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Analisis de las fuerzas estocasticas que actuan sobre la poblacion de particulas en la magnetosfera de Saturno

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❆♥á❧✐s✐s ❞❡ ❧❛s ❢✉❡r③❛s ❡st♦❝ást✐❝❛s q✉❡ ❛❝tú❛♥ s♦❜r❡ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❡♥ ❧❛ ♠❛❣♥❡t♦s❢❡r❛ ❞❡ ❙❛t✉r♥♦ ▼✳ ❡♥ ❈✳ ❊❧✐③❛❜❡t❤ ▼❛rtí♥❡③ ●ó♠❡③ ❚❡s✐s ♣r❡s❡♥t❛❞❛ ♣❛r❛ ♦❜t❡♥❡r ❡❧ ❣r❛❞♦ ❞❡ ❉♦❝t♦r❛ ❡♥ ❈✐❡♥❝✐❛s ✭❋ís✐❝❛ ❊s♣❛❝✐❛❧✮ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❋ís✐❝❛ ❊s♣❛❝✐❛❧ ■♥st✐t✉t♦ ❞❡ ●❡♦❢ís✐❝❛ ❯♥✐✈❡rs✐❞❛❞ ◆❛❝✐♦♥❛❧ ❆✉tó♥♦♠❛ ❞❡ ▼é①✐❝♦ ▼é①✐❝♦ ▼❛②♦ ✷✵✵✼ UNAM – Dirección General de Bibliotecas Tesis Digitales Restricciones de uso DERECHOS RESERVADOS © PROHIBIDA SU REPRODUCCIÓN TOTAL O PARCIAL Todo el material contenido en esta tesis esta protegido por la Ley Federal del Derecho de Autor (LFDA) de los Estados Unidos Mexicanos (México). El uso de imágenes, fragmentos de videos, y demás material que sea objeto de protección de los derechos de autor, será exclusivamente para fines educativos e informativos y deberá citar la fuente donde la obtuvo mencionando el autor o autores. Cualquier uso distinto como el lucro, reproducción, edición o modificación, será perseguido y sancionado por el respectivo titular de los Derechos de Autor. ❉❡❞✐❝❛❞❛ ❛ ▼✐s ♣❛❞r❡s✱ ❊❧✐③❛❜❡t❤ ② ●❡r❛r❞♦ ▼✐ ❤❡r♠❛♥♦✱ ●❡r❛r❞♦ ✭❘❡◆♦✮ ▼✐ ❛❜✉❡❧✐t❛✱ ♠✐s tí♦s ② ♣r✐♠♦s ▼✐s ♣r♦❢❡s♦r❡s ② ❛♠✐❣♦s ▲❛ ♠❡♠♦r✐❛ ❞❡ ❧♦s q✉❡ ②❛ ♥♦ ❡stá♥ ❝♦♥♠✐❣♦ ▲❛ ♠❡♠♦r✐❛ ❞❡ ♠✐ ✜❡❧ ② ❛♠♦r♦s❛ ♠❛s❝♦t❛ ♣♦r ♠✉❝❤♦s ❛ñ♦s✱ ❇❡t♦ ❆❣r❛❞❡❝✐♠✐❡♥t♦s ▲❛s s✐❣✉✐❡♥t❡s ❧í♥❡❛s s♦♥ ♣❛r❛ ❡①♣r❡s❛r ♠✐ ♠ás ♣r♦❢✉♥❞♦ ② s✐♥❝❡r♦ ❛❣r❛❞❡❝✐♠✐❡♥t♦ ❛ t♦❞❛s ❛q✉❡❧❧❛s ♣❡rs♦♥❛s q✉❡ ❤❛♥ ❡st❛❞♦ ❛ ♠✐ ❧❛❞♦ ② ❤❛♥ ❤❡❝❤♦ ❞❡ ♠í ❧❛ ♣❡rs♦♥❛ ② ♣r♦❢❡s✐♦♥✐st❛ q✉❡ ❛❤♦r❛ s♦②✳ ❊❧ ♣✐❧❛r ❞❡ t♦❞♦ ❡st♦ ❡s ♠✐ ❢❛♠✐❧✐❛✱ q✉❡✱ ❛ tr❛✈és ❞❡ s✉s s❛❜✐♦s ❝♦♥s❡❥♦s ♠❡ ❤❛♥ ❛②✉❞❛❞♦ ❛ ♠❡❥♦r❛r ❡♥ t♦❞♦s ❧♦s ❛s♣❡❝t♦s✳ ❨ t❛♠❜✐é♥ ♣♦r ❛❣✉❛♥t❛r♠❡ ❡♥ ❧♦s ♠♦♠❡♥t♦s ♠ás t❡♥s♦s ❞♦♥❞❡ ♣❡r❞í❛ ❧❛ ❝❛❜❡③❛✳ ❆ ♠✐s s✐♥♦❞❛❧❡s✿ ❉r✳ ❍é❝t♦r ❆♥t♦♥✐♦ Pér❡③ ❞❡ ❚❡❥❛❞❛ ✭❛s❡s♦r ❡ ✐♥✈❡st✐❣❛❞♦r ❞❡❧ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❋ís✐❝❛ ❊s♣❛❝✐❛❧✱ ■●✲❯◆❆▼✮✱ ❉r✳ ❏♦r❣❡ ❈❛♥tó ■❧❧❛ ✭✐♥✈❡st✐❣❛❞♦r ❞❡❧ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❆str♦❢ís✐❝❛ ❚❡ór✐❝❛✱ ■❆✲❯◆❆▼✮✱ ❉r✳ ❏✉❧✐♦ ❍❡rr❡r❛ ❱❡❧á③q✉❡③ ✭✐♥✈❡st✐❣❛❞♦r ❞❡❧ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❋ís✐❝❛ ❞❡ P❧❛s♠❛s ② ❞❡ ■♥t❡r❛❝❝✐ó♥ ❞❡ ❘❛❞✐❛❝✐ó♥ ❝♦♥ ▼❛t❡r✐❛✱ ■❈◆✲❯◆❆▼✮✱ ❉r✳ ❏♦sé ❋r❛♥❝✐s❝♦ ❱❛❧❞és ●❛❧✐❝✐❛ ✭❞✐r❡❝t♦r ❡ ✐♥✈❡st✐❣❛✲ ❞♦r ❞❡❧ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ■♥✈❡st✐❣❛❝✐♦♥❡s ❙♦❧❛r❡s ② P❧❛♥❡t❛r✐❛s✱ ■●✲❯◆❆▼✮✱ ❉r❛✳ ❉♦❧♦r❡s ▼❛r❛✈✐❧❧❛ ▼❡③❛ ✭✐♥✈❡st✐❣❛❞♦r❛ ❞❡❧ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ■♥✈❡st✐❣❛❝✐♦♥❡s ❙♦❧❛r❡s ② P❧❛♥❡t❛r✐❛s✱ ■●✲❯◆❆▼✮✱ ❉r✳ ❏♦r❣❡ Pér❡③ P❡r❛③❛ ✭✐♥✈❡st✐❣❛❞♦r ❞❡❧ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ■♥✈❡st✐❣❛❝✐♦♥❡s ❙♦❧❛r❡s ② P❧❛♥❡t❛r✐❛s✱ ■●✲❯◆❆▼✮ ② ❛❧ ❉r✳ ❍é❝t♦r ❏❛✈✐❡r ❉✉r❛♥❞ ▼❛♥t❡r♦❧❛ ✭✐♥✈❡st✐❣❛❞♦r ❞❡❧ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❋ís✐❝❛ ❊s♣❛❝✐❛❧✱ ■●✲❯◆❆▼✮✳ ❈❛❞❛ ✉♥♦ ❞❡ ❡❧❧♦s ❝♦♥tr✐❜✉②ó ❡♥ ❧❛ ♠❡❥♦r❛ ❞❡ ❡st❡ tr❛❜❛❥♦ ❛ tr❛✈és ❞❡ s✉s ♠❛❣♥í✜❝❛s ✐❞❡❛s ② s✉❣❡r❡♥❝✐❛s✳ ❉❡ ♠❛♥❡r❛ ❡s♣❡❝✐❛❧ ❛❣r❛❞❡③❝♦ ❛❧ ❉r✳ ❏♦sé ❋r❛♥❝♦ ▲ó♣❡③ ✭❞✐r❡❝t♦r ■❆✲ ❯◆❆▼✮ ♣♦r ❛②✉❞❛r♠❡ ❡♥ ❧♦s ♠♦♠❡♥t♦s ❝r✉❝✐❛❧❡s ❝✉❛♥❞♦ r❡❝✉rrí ❛ é❧ ② ❛❧ ❉r✳ ❍é❝t♦r ❉✉r❛♥❞ ▼❛♥t❡r♦❧❛ ♣♦r ❡st❛r s✐❡♠♣r❡ r❡✈✐s❛♥❞♦ ♠✐ tr❛❜❛❥♦✱ ♣♦r s✉s s✉❣❡r❡♥❝✐❛s ② ♣♦r ❝♦♠❡♥t❛r ❝❛❞❛ ✉♥♦ ❞❡ ❧♦s ❛r❜✐tr❛❥❡s ❞❡ ❧♦s ❛rtí❝✉❧♦s✳ ❆ ♠✐s ♣r♦❢❡s♦r❡s ② t❛♠❜✐é♥ ❛♠✐❣♦s q✉❡ ♠❡ ❤❛♥ ❡♥s❡ñ❛❞♦ t❛♥t❛s ❝♦s❛s ❞❡s❞❡ ❧♦ ❛❝❛❞é♠✐❝♦ ❤❛st❛ ❧♦ ♣❡rs♦♥❛❧✿ ❉r✳ ❏✉❛♥ ▼❛♥✉❡❧ ▲♦③❛♥♦ ▼❡❥í❛ ✭✐♥✈❡st✐❣❛❞♦r ❞❡❧ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❋ís✐❝❛ ❚❡ór✐❝❛✱ ■❋✲❯◆❆▼✮✱ ❉r✳ ●❡r❛r❞♦ ❱á③q✉❡③ ❋♦♥s❡❝❛ ✭✐♥✈❡s✲ ①✐ ①✐✐ t✐❣❛❞♦r ❞❡❧ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❊st❛❞♦ ❙ó❧✐❞♦✱ ■❋✲❯◆❆▼✮✱ ❉r✳ ▲✉✐s ❋❡r♥❛♥❞♦ ▼❛❣❛ñ❛ ❙♦❧ís ✭✐♥✈❡st✐❣❛❞♦r ❞❡❧ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❊st❛❞♦ ❙ó❧✐❞♦✱ ■❋✲❯◆❆▼✮✱ ② ❛❧ ❋ís✳ ❏✉❛♥ ❆♠ér✐❝♦ ●♦♥③á❧❡③ ▼❡♥é♥❞❡③ ✭♣r♦❢❡s♦r r❡t✐r❛❞♦ ❞❡ ❧❛ ❋❛❝✉❧t❛❞ ❞❡ ❈✐❡♥❝✐❛s✱ ❯◆❆▼✮✳ ❆ ♠✐ ❣r✉♣♦ ❞❡ ❛♠✐❣♦s q✉❡ s✐❡♠♣r❡ ♠❡ ❡stá♥ ❛♣♦②❛♥❞♦ ② ❛❝♦♥s❡❥❛♥❞♦✿ P✐❧❛r ❖✈❛✲ ❧❧❡✱ ❈❛r❧♦s ▼❡♥❞♦③❛✱ ❍é❝t♦r ❱❡r❞✐❣✉❡❧✱ ❋❡r♥❛♥❞♦ ❈❛♠❛❝❤♦✱ ❆rt✉r♦ ❩úñ✐❣❛✱ ❖s❝❛r ▼❡♥❞♦③❛ ✧❊❧ P♦❧❧♦✧✱ ❚❛♥✐❛ ❙❛♥t✐❛❣♦✱ ❱❛♥❡③❛ P❡ñ❛✱ ❘♦s❛ ❙á♥❝❤❡③✱ ❈❛r❧♦s ❇❛rr❛✲ ❣á♥✱ ❆❧❡❥❛♥❞r♦ ▲✉❣♦✱ ❆r♠❛♥❞♦ ❘❡s❡♥❞✐③✱ ❲❛❧t❡r ●❛❧✈á♥✱ ❊❧✐♦ ▼❛rtí♥❡③✱ ❋❡r♥❛♥❞♦ ●✉❛❞❛❧✉♣❡✱ ❋❡❧✐♣❡ ❘✐✈❡r❛✱ ▼❛r❝♦ ❇❛rr❛❣á♥✱ ❉❛✈✐❞ ❇✉❝✐♦✱ ◆♦r♠❛ ❙á♥❝❤❡③✱ ❊r✐❝❦ ❙á♥❝❤❡③✱ ❖r❧❛♥❞♦ ❇❛❝❛✱ P❡❞r♦ ❈❡r✈❡r❛✱ ❖r❧❛♥❞♦ ❍❡r♥á♥❞❡③✱ ●❡r♠á♥ Pér❡③✱ ❈❛r❧♦s ❆✈❡♥❞❛ñ♦✱ ❊❞❣❛r ❉á✈✐❧❛✱ ❖s❝❛r ❞❡ ❧❛ ❘♦s❛✱ ▼✐❣✉❡❧ ❘♦❥♦ ② ❆❧❡① ❲❤✐t♠♦r❡✳ ❆ ❧❛ ❉r❛✳ ❇❧❛♥❝❛ ❊♠♠❛ ▼❡♥❞♦③❛ ❖rt❡❣❛ ✭❝♦♦r❞✐♥❛❞♦r❛ ❞❡❧ ♣♦s❣r❛❞♦ ❡♥ ❈✐❡♥❝✐❛s ❞❡ ❧❛ ❚✐❡rr❛✮ ♣♦r ❛♣♦②❛r♠❡ ❞✉r❛♥t❡ ❡st❡ ♣❡r✐♦❞♦✱ ❛sí ❝♦♠♦ ❛ ❆r❛❝❡❧✐ ❈❤❛♠á♥ ② ❛ ▼ó♥✐❝❛ ❙❛❧❣❛❞♦ ✭❛✉①✐❧✐❛r❡s ❞❡ ❧❛ ❝♦♦r❞✐♥❛❝✐ó♥✮ ♣♦r ❛②✉❞❛r♠❡ ❛♠❛❜❧❡♠❡♥t❡ ❡♥ t♦❞♦s ❧♦s trá♠✐t❡s✳ ❋✐♥❛❧♠❡♥t❡ ❛❣r❛❞❡③❝♦ ❛ ❧❛s ❛✉t♦r✐❞❛❞❡s ❞❡❧ ■●✲❯◆❆▼ ♣♦r ❛s✐❣♥❛r♠❡ ✉♥❛ ♣❡q✉❡ñ❛ ♦✜❝✐♥❛ ❞♦♥❞❡ tr❛❜❛❥❛r ② ❛❧ ❈♦♥s❡❥♦ ◆❛❝✐♦♥❛❧ ❞❡ ❈✐❡♥❝✐❛ ② ❚❡❝♥♦❧♦❣í❛ ✭❈❖◆❆❈②❚✮ ♣♦r ❡❧ ❛♣♦②♦ ❡❝♦♥ó♠✐❝♦ ❜r✐♥❞❛❞♦ ❞✉r❛♥t❡ ♠✐s ❡st✉❞✐♦s ❞♦❝t♦r❛❧❡s✳ ❨ ♣♦r q✉é ♥♦❄❄ ▼❡ ❛❣r❛❞❡③❝♦ ❡❧ s❡r ♣❡rs❡✈❡r❛♥t❡ ❡♥ t♦❞♦ ❧♦ q✉❡ ♠❡ ♣r♦♣♦♥❣♦✱ ♣♦r t❡♥❡r ♠❡t❛s ❞❡✜♥✐❞❛s ② s❛❜❡r q✉❡ ♣✉❡❞♦ ❧❧❡❣❛r ❛ ❡❧❧❛s✳✳✳② ❡st❛ t❡s✐s ❡s ♣r✉❡❜❛ ❞❡ ❡❧❧♦✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❮♥❞✐❝❡ ❣❡♥❡r❛❧ ✐✐✐ ❘❡s✉♠❡♥ ① ❉❡❝❧❛r❛❝✐ó♥ ①✐ ❆❣r❛❞❡❝✐♠✐❡♥t♦s ✶✳ ■♥tr♦❞✉❝❝✐ó♥ ✶✳✶✳ ✶ ▼❡❝❛♥✐s♠♦s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❣❡♥❡r❛❧❡s ✶✳✶✳✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽ ❆❝❡❧❡r❛❝✐ó♥ ❛❞✐❛❜át✐❝❛ ② ♦tr❛s ❢♦r♠❛s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ♥♦ ❡st♦✲ ❝ást✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽ ✶✳✶✳✷✳ ❆❝❡❧❡r❛❝✐ó♥ ❡st♦❝ást✐❝❛ ② ❛❧♠❛❝❡♥❛♠✐❡♥t♦ ❞❡ ❡♥❡r❣í❛ ♠❛❣♥ét✐❝❛ ✾ ✶✳✶✳✸✳ ❆❝❡❧❡r❛❝✐ó♥ ♣♦r ❝❤♦q✉❡s ✶✳✶✳✹✳ ❆❝❡❧❡r❛❝✐ó♥ t✉r❜✉❧❡♥t❛ ② ♣♦r ♦♥❞❛s ❞❡ ♣❧❛s♠❛ ✶✳✶✳✺✳ ▼❡❝❛♥✐s♠♦s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❡♥ ♠❛❣♥❡tós❢❡r❛s ♣❧❛✲ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ♥❡t❛r✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✳✶✳✺✳✶✳ P♦s✐❜❧❡s ♠❡❝❛♥✐s♠♦s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❛♣❧✐❝❛❞♦s ❛ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶ ✶✶ ✶✷ ✶✺ ✷✳ P♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ② ♥❡✉tr❛s ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦ ✶✽ ✷✳✶✳ ❆♥t❡❝❡❞❡♥t❡s✿ ❘❡s✉❧t❛❞♦s ❞❡ ❧❛ ♠✐s✐ó♥ ❱♦②❛❣❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾ ✷✳✶✳✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺ ◆✉❡✈❛s ♦❜s❡r✈❛❝✐♦♥❡s✿ ▼✐s✐ó♥ ❈❛ss✐♥✐ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽ ✷✳✷✳ ❈❛r❛❝t❡ríst✐❝❛s ❞❡ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ✷✳✶✳✶✳✶✳ ▼❡❞✐❝✐♦♥❡s ❞❡ ♣❧❛s♠❛ ✷✳✶✳✶✳✷✳ P❛rtí❝✉❧❛s ♥❡✉tr❛s ①✐✐✐ ❮♥❞✐❝❡ ❣❡♥❡r❛❧ ①✐✈ ✸✳ ▼♦❞❡❧♦ ❞❡ ❡♥❡r❣✐③❛❝✐ó♥ ♣❛r❛ ♣❛rtí❝✉❧❛s ❜❛❥♦ ❧❛ ❛❝❝✐ó♥ ❞❡ ❝❛♠♣♦s ❞❡ ❢✉❡r③❛ ❡st♦❝ást✐❝♦s ✹✹ ✸✳✶✳ ▼♦❞❡❧♦ ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ♣❛r❛ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ✳ ✳ ✳ ✳ ✹✻ ✸✳✶✳✶✳ ▲❛ ❡❝✉❛❝✐ó♥ ❞❡ ♠♦✈✐♠✐❡♥t♦ ♣❛r❛ ✉♥❛ ♣❛rtí❝✉❧❛ ❝❛r❣❛❞❛ ✳ ✳ ✳ ✳ ✹✻ ✸✳✶✳✶✳✶✳ ▲❛ ❛❝❡❧❡r❛❝✐ó♥ ❡st♦❝ást✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✾ ✸✳✶✳✶✳✷✳ ▲❛ ❛❝❡❧❡r❛❝✐ó♥ ❞❡ ▲♦r❡♥t③ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✸✳✶✳✶✳✸✳ ▲❛ ❛❝❡❧❡r❛❝✐ó♥ ❣r❛✈✐t❛❝✐♦♥❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✸✳✶✳✶✳✹✳ ➽❯♥ tér♠✐♥♦ ❝♦❧✐s✐♦♥❛❧❄ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✸ ✸✳✶✳✷✳ ▲❛ ❡♥❡r❣í❛ ✜♥❛❧ ② ❧❛ ✈❡❧♦❝✐❞❛❞ ✜♥❛❧ ♣❛r❛ ❧❛ ❞✐str✐❜✉❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✹ ✸✳✷✳ ▼♦❞❡❧♦ ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ♣❛r❛ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ♥❡✉tr❛s ✳ ✳ ✳ ✳ ✺✼ ✸✳✷✳✶✳ ▲❛ ❡❝✉❛❝✐ó♥ ❞❡ ♠♦✈✐♠✐❡♥t♦ ♣❛r❛ ✉♥❛ ♣❛rtí❝✉❧❛ ❞❡ ♣♦❧✈♦ ♥❡✉tr❛ ✺✼ ✸✳✷✳✶✳✶✳ ▲❛ ❛❝❡❧❡r❛❝✐ó♥ ❣r❛✈✐t❛❝✐♦♥❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✸✳✷✳✶✳✷✳ ▲❛ ❛❝❡❧❡r❛❝✐ó♥ ❣r❛✈✐t❛❝✐♦♥❛❧ ❡st♦❝ást✐❝❛ ❡♥tr❡ ❣r❛♥♦s ❞❡ ♣♦❧✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✽ ✸✳✷✳✶✳✸✳ ▲❛ ❛❝❡❧❡r❛❝✐ó♥ ❞❡❜✐❞❛ ❛ ❧❛ ❢✉❡r③❛ ❞❡ ♣r❡s✐ó♥ ❞❡ r❛✲ ❞✐❛❝✐ó♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✸✳✷✳✷✳ ▲❛ ❡♥❡r❣í❛ ✜♥❛❧ ② ❧❛ ✈❡❧♦❝✐❞❛❞ ✜♥❛❧ ♣❛r❛ ❧❛ ❞✐str✐❜✉❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❞❡ ♣♦❧✈♦ ♥❡✉tr❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✾ ✹✳ ❆♣❧✐❝❛❝✐ó♥ ❞❡❧ ♠♦❞❡❧♦ ❛ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❡♥ ❧❛ ♠❛❣♥❡tós✲ ❢❡r❛ ❞❡ ❙❛t✉r♥♦ ✻✵ ✹✳✶✳ P❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ✭♣r♦t♦♥❡s✱ ✐♦♥❡s ♣❡s❛❞♦s ② ❣r❛♥♦s ❞❡ ♣♦❧✈♦✮ ✳ ✳ ✳ ✻✶ ✹✳✶✳✶✳ ❊❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❡st♦❝ást✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✶ ✹✳✶✳✷✳ ❈❛r❛❝t❡ríst✐❝❛s ❞❡ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ✹✳✶✳✷✳✶✳ ▼❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✻ ✹✳✶✳✷✳✷✳ ▼❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾ ✹✳✶✳✷✳✸✳ ❆♥✐❧❧♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵ ✹✳✷✳ P❛rtí❝✉❧❛s ♥❡✉tr❛s ✭❣r❛♥♦s ❞❡ ♣♦❧✈♦✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✹ ✹✳✷✳✶✳ ❊❧ ❝❛♠♣♦ ❣r❛✈✐t❛❝✐♦♥❛❧ ❡st♦❝ást✐❝♦ ❡♥tr❡ ♣❛rtí❝✉❧❛s ❞❡ ♣♦❧✈♦ ✳ ✽✹ ✹✳✷✳✷✳ ❈❛r❛❝t❡ríst✐❝❛s ❞❡ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ❣r❛♥♦s ❞❡ ♣♦❧✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺ ✹✳✷✳✷✳✶✳ ❉✐str✐❜✉❝✐ó♥ ❞❡ ♠❛s❛s ♣❛r❛ ❧♦s ❣r❛♥♦s ❞❡ ♣♦❧✈♦ ✳ ✳ ✳ ✽✼ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ①✈ ❮♥❞✐❝❡ ❣❡♥❡r❛❧ ✹✳✷✳✷✳✷✳ ❉✐str✐❜✉❝✐ó♥ ❞❡ ❧❛s ❞✐st❛♥❝✐❛s ❡♥tr❡ ❣r❛♥♦s ❞❡ ♣♦❧✈♦ ✳ ✽✽ ✺✳ ❘❡s✉❧t❛❞♦s ② ❉✐s❝✉s✐ó♥ ✾✷ ✺✳✶✳ ▼❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✷ ✺✳✷✳ ▼❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✼ ✺✳✸✳ ❙✐st❡♠❛ ❞❡ ❛♥✐❧❧♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✷ ✺✳✸✳✶✳ P♦❧✈♦ ❝❛r❣❛❞♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✷ ✺✳✸✳✷✳ P♦❧✈♦ ♥❡✉tr♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✷ ✻✳ ❈♦♥❝❧✉s✐♦♥❡s ✶✸✵ ✻✳✶✳ P❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ✭❈❛♠♣♦ ❊❧é❝tr✐❝♦ ❊st♦❝ást✐❝♦✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✶ ✻✳✶✳✶✳ ▼❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✶ ✻✳✶✳✷✳ ▼❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✹ ✻✳✶✳✸✳ ❙✐st❡♠❛ ❞❡ ❛♥✐❧❧♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✺ ✻✳✷✳ P❛rtí❝✉❧❛s ♥❡✉tr❛s ✭❈❛♠♣♦ ●r❛✈✐t❛❝✐♦♥❛❧ ❊st♦❝ást✐❝♦✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✻ ✻✳✷✳✶✳ ❙✐st❡♠❛ ❞❡ ❛♥✐❧❧♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✻ ❇✐❜❧✐♦❣r❛❢í❛ ✶✸✾ ❆♣é♥❞✐❝❡ ✶✻✶ ❆✳ Pr✉❡❜❛s ❞❡ ❤✐♣ót❡s✐s ❞❡ ❜♦♥❞❛❞ ❞❡ ❛ ❥✉st❡ ✶✻✶ ❆✳✵✳✷✳ Pr✉❡❜❛ χ2 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✷ ❆✳✵✳✸✳ Pr✉❡❜❛ ❞❡ ❑♦❧♠♦❣♦r♦✈✲❙♠✐r♥♦✈ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✸ ❇✳ ❋✉♥❝✐ó♥ ❞❡ ❞✐str✐❜✉❝✐ó♥ ❧♦❣íst✐❝❛ ✶✻✺ ❇✳✵✳✹✳ ❉❡✜♥✐❝✐ó♥ ♠❛t❡♠át✐❝❛✳ ▲❛ ❢✉♥❝✐ó♥ ❞❡ ❞❡♥s✐❞❛❞ ❞❡ ♣r♦❜❛❜✐❧✐✲ ❞❛❞ ② ❧❛ ❢✉♥❝✐ó♥ ❞❡ ❞✐str✐❜✉❝✐ó♥ ❛❝✉♠✉❧❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✺ ❇✳✵✳✺✳ Pr♦♣✐❡❞❛❞❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✻ ❇✳✵✳✻✳ ▼♦♠❡♥t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✼ ❇✳✵✳✻✳✶✳ ❋✉♥❝✐ó♥ ❣❡♥❡r❛❞♦r❛ ❞❡ ♠♦♠❡♥t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✼ ❇✳✵✳✼✳ ●❡♥❡r❛❝✐ó♥ ❞❡ ♥ú♠❡r♦s ❛❧❡❛t♦r✐♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✽ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❮♥❞✐❝❡ ❣❡♥❡r❛❧ ①✈✐ ❈✳ ▼ét♦❞♦ ❞❡ ❇♦①✲▼ü❧❧❡r ♣❛r❛ ❣❡♥❡r❛r ♥ú♠❡r♦s ❛❧❡❛t♦r✐♦s ❝♦♥ ❞✐str✐✲ ❜✉❝✐ó♥ ♥♦r♠❛❧ ✶✼✵ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❮♥❞✐❝❡ ❞❡ ✜❣✉r❛s ✷✳✶✳ ❊sq✉❡♠❛ ❣❡♥❡r❛❧ ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦ ❜❛s❛❞♦ ❡♥ ❧❛s ♦❜s❡r✲ ✈❛❝✐♦♥❡s ❞❡❧ P✐♦♥❡❡r ② ❞❡ ❧♦s ❱♦②❛❣❡r ✶ ② ✷ ❬❑r✐♠✐❣✐s✱ ✶✾✽✷❪✳ ✳ ✳ ✳ ✳ ✳ ✷✵ ✷✳✷✳ ❉✐❛❣r❛♠❛ ❞❡ ❧♦s ❛♥✐❧❧♦s ② s❛té❧✐t❡s ✐♥t❡r♥♦s ❞❡ ❙❛t✉r♥♦✳ ❊❧ s✐st❡♠❛ ❞❡ ❛♥✐❧❧♦s ② s❛té❧✐t❡s ❤❛ s✐❞♦ ❡s❝❛❧❛❞♦ ❞❡ ❛❝✉❡r❞♦ ❝♦♥ ❡❧ r❛❞✐♦ ♣❧❛♥❡t❛r✐♦ ❡❝✉❛t♦r✐❛❧✳ ❚❛♠❜✐é♥ s❡ ✐❧✉str❛ ❡❧ r❛❞✐♦ ❛❧ ❝✉❛❧ ❡❧ ♠♦✈✐♠✐❡♥t♦ ♦r❜✐t❛❧ ❡s s✐♥❝ró♥✐❝♦ ❝♦♥ ❧❛ r♦t❛❝✐ó♥ ♣❧❛♥❡t❛r✐❛ ② ❧❛ ❧♦❝❛❧✐③❛❝✐ó♥ ❞❡ ❧í♠✐t❡ ❞❡ ❘♦❝❤❡ ♣❛r❛ ♣❛rtí❝✉❧❛s ❝♦♥ ❞❡♥s✐❞❛❞ ❞❡ 1 g cm−3 ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✻ ✹✳✶✳ ❱✐st❛ ❡❝✉❛t♦r✐❛❧ ❞❡ ❧❛ tr❛②❡❝t♦r✐❛ ❞❡ ❧❛s ♥❛✈❡s ❱♦②❛❣❡r ❡♥ s✉ ❡♥❝✉❡♥✲ tr♦ ❝♦♥ ❙❛t✉r♥♦✳ ❙♦❜r❡ ❧❛s tr❛②❡❝t♦r✐❛s ❧♦s ♣✉♥t♦s ♥❡❣r♦s ♠❛r❝❛❞♦s ❝♦♠♦ ❙ ✐♥❞✐❝❛♥ ❧♦s ❝r✉❝❡s ♣♦r ❡❧ ❢r❡♥t❡ ❞❡ ❝❤♦q✉❡ ② ❧♦s r❡❝tá♥❣✉❧♦s ♥❡❣r♦s ♠❛r❝❛❞♦s ❝♦♠♦ ▼ ✐♥❞✐❝❛♥ ❧♦s ❝r✉❝❡s ♣♦r ❧❛ ♠❛❣♥❡t♦♣❛✉s❛✳ ▲❛ ❞✐r❡❝❝✐ó♥ ❤❛❝✐❛ ❡❧ ❙♦❧ ❡s ♣♦s✐t✐✈❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✸ ✹✳✷✳ ❈❛♠♣♦ ♠❛❣♥ét✐❝♦ r❡s✐❞✉❛❧ ♦❜t❡♥✐❞♦ ♣❛r❛ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦ ❜❛s❛❞♦ ❡♥ ❧❛s ♦❜s❡r✈❛❝✐♦♥❡s ❞❡❧ ❱♦②❛❣❡r ✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✹ ✹✳✸✳ ❈❛♠♣♦ ♠❛❣♥ét✐❝♦ r❡s✐❞✉❛❧ ♦❜t❡♥✐❞♦ ♣❛r❛ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦ ❜❛s❛❞♦ ❡♥ ❧❛s ♦❜s❡r✈❛❝✐♦♥❡s ❞❡❧ ❱♦②❛❣❡r ✷✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✺ ✹✳✹✳ ❈♦♠♣❛r❛❝✐ó♥ ❡♥tr❡ ❧❛s ✢✉❝t✉❛❝✐♦♥❡s t❡♠♣♦r❛❧❡s ② ❧❛s ✢✉❝t✉❛❝✐♦♥❡s ❡s♣❛❝✐❛❧❡s ♦❜t❡♥✐❞❛s ♣❛r❛ ❧❛s ♠❡❞✐❝✐♦♥❡s ❞❡❧ ❱♦②❛❣❡r ✶ ❞❡♥tr♦ ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ✹✳✺✳ ❋❧✉❝t✉❛❝✐♦♥❡s t❡♠♣♦r❛❧❡s ❞❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛ ❞❡ ❙❛t✉r♥♦ ♦❜t❡♥✐❞❛s ♠❡❞✐❛♥t❡ ❧❛s ♠❡❞✐❝✐♦♥❡s ❞❡❧ ❱♦②❛❣❡r ✷✳ ✳ ✻✼ ①✈✐✐ ❮♥❞✐❝❡ ❞❡ ✜❣✉r❛s ①✈✐✐✐ ✹✳✻✳ ❋❧✉❝t✉❛❝✐♦♥❡s t❡♠♣♦r❛❧❡s ❞❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ ❞❡ ❙❛t✉r♥♦ ♦❜t❡♥✐❞❛s ♠❡❞✐❛♥t❡ ❧❛s ♠❡❞✐❝✐♦♥❡s ❞❡❧ ❱♦②❛❣❡r ✷ ❡♥ s✉ tr❛②❡❝t♦r✐❛ ❞❡ ❡♥tr❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✽ ✹✳✼✳ ❋❧✉❝t✉❛❝✐♦♥❡s t❡♠♣♦r❛❧❡s ❞❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ ❞❡ ❙❛t✉r♥♦ ♦❜t❡♥✐❞❛s ♠❡❞✐❛♥t❡ ❧❛s ♠❡❞✐❝✐♦♥❡s ❞❡❧ ❱♦②❛❣❡r ✷ ❡♥ s✉ tr❛②❡❝t♦r✐❛ ❞❡ s❛❧✐❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✾ ✹✳✽✳ ❍✐st♦❣r❛♠❛ ❞❡ ❢r❡❝✉❡♥❝✐❛s ♣❛r❛ ❧❛ ❞✐str✐❜✉❝✐ó♥ ❞❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❡♥ ❧❛ ❝♦♠♣♦♥❡♥t❡ ✏①✑ ② s✉ ❝✉r✈❛ ❞❡ ❛❥✉st❡ ✭❢✉♥❝✐ó♥ ❧♦❣íst✐❝❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ✹✳✾✳ ❉✐str✐❜✉❝✐ó♥ ❞❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❡st♦❝ást✐❝♦ ❜❛s❛❞♦ ❡♥ ❧❛s ♦❜s❡r✈❛❝✐♦✲ ♥❡s ❞❡❧ ❱♦②❛❣❡r ✶ ❡♥ s✉ ♣❛s♦ ♣♦r ❧❛ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛ ❞❡ ❙❛t✉r♥♦✳ ✼✹ ✹✳✶✵✳ ❉✐str✐❜✉❝✐ó♥ ❞❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❡st♦❝ást✐❝♦ ❜❛s❛❞♦ ❡♥ ❧❛s ♦❜s❡r✈❛❝✐♦✲ ♥❡s ❞❡❧ ❱♦②❛❣❡r ✷ ❡♥ s✉ ♣❛s♦ ♣♦r ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ ❞❡ ❙❛t✉r♥♦ ✭tr❛②❡❝t♦r✐❛ ❞❡ s❛❧✐❞❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✺ ✹✳✶✶✳ ❊❧ ♣♦t❡♥❝✐❛❧ s✉♣❡r✜❝✐❛❧ ❞❡ ❡q✉✐❧✐❜r✐♦ ❞❡ ✉♥ ❣r❛♥♦ ❞❡ ♣♦❧✈♦ ❞✐❡❧é❝tr✐❝♦ q✉❡ s❡ ♠✉❡✈❡ ❡♥ ✉♥❛ ór❜✐t❛ ❝✐r❝✉❧❛r ❑❡♣❧❡r✐❛♥❛ ② ♥♦✲♣❡rt✉r❜❛❞❛ ❡♥ ❡❧ ♣❧❛♥♦ ❡❝✉❛t♦r✐❛❧ ❞❡ ❙❛t✉r♥♦ ❝♦♠♦ ❢✉♥❝✐ó♥ ❞❡ ❧❛ ❞✐st❛♥❝✐❛ ❛❧ ♣❧❛♥❡t❛✳ ❙❡ ❛s✉♠❡ q✉❡ Em = 500 eV✱ δm = 1 ✭❧í♥❡❛ ❝♦♥t✐♥✉❛✮ ② δm = 2 ✭❧í♥❡❛ ♣✉♥t❡❛❞❛✮✳ ❚♦♠❛❞♦ ❞❡ ❍♦r❛♥②✐ ❬✶✾✾✻❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸ ✹✳✶✷✳ P❡r✜❧ ❞❡❧ ❝❛♠♣♦ ❣r❛✈✐t❛❝✐♦♥❛❧ ❡st♦❝ást✐❝♦ ♣❛r❛ ♣❛rtí❝✉❧❛s ❧♦❝❛❧✐③❛❞❛s ❡♥ ❡❧ ❛♥✐❧❧♦ ❊✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✾ ✺✳✶✳ ●❛♥❛♥❝✐❛ ❡st♦❝ást✐❝❛ ❞❡ ❡♥❡r❣í❛ ♣r♦♠❡❞✐❛❞❛ s♦❜r❡ t♦❞❛ ❧❛ ❞✐str✐❜✉✲ ❝✐ó♥ ✈s✳ ❡❧ t✐❡♠♣♦ ♣❛r❛ ✉♥❛ ♠✉❡str❛ ❞❡ ♣r♦t♦♥❡s ② ✉♥❛ ❞❡ ✐♦♥❡s ♣❡✲ s❛❞♦s ❧♦❝❛❧✐③❛❞♦s ❡♥ ❡❧ ♣♦❧♦ ♥♦rt❡ ❞❡ ❙❛t✉r♥♦✳ ❘❡s✉❧t❛❞♦s ❜❛s❛❞♦s ❡♥ ♠❡❞✐❝✐♦♥❡s ❞❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ r❡❛❧✐③❛❞♦s ♣♦r ❡❧ ❱♦②❛❣❡r ✶✳ ✳ ✳ ✳ ✳ ✾✸ ✺✳✷✳ ●❛♥❛♥❝✐❛ ❡st♦❝ást✐❝❛ ❞❡ ❡♥❡r❣í❛ ♣r♦♠❡❞✐❛❞❛ s♦❜r❡ t♦❞❛ ❧❛ ❞✐str✐❜✉✲ ❝✐ó♥ ✈s✳ ❡❧ t✐❡♠♣♦ ♣❛r❛ ✉♥❛ ♠✉❡str❛ ❞❡ ♣r♦t♦♥❡s ② ✈❛r✐❛s ♠✉❡str❛s ❞❡ ✐♦♥❡s ♣❡s❛❞♦s ❧♦❝❛❧✐③❛❞♦s s♦❜r❡ ❡❧ ❛♥✐❧❧♦ ❈✳ ❘❡s✉❧t❛❞♦s ❜❛s❛❞♦s ❡♥ ♠❡✲ ❞✐❝✐♦♥❡s ❞❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ r❡❛❧✐③❛❞♦s ♣♦r ❡❧ ❱♦②❛❣❡r ✷✳ ❖❜sér✈❡s❡ q✉❡ ♥♦ ❤❛② ✉♥❛ ♠❛r❝❛❞❛ t❡♥❞❡♥❝✐❛ ❛ ❣❛♥❛r ❡♥❡r❣í❛ t♦❞♦ ❡❧ t✐❡♠♣♦✳ ✳ ✾✹ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❮♥❞✐❝❡ ❞❡ ✜❣✉r❛s ①✐① ✺✳✸✳ ●❛♥❛♥❝✐❛ ❡st♦❝ást✐❝❛ ❞❡ ❡♥❡r❣í❛ ♣r♦♠❡❞✐❛❞❛ s♦❜r❡ t♦❞❛ ❧❛ ❞✐str✐❜✉✲ ❝✐ó♥ ✈s✳ ❡❧ t✐❡♠♣♦ ♣❛r❛ ✉♥❛ ♠✉❡str❛ ❞❡ ♣r♦t♦♥❡s ② ✉♥❛ ❞❡ ✐♦♥❡s ♣❡✲ s❛❞♦s ❧♦❝❛❧✐③❛❞♦s ❡♥ ❡❧ ♣♦❧♦ s✉r ❞❡ ❊♥❝❡❧❛❞♦✳ ❘❡s✉❧t❛❞♦s ❜❛s❛❞♦s ❡♥ ♠❡❞✐❝✐♦♥❡s ❞❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ r❡❛❧✐③❛❞♦s ♣♦r ❡❧ ❱♦②❛❣❡r ✶✳ ✳ ✳ ✳ ✳ ✾✺ ✺✳✹✳ ●❛♥❛♥❝✐❛ ❡st♦❝ást✐❝❛ ❞❡ ❡♥❡r❣í❛ ♣r♦♠❡❞✐❛❞❛ s♦❜r❡ t♦❞❛ ❧❛ ❞✐str✐❜✉✲ ❝✐ó♥ ✈s✳ ❡❧ t✐❡♠♣♦ ♣❛r❛ ✉♥❛ ♠✉❡str❛ ❞❡ ♣r♦t♦♥❡s ② ✉♥❛ ❞❡ ✐♦♥❡s ♣❡✲ s❛❞♦s ❧♦❝❛❧✐③❛❞♦s ❡♥ ❉✐♦♥❡✳ ❘❡s✉❧t❛❞♦s ❜❛s❛❞♦s ❡♥ ♠❡❞✐❝✐♦♥❡s ❞❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ r❡❛❧✐③❛❞♦s ♣♦r ❡❧ ❱♦②❛❣❡r ✷✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✻ ✺✳✺✳ ●❛♥❛♥❝✐❛ ❡st♦❝ást✐❝❛ ❞❡ ❡♥❡r❣í❛ ♣r♦♠❡❞✐❛❞❛ s♦❜r❡ t♦❞❛ ❧❛ ❞✐str✐❜✉✲ ❝✐ó♥ ✈s✳ ❡❧ t✐❡♠♣♦ ♣❛r❛ ✉♥❛ ♠✉❡str❛ ❞❡ ♣r♦t♦♥❡s ② ✉♥❛ ❞❡ ✐♦♥❡s ♣❡✲ s❛❞♦s ❧♦❝❛❧✐③❛❞♦s s♦❜r❡ ❡❧ ❛♥✐❧❧♦ ❊✳ ❘❡s✉❧t❛❞♦s ❜❛s❛❞♦s ❡♥ ♠❡❞✐❝✐♦♥❡s ❞❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ r❡❛❧✐③❛❞♦s ♣♦r ❡❧ ❱♦②❛❣❡r ✶✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✼ ✺✳✻✳ ●❛♥❛♥❝✐❛ ❡st♦❝ást✐❝❛ ❞❡ ❡♥❡r❣í❛ ♣r♦♠❡❞✐❛❞❛ s♦❜r❡ t♦❞❛ ❧❛ ❞✐str✐❜✉✲ ❝✐ó♥ ✈s✳ ❡❧ t✐❡♠♣♦ ♣❛r❛ ✉♥❛ ♠✉❡str❛ ❞❡ ♣r♦t♦♥❡s ② ✉♥❛ ❞❡ ✐♦♥❡s ♣❡s❛✲ ❞♦s ❧♦❝❛❧✐③❛❞♦s ❡♥ ❘❡❛✳ ❘❡s✉❧t❛❞♦s ❜❛s❛❞♦s ❡♥ ♠❡❞✐❝✐♦♥❡s ❞❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ r❡❛❧✐③❛❞♦s ♣♦r ❡❧ ❱♦②❛❣❡r ✷✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✽ ✺✳✼✳ ●❛♥❛♥❝✐❛ ❞❡ ❡♥❡r❣í❛ ❝✐♥ét✐❝❛ ❞❡ ❧♦s ♣r♦t♦♥❡s ✈s✳ ❧❛ ❞✐st❛♥❝✐❛ ❛❧ ♣❧❛✲ ♥❡t❛ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛✳ ❙❡ ♠✉❡str❛ ❧❛ ❣❛♥❛♥❝✐❛ ❞❡ ❡♥❡r❣í❛ ❡st♦❝ást✐❝❛✱ ❧❛ ❣❛♥❛♥❝✐❛ ❞❡ ❡♥❡r❣í❛ ❞❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ ② ❧❛ ❣❛♥❛♥❝✐❛ ❞❡ ❡♥❡r❣í❛ ❞❡❜✐❞❛ ❛❧ ❡❢❡❝t♦ ❝♦♠❜✐♥❛❞♦ ❞❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ ✰ ❝♦rr♦t❛❝✐ó♥✳ ✳ ✶✵✵ ✺✳✽✳ P❡r✜❧ ❞❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ ❞❡ ✈❡❧♦❝✐❞❛❞❡s ✜♥❛❧ ♣❛r❛ ♣r♦t♦♥❡s ❧♦❝❛❧✐③❛❞♦s ❡♥ ❡❧ ❛♥✐❧❧♦ ❈ ② ❡♥ ❡❧ ♣♦❧♦ s✉r ❞❡ ❊♥❝❡❧❛❞♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✷ ✺✳✾✳ ❊s♣❡❝tr♦ ❞❡ ❡♥❡r❣í❛ tí♣✐❝♦ ♣❛r❛ ✐♦♥❡s ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦ ♠❡❞✐❞♦ ♣♦r ❡❧ ✐♥str✉♠❡♥t♦ ▲❊❈P ❛❜♦r❞♦ ❞❡❧ ❱♦②❛❣❡r ✷ ❛ 10 RS ❬❑r✐✲ ♠✐❣✐s✱ ✶✾✽✷❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✸ ✺✳✶✵✳ ❍✐st♦❣r❛♠❛ ❞❡ ❢r❡❝✉❡♥❝✐❛s ♣❛r❛ ❧❛ ❡♥❡r❣í❛ ❝✐♥ét✐❝❛ ✜♥❛❧ ❛❧❝❛♥③❛❞❛ ♣♦r ✉♥❛ ♠✉❡str❛ ❞❡ ♣r♦t♦♥❡s ❞❡s♣✉és ❞❡ 5x107 ✐♥t❡r❛❝❝✐♦♥❡s ② s✉ ❢✉♥❝✐ó♥ ❞❡ ❛❥✉st❡ ❡♥ ❡❧ ♣♦❧♦ ♥♦rt❡ ❞❡ ❙❛t✉r♥♦✳ ▲❛s ♣❛rtí❝✉❧❛s ❣❛♥❛♥ ∼ 1 eV ❞❡s♣✉és ❞❡ 1 s❡❣✉♥❞♦ ② ❡❧ ❡s♣❡❝tr♦ ❞❡ ❡♥❡r❣í❛ q✉❡❞❛ ❜✐❡♥ ❞❡s❝r✐t♦ ♣♦r ✉♥❛ ❢✉♥❝✐ó♥ s✐❣♠♦✐❞❛❧ ❛s✐♠étr✐❝❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✹ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ①① ❮♥❞✐❝❡ ❞❡ ✜❣✉r❛s ✺✳✶✶✳ ❍✐st♦❣r❛♠❛ ❞❡ ❢r❡❝✉❡♥❝✐❛s ♣❛r❛ ❧❛ ❡♥❡r❣í❛ ❝✐♥ét✐❝❛ ✜♥❛❧ ❛❧❝❛♥③❛❞❛ ♣♦r ✉♥❛ ♠✉❡str❛ ❞❡ ♣r♦t♦♥❡s ❞❡s♣✉és ❞❡ 5x107 ✐♥t❡r❛❝❝✐♦♥❡s ② s✉ ❢✉♥❝✐ó♥ ❞❡ ❛❥✉st❡ ❡♥ ❧❛ ✈❡❝✐♥❞❛❞ ❞❡ ❊♥❝❡❧❛❞♦✳ ■♥✐❝✐❛❧♠❡♥t❡ ❧❛s ♣❛rtí❝✉❧❛s t✐❡✲ ♥❡♥ ✉♥❛ ❡♥❡r❣í❛ ❞❡ ✵✳✵✷ ▼❡❱ ② ❞❡s♣✉és ❞❡ ✺ ♠✐❧✐s❡❣✉♥❞♦s ❡❧ ❡s♣❡❝tr♦ ❞❡ ❡♥❡r❣í❛ ♣✉❡❞❡ s❡r ❞❡s❝r✐t♦ ♣♦r ✉♥❛ ❢✉♥❝✐ó♥ ❞❡ ❧❡② ❞❡ ♣♦t❡♥❝✐❛s ❝♦♥ í♥❞✐❝❡ ❞❡ ✲✷✳✸✽ ♣❛r❛ E >✵✳✵✻ ▼❡❱✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✺ ✺✳✶✷✳ ❍✐st♦❣r❛♠❛ ❞❡ ❢r❡❝✉❡♥❝✐❛s ♣❛r❛ ❧❛ ❡♥❡r❣í❛ ❝✐♥ét✐❝❛ ✜♥❛❧ ❛❧❝❛♥③❛❞❛ ♣♦r ✉♥❛ ♠✉❡str❛ ❞❡ ♣r♦t♦♥❡s ❞❡s♣✉és ❞❡ 5x107 ✐♥t❡r❛❝❝✐♦♥❡s ② s✉ ❢✉♥❝✐ó♥ ❞❡ ❛❥✉st❡ ❡♥ ❘❡❛✳ ❊❧ ❡s♣❡❝tr♦ ❞❡ ❡♥❡r❣í❛ q✉❡❞❛ ❜✐❡♥ ❞❡s❝r✐t♦ ♣♦r ❞♦s ❢✉♥❝✐♦♥❡s ❞❡ ❞✐str✐❜✉❝✐ó♥✱ ❡st♦ ❡s✱ ♣❛r❛ E 11 eV ✉♥❛ ❢✉♥❝✐ó♥ ❡①♣♦♥❡♥❝✐❛❧ ❞❡❝r❡❝✐❡♥t❡ s♦♥ ❧❛s ♠ás ❛❞❡❝✉❛❞❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✻ ✺✳✶✸✳ ❍✐st♦❣r❛♠❛ ❞❡ ❢r❡❝✉❡♥❝✐❛s ♣❛r❛ ❧❛ ❞✐str✐❜✉❝✐ó♥ ❞❡ ❧❛ ❝♦♠♣♦♥❡♥t❡ ✏②✑ ❞❡ ❧❛ ✈❡❧♦❝✐❞❛❞ ✜♥❛❧ ❛s♦❝✐❛❞❛ ❛ ❧♦s ♣r♦t♦♥❡s q✉❡ ♣r♦✈✐❡♥❡♥ ❞❡ ❧❛ ✐♦✲ ♥ós❢❡r❛ ❞❡ ❙❛t✉r♥♦ ② ❞❡ ❧❛ s✉♣❡r✜❝✐❡ ❞❡ ❘❡❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✽ ✺✳✶✹✳ ●❛♥❛♥❝✐❛ ❡st♦❝ást✐❝❛ ❞❡ ❡♥❡r❣í❛ ♣r♦♠❡❞✐❛❞❛ s♦❜r❡ t♦❞❛ ❧❛ ❞✐str✐❜✉✲ ❝✐ó♥ ✈s✳ ❡❧ t✐❡♠♣♦ ♣❛r❛ ✉♥❛ ♠✉❡str❛ ❞❡ ♣r♦t♦♥❡s ❧♦❝❛❧✐③❛❞♦s ❡♥ ❞✐❢❡✲ r❡♥t❡s ♣♦s✐❝✐♦♥❡s ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛✳ ❘❡s✉❧t❛❞♦s ❜❛s❛❞♦s ❡♥ ❧❛s ♠❡❞✐❝✐♦♥❡s ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ r❡❛❧✐③❛❞♦s ♣♦r ❡❧ ❱♦②❛❣❡r ✶ ❡♥ ❧❛ tr❛②❡❝t♦r✐❛ ❞❡ ❡♥tr❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✾ ✺✳✶✺✳ ●❛♥❛♥❝✐❛ ❡st♦❝ást✐❝❛ ❞❡ ❡♥❡r❣í❛ ♣r♦♠❡❞✐❛❞❛ s♦❜r❡ t♦❞❛ ❧❛ ❞✐str✐❜✉✲ ❝✐ó♥ ✈s✳ ❡❧ t✐❡♠♣♦ ♣❛r❛ ✉♥❛ ♠✉❡str❛ ❞❡ ♣r♦t♦♥❡s ❧♦❝❛❧✐③❛❞♦s ❡♥ ❞✐❢❡✲ r❡♥t❡s ♣♦s✐❝✐♦♥❡s ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛✳ ❘❡s✉❧t❛❞♦s ❜❛s❛❞♦s ❡♥ ❧❛s ♠❡❞✐❝✐♦♥❡s ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ r❡❛❧✐③❛❞♦s ♣♦r ❡❧ ❱♦②❛❣❡r ✶ ❡♥ ❧❛ tr❛②❡❝t♦r✐❛ ❞❡ ❡♥tr❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✵ ✺✳✶✻✳ ●❛♥❛♥❝✐❛ ❡st♦❝ást✐❝❛ ❞❡ ❡♥❡r❣í❛ ♣r♦♠❡❞✐❛❞❛ s♦❜r❡ t♦❞❛ ❧❛ ❞✐str✐❜✉✲ ❝✐ó♥ ✈s✳ ❡❧ t✐❡♠♣♦ ♣❛r❛ ✉♥❛ ♠✉❡str❛ ❞❡ ♣r♦t♦♥❡s ② ❞❡ ♥✐tró❣❡♥♦ ❛tó✲ ♠✐❝♦ ✐♦♥✐③❛❞♦ ✭N+ ✮ ❧♦❝❛❧✐③❛❞♦s ❡♥ ❧❛ ❛t♠ós❢❡r❛ s✉♣❡r✐♦r ❞❡ ❚✐tá♥✳ ❘❡s✉❧t❛❞♦s ❜❛s❛❞♦s ❡♥ ❧❛s ♠❡❞✐❝✐♦♥❡s ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ r❡❛❧✐③❛❞♦s ♣♦r ❡❧ ❱♦②❛❣❡r ✶ ❡♥ ❧❛ tr❛②❡❝t♦r✐❛ ❞❡ ❡♥tr❛❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✶ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❮♥❞✐❝❡ ❞❡ ✜❣✉r❛s ①①✐ ✺✳✶✼✳ ●❛♥❛♥❝✐❛ ❡st♦❝ást✐❝❛ ❞❡ ❡♥❡r❣í❛ ♣r♦♠❡❞✐❛❞❛ s♦❜r❡ t♦❞❛ ❧❛ ❞✐str✐❜✉✲ ❝✐ó♥ ✈s✳ ❡❧ t✐❡♠♣♦ ♣❛r❛ ✉♥❛ ♠✉❡str❛ ❞❡ ♣r♦t♦♥❡s ❧♦❝❛❧✐③❛❞♦s ❡♥ ❞✐❢❡✲ r❡♥t❡s ♣♦s✐❝✐♦♥❡s ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛✳ ❘❡s✉❧t❛❞♦s ❜❛s❛❞♦s ❡♥ ❧❛s ♠❡❞✐❝✐♦♥❡s ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ r❡❛❧✐③❛❞♦s ♣♦r ❡❧ ❱♦②❛❣❡r ✷ ❡♥ ❧❛ tr❛②❡❝t♦r✐❛ ❞❡ s❛❧✐❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✷ ✺✳✶✽✳ ●❛♥❛♥❝✐❛ ❡st♦❝ást✐❝❛ ❞❡ ❡♥❡r❣í❛ ♣r♦♠❡❞✐❛❞❛ s♦❜r❡ t♦❞❛ ❧❛ ❞✐str✐❜✉✲ ❝✐ó♥ ✈s✳ ❡❧ t✐❡♠♣♦ ♣❛r❛ ✉♥❛ ♠✉❡str❛ ❞❡ ♣r♦t♦♥❡s ❧♦❝❛❧✐③❛❞♦s ❡♥ ❞✐❢❡✲ r❡♥t❡s ♣♦s✐❝✐♦♥❡s ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛✳ ❘❡s✉❧t❛❞♦s ❜❛s❛❞♦s ❡♥ ❧❛s ♠❡❞✐❝✐♦♥❡s ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ r❡❛❧✐③❛❞♦s ♣♦r ❡❧ ❱♦②❛❣❡r ✷ ❡♥ ❧❛ tr❛②❡❝t♦r✐❛ ❞❡ s❛❧✐❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✸ ✺✳✶✾✳ ●❛♥❛♥❝✐❛ ❡st♦❝ást✐❝❛ ❞❡ ❡♥❡r❣í❛ ♣r♦♠❡❞✐❛❞❛ s♦❜r❡ t♦❞❛ ❧❛ ❞✐str✐❜✉✲ ❝✐ó♥ ✈s✳ ❡❧ t✐❡♠♣♦ ♣❛r❛ ✉♥❛ ♠✉❡str❛ ❞❡ ♣r♦t♦♥❡s ② ❞❡ ♥✐tró❣❡♥♦ ❛tó✲ ♠✐❝♦ ✐♦♥✐③❛❞♦ ✭N+ ✮ ❧♦❝❛❧✐③❛❞♦s ❡♥ ❧❛ ❛t♠ós❢❡r❛ s✉♣❡r✐♦r ❞❡ ❚✐tá♥✳ ❘❡s✉❧t❛❞♦s ❜❛s❛❞♦s ❡♥ ❧❛s ♠❡❞✐❝✐♦♥❡s ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ r❡❛❧✐③❛❞♦s ♣♦r ❡❧ ❱♦②❛❣❡r ✷ ❡♥ ❧❛ tr❛②❡❝t♦r✐❛ ❞❡ s❛❧✐❞❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✹ ✺✳✷✵✳ ●❛♥❛♥❝✐❛ ❞❡ ❡♥❡r❣í❛ ❝✐♥ét✐❝❛ ❞❡ ❧♦s ♣r♦t♦♥❡s ✈s✳ ❧❛ ❞✐st❛♥❝✐❛ ❛❧ ♣❧❛✲ ♥❡t❛ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛✳ ❙❡ ♠✉❡str❛ ❧❛ ❣❛♥❛♥❝✐❛ ❞❡ ❡♥❡r❣í❛ ❡st♦❝ást✐❝❛✱ ❧❛ ❣❛♥❛♥❝✐❛ ❞❡ ❡♥❡r❣í❛ ❞❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ ② ❧❛ ❣❛♥❛♥❝✐❛ ❞❡ ❡♥❡r❣í❛ ❞❡❜✐❞❛ ❛❧ ❡❢❡❝t♦ ❝♦♠❜✐♥❛❞♦ ❞❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ ✰ ❝♦rr♦t❛❝✐ó♥✳ ✳ ✶✶✻ ✺✳✷✶✳ ❍✐st♦❣r❛♠❛ ❞❡ ❢r❡❝✉❡♥❝✐❛s ♣❛r❛ ❧❛ ❞✐str✐❜✉❝✐ó♥ ✜♥❛❧ ❞❡ ✈❡❧♦❝✐❞❛❞❡s ❛s♦❝✐❛❞❛ ❛ ❧♦s ♣r♦t♦♥❡s ❧♦❝❛❧✐③❛❞♦s ❝❡r❝❛ ❞❡ ❧❛ ór❜✐t❛ ❞❡ ❚✐tá♥ ✭tr❛✲ ②❡❝t♦r✐❛ ❞❡ s❛❧✐❞❛✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✼ ✺✳✷✷✳ ❍✐st♦❣r❛♠❛ ❞❡ ❢r❡❝✉❡♥❝✐❛s ♣❛r❛ ❧❛ ❡♥❡r❣í❛ ❝✐♥ét✐❝❛ ✜♥❛❧ ❛❧❝❛♥③❛❞❛ ♣♦r ✉♥❛ ♠✉❡str❛ ❞❡ ♣r♦t♦♥❡s ❞❡s♣✉és ❞❡ 5x107 ✐♥t❡r❛❝❝✐♦♥❡s ② s✉ ❢✉♥❝✐ó♥ ❞❡ ❛❥✉st❡ ❡♥ 10 RS ✭tr❛②❡❝t♦r✐❛ ❞❡ s❛❧✐❞❛✮✳ ❊❧ ❡s♣❡❝tr♦ ❞❡ ❡♥❡r❣í❛ q✉❡❞❛ ❜✐❡♥ ❞❡s❝r✐t♦ ♣♦r ✉♥❛ ●❛✉ss✐❛♥❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✽ ✺✳✷✸✳ ❍✐st♦❣r❛♠❛ ❞❡ ❢r❡❝✉❡♥❝✐❛s ♣❛r❛ ❧❛ ❡♥❡r❣í❛ ❝✐♥ét✐❝❛ ✜♥❛❧ ❛❧❝❛♥③❛❞❛ ♣♦r ✉♥❛ ♠✉❡str❛ ❞❡ ♣r♦t♦♥❡s ❞❡s♣✉és ❞❡ 5x107 ✐♥t❡r❛❝❝✐♦♥❡s ② s✉ ❢✉♥❝✐ó♥ ❞❡ ❛❥✉st❡ ❡♥ 15 RS ✭tr❛②❡❝t♦r✐❛ ❞❡ s❛❧✐❞❛✮✳ ❊❧ ❡s♣❡❝tr♦ ❞❡ ❡♥❡r✲ ❣í❛ q✉❡❞❛ ❜✐❡♥ ❞❡s❝r✐t♦ ♣♦r ✉♥❛ ❢✉♥❝✐ó♥ ❡①♣♦♥❡♥❝✐❛❧ ❞❡❝r❡❝✐❡♥t❡ ♣❛r❛ E > 100 eV ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✾ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❮♥❞✐❝❡ ❞❡ ✜❣✉r❛s ①①✐✐ ✺✳✷✹✳ ❍✐st♦❣r❛♠❛ ❞❡ ❢r❡❝✉❡♥❝✐❛s ♣❛r❛ ❧❛ ❡♥❡r❣í❛ ❝✐♥ét✐❝❛ ✜♥❛❧ ❛❧❝❛♥③❛❞❛ ♣♦r ✉♥❛ ♠✉❡str❛ ❞❡ ♣r♦t♦♥❡s ❞❡s♣✉és ❞❡ 5x107 ✐♥t❡r❛❝❝✐♦♥❡s ② s✉ ❢✉♥❝✐ó♥ ❞❡ ❛❥✉st❡ ❡♥ ❚✐tá♥ ✭tr❛②❡❝t♦r✐❛ ❞❡ s❛❧✐❞❛✮✳ ❊❧ ❡s♣❡❝tr♦ ❞❡ ❡♥❡r❣í❛ q✉❡❞❛ ❜✐❡♥ ❞❡s❝r✐t♦ ♣♦r ❞♦s ❢✉♥❝✐♦♥❡s ▲♦r❡♥t③✐❛♥❛s ❡♥ E < 117 eV ② E > 122 eV✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✵ ✺✳✷✺✳ ●❛♥❛♥❝✐❛ ❡st♦❝ást✐❝❛ ❞❡ ❡♥❡r❣í❛ ♣❛r❛ ❧♦s ❣r❛♥♦s ❞❡ ♣♦❧✈♦ ❝❛r❣❛❞♦s ❡♥ ❡❧ ❛♥✐❧❧♦ ❊ ❛ ❞✐❢❡r❡♥t❡s ❞✐st❛♥❝✐❛s✳ ❘❡s✉❧t❛❞♦s ❜❛s❛❞♦s ❡♥ ❧❛s ♠❡❞✐❝✐♦✲ ♥❡s ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❞❡❧ ❱♦②❛❣❡r ✶ ❡♥ s✉ ♣❛s♦ ♣♦r ❧❛ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✸ ✺✳✷✻✳ ●❛♥❛♥❝✐❛ ❡st♦❝ást✐❝❛ ❞❡ ❡♥❡r❣í❛ ♣❛r❛ ❧♦s ❣r❛♥♦s ❞❡ ♣♦❧✈♦ ♥❡✉tr♦s ❡♥ ❡❧ s✐st❡♠❛ ❞❡ ❛♥✐❧❧♦s ❞❡ ❙❛t✉r♥♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✹ ✺✳✷✼✳ ●❛♥❛♥❝✐❛ ❡st♦❝ást✐❝❛ ❞❡ ❡♥❡r❣í❛ ♣r♦♠❡❞✐❛❞❛ s♦❜r❡ t♦❞❛ ❧❛ ❞✐str✐❜✉✲ ❝✐ó♥ ✈s✳ ❡❧ t✐❡♠♣♦ ♣❛r❛ ✉♥❛ ♠✉❡str❛ ❞❡ ♣r♦t♦♥❡s ② ✉♥❛ ❞❡ ✐♦♥❡s ♣❡s❛✲ ❞♦s ❧♦❝❛❧✐③❛❞♦s s♦❜r❡ ❡❧ ❛♥✐❧❧♦ ❊✳ ▲❛s ✢✉❝t✉❛❝✐♦♥❡s ❞❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ t✐❡♥❡♥ ✉♥ ♣❡r✜❧ ❧✐♥❡❛❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✼ ✺✳✷✽✳ ●❛♥❛♥❝✐❛ ❡st♦❝ást✐❝❛ ❞❡ ❡♥❡r❣í❛ ♣r♦♠❡❞✐❛❞❛ s♦❜r❡ t♦❞❛ ❧❛ ❞✐str✐❜✉✲ ❝✐ó♥ ✈s✳ ❡❧ t✐❡♠♣♦ ♣❛r❛ ✉♥❛ ♠✉❡str❛ ❞❡ ♣r♦t♦♥❡s ❧♦❝❛❧✐③❛❞♦s ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ ❞✉r❛♥t❡ ❧❛ tr❛②❡❝t♦r✐❛ ❞❡ s❛❧✐❞❛✳ ▲❛s ✢✉❝t✉❛❝✐♦✲ ♥❡s ❞❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ t✐❡♥❡♥ ✉♥ ♣❡r✜❧ ✉♥✐❢♦r♠❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✽ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❮♥❞✐❝❡ ❞❡ ❝✉❛❞r♦s ✶✳✶✳ ❈❛r❛❝t❡ríst✐❝❛s ♣r✐♥❝✐♣❛❧❡s ❞❡❧ ♣❧❛s♠❛ ♣r❡s❡♥t❡ ❡♥ ❧❛s ♠❛❣♥❡tós❢❡r❛s ♣❧❛♥❡t❛r✐❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸ ✶✳✷✳ ❋✉❡♥t❡s ❞❡ ✐♦♥❡s ② ♠❡❝❛♥✐s♠♦s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❡♥ ❧❛s ♠❛❣♥❡tós❢❡r❛s ♣❧❛♥❡t❛r✐❛s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻ ✶✳✸✳ ❋✉❡♥t❡s ❞❡ ❡♥❡r❣í❛ ♣❛r❛ ❡❧ tr❛♥s♣♦rt❡ ② ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s✳ ✳ ✼ ✷✳✶✳ Pr♦♣✐❡❞❛❞❡s ❢✉♥❞❛♠❡♥t❛❧❡s ❞❡ ❧♦s s❛té❧✐t❡s r❡❣✉❧❛r❡s ❞❡ ❙❛t✉r♥♦✳ ❚♦✲ ♠❛❞♦ ❞❡ ▼♦rr✐s♦♥ ❡t ❛❧✳ ❬✶✾✽✻❪ ② ❙❤❡♣♣❛r❞ ❬✷✵✵✼❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵ ✷✳✷✳ Pr♦♣✐❡❞❛❞❡s ❢✉♥❞❛♠❡♥t❛❧❡s ❞❡ ❧♦s s❛té❧✐t❡s ✐rr❡❣✉❧❛r❡s ❞❡ ❙❛t✉r♥♦✳ ❚♦♠❛❞♦ ❞❡ ❙❤❡♣♣❛r❞ ❬✷✵✵✼❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✷✳✸✳ ✭❝♦♥t✐♥✉❛❝✐ó♥✮ Pr♦♣✐❡❞❛❞❡s ❢✉♥❞❛♠❡♥t❛❧❡s ❞❡ ❧♦s s❛té❧✐t❡s ✐rr❡❣✉❧❛r❡s ❞❡ ❙❛t✉r♥♦✳ ❚♦♠❛❞♦ ❞❡ ❙❤❡♣♣❛r❞ ❬✷✵✵✼❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷ ✷✳✹✳ Pr♦♣✐❡❞❛❞❡s ❢ís✐❝❛s ❞❡❧ s✐st❡♠❛ ❞❡ ❛♥✐❧❧♦s ❞❡ ❙❛t✉r♥♦ ❬❈✉③③✐✱ ✶✾✽✸❀ ❈✉③③✐ ❡t ❛❧✳✱ ✶✾✽✹❀ ❩❡❜❦❡r ❡t ❛❧✳✱ ✶✾✽✺❀ ❊s♣♦s✐t♦✱ ✶✾✽✻❀ ❘♦s❡♥✱ ✶✾✽✾❀ ▼✉rr❛② ❛♥❞ ❉❡r♠♦tt✱ ✶✾✾✾❀ ❍❛rtq✉✐st ❡t ❛❧✳✱ ✷✵✵✸❪✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✹ ✷✳✺✳ ✭❝♦♥t✐♥✉❛❝✐ó♥✮ Pr♦♣✐❡❞❛❞❡s ❢ís✐❝❛s ❞❡❧ s✐st❡♠❛ ❞❡ ❛♥✐❧❧♦s ❞❡ ❙❛t✉r♥♦✳ ✳ ✸✺ ✹✳✶✳ ❱❛❧♦r❡s ❞❡ α ② β ♦❜t❡♥✐❞♦s ♣❛r❛ ❡❧ ❱♦②❛❣❡r ✶ ② ❱♦②❛❣❡r ✷ ❡♥ s✉s ❡♥❝✉❡♥tr♦s ❝♦♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛ ② ❡①t❡r♥❛ ❞❡ ❙❛t✉r♥♦✳ ✳ ✳ ✳ ✳ ✳ ✼✸ ✹✳✷✳ Pr♦♣✐❡❞❛❞❡s ♣r✐♥❝✐♣❛❧❡s ❞❡ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❡♥ ❧❛ ♠❛❣♥❡tós✲ ❢❡r❛ ✐♥t❡r♥❛ ❞❡ ❙❛t✉r♥♦ ✭1 amu =✶✳✻✻x10−27 kg✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✽ ✹✳✸✳ Pr♦♣✐❡❞❛❞❡s ♣r✐♥❝✐♣❛❧❡s ❞❡ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❡♥ ❧❛ ♠❛❣♥❡tós✲ ❢❡r❛ ❡①t❡r♥❛ ❞❡ ❙❛t✉r♥♦ ✭1 amu =✶✳✻✻x10−27 kg✮✳ ①①✐✐✐ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶ ❮♥❞✐❝❡ ❞❡ ❝✉❛❞r♦s ①①✐✈ ✹✳✹✳ Pr♦♣✐❡❞❛❞❡s ❞❡r✐✈❛❞❛s ❞❡ ❧❛s ♣❛rtí❝✉❧❛s q✉❡ ❝♦♥st✐t✉②❡♥ ❛ ❧♦s ❛♥✐❧❧♦s ❞❡ ❙❛t✉r♥♦✳ ❙❡ ❤❛ s✉♣✉❡st♦ q✉❡ ❡♥ t♦❞♦s ❧♦s ❛♥✐❧❧♦s ✭❡①❝❡♣t♦ ❡♥ ❡❧ ❛♥✐❧❧♦ ❊✮ ❧❛s ♣❛rtí❝✉❧❛s ❡stá♥ ❢♦r♠❛❞❛s ♣♦r ✉♥❛ ♠❡③❝❧❛ ❞❡ ❤✐❡❧♦✲s✐❧✐❝❛t♦s✳ ✽✻ ✺✳✶✳ ❊♥❡r❣í❛ ❝✐♥ét✐❝❛ ♠í♥✐♠❛ ✭❡❱✮ q✉❡ t✐❡♥❡♥ ❧♦s ♣r♦t♦♥❡s ② ❧♦s ✐♦♥❡s ♣❡✲ s❛❞♦s ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✹ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❆♥á❧✐s✐s ❞❡ ❧❛s ❢✉❡r③❛s ❡st♦❝ást✐❝❛s q✉❡ ❛❝tú❛♥ s♦❜r❡ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦ ▼✳ ❡♥ ❈✳ ❊❧✐③❛❜❡t❤ ▼❛rtí♥❡③ ●ó♠❡③ Pr❡s❡♥t❛❞❛ ♣❛r❛ ♦❜t❡♥❡r ❡❧ ❣r❛❞♦ ❞❡ ❉♦❝t♦r❛ ❡♥ ❈✐❡♥❝✐❛s ✭❋ís✐❝❛ ❊s♣❛❝✐❛❧✮ ▼❛②♦ ✷✵✵✼ ❘❡s✉♠❡♥ ❈♦♥t❡①t♦✿ ❊❧ ❝♦♥♦❝✐♠✐❡♥t♦ ❛❝t✉❛❧ s♦❜r❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦ s❡ ❜❛s❛ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ❡♥ ❧❛s ♠❡❞✐❝✐♦♥❡s ❞❡ ♣❧❛s♠❛✱ ♣❛rtí❝✉❧❛s ❡♥❡r❣ét✐❝❛s✱ ♦♥❞❛s ② ❝❛♠♣♦ ♠❛❣♥ét✐❝♦❀ r❡❛❧✐③❛❞❛s ♣♦r tr❡s ♠✐s✐♦♥❡s P✐♦♥❡❡r ✶✶✱ ❱♦②❛❣❡r ✶ ② ❱♦②❛❣❡r ✷✳ ❊❧ ♣❛s❛❞♦ ✶ ❞❡ ❥✉❧✐♦ ❞❡ ✷✵✵✹ ❧❛ ♥❛✈❡ ❈❛ss✐♥✐ ❡♥tró ❡①✐t♦s❛♠❡♥t❡ ❡♥ ór❜✐t❛ ❛❧r❡❞❡❞♦r ❞❡ ❙❛t✉r♥♦ ② ❡stá ♣r♦♣♦r❝✐♦♥❛♥❞♦ ❧❛ ❝♦❜❡rt✉r❛ ❝❛s✐ ❣❧♦❜❛❧ ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❑r♦♥✐❛♥❛✳ ❆❝t✉❛❧♠❡♥t❡ ❡s ❛❝❡♣t❛❞♦ q✉❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦ ♣✉❡❞❡ s❡r ❞✐✈✐❞✐❞❛ ❡♥ ❝✉❛tr♦ r❡❣✐♦♥❡s ❞❡ ♣❧❛s♠❛ ❝♦♥ ❞✐❢❡r❡♥t❡s ❝❛r❛❝t❡ríst✐❝❛s ❢ís✐❝❛s ② q✉í♠✐❝❛s ❬❨♦✉♥❣ ❡t ❛❧✳✱ ✷✵✵✺❪✿ ✭✐✮ ❧❛ ❡①t❡r♥❛ q✉❡ ❝♦♥t✐❡♥❡ ♣❧❛s♠❛ ❝❛❧✐❡♥t❡ ❞♦♠✐♥❛❞♦ ♣♦r ♣r♦t♦♥❡s ✭H+ ✮✱ ✭✐✐✮ ✉♥❛ r❡❣✐ó♥ ❧❧❛♠❛❞❛ ❧❛ ♣❧❛s♠❛s❢❡r❛ ❡①t❡r♥❛ q✉❡ ❝♦♥s✐st❡ ❞❡ ♣❧❛s♠❛ ❛❧t❛♠❡♥t❡ ✈❛✲ r✐❛❜❧❡ q✉❡ ❝♦rr♦t❛ ♣❛r❝✐❛❧♠❡♥t❡ ② q✉❡ ❝♦♥t✐❡♥❡ ✉♥❛ ♠❡③❝❧❛ ❞❡ ♣r♦t♦♥❡s ✭H+ ✮✱ ♦①í❣❡♥♦ ❛tó♠✐❝♦ ✐♦♥✐③❛❞♦ ✭O+ ✮ ❡ ✐♦♥❡s ❞❡ ♣r♦❞✉❝t♦s ❞❡ ❛❣✉❛ ✭♣♦r ❡❥❡♠♣❧♦✱ ♣r♦t♦♥❡s ✭H+ )✱ + ♦①í❣❡♥♦ ♠♦❧❡❝✉❧❛r ✐♦♥✐③❛❞♦ ✭O2 , O+ 3 ✮✮✱ ✭✐✐✐✮ ❧❛ ♣❧❛s♠❛s❢❡r❛ ✐♥t❡r♥❛ q✉❡ ❡s ♠❡♥♦s ✈❛✲ r✐❛❜❧❡ ② ❝♦♥ ✉♥❛ r♦t❛❝✐ó♥ ❝❛s✐ rí❣✐❞❛ q✉❡ ❝♦♥t✐❡♥❡ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♦①í❣❡♥♦ ❛tó♠✐❝♦ ✐✈ ✐♦♥✐③❛❞♦ ✭O+ ✮ ❡ ✐♦♥❡s ❞❡ ♣r♦❞✉❝t♦s ❞❡ ❛❣✉❛✱ ② ✭✐✈✮ ✉♥❛ ❝❛♣❛ ❞❡ ♣❧❛s♠❛ q✉❡ ❝♦♥s✐st❡ ❞❡ ♦①í❣❡♥♦ ❛tó♠✐❝♦ ✐♦♥✐③❛❞♦ ✭O+ ✮ ② ❞❡ ♦①í❣❡♥♦ ♠♦❧❡❝✉❧❛r ✐♦♥✐③❛❞♦ ✭O+  ✮ ❧♦❝❛❧✐③❛❞❛ ❞✐r❡❝t❛♠❡♥t❡ s♦❜r❡ ❧♦s ❛♥✐❧❧♦s ❆ ② ❇✳ ❊♥ ❧❛ r❡❣✐ó♥ ✐♥t❡r♥❛ s❡ ❡♥❝✉❡♥tr❛ ❡❧ s✐st❡♠❛ ❞❡ ❛♥✐❧❧♦s✳ ❊❧ s✐st❡♠❛ ❞❡ ❛♥✐❧❧♦s ❞❡ ❙❛t✉r♥♦ ❡s ❡❧ ♠ás ♠❛s✐✈♦✱ ❡①t❡♥s♦✱ ❜r✐❧❧❛♥t❡ ② ❞✐✈❡rs♦ ❞❡❧ ❙✐st❡♠❛ ❙♦❧❛r ② ♣♦r ❡st❛s r❛③♦♥❡s ❡s ❡❧ ♠ás ❡st✉❞✐❛❞♦✳ ❚✐❡♥❡ ✉♥ ❞✐á♠❡tr♦ q✉❡ ❝✉❜r❡ ✉♥❛ ❞✐st❛♥❝✐❛ r❛❞✐❛❧ ❞❡s❞❡ ∼✶✳✶✶ RS ❤❛st❛ ∼✽ RS ✭1 RS = 60 268 km✮✱ s✉ ❡s♣❡s♦r ✈❛rí❛ ❞❡s❞❡ ✉♥♦s ✺ ♠❡tr♦s ❤❛st❛ ❧♦s 107 ♠❡tr♦s ❡♥ ❡❧ ❛♥✐❧❧♦ ❊ ② ❧❛ ♠❛s❛ t♦t❛❧ ❡s ∼ 3x1022 g.✱ s✐♠✐❧❛r ❛ ❧❛ ♠❛s❛ ❞❡ ▼✐♠❛s✳ ▲❛s ♣❛rtí❝✉❧❛s q✉❡ ❧♦s ❝♦♥st✐t✉②❡♥ s♦♥ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ❞❡ ❤✐❡❧♦ ❞❡ ❛❣✉❛ ② s✉s t❛♠❛ñ♦s ✈❛rí❛♥ ❞❡s❞❡ ✉♥❛s ♠✐❝r❛s ❤❛st❛ ✈❛r✐♦s ♠❡tr♦s ❞❡ ❞✐á♠❡tr♦✳ ▲❛s ❝❛r❛❝t❡ríst✐❝❛s ♠ás s♦❜r❡s❛❧✐❡♥t❡s ❞❡ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❡♥❡r❣ét✐❝❛s ❡♥ ❧❛ r❡❣✐ó♥ ♠❛❣♥❡t♦s❢ér✐❝❛ ✐♥t❡r♥❛ s♦♥✿ ✶✮ ❧♦s ❛♥✐❧❧♦s ② ❧♦s s❛té❧✐t❡s ♣❡q✉❡ñ♦s q✉❡ ❛❧❧í s❡ ❡♥❝✉❡♥tr❛♥ r❡❞✉❝❡♥ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❝✉②❛s ❡♥❡r❣í❛s s♦♥ ♠❛②♦r❡s ❛ ✵✳✺ ▼❡❱ ❛ ✈❛❧♦r❡s ❞❡❧ ♦r❞❡♥ ❞❡ 103 ✈❡❝❡s ♠❡♥♦r q✉❡ ❞❡ ♦tr❛ ♠❛♥❡r❛ ❡st❛rí❛♥ ♣r❡s❡♥t❡s✱ ✷✮ ❧❛ s❛❧♣✐❝❛❞✉r❛ ② ❞❡❣❛s❛♠✐❡♥t♦ ❞❡ ❧❛ s✉♣❡r✜❝✐❡ ❞❡ ❧♦s s❛té❧✐t❡s ✐♥②❡❝t❛ ♣❛rtí❝✉❧❛s ❛❧ s✐st❡♠❛ ②✱ ♠❡❞✐❛♥t❡ ❛❧❣ú♥ ♣r♦❝❡s♦ ❢ís✐❝♦✱ ❧❛s ♣❛rtí❝✉❧❛s s♦♥ ❛❝❡❧❡r❛❞❛s ❛ ❡♥❡r❣í❛s ❞❡❧ ♦r❞❡♥ ❞❡ ❞❡❝❡♥❛s ❞❡ ❦❡❱✱ ✸✮ ❧❛ ❞✐str✐❜✉❝✐ó♥ r❛❞✐❛❧ ❞❡ ♣r♦t♦♥❡s ♠✉② ❡♥❡r❣ét✐❝♦s✱ EP > ❞❡❝❡♥❛s ❞❡ ▼❡❱✱ ❡①❤✐❜❡ tr❡s ♣✐❝♦s ❛s♦❝✐❛❞♦s ❝♦♥ ❧♦s ❛♥✐❧❧♦s ② s❛té❧✐t❡s✱ ✹✮ ✉♥❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣r♦t♦♥❡s✱ EP ∼✶ ▼❡❱ ✱ ②❛❝❡ ❢✉❡r❛ ❞❡ ❧❛ ór❜✐t❛ ❞❡ ❊♥❝❡❧❛❞♦✱ ✺✮ ✉♥❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣r♦t♦♥❡s EP < ✵✳✷✺ ▼❡❱ t✐❡♥❡ ❛♣❛r❡♥t❡♠❡♥t❡ ✉♥ ♦r✐❣❡♥ ❛s♦❝✐❛❞♦ ❝♦♥ ❉✐♦♥❡✱ ❚❡t✐s✱ ❊♥❝❡❧❛❞♦✱ ❡❧ ❛♥✐❧❧♦ ❊✱ ▼✐♠❛s ② ❡❧ ❛♥✐❧❧♦ ●✱ ✻✮ ✉♥❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ❡❧❡❝tr♦♥❡s ❞❡ ❜❛❥❛ ❡♥❡r❣í❛ ❡stá ❛s♦❝✐❛❞❛ ❝♦♥ ❧♦s s❛té❧✐t❡s✳ ▲❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ s❡ ❞✐st✐♥❣✉❡ ♣♦r ❧❛ ❡①✐st❡♥❝✐❛ ❞❡ ♣❧❛s♠❛ tér♠✐❝♦ ❝♦♥ ✉♥❛ ❞❡♥s✐❞❛❞ ❞❡ 2x10−2 ❛ 5x10−1 iones cm−3 ❝❡r❝❛ ❞❡❧ ❡❝✉❛❞♦r ② ❛ ✉♥❛ t❡♠♣❡r❛t✉r❛ ∼ 106 K✳ ▲❛ ❢✉❡♥t❡ ♣r✐♥❝✐♣❛❧ ❞❡ ❡st❡ ♣❧❛s♠❛ ❡s ❚✐tá♥ ② s✉ ❞❡♥s❛ ❛t♠ós❢❡r❛ q✉❡ ✲❛ tr❛✈és ❞❡ ♣r♦❝❡s♦s ❞❡ ❢♦t♦✐♦♥✐③❛❝✐ó♥ ❞❡ ♥❡✉tr♦s q✉❡ ❡s❝❛♣❛♥ ❞❡❧ s❛té❧✐t❡ ♦ ❞❡ ❧❛ ✐♥t❡r✲ ❛❝❝✐ó♥ ❞✐r❡❝t❛ ❞❡ ❧❛ ✐♦♥ós❢❡r❛ ❞❡❧ s❛té❧✐t❡ ❝♦♥ ❧❛ ♠❛❣♥❡tós❢❡r❛✲ ✐♥②❡❝t❛♥ ♣❛rtí❝✉❧❛s ❛ ❧❛ r❡❣✐ó♥✳ ❊st❡ ♣❧❛s♠❛✱ ❡♥ ❣❡♥❡r❛❧✱ s❡ ♠✉❡✈❡ ❡♥ ❧❛ ❞✐r❡❝❝✐ó♥ ❞❡ ❝♦rr♦t❛❝✐ó♥ ② ❛ ✉♥❛ ✈❡❧♦❝✐❞❛❞ ❝❡r❝❛♥❛ ❛ ❧❛ r♦t❛❝✐ó♥ rí❣✐❞❛✳ ▲❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❡♥❡r❣ét✐❝❛s ❝♦♥s✐s✲ t❡ ❞❡ ❡❧❡❝tr♦♥❡s✱ ❞❡ ♣r♦t♦♥❡s ② ❞❡ ✐♦♥❡s ♠ás ♣❡s❛❞♦s✳ ❙✉s ❡♥❡r❣í❛s ✈❛♥ ❞❡ < 2 MeV ❛ 10 RS ❤❛st❛ < 1 MeV ❝❡r❝❛ ❞❡ ❧❛ ♠❛❣♥❡t♦♣❛✉s❛✱ ♣❡r♦ ❧♦s r❛②♦s ❝ós♠✐❝♦s ♠✉② ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✈ ❡♥❡r❣ét✐❝♦s t✐❡♥❡♥ ❧✐❜r❡ ❛❝❝❡s♦ ❛ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛✳ ❈♦♠♦ ✉♥❛ ❝♦♥s❡❝✉❡♥❝✐❛✱ ❡❧ ❡s♣❡❝tr♦ ❞❡ ❡♥❡r❣í❛ ❞❡ ❧♦s ♣r♦t♦♥❡s t✐❡♥❡ ❞♦s ❝♦♠♣♦♥❡♥t❡s✿ ✉♥❛ ❝♦♠♣♦♥❡♥t❡ q✉❡ s✐❣✉❡ ✉♥❛ ❧❡② ❞❡ ♣♦t❡♥❝✐❛s E −γ ❝♦♥ γ ∼ 7 q✉❡ ❧❧❡❣❛ ❛ s❡r ♠❡♥♦r ♣❛r❛ ❡♥❡r❣í❛s ❛❜❛❥♦ ❞❡ 100 keV❀ ② ✉♥❛ ❝♦♠♣♦♥❡♥t❡ ❞❡ ❛❧t❛ ❡♥❡r❣í❛ ✐♥t❡r♣❧❛♥❡t❛r✐❛ ❝♦♥ γ ∼ 2✳ ▲❛ r❡❣✐ó♥ ❞❡ ❜❛❥❛s ❡♥❡r❣í❛s ❞❡❧ ❡s♣❡❝tr♦ ❞❡ ♣r♦t♦♥❡s s❡ ♣❛r❡❝❡ ❛ ✉♥❛ ❞✐str✐❜✉❝✐ó♥ ▼❛①✇❡❧❧✐❛♥❛ ❝♦♥ ✉♥❛ ❝♦❧❛ ❞❡ ❛❧t❛ ❡♥❡r❣í❛ ② ♣✉❡❞❡ s❡r ❛❥✉st❛❞❛ ♣♦r ✉♥❛ ❞✐str✐❜✉❝✐ó♥ κ ✭❦❛♣♣❛✮ ❬❑r✐♠✐❣✐s ❡t ❛❧✳✱ ✶✾✽✸❪✳ ❊♥ ❧❛s ♠❡❞✐❝✐♦♥❡s ❞❡❧ ❱♦②❛❣❡r s❡ ❡♥❝♦♥tró q✉❡ ❛❞❡♠ás ❞❡ ♣r♦t♦♥❡s✱ ❧❛ r❡❣✐ó♥ ❡①t❡r♥❛ ❝♦♥t✐❡♥❡ ❝❛r❜♦♥♦ ❛tó♠✐❝♦ ✐♦♥✐③❛❞♦ ✭C+ ✮✱ ♥✐tró❣❡♥♦ ❛tó✲ ♠✐❝♦ ✐♦♥✐③❛❞♦ ✭N+ ✮✱ ♥✐tró❣❡♥♦ ♠♦❧❡❝✉❧❛r ✐♦♥✐③❛❞♦ ✭N+ 2 ✮ ② ♦①í❣❡♥♦ ❛tó♠✐❝♦ ✐♦♥✐③❛❞♦ ✭O+ ✮❀ s✐♥ ❡♠❜❛r❣♦ ❈❛ss✐♥✐ ♥♦ ❧♦s ❞❡t❡❝tó ❡♥ ❛❜✉♥❞❛♥❝✐❛s ❝♦♥s✐❞❡r❛❜❧❡s✳ P♦s✐❜❧❡s ❡①♣❧✐❝❛❝✐♦♥❡s ❛ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❞❡ ❛❧t❛s ❡♥❡r❣í❛s ♣r❡s❡♥t❡s ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦ ✐♥✈♦❧✉❝r❛♥ ❧❛ ❧✐❜❡r❛❝✐ó♥ ❞❡ ❡♥❡r❣í❛ ♠❛❣♥ét✐❝❛ ✲❝♦♠♦ ❝♦♥s❡❝✉❡♥❝✐❛ ❞❡ ❧❛ r❡❝♦♥❡①✐ó♥✲ q✉❡ ❝❛❧✐❡♥t❛ ❛ ❧❛ ❝♦♠♣♦♥❡♥t❡ ✐ó♥✐❝❛ ❞❡❧ ♣❧❛s♠❛ ② ❡♥✲ t♦♥❝❡s ❧❛ ❛❝❡❧❡r❛ ❤❛st❛ ❛❧❝❛♥③❛r ❡♥❡r❣í❛s ❞❡❧ ♦r❞❡♥ ❞❡ ✷ ▼❡❱ ❬❙❝❤❛r❞t ❡t ❛❧✳✱ ✶✾✽✺❪✳ ❖tr❛ ♣♦s✐❜✐❧✐❞❛❞ ❡s ❧❛ ♠❛❣♥❡t♦❝♦❧❛ ❞❡ ❙❛t✉r♥♦ ❡♥ ❞♦♥❞❡ ❧♦s ❝❛♠❜✐♦s ❡♥ ❧❛ ❝♦♥✜❣✉r❛✲ ❝✐ó♥ ✐♥❞✉❝✐❞♦s ♣♦r ♣❡rt✉r❜❛❝✐♦♥❡s ❡♥ ❡❧ ♠❡❞✐♦ ✐♥t❡r♣❧❛♥❡t❛r✐♦ ♣✉❡❞❡♥ ❛❝❡❧❡r❛r t❛♥t♦ ❛ ❧♦s ✐♦♥❡s ❝♦♠♦ ❛ ❧♦s ❡❧❡❝tr♦♥❡s ❤❛st❛ ✈❛r✐♦s ❝✐❡♥t♦s ❞❡ ❦❡❱ ❬❑r✐♠✐❣✐s ❡t ❛❧✳✱ ✶✾✽✶❀ ✶✾✽✷❪✳ ❖❜❥❡t✐✈♦ ✿ ▲♦s ♠❡❝❛♥✐s♠♦s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ♣♦r ♦♥❞❛s ❞❡ ❝❤♦q✉❡✱ ♣♦r ♦♥❞❛s ❞❡ ♣❧❛s♠❛ ② ♣♦r ❝❛♠♣♦s ❡❧é❝tr✐❝♦s ✉♥✐❞✐r❡❝❝✐♦♥❛❧❡s s♦♥ ❛❧❣✉♥♦s ❞❡ ❧♦s q✉❡ s❡ ❛♣❧✐❝❛♥ ♣❛r❛ ❡①♣❧✐❝❛r ❧❛ ❡♥❡r❣✐③❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❡♥ ❆str♦❢ís✐❝❛✳ ❆❞❡♠ás ❞❡ ❧♦s ❛♥t❡r✐♦r❡s✱ ❞❡st❛❝❛ ❡❧ ♠❡❝❛♥✐s♠♦ ❡st♦❝ást✐❝♦ q✉❡ r❡❣✉❧❛r♠❡♥t❡ ❝♦♥s✐❞❡r❛ ❧❛s ✐♥t❡r❛❝❝✐♦♥❡s ♦♥❞❛✲ ♣❛rtí❝✉❧❛ ② ❡❧ ♣r♦❝❡s♦ ❛❧❡❛t♦r✐♦ s❡ ❜❛s❛ ❡♥ r❡s♦❧✈❡r ❧❛ ❡❝✉❛❝✐ó♥ ❞❡ ❋♦❦❦❡r✲P❧❛♥❝❦✱ ♦ ❜✐❡♥✱ ❡♥ ❝♦♥s✐❞❡r❛r ❛ ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ❝♦♠♦ ✉♥❛ ❞✐❢✉s✐ó♥ ❡♥ ❡❧ ❡s♣❛❝✐♦ ❞❡ ♠♦♠❡♥t♦s ❛ tr❛✈és ❞❡ ❧❛ ❛♣r♦①✐♠❛❝✐ó♥ ❝✉❛s✐✲❧✐♥❡❛❧✳ ▲❛ ✈❡♥t❛❥❛ ❞❡ ❧♦s ♠❡❝❛♥✐s♠♦s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❡st♦❝ást✐❝❛ ❡s q✉❡ ❣❡♥❡r❛♥ ❡s♣❡❝tr♦s ❞❡ ❡♥❡r❣í❛ ❞❡s❝r✐t♦s ♣♦r ✉♥❛ ❧❡② ❞❡ ♣♦t❡♥❝✐❛s✱ ♣❡r♦ ❛❞❡♠ás ❞❡ r❡q✉❡r✐r ❞❡ ♠✉❝❤♦ t✐❡♠♣♦ ♣❛r❛ ❛❧❝❛♥③❛r ❡s❛s ❡♥❡r❣í❛s✱ s❡ s✉♣♦♥❡ ✉♥ ♣❡r✜❧ ❞❡ ♦♥❞❛s ❝♦♥♦❝✐❞♦✳ ❊♥ ❡s♦s ♠♦❞❡❧♦s ❧❛ ❡st♦❝❛st✐❝✐❞❛❞ ❡s ♣r♦❞✉❝✐❞❛ ♣♦r ❡❧ ♠♦✈✐♠✐❡♥t♦ ❣✐r♦tró♣✐❝♦ ❞❡ ❧❛s ♣❛rtí❝✉❧❛s ②✱ ❝✉❛♥❞♦ ❡❧ ♣❡r✐♦❞♦ ❞❡ ❣✐r♦ ❡s ♠❛②♦r q✉❡ ❡❧ t✐❡♠♣♦ ❡♠♣❧❡❛❞♦ ♣❛r❛ ❧❛ ❛❝❡❧❡r❛❝✐ó♥✱ ❡s ♥❡❝❡s❛r✐♦ ♣❧❛♥t❡❛r ✉♥❛ ♥✉❡✈❛ ❢♦r♠✉❧❛❝✐ó♥ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✈✐ ❜❛s❛❞❛ ❡♥ ❧❛s ✢✉❝t✉❛❝✐♦♥❡s ❡st♦❝ást✐❝❛s ❞❡ ❛❧❣ú♥ ❝❛♠♣♦ ❞❡ ❢✉❡r③❛s✳ ❊♥ ❡st❡ tr❛❜❛❥♦ s❡ ♣r♦♣♦♥❡ ② s❡ ❞❡s❛rr♦❧❧❛ ✉♥ ♠♦❞❡❧♦ ❣❡♥❡r❛❧ ❞❡ ❡♥❡r❣✐③❛❝✐ó♥ ❜❛s❛❞♦ ❡♥ ❧❛ ❡st♦❝❛st✐❝✐❞❛❞ ✭♦ ❛❧❡❛t♦r✐❡❞❛❞✮ ❞❡❧ ❝❛♠♣♦ ❞❡ ❢✉❡r③❛s q✉❡ ❛❝tú❛ s♦❜r❡ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ② ♥❡✉tr❛s ❡♥ ✉♥❛ ♠❛❣♥❡tós❢❡r❛ ♣❧❛♥❡t❛r✐❛✳ ❊❧ ♠♦❞❡❧♦ ❝♦♥s✐❞❡r❛ q✉❡ ❧❛s ✢✉❝t✉❛❝✐♦♥❡s ❡st♦❝ást✐❝❛s ❞❡❧ ❝❛♠♣♦ ❞❡ ❢✉❡r③❛s ✭❡❧é❝tr✐❝♦ ♦ ❣r❛✈✐t❛❝✐♦♥❛❧✮ t✐❡♥❞❡♥✱ ❡♥ ♣r♦♠❡❞✐♦✱ ❛ ✐♥❝r❡♠❡♥t❛r ❧❛ ❡♥❡r❣í❛ ❞❡ ❧❛s ♣❛rtí❝✉❧❛s✳ ❊❧ ❝❛rá❝t❡r ❛❧❡❛t♦r✐♦ ❞❡ ❧❛s ✢✉❝t✉❛❝✐♦♥❡s s❡ s✐♠✉❧❛ ❛ tr❛✈és ❞❡ ✉♥ ♠ét♦❞♦ ❡st❛❞íst✐❝♦ ❞❡ ▼♦♥t❡ ❈❛r❧♦✳ ▼❡t♦❞♦❧♦❣í❛✿ ❙❡ r❡s✉❡❧✈❡ ❧❛ ❡❝✉❛❝✐ó♥ ❞❡ ♠♦✈✐♠✐❡♥t♦ ♣❛r❛ ✉♥❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ✭❝❛r❣❛❞❛s ♦ ♥❡✉tr❛s✮ q✉❡ ✐♥❝❧✉②❡ ❛ ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ❞❡❜✐❞❛ ❛❧ ❝❛♠♣♦ ❞❡ ❢✉❡r③❛s ❡st♦❝ást✐❝♦ ✭❞❡ ♦r✐❣❡♥ ❡❧❡❝tr♦♠❛❣♥ét✐❝♦ ♦ ❣r❛✈✐t❛❝✐♦♥❛❧✱ s❡❣ú♥ s❡❛ ❡❧ ❝❛s♦✮✱ ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ❣r❛✈✐t❛❝✐♦♥❛❧ ❡♥tr❡ ❧❛ ♣❛rtí❝✉❧❛ ② ❡❧ ♣❧❛♥❡t❛✱ ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ❞❡ ▲♦r❡♥t③ q✉❡ ❝♦♥t✐❡♥❡ ❛❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❧♦❝❛❧ ② ❛❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❝♦rr♦t❛❝✐♦♥❛❧ ✭❡♥ ❡❧ ❝❛s♦ ❞❡ ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s✮ ② ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ❞❡❜✐❞❛ ❛ ❧❛ ❢✉❡r③❛ ❞❡ ♣r❡s✐ó♥ ❞❡ r❛❞✐❛❝✐ó♥ ✭q✉❡ ❡❥❡r❝❡ ❡❧ ❙♦❧ s♦❜r❡ ❧❛s ♣❛rtí❝✉❧❛s ❞❡ ♣♦❧✈♦✮✳ ❙❡ ❝♦♥s✐❞❡r❛♥ ❞✐❢❡r❡♥t❡s ❝♦♥❞✐❝✐♦♥❡s ✐♥✐❝✐❛❧❡s ❝♦♠♦ ❧❛ ❡s♣❡❝✐❡ ✐ó♥✐❝❛✱ ❧❛s ♣r♦♣✐❡❞❛❞❡s ❡s♣❡❝í✜❝❛s ❞❡ ❧❛s ♣❛rtí❝✉❧❛s ❞❡ ♣♦❧✈♦ ❡♥ ❝❛❞❛ ❛♥✐❧❧♦ ② ❧❛ ❞✐str✐❜✉❝✐ó♥ ❞❡ ✈❡❧♦❝✐❞❛❞❡s ❞❡ ❧❛s ♣❛rtí❝✉❧❛s q✉❡ ❛ s✉ ✈❡③ ❞❡♣❡♥❞❡ ❞❡ ❧❛s ❢✉❡♥t❡s ❞❡ ❧❛s ❝✉❛❧❡s ♣r♦✈✐❡♥❡♥ ✭❧❛ ✐♦♥ós❢❡r❛ ❞❡❧ ♣❧❛♥❡t❛✱ ❡❧ ❣❛s ❡♠✐t✐❞♦ ♣♦r ❧♦s s❛té❧✐t❡s ② ❡❧ ♠❛t❡r✐❛❧ ❞❡ ❧♦s ❛♥✐❧❧♦s✮✳ ❘❡s✉❧t❛❞♦s✿ ❊st❡ ♠♦❞❡❧♦ ❡s ❛♣❧✐❝❛❞♦ ❛ ❧❛ ♠❛❣♥❡tós❢❡r❛ ✭✐♥t❡r♥❛ ② ❡①t❡r♥❛✮ ❞❡ ❙❛t✉r♥♦ ❛sí ❝♦♠♦ ❛❧ s✐st❡♠❛ ❞❡ ❛♥✐❧❧♦s✳ ❙❡ ❝♦♥s✐❞❡r❛ ✉♥❛ ♠✉❡str❛ ❞❡ ♣r♦t♦♥❡s ✭H+ ✮ ② + + ❞❡ ✐♦♥❡s ♣❡s❛❞♦s✿ ♠❡t❛♥♦ ✭CH+ 4 ✮✱ ❤✐❞ró❣❡♥♦ ♠♦❧❡❝✉❧❛r ✭H2 ✮✱ ❛❣✉❛ ✭H2 O ✮✱ ♥✐tró❣❡♥♦ + + ❛tó♠✐❝♦ ✭N+ ✮✱ ♥✐tró❣❡♥♦ ♠♦❧❡❝✉❧❛r ✭N+ 2 ✮✱ ♦①í❣❡♥♦ ❛tó♠✐❝♦ ✭O ✮ ❡ ❤✐❞ró①✐❞♦ ✭OH ✮✱ s✐t✉❛❞♦s ✐♥✐❝✐❛❧♠❡♥t❡ s♦❜r❡ ❡❧ ♣♦❧♦ ♥♦rt❡ ❞❡ ❙❛t✉r♥♦✱ s♦❜r❡ ❡❧ ❛♥✐❧❧♦ ❈✱ ❡♥ ❡❧ ♣♦❧♦ s✉r ❞❡ ❊♥❝❡❧❛❞♦✱ ❡♥ ❡❧ ♣♦❧♦ ♥♦rt❡ ❞❡ ❉✐♦♥❡✱ s♦❜r❡ ❡❧ ❛♥✐❧❧♦ ❊✱ ❡♥ ❡❧ ♣♦❧♦ ♥♦rt❡ ❞❡ ❘❡❛✱ ❡♥ ❞✐❢❡r❡♥t❡s ♣♦s✐❝✐♦♥❡s ❞❡ ❧❛ r❡❣✐ó♥ ❡①t❡r♥❛ ② ❡♥ ❧❛ ❛t♠ós❢❡r❛ s✉♣❡r✐♦r ❞❡ ❚✐tá♥✳ ▲♦s r❡s✉❧t❛❞♦s ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛ ♠✉❡str❛♥ q✉❡ ❧❛ ❡♥❡r❣í❛ ❝✐♥ét✐❝❛ ❞❡ ❧❛s ♣❛rtí❝✉❧❛s t✐❡♥❞❡ ❛ ❛✉♠❡♥t❛r ❝♦♥ ❡❧ t✐❡♠♣♦✱ ❛❧❝❛♥③❛♥❞♦ ❛❧❣✉♥♦s ❡❱ ❡♥ ♣♦❝♦s s❡❣✉♥✲ ❞♦s✳ ▲❛ ❞✐str✐❜✉❝✐ó♥ ✜♥❛❧ ❞❡ ✈❡❧♦❝✐❞❛❞❡s ♠❛♥t✐❡♥❡ s✉ ♣❡r✜❧ ▼❛①✇❡❧❧✐❛♥♦✱ ❛ ❡①❝❡♣❝✐ó♥ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✈✐✐ ❞❡ ❧♦s ♣r♦t♦♥❡s ❡ ✐♦♥❡s ♣❡s❛❞♦s q✉❡ ♣r♦✈✐❡♥❡♥ ❞❡❧ ❛♥✐❧❧♦ ❈ ② ❞❡ ❧♦s ♣r♦t♦♥❡s ❞❡❧ ♣♦❧♦ s✉r ❞❡ ❊♥❝❡❧❛❞♦✳ ❙❡ ❞✐st✐♥❣✉❡♥ ❞✐❢❡r❡♥t❡s r❡❣✐♦♥❡s ❞❡ ❡♥❡r❣✐③❛❝✐ó♥ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡✲ r❛ ✐♥t❡r♥❛✿ ✶✮ r❡❣✐ó♥ ❞❡ ❜❛❥❛ ❡♥❡r❣✐③❛❝✐ó♥ ✭♣♦❧♦ ♥♦rt❡ ❞❡ ❙❛t✉r♥♦✱ ❊♥❝❡❧❛❞♦ ② ❘❡❛✮❀ ✷✮ r❡❣✐ó♥ ❞❡ ✐♥❡st❛❜✐❧✐❞❛❞ ✭❆♥✐❧❧♦ ❈✮❀ ✸✮ r❡❣✐ó♥ ❞❡ ❡♥❡r❣✐③❛❝✐ó♥ ✐♥t❡r♠❡❞✐❛ ✭❉✐♦♥❡✮ ② ✹✮ r❡❣✐ó♥ ❞❡ ❛❧t❛ ❡♥❡r❣✐③❛❝✐ó♥ ✭❆♥✐❧❧♦ ❊✮✳ ❊♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ ♥♦ ❡s ♣♦s✐❜❧❡ ❞✐st✐♥❣✉✐r ❡♥tr❡ ❞✐st✐♥t❛s r❡❣✐♦♥❡s ❞❡ ❡♥❡r❣✐③❛❝✐ó♥✱ ♣♦r ❡❧ ❝♦♥tr❛r✐♦✱ ❧❛ ❝♦♥tr✐❜✉❝✐ó♥ ❛ ❧❛ ❡❝✉❛❝✐ó♥ ❞❡ ❡♥❡r❣í❛ ❞❡ ❧❛ ❛❝❡❧❡✲ r❛❝✐ó♥ ❡st♦❝ást✐❝❛ ❡s ♠❛②♦r ❝♦♥❢♦r♠❡ ❧❛s ♣❛rtí❝✉❧❛s s❡ ❛❧❡❥❛♥ ❞❡❧ ♣❧❛♥❡t❛✳ ❉❡♥tr♦ ❞❡❧ s✐st❡♠❛ ❞❡ ❛♥✐❧❧♦s s❡ ❡♥❝✉❡♥tr❛♥ ❞✐❢❡r❡♥t❡s r❡❣✐♦♥❡s ❞❡ ❡♥❡r❣✐③❛❝✐ó♥✱ ❞❡♣❡♥❞✐❡♥❞♦ s✐ ❧♦s ❣r❛♥♦s ❞❡ ♣♦❧✈♦ ❡stá♥ ❝❛r❣❛❞♦s ♦ ♥❡✉tr♦s✳ P❛r❛ ❧♦s ❣r❛♥♦s ❞❡ ♣♦❧✲ ✈♦ ❝❛r❣❛❞♦s s❡ ✐❞❡♥t✐✜❝❛♥ ❞♦s r❡❣✐♦♥❡s✿ ❡♥ ❡❧ ❜♦r❞❡ ❡①t❡r♥♦ ❞❡❧ ❛♥✐❧❧♦ ❊ ❧♦s ❣r❛♥♦s ❞❡ ♣♦❧✈♦ t✐❡♥❞❡♥ ❛ ♣❡r❞❡r ❡♥❡r❣í❛ ② ❡♥ ❡❧ ❜♦r❞❡ ✐♥t❡r♥♦ t✐❡♥❞❡♥ ❛ ❣❛♥❛r ♠ás ❡♥❡r❣í❛✳ P❛r❛ ❧♦s ❣r❛♥♦s ❞❡ ♣♦❧✈♦ ♥❡✉tr♦s s❡ ✐❞❡♥t✐✜❝❛♥ tr❡s r❡❣✐♦♥❡s✿ ❛✮ ❆❧t❛ ❡♥❡r❣✐③❛❝✐ó♥ ✭❉✐✈✐s✐ó♥ ❞❡ ❈❛ss✐♥✐ ② ❛♥✐❧❧♦ ❆✮❀ ❜✮ ❇❛❥❛ ❡♥❡r❣✐③❛❝✐ó♥ ✭❛♥✐❧❧♦ ❇ ② ❛♥✐❧❧♦ ❊ ✮ ② ❝✮ ❡♥❡r❣✐③❛❝✐ó♥ ✐♥t❡r♠❡❞✐❛ ✭❛♥✐❧❧♦ ❈✮✳ ❈♦♥tr✐❜✉❝✐♦♥❡s ❞❡ ❧❛ t❡s✐s✿ ❍❛st❛ ❡❧ ♠♦♠❡♥t♦✱ ❧♦s ♠❡❝❛♥✐s♠♦s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❡st♦❝ást✐❝❛ tr❛❞✐❝✐♦♥❛❧❡s r❡q✉✐❡r❡♥ ❡s❡♥❝✐❛❧♠❡♥t❡ ❞❡ tr❡s ❝♦s❛s✿ ✶✮ ❞❡ ❧❛s ✐♥t❡r❛❝❝✐♦♥❡s ❡❧❡♠❡♥t❛❧❡s ♦♥❞❛✲♣❛rtí❝✉❧❛✱ ✷✮ ❞❡ ❧❛ ❞✐s♣❡rs✐ó♥ ❡❢❡❝t✐✈❛ ❛tr✐❜✉✐❞❛ ❛ ❡s❛s ✐♥t❡r❛❝❝✐♦♥❡s✱ ② ✸✮ ❞❡ ✉♥ ♣r♦❝❡s♦ ❛❧❡❛t♦r✐♦ ✭tr❛t❛♠✐❡♥t♦ ❡st❛❞íst✐❝♦✮✳ ❙✐ ❧❛s ♦♥❞❛s q✉❡ ♣r♦❞✉❝❡♥ ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s s♦♥ ❧♦ s✉✜❝✐❡♥t❡♠❡♥t❡ ❛❧❡❛t♦r✐❛s ✭❡st♦ ❡s✱ ♦♥❞❛s ❝♦♥ ❢❛s❡ ❛❧❡❛t♦r✐❛✮✱ ❡♥t♦♥❝❡s ♦❝✉rr❡ ❡❧ ♣r♦❝❡s♦ ❞❡ ❞✐❢✉s✐ó♥ ❡♥ ❡❧ ❡s♣❛❝✐♦ ❞❡ ✈❡❧♦❝✐❞❛❞❡s ② ❡❧ ❢❡♥ó♠❡♥♦ ❡s ❝♦♥♦❝✐❞♦ ❝♦♠♦ ❞✐❢✉s✐ó♥ ❝✉❛s✐✲❧✐♥❡❛❧✳ ❊st❡ ❡❢❡❝t♦ ❡s tr❛t❛❞♦ ❝♦♠♦ ✉♥ ♦♣❡r❛❞♦r ❞❡ ❞✐❢✉s✐ó♥ ❡♥ ❧❛ ❡❝✉❛❝✐ó♥ ❞❡ ❋♦❦❦❡r✲P❧❛♥❝❦✱ ❧❛ ❝✉❛❧ ♣✉❡❞❡ s❡r r❡❡♠♣❧❛③❛❞❛ ♣♦r ✉♥ ❝♦♥❥✉♥t♦ ❞❡ ❡❝✉❛❝✐♦♥❡s ❞✐❢❡r❡♥❝✐❛❧❡s ❡st♦❝ást✐❝❛s✳ ❆❞❡♠ás✱ ❡s ♥❡❝❡s❛r✐♦ q✉❡ ❧❛ ♣❛rtí❝✉❧❛ ❝♦♠♣❧❡t❡ ✉♥ r❛❞✐♦ ❞❡ ❣✐r♦ ✭♠♦✈✐♠✐❡♥t♦ ❣✐r♦tró♣✐❝♦✮ ♣❛r❛ q✉❡ ♣✉❡❞❛ r❡s♦♥❛r ❝♦♥ ❧❛ ♦♥❞❛ ❝♦rr❡s♣♦♥❞✐❡♥t❡ ② ❡♥t♦♥❝❡s s❡r ❛❝❡❧❡r❛❞❛ ♦ ❞❡s❛❝❡❧❡r❛❞❛✳ P♦r ❡❥❡♠♣❧♦✱ ❡st❛ ❛♣r♦①✐♠❛❝✐ó♥ ♥♦ ♣✉❡❞❡ ❡①♣❧✐❝❛r ❡❧ rá♣✐❞♦ ✐♥❝r❡♠❡♥t♦ ❞❡ ❡♥❡r❣í❛ ❞❡ ❧♦s ✐♦♥❡s ❞❡ ♦①í❣❡♥♦ ❧♦❝❛❧✐③❛❞♦s ❡♥ ❧❛ ✐♦♥ós❢❡r❛ ❞❡ ❱❡♥✉s✱ ♣✉❡s ❧♦s r❛❞✐♦s ❞❡ ❣✐r♦ ✭② ❧♦s ♣❡r✐♦❞♦s✮ s♦♥ ♠✉② ❣r❛♥❞❡s ❡♥ ❝♦♠♣❛r❛❝✐ó♥ ❝♦♥ ❡❧ t✐❡♠♣♦ ❡♠♣❧❡❛❞♦ ♣❛r❛ ❛❝❡❧❡r❛r❧♦s ❬Pér❡③ ❞❡ ❚❡❥❛❞❛ ❡t ❛❧✳✱ ✶✾✾✺❪✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✈✐✐✐ ❊st❡ tr❛❜❛❥♦ ❝♦♥st✐t✉②❡ ✉♥❛ ♠❛♥❡r❛ ❣❡♥❡r❛❧ ② ♥♦✈❡❞♦s❛ ❞❡ ❡st✉❞✐❛r ❡❧ ♣r♦❜❧❡♠❛ ❞❡ ❡♥❡r❣✐③❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❡♥ ♠❛❣♥❡tós❢❡r❛s ♣❧❛♥❡t❛r✐❛s✳ ❊♥ ❡❧ ♠♦❞❡❧♦ q✉❡ s❡ ♣r❡s❡♥t❛✱ ♥♦ s❡ ❝♦♥s✐❞❡r❛ ✉♥ ❡s♣❡❝tr♦ ❞❡ ♦♥❞❛ ❡♥ ♣❛rt✐❝✉❧❛r s✐♥♦ ❡❧ ❡s♣❡❝tr♦ ❞❡ ✢✉❝t✉❛❝✐♦♥❡s ❞❡ ❝❛♠♣♦ ✭♠❛❣♥ét✐❝♦ ♦ ❣r❛✈✐t❛❝✐♦♥❛❧✮ ❝❛r❛❝t❡ríst✐❝♦ ❞❡ ❧❛ r❡❣✐ó♥ ❡♥ ❡st✉❞✐♦✳ ❆❞❡♠ás✱ ♥♦ ❡s ♥❡❝❡s❛r✐♦ ❝♦♥♦❝❡r ❧♦s ✈❛❧♦r❡s ♣r♦♠❡❞✐♦ ♣❛r❛ ❧❛ ✈❡❧♦❝✐❞❛❞✱ ♣❛r❛ ❧❛ ❞❡♥s✐❞❛❞ ② ♣❛r❛ ❧❛ t❡♠♣❡r❛t✉r❛ ✭q✉❡ ♣✉❡❞❡♥ ♦❜t❡♥❡rs❡ ❛ ♣❛rt✐r ❞❡ ❧❛s ♠❡❞✐❝✐♦♥❡s ♦ ❞❡ ❧♦s ❝á❧❝✉❧♦s t❡ór✐❝♦s✮❀ ❡♥ ❡st❡ ♠♦❞❡❧♦ s❡ r❡q✉✐❡r❡ ❞❡r✐✈❛r ❧❛ ❢✉♥❝✐ó♥ ❞❡ ❞✐str✐❜✉❝✐ó♥ ❞❡ ✈❡❧♦❝✐❞❛❞❡s ♣❛r❛ ❧❛s ❞✐st✐♥t❛s ♣♦❜❧❛❝✐♦♥❡s✳ ❊st❡ ♠❡❝❛♥✐s♠♦ ♣✉❡❞❡ s❡r ❝♦♥s✐❞❡r❛❞♦ ❝♦♠♦ ✉♥ ♣r♦❝❡s♦ ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ♣r✐♠❛r✐♦✳ ❊st♦ ❡s✱ ❧♦s ♣r♦t♦♥❡s ✲q✉❡ s♦♥ ♠ás s✉s❝❡♣t✐❜❧❡s ❞❡ s❡r ❛❝❡❧❡r❛❞♦s✲ ❣❛♥❛♥ ❡♥❡r❣í❛ ❝♦♠♦ ❝♦♥s❡❝✉❡♥❝✐❛ ❞❡ ❧❛ ❛❝❝✐ó♥ ❞❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❡st♦❝ást✐❝♦✳ ❊st♦s ♣r♦t♦♥❡s s❡rá♥ ❝❛♣❛❝❡s ❞❡ tr❛♥s❢❡r✐r ❡♥❡r❣í❛ ❛ ❧❛s ❞✐st✐♥t❛s ♣♦❜❧❛❝✐♦♥❡s ❞❡ ✐♦♥❡s ♣r❡s❡♥t❡s ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛✱ q✉❡ ❛❞❡♠ás✱ ❡stá♥ ❣❛♥❛♥❞♦ ❡♥❡r❣í❛ ♣♦r ❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❡st♦❝ást✐❝♦ ❞❡ ❢♦♥❞♦✳ ❋✐♥❛❧♠❡♥t❡ s❡ ❡s♣❡r❛ q✉❡ ❡❧ ♣❧❛s♠❛ s❡ ✈❛②❛ ❡♥❡r❣✐③❛♥❞♦ ♣❛r❛ ❛❧❝❛♥③❛r ❧❛ ❡♥❡r❣í❛ ♦❜s❡r✈❛❞❛ ♣♦r ❧❛s ♥❛✈❡s✳ ❖tr❛ ❝♦♥tr✐❜✉❝✐ó♥ ✐♠♣♦rt❛♥t❡ ❡s ❡❧ ❤❛❜❡r ✐❞❡♥t✐✜❝❛❞♦ ❞✐❢❡r❡♥t❡s r❡❣✐♦♥❡s ❞❡ ❡♥❡r✲ ❣✐③❛❝✐ó♥ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛✱ ♣✉❡s ❤❛st❛ ❡❧ ♠♦♠❡♥t♦ ♥♦ s❡ ❤❛❜í❛ r❡♣♦rt❛❞♦ ❡♥ tr❛❜❛❥♦s ❛♥t❡r✐♦r❡s ❡st❛ ♣♦s✐❜✐❧✐❞❛❞✳ ❙❡ ❤❛ ♣r♦♣✉❡st♦ ❧❛ ❛❝❝✐ó♥ ❞❡ ✉♥ ❝❛♠♣♦ ❣r❛✈✐t❛❝✐♦♥❛❧ ❡st♦❝ást✐❝♦ ♣❛r❛ ❡①♣❧✐❝❛r ❧❛ ❞✐♥á♠✐❝❛ ❞❡ ❧♦s ❣r❛♥♦s ❞❡ ♣♦❧✈♦ ❡♥ ❧♦s ❛♥✐❧❧♦s✳ ❊st❛ ❡s ✉♥❛ ✐❞❡❛ ♥♦✈❡❞♦s❛ q✉❡ ♣✉❡❞❡ ❝♦♥tr✐❜✉✐r ❛❧ ❡st✉❞✐♦ ❞❡ ❧❛ ✐♦♥ós❢❡r❛ q✉❡ s❡ ♦❜s❡r✈❛ s♦❜r❡ ❧♦s ❛♥✐❧❧♦s✳ ❆❝t✉❛❧♠❡♥t❡ s❡ ♣✐❡♥s❛ q✉❡ s♦♥ ❧❛s ❝♦❧✐s✐♦♥❡s ❡♥tr❡ ❣r❛♥♦s ❞❡ ♣♦❧✈♦ ❧❛s q✉❡ ❢♦r♠❛♥ ❡st❛ ❡str✉❝t✉r❛✳ ❖r❣❛♥✐③❛❝✐ó♥ ❞❡ ❧❛ t❡s✐s✿ ❊❧ tr❛❜❛❥♦ q✉❡ s❡ ♣r❡s❡♥t❛ ❝♦♥st❛ ❞❡ s❡✐s ❈❛♣ít✉❧♦s ② ❞❡ tr❡s ❆♣é♥❞✐❝❡s✳ ❊♥ ❡❧ ❈❛♣ít✉❧♦ ✶ s❡ ❞❡s❝r✐❜❡♥ ❧♦s ♠❡❝❛♥✐s♠♦s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ♠ás ❝♦♠✉♥❡s ❡♥ ❆s✲ tr♦❢ís✐❝❛ ② ♣♦st❡r✐♦r♠❡♥t❡ ❧♦s ♠❡❝❛♥✐s♠♦s q✉❡ s❡ ❛♣❧✐❝❛♥ ♣❛r❛ ❡❧ ❡st✉❞✐♦ ❞❡ ♣❛rtí❝✉❧❛s ❡♥❡r❣ét✐❝❛s ❡♥ ❧❛s ♠❛❣♥❡tós❢❡r❛s ♣❧❛♥❡t❛r✐❛s✱ ❤❛❝✐❡♥❞♦ é♥❢❛s✐s ❡♥ ❧♦s ♠❡❝❛♥✐s♠♦s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ♣r♦♣✉❡st♦s ✲❤❛st❛ ❡❧ ♠♦♠❡♥t♦✲ ♣❛r❛ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦✳ ❊♥ ❡❧ ❈❛♣ít✉❧♦ ✷ s❡ r❡s✉♠❡♥ ❧❛s ♣r♦♣✐❡❞❛❞❡s ♠ás ✐♠♣♦rt❛♥t❡s ♦❜s❡r✈❛❞❛s ❡♥ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ② ♥❡✉tr❛s ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦✳ ❊st❛ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✐① ❞❡s❝r✐♣❝✐ó♥ ❡stá ❜❛s❛❞❛ ❡♥ ❧❛s ♠❡❞✐❝✐♦♥❡s r❡❛❧✐③❛❞❛s ❤❛❝❡ ♠ás ❞❡ ❞♦s ❞é❝❛❞❛s ♣♦r ❡❧ ❱♦②❛❣❡r ✶ ② ❡❧ ❱♦②❛❣❡r ✷✱ ② ❡♥ ❧❛s r❡❝✐❡♥t❡s ♠❡❞✐❝✐♦♥❡s r❡❛❧✐③❛❞❛s ♣♦r ❧❛ ♥❛✈❡ ❈❛ss✐♥✐✳ ❊♥ ❡❧ ❈❛♣ít✉❧♦ ✸ s❡ ❞❡s❛rr♦❧❧❛ ❡❧ ♠♦❞❡❧♦ ❣❡♥❡r❛❧ ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❡st♦❝ást✐❝❛ ♣❛r❛ ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ② ♣❛r❛ ♣❛rtí❝✉❧❛s ♥❡✉tr❛s✳ ❊♥ ❡❧ ❈❛♣ít✉❧♦ ✹ s❡ ❛♣❧✐❝❛ ❡❧ ♠♦❞❡❧♦ ❞❡s❛rr♦❧❧❛❞♦ ❛❧ ❝❛s♦ ♣❛rt✐❝✉❧❛r ❞❡ ❧❛ ♠❛❣✲ ♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦✳ P❛r❛ ❧♦ ❝✉❛❧✱ s❡ ❝♦♥s✐❞❡r❛♥ ❞♦s r❡❣✐♦♥❡s✿ ✐♥t❡r♥❛ ② ❡①t❡r♥❛✳ ❆❞✐❝✐♦♥❛❧♠❡♥t❡ s❡ ✐♥❝❧✉②❡ ❛❧ s✐st❡♠❛ ❞❡ ❛♥✐❧❧♦s ♣❛r❛ ❡①♣❧✐❝❛r s✉ ❞✐♥á♠✐❝❛✳ ❊♥ ❡❧ ❈❛♣ít✉❧♦ ✺ s❡ ❞✐s❝✉t❡♥ ❧♦s r❡s✉❧t❛❞♦s ♦❜t❡♥✐❞♦s✱ ❝♦♥ ❡❧ ♠♦❞❡❧♦ ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❡st♦❝ást✐❝❛✱ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛ ② ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ ❞❡ ❙❛t✉r♥♦✳ ❚❛♠❜✐é♥ ♣❛r❛ ❧♦s ❣r❛♥♦s ❞❡ ♣♦❧✈♦ ❡♥ ❡❧ s✐st❡♠❛ ❞❡ ❛♥✐❧❧♦s✳ ❊♥ ❡❧ ❈❛♣ít✉❧♦ ✻ s❡ ♣r❡s❡♥t❛♥ ❧❛s ❝♦♥❝❧✉s✐♦♥❡s ❣❡♥❡r❛❧❡s ❞❡❧ tr❛❜❛ ❥♦ ② ❡♥ s❡❝❝✐♦♥❡s s❡♣❛r❛❞❛s ❧❛s ❝♦rr❡s♣♦♥❞✐❡♥t❡s ❛ ❝❛❞❛ r❡❣✐ó♥ ❡st✉❞✐❛❞❛✳ ▲♦s ❆♣é♥❞✐❝❡s ❡①♣❧✐❝❛♥ ❡♥ ❞❡t❛❧❧❡ ❛s♣❡❝t♦s ✐♠♣♦rt❛♥t❡s r❡❧❛❝✐♦♥❛❞♦s ❝♦♥ ❧❛ ♣❛rt❡ ♠❛t❡♠át✐❝❛ ② ❡st❛❞íst✐❝❛ ❞❡❧ ♣r♦❜❧❡♠❛ ❛ r❡s♦❧✈❡r✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❈❛♣ít✉❧♦ ✶ ■♥tr♦❞✉❝❝✐ó♥ ▲❛ ❛❝❡❧❡r❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ❛ ❡♥❡r❣í❛s s✉♣r❛t❡r♠❛❧❡s ♦❝✉rr❡ ❡♥ ♣rá❝t✐✲ ❝❛♠❡♥t❡ ❝❛❞❛ ♣❧❛s♠❛ ❞❡ ✐♥t❡rés ❛str♦❢ís✐❝♦✳ ▼✉❝❤♦ ❞❡ ❧♦ q✉❡ s❡ ❝♦♥♦❝❡ s♦❜r❡ ♣r♦❝❡s♦s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❤❛ s✐❞♦ ❞❡r✐✈❛❞♦ ❛ ♣❛rt✐r ❞❡ ❧♦s ❡①♣❡r✐♠❡♥t♦s ❞❡ ❧❛❜♦r❛t♦r✐♦ ② ❞❡ ❧♦s ❡st✉❞✐♦s t❡ór✐❝♦s ❛s♦❝✐❛❞♦s ❛ ❡❧❧♦s✳ ❊❧ ❡st✉❞✐♦ ❞❡ ❡st♦s ♣r♦❝❡s♦s ❞❡♥tr♦ ❞❡ r❡❣✐♦♥❡s ❛❝✲ ❝❡s✐❜❧❡s ❝♦♠♦ ❡❧ ❙✐st❡♠❛ ❙♦❧❛r✱ ♣❛rt✐❝✉❧❛r♠❡♥t❡ ❡❧ ❣❡♦❡s♣❛❝✐♦✱ ♦❢r❡❝❡ ❧❛ ♦♣♦rt✉♥✐❞❛❞ ♣❛r❛ ❡♥t❡♥❞❡r ❛❧❣✉♥♦s ♣r♦❝❡s♦s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ❡♥ ❞❡t❛❧❧❡ ② ❛sí ❡st❛❜❧❡❝❡r ❝♦♥❝❡♣t♦s q✉❡ ❡stá♥ s✉❥❡t♦s ❛ r✐❣✉r♦s❛s ♦❜s❡r✈❛❝✐♦♥❡s ❡①♣❡r✐♠❡♥t❛❧❡s✳ ❊s ❞✐❢í❝✐❧ ❡st❛❜❧❡❝❡r ✉♥❛ ❝❧❛s✐✜❝❛❝✐ó♥ ú♥✐❝❛ ❞❡ ❧♦s ♠❡❝❛♥✐s♠♦s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s✳ P♦r ❡❥❡♠♣❧♦✱ ❏♦❦✐♣✐✐ ❬✶✾✼✾❪ ❝❛t❛❧♦❣❛ ❛ ❧❛s ❛♣r♦①✐♠❛❝✐♦♥❡s ❜ás✐❝❛s ♣❛✲ r❛ ❡st✉❞✐❛r ❡❧ ♣r♦❜❧❡♠❛ ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❡♥ ❞❡t❡r♠✐♥íst✐❝❛s ✭t❛♠❜✐é♥ ❝♦♥♦❝✐❞❛ ❝♦♠♦ ❛❝❡❧❡r❛❝✐ó♥ s❡❝✉❧❛r ♦ ❞❡ ❣❛♥❛♥❝✐❛ s✐st❡♠át✐❝❛ ❞♦♥❞❡ ❧♦s ❝❛♠♣♦s ❡❧é❝tr✐❝♦s s♦♥ ✉♥✐❞✐✲ r❡❝❝✐♦♥❛❧❡s✱ ♣♦r ❡❥❡♠♣❧♦ ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ♣♦r ♦♥❞❛s ❞❡ ❝❤♦q✉❡ ♦ ♣♦r ❝❛♠♣♦s ❡❧é❝tr✐❝♦s ♣❛r❛❧❡❧♦s✮ ② ❡♥ ❡st♦❝ást✐❝❛s ✭❞♦♥❞❡ ❧❛s ♣❛rtí❝✉❧❛s ❣❛♥❛♥ ♦ ♣✐❡r❞❡♥ ❡♥❡r❣í❛ ❛ tr❛✈és ❞❡ ❧❛ ❛❝❝✐ó♥ ❞❡ ❝❛♠♣♦s ❡❧é❝tr✐❝♦s q✉❡ ♥♦ t✐❡♥❡♥ ✉♥❛ ❞✐r❡❝❝✐ó♥ ♣r❡❢❡r❡♥❝✐❛❧ ❝♦♠♦ ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ♣♦r t✉r❜✉❧❡♥❝✐❛✱ ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ❞❡ ❋❡r♠✐ ② s✉s ❞❡s❝❡♥❞✐❡♥t❡s✮✳ ■♥❞❡♣❡♥✲ ❞✐❡♥t❡♠❡♥t❡ ❞❡ ❧❛ ❝❧❛s✐✜❝❛❝✐ó♥ q✉❡ s❡ ❞é ❡s ✐♠♣♦rt❛♥t❡ ❞❡st❛❝❛r q✉❡ ❝❛❞❛ ✉♥♦ ❞❡ ❡st♦s ♣r♦❝❡s♦s ♦♣❡r❛ s❡❧❡❝t✐✈❛♠❡♥t❡ s♦❜r❡ ♣❛rtí❝✉❧❛s ❡s♣❡❝í✜❝❛s✿ ❧❛s ♦♥❞❛s ♣✉❡❞❡♥ ❛❝❡❧❡r❛r ♣❛rtí❝✉❧❛s ❝✉❛♥❞♦ s❡ ❝✉♠♣❧❡ ✉♥❛ ❝♦♥❞✐❝✐ó♥ ❞❡ r❡s♦♥❛♥❝✐❛❀ ❧♦s ❝❤♦q✉❡s s♦❧❛✲ ♠❡♥t❡ ♣✉❡❞❡♥ ❛❝❡❧❡r❛r ♣❛rtí❝✉❧❛s ❛ ♣❛rt✐r ❞❡ ❞❡t❡r♠✐♥❛❞♦ ✉♠❜r❛❧ ❧❧❛♠❛❞♦ ❡♥❡r❣í❛ ❞❡ ✐♥②❡❝❝✐ó♥❀ ❧♦s ❝❛♠♣♦s ❡❧é❝tr✐❝♦s ❡♥ ✉♥ ♣❧❛s♠❛ ♥♦✲❝♦❧✐s✐♦♥❛❧ ♣✉❡❞❡♥ ♦❝❛s✐♦♥❛r ❛❝❡✲ ❧❡r❛❝✐ó♥ ✏r✉♥❛✇❛②✑ ❡♥ ✉♥❛ ♣❡q✉❡ñ❛ ❢r❛❝❝✐ó♥ ♦ ❡♥ t♦❞❛ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s✱ ✶ ❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉❝❝✐ó♥ ✷ ♣♦r ♠❡♥❝✐♦♥❛r ❛❧❣✉♥♦s✳ ❊♥ ❡st❡ ❝❛♣ít✉❧♦ s❡ ❞❡s❝r✐❜❡♥ ❧♦s ♠❡❝❛♥✐s♠♦s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ♠ás ❝♦♠✉♥❡s ❡♥ ❆s✲ tr♦❢ís✐❝❛ ② ♣♦st❡r✐♦r♠❡♥t❡ ❧♦s ♠❡❝❛♥✐s♠♦s q✉❡ s❡ ❛♣❧✐❝❛♥ ♣❛r❛ ❡❧ ❡st✉❞✐♦ ❞❡ ♣❛rtí❝✉❧❛s ❡♥❡r❣ét✐❝❛s ❡♥ ❧❛s ♠❛❣♥❡tós❢❡r❛s ♣❧❛♥❡t❛r✐❛s✱ ❤❛❝✐❡♥❞♦ é♥❢❛s✐s ❡♥ ❧♦s ♠❡❝❛♥✐s♠♦s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ♣r♦♣✉❡st♦s ✲❤❛st❛ ❡❧ ♠♦♠❡♥t♦✲ ♣❛r❛ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦✳ ▲❛s ♠❛❣♥❡tós❢❡r❛s ❡stá♥ ♣♦❜❧❛❞❛s ❝♦♥ ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ❝♦♠♦ ♣r♦t♦♥❡s✱ ❡❧❡❝✲ tr♦♥❡s ❡ ✐♦♥❡s ♣❡s❛❞♦s✳ ▲❛s ❡s♣❡❝✐❡s ❞♦♠✐♥❛♥t❡s ❞❡t❡❝t❛❞❛s ❡♥ ❧❛s ♠❛❣♥❡tós❢❡r❛s ♣❧❛♥❡t❛r✐❛s s❡ r❡s✉♠❡♥ ❡♥ ❡❧ ❈✉❛❞r♦ ✶✳✶✳ ▲❛s ♣❛rtí❝✉❧❛s ❡♥❡r❣ét✐❝❛s ② ❧♦s ♣❧❛s♠❛s ♠♦❞✐✜❝❛♥ ❧❛s ❛t♠ós❢❡r❛s s✉♣❡r✐♦r❡s ✭❧❧❡✈❛♥❞♦ ❛ ❧❛ ✐♦♥✐③❛❝✐ó♥✱ ❝❛❧❡♥t❛♠✐❡♥t♦ ② ♠♦✲ ❞✐✜❝❛❝✐ó♥ q✉í♠✐❝❛✮✱ ❧❛ s✉♣❡r✜❝✐❡ ❞❡ ❧♦s s❛té❧✐t❡s ✭r❡♠♦✈✐❡♥❞♦ ♠❛t❡r✐❛❧ ❛ tr❛✈és ❞❡❧ ♣r♦❝❡s♦ ❞❡♥♦♠✐♥❛❞♦ ✏s♣✉tt❡r✐♥❣✑ ✮ ② ❧♦s ❛♥✐❧❧♦s ✭♣❛rt✐❝✐♣❛♥❞♦ ❡♥ ❡❧ tr❛♥s♣♦rt❡ ❞❡ ♠❛t❡r✐❛❧ ② ❡♥ ❧♦s ♣r♦❝❡s♦s ❞❡ ❛❞q✉✐s✐❝✐ó♥ ❞❡ ❝❛r❣❛ ❡❧é❝tr✐❝❛✮✳ P♦r ❡❥❡♠♣❧♦✱ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❧❛ ❚✐❡rr❛ s❡ ❡♥❝✉❡♥tr❛♥ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ✐♦♥❡s ❞❡ ♦①í❣❡♥♦ ② ♣r♦t♦✲ ♥❡s❀ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❏ú♣✐t❡r ❛❞❡♠ás ❞❡ ❡st♦s ✐♦♥❡s s❡ ❞❡t❡❝t❛♥ ♣❛rtí❝✉❧❛s ❞❡ ❛③✉❢r❡ ♦r✐❣✐♥❛❞❛s ❡♥ s✉ s❛té❧✐t❡ ■♦❀ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦ s❡ ✐♥❝❧✉②❡♥ ✐♦♥❡s✱ ♣r♦❞✉❝t♦ ❞❡❧ ❛❣✉❛✱ ♣r♦✈❡♥✐❡♥t❡s ❞❡ s✉s s❛té❧✐t❡s ② ❛♥✐❧❧♦s✱ ❛❞❡♠ás ❞❡ ✐♦♥❡s ❞❡ ♥✐✲ tró❣❡♥♦ ❝✉②❛ ❢✉❡♥t❡ ♣r✐♥❝✐♣❛❧ ❡s ❚✐tá♥ ❬❨♦✉♥❣ ❡t ❛❧✳✱ ✷✵✵✺❪ ② ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ◆❡♣t✉♥♦ s❡ ❤❛♥ ❞❡t❡❝t❛❞♦ ✐♦♥❡s ❞❡ ♥✐tró❣❡♥♦ ② ♣r♦t♦♥❡s✳ ❊❧ ♣❡r✜❧ ❞❡ ❧❛s ❢✉♥❝✐♦♥❡s ❞❡ ❞✐str✐❜✉❝✐ó♥ ❞❡ ❧❛s ❡♥❡r❣í❛s ❞❡ ❧❛s ♣❛rtí❝✉❧❛s ❡s ❝❡r❝❛♥♦ ❛❧ ❞❡ ✉♥❛ ▼❛①✇❡❧❧✐❛♥❛✱ ♦ tér♠✐❝❛✱ ❛✉♥q✉❡ ❡♥ ❛❧❣✉♥❛s ♠❛❣♥❡tós❢❡r❛s ❡①✐st❡ ✉♥❛ ♣r♦♥✉♥❝✐❛❞❛ ❝♦❧❛ ❞❡ ❛❧t❛s ❡♥❡r❣í❛s ❢♦r♠❛❞❛ ♣♦r ♣❛rtí❝✉❧❛s ❝♦♥ ❡♥❡r❣í❛s q✉❡ ❛❧❝❛♥③❛♥ ✈❛r✐❛s ❝❡♥t❡♥❛s ❞❡ ▼❡❱✳ P♦r ❡st❛ r❛③ó♥ ❛ ❧❛s ♠❛❣♥❡tós❢❡r❛s ♣❧❛♥❡t❛r✐❛s s❡ ❧❡s ❝♦♥s✐❞❡r❛ ❝♦♠♦ ♣r♦❞✐❣✐♦s♦s ❛❝❡❧❡r❛❞♦r❡s ❞❡ ♣❛rtí❝✉❧❛s❀ ✈❡r ♣♦r ❡❥❡♠♣❧♦✱ P❡r❦✐♥s ❬✶✾✻✽❪❀ ❙❝❤❛r❞t ❡t ❛❧✳✱ ❬✶✾✽✺❪❀ ❊r❛❦❡r ❛♥❞ ❙✐♠♣s♦♥ ❬✶✾✽✻❪✳ ▲❛s ❝♦♥s✐❞❡r❛❝✐♦♥❡s ❜ás✐❝❛s q✉❡ ❞❡❜❡♥ ❤❛❝❡rs❡ ❡♥ ❝✉❛❧q✉✐❡r ♠❡❝❛♥✐s♠♦ ❞❡ ❛❝❡❧❡✲ r❛❝✐ó♥ s❡ ❡♥✉♥❝✐❛♥ ❛ ❝♦♥t✐♥✉❛❝✐ó♥✿ ▲❛s ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s s♦♥ ❛❝❡❧❡r❛❞❛s s♦❧❛♠❡♥t❡ ♣♦r ❝❛♠♣♦s ❡❧é❝tr✐❝♦s ✭❧♦s ❝❛♠♣♦s ♠❛❣♥ét✐❝♦s ♥♦ r❡❛❧✐③❛♥ tr❛❜❛❥♦ s♦❜r❡ ❧❛s ♣❛rtí❝✉❧❛s✮ ②❛ q✉❡ ❧❛ ♣r♦❞✉❝✐✲ ❞❛ ♣♦r ♦tr♦s ❝❛♠♣♦s ♣✉❡❞❡ ♥♦ s❡r ✐♠♣♦rt❛♥t❡ ❡♥ ❧❛ ❣❡♥❡r❛❝✐ó♥ ❞❡ ❧❛s ♣❛rtí❝✉❧❛s ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉❝❝✐ó♥ ❈✉❛❞r♦ ✶✳✶✿ ✸ ❈❛r❛❝t❡ríst✐❝❛s ♣r✐♥❝✐♣❛❧❡s ❞❡❧ ♣❧❛s♠❛ ♣r❡s❡♥t❡ ❡♥ ❧❛s ♠❛❣♥❡tós❢❡r❛s ♣❧❛♥❡t❛r✐❛s✳ Planeta Tamaño de la magnetósfera (RP) a Composición iónica y fuente dominante b Densidad máxima (cm-3) Agente que controla el movimiento del plasma c Tiempo de residencia de las partículas energéticas d Mercurio 1.4 H+ (VS) 1 VS ? Tierra 8-12 O+, H+, N+, He+ (I) 1000-4000 VS (fuera) R (dentro) días-horas Júpiter 50-100 On+, Sn+, SO2+, Cl+ (S) >3000 R 10-100 días Saturno 16-22 O+, H2O+, H+ (A, S) ~100 R 30 días-años Urano 18 H+ (ATM) 3 VS y R 1-30 días Neptuno 23-26 N+, H+ (S) 2 R y VS? ~ 1 día ❛ ❙❡ r❡✜❡r❡ ❛❧ t❛♠❛ñ♦ ♦❜s❡r✈❛❞♦ ❡♥ ❡❧ ❧❛❞♦ ❞í❛ ② ❡stá ♠❡❞✐❞♦ ❡♥ r❛❞✐♦s ♣❧❛♥❡t❛r✐♦s✿ ▼❡r❝✉r✐♦ ✭✷ ✹✹✵ ❦♠✮✱ ❚✐❡rr❛ ✭✻ ✸✼✽❦♠✮✱ ❏ú♣✐t❡r ✭✼✶ ✾✵✵ ❦♠✮✱ ❙❛t✉r♥♦ ✭✻✵ ✷✻✽ ❦♠✮✱ ❯r❛♥♦ ✭✷✺ ✺✻✵ ❦♠✮✱ ◆❡♣t✉♥♦ ✭✷✹ ✼✺✵ ❦♠✮✳ ❜ ▲❛s ♣r✐♥❝✐♣❛❧❡s ❢✉❡♥t❡s ❞❡ ♣❛rtí❝✉❧❛s s♦♥✿ ❡❧ ✈✐❡♥t♦ s♦❧❛r ✭❱❙✮✱ ❧❛ ✐♦♥ós❢❡r❛ ❞❡ ❧♦s ♣❧❛♥❡t❛s ✭■✮✱ ❧♦s s❛té❧✐t❡s ✭❙✮✱ ❧♦s ❛♥✐❧❧♦s ✭❆✮ ② ❧❛ ❛t♠ós❢❡r❛ ❞❡ ❧♦s ♣❧❛♥❡t❛s ✭❆❚▼✮✳ ❊♥ ❡❧ ❝❛s♦ ❞❡ ❧♦s s❛té❧✐t❡s s❡ t✐❡♥❡ q✉❡✿ ■♦ ✭❏ú♣✐t❡r✮❀ ❊♥❝❡❧❛❞♦✱ ❉✐♦♥❡✱ ▼✐♠❛s✱ ❚✐tá♥ ✭❙❛t✉r♥♦✮ ② ❚r✐tó♥ ✭◆❡♣t✉♥♦✮ s♦♥ ❧♦s q✉❡ ❝♦♥tr✐❜✉②❡♥ ♠❛②♦r♠❡♥t❡ ❛ ❧❛ ♣♦❜❧❛❝✐ó♥ ♦❜s❡r✈❛❞❛ ❞❡ ♣❛rtí❝✉❧❛s ❡♥ s✉s r❡s♣❡❝t✐✈❛s ♠❛❣♥❡tós❢❡r❛s✳ ❝ ▲♦s ❛❣❡♥t❡s q✉❡ ❝♦♥tr♦❧❛♥ ❡❧ ♠♦✈✐♠✐❡♥t♦ ❞❡❧ ♣❧❛s♠❛ ❞❡♥tr♦ ❞❡ ❧❛s ♠❛❣♥❡tós❢❡r❛s ♣❧❛♥❡t❛✲ r✐❛s ♣✉❡❞❡♥ s❡r ❡❧ ✈✐❡♥t♦ s♦❧❛r ✭❱❙✮ ② ❧❛ r♦t❛❝✐ó♥ ✭❘✮✳ ❞ ▲♦s t✐❡♠♣♦s ❞❡ r❡s✐❞❡♥❝✐❛ s❡ ❝❛❧❝✉❧❛♥ ❞❡ ❛❝✉❡r❞♦ ❝♦♥ ❧♦s ♣r♦❝❡s♦s ❞❡ ♣ér❞✐❞❛ ✭❞✐s♦❝✐❛❝✐ó♥✮ q✉❡ ♦♣❡r❛♥ ❡♥ ❧❛ r❡❣✐ó♥ ♠❛❣♥❡t♦s❢ér✐❝❛✳ ❊st♦s t✐❡♠♣♦s ❡stá♥ t♦♠❛❞♦s ❞❡❧ tr❛❜❛❥♦ ❞❡ ❇❧❛♥❝ ❡t ❛❧✳ ❬✷✵✵✷❪✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉❝❝✐ó♥ ✹ ❛❧t❛♠❡♥t❡ ❡♥❡r❣ét✐❝❛s ♦❜s❡r✈❛❞❛s ❡♥ ❧❛s ♠❛❣♥❡tós❢❡r❛s✳ ❊①✐st❡♥ ✈❛r✐♦s ❡❢❡❝t♦s q✉❡ ❞❡❜❡♥ s❡r t♦♠❛❞♦s ❡♥ ❝✉❡♥t❛ ♣❛r❛ r❡❧❛❝✐♦♥❛r ❧❛ t❡♦✲ rí❛ ❝♦♥ ❧❛s ♦❜s❡r✈❛❝✐♦♥❡s✳ ❊st♦s s♦♥✿ ❧❛s ♣ér❞✐❞❛s ♣♦r ♣r♦❝❡s♦s ❞❡ r❛❞✐❛❝✐ó♥ ♦ ✐♦♥✐③❛❝✐ó♥❀ ❧❛ ❡♠✐s✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s s❡❝✉♥❞❛r✐❛s ② ♠❡❝❛♥✐s♠♦s ❞❡ ♣r❡❛❝❡❧❡r❛✲ ❝✐ó♥✳ ▲❛s ❢✉❡♥t❡s ♣♦t❡♥❝✐❛❧❡s ❞❡ ❡♥❡r❣í❛ ② ❞❡ ♣❛rtí❝✉❧❛s ♠ás ✐♠♣♦rt❛♥t❡s q✉❡ ♦♣❡r❛♥ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ♣❧❛♥❡t❛r✐❛ ❡♥ ❡st✉❞✐♦✳ ❋✉❡♥t❡s ❞❡ ♣❛rtí❝✉❧❛s ② ❞❡ ❡♥❡r❣í❛ ▲❛s ♠❛❣♥❡tós❢❡r❛s ♣❧❛♥❡t❛r✐❛s ✐♥②❡❝t❛♥ át♦♠♦s ♥❡✉tr♦s rá♣✐❞♦s✱ ♣❧❛s♠❛s ② ♣❛rtí✲ ❝✉❧❛s ❡♥❡r❣ét✐❝❛s ❤❛❝✐❛ ❡❧ ♠❡❞✐♦ ✐♥t❡r♣❧❛♥❡t❛r✐♦✳ ➱st❡ ❛ s✉ ✈❡③ ✲❛ tr❛✈és ❞❡ ❧❛ ♣r❡s✐ó♥ s✉♣❡rsó♥✐❝❛ ❞❡❧ ✈✐❡♥t♦ s♦❧❛r✱ ❞❡ ❝❛♠♣♦s ♠❛❣♥ét✐❝♦s✱ ❡t❝✳✲ ❛②✉❞❛ ❛ ❡st❛❜❧❡❝❡r ❧❛ ❝♦♥✲ ✜❣✉r❛❝✐ó♥ ♠❛❣♥❡t♦s❢ér✐❝❛ q✉❡ ✐♥❝❧✉②❡ ❛❧ ❢r❡♥t❡ ❞❡ ❝❤♦q✉❡✱ ❛ ❧❛ ♠❛❣♥❡t♦♣❛✉s❛✱ ❛ ❧❛ ♠❛❣♥❡t♦❝♦❧❛ ② ❛♣❛r❡♥t❡♠❡♥t❡ ❡♥❡r❣✐③❛ ❡✈❡♥t♦s ❞✐♥á♠✐❝♦s ❝♦♠♦ ❧❛s s✉❜t♦r♠❡♥t❛s ♠❛❣♥❡t♦s❢ér✐❝❛s ✭r❡❝♦♥✜❣✉r❛❝✐♦♥❡s ♠❛❣♥❡t♦s❢ér✐❝❛s ❣❧♦❜❛❧❡s q✉❡ r❡s✉❧t❛♥ ❞❡ ❧❛ ❝♦♥✲ ✈❡rs✐ó♥ ❞❡ ❧❛ ❡♥❡r❣í❛ ❡❧❡❝tr♦♠❛❣♥ét✐❝❛ ❡♥ ❛❝❡❧❡r❛❝✐ó♥ ② ❝❛❧❡♥t❛♠✐❡♥t♦ ❞❡ ♣❛rtí❝✉❧❛s✮✳ ▲❛s ❢✉❡♥t❡s ✐♠♣♦rt❛♥t❡s ❞❡ ♣❛rtí❝✉❧❛s ❡♥❡r❣ét✐❝❛s q✉❡ ❝♦♥tr✐❜✉②❡♥ ❡♥ ❛❧❣✉♥❛ ♠❡❞✐❞❛ ❛ ❧❛ ♣♦❜❧❛❝✐ó♥ ♦❜s❡r✈❛❞❛ ❡♥ ✉♥❛ ♠❛❣♥❡tós❢❡r❛ ♣❧❛♥❡t❛r✐❛ s♦♥ ❧❛s s✐❣✉✐❡♥t❡s✿ ❛✮ ❡❧ ✈✐❡♥t♦ s♦❧❛r❀ ❜✮ ❧❛s ♣❛rtí❝✉❧❛s s♦❧❛r❡s ❡♥❡r❣ét✐❝❛s❀ ❝✮ ❧♦s r❛②♦s ❝ós♠✐❝♦s❀ ❞✮ ❧❛s ♣❛rtí❝✉❧❛s s❡❝✉♥❞❛r✐❛s q✉❡ s❡ ♣r♦❞✉❝❡♥ ❡♥ ❧❛s ✐♥t❡r❛❝❝✐♦♥❡s ❞❡ ❧♦s r❛②♦s ❝ós♠✐❝♦s ❝♦♥ ❧❛ ❛t♠ós❢❡r❛ ♣❧❛♥❡t❛r✐❛✱ ❝♦♥ ❧♦s ❛♥✐❧❧♦s ② ❝♦♥ ❧♦s s❛té❧✐t❡s❀ ❡✮ ❡❧ ❣❛s ✐♦♥✐③❛❞♦ q✉❡ ♣r♦✈✐❡♥❡ ❞❡ ❧❛ ✐♦♥ós❢❡r❛ ♣❧❛♥❡t❛r✐❛❀ ❢ ✮ ❡❧ ❣❛s ✏s❛❧♣✐❝❛❞♦✑ ❞❡ ❧♦s ❛♥✐❧❧♦s ② s❛té❧✐t❡s ♣♦r ❡❧ ❜♦♠❜❛r❞❡♦ ❞❡ ♣❛rtí❝✉❧❛s ② ❢♦t♦♥❡s✱ ②❀ ❣✮ ❡❧ ❣❛s ❡♠✐t✐❞♦ ♣♦r ❧♦s ✈♦❧❝❛♥❡s ♦ ❡❧ ❞❡❣❛s❛❞♦ ♣♦r ❧♦s s❛té❧✐t❡s✳ ▲❛s ❢✉❡♥t❡s ♣♦t❡♥❝✐❛❧❡s ② ♦❜s❡r✈❛❞❛s ❞❡ ♣❛rtí❝✉❧❛s ❛sí ❝♦♠♦ ❧♦s ♠❡❝❛♥✐s♠♦s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ s❡ r❡s✉♠❡♥ ❡♥ ❡❧ ❈✉❛❞r♦ ✶✳✷ ♣❛r❛ t♦❞❛s ❧❛s ♠❛❣♥❡tós❢❡r❛s ❞❡❧ ❙✐st❡♠❛ ❙♦❧❛r ❬▼ö❜✐✉s✱ ✶✾✾✹❪✳ ❚♦❞❛s ❧❛s ♣♦❜❧❛❝✐♦♥❡s ❞❡ ♣❛rtí❝✉❧❛s ✜♥❛❧♠❡♥t❡ s✉❢r❡♥ ❞✐❢✉s✐ó♥ r❛❞✐❛❧ ❝♦♠♦ r❡s✉❧t❛❞♦ ❞❡ ❧❛ ❝♦♠❜✐♥❛❝✐ó♥ ❞❡ ❧♦s ♣r♦❝❡s♦s ❞❡ tr❛♥s♣♦rt❡ ② ❞❡ ❛❝❡❧❡✲ r❛❝✐ó♥ q✉❡ ❞❡t❡r♠✐♥❛ ❧❛s ❞✐str✐❜✉❝✐♦♥❡s ❡♥ ❡❧ ❛♥✐❧❧♦ ❞❡ ❝♦rr✐❡♥t❡ ② ❡♥ ❧♦s ❝✐♥t✉r♦♥❡s ❞❡ r❛❞✐❛❝✐ó♥ ❞❡ ❧❛s ♠❛❣♥❡tós❢❡r❛s ✐♥t❡r♥❛s✳ ❙♦❧❛♠❡♥t❡ ❧❛s ♣❛rtí❝✉❧❛s ✐♥②❡❝t❛❞❛s ♣♦r ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉❝❝✐ó♥ ✺ ❈❘❆◆❉ ✭❈♦s♠✐❝ ❘❛② ❆❧❜❡❞♦ ◆❡✉tr♦♥ ❉❡❝❛② ✮ ♦ ♣♦r ❧❛ ❝♦♠♣♦♥❡♥t❡ ❛♥ó♠❛❧❛ ❞❡ ❧♦s r❛②♦s ❝ós♠✐❝♦s ✭❆❈❘✱ ❆♥♦♠❛❧♦✉s ❈♦s♠✐❝ ❘❛②s ✮ s♦♥ ❧♦ s✉✜❝✐❡♥t❡♠❡♥t❡ ❡♥❡r❣ét✐❝❛s ❞❡s❞❡ ❡❧ ✐♥✐❝✐♦ q✉❡ ♥♦ ♥❡❝❡s✐t❛♥ ♣r♦❝❡s♦s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❛❞✐❝✐♦♥❛❧❡s✳ ▲❛ ❢✉❡♥t❡ ❞❡ ❈❘❆◆❉ ♣❛r❡❝❡ s❡r ❝♦♥s✐st❡♥t❡ ❝♦♥ ❧❛ ❞✐str✐❜✉❝✐ó♥ ❞❡ ♣r♦t♦♥❡s ♠ás ❡♥❡r❣ét✐❝♦s ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❧❛ ❚✐❡rr❛ ❬❍❡ss✱ ✶✾✻✽❪✱ ❬▲❛✈✐♥❡ ❛♥❞ ❱❡tt❡✱ ✶✾✼✵❪ ② ❙❝❤❛r❞t ❛♥❞ ▼❝❉♦♥❛❧❞ ❬✶✾✽✸❪ ❤❛♥ ♠♦str❛❞♦ q✉❡ ✉♥❛ ♣r♦❞✉❝❝✐ó♥ ❈❘❆◆❉ ❡♥ ❧♦s ❛♥✐❧❧♦s ❡s ❝♦♠✲ ♣❛t✐❜❧❡ ❝♦♥ ❧❛ ❞✐str✐❜✉❝✐ó♥ ❞❡ ♣r♦t♦♥❡s ♦❜s❡r✈❛❞❛ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦✳ ▲♦s ✐♦♥❡s ❆❈❘ ❤❛♥ s✐❞♦ r❡♣♦rt❛❞♦s ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❧❛ ❚✐❡rr❛ ❬●r✐❣♦r♦✈ ❡t ❛❧✳✱ ✶✾✾✶❪✳ ▲❛s ❢✉❡♥t❡s r❡st❛♥t❡s r❡q✉✐❡r❡♥ ❞❡ ✉♥❛ ❛❝❡❧❡r❛❝✐ó♥ ✐♥✐❝✐❛❧ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ q✉❡ s❡ ❡s❝❛❧❛ ❡♥ ❊✴◗ ✭❡♥❡r❣í❛✴❝❛r❣❛✮ ♣❛r❛ ❡①♣❧✐❝❛r ❡❧ ❡s♣❡❝tr♦ ♦❜s❡r✈❛❞♦ ❞❡ ❡♥❡r❣í❛✳ P❛r❛ ❧❛ ♠❛②♦rí❛ ❞❡ ❧❛s ♠❛❣♥❡tós❢❡r❛s ❡st❡ ♣❛s♦ ❡s ✐♥❢❡r✐❞♦ ✐♥❞✐r❡❝t❛♠❡♥t❡ ❛ ♣❛rt✐r ❞❡ ❧❛ ✐♥❤❛❜✐❧✐❞❛❞ ❞❡ ❧❛ ❞✐❢✉s✐ó♥ r❛❞✐❛❧ ♣✉r❛ ♣❛r❛ r❡♣r♦❞✉❝✐r ❧❛s ♦❜s❡r✈❛❝✐♦♥❡s✳ ❙♦❧❛♠❡♥t❡ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❧❛ ❚✐❡rr❛ ❧♦s ♣❛s♦s ✐♥❞✐✈✐❞✉❛❧❡s ❤❛♥ s✐❞♦ ♠❛r❝❛❞♦s ❝♦♥ ♠❡❞✐❝✐♦♥❡s ❡♥ t♦❞❛s ❧❛s r❡❣✐♦♥❡s ❝❧❛✈❡✳ ❚❛♠❜✐é♥ ❞❡❜❡♥ s❡r t♦♠❛❞♦s ❡♥ ❝✉❡♥t❛ ❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❝♦♥✈❡❝t✐✈♦ ❞❡❧ ✈✐❡♥t♦ s♦❧❛r ✭ECON ✮ ② ❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❞❡ ❝♦rr♦t❛❝✐ó♥ ✭EωR ✮ ❞❡❜✐❞♦ ❛ ❧❛ r♦t❛❝✐ó♥ ♣❧❛♥❡✲ t❛r✐❛✳ ❊♥ ❡❧ ❈✉❛❞r♦ ✶✳✸ ❧♦s ❡❢❡❝t♦s ❞❡ ❡st♦s ❝❛♠♣♦s s♦♥ ❝♦♥s✐❞❡r❛❞♦s ♣❛r❛ t♦❞❛s ❧❛s ♠❛❣♥❡tós❢❡r❛s ❛ tr❛✈és ❞❡ ❧❛s ❡❝✉❛❝✐♦♥❡s✿ EωR = B (R) ωR ✭✶✳✶✮ ❊♥ ❧❛ ❊❝✳ ✶✳✶✱ B (R) ❡s ❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ♠❡❞✐❞♦ ❛ ✉♥❛ ❞✐st❛♥❝✐❛ R ❞❡❧ ♣❧❛♥❡t❛✱ ω ❡s ❧❛ ❢r❡❝✉❡♥❝✐❛ ❛♥❣✉❧❛r ❞❡ r♦t❛❝✐ó♥ ❞❡❧ ♣❧❛♥❡t❛✱ ECON = αBSW (r) vSW ✭✶✳✷✮ ❉♦♥❞❡ BSW ❡s ❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ✐♥t❡r♣❧❛♥❡t❛r✐♦ ❧♦❝❛❧ ② vSW ❡s ❧❛ ✈❡❧♦❝✐❞❛❞ ❞❡❧ ✈✐❡♥t♦ s♦❧❛r ♠❡❞✐❞❛ ❛ ❧❛ ❞✐st❛♥❝✐❛ r ❞❡❧ ♣❧❛♥❡t❛✳ ❊❧ ❢❛❝t♦r α ❞❡♥♦t❛ ❧❛ ❡✜❝✐❡♥❝✐❛ ❝♦♥ ❧❛ ❝✉❛❧ ❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ✐♥t❡r♣❧❛♥❡t❛r✐♦ ✭❞❡❧ ✈✐❡♥t♦ s♦❧❛r✮ s❡ ❛❝♦♣❧❛ ❛ ❧❛ ♠❛❣♥❡tós❢❡r❛✳ ❆❞✐❝✐♦♥❛❧♠❡♥t❡ s❡ ❞❛♥ ❡❧ ♣♦t❡♥❝✐❛❧ ❝♦♥✈❡❝t✐✈♦ s♦❜r❡ ❡❧ ♣♦❧♦ ② ❧❛ ❡♥❡r❣í❛ t♦t❛❧ ❛❧♠❛❝❡♥❛❞❛ ♣♦r ❧❛ ❝♦rr♦t❛❝✐ó♥✳ ▼✐❡♥tr❛s q✉❡ ❡♥ ❧❛s ♠❛❣♥❡tós❢❡r❛s ❞❡ ❧❛ ❚✐❡rr❛ ② ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉❝❝✐ó♥ ✻ ❈✉❛❞r♦ ✶✳✷✿ ❋✉❡♥t❡s ❞❡ ✐♦♥❡s ② ♠❡❝❛♥✐s♠♦s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❡♥ ❧❛s ♠❛❣♥❡tós❢❡r❛s ♣❧❛♥❡t❛r✐❛s✳ Fuente Aceleración Planeta Región M T X J I S I U I N I E || B Aurora Reconexión Magnetocola X I I X I Difusión radial Magnetósfera interna X X X X X Reconexión Magnetocola X I I X I Difusión radial Magnetósfera interna X X X X X CRAND Difusión radial Magnetósfera interna X ACR Difusión radial Magnetósfera interna X Reconexión Magnetocola I I I Difusión radial Magnetósfera interna X X X Reconexión Magnetocola I Difusión radial Magnetósfera interna X Ionósfera Viento Solar Satélites Anillos X X ◆❖❚❆✿ ✏❳✑ ✐♥❞✐❝❛ ❡✈✐❞❡♥❝✐❛ ♦❜s❡r✈❛❝✐♦♥❛❧ ❞✐r❡❝t❛ t❛♥t♦ ❞❡ ❧❛ ❢✉❡♥t❡ ❝♦♠♦ ❞❡❧ ♠❡❝❛♥✐s♠♦ ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s❀ ✏■✑ ✐♥❞✐❝❛ ✐♥❢❡r❡♥❝✐❛✳ ▲♦s ♣❧❛♥❡t❛s s♦♥✿ ▼ ✭▼❡r❝✉r✐♦✮✱ ❚ ✭❚✐❡rr❛✮✱ ❏ ✭❏ú♣✐t❡r✮✱ ❙ ✭❙❛t✉r♥♦✮✱ ❯ ✭❯r❛♥♦✮ ② ◆ ✭◆❡♣t✉♥♦✮✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❈❛♣ít✉❧♦ ✶✳ ■♥tr♦❞✉❝❝✐ó♥ ✼ ❈✉❛❞r♦ ✶✳✸✿ ❋✉❡♥t❡s ❞❡ ❡♥❡r❣í❛ ♣❛r❛ ❡❧ tr❛♥s♣♦rt❡ ② ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s✳ Planeta Bsup (T) Periodo (hr) Tierra 3.0x10-5 Mercurio Viento solar Rotación planetaria EωR / ECON magnetopausa ECON (V m-1) Umax (KV) EωR (V m-1) Wmax (keV) 24 5.0x10-4 9.6 1.4x10-4 4.4x10-4 0.3 2.6x10-7 1406 1.3x10-3 1.4 3.4x10-7 4.1x10-10 2.6x10-4 Júpiter 9.6x10-4 9.5 9.6x10-5 114.2 4.2x10-3 11 43.7 Saturno -5 4.9x10 10.1 5.3x10 23.7 -4 8.2x10 1.4 15.6 Urano 9.1x10-6 17.1 2.6x10-5 3.7 7.5x10-5 4.7x10-2 2.9 Neptuno 1.8x10-5 16.3 1.7x10-5 3.3 7.0x10-5 1.0x10-1 4.2 0.0 8 v→c sólo rotación Pulsar 8 1.0x10 -5 -5 2.8x10 0.0 2.8x10 ❞❡ ▼❡r❝✉r✐♦ ❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❝♦♥✈❡❝t✐✈♦ ❡s ❡❧ ❞♦♠✐♥❛♥t❡✱ ❡♥ ❧❛s ♠❛❣♥❡tós❢❡r❛s ❞❡ ❏ú♣✐t❡r ② ❞❡ ❙❛t✉r♥♦ ❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❝♦rr♦t❛❝✐♦♥❛❧ ❡s ❡❧ ♠ás ✐♠♣♦rt❛♥t❡✳ ❊♥ ❧❛s ♠❛❣♥❡tós❢❡r❛s ❞❡ ❯r❛♥♦ ② ◆❡♣t✉♥♦ ❛♠❜❛s ❢✉❡♥t❡s ❞❡ ❡♥❡r❣í❛ ♣❛r❡❝❡♥ ❝♦♥tr✐❜✉✐r ❞❡ ♠❛♥❡r❛ s✐❣♥✐✜❝❛t✐✈❛✳ ▲❛ ✐♠♣♦rt❛♥❝✐❛ r❡❧❛t✐✈❛ ❞❡ ❛♠❜❛s ❢✉❡♥t❡s ❞❡ ❡♥❡r❣í❛ ❞❡♣❡♥❞❡ ❞❡❧ ❝♦❡✜❝✐❡♥t❡ ❞❡ ❛❝♦♣❧❛♠✐❡♥t♦✱ α ✱ ❡♥tr❡ ❡❧ ✈✐❡♥t♦ s♦❧❛r ② ❧❛ ♠❛❣♥❡tós❢❡r❛✳ ❊♥ ❡❧ ❈✉❛❞r♦ ✶✳✸ s❡ ❤❛ ✐♥❝❧✉✐❞♦ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ✉♥ ♣✉❧s❛r só❧♦ ♣♦r ❝♦♠♣❛r❛❝✐ó♥✱ ❡♥ ❧❛ ❝✉❛❧ ú♥✐❝❛♠❡♥t❡ ❧❛ r♦t❛❝✐ó♥ ❥✉❡❣❛ ✉♥ ♣❛♣❡❧ ❡♥ ❡❧ tr❛♥s♣♦rt❡ ❞❡ ♣❛rtí❝✉❧❛s ② ❡♥ ❧❛ ❡♥❡r❣✐③❛❝✐ó♥ ✭♥♦ ❤❛② ✉♥ ✢✉❥♦ ❡①t❡r♥♦ ✐♠♣♦rt❛♥t❡ ❝♦♠♦ ❡❧ ✈✐❡♥t♦ s♦❧❛r✮✳ ❊♥ ♣r✐♥❝✐♣✐♦✱ ❧❛s ♣❛rtí❝✉❧❛s ♣✉❡❞❡♥ s❡r ❛❝❡❧❡r❛❞❛s ❛ ❧♦ ❧❛r❣♦ ❞❡❧ ❝✐❧✐♥❞r♦ ❞❡ ❧✉③✶ ♣♦r ❧♦ q✉❡ ❧❛ ❣❛♥❛♥❝✐❛ ❞❡ ❡♥❡r❣í❛ ❡stá ❞❡t❡r♠✐♥❛❞❛ ♣♦r ❡❢❡❝t♦s r❡❧❛t✐✈✐st❛s✳ ❊♥ ❡❧ ❙✐st❡♠❛ ❙♦❧❛r✱ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❏ú♣✐t❡r ❡s ❧♦ ♠ás ❝❡r❝❛♥♦ ❛ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ✉♥ ♣✉❧s❛r✳ ✶ ❊❧ ✏❝✐❧✐♥❞r♦ ❞❡ ❧✉③✑ ❡s ✉♥ tér♠✐♥♦ ❝♦♠ú♥♠❡♥t❡ ❡♠♣❧❡❛❞♦ ❡♥ ❆str♦♥♦♠í❛ ② s❡ r❡✜❡r❡ ❛❧ ❝✐❧✐♥❞r♦ ❝✉②♦ ❡❥❡ ❡s ❡❧ ❡❥❡ ❞❡ r♦t❛❝✐ó♥ ❞❡ ✉♥❛ ❡str❡❧❧❛ ❞❡ ♥❡✉tr♦♥❡s ✭♦ ❞❡ ✉♥ ♣✉❧s❛r✮ ② ❝✉②♦ r❛❞✐♦ ❡s t❛❧ q✉❡ ❧❛ ✈❡❧♦❝✐❞❛❞ ❞❡ ✉♥ ♣❧❛s♠❛ q✉❡ r♦t❛ ❝♦♥ ❡s❛ ❡str❡❧❧❛ ✐❣✉❛❧❛rí❛ ❛ ❧❛ ✈❡❧♦❝✐❞❛❞ ❞❡ ❧❛ ❧✉③ ❡♥ ❧❛ s✉♣❡r✜❝✐❡ ❞❡❧ ❝✐❧✐♥❞r♦✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✶✳✶✳ ▼❡❝❛♥✐s♠♦s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❣❡♥❡r❛❧❡s ✶✳✶✳ ✽ ▼❡❝❛♥✐s♠♦s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❣❡♥❡r❛❧❡s ▲♦s ♠❡❝❛♥✐s♠♦s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ♣✉❡❞❡♥ s❡r ❝❧❛s✐✜❝❛❞♦s ❡♥ ❝✉❛tr♦ ❣r❛♥❞❡s ❝❛t❡❣♦✲ rí❛s ❬●❛❧❧❛❣❤❡r ❡t ❛❧✳ ✷✵✵✺❪✳ ✶✳✶✳✶✳ ❆❝❡❧❡r❛❝✐ó♥ ❛❞✐❛❜át✐❝❛ ② ♦tr❛s ❢♦r♠❛s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ♥♦ ❡st♦❝ást✐❝❛ ❊❧ ♠❡❝❛♥✐s♠♦ ♠ás s✐♠♣❧❡ ❡s ❧❛ ❛❝❡❧❡r❛❝✐ó♥ s✐st❡♠át✐❝❛ ❡♥ ✉♥ ❝❛♠♣♦ ❡❧❡❝tr♦stá✲ t✐❝♦ ♣❛r❛❧❡❧♦ ❛❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦✳ ❙✐♥ ❡♠❜❛r❣♦✱ ❡①✐st❡ ✉♥ ❛r❣✉♠❡♥t♦ ♦❜s❡r✈❛❝✐♦♥❛❧ ❡♥ ❝♦♥tr❛ ❞❡ ❡st❡ ♠❡❝❛♥✐s♠♦✿ ❝✉❛♥❞♦ ❧❛s ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s t✐❡♥❡♥ ✉♥❛ ❝❛í❞❛ ❞❡ ♣♦t❡♥❝✐❛❧ t♦❞❛s ❡❧❧❛s ❣❛♥❛♥ ❧❛ ♠✐s♠❛ ❡♥❡r❣í❛✳ ❖❜s❡r✈❛❝✐♦♥❛❧♠❡♥t❡ ❧❛s ♣❛rtí❝✉❧❛s rá✲ ♣✐❞❛s t✐❡♥❞❡♥ ❛ ♠♦str❛r ✉♥ ❡s♣❡❝tr♦ ❞❡ ❡♥❡r❣í❛s q✉❡ s✐❣✉❡ ✉♥❛ ❧❡② ❞❡ ♣♦t❡♥❝✐❛s✱ ② ♥♦ ✉♥ ❡s♣❡❝tr♦ ❝✉❛s✐♠♦♥♦❝r♦♠át✐❝♦ q✉❡ s❡ ❡s♣❡r❛rí❛ ❞❡ ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ❡❧❡❝tr♦stát✐❝❛✳ ❖tr♦ t✐♣♦ ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ♦❝✉rr❡ ❝✉❛♥❞♦ ❧♦s ✐♥✈❛r✐❛♥t❡s ❛❞✐❛❜át✐❝♦s s♦♥ ❝♦♥s❡r✲ ✈❛❞♦s ❞✉r❛♥t❡ ❡❧ ♠♦✈✐♠✐❡♥t♦ ❡♥ ❝❛♠♣♦s ♠❛❣♥ét✐❝♦s ♥♦ ✉♥✐❢♦r♠❡s✳ ❘❡❝✉ér❞❡s❡✱ ♣♦r ❡❥❡♠♣❧♦✱ q✉❡ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ t❡rr❡str❡ ✐♥t❡r♠❡❞✐❛ ❧❛s ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s s♦♥ ♠♦✈✐❞❛s ❤❛❝✐❛ r❡❣✐♦♥❡s ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ✐♥t❡♥s♦ ✲❛ tr❛✈és ❞❡ ❝❛♠♣♦s ❡❧é❝tr✐❝♦s ❝♦♥✈❡❝t✐✈♦s✲ ❝♦♥s❡r✈❛♥❞♦ ❡❧ ♣r✐♠❡r ✐♥✈❛r✐❛♥t❡ ❛❞✐❛❜át✐❝♦✳ P❛r❛ ♣❛rtí❝✉❧❛s q✉❡ ❞❡r✐✲ ✈❛♥ ❛ ❧♦ ❧❛r❣♦ ❞❡ ✉♥❛ ❧í♥❡❛ ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ② ❧✉❡❣♦ s♦♥ tr❛♥s♣♦rt❛❞❛s ❤❛❝✐❛ ❧í♥❡❛s ❞❡ ❝❛♠♣♦ ♠ás ❝♦rt❛s✱ s✉ ❡♥❡r❣í❛ ♣❛r❛❧❡❧❛ s❡ ✐♥❝r❡♠❡♥t❛ ❝♦♥s❡r✈❛♥❞♦ ❡❧ s❡❣✉♥❞♦ ✐♥✈❛r✐❛♥t❡ ❛❞✐❛❜át✐❝♦✳ ❋✐♥❛❧♠❡♥t❡✱ s✐ ❧♦s ❝❛♠❜✐♦s ❡♥ ❛❣❡♥t❡s ❡①t❡r♥♦s ♥♦ ♦❝✉rr❡♥ ♠ás rá♣✐❞♦ q✉❡ ❧♦s ♣❡r✐♦❞♦s ❝♦♠♣❧❡t♦s ♣❛r❛ ❧♦s ❛rr❛str❡s ❞❡ ❧❛s ♣❛rtí❝✉❧❛s q✉❡ ❞❡r✐✈❛♥ ❛❧r❡❞❡❞♦r ❞❡ ❧❛ ❚✐❡rr❛✱ ❡❧ t❡r❝❡r ✐♥✈❛r✐❛♥t❡ ❛❞✐❛❜át✐❝♦ t✐❡♥❞❡ ❛ ❝♦♥s❡r✈❛rs❡✳ ▲❛ ❛❝❡❧❡r❛❝✐ó♥ ✏❝❡♥trí❢✉❣❛✑ ❬❈❧❛❞✐s✱ ✶✾✽✻❀ ❍♦r✇✐t③ ❡t ❛❧✳✱ ✶✾✾✹❪ ❡s ❛q✉❡❧❧❛ ❡♥ ❧❛ ❝✉❛❧ ❧❛ ❝♦♥✈❡❝❝✐ó♥ ❞❡ ❧í♥❡❛s ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❝♦♥ ❞✐r❡❝❝✐♦♥❡s ✈❛r✐❛❜❧❡s ✏❛③♦t❛✑ ❧❛s ♣❛rtí❝✉❧❛s ❤❛❝✐❛ ❛❢✉❡r❛ ❛ ❧♦ ❧❛r❣♦ ❞❡ ❧❛s ❧í♥❡❛s ❞❡ ❝❛♠♣♦✳ ❊st❛ ❡♥❡r❣✐③❛❝✐ó♥ ♣✉❡❞❡ s❡r r❡❧❡✈❛♥t❡ ♣❛r❛ ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ❞❡ ✢✉❥♦s ❡♥ ❧♦s ❡✈❡♥t♦s ❞❡ s✉❜t♦r♠❡♥t❛s✱ ❝♦♠♦ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ t❡rr❡str❡ ②✱ q✉✐③ás✱ ❡♥ ♠❛❣♥❡tós❢❡r❛s q✉❡ r♦t❛♥ rá♣✐❞❛♠❡♥t❡ ❝♦♠♦ ❧❛ ❞❡ ❏ú♣✐t❡r✳ ❯♥❛ ❝❛r❛❝t❡ríst✐❝❛ ❞❡ ❡st❡ t✐♣♦ ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❡s q✉❡ ❧❛ ✈❡❧♦❝✐❞❛❞ ❣❛♥❛❞❛ t✐❡♥❞❡ ❛ s❡r ❝♦♥st❛♥t❡ ♣❛r❛ ❧❛s ❞✐❢❡r❡♥t❡s ❡s♣❡❝✐❡s ✐ó♥✐❝❛s✳ ❖tr❛ ❛❝❡❧❡r❛❝✐ó♥ ♥♦ ❡st♦❝ást✐❝❛ ♣♦r ❝❛♠♣♦s ❡❧é❝tr✐❝♦s ♣❛r❛❧❡❧♦s ♦❝✉rr✐❞❛ ❡♥ ❡❧ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✶✳✶✳ ▼❡❝❛♥✐s♠♦s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❣❡♥❡r❛❧❡s ✾ ♣❧❛s♠❛ ✐♦♥♦s❢ér✐❝♦ ♣✉❡❞❡ r❡s✉❧t❛r ❞❡ ❧♦s ❡❢❡❝t♦s ❞❡ ❧♦s ❢♦t♦❡❧❡❝tr♦♥❡s✳ ❊♥ ❡st❡ ❢❡♥ó✲ ♠❡♥♦✱ ♣❛r❛ ❧✐♠✐t❛r ❧❛ ❝♦rr✐❡♥t❡ ♥❡t❛ ② ♠❛♥t❡♥❡r ❧❛ ❝✉❛s✐♥❡✉tr❛❧✐❞❛❞ ❡♥ ❡❧ tr❛♥s♣♦rt❡ ❞❡ ♣❧❛s♠❛ ♣♦❧❛r ✐♦♥♦s❢ér✐❝♦ ❛♥t❡ ❧❛ ♣r❡s❡♥❝✐❛ ❞❡ ❢♦t♦❡❧❡❝tr♦♥❡s q✉❡ s❡ ♠✉❡✈❡♥ ❛ ♠❛✲ ②♦r❡s ❛❧t✉r❛s✱ s❡ ❣❡♥❡r❛ ✉♥ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❤❛❝✐❛ ❛rr✐❜❛ ♣❛r❛ s✉♣r✐♠✐r ❡❧ ✢✉❥♦ ❞❡ ❢♦t♦❧❡❝tr♦♥❡s❀ ❝♦♥s❡❝✉❡♥t❡♠❡♥t❡ ❧♦s ✐♦♥❡s s♦♥ ❛❝❡❧❡r❛❞♦s ❡♥ ❧❛ ♠✐s♠❛ ❞✐r❡❝❝✐ó♥ ❞❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦✳ ✶✳✶✳✷✳ ❆❝❡❧❡r❛❝✐ó♥ ❡st♦❝ást✐❝❛ ② ❛❧♠❛❝❡♥❛♠✐❡♥t♦ ❞❡ ❡♥❡r❣í❛ ♠❛❣♥ét✐❝❛ ❯♥ ♣r♦❝❡s♦ ❢✉♥❞❛♠❡♥t❛❧ ❡♥ ❧♦s ♣❧❛s♠❛s ❡s ❡❧ ❛❧♠❛❝❡♥❛♠✐❡♥t♦ ❞❡ ❡♥❡r❣í❛ ❡♥ ❝❛♠♣♦s ♠❛❣♥ét✐❝♦s ② s✉ s✉❜s❡❝✉❡♥t❡ ❝♦♥✈❡rs✐ó♥ ❛ ❡♥❡r❣í❛ ❝✐♥ét✐❝❛ ❞❡ ❧❛s ♣❛rtí❝✉❧❛s✳ ▲❛ ✐❞❡❛ q✉❡ s❡ t✐❡♥❡ ❡s q✉❡ ❧❛ r❡❝♦♥❡①✐ó♥ ♠❛❣♥ét✐❝❛ ❥✉❡❣❛ ✉♥ ♣❛♣❡❧ ❝❧❛✈❡ ❡♥ ❡st❡ ♣r♦❝❡s♦ q✉❡ ❢✉❡ ❛❞✈❡rt✐❞♦ ♣r✐♠❡r♦ ♣♦r ●✐♦✈❛♥❡❧❧✐ ❬✶✾✹✼❪ ♣❛r❛ ❡①♣❧✐❝❛r ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❡♥ ❢✉❧❣✉r❛❝✐♦♥❡s s♦❧❛r❡s✳ ▲❛ r❡❝♦♥❡①✐ó♥ ♠❛❣♥ét✐❝❛ ✐♥✈♦❧✉❝r❛ ✉♥❛ r✉♣t✉r❛ ❞❡ ❧❛ ❛♣r♦①✐♠❛❝✐ó♥ ♠❛❣♥❡t♦❤✐✲ ❞r♦❞✐♥á♠✐❝❛ ✐❞❡❛❧ ❞❡❧ ❝❛♠♣♦ ❝♦♥❣❡❧❛❞♦ ❡♥ ❧❛ ❝✉❛❧ ❧❛s ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s q✉❡ ❡stá♥ ❝♦♥❡❝t❛❞❛s ♣♦r ✉♥❛ ❧í♥❡❛ ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❡♥ ✉♥ ✐♥st❛♥t❡ ❞❡ t✐❡♠♣♦ ❞❛❞♦✱ ❞❡❜❡ ♣❡r♠❛♥❡❝❡r ❝♦♥❡❝t❛❞❛ ♣♦r ✉♥❛ ❧í♥❡❛ ❞❡ ❝❛♠♣♦ ♣♦r t♦❞♦ ❡❧ t✐❡♠♣♦✳ ❊st❡ ♣r♦❝❡s♦ ✐♥❞✉❝❡ ❝❛♠♣♦s ❡❧é❝tr✐❝♦s ♣❛r❛❧❡❧♦s ❛❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ② ❡♥t♦♥❝❡s ❛❝❡❧❡r❛ ❛ ❧❛s ♣❛r✲ tí❝✉❧❛s ❞❡❧ ♣❧❛s♠❛✳ ❈♦♥s❡❝✉❡♥t❡♠❡♥t❡ s❡ ❧❧❡❣❛ ❛❧ ❝♦♥❝❡♣t♦ ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❡st♦❝ást✐❝❛ ✭♦ ❛❝❡❧❡r❛❝✐ó♥ ❞❡ ❋❡r♠✐ ❞❡ s❡❣✉♥❞♦ ♦r❞❡♥✮✳ ▲❛ ✐❞❡❛ ♣r✐♥❝✐♣❛❧ ❡s q✉❡ ❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❡s ❛❧❡❛t♦r✐♦ ❞❡ ❛❧❣✉♥❛ ♠❛♥❡r❛✱ ② q✉❡✱ ❛✉♥q✉❡ ❧❛s ♣❛rtí❝✉❧❛s ❣❛♥❛♥ ② ♣✐❡r❞❡♥ ❡♥❡r❣í❛ ❡♥ ❝❛❞❛ ✐♥t❡r❛❝❝✐ó♥✱ ❡♥ ♣r♦♠❡❞✐♦ ❧❛s ♣❛rtí❝✉❧❛s ❣❛♥❛♥ ❡♥❡r❣í❛✳ ❊❧ ♣r✐♠❡r♦ ❞❡ ❡st♦s ♠❡❝❛♥✐s✲ ♠♦s ❢✉❡ ❡①♣❧♦r❛❞♦ ❡♥ ❞❡t❛❧❧❡ ♣♦r ❋❡r♠✐ ❬✶✾✹✾❪ q✉✐❡♥ ✐♥✈♦❧✉❝ró ❝♦❧✐s✐♦♥❡s ❞❡ r❛②♦s ❝ós♠✐❝♦s ❝♦♥ ♥✉❜❡s ✐♥t❡r❡st❡❧❛r❡s ♠❛❣♥❡t✐③❛❞❛s✱ ❡♥ ❞♦♥❞❡ s❡ ❣❛♥❛❜❛ ♦ ♣❡r❞í❛ ❡♥❡r❣í❛ ❞❡♣❡♥❞✐❡♥❞♦ ❞❡ s✐ ❡❧ ✏❡s♣❡❥♦ ♠❛❣♥ét✐❝♦✑ s❡ ❛❝❡r❝❛❜❛ ♦ ❛❧❡❥❛❜❛✳ ▲❛ ❛❝❡❧❡r❛❝✐ó♥ ❡st♦❝ást✐❝❛✱ ♣♦r ♦tr♦ ❧❛❞♦✱ s❡ ❤❛ s❛❜✐❞♦ q✉❡ ❡①✐st❡ ② ❡stá ♣r❡s❡♥t❡ ❡♥ ❧❛ r❡❣✐ó♥ ✏rí♦ ❛❜❛❥♦✑ ❞❡ ❧♦s ❝❤♦q✉❡s✱ ♣❡r♦ ❝♦♠♦ ❡st❡ ♠❡❝❛♥✐s♠♦ tr❛❜❛❥❛ ❡♥ ❡s❝❛❧❛s t❡♠♣♦r❛❧❡s ♠✉❝❤♦ ♠❛②♦r❡s q✉❡ ❧❛s ❝♦rr❡s♣♦♥❞✐❡♥t❡s ❛❧ ♠❡❝❛♥✐s♠♦ ❞❡ ❋❡r♠✐ ❬✶✾✺✹❪ ❞❡ ♣r✐♠❡r ♦r❞❡♥✱ ❤❛ s✐❞♦ ❢r❡❝✉❡♥t❡♠❡♥t❡ ❞❡s♣r❡❝✐❛❞♦ ❡♥ ❡st✉❞✐♦s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✶✳✶✳ ▼❡❝❛♥✐s♠♦s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❣❡♥❡r❛❧❡s ✶✵ ❞❡ ♣❛rtí❝✉❧❛s r❡❧❛t✐✈✐st❛s ❬✈é❛s❡ ♣♦r ❡❥❡♠♣❧♦ ❖str♦✇s❦✐ ❛♥❞ ❙❝❤❧✐❝❦❡✐s❡r✱ ✶✾✾✸❪✳ ❙✐♥ ❡♠❜❛r❣♦✱ ❛❧❣✉♥♦s ❛✉t♦r❡s ❤❛♥ ❛♣❧✐❝❛❞♦ ❡①✐t♦s❛♠❡♥t❡ ❡st❡ ♠❡❝❛♥✐s♠♦ ❛❧ ❡st✉❞✐♦ ❞❡ ♣❛rtí❝✉❧❛s ❡♥❡r❣ét✐❝❛s ❡♥ ❢✉❧❣✉r❛❝✐♦♥❡s s♦❧❛r❡s ❬♣♦r ❡❥❡♠♣❧♦ ❙❡❧❦♦✇✐t③ ❛♥❞ ❇❧❛❝❦♠❛♥✱ ✷✵✵✹❪✳ ▲♦s r❡q✉✐s✐t♦s ❡s❡♥❝✐❛❧❡s ❞❡ ✉♥ ♠❡❝❛♥✐s♠♦ ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❡st♦❝ást✐❝❛ s♦♥✿ ✶✮ ✐♥t❡r❛❝❝✐♦♥❡s ❡❧❡♠❡♥t❛❧❡s q✉❡ ❝❛✉s❛♥ q✉❡ ❧❛ ❡♥❡r❣í❛ ❞❡ ❧❛s ♣❛rtí❝✉❧❛s ❝❛♠❜✐❡ ❞❡❜✐❞♦ ❛❧ ❡❢❡❝t♦ ❜❡t❛tró♥ ❬❙✇❛♥♥✱ ✶✾✸✸❪✱ ❛ ❧❛ r❡✢❡①✐ó♥ ❞❡ ❧❛s ✐♥❤♦♠♦❣❡♥❡✐❞❛❞❡s ♠❛❣♥ét✐❝❛s ❬❋❡r♠✐✱ ✶✾✹✾❪ ♦ ❛❧ ❛♠♦rt✐❣✉❛♠✐❡♥t♦ ❞❡ tr❛♥s✐❝✐ó♥ ❬❙❤❡♥✱ ✶✾✻✺❪❀ ✷✮ ❞✐s♣❡rs✐ó♥ ❡❢❡❝t✐✈❛ ❛tr✐❜✉✐❞❛ ❛ ❧❛s ✐♥t❡r❛❝❝✐♦♥❡s ♦♥❞❛✲♣❛rtí❝✉❧❛ ②✱ ✸✮ ✉♥ ♣r♦❝❡s♦ ❛❧❡❛t♦r✐♦ ✭tr❛t❛♠✐❡♥t♦ ❡st❛❞íst✐❝♦✮ ❜❛s❛❞♦ ❡♥ ✉♥❛ ❛♣r♦①✐♠❛❝✐ó♥ ❞❡ ❧❛ ❡❝✉❛❝✐ó♥ ❞❡ ❋♦❦❦❡r✲P❧❛♥❝❦ ♦ ❡♥ ✉♥❛ ❛♣r♦①✐♠❛❝✐ó♥ ❝✉❛s✐❧✐♥❡❛❧ q✉❡ ✐♠♣❧✐❝❛ q✉❡ ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ♣✉❡❞❡ s❡r ❝♦♥s✐❞❡r❛❞❛ ❝♦♠♦ ✉♥❛ ❞✐❢✉s✐ó♥ ❡♥ ❡❧ ❡s♣❛❝✐♦ ❞❡ ♠♦♠❡♥t♦s✳ ❊st❡ s❡❣✉♥❞♦ ♠❡❝❛♥✐s♠♦ ♣✉❡❞❡ s❡r ♦ ♥♦ ✐♥❞❡♣❡♥❞✐❡♥t❡ ❞❡ ❧♦s ❝❛♠❜✐♦s ❞❡ ❡♥❡r❣í❛✳ ❊♥ ❡❧ ♠❡❝❛♥✐s♠♦ ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❡st♦❝ást✐❝❛ ♥♦ ❡s ♥❡❝❡s❛r✐❛♠❡♥t❡ ♦❜✈✐♦ q✉❡ ❡♥ ♣r♦♠❡❞✐♦ s❡ ❣❛♥❡ ❡♥❡r❣í❛ ✭❡♥ ❧✉❣❛r ❞❡ ♣❡r❞❡r❧❛✮✳ ❊♥ tér♠✐♥♦s t❡r♠♦❞✐♥á♠✐❝♦s✱ ❧❛ ❡♥❡r❣í❛ ❞❡ ❧❛s ♣❛rtí❝✉❧❛s ❞❡❜❡rí❛ t❡♥❞❡r ❤❛❝✐❛ ❧❛ ❡♥❡r❣í❛ ♣r♦♠❡❞✐♦ ♦ ❤❛❝✐❛ ❧❛ t❡♠♣❡✲ r❛t✉r❛ ❡❢❡❝t✐✈❛ ❞❡ ❧♦s ♠♦✈✐♠✐❡♥t♦s t✉r❜✉❧❡♥t♦s✳ ❆❞❡♠ás✱ ❡s ♥❡❝❡s❛r✐♦ q✉❡ ❧❛ ♣❛rtí❝✉❧❛ ❝♦♠♣❧❡t❡ ✉♥ r❛❞✐♦ ❞❡ ❣✐r♦ ✭♠♦✈✐♠✐❡♥t♦ ❣✐r♦tró♣✐❝♦✮ ♣❛r❛ q✉❡ ♣✉❡❞❛ r❡s♦♥❛r ❝♦♥ ❧❛ ♦♥❞❛ ❝♦rr❡s♣♦♥❞✐❡♥t❡ ② ❡♥t♦♥❝❡s s❡r ❛❝❡❧❡r❛❞❛ ♦ ❞❡s❛❝❡❧❡r❛❞❛ ❬❈❤❡✇ ❡t ❛❧✳✱ ✶✾✻✾❪✳ P♦r ❡❥❡♠♣❧♦✱ ❡st❛ ❛♣r♦①✐♠❛❝✐ó♥ ♥♦ ♣✉❡❞❡ ❡①♣❧✐❝❛r ❡❧ rá♣✐❞♦ ✐♥❝r❡♠❡♥t♦ ❞❡ ❡♥❡r❣í❛ ❞❡ ❧♦s ✐♦♥❡s ❞❡ ♦①í❣❡♥♦ ❧♦❝❛❧✐③❛❞♦s ❡♥ ❧❛ ✐♦♥ós❢❡r❛ ❞❡ ❱❡♥✉s✱ ♣✉❡s ❧♦s r❛❞✐♦s ❞❡ ❣✐✲ r♦ ✭② ❧♦s ♣❡r✐♦❞♦s✮ s♦♥ ♠✉② ❣r❛♥❞❡s ❡♥ ❝♦♠♣❛r❛❝✐ó♥ ❝♦♥ ❡❧ t✐❡♠♣♦ ❡♠♣❧❡❛❞♦ ♣❛r❛ ❛❝❡❧❡r❛r❧♦s ❬Pér❡③ ❞❡ ❚❡❥❛❞❛ ❡t ❛❧✳✱ ✶✾✾✺❪✳ P❛r❛ ❡s♦s ❝❛s♦s✱ ❡s ♥❡❝❡s❛r✐♦ ❞❡s❛rr♦❧❧❛r ✉♥❛ ♥✉❡✈❛ ❢♦r♠✉❧❛❝✐ó♥ ❜❛s❛❞❛ ❡♥ ❧❛s ✢✉❝t✉❛❝✐♦♥❡s ❡st♦❝ást✐❝❛s ❞❡ ❛❧❣ú♥ ❝❛♠♣♦ ❞❡ ❢✉❡r③❛s✱ ❡♥ ❧✉❣❛r ❞❡❧ ♠♦✈✐♠✐❡♥t♦ ❡st♦❝ást✐❝♦ ❞❡ ❣✐r♦ ❞❡s❝r✐t♦ ♣♦r ❧❛ ♣❛rtí❝✉❧❛ ❛ tr❛✈és ❞❡ ❧❛s ❧í♥❡❛s ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦✳ ❊♥ ❡❧ ♣r❡s❡♥t❡ tr❛❜❛❥♦ s❡ ♣r♦♣♦♥❡ ✉♥ ♠❡❝❛♥✐s♠♦ ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❡♥ ❞♦♥❞❡ ❧❛ ❡st♦❝❛st✐❝✐❞❛❞ r❡❝❛❡ ❡♥ ✉♥ ❝❛♠♣♦ ❞❡ ❢✉❡r③❛s ❝✉②❛ ♥❛t✉r❛❧❡③❛ ♣✉❡❞❡ s❡r ♦ ♥♦ ❡❧❡❝tr♦✲ ♠❛❣♥ét✐❝❛ ② ❧❛ ❡❝✉❛❝✐ó♥ ❞❡ ♠♦✈✐♠✐❡♥t♦ ❛ r❡s♦❧✈❡r ✐♥❝❧✉②❡ ✲❡♥tr❡ ♦tr❛s✲ ❛ ❧❛ ❢✉❡r③❛ ❞❡ ❡st❡ ❝❛♠♣♦ ❡st♦❝ást✐❝♦✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✶✳✶✳ ▼❡❝❛♥✐s♠♦s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❣❡♥❡r❛❧❡s ✶✳✶✳✸✳ ✶✶ ❆❝❡❧❡r❛❝✐ó♥ ♣♦r ❝❤♦q✉❡s ▲❛ ❛❝❡❧❡r❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ♣♦r ♦♥❞❛s ❞❡ ❝❤♦q✉❡ ♣✉❡❞❡ s❡r ♦❜s❡r✈❛❞❛ ❡♥ ❧♦s ❢r❡♥✲ t❡s ❞❡ ❝❤♦q✉❡ ♣❧❛♥❡t❛r✐♦s ② ❡♥ ❧♦s ❝❤♦q✉❡s ✏✈✐❛❥❡r♦s✑ ✐♥t❡r♣❧❛♥❡t❛r✐♦s✳ P♦r ❡❥❡♠♣❧♦✱ ♣✉❡❞❡ ♦❝✉rr✐r ❡♥ ❡❧ ❢r❡♥t❡ ❞❡ ❝❤♦q✉❡ t❡rr❡str❡✱ ❞❡♥tr♦ ❞❡❧ ✈✐❡♥t♦ s♦❧❛r ❝♦♥❞✉❝✐❞♦ ♣♦r ❡②❡❝❝✐♦♥❡s ❞❡ ♠❛s❛ ❝♦r♦♥❛❧✱ ❡♥ ❢✉❧❣✉r❛❝✐♦♥❡s s♦❧❛r❡s✱ ❡♥ r❡♠❛♥❡♥t❡s ❞❡ s✉♣❡r♥♦✈❛ ❙✉♣❡r♥♦✈❛ ❘❡♠♥❛♥ts ✮✱ ❡♥ ❥❡ts ❞❡ ◆ú❝❧❡♦s ❆❝t✐✈♦s ❞❡ ●❛❧❛①✐❛s ✭❆●◆✱ ❆❝t✐✈❡ ●❛❧❛❝t✐❝ ◆✉❝❧❡✐ ✮✱ ❡♥ ❝❤♦q✉❡s r❡❧❛t✐✈✐st❛s ❛s♦❝✐❛❞♦s ❝♦♥ ❡st❛❧❧✐❞♦s ❞❡ r❛②♦s γ ② ❡♥ ❡❧ ✭❙◆❘✱ ❣❛s q✉❡ s❡ ❡♥❝✉❡♥tr❛ ❡♥tr❡ ❧♦s ❝ú♠✉❧♦s ❞❡ ❣❛❧❛①✐❛s✳ ❊①✐st❡♥ ❞✐❢❡r❡♥t❡s ♠❡❝❛♥✐s♠♦s ❢ís✐❝♦s ✐♥✈♦❧✉❝r❛❞♦s ❡♥ ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❡♥ ❧♦s ❝❤♦q✉❡s✿ ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ♣♦r ❛rr❛str❡ ✭❛❧❣✉♥❛s ✈❡❝❡s ❧❧❛♠❛❞❛ ❛❝❡❧❡r❛❝✐ó♥ ❧✐❜r❡ ❞❡ ❞✐s♣❡rs✐ó♥✮ ❞❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❞❡ ✐♥❞✉❝❝✐ó♥ ❡♥ ❡❧ ❢r❡♥t❡ ❞❡ ❝❤♦q✉❡❀ ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ♣♦r ❝❤♦q✉❡ ❞✐❢✉s✐✈♦ ❞❡❜✐❞♦ ❛ ❧❛s r❡♣❡t✐❞❛s r❡✢❡①✐♦♥❡s ❡♥ ❡❧ ❢r❡♥t❡ ❞❡ ❝❤♦q✉❡❀ ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ❡st♦❝ást✐❝❛ ❡♥ ❧❛ r❡❣✐ó♥ ❞❡ t✉r❜✉❧❡♥❝✐❛ ❧♦❝❛❧✐③❛❞❛ ❞❡trás ❞❡❧ ❢r❡♥t❡ ❞❡ ❝❤♦q✉❡ ② ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ♣♦r ❝♦♠♣r❡s✐ó♥ ❞✐❢✉s✐✈❛ q✉❡ ♥♦ ♦❝✉rr❡ ❡①❛❝t❛♠❡♥t❡ ❡♥ ❧♦s ❝❤♦q✉❡s s✐♥♦ ❝✉❛♥❞♦ ❡❧ ♣❧❛s♠❛ ❡s ❣r❛❞✉❛❧♠❡♥t❡ ❝♦♠♣r✐♠✐❞♦ ❬❙❝❤❛t③♠❛♥♥✱ ✶✾✻✸❀ ❏♦♥❡s✱ ✶✾✾✹❀ ❏♦❦✐♣✐✐ ❡t ❛❧✳✱ ✷✵✵✶❪✳ ✶✳✶✳✹✳ ❆❝❡❧❡r❛❝✐ó♥ t✉r❜✉❧❡♥t❛ ② ♣♦r ♦♥❞❛s ❞❡ ♣❧❛s♠❛ ❉❡♥tr♦ ❞❡ ❡st❡ ❝♦♥t❡①t♦✱ ❧❛ r❡❧❛❝✐ó♥ ♦♥❞❛✲♣❛rtí❝✉❧❛ ❡s ❡①♣r❡s❛❞❛ ❛ tr❛✈és ❞❡ ❧❛s ❝♦♥❞✐❝✐♦♥❡s ❞❡ r❡s♦♥❛♥❝✐❛ q✉❡ ❞❡♣❡♥❞❡♥ ❞❡ ❧❛ ❢r❡❝✉❡♥❝✐❛ ❞❡ ❧❛ ♦♥❞❛✱ ❞❡ ❧❛ ✈❡❧♦❝✐❞❛❞ ❞❡ ❧❛ ♣❛rtí❝✉❧❛ ② ❞❡❧ ♥ú♠❡r♦ ❞❡ ♦♥❞❛s ♣♦s✐❜❧❡s q✉❡ ✐♥t❡r❛❝❝✐♦♥❛♥ ❝♦♥ ❧❛ ♣❛rtí❝✉❧❛✳ ❈✉❛♥❞♦ ❧❛s ♦♥❞❛s s♦♥ ❛♠♦rt✐❣✉❛❞❛s✱ s✉ ❡♥❡r❣í❛ ❡s tr❛♥s❢❡r✐❞❛ ❛ ❧❛s ♣❛rtí❝✉❧❛s ② ❣❡♥❡r❛❧♠❡♥t❡ s❡ ❡s♣❡r❛ q✉❡ ❧❛ ❡♥❡r❣í❛ ❞❡ ❧❛ ♦♥❞❛ s❡ ❝♦♥✈✐❡rt❛ ❡♥ ❝❛❧♦r✱ ❡st♦ ❡s✱ q✉❡ s❡ ❞✐str✐❜✉②❛ ❡♥tr❡ ❧❛s ♣❛rtí❝✉❧❛s tér♠✐❝❛s✳ ❙✐♥ ❡♠❜❛r❣♦✱ s✐ só❧♦ ✉♥❛ ❢r❛❝❝✐ó♥ ❞❡ ❧❛s ♣❛rtí❝✉❧❛s ♣✉❡❞❡ ✐♥t❡r❛❝t✉❛r ❝♦♥ ❧❛s ♦♥❞❛s✱ ❡♥t♦♥❝❡s ❧❛ ❡♥❡r❣í❛ ❞❡❜❡ ✐rs❡ ✐♥✐❝✐❛❧♠❡♥t❡ ❡♥ ❡s❛ ❢r❛❝❝✐ó♥✳ ❊st♦s ♠❡❝❛♥✐s♠♦s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ♣♦r ♦♥❞❛s s♦♥ út✐❧❡s ♣❛r❛ ❡①♣❧✐❝❛r ❧❛ ❡♥❡r❣✐③❛❝✐ó♥ ❞❡ ❧♦s ❡❧❡❝tr♦♥❡s ❡♥ ❧♦s ❛♥✐❧❧♦s ❞❡ r❛❞✐❛❝✐ó♥ ❞❡ ❱❛♥ ❆❧❧❡♥✱ ♣❛r❛ ❧♦s ❡st❛❧❧✐❞♦s ❞❡ r❛❞✐♦ s♦❧❛r❡s t✐♣♦ ■■■✱ ❡♥tr❡ ♦tr♦s✳ ❆❞❡♠ás ❞❡ ❧❛s ❝♦♥❞✐❝✐♦♥❡s ❞❡ r❡s♦♥❛♥❝✐❛ ❡s ♥❡❝❡s❛r✐♦ ❝♦♥s✐❞❡r❛r ❧❛s ✐♥❡st❛❜✐❧✐❞❛✲ ❞❡s ❡♥ ❡❧ ♣❧❛s♠❛ q✉❡ ❧❧❡✈❛♥ t❛♠❜✐é♥ ❛ ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ❞❡ ❧❛s ♣❛rtí❝✉❧❛s✳ ❊st❛s ✐♥❡st❛❜✐✲ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✶✳✶✳ ▼❡❝❛♥✐s♠♦s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❣❡♥❡r❛❧❡s ✶✷ ❧✐❞❛❞❡s ♣✉❡❞❡♥ s❡r ❝❧❛s✐✜❝❛❞❛s ❣❡♥❡r❛❧♠❡♥t❡ ❡♥ ❝✉❛tr♦ ❝❛t❡❣♦rí❛s✿ ✶✮ ✐♥❡st❛❜✐❧✐❞❛❞❡s ❞❡ ✢✉❥♦✱ ✷✮ ✐♥❡st❛❜✐❧✐❞❛❞❡s ❞❡ ❘❛②❧❡✐❣❤✲❚❛②❧♦r✱ ✸✮ ✐♥❡st❛❜✐❧✐❞❛❞❡s ✉♥✐✈❡rs❛❧❡s ❡✱ ✹✮ ✐♥❡st❛❜✐❧✐❞❛❞❡s ❝✐♥ét✐❝❛s✳ ❈♦♠♦ ❡❥❡♠♣❧♦s s❡ ❝✐t❛♥ ❧❛ ❞✐sr✉♣❝✐ó♥ ❞❡ ❧❛ ♠❛❣♥❡t♦❝♦❧❛ t❡rr❡str❡ ✲♣♦s✐❜❧❡♠❡♥t❡ ♦❝❛s✐♦♥❛❞❛ ♣♦r ✐♥❡st❛❜✐❧✐❞❛❞❡s✲ q✉❡ ❧❧❡✈❛ ❛ ❧❛ ❧✐❜❡r❛❝✐ó♥ ✐♠✲ ♣✉❧s✐✈❛ ❞❡ ❡♥❡r❣í❛ ❡♥ ❧❛ ❢♦r♠❛ ❞❡ ♣❛rtí❝✉❧❛s ❛❝❡❧❡r❛❞❛s✱ ❧❛ ✐♥❡st❛❜✐❧✐❞❛❞ ❞❡r✐✈❛❞❛ ❞❡ ❧❛ ❝♦♠♣r❡s✐ó♥ ❞❡ ❧❛ ♠❛❣♥❡t♦❢✉♥❞❛ t❡rr❡str❡ ♣♦r ❡❧ ✈✐❡♥t♦ s♦❧❛r q✉❡ ❝❛❧✐❡♥t❛ ❛❧ ♣❧❛s♠❛ ❞❡ ❧❛ ❢✉♥❞❛✱ ❡♥tr❡ ♦tr♦s✳ ❊♥ ❝✉❛♥t♦ ❛ ❧❛ t✉r❜✉❧❡♥❝✐❛ ❤✐❞r♦♠❛❣♥ét✐❝❛ ést❛ ❡s r❡❣✉❧❛r♠❡♥t❡ tr❛t❛❞❛ ❡♥ ❧❛ ❛♣r♦①✐♠❛❝✐ó♥ ❝✉❛s✐❧✐♥❡❛❧ ❬♣♦r ❡❥❡♠♣❧♦ ❙❝❤❧✐❝❦❡✐s❡r✱ ✶✾✽✾❪ ❞❡ ❧❛ ❝✉❛❧ s❡ ♦❜t✐❡♥❡ ❧❛ ❡❝✉❛❝✐ó♥ ❞❡ ❋♦❦❦❡r✲P❧❛♥❝❦ ❝♦♥ ✉♥ ❝♦❡✜❝✐❡♥t❡ ❞❡ ❞✐❢✉s✐ó♥ ❝✉②❛ ♠❛❣♥✐t✉❞ ② ❢♦r♠❛ ❞❡♣❡♥❞❡ ❞❡❧ ❡s♣❡❝tr♦ ❞❡ ♣♦t❡♥❝✐❛s ② ❞❡ ♦tr❛s ❝❛r❛❝t❡ríst✐❝❛s ❞❡ ❧❛ t✉r❜✉❧❡♥❝✐❛ ♠❛❣✲ ♥ét✐❝❛ ❡♥ ❡❧ ♣❧❛s♠❛✳ ●❡♥❡r❛❧♠❡♥t❡✱ ❧❛ ❡❝✉❛❝✐ó♥ r❡s✉❧t❛♥t❡ ❡s ❜❛st❛♥t❡ ❝♦♠♣❧✐❝❛❞❛ ② ♣❛r❛ r❡s♦❧✈❡r❧❛ s❡ r❡q✉✐❡r❡♥ ❞❡ ❛❧❣✉♥❛s s✐♠♣❧✐✜❝❛❝✐♦♥❡s ❬P❛r❦ ❛♥❞ P❡tr♦s✐❛♥✱ ✶✾✾✻❪✳ ❆ ❡st❡ t✐♣♦ ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ♠✉❝❤❛s ✈❡❝❡s s❡ ❧❡ ❧❧❛♠❛ ❛❝❡❧❡r❛❝✐ó♥ ❡st♦❝ást✐❝❛✳ ✶✳✶✳✺✳ ▼❡❝❛♥✐s♠♦s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❡♥ ♠❛❣♥❡tós✲ ❢❡r❛s ♣❧❛♥❡t❛r✐❛s ❯♥♦ ❞❡ ❧♦s ♣r✐♥❝✐♣❛❧❡s ♣r♦❜❧❡♠❛s ❡♥ ❧❛ ❞é❝❛❞❛ ❞❡ ❧♦s ❛ñ♦s s❡s❡♥t❛ ❢✉❡ ❡①♣❧✐❝❛r ❞❡ q✉é ♠❛♥❡r❛ ❧❛ ❡♥❡r❣í❛ ❞❡❧ ✈✐❡♥t♦ s♦❧❛r ♣♦❞í❛ s❡r tr❛♥s❢❡r✐❞❛ ❛❧ ✐♥t❡r✐♦r ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ t❡rr❡str❡✳ ❍♦② s❡ s❛❜❡ q✉❡ ❡s ❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ✐♥t❡r♣❧❛♥❡t❛r✐♦ ❡❧ q✉❡ ❞❡s❡♠♣❡ñ❛ ❡❧ ♣❛♣❡❧ ♠ás ✐♠♣♦rt❛♥t❡ ❡♥ ❞✐❝❤❛ tr❛♥s❢❡r❡♥❝✐❛✳ ❊♥ ♣❛rt✐❝✉❧❛r✱ ❉✉♥❣❡② ❬✶✾✺✵❪ ♣r♦♣✉s♦ ❡❧ s✐❣✉✐❡♥t❡ ♠❡❝❛♥✐s♠♦✿ ❙✐ ❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ✐♥t❡r♣❧❛♥❡t❛r✐♦ t✐❡♥❡ ✉♥❛ ❝♦♠♣♦♥❡♥t❡ ❞✐r✐❣✐❞❛ ❤❛❝✐❛ ❡❧ s✉r✱ ést❡ ♣✉❡❞❡ ❝♦♥❡❝t❛rs❡ ❝♦♥ ❧❛s ❧í♥❡❛s ❞❡ ❛❧t❛ ❧❛t✐t✉❞ ❞❡❧ ❝❛♠♣♦ ❞✐♣♦❧❛r ❞❡ ❧❛ ❚✐❡rr❛✱ ❛❧ ❢r❡♥t❡ ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛✳ ❯♥❛ ✈❡③ q✉❡ ❡st♦ s✉❝❡❞❡ ❧❛s ❧í♥❡❛s ❛sí ✉♥✐❞❛s s♦♥ ❛rr❛str❛❞❛s ♣♦r ❡❧ ✈✐❡♥t♦ s♦❧❛r ❤❛❝✐❛ ❧❛ ♣❛rt❡ ♣♦st❡r✐♦r✱ ❢♦r♠❛♥❞♦ ✉♥❛ ❡str✉❝t✉r❛ ❧❧❛♠❛❞❛ ❝♦❧❛ ♠❛❣♥ét✐❝❛✳ ❊st❛ ❡str✉❝t✉r❛ ❤❛ s✐❞♦ ❞❡t❡❝t❛❞❛ ✉t✐❧✐③❛♥❞♦ ❧♦s ✐♥str✉♠❡♥t♦s ❛ ❜♦r❞♦ ❞❡ ❧♦s s❛té❧✐t❡s ❛rt✐✜❝✐❛❧❡s✳ ❙♣❡✐s❡r ❬✶✾✻✺❪ ❛♠♣❧✐ó ❡st❡ ❝♦♥❝❡♣t♦ s✉❣✐r✐❡♥❞♦ q✉❡ ❧❛s ❧í♥❡❛s ❞❡ ❝❛♠♣♦ ❞❡ ❧❛ ❝♦❧❛ ♠❛❣♥❡t♦s❢ér✐❝❛ ♣✉❡❞❡♥ r❡❝♦♥❡❝t❛rs❡ ② r❡❣r❡s❛r ❞❡ ♥✉❡✈♦ ❛ ❧❛ ❝♦♥✜❣✉r❛❝✐ó♥ ❞❡ ❧í♥❡❛s ❞❡ ❝❛♠♣♦ ❞✐♣♦❧❛r ✐♥t❡r♥♦ q✉❡ ❡①✐stí❛ ❛♥t❡s ❞❡ ❧❛ ❝♦♥❡①✐ó♥✳ ❊st❛ ❛♥✐q✉✐❧❛❝✐ó♥ ♠❛❣✲ ♥ét✐❝❛ ♣r♦✈♦❝❛ q✉❡ ❡❧ ♣❧❛s♠❛ ✢✉②❛ ❤❛❝✐❛ ✉♥❛ ❤♦❥❛ ♥❡✉tr❛ ② ❛sí ❧❛ ❡♥❡r❣í❛ ♠❛❣♥ét✐❝❛ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✶✳✶✳ ▼❡❝❛♥✐s♠♦s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❣❡♥❡r❛❧❡s ✶✸ ❧✐❜❡r❛❞❛ s❡ ✈❛ ❡♥ ❝❛❧❡♥t❛r ♦ ❡♥ ❛❝❡❧❡r❛r ❛❧❣✉♥❛s ♣❛rtí❝✉❧❛s ♣r❡s❡♥t❡s ❡♥ ❡❧ ♣❧❛s♠❛ ♠❛❣♥❡t♦s❢ér✐❝♦ ❬❏❛r❞✐♥❡ ❛♥❞ ❆❧❧❡♥✱ ✶✾✾✻❪✳ ❙❡ ❤❛ s✉❣❡r✐❞♦ q✉❡ ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ❞❡ ♣❛r✲ tí❝✉❧❛s ❡♥ ❧❛s ❤♦❥❛s ❞❡ ❝♦rr✐❡♥t❡✱ ♦❝✉rr❡ ❞❡ ✉♥❛ ♠❛♥❡r❛ ❡①♣❧♦s✐✈❛ ❡♥ ❧❛ ♠❛❣♥❡t♦❝♦❧❛✱ ❝❛✉s❛♥❞♦ ♣❡rt✉r❜❛❝✐♦♥❡s ♠❛❣♥ét✐❝❛s ♣♦❧❛r❡s✱ ❝♦♥♦❝✐❞❛s t❛♠❜✐é♥ ❝♦♠♦ s✉❜t♦r♠❡♥t❛s ♣♦❧❛r❡s ② ❧❛ ❛♣❛r✐❝✐ó♥ ❞❡ ❛✉r♦r❛s ❬P❡r❦✐♥s✱ ✶✾✻✽❪✳ ▲❛ r❡❝♦♥❡①✐ó♥ ♠❛❣♥ét✐❝❛ t❛♠❜✐é♥ ❤❛ s✐❞♦ ♣r♦♣✉❡st❛ ♣❛r❛ ❡①♣❧✐❝❛r ❡❧ ♦r✐❣❡♥ ❞❡ ❧❛s ❡①♣❧♦s✐♦♥❡s ❞❡ ❡❧❡❝tr♦♥❡s ❞❡ ❛❧t❛s ❡♥❡r❣í❛s ✭∼ 600 keV✮ ❞❡s❝✉❜✐❡rt♦s ❡♥ ❧❛ ♠❛❣♥❡tós✲ ❢❡r❛ ❞❡ ▼❡r❝✉r✐♦ ❬❊r❛❦❡r ❛♥❞ ❙✐♠♣s♦♥✱ ✶✾✽✻❪✳ ❊st♦s ❛✉t♦r❡s ❡♥❝♦♥tr❛r♦♥ ❡✈✐❞❡♥❝✐❛ ❞❡ ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❞❡♥tr♦ ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ▼❡r❝✉r✐♦ ❞✉r❛♥t❡ ❧❛ r❡❝♦✲ ♥❡①✐ó♥ ♠❛❣♥ét✐❝❛ ♦❝✉rr✐❞❛ ❡♥ ❧❛ ♠❛❣♥❡t♦❝♦❧❛ ② s✉❣✐r✐❡r♦♥ q✉❡ ❤❛❜í❛ ✉♥❛ ❧✐❜❡r❛❝✐ó♥ rá♣✐❞❛ ❞❡ ❡♥❡r❣í❛ ♠❛❣♥ét✐❝❛ ❛ tr❛✈és ❞❡ ❧❛s ✐♥❡st❛❜✐❧✐❞❛❞❡s ❡♥ ❡❧ ♣❧❛s♠❛✳ ❆❞❡♠ás ❞❡ ❡st♦s ♠❡❝❛♥✐s♠♦s✱ s❡ ❤❛♥ ♣r♦♣✉❡st♦ ♦tr♦s ♣❛r❛ ❡①♣❧✐❝❛r ❧❛ ❡♥❡r❣✐③❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❡♥ ♠❛❣♥❡tós❢❡r❛s ♣❧❛♥❡t❛r✐❛s✱ ♣♦r ❡❥❡♠♣❧♦✱ ❧❛s ♣❛rtí❝✉❧❛s q✉❡ s❡ ♠✉❡✈❡♥ ❡♥ ❡s♣✐r❛❧ ❛ ❧♦ ❧❛r❣♦ ❞❡ ❧❛s ❧í♥❡❛s ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ s♦♥ ❛❝❡❧❡r❛❞❛s ❛ tr❛✈és ❞❡ ✐♥t❡r❛❝❝✐♦♥❡s r❡s♦♥❛♥t❡s ❝♦♥ ♦♥❞❛s ❞❡ ♣❧❛s♠❛ ❬❆❜❡ ❛♥❞ ◆✐s❤✐❞❛✱ ✶✾✽✻❀ ❇❛r❜♦s❛ ✶✾✽✻❪ ▲♦s ♠❡❝❛♥✐s♠♦s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ♣✉❡❞❡♥ s❡r ❞❡♣❡♥❞✐❡♥t❡s ❞❡ ❧❛ ♠❛s❛ ② ❞❡ ❧❛ ❡♥❡r❣í❛ ❞❡ ❧❛s ♣❛rtí❝✉❧❛s✳ ❊♥tr❡ ❡❧❧♦s s❡ ✐♥❝❧✉②❡♥ ❧❛ ❞✐❢✉s✐ó♥ r❛❞✐❛❧ ② ❞❡❧ á♥❣✉❧♦ ❞❡ ♣❛s♦✱ ✐♥t❡r❝❛♠❜✐♦ ❞❡ ❝❛r❣❛ ② ✈❛r✐♦s ♣r♦❝❡s♦s q✉❡ ✐♥✈♦❧✉❝r❛♥ ❧❛ r❡❝✐r❝✉❧❛❝✐ó♥ ❡s♣❛❝✐❛❧ ❞❡ ✐♦♥❡s✳ ▲❛ ❞✐❢✉s✐ó♥ s❡ r❡✜❡r❡ ❛ ❧❛ ❡①t❡♥s✐ó♥ ❞❡ ✉♥❛ ❞✐str✐❜✉❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❞❡ ♣❧❛s♠❛ t❛♥t♦ ❡♥ ❡❧ ❡s♣❛❝✐♦ ❞❡ ✈❡❧♦❝✐❞❛❞❡s ❝♦♠♦ ❡♥ ❡❧ ❞❡ ❝♦♥✜❣✉r❛❝✐ó♥ ❛ tr❛✈és ❞❡ ❧❛ ❛❝❝✐ó♥ ❞❡ ❝❛♠♣♦s q✉❡ ✢✉❝tú❛♥ ❛❧❡❛t♦r✐❛♠❡♥t❡✳ ❊❧ ✐♥t❡r❝❛♠❜✐♦ ❞❡ ❝❛r❣❛ s❡ r❡✜❡r❡ ❛ ✉♥ ♣r♦❝❡s♦ ❡♥ ❡❧ ❝✉❛❧ ✉♥❛ ♣❛rtí❝✉❧❛ ♥❡✉tr❛ q✉❡ s❡ ♠✉❡✈❡ ❛ ✉♥❛ ✈❡❧♦❝✐❞❛❞ vn ✐♥t❡r❝❛♠❜✐❛ ✉♥❛ ❝❛r❣❛ ❝♦♥ ✉♥ ✐ó♥ q✉❡ s❡ ♠✉❡✈❡ ❛ ❧❛ ✈❡❧♦❝✐❞❛❞ vi ✱ ❞❡ ❛❧❧í q✉❡ s❡ ♠♦❞✐✜❝❛ ❧❛ ❞✐str✐❜✉❝✐ó♥ ❞❡ ❡♥❡r❣í❛ ❡♥ ❡❧ ♣❧❛s♠❛ ② ♣r♦♣♦r❝✐♦♥❛ ✉♥❛ ❢✉❡♥t❡ ❞❡ ♥❡✉tr♦s q✉❡ s❡ ♠✉❡✈❡♥ ❛ ❧❛ ✈❡❧♦❝✐❞❛❞ ❞❡❧ ♣❧❛s♠❛ ❧♦❝❛❧✳ ❊st❡ ♣r♦❝❡s♦ ❡♥ ❧❛ ❚✐❡rr❛ s✐r✈❡ ❝♦♠♦ ✉♥ ♠❡❝❛♥✐s♠♦ ❞❡ ♣ér❞✐❞❛ ♣❛r❛ ❧♦s ✐♦♥❡s ❞❡❧ ❛♥✐❧❧♦ ❞❡ ❝♦rr✐❡♥t❡✳ ❊♥ ❏ú♣✐t❡r ❡st❡ ✐♥t❡r❝❛♠❜✐♦ ❞❡ ❝❛r❣❛ r❡s✉❧t❛ ❡♥ ✉♥ ♠❡❝❛♥✐s♠♦ ❞❡ tr❛♥s♣♦rt❡ ✐♠♣♦rt❛♥t❡✳ ❊♥ ❙❛t✉r♥♦ ❧♦s ♥❡✉tr♦s ❧✐❜❡r❛❞♦s ❞❡ ❧♦s ❛♥✐❧❧♦s ② ❞❡ ❧♦s s❛té❧✐t❡s t❛♠❜✐é♥ ♣❛rt✐❝✐♣❛♥ ❡♥ ❡st❡ ✐♥t❡r❝❛♠❜✐♦✳ ▲❛ r❡❝✐r❝✉❧❛❝✐ó♥ ❡s ✉♥ ♠❡❝❛♥✐s♠♦ ♣❛r❛ ❛❝❡❧❡r❛r ✐♦♥❡s ❤❛st❛ ❛❧❝❛♥③❛r ❛❧t❛s ❡♥❡r✲ ❣í❛s✳ ❯♥❛ ✐❞❡❛✱ q✉❡ t♦❞❛✈í❛ ♥♦ ❤❛ s✐❞♦ ❝♦♥✜r♠❛❞❛ ♣♦r ❧❛s ♦❜s❡r✈❛❝✐♦♥❡s✱ ❢✉❡ ♣r♦✲ ♣✉❡st❛ ♣♦r ◆✐s❤✐❞❛ ❬✶✾✼✻❪ q✉✐❡♥ ♦❜s❡r✈ó q✉❡ ❧♦s ✐♦♥❡s ❞❡❧ ✈✐❡♥t♦ s♦❧❛r ✭❝♦♥ ❡♥❡r❣í❛s ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✶✳✶✳ ▼❡❝❛♥✐s♠♦s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❣❡♥❡r❛❧❡s ✶✹ ❞❡ ❛❧❣✉♥♦s ❡❱✮ ♣♦❞rí❛♥ s❡r ❛❞✐❛❜át✐❝❛♠❡♥t❡ ❛❝❡❧❡r❛❞♦s ❤❛st❛ > 1 keV ♠❡❞✐❛♥t❡ ❧❛ ❞✐❢✉s✐ó♥ ❤❛❝✐❛ ❛❞❡♥tr♦ ❡♥ ❏ú♣✐t❡r ♣❡r♦ q✉❡ ❡st❛ ❛❝❡❧❡r❛❝✐ó♥ ❛❞✐❛❜át✐❝❛ ♣♦❞rí❛ ♥♦ ❡①♣❧✐❝❛r ❧❛ ♣r❡s❡♥❝✐❛ ❞❡ ✐♦♥❡s ❝♦♥ ❡♥❡r❣í❛s > 1 MeV ❡♥ ❡❧ r❡st♦ ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛✳ ❯♥ ♣r♦❝❡s♦ ❧✐❣❡r❛♠❡♥t❡ ❞✐st✐♥t♦ ❢✉❡ ❞✐s❝✉t✐❞♦ ♣♦r ❇❛r❜♦s❛ ❡t ❛❧✳ ❬✶✾✽✹❪ ♣❛r❛ ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ❞❡ ✐♦♥❡s ♣❡s❛❞♦s✳ ❊❧❧♦s s❡ ❛♣♦②❛r♦♥ ❡♥ q✉❡ ❡❧ ✐♥t❡r❝❛♠❜✐♦ ❞❡ ❝❛r❣❛ ❝❡r❝❛ ❞❡ ❧❛ ór❜✐t❛ ❞❡ ■♦ ♣r♦❞✉❝❡ ✐♦♥❡s ♣❡s❛❞♦s q✉❡ s♦♥ ❧❛♥③❛❞♦s ❡♥ tr❛②❡❝t♦r✐❛s ❜❛❧íst✐❝❛s✳ ❊st❛s ♣❛rtí❝✉❧❛s ♣✉❡❞❡♥ s✉❢r✐r ✉♥ s❡❣✉♥❞♦ ✐♥t❡r❝❛♠❜✐♦ ❞❡ ❝❛r❣❛ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ ❞❡ ❏ú♣✐t❡r✱ ❞♦♥❞❡ ❧❛ ✈❡❧♦❝✐❞❛❞ ❞❡❧ ✢✉❥♦ ❛③✐♠✉t❛❧ ❡♥❡r❣✐③❛rí❛ ❛ ❧♦s ✐♦♥❡s ❤❛st❛ ❛❧❝❛♥③❛r ❝✐❡♥t♦s ❞❡ ❦❡❱✱ ✜♥❛❧♠❡♥t❡ ❧❛ ❞✐❢✉s✐ó♥ ❛❞✐❛❜át✐❝❛ ❤❛❝✐❛ ❛❞❡♥tr♦ ❧♦s ♣♦❞rí❛ ❛❝❡❧❡r❛r ❛ ❡♥❡r❣í❛s ❞❡ ✈❛r✐♦s ▼❡❱✳ ❇❛r❜♦s❛ ❬✶✾✾✹❪ ❞❡s❛rr♦❧❧ó ✉♥ ♠♦❞❡❧♦ ❡♥ ❡❧ ❝✉❛❧ ❝♦♠❜✐♥ó ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ❡st♦❝ást✐❝❛ ② ❧❛ ❞✐❢✉s✐ó♥ r❛❞✐❛❧ ❡♥ ✉♥❛ ❡❝✉❛❝✐ó♥ ♣❛r❛ ✐♦♥❡s ❡♥❡r❣ét✐❝♦s q✉❡ ✐♥t❡r❛❝tú❛♥ ❝♦♥ ♦♥❞❛s ▼❍❉ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ ❞❡ ❏ú♣✐t❡r✳ ❙✉s r❡s✉❧t❛❞♦s ♣r♦♣♦r❝✐♦♥❛r♦♥ ✉♥❛ ❡①♣❧✐❝❛❝✐ó♥ ❝✉❛♥t✐t❛t✐✈❛ ❞❡ ❧❛ ❝♦♠♣♦♥❡♥t❡ ✐ó♥✐❝❛ ❞❡ ❛❧t❛ ❡♥❡r❣í❛ ♦❜s❡r✈❛❞❛ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❏ú♣✐t❡r✳ ❙✉♠♠❡rs ② ❈❤✉♥✲②✉ ❬✷✵✵✵❪ ❤❛♥ ❡①❛♠✐♥❛❞♦ ❡❧ ♠❡❝❛♥✐s♠♦ ❞❡ ❛❝❡❧❡r❛❝✐ó♥ tr❛♥s✐t♦✲ r✐♦ ❞❡ ❡❧❡❝tr♦♥❡s ♠❡❞✐❛♥t❡ ♦♥❞❛s ♠❛❣♥❡t♦❤✐❞r♦❞✐♥á♠✐❝❛s rá♣✐❞❛s ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛ ❞❡ ❧❛ ❚✐❡rr❛✳ ❙✉s ❝á❧❝✉❧♦s ♠♦str❛r♦♥ q✉❡ ❧❛s ♦♥❞❛s rá♣✐❞❛s ❝✉②❛s ❢r❡❝✉❡♥❝✐❛s s❡ ❡♥❝✉❡♥tr❛♥ ❡♥ ❧♦s r❛♥❣♦s ❞❡ 7 − 22 MHz ❛ 2 − 7 MHz ② ❝♦♥ ❝❛♠♣♦s ♠❛❣♥ét✐❝♦s ♦❜s❡r✈❛❞♦s ❞❡ 10 − 20 nT ♣✉❡❞❡♥ ❛❝❡❧❡r❛r ❛ ❧♦s ❡❧❡❝tr♦♥❡s ❤❛st❛ ❛❧❝❛♥③❛r ❡♥❡r❣í❛s ❞❡❧ ♦r❞❡♥ ❞❡ ▼❡❱ ❡♥ ♣♦❝❛s ❤♦r❛s✳ ❖tr♦s ♠❡❝❛♥✐s♠♦s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ✐♥❝❧✉②❡♥ ❧❛ ✐♥t❡r❛❝❝✐ó♥ ❞❡ ♦♥❞❛s ❞❡ ❆❧❢✈é♥ ❝♦♥ ✉♥❛ ✐♥❤♦♠♦❣❡♥❡✐❞❛❞ ❞❡❧ ♣❧❛s♠❛ ❡♥ ✉♥❛ ❞✐r❡❝❝✐ó♥ tr❛♥s✈❡rs❛❧ ❛❧ ❝❛♠♣♦ ♠❛❣♥❡t♦s✲ tát✐❝♦ ❬▼♦tt❡③ ❡t ❛❧✳✱ ✷✵✵✹❪✳ ❊♥ ❡s❡ ❡st✉❞✐♦ ❧♦s ❛✉t♦r❡s ♠♦str❛r♦♥ q✉❡ ❧❛s ♦♥❞❛s ❞❡ ❆❧❢✈é♥ s❡ ♣r♦♣❛❣❛♥ s♦❜r❡ ❣r❛❞✐❡♥t❡s ❞❡ ❞❡♥s✐❞❛❞ ♠✉② ♠❛r❝❛❞♦s✱ ② ❣r❛❝✐❛s ❛ ❧♦s ❡❢❡❝t♦s ✐♥❡r❝✐❛❧❡s✱ ❝♦♥❞✉❝❡♥ ❛ ❧❛ ❢♦r♠❛❝✐ó♥ ❞❡ ✉♥ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ♣❛r❛❧❡❧♦ ❛❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦✳ ❊st❡ ❝❛♠♣♦ ♣❛r❛❧❡❧♦ ❡s ❝❛♣❛③ ❞❡ ❛❝❡❧❡r❛r ❡❧❡❝tr♦♥❡s ❛ ❡♥❡r❣í❛s ♣♦r ❛rr✐❜❛ ❞❡ ❦❡❱ ❡♥ ✉♥❛ ❞✐st❛♥❝✐❛ ❞❡ ❛❧❣✉♥♦s ❝✐❡♥t♦s ❞❡ ❧♦♥❣✐t✉❞❡s ❞❡ ❉❡❜②❡✱ ② q✉❡ ❛❞❡♠ás ✐♥❞✉❝❡ ❧❛ ❢♦r♠❛❝✐ó♥ ❞❡ ❤❛❝❡s ❞❡ ❡❧❡❝tr♦♥❡s✳ ▲♦s ✐♥❝r❡♠❡♥t♦s s✐❣♥✐✜❝❛t✐✈♦s ❡ ✐♥t❡r♠✐t❡♥t❡s ❞❡ ✢✉❥♦s ❞❡ ❡❧❡❝tr♦♥❡s r❡❧❛t✐✈✐st❛s ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ t❡rr❡str❡ ♣r♦❞✉❝❡♥ ✉♥❛ ❣r❛♥ ✈❛r✐❡❞❛❞ ❞❡ ❢❡♥ó♠❡♥♦s q✉❡ ❛❢❡❝t❛♥✱ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✶✳✶✳ ▼❡❝❛♥✐s♠♦s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❣❡♥❡r❛❧❡s ✶✺ ♣♦r ❡❥❡♠♣❧♦✱ ❛ ❧❛s ❝♦♠✉♥✐❝❛❝✐♦♥❡s✳ ❉✉r❛♥t❡ ✉♥❛ t♦r♠❡♥t❛ ❣❡♦♠❛❣♥ét✐❝❛✱ ❧♦s ✢✉❥♦s ❞❡ ❡❧❡❝tr♦♥❡s s❡ ✐♥❝r❡♠❡♥t❛♥ ♣♦r ✈❛r✐♦s ór❞❡♥❡s ❞❡ ♠❛❣♥✐t✉❞ ② ♥♦ ❡s ❝❧❛r♦ ❝ó♠♦ s❡ r❡❛❧✐③❛ ❧❛ ❛❝❡❧❡r❛❝✐ó♥✳ ❊❧ ❛rr❛str❡ ❡♥ ❧❛ ❞✐r❡❝❝✐ó♥ ❛♠❛♥❡❝❡r✴❛t❛r❞❡❝❡r ✲♣❛r❛❧❡❧♦ ♦ ❛♥t✐♣❛r❛❧❡❧♦ ❛❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ♠❛❣♥❡t♦s❢ér✐❝♦✲ ♣✉❡❞❡ ❛❝❡❧❡r❛r ♣❛rtí❝✉❧❛s✳ ❊st❛ ❛❝❡❧❡r❛❝✐ó♥ ❧❧❡✈❛ ❛ ❡♥❡r❣í❛s ❞❡❧ ♦r❞❡♥ ❞❡ 100 keV✳ ❙✐♥ ❡♠❜❛r❣♦✱ ❡s ♥❡❝❡s❛r✐♦ q✉❡ ♦tr♦ ♠❡❝❛♥✐s♠♦ ❛❝tú❡ ♣❛r❛ q✉❡ ❧♦s ❡❧❡❝tr♦♥❡s ❛❧❝❛♥❝❡♥ ❧❛s ❡♥❡r❣í❛s ♠❡❞✐❞❛s ❞❡s♣✉és ❞❡ ✉♥❛ t♦r♠❡♥t❛ ❣❡♦♠❛❣♥ét✐❝❛✳ ❙❡ ❤❛♥ ♣r♦♣✉❡st♦ ❞✐✈❡rs♦s ♠❡❝❛♥✐s♠♦s q✉❡ s❡ ❝❧❛s✐✜❝❛♥ ❡♥ ❞♦s ❝❧❛s❡s ❬❑✐✈❡❧s♦♥✱ ✷✵✵✺❪✿ ❛✮ ❧❛s q✉❡ ❞❡s❝r✐❜❡♥ ❝ó♠♦ ✉♥❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ♣✉❡❞❡ s❡r ❝♦♥❞✉❝✐❞❛ ❤❛❝✐❛ ❡❧ ✐♥t❡r✐♦r ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ② ❧✉❡❣♦ ❛❝❡❧❡r❛❞❛ ♣♦r ❧❛ ❞✐❢✉s✐ó♥ ❤❛❝✐❛ ❛❞❡♥tr♦ ❛ tr❛✈és ❞❡ ✢✉❝t✉❛❝✐♦♥❡s ❞❡ ❝❛♠♣♦s ❡❧é❝tr✐❝♦s ♦ ♠❛❣♥ét✐❝♦s ❞❡ ❢r❡❝✉❡♥❝✐❛ ✉❧tr❛❜❛❥❛ ✭❯▲❋✱ ♠❡♥♦r q✉❡ ❧❛ ❣✐r♦❢r❡❝✉❡♥❝✐❛ ❞❡ ❧♦s ✐♦♥❡s✮❀ ❜✮ ❧❛s q✉❡ ❞❡s❝r✐❜❡♥ ♠❛♥❡r❛s ❡♥ ❧❛s ❝✉❛❧❡s ✉♥❛ ♣♦❜❧❛❝✐ó♥ ♣r❡❡①✐st❡♥t❡ ♣✉❡❞❡ s❡r ❛❝❡❧❡r❛❞❛ s✐t✉ ✐♥ ♣♦r ♦♥❞❛s ❞❡ ♠✉② ❜❛❥❛ ❢r❡❝✉❡♥❝✐❛ ✭❱▲❋✱ ♠❛②♦r q✉❡ ❧❛ ❣✐r♦❢r❡❝✉❡♥❝✐❛ ❞❡ ❧♦s ✐♦♥❡s✮✳ ✶✳✶✳✺✳✶✳ P♦s✐❜❧❡s ♠❡❝❛♥✐s♠♦s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❛♣❧✐❝❛❞♦s ❛ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦ ❙❛t✉r♥♦ ❡s ✉♥ ♣❧❛♥❡t❛ q✉❡ ❞✐♥á♠✐❝❛♠❡♥t❡ s❡ ♣❛r❡❝❡ ❛ ❏ú♣✐t❡r ② ❧❛ ❚✐❡rr❛✳ ❈♦♠♦ ❏ú♣✐t❡r✱ ❡stá ❞♦♠✐♥❛❞♦ ♣♦r ❧❛ r♦t❛❝✐ó♥✱ ❛sí q✉❡ ❡s r❛③♦♥❛❜❧❡ ❜✉s❝❛r ❡✈✐❞❡♥❝✐❛ ❞❡ ✐♥✲ t❡r❝❛♠❜✐♦ ❝♦♠♦ ✉♥ ♠❡❝❛♥✐s♠♦ ❞❡ tr❛♥s♣♦rt❡✳ ▲❛ ❞❡♥s✐❞❛❞ ❞❡❧ ♣❧❛s♠❛ ❡♥ ❙❛t✉r♥♦ ❡s ❣❡♥❡r❛❧♠❡♥t❡ ♠❡♥♦r q✉❡ ❧❛ ❞❡ ❏ú♣✐t❡r✱ ❡s♣❡❝✐❛❧♠❡♥t❡ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛✱ ❧♦ ❝✉❛❧ ✐♠♣❧✐❝❛ q✉❡ ❧❛s t❡♥s✐♦♥❡s ✐♥❡r❝✐❛❧❡s ✉♥✐❞❛s ❛ ❧❛ r♦t❛❝✐ó♥ s♦♥ ♠❡♥♦s s✐❣♥✐✜❝❛t✐✈❛s✳ ❊❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❞❡❧ ❧❛❞♦ ❞í❛✱ ♣♦r ❡❥❡♠♣❧♦✱ ❡stá ❧✐❣❡r❛♠❡♥t❡ ❞✐st♦rs✐♦♥❛❞♦ ♣♦r ❧❛ r♦t❛❝✐ó♥✳ ❉❡ ♣❛rt✐❝✉❧❛r ✐♠♣♦rt❛♥❝✐❛ ❡s ❧❛ ✈❛r✐❡❞❛❞ ❞❡ ❢✉❡♥t❡s ❞❡ ♣❛rtí❝✉❧❛s ② ❧❛ ♣r❡s❡♥❝✐❛ ❞❡ ❧♦s ❛♥✐❧❧♦s ❝♦♥t❡♥✐❡♥❞♦ ♠❛t❡r✐❛ só❧✐❞❛ q✉❡ s✐r✈❡ ❝♦♠♦ ❢✉❡♥t❡ ② s✉♠✐❞❡r♦ ❞❡ ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s✳ P♦s✐❜❧❡s ❡①♣❧✐❝❛❝✐♦♥❡s ❞❡ ❧❛ ♣♦❜❧❛❝✐ó♥ ♦❜s❡r✈❛❞❛ ❞❡ ♣❛rtí❝✉❧❛s ❡♥❡r❣ét✐❝❛s ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦ ✐♠♣❧✐❝❛♥ ❧❛ ❧✐❜❡r❛❝✐ó♥ ❞❡ ❧❛ ❡♥❡r❣í❛ ♠❛❣♥ét✐❝❛ q✉❡ ❝❛❧✐❡♥t❛ ❧❛ ❝♦♠♣♦♥❡♥t❡ ✐ó♥✐❝❛ ❞❡❧ ♣❧❛s♠❛ ② ❞❡s♣✉és ❛❝❡❧❡r❛ ❛ ❧♦s ❡❧❡❝tr♦♥❡s ❤❛st❛ ❛❧❝❛♥③❛r ❡♥❡r❣í❛s ❞❡❧ ♦r❞❡♥ ❞❡ 2 MeV ❬❙❝❤❛r❞t ❡t ❛❧✳✱ ✶✾✽✺❪✳ ❖tr❛ ♣♦s✐❜✐❧✐❞❛❞ ❡s ❧❛ ♠❛❣♥❡t♦✲ ❝♦❧❛ ❞❡ ❙❛t✉r♥♦✳ ❊♥ ❡st❛ r❡❣✐ó♥✱ ❝♦♠♦ ❡♥ ❧❛ ❚✐❡rr❛ ② ❡♥ ❏ú♣✐t❡r✱ ❧♦s ❝❛♠❜✐♦s ❡♥ ❧❛ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✶✳✶✳ ▼❡❝❛♥✐s♠♦s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❣❡♥❡r❛❧❡s ✶✻ ❝♦♥✜❣✉r❛❝✐ó♥ ❞❡ ❧❛ ❝♦❧❛ ✐♥❞✉❝✐❞❛ ♣♦r ♣❡rt✉r❜❛❝✐♦♥❡s ✐♥t❡r♣❧❛♥❡t❛r✐❛s ♣✉❡❞❡♥ ❝♦♥❞✉✲ ❝✐r ❛ ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ❞❡ ✐♦♥❡s ② ❞❡ ❡❧❡❝tr♦♥❡s ❛ ✈❛r✐♦s ❝✐❡♥t♦s ❞❡ ❦❡❱ ❬❑r✐♠✐❣✐s ❡t ❛❧✳✱ ✶✾✽✶❀ ✶✾✽✷❪✳ ❉❡❜✐❞♦ ❛ q✉❡ ❙❛t✉r♥♦ ❡s ♠✉② ♣❛r❡❝✐❞♦ ❛ ❧❛ ❚✐❡rr❛✱ ❧❛s r❡s♣✉❡st❛s ❛ ❧♦s ❢❡♥ó♠❡♥♦s ❝♦♥❞✉❝✐❞♦s ♣♦r ❡❧ ✈✐❡♥t♦ s♦❧❛r ♣r♦❜❛❜❧❡♠❡♥t❡ s❡❛♥ s❡♠❡❥❛♥t❡s ❡♥tr❡ sí✳ ◆♦ ❡s ❝❧❛r♦ q✉❡ ❧❛ r❡❝♦♥❡①✐ó♥ ❡♥ ❡❧ ❧❛❞♦ ❞í❛ ❧❧❡✈❡ ❛ ❧❛ ❢♦r♠❛❝✐ó♥ ❞❡ s✉❜t♦r♠❡♥t❛s✱ ♣❡r♦ ❤❛② ✐♥❞✐✲ ❝✐♦s ❞❡ q✉❡ ❡s ✈❡r❞❛❞✳ ❍❛② ❛❧❣✉♥♦s r❡♣♦rt❡s s♦❜r❡ ❝❛r❛❝t❡ríst✐❝❛s ❛✉r♦r❛❧❡s ❡♥ ❏ú♣✐t❡r ❬●❧❛❞st♦♥❡ ❡t ❛❧✳✱ ✷✵✵✷❪✱ ❞❡ ✜r♠❛s ❞❡ r❡❝♦♥❡①✐ó♥ ❛ ♣❡q✉❡ñ❛ ❡s❝❛❧❛ ❡♥ ❏ú♣✐t❡r ❬●r♦✲ ❞❡♥t✱ ✷✵✵✹❀ ●r♦❞❡♥t ❡t ❛❧✳✱ ✷✵✵✹❪ ② ❞❡ ❧❛ ✈❛r✐❛❜✐❧✐❞❛❞ ❛✉r♦r❛❧ ❡♥ ❙❛t✉r♥♦ ❬●r♦❞❡♥t✱ ✷✵✵✹❪✳ ❆❧❣✉♥❛s ❞❡ ❡st❛s ❝❛r❛❝t❡ríst✐❝❛s ❞❡ ❧❛ ✈❛r✐❛❜✐❧✐❞❛❞ ♣♦❞rí❛♥ ❡st❛r r❡❧❛❝✐♦♥❛❞❛s ❝♦♥ ❧❛ r❡❝♦♥❡①✐ó♥ ❞❡ t✉❜♦s ❞❡ ✢✉❥♦✳ ❙✐ ❧❛s s✉❜t♦r♠❡♥t❛s s♦♥ s✐❣♥✐✜❝❛t✐✈❛s✱ ❧♦s ✐♥✲ t❡r✈❛❧♦s ❞❡ t♦r♠❡♥t❛s ♣♦❞rí❛♥ ❡st❛r t❛♠❜✐é♥ ❝♦♥tr♦❧❛❞♦s ♣♦r ❧❛ ✐♥✉s✉❛❧ r❡❝♦♥❡①✐ó♥ ❡♥ ❡❧ ❧❛❞♦ ❞í❛✳ ❆❞❡♠ás s❡rí❛ ♣♦s✐❜❧❡ ♣❡♥s❛r ❡♥ q✉❡ ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ❡stá ❝❛✉s❛❞❛ ♣♦r ♦♥❞❛s ❞❡ ♠✉② ❜❛❥❛ ❢r❡❝✉❡♥❝✐❛ ✭❱▲❋✮ ❝♦♠♦ ♣❛r❡❝❡ s❡r ❡♥ ❡❧ ❝❛s♦ t❡rr❡str❡✳ ❆ ❞✐❢❡r❡♥❝✐❛ ❞❡ ❧♦s ♠❡❝❛♥✐s♠♦s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❡st♦❝ást✐❝❛ tr❛❞✐❝✐♦♥❛❧❡s ✭✈❡r ❙❡❝✲ ❝✐ó♥ ✶✳✶✳✷✮✱ ❡♥ ❡st❡ tr❛❜❛❥♦ s❡ ♣r♦♣♦♥❡ q✉❡ ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ♣r♦❞✉❝✐❞❛ ♣♦r ✉♥ ❝❛♠♣♦ ❞❡ ❢✉❡r③❛s ❡st♦❝ást✐❝♦ ❬❉✉r❛♥❞✲▼❛♥t❡r♦❧❛✱ ✷✵✵✸❪ ❡s ❝❛♣❛③ ❞❡ ❡♥❡r❣✐③❛r ❛ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛ ❬▼❛rtí♥❡③✲●ó♠❡③ ❡t ❛❧✳✱ ✷✵✵✻❪ ② ❡①t❡r♥❛ ❞❡ ❙❛t✉r♥♦ ❡♥ ✉♥♦s ❝✉❛♥t♦s s❡❣✉♥❞♦s✳ P❛r❛ ❡①♣❧✐❝❛r ❧❛ ❞✐♥á♠✐❝❛ ❞❡ ❧♦s ❣r❛♥♦s ❞❡ ♣♦❧✈♦ ♥❡✉tr♦ ❡♥ ❧♦s ❛♥✐❧❧♦s ❞❡ ❙❛t✉r♥♦✱ s❡ ♣r♦♣♦♥❡ q✉❡ ❧❛ ❢✉❡r③❛ ❣r❛✈✐t❛❝✐♦♥❛❧ ❡st♦❝ást✐❝❛ ❡♥tr❡ ❣r❛♥♦s ❞❡ ♣♦❧✈♦ ❡s ✉♥❛ ❞❡ ❧❛s r❡s♣♦♥s❛❜❧❡s✳ ❊st❡ ♠❡❝❛♥✐s♠♦ ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❡st♦❝ást✐❝❛ ❡s ✉♥❛ ♠❛♥❡r❛ ❛❧t❡r♥❛t✐✈❛ ❞❡ ❡st✉❞✐❛r ❡❧ ♣r♦❜❧❡♠❛ ❞❡ ❡♥❡r❣✐③❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ✭❝❛r❣❛❞❛s ② ♥❡✉tr❛s✮ ❡♥ ❝✉❛❧q✉✐❡r ❛♠❜✐❡♥✲ t❡ ❛str♦❢ís✐❝♦✳ ▲❛s ♣❛rt✐❝✉❧❛r✐❞❛❞❡s ❡stá♥ ❡♥ ❧❛s ✢✉❝t✉❛❝✐♦♥❡s ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ♠❡❞✐❞❛s ❡♥ ❧❛ r❡❣✐ó♥ ❞❡ ✐♥t❡rés ② ❡♥ ❧❛s ❝❛r❛❝t❡ríst✐❝❛s ❞❡ ❧❛s ❢✉❡♥t❡s ❞❡ ♣❛rtí❝✉❧❛s✳ ❊s ✐♠♣♦rt❛♥t❡ ❞❡st❛❝❛r q✉❡ ❧❛ ❡❝✉❛❝✐ó♥ ❢✉♥❞❛♠❡♥t❛❧ ❡♥ ❧❛ q✉❡ s❡ ❜❛s❛ ❡❧ ♠♦❞❡❧♦ ❡s ❧❛ ❡❝✉❛❝✐ó♥ ❞❡ ♠♦✈✐♠✐❡♥t♦ ♣❛r❛ ✉♥❛ ♣❛rtí❝✉❧❛✱ ♣♦r ❧♦ q✉❡ ♥♦ ❡s ♥❡❝❡s❛r✐♦ ♣❧❛♥t❡❛r ② r❡s♦❧✈❡r ❧❛s ❡❝✉❛❝✐♦♥❡s ♠❛❣♥❡t♦❤✐❞r♦❞✐♥á♠✐❝❛s ❛s♦❝✐❛❞❛s ❛❧ s✐st❡♠❛ ❡♥ ❡st✉❞✐♦✳ ❊♥ ❡st❡ ❝❛♣ít✉❧♦ s❡ r❡✈✐s❛r♦♥ ❧♦s ♠❡❝❛♥✐s♠♦s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ♠ás ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✶✳✶✳ ▼❡❝❛♥✐s♠♦s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❣❡♥❡r❛❧❡s ✶✼ ❝♦♠✉♥❡s ❡♥ ❆str♦❢ís✐❝❛✱ ❡♥tr❡ ❡❧❧♦s ❞❡st❛❝❛♥ ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ❡st♦❝ást✐❝❛✱ ❧❛ ❛❝❡❧❡r❛✲ ❝✐ó♥ ♣♦r ♦♥❞❛s✱ ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ♣♦r ❝❤♦q✉❡s✱ ❡♥tr❡ ♦tr♦s✳ ❆❞❡♠ás s❡ ❞❡s❝r✐❜✐❡r♦♥ ❧❛s ❢✉❡♥t❡s ♠ás ✐♠♣♦rt❛♥t❡s q✉❡ ❝♦♥tr✐❜✉②❡♥ ❛ ❧❛ ♣♦❜❧❛❝✐ó♥ ♦❜s❡r✈❛❞❛ ❞❡ ♣❛rtí❝✉❧❛s ❡♥ ✉♥❛ ♠❛❣♥❡tós❢❡r❛ ♣❧❛♥❡t❛r✐❛✳ ❋✐♥❛❧♠❡♥t❡ s❡ ❡①♣❧✐❝❛r♦♥ ❧♦s ♣♦s✐❜❧❡s ♠❡❝❛♥✐s♠♦s ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s q✉❡ ❛❝tú❛♥ ❡♥ ❡❧ ❝❛s♦ ♣❛rt✐❝✉❧❛r ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛✲ t✉r♥♦✳ ❊❧ s✐❣✉✐❡♥t❡ ❝❛♣ít✉❧♦ tr❛t❛rá s♦❜r❡ ❧❛s ♦❜s❡r✈❛❝✐♦♥❡s r❡❛❧✐③❛❞❛s✱ ♣♦r ❧❛s ♥❛✈❡s ❱♦②❛❣❡r ② ❈❛ss✐♥✐✱ ❞❡ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❡♥❡r❣ét✐❝❛s ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❈❛♣ít✉❧♦ ✷ P♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ② ♥❡✉tr❛s ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦ ▲❛s ♣r✐♠❡r❛s ♦❜s❡r✈❛❝✐♦♥❡s ✐♥ s✐t✉ ❞❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ② ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦ ❢✉❡r♦♥ ♦❜t❡♥✐❞❛s ♣♦r ❧❛ ♥❛✈❡ P✐♦♥❡❡r ✶✶ ❡♥ ❙❡♣t✐❡♠❜r❡ ❞❡ ✶✾✼✾✳ ▲❛s ✐♥✈❡st✐❣❛❝✐♦♥❡s r❡✈❡❧❛r♦♥ q✉❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡s s✐♠✐❧❛r ❛ ❧❛ t❡rr❡str❡ ② ❛ ❧❛ ❏♦✈✐❛♥❛✱ ♣❡r♦ q✉❡ t✐❡♥❡ ❢ís✐❝❛♠❡♥t❡ ❞✐❢❡r❡♥❝✐❛s ♥♦t❛❜❧❡s q✉❡ ✈❛♥ ❞❡s❞❡ ❧❛ s✐♠❡trí❛ ✐♥✉s✉❛❧ ❞❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❞❡ ❙❛t✉r♥♦ ❤❛st❛ ❧❛s ❢✉❡♥t❡s ② s✉♠✐❞❡r♦s ❞❡ ♣❧❛s♠❛ ② ❞❡ ♣❛rtí✲ ❝✉❧❛s ❡♥❡r❣ét✐❝❛s ♣❛r❛ ❧❛ ❣❡♥❡r❛❝✐ó♥ ❞❡ ♦♥❞❛s ❞❡ r❛❞✐♦ ❦✐❧♦♠étr✐❝❛s ✭❙❑❘✱ ❙❛t✉r♥ ❑✐❧♦♠❡tr✐❝ ❘❛❞✐❛t✐♦♥ ✮✳ ❆❝✉ñ❛ ❡t ❛❧✳ ❬✶✾✽✵❪ ❛♣r♦①✐♠❛r♦♥ ❡st❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ✐♥✲ t❡r♥♦ ♣♦r ✉♥ ❞✐♣♦❧♦ ❞❡ ♠♦♠❡♥t♦ ✵✳✷ ●❛✉ss R3S ✭✶ RS ❂ ✻✳✵✷✻✽x109 ❝♠✮ q✉❡ ❡stá ❝♦♥✜♥❛❞♦ ② ❞✐st♦rs✐♦♥❛❞♦ ♣♦r ❧❛ ♣r❡s✐ó♥ ❞✐♥á♠✐❝❛ ❞❡❧ ✈✐❡♥t♦ s♦❧❛r✱ ❧♦ q✉❡ ❣❡♥❡r❛ ✉♥❛ ♠❛❣♥❡t♦❝♦❧❛ ❡①t❡♥s❛✳ ❆❞❡♠ás s❡ ♦❜s❡r✈❛r♦♥ tr❡s ✜r♠❛s✶ ❞❡ ❧❛ ♣r❡s❡♥❝✐❛ ❞❡ ✉♥ ❢r❡♥t❡ ❞❡ ❝❤♦q✉❡ ❛ tr❛✈és ❞❡❧ ✐♥str✉♠❡♥t♦ ❞❡ ♣❧❛s♠❛ ② ❞❡❧ ♠❛❣♥❡tó♠❡tr♦ ❝❡r❝❛ ❞❡❧ ♠❡r✐❞✐❛♥♦ ❞í❛ ❞❡❧ ♣❧❛♥❡t❛ ❛ ✉♥❛ ❞✐st❛♥❝✐❛ ❞❡ ✷✹ RS ✱ ✷✸ RS ② ✶✾✳✾ RS ✳ ▲❛ ♣r✐♠❡r❛ ❞❡ ❡st❛s ✜r♠❛s ❢✉❡ ✶ ▲❛s ✑✜r♠❛s✑ ✭♦ ❤✉❡❧❧❛s✮ ❡♥ ❡st❡ ❝♦♥t❡①t♦ s❡ r❡✜❡r❡♥ ❛ ❧♦s ❡❢❡❝t♦s ♣r♦❞✉❝✐❞♦s✱ ♣♦r ❛❧❣ú♥ ❢❡♥ó♠❡♥♦ ❢ís✐❝♦✱ s♦❜r❡ ❧❛s ♣r♦♣✐❡❞❛❞❡s q✉❡ ❞❡s❝r✐❜❡♥ ❛❧ s✐st❡♠❛ ❡♥ ❡st✉❞✐♦✳ ❊st❛s ✜r♠❛s ♣✉❡❞❡♥ ✈❡rs❡ r❡✢❡❥❛❞❛s ❝♦♠♦ ✉♥ ✐♥❝r❡♠❡♥t♦ ♦ ❞❡❝r❡♠❡♥t♦ ❡♥ ❧❛ t❡♠♣❡r❛t✉r❛ ✭♦ ❞❡♥s✐❞❛❞✮ ❞❡❧ ♣❧❛s♠❛✱ ❡♥ ❧❛ ✐♥✈❡rs✐ó♥ ❞❡ ♣♦❧❛r✐❞❛❞ ❞❡ ❛❧❣ú♥ ❝♦♠♣♦♥❡♥t❡ ❞❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦✱ ❡♥tr❡ ♦tr♦s✳ ✶✽ ✷✳✶✳ ❆♥t❡❝❡❞❡♥t❡s✿ ❘❡s✉❧t❛❞♦s ❞❡ ❧❛ ♠✐s✐ó♥ ❱♦②❛❣❡r ✶✾ t❛♠❜✐é♥ ✐❞❡♥t✐✜❝❛❞❛ ❝♦♠♦ ✉♥❛ ♣❡q✉❡ñ❛ ❡①♣❧♦s✐ó♥ ❞❡ ❡❧❡❝tr♦♥❡s ❝♦♥ ❡♥❡r❣í❛s >✵✳✵✹ ▼❡❱✳ ▲❛ ♠❛❣♥❡t♦♣❛✉s❛ ❢✉❡ ♦❜s❡r✈❛❞❛ ♣♦r ❧♦s ♠✐s♠♦s ✐♥str✉♠❡♥t♦s ❡♥ ✶✼✳✷ RS ② ❢✉❡ ❝♦♥✜r♠❛❞❛ ❝♦♠♦ ❧❛ ❢r♦♥t❡r❛ ❡❢❡❝t✐✈❛ ♣❛r❛ ❛tr❛♣❛r ♣❛rtí❝✉❧❛s ❡♥❡r❣ét✐❝❛s ❡①t❡r♥❛s✳ ❊❧ P✐♦♥❡❡r ✶✶ t❛♠❜✐é♥ ♣r♦♣♦r❝✐♦♥ó ✐♥❢♦r♠❛❝✐ó♥ s♦❜r❡ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ✐♦♥❡s ❡♥❡r✲ ❣ét✐❝♦s ❡♥ ❡❧ ✐♥t❡r✈❛❧♦ ❞❡ ✶✵✵ ❡❱ ❤❛st❛ ✽ ❦❡❱ ❛ ❞✐st❛♥❝✐❛s ❞❡ ✹ RS ❛ ✶✻ RS ✱ ♠❡❞✐❞❛s ❞❡s❞❡ ❙❛t✉r♥♦✱ ② ❛ ✉♥❛ ❞✐st❛♥❝✐❛ ❞❡ ✶ RS ❞❡❧ ♣❧❛♥♦ ❡❝✉❛t♦r✐❛❧ ❬❋r❛♥❦ ❡t ❛❧✳✱ ✶✾✽✵❪✳ ❊s✲ t♦s ❞❛t♦s ✐♥❞✐❝❛r♦♥ ❧❛ ♣r❡s❡♥❝✐❛ ❞❡ ✉♥❛ ♠❛❣♥❡tós❢❡r❛ ❞❡♥s❛ ✭> 1 cm−3 ✮ ② q✉❡ ❝♦rr♦t❛ rí❣✐❞❛♠❡♥t❡ ❛ ✉♥❛ ❞✐st❛♥❝✐❛ ❞❡ ✶✵ RS ✳ ▲❛ ❞❡♥s✐❞❛❞ ♠á①✐♠❛ ❞❡ ✐♦♥❡s ✭∼ 50 cm−3 ✮ ❢✉❡ ♠❡❞✐❞❛ ❝❡r❝❛ ❞❡ ❧❛s ór❜✐t❛s ❞❡ ❚❡t✐s ② ❞❡ ❉✐♦♥❡✱ ✐♥❞✐❝❛♥❞♦ q✉❡ ❡st❛❜❛♥ r♦❞❡❛❞♦s ♣♦r ❡❧ t♦r♦ ❞❡ ♣❧❛s♠❛✳ ▲❛s s✐❣✉✐❡♥t❡s ♦❜s❡r✈❛❝✐♦♥❡s ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❢✉❡r♦♥ ❤❡❝❤❛s ♣♦r ❡❧ ❱♦②❛❣❡r ✶ ❡♥ ◆♦✈✐❡♠❜r❡ ❞❡ ✶✾✽✵✱ ♣♦r ❡❧ ❱♦②❛❣❡r ✷ ❡♥ ❆❣♦st♦ ❞❡ ✶✾✽✶ ② ♣♦r ❈❛ss✐♥✐ ❡♥ ❏✉❧✐♦ ❞❡ ✷✵✵✹✳ ▲❛s ❞✐✈❡rs❛s ✐♥✈❡st✐❣❛❝✐♦♥❡s ❝✐❡♥tí✜❝❛s r❡❛❧✐③❛❞❛s ♣♦r ❝❛❞❛ ♥❛✈❡ ❝♦♥tr✐❜✉✲ ②❡♥ ❣r❛♥❞❡♠❡♥t❡ ❛❧ ❡♥t❡♥❞✐♠✐❡♥t♦ ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦ ♦ ♠❛❣♥❡tós❢❡r❛ ❑r♦♥✐❛♥❛✳ ❊♥ ❡❧ ♣r❡s❡♥t❡ ❈❛♣ít✉❧♦ s❡ ❞❡s❝r✐❜✐rá♥ ❧❛s ♣r♦♣✐❡❞❛❞❡s ♠ás ✐♠♣♦rt❛♥t❡s ♦❜s❡r✲ ✈❛❞❛s ❡♥ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ② ♥❡✉tr❛s ❡♥ ❡st❛ ♠❛❣♥❡tós❢❡r❛✳ ❊st❛ ❞❡s❝r✐♣❝✐ó♥ ❡stá ❜❛s❛❞❛ ❡♥ ❧❛s ♠❡❞✐❝✐♦♥❡s r❡❛❧✐③❛❞❛s ❤❛❝❡ ♠ás ❞❡ ❞♦s ❞é❝❛❞❛s ♣♦r ❡❧ ❱♦②❛❣❡r ✶ ② ❡❧ ❱♦②❛❣❡r ✷✱ ② ❡♥ ❧❛s r❡❝✐❡♥t❡s ♠❡❞✐❝✐♦♥❡s r❡❛❧✐③❛❞❛s ♣♦r ❧❛ ♥❛✈❡ ❈❛ss✐♥✐✳ ✷✳✶✳ ❆♥t❡❝❡❞❡♥t❡s✿ ❘❡s✉❧t❛❞♦s ❞❡ ❧❛ ♠✐s✐ó♥ ❱♦②❛❣❡r ❉✉r❛♥t❡ ❧♦s ❡♥❝✉❡♥tr♦s ❞❡ ❧❛s ♥❛✈❡s ❱♦②❛❣❡r ❝♦♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦✱ ❡❧ ❡st❛❞♦ ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❢✉❡ ♠ás q✉✐❡t♦ ♣❡r♦ ❝♦♥ ✈❛r✐❛❝✐♦♥❡s t❡♠♣♦r❛❧❡s s✐❣♥✐✜❝❛✲ t✐✈❛s ❬❑r✐♠✐❣✐s ❡t ❛❧✳✱ ✶✾✽✸❪✳ ▲❛s tr❛②❡❝t♦r✐❛s ❞❡ ❡st❛s ♥❛✈❡s ♥♦ ♣❡r♠✐t✐❡r♦♥ q✉❡ ❡❧ ✐♥str✉♠❡♥t♦ ❞❡ ♣❧❛s♠❛ ✭P▲❙✱ P❧❛s♠❛ ❙♣❡❝tr♦♠❡t❡r ✮ ❝♦♥✜r♠❛r❛ ❡❧ ❝♦♠♣♦rt❛♠✐❡♥t♦ ❝♦rr♦t❛♥t❡ ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ♠ás ❛❧❧á ❞❡ ✹ RS ❬❇r✐❞❣❡ ❡t ❛❧✳✱ ✶✾✽✷❀ ❙✐tt❧❡r ❡t ❛❧✳✱ ✶✾✽✸❀ ❘✐❝❤❛r❞s♦♥✱ ✶✾✽✻❪✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✷✳✶✳ ❆♥t❡❝❡❞❡♥t❡s✿ ❘❡s✉❧t❛❞♦s ❞❡ ❧❛ ♠✐s✐ó♥ ❱♦②❛❣❡r ✷✵ ❋✐❣✉r❛ ✷✳✶✿ ❊sq✉❡♠❛ ❣❡♥❡r❛❧ ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦ ❜❛s❛❞♦ ❡♥ ❧❛s ♦❜s❡r✈❛✲ ❝✐♦♥❡s ❞❡❧ P✐♦♥❡❡r ② ❞❡ ❧♦s ❱♦②❛❣❡r ✶ ② ✷ ❬❑r✐♠✐❣✐s✱ ✶✾✽✷❪✳ ❙❡ ✐❞❡♥t✐✜❝❛r♦♥ ❝✉❛tr♦ r❡❣✐♦♥❡s✿ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛✱ ❧❛ ✑r❛♥✉r❛✑ ✱ ❧❛ ♠❛❣♥❡✲ tós❢❡r❛ ✐♥t❡r♥❛ ② ❧♦s ❛♥✐❧❧♦s✳ ❊❧ ❡sq✉❡♠❛ ❣❡♥❡r❛❧ ❞❡ ❧❛ ❝♦♥✜❣✉r❛❝✐ó♥ ♠❛❣♥❡t♦s❢ér✐❝❛ s❡ ♠✉❡str❛ ❡♥ ❧❛ ❋✐❣✉r❛ ✷✳✶✳ ▲❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ ❡①✐st❡ ❛ ♣❛rt✐r ❞❡ ❧♦s ✼✳✺ RS ❤❛st❛ ✶✼ RS ② s❡ ❝❛r❛❝t❡r✐③❛ ♣♦r s❡r r✐❝❛ ❡♥ ♦①í❣❡♥♦ ❛tó♠✐❝♦ ✐♦♥✐③❛❞♦ ✭O+ ✮ ② ❡♥ ❤✐❞ró①✐❞♦ ✐♦♥✐③❛❞♦ ✭OH+ ✮✳ ▲❛ ✏r❛♥✉r❛✑ s❡ ✉❜✐❝❛ ❡♥tr❡ ✹ RS ② ✼✳✺ RS ② ❡s ✉♥❛ ár❡❛ q✉❡ ❝❛r❡❝❡ ❞❡ ♣❛rtí❝✉❧❛s q✉❡ ❝♦♥st✐t✉②❡♥ ❛ ❧❛ ♠❛❣♥❡tós❢❡r❛✱ q✉✐③á ♣♦r ❧❛ ♣r❡s❡♥❝✐❛ ❞❡ ❧♦s s❛té❧✐t❡s ❉✐♦♥❡✱ ❚❡t✐s✱ ② ❊♥❝❡❧❛❞♦✳ ▲❛ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛ ❡stá ❞❡♥tr♦ ❞❡ ❧♦s ✹ RS ② ❝♦♥t✐❡♥❡ ♣❛rtí❝✉❧❛s ❞❡ ❛❧t❛s ❡♥❡r❣í❛s✳ ▲❛ r❡❣✐ó♥ ❞❡ ❧♦s ❛♥✐❧❧♦s s❡ ❡①t✐❡♥❞❡ ❤❛st❛ ✶✵ RS ② ❡stá ❞❡s♣r♦✈✐st❛ ❞❡ ♣❛rtí❝✉❧❛s q✉❡ ❝♦♥st✐t✉②❡♥ ❛ ❧❛ ♠❛❣♥❡tós❢❡r❛ ✭❡st♦ ❡s ✉♥ r❡s✉❧t❛❞♦ ❞❡❧ ❤❡❝❤♦ ❞❡ q✉❡ ❝✉❛♥❞♦ ❧❛s ♣❛rtí❝✉❧❛s ❝❤♦❝❛♥ ❝♦♥tr❛ ❧♦s ❡❧❡♠❡♥t♦s ❞❡ ❧♦s ❛♥✐❧❧♦s✱ ést♦s ❛tr❛♣❛♥ ❛ ❧❛s ♣❛rtí❝✉❧❛s ② ❧❡s ✐♠♣✐❞❡♥ ❡s❝❛♣❛r✮✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✷✳✶✳ ❆♥t❡❝❡❞❡♥t❡s✿ ❘❡s✉❧t❛❞♦s ❞❡ ❧❛ ♠✐s✐ó♥ ❱♦②❛❣❡r ✷✳✶✳✶✳ ✷✶ ❈❛r❛❝t❡ríst✐❝❛s ❞❡ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❊♥ ❝✉❛♥t♦ ❛ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❡♥❡r❣ét✐❝❛s s❡ ❞❡t❡r♠✐♥ó q✉❡✿ ✶✳ ▲❛ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛ ❞❡ ❙❛t✉r♥♦✱ ❛sí ❝♦♠♦ ❧❛ t❡rr❡str❡✱ s❡ ❞✐st✐♥❣✉❡ ♣♦r ❧❛ ♣r❡s❡♥❝✐❛ ❞❡ ✉♥❛ ♣♦❜❧❛❝✐ó♥ ❡st❛❜❧❡ ❞❡ ♣r♦t♦♥❡s ❛tr❛♣❛❞♦s ❝♦♥ ❡♥❡r❣í❛s s✉♣❡✲ r✐♦r❡s ❛ ✈❛r✐❛s ❞❡❝❡♥❛s ❞❡ ▼❡❱ ❬❱❛♥ ❆❧❧❡♥✱ ✶✾✽✹❪✳ ✷✳ ▲❛ ❡①✐st❡♥❝✐❛ ❞❡ ❧♦s ♣r♦t♦♥❡s ❞❡ ❛❧t❛ ❡♥❡r❣í❛ ❡♥ ❡st❛ r❡❣✐ó♥ s❡ ❞❡❜❡ ❛ q✉❡ s♦♥ ❧♦s ♣r♦❞✉❝t♦s ❞❡ ❞❡❝❛✐♠✐❡♥t♦ ❞❡ ❧♦s ♥❡✉tr♦♥❡s q✉❡ s❡ ♦r✐❣✐♥❛♥ ❡♥ ❧❛s ✐♥t❡r❛❝❝✐♦♥❡s ♥✉❝❧❡❛r❡s ❞❡ ❧♦s r❛②♦s ❝ós♠✐❝♦s ♣r✐♠❛r✐♦s✱ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ❡♥ ❡❧ ♠❛t❡r✐❛❧ ❞❡ ❧♦s ❛♥✐❧❧♦s ❆ ② ❇ ❬❋✐❧❧✐✉s ❡t ❛❧✳✱ ✶✾✽✵❪✳ ✸✳ ▲♦s ♣r♦t♦♥❡s ❝♦♥ ❡♥❡r❣í❛s ❡♥ ❡❧ ✐♥t❡r✈❛❧♦ ✵✳✵✷✽ ▼❡❱< EP 103 eV✳ ❊st❛s ❞♦s ❢♦r♠❛s ❡s♣❡❝tr❛❧❡s ♣✉❡❞❡♥ ❝♦♠❜✐♥❛rs❡ ❡♥ ✉♥❛ ❞✐str✐❜✉❝✐ó♥ ❦❛♣♣❛✳ ❆ ♣❛rt✐r ❞❡ ❡s♦s ❛❥✉st❡s ❡s♣❡❝tr❛❧❡s s❡ ❡♥❝♦♥tró ✉♥❛ t❡♠♣❡r❛t✉r❛ ❝❛r❛❝t❡ríst✐❝❛ ❞❡ 6x108 K ✭55 keV✮ ❬❑r✐♠✐❣✐s✱ ✶✾✽✷❪✳ ✽✳ ❙❡ ❡♥❝♦♥tr❛r♦♥ ❞♦s ❝♦♠♣♦♥❡♥t❡s ❡s♣❡❝tr❛❧❡s ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛ ❬❑r✐♠✐✲ ❣✐s ❛♥❞ ❆r♠str♦♥❣✱ ✶✾✽✷❪✱ ✉♥❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ❜❛❥❛✲❡♥❡r❣í❛ ✭< 500 keV✮ ❞❡s❝r✐t❛ ♣♦r ✉♥❛ ❧❡② ❞❡ ♣♦t❡♥❝✐❛s ❝♦♥ í♥❞✐❝❡ ✷✳✺ ② ✉♥❛ ♣❛rt❡ ❞❡ ❛❧t❛ ❡♥❡r❣í❛ ✭> 16 MeV✮ ❝♦♥ ✉♥ ♣❡r✜❧ s✐♠✐❧❛r ❛❧ ❡s♣❡r❛❞♦ ❞❡❧ ❈❘❆◆❉ ✭❈♦s♠✐❝ ❘❛② ◆❡✉tr♦♥ ❆❧❜❡❞♦ ❉❡✲ ❝❛② ✮ ❬❋✐❧❧✐✉s ❛♥❞ ▼❝■❧✇❛✐♥✱ ✶✾✽✵❀ ❑r✐♠✐❣✐s✱ ✶✾✽✶❪✳ ❊st♦ ❡s ✐♥❞✐❝❛t✐✈♦ ❞❡ ❧❛ ♣r❡✲ s❡♥❝✐❛ ❞❡ ❞✐st✐♥t❛s ❢✉❡♥t❡s ❞❡ ♣❛rtí❝✉❧❛s q✉❡ ❛❝tú❛♥ ❡♥ ❡❧ s✐st❡♠❛ ❞❡ ❙❛t✉r♥♦✿ ❡❧ ✈✐❡♥t♦ s♦❧❛r✱ ❧❛ ✐♦♥ós❢❡r❛ ♣❧❛♥❡t❛r✐❛✱ ❚✐tá♥✱ ❧❛ s✉♣❡r✜❝✐❡ ② ❧❛ ❛t♠ós❢❡r❛ ❞❡ ❧♦s s❛té❧✐t❡s ❞❡ ❤✐❡❧♦ ② ❧♦s ❛♥✐❧❧♦s ❬❊✈✐❛t❛r✱ ✶✾✽✹ ❀ ❏✉r❛❝✱ ✷✵✵✷❀ ❑r✉♣♣✱ ✷✵✵✺❀ ❑r✐♠✐❣✐s ❡t ❛❧✳✱ ✷✵✵✺❀ ❙✐tt❧❡r ❡t ❛❧✳✱ ✷✵✵✻❪✳ ✾✳ ▲❛ ❢r♦♥t❡r❛ ❡♥tr❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛ ② ❡①t❡r♥❛ ♥♦ ❡stá ♠✉② ♠❛r❝❛❞❛ ② ❝✉❜r❡ ✉♥ ✐♥t❡r✈❛❧♦ ❞❡ 6 RS ❛ 10 RS ❬❙❝❤❛r❞t ❡t ❛❧✳✱ ✶✾✽✹❪✳ ✶✵✳ ▲❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❡♥❡r❣ét✐❝❛s ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ ❝♦♥s✐st❡ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ❞❡ ❡❧❡❝tr♦♥❡s✱ ♣r♦t♦♥❡s ② ❛❧❣✉♥♦s ✐♦♥❡s ♣❡s❛❞♦s ❝♦♥ ❡♥❡r❣í❛s < 2 MeV ❛ ✶✵ RS ② < 1 MeV ❝❡r❝❛ ❞❡ ❧❛ ♠❛❣♥❡t♦♣❛✉s❛✳ ✶✶✳ ▲♦s t✐❡♠♣♦s ❞❡ r❡s✐❞❡♥❝✐❛ ✲♣r♦♠❡❞✐♦✲ ♣❛r❛ ✐♦♥❡s ❡♥❡r❣ét✐❝♦s ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ s♦♥ ∼ 10 − 100 ❞í❛s✳ ❍❛♠✐❧t♦♥ ❡t ❛❧✳ ❬✶✾✽✸❪ ❞❡t❡r♠✐♥❛r♦♥ ✉♥ ❧í♠✐t❡ ❞❡ ∼✷✸ ❞í❛s ♣❛r❛ ♠♦❧é❝✉❧❛s ✐♦♥✐③❛❞❛s ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛✳ ❊st♦s t✐❡♠♣♦s ❞❡♣❡♥❞❡♥ ❞❡ ❧♦s ❡st❛❞♦s ❝✉á♥t✐❝♦s ✈✐❜r❛❝✐♦♥❛❧❡s ② ❞❡ ❧♦s ♣r♦❝❡s♦s ❞❡ ❢♦t♦❞✐s♦❝✐❛❝✐ó♥✳ ✷✳✶✳✶✳✶✳ ▼❡❞✐❝✐♦♥❡s ❞❡ ♣❧❛s♠❛ ▲♦s r❡s✉❧t❛❞♦s ♠ás s♦❜r❡s❛❧✐❡♥t❡s ❡♥ r❡❧❛❝✐ó♥ ❝♦♥ ❧❛s ♣r♦♣✐❡❞❛❞❡s ❞❡❧ ♣❧❛s♠❛ ♠❛❣♥❡t♦s❢ér✐❝♦ s❡ r❡s✉♠❡♥ ❛ ❝♦♥t✐♥✉❛❝✐ó♥✿ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✷✳✶✳ ❆♥t❡❝❡❞❡♥t❡s✿ ❘❡s✉❧t❛❞♦s ❞❡ ❧❛ ♠✐s✐ó♥ ❱♦②❛❣❡r ✷✸ ✶✳ ❊❧ s✐st❡♠❛ ❞❡ ❙❛t✉r♥♦ ❡s ❝❧❛r❛♠❡♥t❡ ❡❧ ♠ás ❞✐✈❡rs♦ ❡♥ tér♠✐♥♦s ❞❡ ❢✉❡♥t❡s ❞❡ ♣❧❛s♠❛✿ ❛❞✐❝✐♦♥❛❧♠❡♥t❡ ❛❧ ✈✐❡♥t♦ s♦❧❛r ② ❛ ❧❛ ✐♦♥ós❢❡r❛ ♣❧❛♥❡t❛r✐❛✱ ❧❛s ❞♦s ❢✉❡♥t❡s ❞♦♠✐♥❛♥t❡s ♣❛r❡❝❡♥ ❡st❛r ❧♦❝❛❧✐③❛❞❛s ❡♥ ❧❛ ✈❡❝✐♥❞❛❞ ❞❡❧ ♣❧❛♥♦ ❡❝✉❛t♦✲ r✐❛❧✱ ✉♥❛ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ ② r❡❧❛❝✐♦♥❛❞❛ ❝♦♥ ❚✐tá♥✱ ♣r♦♣♦r❝✐♦♥❛♥❞♦ + + ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♣r♦t♦♥❡s ✭H ✮ ② ♥✐tró❣❡♥♦ ❛tó♠✐❝♦ ✐♦♥✐③❛❞♦ ✭N ✮✱ ② ❧❛ ♠ás ✐♠♣♦rt❛♥t❡ ✭❛❧ ♠❡♥♦s ♣❛r❛ ❧❛ ❝♦♠♣♦♥❡♥t❡ ✏❢rí❛✑ ❞❡❧ ♣❧❛s♠❛✮ ❧♦❝❛❧✐③❛❞❛ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛ ② r❡❧❛❝✐♦♥❛❞❛ ❝♦♥ ❧❛ s✉♣❡r✜❝✐❡ ❞❡ ❧♦s s❛té❧✐t❡s ❞❡ ❤✐❡❧♦ ② ❞❡ s✉s ❛t♠ós❢❡r❛s ❞❡❧❣❛❞❛s✳ ✷✳ ▲❛ ❝♦♠♣♦s✐❝✐ó♥ ❞❡ ✐♦♥❡s tér♠✐❝♦s ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ s❡ ❞❡❜❡ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ❛ ❧❛ ♥✉❜❡ ❞❡ ❣❛s ♥❡✉tr♦ ❝✉②❛ ❞❡♥s✐❞❛❞ ♠á①✐♠❛ s❡ ❧♦❝❛❧✐③❛ ❝❡r❝❛ ❞❡ ❧❛ ór❜✐t❛ ❞❡ 4 ❊♥❝❡❧❛❞♦ ✭10 cm−3 ✮✱ ♣♦r ❧♦ q✉❡ ❡❧ ❤✐❞ró①✐❞♦ ✐♦♥✐③❛❞♦ ✭OH+ ✮ ② ❡❧ ❛❣✉❛ ✐♦♥✐③❛❞❛ + + ✭H2 O ✮ ♣♦❞rí❛♥ s❡r t❛♥ ❛❜✉♥❞❛♥t❡s ❝♦♠♦ ❡❧ ♦①í❣❡♥♦ ❛tó♠✐❝♦ ✐♦♥✐③❛❞♦ ✭O ✮ ❡♥ t♦❞❛ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❬■♣✱ ✷✵✵✵❪✳ ✸✳ ❇r✐❞❣❡ ❡t ❛❧✳ ❬✶✾✽✶✱ ✶✾✽✷❪ r❡♣♦rt❛r♦♥ q✉❡ ❡❧ ♣❧❛s♠❛ ♠❛❣♥❡t♦s❢ér✐❝♦ s❡ ❞❡st❛❝❛ ♣♦rq✉❡ ❡①✐st❡ ✉♥ ré❣✐♠❡♥ ❛❧t❛♠❡♥t❡ ✈❛r✐❛❜❧❡ ❢✉❡r❛ ❞❡ t❡♥❞✐❞❛ ❞❡ ♣❧❛s♠❛ ❡♥tr❡ L=7 t♦r♦ ❞❡ ♣❧❛s♠❛ ❞❡♥tr♦ ❞❡ L = 7 ❝♦♥ ✉♥ ❡s♣❡s♦r ♠❡❞✐♦ ❞❡ ✶ RS ✵✳✷ RS ✭❡♥ L= ② L = 15 L = 15 ✷ ✱ ✉♥❛ ❤♦❥❛ ❡①✲ ❝♦♥ ✉♥ ❡s♣❡s♦r ♠❡❞✐♦ > 4 RS ✭❡♥ ② ✉♥ L = 5✮ ② ❞❡ ✷✳✽✽✮✳ ✹✳ ▲❛s ♠❡❞✐❝✐♦♥❡s ❡❧❡❝tró♥✐❝❛s ❞❡❧ ❱♦②❛❣❡r ♠✉❡str❛♥ ❣r❛❞✐❡♥t❡s ❛ ❣r❛♥ ❡s❝❛❧❛ ❡♥ ❧❛ t❡♠♣❡r❛t✉r❛ ❡❧❡❝tró♥✐❝❛ ❝♦♥ ✉♥ ✐♥❝r❡♠❡♥t♦ ❞❡s❞❡ ✐♥t❡r♥❛ ❤❛st❛ > 800 eV < 1 eV ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛✳ ❊st❡ ✐♥❝r❡♠❡♥t♦ ❡♥ ❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧ ♣❧❛s♠❛ ✲♣♦r ❝❡r❝❛ ❞❡ tr❡s ór❞❡♥❡s ❞❡ ♠❛❣♥✐t✉❞✲ ♣r♦✈♦❝❛ q✉❡ ❡❧ ❡s♣❡s♦r ❞❡ ❧❛ ❤♦❥❛ ❞❡ ♣❧❛s♠❛ ❛✉♠❡♥t❡ ❝♦♥ ❧❛ ❞✐st❛♥❝✐❛ r❛❞✐❛❧✳ ✺✳ ▲❛ r❡❞✉❝❝✐ó♥ ❡♥ ❧❛ t❡♠♣❡r❛t✉r❛ ❡❧❡❝tró♥✐❝❛ ② ❧❛ ❛t❡♥✉❛❝✐ó♥ ❞❡ ❧♦s ❡❧❡❝tr♦♥❡s s✉♣r❛t❡r♠❛❧❡s ❢✉❡r♦♥ t❛♠❜✐é♥ ♦❜s❡r✈❛❞❛s ❝❡r❝❛ ❞❡ ❧❛ ór❜✐t❛ ❞❡ ❚❡t✐s✱ ❞❡ ❉✐♦♥❡ ② ♣♦s✐❜❧❡♠❡♥t❡ ❞❡ ❘❡❛✳ ❚❛❧❡s ❡❢❡❝t♦s ✐♥❞✐❝❛♥ ❧❛ ✐♥t❡r❛❝❝✐ó♥ ❡♥tr❡ ❧♦s ❡❧❡❝tr♦♥❡s ✷ ❊❧ ♣❛rá♠❡tr♦ ✑▲✑ ❡s ❧❛ ❞✐st❛♥❝✐❛ ❛ ❧❛ ❝✉❛❧ ✉♥❛ ❧í♥❡❛ ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❝♦rt❛ ❛❧ ♣❧❛♥♦ ❡❝✉❛t♦r✐❛❧ ② ❡stá ♠❡❞✐❞❛ ❞❡s❞❡ ❡❧ ❝❡♥tr♦ ❞❡ ♠❛s❛ ❞❡❧ ♣❧❛♥❡t❛✳ ❊s ✉♥❛ ❝❛♥t✐❞❛❞ ❛❞✐♠❡♥s✐♦♥❛❧✱ ♣❡r♦ s❡ ❡♥t✐❡♥❞❡ q✉❡ ❡stá r❡❢❡r✐❞❛ ❛ r❛❞✐♦s ♣❧❛♥❡t❛r✐♦s✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✷✳✶✳ ❆♥t❡❝❡❞❡♥t❡s✿ ❘❡s✉❧t❛❞♦s ❞❡ ❧❛ ♠✐s✐ó♥ ❱♦②❛❣❡r ✷✹ ② ❧❛s ❝♦♥❝❡♥tr❛❝✐♦♥❡s ❧♦❝❛❧✐③❛❞❛s ❞❡ ♣♦❧✈♦✱ ❣❛s ♥❡✉tr♦✱ ✐♦♥❡s ②✴♦ ♦♥❞❛s ❞❡ ♣❧❛s♠❛ ❬❑r✐♠✐❣✐s ❡t ❛❧✳✱ ✶✾✽✶❀ ✶✾✽✷❪✳ ✻✳ ❊❧ ❤❡❝❤♦ ❞❡ q✉❡ ✉♥❛ ❝♦♠♣♦♥❡♥t❡ ✐ó♥✐❝❛ t❡♠♣❧❛❞❛ s❡❛ ♠ás ♥♦t❛❜❧❡ ❡♥ ❧❛ ♠❛❣✲ ♥❡tós❢❡r❛ ❡①t❡r♥❛ ✐♥❞✐❝❛ q✉❡ ❡♥ ❧❛ ✈❡❝✐♥❞❛❞ ❞❡ ❧❛ ♥✉❜❡ ♥❡✉tr❛ ❞❡ ❤✐❞ró❣❡♥♦ s❡ ❢♦r♠❛ ✉♥❛ ❡str✉❝t✉r❛ ❝♦♠♣✉❡st❛ ♣♦r ✐♦♥❡s ♣❡s❛❞♦s ❬▲❛③❛r✉s ❛♥❞ ▼❝◆✉tt✱ ✶✾✽✸❪ s✐❡♥❞♦ ❧❛s ❢✉❡♥t❡s ❞❡ ♥❡✉tr♦s ♣❡s❛❞♦s✱ ❚✐tá♥ ② ❡❧ s✐st❡♠❛ ❞❡ ❛♥✐❧❧♦s ♣r✐♥✲ ❝✐♣❛❧ ❬❊✈✐❛t❛r ❡t ❛❧✳ ✶✾✽✸❪✳ ❚❛♥t♦ ❡❧ P✐♦♥❡❡r ❝♦♠♦ ❧♦s ❱♦②❛❣❡r ❞❡t❡❝t❛r♦♥ ❡st❡ t♦r♦ ❞❡ ✐♦♥❡s ♣❡s❛❞♦s q✉❡ s❡ ❡①t✐❡♥❞❡ ❞❡s❞❡ ✉♥♦s ✶✵ RS ❤❛❝✐❛ ❛❞❡♥tr♦ ❝♦♥ ✉♥❛ ❞❡♥s✐❞❛❞ ♣✐❝♦ ∼ 50 cm−3 ❝❡r❝❛ ❞❡ ❧❛s ór❜✐t❛s ❞❡ ❧♦s s❛té❧✐t❡s ❞❡ ❤✐❡❧♦✳ ✼✳ ❉❡♥tr♦ ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛✱ ❧♦s ❱♦②❛❣❡r ❡♥❝♦♥tr❛r♦♥ ✈❛r✐♦s ✐♥❝r❡♠❡♥t♦s ❡♥ ❧❛ ❞❡♥s✐❞❛❞ ❜✐❡♥ ❧♦❝❛❧✐③❛❞♦s✳ ❊st♦s ✐♥❝r❡♠❡♥t♦s ❛♣❛r❡♥t❡♠❡♥t❡ ❝♦♥t✐❡♥❡♥ ✐♦♥❡s ♣❡s❛❞♦s ❞❡ 14 ❛ 28 uma ❛ t❡♠♣❡r❛t✉r❛s ❜❛❥❛s ② ♣✉❡❞❡♥ s❡r ✐❞❡♥t✐✜❝❛❞♦s ❝♦♠♦ ✉♥❛ ♣❧✉♠❛ ❞❡ ♣❧❛s♠❛ ♦r✐❣✐♥❛❞❛ ❡♥ ❚✐tá♥✳ ❊st❛ ♣❧✉♠❛ s❡ ❡♥r❡❞❛ ❡♥ ❙❛t✉r♥♦✱ ❢♦r♠❛♥❞♦ ❡❧ t♦r♦ ❞❡ ♣❧❛s♠❛ ❞❡ ❚✐tá♥ ✭✈é❛s❡ ♣♦r ❡❥❡♠♣❧♦ ❙❝❛r❢ ❡t ❛❧✳✱ ✶✾✽✹✱ ② ❙❝❤❛r❞t ❡t ❛❧✳✱ ✶✾✽✹✮✳ ✽✳ ▲❛ ✐♥✢✉❡♥❝✐❛ ❞❡ ❧❛s ♣❡rt✉r❜❛❝✐♦♥❡s ❞❡❧ ✈✐❡♥t♦ s♦❧❛r s♦❜r❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ s❡ ❤❛❝❡ ♠ás ❡✈✐❞❡♥t❡ ❡♥ ❧❛s ♦❜s❡r✈❛❝✐♦♥❡s q✉❡ r❡❛❧✐③ó ❡❧ ❱♦②❛❣❡r ✷✳ P♦r ❡❥❡♠♣❧♦✱ s❡ ❞❡t❡❝tó q✉❡ ❧♦s ✢✉❥♦s ❞❡ ♣r♦t♦♥❡s ② ❞❡ ❡❧❡❝tr♦♥❡s ❡r❛♥ ♠ás ✈❛r✐❛❜❧❡s ❡ ✐♥t❡♥s♦s q✉❡ ❧♦s ❛♥t❡r✐♦r♠❡♥t❡ ♦❜s❡r✈❛❞♦s ❬❱♦❣t ❡t ❛❧✳✱ ✶✾✽✷❪✳ ✾✳ ▲❛ ♠❛❣♥❡tós❢❡r❛ ❡stá ❞♦♠✐♥❛❞❛ ♣♦r ❧❛ ❝♦rr♦t❛❝✐ó♥ ✭❧♦s ♣❧❛s♠❛s ② ❧❛s ♣❛rtí❝✉❧❛s ❝♦rr♦t❛♥ ♣❛r❝✐❛❧♠❡♥t❡ ❝♦♥ ❡❧ ♣❧❛♥❡t❛✮✳ ❆❧❣✉♥♦s ❡st✉❞✐♦s ✐♥❞✐❝❛♥ q✉❡ ❡①✐st❡♥ ♣❧❛s♠❛s q✉❡ ❝♦rr♦t❛♥ rí❣✐❞❛♠❡♥t❡ ❛❧ ♠❡♥♦s ❤❛st❛ ✶✵ RS ❬❋r❛♥❦ ❡t ❛❧✳✱ ✶✾✽✵❪✳ ▼ás ❛❧❧á ❞❡ ❡s❛ ❞✐st❛♥❝✐❛✱ ❧❛s ✈❡❧♦❝✐❞❛❞❡s ✈❛rí❛♥ ❡♥tr❡ 30 ② 80 % ❞❡ ❧❛ ❝♦rr♦✲ t❛❝✐ó♥ rí❣✐❞❛✳ ✶✵✳ ❚❛♠❜✐é♥ s❡ ❤❛ ♦❜s❡r✈❛❞♦ q✉❡ ❥✉st❛♠❡♥t❡ ❞❡s♣✉és ❞❡ ❧❛s ór❜✐t❛s ❞❡ ❉✐♦♥❡ ② ❞❡ ❘❡❛ ❧❛ ✈❡❧♦❝✐❞❛❞ ❞❡ ✢✉❥♦ ❛③✐♠✉t❛❧ ❞❡❧ ♣❧❛s♠❛ ❝❛❡ s✐❣♥✐✜❝❛t✐✈❛♠❡♥t❡✳ ❊st♦ q✉✐③á s❡ ❞❡❜❛ ❛ q✉❡ ❡❧ ♣❧❛s♠❛ ❡s tr❛♥s♣♦rt❛❞♦ r❛❞✐❛❧♠❡♥t❡ ❤❛❝✐❛ ❛❞❡♥tr♦ ❬❙❛✉r ❡t ❛❧✳✱ ✷✵✵✹❪✳ ❊st❡ tr❛♥s♣♦rt❡ ❤❛❝❡ ❣✐r❛r ❛❧ ♣❧❛s♠❛ ❛❧❣✉♥❛s ✈❡❝❡s ❡①❝❡❞✐❡♥❞♦ ❧❛ ❝♦rr♦t❛❝✐ó♥ rí❣✐❞❛✳ ❊♥ ❡st❛❞♦ ❡st❛❝✐♦♥❛r✐♦ ❡st❡ ♠♦✈✐♠✐❡♥t♦ ❤❛❝✐❛ ❛❞❡♥tr♦ só❧♦ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✷✳✶✳ ❆♥t❡❝❡❞❡♥t❡s✿ ❘❡s✉❧t❛❞♦s ❞❡ ❧❛ ♠✐s✐ó♥ ❱♦②❛❣❡r ✷✺ ❡s ♣♦s✐❜❧❡ ❝✉❛♥❞♦ ❡❧ ♣❧❛s♠❛ ❡s ❝♦♥✈❡rt✐❞♦ ❛ ♥❡✉tr♦s ♦ s✐ ❡❧ ♣❧❛s♠❛ ❡s ❛❜s♦r❜✐❞♦ ❡♥ ❛❧❣ú♥ ❧✉❣❛r✳ ❉❡ ❤❡❝❤♦ ❙❛✉r ❡t ❛❧✳ ❬✷✵✵✹❪ ❞❡t❡r♠✐♥❛♥ q✉❡ ❡❧ ♠❛t❡r✐❛❧ só❧♦ ♣✉❡❞❡ ❞❡❥❛r ❧❛ r❡❣✐ó♥ ❝♦♠♦ ♥❡✉tr♦s✳ ✷✳✶✳✶✳✷✳ P❛rtí❝✉❧❛s ♥❡✉tr❛s ▲❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦✱ ❛❧ ✐❣✉❛❧ q✉❡ ❧❛ ❞❡ ❏ú♣✐t❡r✱ ❝♦♥t✐❡♥❡ ♥✉♠❡r♦s❛s ❢✉❡♥✲ t❡s ❞❡ ❣❛s ♥❡✉tr♦✳ ❊st❡ ❣❛s ♥❡✉tr♦ ♣✉❡❞❡ s❡r ✐♦♥✐③❛❞♦ ② ❛sí ❝♦♥tr✐❜✉✐r ❛ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❞❡❧ ♣❧❛s♠❛ tér♠✐❝♦ ② ❛ ❧❛ ❞❡ ❧♦s ❝✐♥t✉r♦♥❡s ❞❡ r❛❞✐❛❝✐ó♥✳ ❊♥ ♣❛rt✐❝✉❧❛r✱ ❧❛ ✏s❛❧♣✐❝❛❞✉r❛✑ ♣r♦✈♦❝❛❞❛ ♣♦r ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ② ♣♦r ❡❧ ❜♦♠❜❛r❞❡♦ ♠❡t❡♦rít✐❝♦ ❞❡❧ ♠❛t❡r✐❛❧ ❞❡ ❧♦s ❛♥✐❧❧♦s ② ❞❡ ❧❛ s✉♣❡r✜❝✐❡ ❤❡❧❛❞❛ ❞❡ s✉s s❛té❧✐t❡s ❢♦r♠❛ ✉♥❛ ❡①✲ t❡♥s❛ ♥✉❜❡ ❞❡ ♠♦❧é❝✉❧❛s ❞❡ ❛❣✉❛ ② ❞❡ ♣r♦❞✉❝t♦s ❞❡ ❧❛ ❞✐s♦❝✐❛❝✐ó♥ ❞❡❧ ❛❣✉❛ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛✳ ❚✐tá♥ ❛❝tú❛ ❝♦♠♦ ✉♥❛ ❢✉❡♥t❡ ❞❡ ❣❛s❡s ♥❡✉tr♦s ② ❞❡ ✐♦♥❡s ♣❛r❛ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛✳ ❚❛♥t♦ ❡❧ ❤✐❞ró❣❡♥♦ ♥❡✉tr♦ ❡ ✐♦♥✐③❛❞♦ ❝♦♠♦ ❡❧ t♦r♦ ❞❡ ♥✐tró❣❡♥♦ r♦❞❡❛♥ ❛ ❙❛t✉r♥♦ ❝❡r❝❛ ❞❡ ❧❛ ór❜✐t❛ ❞❡ ❚✐tá♥ ❡♥ ∼ 20 RS ✱ ② ❧❛s ♣❧✉♠❛s ❞❡ ✐♦♥❡s ♣❡s❛❞♦s s❡ ❡①t✐❡♥❞❡♥ ♠ás ❛❧❧á ❞❡ ❧❛ ór❜✐t❛ ❞❡ ❚✐tá♥✳ ❊❧ ❡sq✉❡♠❛ ❣❡♥❡r❛❧ ❞❡❧ t♦r♦ ❞❡ ♣❧❛s♠❛ ② ♥❡✉tr♦ ❡♥ ❙❛t✉r♥♦ ❡stá ❜❛s❛❞♦ ❡♥ ✉♥❛ s❡r✐❡ ❞❡ ♦❜s❡r✈❛❝✐♦♥❡s ❤❡❝❤❛s ❞❡s❞❡ ❧❛ ❚✐❡rr❛ ❞❡ ❧❛ ❡♠✐s✐ó♥ ▲②✲α✱ ② ❡♥ ❧❛s ♦❜s❡r✈❛✲ ❝✐♦♥❡s r❡❛❧✐③❛❞❛s ♣♦r ❧❛s ♠✐s✐♦♥❡s P✐♦♥❡❡r ② ❱♦②❛❣❡r✳ ▲❛s ♥✉❜❡s ❞❡ ❤✐❞ró❣❡♥♦ ② ❞❡ ♥✐tró❣❡♥♦ ♥❡✉tr♦s s❡ ❡♥❝✉❡♥tr❛♥ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛✱ s❡ ❡①t✐❡♥❞❡♥ r❛❞✐❛❧♠❡♥✲ t❡ ❞❡s❞❡ 8 RS ❤❛st❛ 25 RS ② ❝♦♥ ✉♥ ❡s♣❡s♦r ❛♣r♦①✐♠❛❞♦ ❞❡ ✶✷ RS ✳ ❙❡ ❡♥❝♦♥tró q✉❡ ❧❛s ❞❡♥s✐❞❛❞❡s ♠❡❞✐❛s ❞❡ ❧❛s ♥✉❜❡s ❞❡ ❤✐❞ró❣❡♥♦ ② ❞❡ ♥✐tró❣❡♥♦ ❡r❛♥ ❞❡ 6 cm−3 20 cm−3 ② ❞❡ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ❙❤❡♠❛♥s❦② ❛♥❞ ❍❛❧❧ ❬✶✾✾✷❪ ❡①❛♠✐♥❛r♦♥ ❧❛s ♦❜s❡r✈❛❝✐♦♥❡s ❞❡❧ ❡①♣❡r✐♠❡♥t♦ ❯❱❙ ❞❡❧ ❱♦②❛❣❡r ② ❤❛❧❧❛r♦♥ q✉❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ ❛♥❣✉❧❛r ❞❡ ❧❛ ♥✉❜❡ ❞❡ ❤✐❞ró❣❡♥♦ ❡r❛ ❛s✐♠étr✐❝❛ ❝♦♥ ✉♥❛ ❛❧t❛ ❝♦♥❝❡♥tr❛❝✐ó♥ ❝❡r❝❛ ❞❡❧ ❧❛❞♦ ❝r❡♣✉s❝✉❧❛r✳ ▲❛ ❢✉❡♥t❡ ❞❡ ♠❛t❡r✐❛❧ ♣❛r❛ ❝❛❞❛ ♥✉❜❡ ♣r♦✈✐❡♥❡ ❞❡ ❚✐tá♥✳ ❉❡♥tr♦ ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛ ❧❛s ❡♠✐s✐♦♥❡s ▲②✲α ♣r♦♣♦r❝✐♦♥❛r♦♥ ❡✈✐❞❡♥❝✐❛ ❞❡ ✉♥❛ ❛t♠ós❢❡r❛ ❞❡ ❤✐❞ró❣❡♥♦ ❛s♦❝✐❛❞❛ ❝♦♥ ❧♦s ❛♥✐❧❧♦s ❞❡ ❙❛t✉r♥♦✳ ❊st❛ ❛t♠ós❢❡r❛ ❡stá ❝♦♥✜♥❛❞❛ r❛❞✐❛❧♠❡♥t❡ ❡♥tr❡ ✷ RS s✐❞❛❞ ♠❡❞✐❛ ❞❡ ❡st❛ ❡str✉❝t✉r❛ ❡s ❞❡ ② ✸ RS ❝♦♥ ✉♥ ❡s♣❡s♦r ❞❡ ∼ 400 cm−3 ✳ ∼✵✳✹ RS ✳ ▲❛ ❞❡♥✲ ❆❞✐❝✐♦♥❛❧♠❡♥t❡ s❡ ❤❛ ✐♥❢❡r✐❞♦ ❧❛ ❡①✐st❡♥❝✐❛ ❞❡ ✉♥❛ ♥✉❜❡ ❞❡ ❛❣✉❛ ♥❡✉tr❛ ❝❡r❝❛ ❞❡ ❧♦s ❛♥✐❧❧♦s ② ❞❡ ❧♦s s❛té❧✐t❡s ❞❡ ❤✐❡❧♦✱ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✷✳✶✳ ❆♥t❡❝❡❞❡♥t❡s✿ ❘❡s✉❧t❛❞♦s ❞❡ ❧❛ ♠✐s✐ó♥ ❱♦②❛❣❡r ✷✻ ❜❛s❛❞❛ ❡♥ ❧❛s ♦❜s❡r✈❛❝✐♦♥❡s ❞❡❧ P✐♦♥❡❡r ② ❞❡ ❧♦s ❱♦②❛❣❡r✳ ❊①✐st❡♥ ♦tr❛s ♣♦s✐❜❧❡s ❢✉❡♥t❡s ❞❡ ♥❡✉tr♦s ② ❞❡ ✐♦♥❡s q✉❡ ♣✉❡❞❡♥ ❤❛❝❡r ❧❛ ❞✐❢❡r❡♥❝✐❛ ❡♥tr❡ ❧❛ ❞❡♥s✐❞❛❞ ♦❜s❡r✈❛❞❛ ❞❡❧ t♦r♦ ✐♥t❡r♥♦ ② ❧♦s r❡s✉❧t❛❞♦s ❞❡❧ ♠♦❞❡❧♦ ❞❡ ❧♦s s❛té❧✐t❡s ❞❡ ❤✐❡❧♦ ❞❡s❛rr♦❧❧❛❞❛ ♣♦r ❏♦❤♥s♦♥ ❡t ❛❧✳ ❬✶✾✽✾❪✱ t❛❧❡s ❝♦♠♦ ✉♥❛ s✉♣❡r✜❝✐❡ ❛❝t✐✈❛ s♦❜r❡ ❊♥❝❡❧❛❞♦ ♦ ♣❛rtí❝✉❧❛s ❡♥ ❡❧ ❛♥✐❧❧♦ ❊ ❬P♦s♣✐❡s③❛❧s❦❛ ❛♥❞ ❏♦❤♥s♦♥✱ ✶✾✾✶❪ q✉❡ s❡ ❡①t✐❡♥❞❡ ❞❡s❞❡ ❧♦s ✸ RS ❤❛st❛ ❧♦s ✽ RS ❝♦♥ ✉♥❛ ❞❡♥s✐❞❛❞ ♣✐❝♦ ❝❡r❝❛ ❞❡ ❧❛ ór❜✐t❛ ❞❡ ❊♥❝❡❧❛❞♦ ❛ 4 RS ❬❏✉r❛❝ ❡t ❛❧✳ ✷✵✵✶❪✳ ❆ ❞✐st❛♥❝✐❛s r❛❞✐❛❧❡s ♠❡♥♦r❡s ❛ 4 RS ✱ ❧❛ ❡r♦s✐ó♥ ♠✐❝r♦♠❡t❡♦rít✐❝❛ ❞❡ ❧♦s ❛♥✐❧❧♦s ♣r✐♥❝✐♣❛❧❡s ♣✉❡❞❡ s❡r ✉♥❛ ❢✉❡♥t❡ s✐❣♥✐✜❝❛t✐✈❛ ❞❡ ♠♦❧é❝✉❧❛s ② ❞❡ ✐♦♥❡s ❞❡ ❛❣✉❛✳ ▲❛s ❞❡♥s✐❞❛❞❡s ♣r♦❞✉❝✐❞❛s ♣♦r ❡st❡ ♣r♦❝❡s♦ ♣✉❡❞❡♥ r❡s✉❧t❛r ✐♠♣♦rt❛♥t❡s ✭♣♦r ❡❥❡♠♣❧♦✱ P♦s♣✐❡s③❛❧s❦❛✲❏♦❤♥s♦♥ ❬✶✾✾✶❪ ❡♥❝✉❡♥tr❛♥ ✉♥ ♣✐❝♦ ❞❡ ❛♣r♦①✐♠❛❞❛♠❡♥t❡ 4x104 cm−3 ❧♦❝❛❧✐③❛❞♦ ❛❧r❡❞❡❞♦r ❞❡ ✶✳✹ RS ✮✳ P❡r♦ ♠ás ❛❧❧á ❞❡ ✷✳✸ RS t❛♥t♦ ❧❛ ❞❡♥s✐❞❛❞ ❞❡ ♣❧❛s♠❛ ❝♦♠♦ ❧❛ ❞❡♥s✐❞❛❞ ❞❡ ♥❡✉tr♦s ❡♠♣✐❡③❛ ❛ ❞❡❝r❡❝❡r✳ ❊♥ ❡st❡ ♣✉♥t♦ ❧❛ ✈❡❧♦❝✐❞❛❞ ❞❡ ❧❛ ♣❛rtí❝✉❧❛ ❞❡❧ ♣❧❛s♠❛ q✉❡ ❝♦rr♦t❛ ❝♦♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡s ♠❛②♦r q✉❡ ❧❛ ✈❡❧♦❝✐❞❛❞ ❞❡ ❡s❝❛♣❡ ❞❡ ✉♥❛ ♣❛rtí❝✉❧❛ ♥❡✉tr❛✳ ❯♥❛ ✈❡③ q✉❡ ❡❧ ✐ó♥ ❡s ♥❡✉tr❛❧✐③❛❞♦ ❡s❝❛♣❛ ❞❡❧ s✐st❡♠❛ ❞❡ ❙❛t✉r♥♦ r❡❞✉❝✐❡♥❞♦ ❞❡ ❡st❛ ♠❛♥❡r❛ ❧❛ ❞❡♥s✐❞❛❞ ❞❡ ♥❡✉tr♦s ❡♥ ❧❛ r❡❣✐ó♥ ②✱ ❞❡ ❛q✉í✱ q✉❡ s❡ r❡❞✉③❝❛ ❧❛ ❞❡♥s✐❞❛❞ ✐ó♥✐❝❛ ❞❡❜✐❞♦ ❛ q✉❡ ❤❛② ♠❡♥♦s ♥❡✉tr♦s ♣❛r❛ ✐♦♥✐③❛r✳ ❊st❡ ♣r♦❝❡s♦ ❡s ❡✜❝✐❡♥t❡ ♣❛r❛ r❡♠♦✈❡r ❡s❝♦♠❜r♦s ❞❡ ❧❛ r❡❣✐ó♥ ❝❡r❝❛♥❛ ❛ ❙❛t✉r♥♦ ② ♣✉❡❞❡ s❡r ❡❧ ❢❛❝t♦r ❞❡t❡r♠✐♥❛♥✲ t❡ ❡♥ ❧❛ ❧♦❝❛❧✐③❛❝✐ó♥ ❞❡ ❧❛ ❢r♦♥t❡r❛ ❡①t❡r♥❛ ❞❡❧ ❛♥✐❧❧♦ ♣r✐♥❝✐♣❛❧ ❬P♦s♣✐❡s③❛❧s❦❛ ❛♥❞ ❏♦❤♥s♦♥✱ ✶✾✾✶❪✳ ❚♦r♦ ❞❡ ♣❧❛s♠❛ ② ❣❛s ❞❡ ❚✐tá♥ ❊❧ ❡♥❝✉❡♥tr♦ ❞❡❧ ❱♦②❛❣❡r ✶ ❝♦♥ ❚✐tá♥ ♦❝✉rr✐ó ❡❧ ✶✷ ❞❡ ♥♦✈✐❡♠❜r❡ ❞❡ ✶✾✽✵ ❛❧✲ r❡❞❡❞♦r ❞❡ ❧❛s ✵✺✹✵✿✷✵ ❙❈❊❚ ✭✶✸✸✵ t✐❡♠♣♦ ❧♦❝❛❧ ❡♥ ❙❛t✉r♥♦✮ ❛ ✉♥❛ ❞✐st❛♥❝✐❛ ❞❡ 6969 ❦✐❧ó♠❡tr♦s ❞❡❧ ❝❡♥tr♦ ❞❡❧ s❛té❧✐t❡✱ ♠✐❡♥tr❛s q✉❡ ❚✐tá♥ ❡st❛❜❛ ❞❡♥tr♦ ❞❡❧ ❧❛❞♦ ❞í❛ ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ ❞❡ ❙❛t✉r♥♦ ❬◆❡✉❜❛✉❡r ❡t ❛❧✳✱ ✶✾✽✹❪✳ ❊st♦ ❞✐♦ ❧❛ ❣r❛♥ ♦♣♦rt✉♥✐❞❛❞ ❞❡ ❡♥t❡♥❞❡r t❛♥t♦ ❧❛s ✐♥t❡r❛❝❝✐♦♥❡s ❝♦♠♦ ❧❛ ✐♥✢✉❡♥❝✐❛ ❞❡ ❡st❡ s❛té❧✐t❡ ❝♦♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ♣❧❛♥❡t❛r✐❛✳ ▲❛ ❞✐st❛♥❝✐❛ ♦r❜✐t❛❧ ❞❡ ❚✐tá♥ ✭✷✵✳✷ RS ✮ ❡s t❛❧ q✉❡ ❡❧ s❛té❧✐t❡ s❡ ❡♥❝✉❡♥tr❛ s✐❡♠♣r❡ ❞❡♥tr♦ ❞❡ ❧❛ ♠❛❣♥❡t♦❝♦❧❛ ❞❡ ❙❛t✉r♥♦ ♣❡r♦ ♣✉❡❞❡ ❡st❛r ❞❡♥tr♦ ♦ ❢✉❡r❛ ❞❡❧ ❧❛❞♦ ❢r♦♥t❛❧ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✷✳✶✳ ❆♥t❡❝❡❞❡♥t❡s✿ ❘❡s✉❧t❛❞♦s ❞❡ ❧❛ ♠✐s✐ó♥ ❱♦②❛❣❡r ✷✼ ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡♣❡♥❞✐❡♥❞♦ ❞❡ ❧❛s ❝♦♥❞✐❝✐♦♥❡s ❞❡❧ ✈✐❡♥t♦ s♦❧❛r✳ ❈✉❛♥❞♦ ❚✐tá♥ ❡stá ❢✉❡r❛ ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ s❡ ❡s♣❡r❛ q✉❡ t❡♥❣❛ ✉♥❛ ✐♥t❡r❛❝❝✐ó♥ ❝♦♥ ❡❧ ✈✐❡♥t♦ s♦❧❛r s✐♠✐❧❛r ❛❧ q✉❡ t✐❡♥❡ ❧❛ ❚✐❡rr❛ ✭s✐ ❡stá ♠❛❣♥❡t✐③❛❞♦✮✱ ♦ ❝♦♠♦ ❱❡♥✉s ✭s✐ ♥♦ ❡stá ♠❛❣✲ ♥❡t✐③❛❞♦✮✳ ❊♥ ❝❛♠❜✐♦ ❝✉❛♥❞♦ ❡stá ❞❡♥tr♦ ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛✱ ❧❛ ✐♥t❡r❛❝❝✐ó♥ ♣♦❞rí❛ s❡r s✐♠✐❧❛r ❛❧ ❞❡ ❧♦s s❛té❧✐t❡s ❣❛❧✐❧❡❛♥♦s ❝♦♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❏♦✈✐❛♥❛ ❝♦rr♦t❛♥t❡✳ ❉❛❞♦ q✉❡ t♦❞❛✈í❛ ♥♦ ❤❛② ✐♥❞✐❝✐♦s ❞❡ q✉❡ ❚✐tá♥ t❡♥❣❛ ✉♥ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ✐♥trí♥✲ s❡❝♦ ❛♣r❡❝✐❛❜❧❡ ♥✐ ✉♥❛ ♠❛❣♥❡tós❢❡r❛ ❛s♦❝✐❛❞❛✱ ❡①✐st❡ ✉♥❛ ✐♥t❡r❛❝❝✐ó♥ ❞✐r❡❝t❛ ❡♥tr❡ ❡❧ ♣❧❛s♠❛ ♠❛❣♥❡t♦s❢ér✐❝♦ ❞❡ ❙❛t✉r♥♦ ② ❡❧ s✐st❡♠❛ ✐♦♥ós❢❡r❛✲❛t♠ós❢❡r❛ ❞❡ ❚✐tá♥✳ ❆ ❞✐❢❡r❡♥❝✐❛ ❞❡ ❧♦s s❛té❧✐t❡s ❞❡ ❤✐❡❧♦✱ ❚✐tá♥ ♣♦s❡❡ ✉♥❛ ❞❡♥s❛ ❛t♠ós❢❡r❛ ❝♦♠♣✉❡st❛ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♣♦r ♥✐tró❣❡♥♦ ② ♠❡t❛♥♦✱ ❛❞❡♠ás ❞❡ ♦tr♦s ❤✐❞r♦❝❛r❜✉r♦s✳ ❉❡ ❛q✉í✱ q✉❡ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s q✉❡ ✐♥t❡r❛❝tú❛ ❝♦♥ ❧❛ ❛t♠ós❢❡r❛ s✉♣❡r✐♦r ❞❡ ❚✐tá♥ ② ❝♦♥ ❧❛ ✐♦♥ós❢❡r❛ ♣✉❡❞❡ ❝❛♠❜✐❛r ❝♦♥s✐❞❡r❛❜❧❡♠❡♥t❡ ❡♥ ❡❧ tr❛♥s❝✉rs♦ ❞❡ ✉♥❛ ór❜✐t❛✳ ❚❛❧❡s ❝♦♥s✐❞❡r❛❝✐♦♥❡s s♦♥ ❡①tr❡♠❛❞❛♠❡♥t❡ ✐♠♣♦rt❛♥t❡s ♣❛r❛ ❡♥t❡♥❞❡r ❧❛ ❞✐♥á♠✐❝❛ ❞❡ ❧❛ ❛t♠ós❢❡r❛ ❞❡ ❚✐tá♥ ② s✉ r❡❧❛❝✐ó♥ ❝♦♥ ❡❧ ♠❡❞✐♦ ❝✐r❝✉♥❞❛♥t❡✳ ◆❡ss ❡t ❛❧✳ ❬✶✾✽✶❪ ♠✉❡str❛♥ q✉❡ ❢ís✐❝❛♠❡♥t❡ ✉♥❛ ✐♥t❡r❛❝❝✐ó♥ ❡♥tr❡ ❧❛ ❛t♠ós❢❡r❛ ❞❡ ❚✐tá♥ ② ❡❧ ♣❧❛s♠❛ ❝♦♥❞✉❝❡ ❛ ✉♥❛ ♠❛❣♥❡tós❢❡r❛ ✐♥❞✉❝✐❞❛ ❝♦♥ ❧❛s ❧í♥❡❛s ❞❡ ❝❛♠♣♦ ❡♥r♦❧❧á♥❞♦s❡ ❛❧r❡❞❡❞♦r ❞❡ ❧❛ ✐♦♥♦♣❛✉s❛✳ ❊✈✐❛t❛r ❡t ❛❧✳ ❬✶✾✽✷❪ s✉❣✐❡r❡♥ q✉❡ ❧❛ t❛s❛ ❞❡ ♣ér❞✐❞❛ ❞❡ ✐♦♥❡s ❡♥ ❧❛ ♠❛❣♥❡t♦❝♦❧❛ ✐♥❞✉❝✐❞❛ ❡s ❞❡ ❞❡ 3x1027 1024 s−1 ② q✉❡ ❛❞❡♠ás ❛❧r❡❞❡❞♦r át♦♠♦s ② ♠♦❧é❝✉❧❛s ❞❡ ❤✐❞ró❣❡♥♦ ② ❛♣r♦①✐♠❛❞❛♠❡♥t❡ 3x1026 át♦♠♦s ❞❡ ♥✐tró❣❡♥♦ ❡s❝❛♣❛♥ ❞❡ ❚✐tá♥ ❝❛❞❛ s❡❣✉♥❞♦✳ ❊st♦s át♦♠♦s ② ♠♦❧é❝✉❧❛s ❞❡ ❤✐❞ró❣❡♥♦✱ ❛sí ❝♦♠♦ ❞❡ ♥✐tró❣❡♥♦✱ ❡s❝❛♣❛♥ ❤❛❝✐❛ ❧❛ ♠❛❣♥❡tós❢❡r❛ ② ❢♦r♠❛♥ ❡❧ t♦r♦ ❞❡ ❚✐tá♥✱ ✉♥❛ ✈❛st❛ ♥✉❜❡ ❞❡ ❣❛s ♥❡✉tr♦ q✉❡ r♦❞❡❛ ❛ ❙❛t✉r♥♦✳ ❊❧ ❡s♣❡❝tró♠❡tr♦ ✉❧tr❛✈✐♦❧❡t❛ ✭❯❱❙✮ ❞❡❧ ❱♦②❛❣❡r ♦❜s❡r✈ó q✉❡ ❧❛ ♥✉❜❡ ❞❡ ❤✐❞ró❣❡♥♦ ❛tó♠✐❝♦ ❞❡❧ t♦r♦ ❞❡ ❚✐tá♥ s❡ ❡①t✐❡♥❞❡ r❛❞✐❛❧♠❡♥t❡ ❞❡s❞❡ ❧♦s ❛ 20 cm−3 8 RS ❤❛st❛ ❧♦s ✷✺ RS ❝♦♥ ✉♥❛ ❞❡♥s✐❞❛❞ ♣r♦♠❡❞✐♦ ❞❡ 10 cm−3 ❬❙❛♥❞❡❧ ❡t ❛❧✳✱✶✾✽✷❪✳ ❙❤❡♠❛♥s❦② ② ❙♠✐t❤ ❬✶✾✽✸❪ ❤❛♥ s✉❣❡r✐❞♦ q✉❡ ❧❛ ❛t♠ós❢❡r❛ ❞❡ ❙❛t✉r♥♦ ❡s ❧❛ ❢✉❡♥t❡ ❞♦♠✐♥❛♥t❡ ❞❡ ❤✐❞ró❣❡♥♦ ♣❛r❛ ❡❧ t♦r♦ ❞❡ ❚✐tá♥✱ ♣❡r♦ ❘✐❝❤❛r❞s♦♥ ② ❊✈✐❛t❛r ❬✶✾✽✽❪ ❤❛♥ ❝r✐t✐❝❛❞♦ ❡st❛ ✐❞❡❛ ❜❛sá♥❞♦s❡ ❡♥ ❡❧ ❤❡❝❤♦ ❞❡ q✉❡ ✉♥❛ ❛❧t❛ ❞❡♥s✐❞❛❞ ❞❡ ❍ ❡♥ ❧❛ r❡❣✐ó♥ ❞❡ ❉✐♦♥❡✲❚❡t✐s✲❘❡❛ s❡rí❛ ✐♥❝♦♠♣❛t✐❜❧❡ ❝♦♥ ❡❧ ♣❧❛s♠❛ ♦❜s❡r✈❛❞♦ ❛❧❧í✳ ▲❛ ✐♦♥✐③❛❝✐ó♥ ❞❡ ♥❡✉tr♦s ❡♥ ❡❧ t♦r♦ ❞❡ ❚✐tá♥ ❡s ❝❧❛r❛♠❡♥t❡ ✉♥❛ ❢✉❡♥t❡ ✐♠♣♦rt❛♥t❡ ❞❡ ♣❧❛s♠❛ ♣❛r❛ ❧❛ ♠❛❣♥❡tós❢❡r❛✱ ♣❡r♦ ♣✉❡❞❡ s❡r ♥♦ ❞♦♠✐♥❛♥t❡✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✷✳✶✳ ❆♥t❡❝❡❞❡♥t❡s✿ ❘❡s✉❧t❛❞♦s ❞❡ ❧❛ ♠✐s✐ó♥ ❱♦②❛❣❡r ✷✽ ▲♦s ✐♦♥❡s ❡♥❡r❣ét✐❝♦s ♣✉❡❞❡♥ ✐♠♣❛❝t❛r ❛ ❧❛ ❛t♠ós❢❡r❛ ❞❡ ❚✐tá♥ ❞❡ ❞♦♥❞❡ ✏s❛❧✲ ♣✐❝❛rá♥✑ át♦♠♦s ✭♦ ♠♦❧é❝✉❧❛s✮ ♥❡✉tr♦s✳ ▲♦s ♥❡✉tr♦s ♣✉❡❞❡♥ s❡r ❧❛♥③❛❞♦s ❞❡ ❚✐tá♥ ❝♦♠♦ ✉♥ r❡s✉❧t❛❞♦ ❞❡ ❧❛s r❡❛❝❝✐♦♥❡s ❢♦t♦q✉í♠✐❝❛s✳ ❊st❛s r❡❛❝❝✐♦♥❡s ♣✉❡❞❡♥ ❡♥❡r❣✐③❛r ❛ ❛❧❣✉♥♦s ❞❡ ❧♦s ♥❡✉tr♦s ♠ás ❛❧❧á ❞❡ ❧❛ ✈❡❧♦❝✐❞❛❞ ❞❡ ❡s❝❛♣❡ ❞❡ ❚✐tá♥✳ ▲♦s ♥❡✉tr♦s ❧❛♥✲ ③❛❞♦s ❝♦♠❡♥③❛rá♥ ❛ ♦r❜✐t❛r ❙❛t✉r♥♦✱ ♣r♦❞✉❝✐❡♥❞♦ ✉♥ t♦r♦ ♥❡✉tr♦✳ ▲♦s ❝♦♠♣♦♥❡♥t❡s ♣r✐♥❝✐♣❛❧❡s ❞❡ ❡st❡ t♦r♦ s♦♥ ❤✐❞ró❣❡♥♦ ② ♥✐tró❣❡♥♦✳ ❆❧ ❛♥❛❧✐③❛r ❧♦s ❞❛t♦s ❞❡❧ ❡s♣❡❝tró♠❡tr♦ ✉❧tr❛✈✐♦❧❡t❛ ✭❯❱❙✱ ❯❧tr❛✈✐♦❧❡t ❙♣❡❝tr♦✲ ♠❡t❡r ✮ ❛❜♦r❞♦ ❞❡❧ ❱♦②❛❣❡r✱ ❙❤❡♠❛♥s❦② ❛♥❞ ❍❛❧❧ ❬✶✾✾✷❪ ❡♥❝♦♥tr❛r♦♥ q✉❡ ❡❧ t♦r♦ ❞❡ ❤✐❞ró❣❡♥♦ ♥♦ t❡♥í❛ s✐♠❡trí❛ ❛①✐❛❧✱ ♣❡r♦ q✉❡ ♠♦str❛❜❛ ✉♥❛ ❢✉❡rt❡ ❞❡♣❡♥❞❡♥❝✐❛ ❡♥ ❡❧ t✐❡♠♣♦ ❧♦❝❛❧✳ ❊st❛ ❞❡♣❡♥❞❡♥❝✐❛ ❢✉❡ ❞❡♠♦str❛❞❛ ♣♦r ■♣ ❬✶✾✾✻❪ ❝♦♠♦ ❡❧ r❡s✉❧t❛❞♦ ❞❡ ❧❛s ♣❡rt✉r❜❛❝✐♦♥❡s ♦r❜✐t❛❧❡s ❞❡ ❧♦s át♦♠♦s ❞❡ ❤✐❞ró❣❡♥♦ ♣r♦✈♦❝❛❞❛s ♣♦r ❧❛ ♣r❡s✐ó♥ ❞❡ r❛❞✐❛❝✐ó♥ s♦❧❛r q✉❡ ❛❝tú❛ s♦❜r❡ ❡❧ t✐❡♠♣♦ ❞❡ ✐♦♥✐③❛❝✐ó♥ ❞❡ ❡s♦s ♥❡✉tr♦s✳ ▲❛ ♣r❡✲ s✐ó♥ ❞❡ r❛❞✐❛❝✐ó♥ s♦❧❛r ❝❛♠❜✐❛ ❧❛ ór❜✐t❛ ❝✐r❝✉❧❛r ✐♥✐❝✐❛❧ ❞❡ ✉♥ át♦♠♦ ❞❡ ❤✐❞ró❣❡♥♦ ♥❡✉tr♦ ❡♥ ✉♥❛ ór❜✐t❛ ❡❧í♣t✐❝❛ ❝♦♥ ✉♥ ❛♣♦❣❡♦ ❧♦❝❛❧✐③❛❞♦ ❡♥ ❧❛ ❞✐r❡❝❝✐ó♥ ❞❡❧ ❛♠❛♥❡❝❡r✳ ❊st❡ ❡❢❡❝t♦ r❡s✉❧t❛ ❡♥ ✉♥❛ ❝❛✈✐❞❛❞ ❡♥ ❧❛ ❞❡♥s✐❞❛❞ ❡♥ ❡❧ ❧❛❞♦ ❛♠❛♥❡❝❡r ❞❡ ❙❛t✉r♥♦ ② ❡♥ ❝♦♥s❡❝✉❡♥❝✐❛✱ ❡❧ t♦r♦ ❞❡ ❤✐❞ró❣❡♥♦ s❡ ❡①t✐❡♥❞❡ r❛❞✐❛❧♠❡♥t❡ ❤❛❝✐❛ ❛❞❡♥tr♦ ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛✳ ❊❧ t♦r♦ ❞❡ ♥✐tró❣❡♥♦ s❡ ❢♦r♠❛ ❞❡ ♠❛♥❡r❛ s✐♠✐❧❛r✳ ▲❛ ❞✐str✐❜✉❝✐ó♥ ❞❡ ❧❛ ❞❡♥s✐❞❛❞ ❞❡❧ t♦r♦ ❞❡ ♥✐tró❣❡♥♦ ❞❡♣❡♥❞❡ ❢✉❡rt❡♠❡♥t❡ ❞❡ ❧❛ t❛s❛ t♦t❛❧ ❞❡ ❡♠✐s✐ó♥✱ ❞❡ ❧❛ ❞✐str✐✲ ❜✉❝✐ó♥ ✐♥✐❝✐❛❧ ❞❡ ✈❡❧♦❝✐❞❛❞❡s ❞❡ ❧♦s ♥❡✉tr♦s q✉❡ ✢✉②❡♥ ❤❛❝✐❛ ❢✉❡r❛ ② ❞❡ ❧❛ t❛s❛ ❞❡ ✐♦♥✐③❛❝✐ó♥ ❞❡❧ ♥✐tró❣❡♥♦ ♥❡✉tr♦✳ ▲♦s ❝á❧❝✉❧♦s ❞❡ ■♣ ❬✶✾✾✷❪ s✉❣✐❡r❡♥ q✉❡ ❧❛ ❞❡♥s✐❞❛❞ ♣✐❝♦ ❝❡r❝❛ ❞❡ ❧❛ ór❜✐t❛ ❞❡ ❚✐tá♥ ♣✉❡❞❡ ❡st❛r ❡♥tr❡ 10 cm−3 ❞❡ ❧❛s ❝♦♥❞✐❝✐♦♥❡s ✐♥✐❝✐❛❧❡s✳ ❊st❡ ✈❛❧♦r ❝❛❡ ❤❛st❛ ✵✳✶ cm−3 ② 40 cm−3 ❞❡♣❡♥❞✐❡♥❞♦ ❡♥ ❧❛ r❡❣✐ó♥ ❡♥tr❡ ❚❡t✐s ② ❉✐♦♥❡✳ ▲♦s át♦♠♦s ② ♠♦❧é❝✉❧❛s ❡♥ ❡❧ t♦r♦ ♥❡✉tr♦ ❞❡ ❚✐tá♥ ♣✉❡❞❡♥ s❡r ✐♦♥✐③❛❞♦s ② r❡❝♦✲ ❣✐❞♦s ♣♦r ❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❞❡ ❙❛t✉r♥♦✳ ❊st❡ ❡s ❥✉st❛♠❡♥t❡ ✉♥♦ ❞❡ ❧♦s ♣r♦❝❡s♦s q✉❡ ♣✉❡❞❡♥ ♣r♦❞✉❝✐r ✉♥ t♦r♦ ❞❡ ♣❧❛s♠❛ ❛❧r❡❞❡❞♦r ❞❡ ❙❛t✉r♥♦✳ ❖tr♦ ♣r♦❝❡s♦ q✉❡ ❝♦♥✲ tr✐❜✉②❡ ❛❧ t♦r♦ ❞❡ ♣❧❛s♠❛ ❞❡ ❚✐tá♥ ❡s ❡❧ ♠✐s♠♦ s❛té❧✐t❡✳ ▲♦s ♥❡✉tr♦s ♣r❡s❡♥t❡s ❡♥ ❧❛ ❛t♠ós❢❡r❛ ❞❡ ❚✐tá♥ ♣✉❡❞❡♥ s❡r ✐♦♥✐③❛❞♦s ♣♦r ✐♠♣❛❝t♦ ❝♦♥ ❡❧❡❝tr♦♥❡s ♠❛❣♥❡t♦s❢ér✐✲ ❝♦s ♦ ❜✐❡♥ ♣♦r ❢♦t♦♥❡s s♦❧❛r❡s✳ ▲♦s ✐♦♥❡s ❝r❡❛❞♦s ❛ ❛❧t✐t✉❞❡s ❜❛❥❛s ♣✉❡❞❡♥ ✢✉✐r ❤❛❝✐❛ ❧❛ ❡st❡❧❛✱ ♠✐❡♥tr❛s q✉❡ ❧♦s ✐♦♥❡s ❝r❡❛❞♦s ❛ ❛❧t✐t✉❞❡s ❡❧❡✈❛❞❛s s♦♥ r❡❝♦❣✐❞♦s ♣♦r ❡❧ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✷✳✶✳ ❆♥t❡❝❡❞❡♥t❡s✿ ❘❡s✉❧t❛❞♦s ❞❡ ❧❛ ♠✐s✐ó♥ ❱♦②❛❣❡r ✷✾ ♣❧❛s♠❛ ❡①t❡r♥♦ ② ♣♦r ❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦✳ ❊st♦s ♣r♦❝❡s♦s ❝♦♥❞✉❝❡♥ ❛ ❧❛ ❢♦r♠❛❝✐ó♥ ❞❡ ❧❛ ♣❧✉♠❛ ❞❡ ♣❧❛s♠❛ ❞❡ ❚✐tá♥ q✉❡ ❡♥✈✉❡❧✈❡ ❛ ❙❛t✉r♥♦✳ ❉❡ ❤❡❝❤♦ ❝♦♥❢♦r♠❡ ❚✐tá♥ ♦r❜✐t❛ ❛❧r❡❞❡❞♦r ❞❡ ❙❛t✉r♥♦ s❡ ♣✉❡❞❡ ❡♥❝♦♥tr❛r ❝♦♥ ♣❧❛s♠❛ ❞❡ ❡st❛ ♣❧✉♠❛✳ ▲♦s s❛té❧✐t❡s ❞❡ ❤✐❡❧♦ ❆❧❣✉♥♦s ❞❡ ❧♦s s❛té❧✐t❡s ❞❡ ❙❛t✉r♥♦ ✭❈✉❛❞r♦ ✷✳✶ ❤❛st❛ ❈✉❛❞r♦ ✷✳✸✮ t✐❡♥❡♥ ✐♠♣♦r✲ t❛♥t❡s ✐♥t❡r❛❝❝✐♦♥❡s ❝♦♥ ❧❛ ♠❛❣♥❡tós❢❡r❛✳ ▼✐♠❛s✱ ❊♥❝❡❧❛❞♦✱ ❚❡t✐s✱ ❉✐♦♥❡ ② ❘❡❛ s♦♥ s❛té❧✐t❡s ❞❡ ❤✐❡❧♦ ❝✉②♦s r❛❞✐♦s ❛♣❡♥❛s s✉♣❡r❛♥ ❧❛ ♠✐t❛❞ ❞❡❧ r❛❞✐♦ ❞❡ ❧❛ ▲✉♥❛✳ ❊st♦s s❛té❧✐t❡s ❡stá♥ ❡♠❜❡❜✐❞♦s ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛ ❡♥tr❡ ❧♦s ✸ RS ② ❧♦s ✾ RS ♣♦r ❧♦ q✉❡ ❝♦♥st❛♥t❡♠❡♥t❡ ❡stá♥ s✐❡♥❞♦ ❜♦♠❜❛r❞❡❛❞♦s ♣♦r ✐♦♥❡s ❡♥❡r❣ét✐❝♦s✱ ✐♦♥❡s ❝♦rr♦✲ t❛♥t❡s✱ ② r❛❞✐❛❝✐ó♥ s♦❧❛r✱ ❧♦ q✉❡ r❡s✉❧t❛ ❡♥ ❧❛ ✐♥②❡❝❝✐ó♥ ❞❡ ❝♦♥s✐❞❡r❛❜❧❡s ❝❛♥t✐❞❛❞❡s ❞❡ ♣r♦❞✉❝t♦s ♥❡✉tr♦s ❞❡ ❧❛ ❞✐s♦❝✐❛❝✐ó♥ ❞❡❧ H2 O ❞❡♥tr♦ ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛✳ ❆ ❞✐❢❡r❡♥❝✐❛ ❞❡ ❚✐tá♥✱ ❡st♦s s❛té❧✐t❡s ♥♦ t✐❡♥❡♥ ✉♥❛ ❛t♠ós❢❡r❛ ❝♦♥s✐❞❡r❛❜❧❡✳ ▲❛ s✉♣❡r✜❝✐❡ ❞❡ ❡st♦s s❛té❧✐t❡s ✐♥t❡r❛❝tú❛ ❞✐r❡❝t❛♠❡♥t❡ ❝♦♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦✳ ❊❧ ❜♦♠❜❛r❞❡♦ ❞❡ ❧♦s s❛té❧✐t❡s ♣♦r ❧♦s ✐♦♥❡s ♣r❡s❡♥t❡s ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ✏s❛❧♣✐❝❛✑ ❞❡ ♥❡✉tr♦s ② ❞❛❞♦ q✉❡ ❧❛ s✉♣❡r✜❝✐❡ ❞❡ ❡st♦s s❛té❧✐t❡s ❡stá ❢♦r♠❛❞❛ ❜ás✐❝❛♠❡♥t❡ ♣♦r ❤✐❡❧♦ ❞❡ ❛❣✉❛ ❬❈r✉✐❦s❤❛♥❦ ❡t ❛❧✳ ✶✾✽✹❪✱ ❡❧ ♠❛t❡r✐❛❧ ♥❡✉tr♦ s❛❧♣✐❝❛❞♦ ❞❡❜❡rí❛ s❡r ♣r✐♥❝✐♣❛❧♠❡♥t❡ ❛❣✉❛✳ ▲❛ ♠❛②♦rí❛ ❞❡ ❡st♦s ♥❡✉tr♦s t✐❡♥❡♥ ❧❛ s✉✜❝✐❡♥t❡ ❡♥❡r❣í❛ ♣❛r❛ ❡s❝❛♣❛r ❞❡ ❧♦s ❝❛♠♣♦s ❣r❛✈✐t❛❝✐♦♥❛❧❡s ❞❡ ❡st♦s ♣❡q✉❡ñ♦s s❛té❧✐t❡s✱ s✐♥ ❡♠❜❛r❣♦✱ ♥♦ t✐❡♥❡♥ ❧❛ s✉✜❝✐❡♥t❡ ❡♥❡r❣í❛ ♣❛r❛ ❡s❝❛♣❛r ❞❡❧ ❝❛♠♣♦ ❣r❛✈✐t❛❝✐♦♥❛❧ ❞❡ ❙❛t✉r♥♦ ♣♦r ❧♦ q✉❡✱ ❡♥ ♣r♦♠❡❞✐♦✱ ❤❛❝❡♥ ✈❛r✐❛s ór❜✐t❛s ❛❧r❡❞❡❞♦r ❞❡❧ ♣❧❛♥❡t❛ ❛♥t❡s ❞❡ s❡r ✐♦♥✐③❛❞♦s ② r❡❝♦❣✐❞♦s ♣♦r s✉ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦✳ ▲❛ s✉❜s✐❣✉✐❡♥t❡ ✐♦♥✐③❛❝✐ó♥ ✭✈í❛ ❢♦t♦♥❡s✱ ✐♠♣❛❝t♦ ♣♦r ❡❧❡❝tr♦♥❡s ♦ ✐♥t❡r❝❛♠❜✐♦ ❞❡ ❝❛r❣❛✮ ② ❞✐s♦❝✐❛❝✐ó♥ ❞❡ ❡st♦s ♥❡✉tr♦s ♣r♦✈❡❡ ❧❛s ❢✉❡♥t❡s ❞❡ ♣❧❛s♠❛ ♣❛r❛ ❧❛ ♠❛❣♥❡tós✲ ❢❡r❛ ✐♥t❡r♥❛✱ ❛❞❡♠ás ❞❡ q✉❡ ♠❛♥t✐❡♥❡ ✉♥ t♦r♦ ❞❡ ♣❧❛s♠❛ ❞❡ ♦①í❣❡♥♦ ❛tó♠✐❝♦ ✐♦♥✐③❛❞♦ + ✭O ✮ ♦❜s❡r✈❛❞♦ t❛♥t♦ ♣♦r ❡❧ P✐♦♥❡❡r ❝♦♠♦ ♣♦r ❧♦s ❱♦②❛❣❡r✳ ▲❛ ♣r❡s❡♥❝✐❛ ❞❡ ✉♥❛ ♥✉❜❡ ❞❡ ❛❣✉❛ ♥❡✉tr❛ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛ ❤❛ s✐❞♦ ✐♥✲ ❢❡r✐❞❛ ❛ ♣❛rt✐r ❞❡ ❧❛s ♦❜s❡r✈❛❝✐♦♥❡s ❞❡ ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ❞❡ ❜❛❥❛s ❡♥❡r❣í❛s ✭▲❊❈P✮ ❞❡❧ ❱♦②❛❣❡r✳ ❊st❛s ♦❜s❡r✈❛❝✐♦♥❡s s♦♥ ❝♦♥s✐st❡♥t❡s ❝♦♥ ❧♦s ✐♥t❡r❝❛♠❜✐♦s ❞❡ ❝❛r❣❛ ❡♥ ✉♥❛ ♥✉❜❡ ❞❡ ❛❣✉❛ q✉❡ s❡ ❡①t✐❡♥❞❡ ❞❡s❞❡ ❧♦s ✸ ❞❡ ✶✳✺ RS ② ✉♥❛ ❞❡♥s✐❞❛❞ ♣r♦♠❡❞✐♦ ❞❡ RS ❤❛st❛ ❧♦s ✶✶RS ❝♦♥ ✉♥ ❡s♣❡s♦r t♦t❛❧ 20 cm−3 ✱ ♠ás ✐♥t❡r❝❛♠❜✐♦s ❞❡ ❝❛r❣❛ ❡♥ ❧❛ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✷✳✶✳ ❆♥t❡❝❡❞❡♥t❡s✿ ❘❡s✉❧t❛❞♦s ❞❡ ❧❛ ♠✐s✐ó♥ ❱♦②❛❣❡r ✸✵ ❈✉❛❞r♦ ✷✳✶✿ Pr♦♣✐❡❞❛❞❡s ❢✉♥❞❛♠❡♥t❛❧❡s ❞❡ ❧♦s s❛té❧✐t❡s r❡❣✉❧❛r❡s ❞❡ ❙❛t✉r♥♦✳ ❚♦♠❛✲ ❞♦ ❞❡ ▼♦rr✐s♦♥ ❡t ❛❧✳ ❬✶✾✽✻❪ ② ❙❤❡♣♣❛r❞ ❬✷✵✵✼❪✳ Nombre a (km)1 Inicio del anillo D Pan Daphnis Atlas Prometeo Pandora Epimeteo Jano Mimas Methone Pallene Encelado Tethys Telesto Calypso Dione Helene Polydeuces Final del anillo E Rea Titán Hyperion Iapeto 66 000 133 583 136 500 137 670 139 353 141 700 151 422 151 472 185 520 194 000 211 000 238 020 294 660 294 660 294 660 294 660 377 400 377 400 480 000 527 040 1 221 830 1 481 100 3 561 300 e2 i ( ° )3 Masa (kg) Radio (km) Año del descubrimiento Satélites regulares 0.000 0.000 0.000 0.002 0.004 0.021 0.007 0.021 0.000 0.000 0.004 0.000 0.001 0.001 0.000 0.005 0.000 0.000 0.000 0.000 0.000 0.000 0.335 0.165 1.566 0.000 0.000 0.01 0.168 1.158 1.473 0.002 0.212 0.000 ? ? ? 1.4 x 1017 1.3 x 1017 5.5 x 1017 2 x 1018 3.7 x 1019 ? ? 6.5 x 1019 6.1 x 1020 ? ? 1.1 x 1021 ? ? 20 7 32 100 84 119 178 397 3 4 499 24 1060 19 1118 32 4 1981 2005 1980 1980 1980 1980 1980 1789 2004 2004 1789 1980 1684 1980 1684 1980 2004 0.001 0.029 0.018 0.028 0.327 1.634 0.568 7.570 2.3 x 1021 1.34 x 1023 1.71 x 1019 1.6 x 1021 1528 5150 266 1436 1672 1655 1848 1671 1 ❙❡ r❡✜❡r❡ ❛❧ s❡♠✐❡❥❡ ♠❛②♦r ♣r♦♠❡❞✐♦ ❞❡ ❧❛ ór❜✐t❛ ♠❡❞✐❞♦ ❞❡s❞❡ ❡❧ ❝❡♥tr♦ ❞❡❧ ♣❧❛♥❡t❛✳ 2 ❙❡ r❡✜❡r❡ ❛ ❧❛ ✐♥❝❧✐♥❛❝✐ó♥ ♣r♦♠❡❞✐♦ ❞❡ ❧❛ ór❜✐t❛✳ 3 ❙❡ r❡✜❡r❡ ❛ ❧❛ ❡①❝❡♥tr✐❝✐❞❛❞ ♣r♦♠❡❞✐♦ ❞❡ ❧❛ ór❜✐t❛✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✷✳✶✳ ❆♥t❡❝❡❞❡♥t❡s✿ ❘❡s✉❧t❛❞♦s ❞❡ ❧❛ ♠✐s✐ó♥ ❱♦②❛❣❡r ✸✶ ❈✉❛❞r♦ ✷✳✷✿ Pr♦♣✐❡❞❛❞❡s ❢✉♥❞❛♠❡♥t❛❧❡s ❞❡ ❧♦s s❛té❧✐t❡s ✐rr❡❣✉❧❛r❡s ❞❡ ❙❛t✉r♥♦✳ ❚♦✲ ♠❛❞♦ ❞❡ ❙❤❡♣♣❛r❞ ❬✷✵✵✼❪✳ Nombre a (km)1 Kiviuq Ijiraq Phoebe Paaliaq Skathi Albiorix Bebhionn Erriapo Siarnaq Skoll Tarvos Hyrokkin Mundilfari Narvi Bergelmir Suttungr Hati Bestla Farbauti Thrymr Regir Kari Fenrir Surtur Ymir Loge Fornjot 11 111 000 11 124 000 12 952 000 15 200 000 15 541 000 16 182 000 17 119 000 17 343 000 17 531 000 17 665 000 17 983 000 18 437 000 18 685 000 19 007 000 19 338 000 19 459 000 19 856 000 20 129 000 20 390 000 20 474 000 20 735 000 22 118 000 22 453 000 22 707 000 23 040 000 23 065 000 25 108 000 e2 i ( ° )3 Masa (kg) Satélites irregulares 0.334 45.71 ? 0.316 46.44 ? 0.164 174.8 3.98 x 1017 0.364 45.13 ? 0.270 152.6 ? 0.478 33.98 ? 0.469 35.01 ? 0.474 34.62 ? 0.295 45.56 ? 0.464 161.2 ? 0.531 33.82 ? 0.333 151.4 ? 0.210 167.3 ? 0.431 145.8 ? 0.142 158.5 ? 0.114 175.8 ? 0.372 165.8 ? 0.521 145.2 ? 0.206 156.4 ? 0.470 176.0 ? 0.252 166.7 ? 0.478 156.3 ? 0.136 164.9 ? 0.451 177.5 ? 0.335 173.1 ? 0.187 167.9 ? 0.206 170.4 ? Radio (km) Año del descubrimiento 16 12 240 22 8 32 6 10 40 6 15 8 7 7 6 7 6 7 5 7 6 7 4 6 18 6 6 2000 2000 1898 2000 2000 2000 2004 2000 2000 2006 2000 2004 2000 2003 2004 2000 2004 2004 2004 2000 2004 2006 2004 2006 2000 2006 2004 1 ❙❡ r❡✜❡r❡ ❛❧ s❡♠✐❡❥❡ ♠❛②♦r ♣r♦♠❡❞✐♦ ❞❡ ❧❛ ór❜✐t❛ ♠❡❞✐❞♦ ❞❡s❞❡ ❡❧ ❝❡♥tr♦ ❞❡❧ ♣❧❛♥❡t❛✳ 2 ❙❡ r❡✜❡r❡ ❛ ❧❛ ✐♥❝❧✐♥❛❝✐ó♥ ♣r♦♠❡❞✐♦ ❞❡ ❧❛ ór❜✐t❛✳ 3 ❙❡ r❡✜❡r❡ ❛ ❧❛ ❡①❝❡♥tr✐❝✐❞❛❞ ♣r♦♠❡❞✐♦ ❞❡ ❧❛ ór❜✐t❛✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✷✳✶✳ ❆♥t❡❝❡❞❡♥t❡s✿ ❘❡s✉❧t❛❞♦s ❞❡ ❧❛ ♠✐s✐ó♥ ❱♦②❛❣❡r ✸✷ ❈✉❛❞r♦ ✷✳✸✿ ✭❝♦♥t✐♥✉❛❝✐ó♥✮ Pr♦♣✐❡❞❛❞❡s ❢✉♥❞❛♠❡♥t❛❧❡s ❞❡ ❧♦s s❛té❧✐t❡s ✐rr❡❣✉❧❛r❡s ❞❡ ❙❛t✉r♥♦✳ ❚♦♠❛❞♦ ❞❡ ❙❤❡♣♣❛r❞ ❬✷✵✵✼❪✳ Nombre a (km)1 S/2004 S07 S/2004 S12 S/2004 S13 S/2004 S17 S/2006 S1 S/2006 S3 S/2006 S4 S/2006 S6 S/2007 S1 19 800 000 19 650 000 18 450 000 18 600 000 18 981 135 21 132 000 18 105 000 18 600 000 17 960 000 e2 i ( ° )3 Masa (kg) Nuevos satélites irregulares por nombrar 0.580 165.1 ? 0.401 164.0 ? 0.273 167.4 ? 0.259 166.6 ? 0.130 154.2 ? 0.471 150.8 ? 0.374 172.7 ? 0.192 162.9 ? 0.108 49.90 ? Radio (km) Año del descubrimiento 6 5 6 4 6 6 6 6 7 2004 2004 2004 2004 2006 2006 2006 2006 2007 1 ❙❡ r❡✜❡r❡ ❛❧ s❡♠✐❡❥❡ ♠❛②♦r ♣r♦♠❡❞✐♦ ❞❡ ❧❛ ór❜✐t❛ ♠❡❞✐❞♦ ❞❡s❞❡ ❡❧ ❝❡♥tr♦ ❞❡❧ ♣❧❛♥❡t❛✳ 2 ❙❡ r❡✜❡r❡ ❛ ❧❛ ✐♥❝❧✐♥❛❝✐ó♥ ♣r♦♠❡❞✐♦ ❞❡ ❧❛ ór❜✐t❛✳ 3 ❙❡ r❡✜❡r❡ ❛ ❧❛ ❡①❝❡♥tr✐❝✐❞❛❞ ♣r♦♠❡❞✐♦ ❞❡ ❧❛ ór❜✐t❛✳ ♥✉❜❡ ❞❡ ❤✐❞ró❣❡♥♦ ❛tó♠✐❝♦ ✭t♦r♦ ❞❡ ❚✐tá♥✮ ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛✳ ❊st❛s ♠✐s✲ ♠❛s ♦❜s❡r✈❛❝✐♦♥❡s ♣✉❡❞❡♥ s❡r ❡①♣❧✐❝❛❞❛s s✐ ❡❧ ❤✐❞ró❣❡♥♦ ♠♦❧❡❝✉❧❛r ❝♦♥ ✉♥❛ ❞❡♥s✐❞❛❞ ❞❡ ∼ 10 cm−3 ❛ 20 cm−3 ❡stá ♣r❡s❡♥t❡ ❥✉♥t♦ ❝♦♥ ❡❧ ❤✐❞ró❣❡♥♦ ❛tó♠✐❝♦ ❡♥ ❡❧ t♦r♦ ❞❡ ❚✐tá♥✳ ▲♦s r❡s✉❧t❛❞♦s ❞❡❧ ♠♦❞❡❧♦ ❞❡ ❏♦❤♥s♦♥ ❡t ❛❧✳ ❬✶✾✽✾❪ ♠✉❡str❛♥ q✉❡ ❧❛s ❞❡♥s✐❞❛❞❡s ❞❡ ❧❛ ♥✉❜❡ ♥❡✉tr❛ ❞❡ ❛❣✉❛ t✐❡♥❡ ✉♥ ♣✐❝♦ ❛❧r❡❞❡❞♦r ❞❡ ❧❛ ♣♦s✐❝✐ó♥ ♦r❜✐t❛❧ ❞❡ ❧♦s s❛té❧✐t❡s ② q✉❡ ❡stá ❝♦♥✜♥❛❞❛ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ❛❧ ♣❧❛♥♦ ♦r❜✐t❛❧✳ ❉❛❞❛ ❡st❛ ❝♦♥✜❣✉r❛❝✐ó♥✱ ❧♦s s❛té❧✐t❡s ❞❡❜❡rí❛♥ ✐♥t❡r❛❝t✉❛r ❝♦♥ s✉ r❡s♣❡❝t✐✈♦ t♦r♦ ♥❡✉tr♦✱ r❡❛❜s♦r❜✐❡♥❞♦ ❛❧❣✉♥♦s ❞❡ ❧♦s ♥❡✉tr♦s✳ ❆❞❡♠ás ❡st❛ ♥✉❜❡ ♥❡✉tr❛ ❡①❤✐❜❡ ❧♦s s✐❣✉✐❡♥t❡s ❡❢❡❝t♦s✳ Pr✐♠❡r♦✱ ❡s ❧❛ ❢✉❡♥t❡ ❞❡ ✐♦♥❡s ♣❡s❛❞♦s ❡♥ ❡❧ ♣❧❛♥♦ ♦r❜✐t❛❧ ❞❡ ❧♦s s❛té❧✐t❡s ②✱ ♣♦r ❧♦ t❛♥t♦✱ s❡ ♣✉❡❞❡ ♣❡♥s❛r q✉❡ ♣♦s❡❡ ✉♥❛ ✐♦♥ós❢❡r❛✳ ❙❡❣✉♥❞♦✱ ❧♦s ✐♦♥❡s rá♣✐❞♦s ❞❡ ❧♦s ❝✐♥t✉r♦♥❡s ❞❡ r❛❞✐❛❝✐ó♥ ♣✉❡❞❡♥ ❡①♣❡r✐♠❡♥t❛r r❡❛❝❝✐♦♥❡s ❞❡ ✐♥t❡r❝❛♠❜✐♦ ❞❡ ❝❛r❣❛ ② ❝♦♥✈❡rt✐rs❡ ❡♥ ♥❡✉tr♦s rá♣✐❞♦s q✉❡ ❡s❝❛♣❡♥ ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛✳ P♦st❡r✐♦r♠❡♥t❡ ❧❛ ♥✉❜❡ ♥❡✉tr❛ ❡s ✐♦♥✐③❛❞❛ ② ❞✐s♦❝✐❛❞❛ ♣❛r❛ ♠❛♥t❡♥❡r ✉♥ t♦r♦ ❞❡ ♣❧❛s♠❛ ✐♥t❡r♥♦ ❞❡ ✐♦♥❡s ❞❡ ♦①í❣❡♥♦ q✉❡ ❢✉❡ ♦❜s❡r✈❛❞❛ t❛♥t♦ ♣♦r ❡❧ P✐♦♥❡❡r ✶✶ ❝♦♠♦ ♣♦r ❧♦s ❱♦②❛❣❡r✳ ❈♦♠♦ ❧❛s ❞❡♥s✐❞❛❞❡s ❡♥ ❡❧ t♦r♦ ♥❡✉tr♦✱ ❧❛s ❞❡♥s✐❞❛❞❡s ❞❡ ❧♦s ✐♦♥❡s ❞❡ ❛❣✉❛ ❡①❤✐❜❡♥ ✉♥ ♣✐❝♦ ❛❧r❡❞❡❞♦r ❞❡ ❧❛s ♣♦s✐❝✐♦♥❡s ♦r❜✐t❛❧❡s ❞❡ ❧♦s s❛té❧✐t❡s✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✷✳✶✳ ❆♥t❡❝❡❞❡♥t❡s✿ ❘❡s✉❧t❛❞♦s ❞❡ ❧❛ ♠✐s✐ó♥ ❱♦②❛❣❡r ✸✸ ❏♦❤♥s♦♥ ❡t ❛❧✳ ❬✶✾✽✾❪ ❝♦♥❝❧✉②❡r♦♥ ❞❡ s✉s ♠♦❞❡❧♦s q✉❡ ❧♦s ✐♦♥❡s q✉❡ ♣r♦✈✐❡♥❡♥ ❞❡ ❧♦s s❛té❧✐t❡s ❞❡ ❤✐❡❧♦ ♥♦ s♦♥ ❞❡❧ t♦❞♦ t♦♠❛❞♦s ❡♥ ❝✉❡♥t❛ ♣❛r❛ ❧❛ ❞❡♥s✐❞❛❞ ♦❜s❡r✈❛❞❛ ❡♥ ❧❛s r❡❣✐♦♥❡s ✐♥t❡r♥❛s ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛✳ ❊❧❧♦s ✐♥✜❡r❡♥ q✉❡ ✉♥❛ ❢✉❡♥t❡ ❛❞✐❝✐♦♥❛❧ ❞❡ ♥❡✉tr♦s ❡s ♥❡❝❡s❛r✐❛ ❡♥ ❧❛ r❡❣✐ó♥ ♣❛r❛ ❝♦♥s✐❞❡r❛r ❡st❛ ❞✐❢❡r❡♥❝✐❛✱ ♣♦s✐❜❧❡♠❡♥t❡ ❧❛ ❡r♦s✐ó♥ ❞❡ ❧♦s ❛♥✐❧❧♦s✳ ❊♥ ❡st❡ s❡♥t✐❞♦ ❧♦s r❡s✉❧t❛❞♦s ❞❡❧ ♠♦❞❡❧♦ ❞❡ P♦s♣✐❡s③❛❧s❦❛ ② ❏♦❤♥s♦♥ ❬✶✾✾✶❪ ✐♥❞✐❝❛♥ q✉❡ ❧❛ ❡r♦s✐ó♥ ♣♦r ♠✐❝r♦♠❡t❡♦r✐t♦s ❞❡ ❧♦s ❛♥✐❧❧♦s ♣r✐♥❝✐♣❛❧❡s ♣✉❡❞❡ ✐♥❝r❡♠❡♥t❛r ❧❛ ❞❡♥s✐❞❛❞ ❞❡ ♥❡✉tr♦s ❡♥ ❧❛ r❡❣✐ó♥ ❡♥tr❡ ✷✳✸ RS < r < ✹ RS ♣♦r ❞♦s ór❞❡♥❡s ❞❡ ♠❛❣♥✐t✉❞ s✉♣❡r✐♦r ❛ ❧❛ ❝♦♥tr✐❜✉❝✐ó♥ ❞❡ ❧♦s s❛té❧✐t❡s ❞❡ ❤✐❡❧♦✳ ▲♦s ❛♥✐❧❧♦s ❊❧ s✐st❡♠❛ ❞❡ ❛♥✐❧❧♦s ❞❡ ❙❛t✉r♥♦ t✐❡♥❡ ✉♥ ❞✐á♠❡tr♦ ❞❡ 270 000km ✭❡st♦ ❡s✱ ❝✉❜r❡♥ ✉♥❛ ❞✐st❛♥❝✐❛ r❛❞✐❛❧ q✉❡ s❡ ❡①t✐❡♥❞❡ ❞❡s❞❡ ✶✳✶✶ RS ❤❛st❛ ✽ RS ✮ ② s✉ ❡s♣❡s♦r ✈❛rí❛ ❞❡s❞❡ ✉♥♦s 5 ♠❡tr♦s ❤❛st❛ ❧♦s 107 ♠❡tr♦s ❡♥ ❡❧ ❛♥✐❧❧♦ ❊✳ ▲❛ ♠❛s❛ t♦t❛❧ ❡s ❛♣r♦①✐✲ ♠❛❞❛♠❡♥t❡ ❞❡ 3x1022 g✳ s✐♠✐❧❛r ❛ ❧❛ ♠❛s❛ ❞❡ ▼✐♠❛s ❬❩❡❜❦❡r ❛♥❞ ❚②❧❡r✱ ✶✾✽✹❪✳ ▲❛ ❡str✉❝t✉r❛ ❞❡❧ s✐st❡♠❛ ❞❡ ❛♥✐❧❧♦s s❡ r❡s✉♠❡ ❡♥ ❡❧ ❈✉❛❞r♦ ✷✳✹ ② ❡♥ ❡❧ ❈✉❛❞r♦ ✷✳✺✳ ▲♦s ❛♥✐❧❧♦s s❡ ❝❧❛s✐✜❝❛♥ ❡♥ ❞♦s ❝❛t❡❣♦rí❛s✱ ❞❡♣❡♥❞✐❡♥❞♦ ❞❡ ❧❛ ♣r♦❢✉♥❞✐❞❛❞ ó♣t✐❝❛ ♣r♦♠❡❞✐♦✳ ❊❧ ❧❧❛♠❛❞♦ s✐st❡♠❛ ❝❧ás✐❝♦ ❝♦♥s✐st❡ ❞❡ ❧♦s ❛♥✐❧❧♦s ❜r✐❧❧❛♥t❡s ❆ ② ❇ ✭q✉❡ ❡stá♥ s❡♣❛r❛❞♦s ♣♦r ❧❛ ❉✐✈✐s✐ó♥ ❞❡ ❈❛ss✐♥✐✮ ② ✉♥ ❛♥✐❧❧♦ ❈ ♠ás t❡♥✉❡ q✉❡ ♦❝✉♣❛♥ ❧❛ r❡❣✐ó♥ ❡♥tr❡ ✶✳✷✸ RS ② ✷✳✻✼ RS ❡♥ ❡❧ ♣❧❛♥♦ ❡❝✉❛t♦r✐❛❧ ❞❡ ❙❛t✉r♥♦✳ ❊❧ s✐st❡♠❛ ❝❧ás✐❝♦ ❞❡ ❛♥✐❧❧♦s r❡s✐❞❡ ❞❡♥tr♦ ♦ ❝❡r❝❛ ❞❡❧ ❧í♠✐t❡ ❞❡ ❘♦❝❤❡ ② t✐❡♥❡ ✉♥❛ ♣r♦❢✉♥❞✐❞❛❞ ó♣t✐❝❛ ❞❡ ✵✳✶ < τ 1 ❡stá♥ ❞♦♠✐♥❛❞♦s ♣♦r ❧❛ ❢✉❡r③❛ ❞❡ ❣r❛✈❡❞❛❞✱ ♠✐❡♥tr❛s q✉❡ ❧♦s ❣r❛♥♦s ❝♦♥ aµ < 1 ❡stá♥ ❞♦♠✐♥❛❞♦s ♣♦r ❢✉❡r③❛s ❡❧❡❝tr♦♠❛❣♥ét✐❝❛s✳ ✸✳✶✳✶✳✶✳ ▲❛ ❛❝❡❧❡r❛❝✐ó♥ ❡st♦❝ást✐❝❛ ❊❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❞❡♥tr♦ ❞❡ ✉♥❛ ♠❛❣♥❡tós❢❡r❛ ♣❧❛♥❡t❛r✐❛ ♣✉❡❞❡ s❡r ❞✐✈✐❞✐❞♦ ❡♥ ❞♦s ❝♦♠♣♦♥❡♥t❡s✿ Bf ❡s ❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❝♦♥st❛♥t❡ ❣❡♥❡r❛❞♦ ♣♦r ❡❧ ❞✐♥❛♠♦ ♣❧❛♥❡t❛r✐♦ ✭❣❡♥❡r❛❧♠❡♥t❡ ❡s ♠✉② ✐♥t❡♥s♦✮ ② Be s♦♥ ❧❛s ✢✉❝t✉❛❝✐♦♥❡s t❡♠♣♦r❛❧❡s ❞❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ✭❣❡♥❡r❛❧♠❡♥t❡ s♦♥ ❡st♦❝ást✐❝❛s ② ♣♦❝♦ ✐♥t❡♥s❛s✮✳ ▲❛ ♣r✐♠❡r❛ ❝♦♠♣♦♥❡♥t❡ ❝♦rr❡s♣♦♥❞❡ ❛❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ♣❧❛♥❡t❛r✐♦ ② ❧❛ s❡❣✉♥❞❛ ❡s ❣❡♥❡r❛❞❛ ♣♦r ❧♦s ❝❛♠❜✐♦s t❡♠♣♦r❛❧❡s ❡♥ ❧❛ ✐♥t❡r❛❝❝✐ó♥ ❡♥tr❡ ❡❧ ✈✐❡♥t♦ s♦❧❛r ② ❧❛ ♠❛❣♥❡tós❢❡r❛ ② q✉❡ ♣♦r ❧♦ t❛♥t♦ ✐♥❝❧✉②❡ ❧♦s ❝❛♠❜✐♦s ❡♥ ❡❧ s✐st❡♠❛ ❞❡ ❝♦rr✐❡♥t❡s ♠❛❣♥❡t♦s❢ér✐❝♦✿ ❡❧ ❛♥✐❧❧♦ ❞❡ ❝♦rr✐❡♥t❡ ❢♦r♠❛❞♦ ♣♦r ♣❧❛s♠❛ ❛tr❛♣❛❞♦ ❛❧r❡❞❡❞♦r ❞❡❧ ♣❧❛♥❡t❛✱ ❧❛ ❝♦rr✐❡♥t❡ ❞❡ ❧❛ ♠❛❣♥❡t♦♣❛✉s❛ q✉❡ ❝♦♥✜♥❛ ❛ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❛ ✉♥❛ ❝❛✈✐❞❛❞ ❡♥ ❡❧ ✈✐❡♥t♦ s♦❧❛r ✭❡s ✉♥❛ ❝♦rr✐❡♥t❡ q✉❡ ✢✉②❡ s♦❜r❡ ❧❛ s✉♣❡r✜❝✐❡ ❞❡ ❞✐❝❤❛ ❝❛✈✐❞❛❞✮✱ ❧❛s ❝♦rr✐❡♥t❡s ❞❡ ❧❛ ♠❛❣♥❡t♦❝♦❧❛✱ ❧❛s ❝♦♥tr✐❜✉❝✐♦♥❡s ❞❡ ❧❛ ❤♦❥❛ ❞❡ ❝♦rr✐❡♥t❡ ② ❧❛s ❝♦rr✐❡♥t❡s ❛❧✐♥❡❛❞❛s ❛❧ ❝❛♠♣♦ q✉❡ ✢✉②❡♥ ❛ ❧♦ ❧❛r❣♦ ❞❡ ❧❛s ❧í♥❡❛s q✉❡ ✉♥❡♥ ❛ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❝♦♥ ❧❛ ✐♦♥♦s❢❡r❛✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✸✳✶✳ ▼♦❞❡❧♦ ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ♣❛r❛ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ✺✵ ❆ tr❛✈és ❞❡ ❧❛ ▲❡② ❞❡ ❋❛r❛❞❛② ❡st❛s ✢✉❝t✉❛❝✐♦♥❡s ❞❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❣❡♥❡r❛♥ ✉♥ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❡st♦❝ást✐❝♦✱ Estoc ✱ q✉❡ ♣♦❞rá ✐♥t❡r❛❝t✉❛r ❝♦♥ ❧❛s ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ❡①✐st❡♥t❡s ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛✳ P❛r❛ s✐♠✉❧❛r ❡❧ ❝❛rá❝t❡r ❡st♦❝ást✐❝♦ ❞❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦✱ ∆E ✱ s❡ ❡♠♣❧❡❛ ✉♥ ♠é✲ t♦❞♦ ❞❡ ▼♦♥t❡ ❈❛r❧♦ ❬❘✉❜✐♥st❡✐♥✱ ✶✾✽✶❪✳ ▼ét♦❞♦s ❞❡ ▼♦♥t❡ ❈❛r❧♦ ▲♦s ♠ét♦❞♦s ❞❡ ▼♦♥t❡ ❈❛r❧♦ s♦♥ ✉♥❛ ❝❧❛s❡ ❞❡ ❛❧❣♦r✐t♠♦s ❝♦♠♣✉t❛❝✐♦♥❛❧❡s ❛♠✲ ♣❧✐❛♠❡♥t❡ ✉t✐❧✐③❛❞♦s ♣❛r❛ s✐♠✉❧❛r ❡❧ ❝♦♠♣♦rt❛♠✐❡♥t♦ ❞❡ ✈❛r✐♦s s✐st❡♠❛s ❢ís✐❝♦s ② ♠❛t❡♠át✐❝♦s✱ ② t❛♠❜✐é♥ ♣❛r❛ ♦tr♦s ❝á❧❝✉❧♦s✳ ❙❡ ❞✐st✐♥❣✉❡♥ ❞❡ ♦tr♦s ♠ét♦❞♦s ❞❡ s✐✲ ♠✉❧❛❝✐ó♥ ✭t❛❧❡s ❝♦♠♦ ❧❛ ❞✐♥á♠✐❝❛ ♠♦❧❡❝✉❧❛r✮ ♣♦r s❡r ❡st♦❝ást✐❝♦s✱ ❡st♦ ❡s✱ ❞❡ ❛❧❣✉♥❛ ♠❛♥❡r❛ s♦♥ ♥♦✲❞❡t❡r♠✐♥íst✐❝♦s ❛❧ ❡♠♣❧❡❛r ♥ú♠❡r♦s ❛❧❡❛t♦r✐♦s ✭♦ ♣s❡✉❞♦❛❧❡❛t♦r✐♦s✮✳ ❉❡❜✐❞♦ ❛ ❧❛ r❡♣❡t✐❝✐ó♥ ❞❡ ❛❧❣♦r✐t♠♦s ② ❡❧ ❣r❛♥ ♥ú♠❡r♦ ❞❡ ❝á❧❝✉❧♦s ✐♥✈♦❧✉❝r❛❞♦s✱ ▼♦♥t❡ ❈❛r❧♦ ❡s ✉♥ ♠ét♦❞♦ q✉❡ r❡q✉✐❡r❡ ❞❡ ❞✐✈❡rs❛s té❝♥✐❝❛s ❞❡ s✐♠✉❧❛❝✐ó♥ ❝♦♠♣✉✲ t❛❝✐♦♥❛❧❡s✳ ❊s ❛sí ❝♦♠♦ ❡st♦s ♠ét♦❞♦s ❡st❛❞íst✐❝♦s ❞❛♥ s♦❧✉❝✐ó♥ ❛ ✉♥❛ ❣r❛♥ ✈❛r✐❡❞❛❞ ❞❡ ♣r♦❜❧❡♠❛s ♠❛t❡♠át✐❝♦s ✭✐♥❝❧✉s✐✈❡ ♣✉❡❞❡♥ s❡r ❞❡ ♠✉❝❤❛s ✈❛r✐❛❜❧❡s✮ q✉❡ ♥♦ ♣✉❡❞❡♥ s❡r ❢á❝✐❧♠❡♥t❡ r❡s✉❡❧t♦s✱ ♣♦r ❡❥❡♠♣❧♦✱ ♠❡❞✐❛♥t❡ ❡❧ ❝á❧❝✉❧♦ ✐♥t❡❣r❛❧ ♦ ♣♦r ♠ét♦❞♦s ♥✉♠ér✐❝♦s✳ ▲❛ ✐❞❡❛ ❜ás✐❝❛ ❡♥ ❝✉❛❧q✉✐❡r ♠ét♦❞♦ ❞❡ ▼♦♥t❡ ❈❛r❧♦✱ ♦ ♠ét♦❞♦ ❡st❛❞íst✐❝♦✱ ❛♣❧✐❝❛✲ ❞♦ ❛ ✉♥ s✐st❡♠❛ ❛r❜✐tr❛r✐♦ ❡s s❡❧❡❝❝✐♦♥❛r ✉♥❛ ♠✉❡str❛ ❛❧ ❛③❛r ❛ ♣❛rt✐r ❞❡ ❧❛s ❢✉♥❝✐♦♥❡s ❞❡ ❞✐str✐❜✉❝✐ó♥ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞ ❝♦♥♦❝✐❞❛s ❝♦♠♦ ♣❞❢✱ f (∆E)✱ ♦ ❜✐❡♥ ❞❡ ❧❛s ❢✉♥❝✐♦♥❡s ❞❡ ❞✐str✐❜✉❝✐ó♥ ❛❝✉♠✉❧❛❞❛ ❝♦♥♦❝✐❞❛s ❝♦♠♦ ❝❞❢✱ F (∆E)✱ q✉❡ ❞❡s❝r✐❜❡♥ ❧❛ ❡✈♦❧✉❝✐ó♥ ❞❡ ❞✐❝❤♦ s✐st❡♠❛✳ P❛r❛ ❡st♦ ♥❡❝❡s✐t❛ ✉♥❛ ♠❛♥❡r❛ rá♣✐❞❛ ② ❡❢❡❝t✐✈❛ ❞❡ ❣❡♥❡r❛r ♥ú♠❡r♦s ❛❧❡❛t♦r✐♦s ξ ✉♥✐❢♦r♠❡♠❡♥t❡ ❞✐str✐❜✉✐❞♦s s♦❜r❡ ❡❧ ✐♥t❡r✈❛❧♦ [0, 1]✶ ✳ ▲✉❡❣♦ ❞❡ q✉❡ s❡ ❤❛ ❡s❝♦❣✐❞♦ ❛❧ ✶ ❊①✐st❡♥ ✉♥ ❣r❛♥ ♥ú♠❡r♦ ❞❡ ♠ét♦❞♦s ♣❛r❛ ❣❡♥❡r❛r ♥ú♠❡r♦s ❝♦♥ ❞✐str✐❜✉❝✐ó♥ ✉♥✐❢♦r♠❡ s♦❜r❡ ❡❧ ✐♥t❡r✈❛❧♦ [0, 1] .▲❛s ❢♦r♠❛s ♠ás ❝♦♠✉♥❡s ❞❡ ❣❡♥❡r❛r❧♦s s♦♥✿ ✉t✐❧✐③❛♥❞♦ t❛❜❧❛s ❞❡ ♥ú♠❡r♦s ❛❧❡❛t♦r✐♦s ✭❡♥ ❧❛ ♠❛②♦rí❛ ❞❡ ❧♦s t❡①t♦s ❞❡ ❡st❛❞íst✐❝❛ ❧❡s ❧❧❛♠❛♥ ♣s❡✉❞♦❛❧❡❛t♦r✐♦s✮❀ ✉t✐❧✐③❛♥❞♦ ❝❛❧❝✉❧❛❞♦r❛s q✉❡ ❧♦s ❣❡♥❡r❡♥ ♠❡❞✐❛♥t❡ ✉♥❛ ❢✉♥❝✐ó♥ ②❛ ❡st❛❜❧❡❝✐❞❛ ❡♥ s✉ ♠❡♠♦r✐❛❀ ❧♦s ❧❡♥❣✉❛❥❡s ❞❡ ♣r♦❣r❛♠❛❝✐ó♥ ② ❧❛s ❤♦❥❛s ❡❧❡❝tró♥✐❝❛s ✐♥❝❧✉②❡♥ ✉♥❛ ❢✉♥❝✐ó♥ ❡s♣❡❝í✜❝❛ ♣❛r❛ ❣❡♥❡r❛r❧♦s❀ ✉t✐❧✐③❛♥❞♦ ●❡♥❡r❛❞♦r❡s ❈♦♥❣r✉❡♥❝✐❛❧❡s✳ ❊❧ ♠ét♦❞♦ ❛ ✉t✐❧✐③❛r✱ ❡♥ sí ♠✐s♠♦✱ ❝❛r❡❝❡ ❞❡ ✐♠♣♦rt❛♥❝✐❛✳ ▲❛ ✐♠♣♦rt❛♥❝✐❛ r❛❞✐❝❛ ❡♥ ❧♦s ♥ú♠❡✲ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✸✳✶✳ ▼♦❞❡❧♦ ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ♣❛r❛ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ✺✶ ❣❡♥❡r❛❞♦r ❞❡ ♥ú♠❡r♦s ❛❧❡❛t♦r✐♦s✱ s❡ ❤❛❝❡ ❧❛ tr❛♥s❢♦r♠❛❝✐ó♥ ♠❛t❡♠át✐❝❛ ❞❡ ❧❛s ❢✉♥✲ ❝✐♦♥❡s ❞❡ ❞❡♥s✐❞❛❞ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞✳ ❊♥ ❡st❡ ♣❛s♦✱ ❧❛ tr❛♥s❢♦r♠❛❝✐ó♥ ❞❡❜❡ ❝♦♥s❡r✈❛r ❧❛ ♣r♦❜❛❜✐❧✐❞❛❞ ❞❡ ❛♠❜❛s ❞✐str✐❜✉❝✐♦♥❡s✱ ❡st♦ ❡s✱ f (∆E) = ξ ✳ ❊♥ ♦tr❛s ♣❛❧❛❜r❛s✱ ❡st♦ s✐❣♥✐✜❝❛ q✉❡ ❧♦s ♥ú♠❡r♦s ❛❧❡❛t♦r✐♦s ②❛ ❣❡♥❡r❛❞♦s ❝♦♥ ❞✐str✐❜✉❝✐ó♥ ✉♥✐❢♦r♠❡ s♦♥ tr❛♥s❢♦r♠❛❞♦s ❡♥ ❧❛ ❞✐str✐❜✉❝✐ó♥ ❞❡s❡❛❞❛✳ ❊♥ ❡st❡ ♣✉♥t♦ s❡ ❜✉s❝❛ ❧❛ ❢✉♥❝✐ó♥ ❞❡ ❞✐s✲ tr✐❜✉❝✐ó♥ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞ q✉❡ ♠❡❥♦r s❡ ❛❥✉st❛ ❛ ❧♦s ❞❛t♦s ❞❡ ❝❛♠♣♦ ❡❧é❝tr✐❝♦✳ ▲❛ ♠❛♥❡r❛ ❞❡ ❤❛❝❡r❧♦ ✲❡st❛❞íst✐❝❛♠❡♥t❡ ❝♦rr❡❝t♦✲ ❡s ❛ tr❛✈és ❞❡ ✉♥❛ t❡s✐s ❞❡ ❜♦♥❞❛❞ ❞❡ ❛❥✉st❡ ♣r✉❡❜❛ ❞❡ ❤✐♣ó✲ ❬❘♦❤❛t❣✐✱ ✷✵✵✸❪ ❜❛s❛❞❛ ❡♥ ❝✉❛❧q✉✐❡r❛ ❞❡ ❧♦s ❡st❛❞íst✐❝♦s ✭♣♦r ❡❥❡♠♣❧♦✱ ❏❛rq✉❡✲❇❡r❛✱ ❆♥❞❡rs♦♥✲❉❛r❧✐♥❣✱ ❑♦❧♠♦❣♦r♦✈✲❙♠✐r♥♦✈✱ χ2 ✮ ② ❝♦♥s✐❞❡✲ r❛♥❞♦ ❞✐❢❡r❡♥t❡s ❞✐str✐❜✉❝✐♦♥❡s ❤✐♣♦tét✐❝❛s ✭✉♥✐❢♦r♠❡✱ ❡①♣♦♥❡♥❝✐❛❧✱ ♥♦r♠❛❧✱ ❧♦❣íst✐❝❛✱ ❲❡✐❜✉❧❧ ♦ ✉♥❛ ❝♦♠❜✐♥❛❝✐ó♥ ❞❡ ❡❧❧♦s✮✳ ❉❡ ❡st❛ ♠❛♥❡r❛ s❡ ♦❜t✐❡♥❡♥ ❧❛s ❢✉♥❝✐♦♥❡s ♠❛✲ t❡♠át✐❝❛s q✉❡ ❞❡s❝r✐❜❡♥ ❛❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ∆E ❡♥ ❝❛❞❛ ❞✐r❡❝❝✐ó♥ ❡s♣❛❝✐❛❧✿ f (∆Ex )✱ f (∆Ey ) ② f (∆Ez )✳ ▲♦s r❡s✉❧t❛❞♦s ❞❡ ❡st❛s ♠✉❡str❛s ❞❡❜❡♥ ❡st❛r ♦r❞❡♥❛❞♦s ❡♥ ✉♥❛ ♠❛♥❡r❛ ❛♣r♦✲ ♣✐❛❞❛ ♣❛r❛ ♣r♦❞✉❝✐r ✉♥❛ ❞✐str✐❜✉❝✐ó♥ ❞❛❞❛ ♣♦r ∆E = f −1 (ξ)✱ ♣❡r♦ ❧❛ ❝❛r❛❝t❡ríst✐❝❛ ❡s❡♥❝✐❛❧ ❞❡ ▼♦♥t❡ ❈❛r❧♦ ❡s ❡❧ ✉s♦ ❞❡ té❝♥✐❝❛s ❞❡ ♠✉❡str❡♦ ❛❧❡❛t♦r✐♦✷ ✭♦ q✉✐③ás ❞❡ ♦tr❛ á❧❣❡❜r❛ q✉❡ ♣❡r♠✐t❛ ♠❛♥✐♣✉❧❛r ❧♦s r❡s✉❧t❛❞♦s✮✳ ▲❛ r❡❣❧❛ ❞❡ ♠✉❡str❡♦ s❡ ❡❧✐❣❡ ❡♥tr❡ ❧❛s s✐❣✉✐❡♥t❡s ❝❛t❡❣♦rí❛s✿ ❣❡♥❡r❛❞♦r ❞❡ ♥ú♠❡r♦s ❛❧❡❛t♦r✐♦s ✭♣❛r❛ ✉♥❛ ♣❞❢ ✉♥✐❢♦r♠❡✮✱ r♦s q✉❡ ❣❡♥❡r❛ ②❛ q✉❡ ést♦s ❞❡❜❡♥ ❝✉♠♣❧✐r ❝✐❡rt❛s ❝❛r❛❝t❡ríst✐❝❛s ♣❛r❛ q✉❡ s❡❛♥ ✈á❧✐❞♦s✳ ❊st❛s ❝❛r❛❝t❡ríst✐❝❛s s♦♥✿ ✶✳ ❯♥✐❢♦r♠❡♠❡♥t❡ ❞✐str✐❜✉✐❞♦s✳ ✷✳ ❊st❛❞íst✐❝❛♠❡♥t❡ ✐♥❞❡♣❡♥❞✐❡♥t❡s✳ ✸✳ ❙✉ ♠❡❞✐❛ ❞❡❜❡ s❡r ❡st❛❞íst✐❝❛♠❡♥t❡ ✐❣✉❛❧ ❛ 12 ✳ ✹✳ ❙✉ ✈❛r✐❛♥③❛ ❞❡❜❡ s❡r ❡st❛❞íst✐❝❛♠❡♥t❡ ✐❣✉❛❧ ❛ 1 12 ✳ ✺✳ ❙✉ ♣❡r✐♦❞♦ ♦ ❝✐❝❧♦ ❞❡ ✈✐❞❛ ❞❡❜❡ s❡r ❧❛r❣♦✳ ✻✳ ❉❡❜❡♥ s❡r ❣❡♥❡r❛❞♦s ❛ tr❛✈és ❞❡ ✉♥ ♠ét♦❞♦ rá♣✐❞♦ ② q✉❡ ♥♦ r❡q✉✐❡r❛ ❞❡ ♠✉❝❤❛ ❝❛♣❛❝✐❞❛❞ ❞❡ ❛❧♠❛❝❡♥❛♠✐❡♥t♦ ❡♥ ✉♥❛ ❝♦♠♣✉t❛❞♦r❛✳ ✷ ▲♦s ♠ét♦❞♦s ❞❡ ♠✉❡str❡♦ s❡ ❝❧❛s✐✜❝❛♥ ❡♥ ❞♦s t✐♣♦s✿ ♣r♦❜❛❜✐❧íst✐❝♦s ② ♥♦ ♣r♦❜❛❜✐❧íst✐❝♦s✳ ❊♥ ❧❛s ♠✉❡str❛s ♣r♦❜❛❜✐❧íst✐❝❛s✱ ❝❛❞❛ ♠✐❡♠❜r♦ ❞❡ ❧❛ ♣♦❜❧❛❝✐ó♥ t✐❡♥❡ ✉♥❛ ♣r♦❜❛❜✐❧✐❞❛❞ ❞✐st✐♥t❛ ❞❡ ❝❡r♦ ❞❡ s❡r ❡s❝♦❣✐❞❛✳ ▲♦s ♠ét♦❞♦s ♣r♦❜❛❜✐❧íst✐❝♦s ✐♥❝❧✉②❡♥ ❡❧ ♠✉❡str❡♦ ❛❧❡❛t♦r✐♦✱ ❡❧ ♠✉❡str❡♦ s✐st❡♠át✐❝♦✱ ❡❧ ♠✉❡str❡♦ ❡str❛t✐✜❝❛❞♦✱ ② ❡❧ ♠✉❡str❡♦ ♣♦r ❝ú♠✉❧♦s✳ ❊♥ ❡❧ ♠✉❡str❡♦ ♥♦ ♣r♦❜❛❜✐❧íst✐❝♦ ❧♦s ♠✐❡♠✲ ❜r♦s s♦♥ s❡❧❡❝❝✐♦♥❛❞♦s ❞❡ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ✉♥❛ ♠❛♥❡r❛ ♥♦ ❛③❛r♦s❛✳ ❆q✉í s❡ ✐♥❝❧✉②❡♥ ❡❧ ♠✉❡str❡♦ ❝♦♥✈❡♥✐❡♥t❡✱ ❡❧ ♠✉❡str❡♦ ❞❡ ♦♣✐♥✐ó♥✱ ❡❧ ♠✉❡str❡♦ ❞❡ ❝✉♦t❛✱ ❡t❝✳ ❊♥ ❝❛♠❜✐♦✱ ❝✉❛❧q✉✐❡r ♠ét♦❞♦ ❞❡ ▼♦♥t❡ ❈❛r❧♦ r❡q✉✐❡r❡ ❞❡ r❡❣❧❛s ❞❡ ♠✉❡str❡♦ ❡s♣❡❝í✜❝❛s ♣❛r❛ ❣❡♥❡r❛r ✈❛r✐❛❜❧❡s ❛❧❡❛t♦r✐❛s ❛ ♣❛rt✐r ❞❡ ✉♥❛ ❞✐str✐❜✉❝✐ó♥ ❞❛❞❛✳ P♦r ❧♦ t❛♥t♦ ❡s ❞✐❢❡r❡♥t❡ ❞❡ ❧♦s ♠ét♦❞♦s ❞❡ ♠✉❡str❡♦ ❡♥✉♥❝✐❛❞♦s ❡♥ ❡❧ ♣árr❛❢♦ ❛♥t❡r✐♦r✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✸✳✶✳ ▼♦❞❡❧♦ ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ♣❛r❛ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ✺✷ ❡❧ ♠✉❡str❡♦ ❛ ♣❛rt✐r ❞❡ ❧❛s ❢✉♥❝✐♦♥❡s ❛♥❛❧ít✐❝❛s ✭♣♦r ❡❥❡♠♣❧♦✱ ♠❛①✇❡❧❧✐❛♥❛✱ ❡①♣♦♥❡♥✲ ❝✐❛❧✮ ② ❡❧ ♠✉❡str❡♦ ❛ ♣❛rt✐r ❞❡ ❧❛s ♣❞❢ t❛❜✉❧❛❞❛s ✭♣♦r ❡❥❡♠♣❧♦✱ ❡s♣❡❝tr❛❧ ② ❛♥❣✉❧❛r✮✳ ❊♥ ❡❧ s❡❣✉♥❞♦ ❝❛s♦ ❧♦s ♥ú♠❡r♦s ❛❧❡❛t♦r✐♦s ♣✉❡❞❡♥ ♦❜t❡♥❡rs❡ ❞✐r❡❝t❛♠❡♥t❡ ♠❡❞✐❛♥t❡ ❧❛ ✐♥✈❡rs✐ó♥ ❞✐r❡❝t❛ ❞❡ ❧❛ ❢✉♥❝✐ó♥ ❞❡ ❞✐str✐❜✉❝✐ó♥ ❛❝✉♠✉❧❛❞❛ ✭❝❞❢✮✱ ♣♦r ♠ét♦❞♦s ❞❡ r❡❝❤❛③♦✱ tr❛♥s❢♦r♠❛❝✐♦♥❡s ② ♦tr♦s ❬❍❛♠♠❡rs❧❡② ❛♥❞ ❍❛♥❞s❝♦♠❜✱ ✶✾✻✹❀ ❘✉❜✐♥st❡✐♥✱ ✶✾✽✶❪✳ P♦r ❧♦ t❛♥t♦✱ s❡ ♦❜t✐❡♥❡♥ ❧❛s ❢✉♥❝✐♦♥❡s q✉❡ r❡♣r❡s❡♥t❛♥ ❡❧ ❝♦♠♣♦rt❛♠✐❡♥t♦ ❡s✲ t♦❝ást✐❝♦ ❞❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ∆Ex (ξ1 ) ✱ ∆Ey (ξ2 ) ② ∆Ez (ξ3 ) ❞♦♥❞❡ ♥ú♠❡r♦s ❛❧❡❛t♦r✐♦s ❡st❛❞íst✐❝❛♠❡♥t❡ ✐♥❞❡♣❡♥❞✐❡♥t❡s ❡♥ ❡❧ ✐♥t❡r✈❛❧♦ ✸✳✶✳✶✳✷✳ ξ1 ✱ ξ2 ② ξ3 s♦♥ [0, 1]✳ ▲❛ ❛❝❡❧❡r❛❝✐ó♥ ❞❡ ▲♦r❡♥t③ ❊♥ ❧❛ ❊❝✳ ✭✸✳✶✮ ❡❧ s❡❣✉♥❞♦ tér♠✐♥♦ ❞❡ ❧❛ ❞❡r❡❝❤❛ ❝♦rr❡s♣♦♥❞❡ ❛ ❧❛ ❢✉❡r③❛ ❞❡ ▲♦r❡♥t③✳ ▲❛ r♦t❛❝✐ó♥ ❞❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❞❡ ❙❛t✉r♥♦ ✐♥❞✉❝❡ ✉♥ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❡♥ ❧❛ ❞✐r❡❝❝✐ó♥ r❛❞✐❛❧✿ ❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❝♦rr♦t❛❝✐♦♥❛❧✱ Ec ✳ P❛r❛ ✉♥❛ ♣❛rtí❝✉❧❛ ♥❡✉tr❛ ♦ ✉♥ ♦❜s❡r✈❛❞♦r ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛✱ ❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ s❡ ♠✉❡✈❡ ❝♦♥ ✉♥❛ ✈❡❧♦❝✐❞❛❞ ❞❡ ❝♦rr♦t❛❝✐ó♥✱ vc = ωrot × r ✱ ❞♦♥❞❡ ωrot ❡s ❧❛ ✈❡❧♦❝✐❞❛❞ ❛♥❣✉❧❛r ❞❡❧ ♣❧❛♥❡t❛ ② r ❡s ❧❛ ❞✐st❛♥❝✐❛✳ ❊st♦ ✐♥❞✉❝❡ ✉♥ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❞❛❞♦ ♣♦r✿ Ec = −vc × B = (r × ωrot ) × B ❊♥ ❧❛ ❊❝✳ ✭✸✳✺✮ B ✭✸✳✺✮ r❡♣r❡s❡♥t❛ ❛❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❞✐♣♦❧❛r ❞❡❧ ♣❧❛♥❡t❛✳ ▲❛ ❢✉❡r③❛ ♠❛❣♥ét✐❝❛ ❛❝tú❛ s♦❜r❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s q✉❡ ❡stá♥ ❝❛r❛❝t❡r✐③❛❞❛s ♣♦r ✉♥❛ ✈❡❧♦❝✐❞❛❞ ② ❡♥❡r❣í❛ ✐♥✐❝✐❛❧❡s✳ ▲❛ ✈❡❧♦❝✐❞❛❞ ✐♥✐❝✐❛❧ ✐♥❝❧✉②❡ ❛ ❧❛ ✈❡❧♦❝✐❞❛❞ ❞❡ ❝♦rr♦t❛❝✐ó♥✱ vc ② ❛ ❧❛ ✈❡❧♦❝✐❞❛❞ ❞❡ ❧❛ ❞✐str✐❜✉❝✐ó♥✱vd ✳ ❆sí s❡ t✐❡♥❡ q✉❡✿ v1 = vc1 + vd1 ✭✸✳✻✮ ❊♥ ❧❛ ❊❝✳ ✭✸✳✻✮ ❡❧ s✉❜í♥❞✐❝❡ ✶ ❡stá r❡❢❡r✐❞♦ ❛❧ ✈❛❧♦r ✐♥✐❝✐❛❧ ② ❡s ❛♣❧✐❝❛❞❛ ❛ ❝❛❞❛ ❞✐r❡❝❝✐ó♥ ❡s♣❛❝✐❛❧✳ ❯s❛♥❞♦ ❡❧ ♠ét♦❞♦ ❞❡ ▼♦♥t❡ ❈❛r❧♦ s❡ s❡❧❡❝❝✐♦♥❛✱ ❛❧❡❛t♦r✐❛♠❡♥t❡✱ ❧❛ ✈❡❧♦❝✐❞❛❞ ❞❡ ❧❛ ♣❛rtí❝✉❧❛ q✉❡ s✐❣✉❡ ❡s❛ ❞✐str✐❜✉❝✐ó♥ ❡♥ ❝❛❞❛ ❞✐r❡❝❝✐ó♥ ❡s♣❛❝✐❛❧✳ ▲❛ ❡♥❡r❣í❛ ❝✐♥ét✐❝❛ ✐♥✐❝✐❛❧ ❞❡ ❧❛s ♣❛rtí❝✉❧❛s ❡stá ❞❛❞❛ ♣♦r ❧❛ ❡①♣r❡s✐ó♥ ❝❧ás✐❝❛✱ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✸✳✶✳ ▼♦❞❡❧♦ ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ♣❛r❛ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s 1 K1 = mv12 2 ✺✸ ✭✸✳✼✮ ▲❛s ❊❝s✳ ✭✸✳✻✮ ② ✭✸✳✼✮ s❡ ❝❛❧❝✉❧❛♥ ✐♥✐❝✐❛❧♠❡♥t❡ ♣❛r❛ ❝❛❞❛ ♣❛rtí❝✉❧❛ ❞❡ ❧❛ ♠✉❡str❛✳ ❈❛s♦ ❡s♣❡❝✐❛❧✿ ●r❛♥♦s ❞❡ ♣♦❧✈♦ ❝❛r❣❛❞♦s ▲❛s ♣❛rtí❝✉❧❛s ❞❡ ♣♦❧✈♦ ♥♦ s✐❣✉❡♥ ✉♥❛ ❞✐str✐❜✉❝✐ó♥ ❞❡ ✈❡❧♦❝✐❞❛❞❡s ❝♦♠♦ ❡♥ ❡❧ ❝❛s♦ ❞❡ ❧♦s ✐♦♥❡s✳ ❊❧ ♠♦✈✐♠✐❡♥t♦ ♦r❜✐t❛❧ q✉❡ ❞❡s❝r✐❜❡♥ ❛❧r❡❞❡❞♦r ❞❡❧ ♣❧❛♥❡t❛ ❡stá ❣♦❜❡r♥❛❞♦ ♣♦r ❧❛s ❧❡②❡s ❞❡ ❑❡♣❧❡r✳ ❙✉♣♦♥✐❡♥❞♦ q✉❡ ❧❛s ór❜✐t❛s ❞❡s❝r✐t❛s s♦♥ ❝❛s✐ ❝✐r❝✉❧❛r❡s ❧❛ ✈❡❧♦❝✐❞❛❞ ✐♥✐❝✐❛❧ ❑❡♣❧❡r✐❛♥❛✱ vK1 ✱ vK1 = ❞♦♥❞❡ r ❡stá ❞❛❞❛ ♣♦r✿ 2πr T ✭✸✳✽✮ ❡s ❧❛ ❞✐st❛♥❝✐❛ ♠❡❞✐❞❛ ✭s♦❜r❡ ❡❧ ♣❧❛♥♦ ♦r❜✐t❛❧✮ ❞❡s❞❡ ❡❧ ❝❡♥tr♦ ❞❡ ♠❛s❛ ❞❡❧ ♣❧❛♥❡t❛ ❤❛st❛ ❡❧ ❝❡♥tr♦ ❞❡ ♠❛s❛ ❞❡ ❧❛ ♣❛rtí❝✉❧❛ ❞❡ ♣♦❧✈♦ ② T ❡s ❡❧ ♣❡r✐♦❞♦ ♦r❜✐t❛❧ ♦❜t❡♥✐❞♦ ❛ tr❛✈és ❞❡ ❧❛ t❡r❝❡r❛ ▲❡② ❞❡ ❑❡♣❧❡r ❞❡❧ ♠♦✈✐♠✐❡♥t♦ ♣❧❛♥❡t❛r✐♦✳ ✸✳✶✳✶✳✸✳ ▲❛ ❛❝❡❧❡r❛❝✐ó♥ ❣r❛✈✐t❛❝✐♦♥❛❧ ❙❡ ❝❛❧❝✉❧❛ ❧❛ ✐♥t❡r❛❝❝✐ó♥ ❡♥tr❡ ❝❛❞❛ ♣❛rtí❝✉❧❛ ② ❡❧ ♣❧❛♥❡t❛ ❞❡❜✐❞♦ ❛ ❧❛ ❛tr❛❝❝✐ó♥ ❣r❛✈✐t❛❝✐♦♥❛❧ ❡♥tr❡ ❡❧❧♦s✳ ❊♥ ❡❧ ú❧t✐♠♦ tér♠✐♥♦ ❞❡ ❧❛ ❊❝✳ ✭✸✳✶✮ s❡ ❡①♣r❡s❛ ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ♣r♦❞✉❝✐❞❛ ♣♦r ❡st❛ ❢✉❡r③❛ ❞♦♥❞❡ G ❡s ❧❛ ❝♦♥st❛♥t❡ ❣r❛✈✐t❛❝✐♦♥❛❧ ② MP ❡s ❧❛ ♠❛s❛ ❞❡❧ ♣❧❛♥❡t❛✳ ✸✳✶✳✶✳✹✳ ➽❯♥ tér♠✐♥♦ ❝♦❧✐s✐♦♥❛❧❄ ❊s ✐♠♣♦rt❛♥t❡ ❞❡t❡r♠✐♥❛r ❧❛ ♥❛t✉r❛❧❡③❛ ❝♦❧✐s✐♦♥❛❧ ♦ ♥♦✲❝♦❧✐s✐♦♥❛❧ ❞❡ ❧❛ r❡❣✐ó♥ ♠❛❣♥❡t♦s❢ér✐❝❛ ❡♥ ❡st✉❞✐♦✳ P❛r❛ ❡st❡ ♣r♦♣ós✐t♦ s❡ s✐♠✉❧❛ ✉♥❛ ♠❛❣♥❡tós❢❡r❛ ❝♦♥ s✐✲ ♠❡trí❛ ❡s❢ér✐❝❛ ❞❡ r❛❞✐♦ Rm ✭❡st❡ r❛❞✐♦ ❞❡♣❡♥❞❡rá ❞❡ ❧❛ r❡❣✐ó♥ q✉❡ s❡ ❞❡s❡❡ ❡st✉❞✐❛r✱ ❡st♦ ❡s✱ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛✱ ✐♥t❡r♠❡❞✐❛ ✭s✐ ❡s ❡❧ ❝❛s♦✮ ② ❡①t❡r♥❛✮ ② s❡ ❛♥❛❧✐③❛ ❡❧ ❝❛♠✐♥♦ ❧✐❜r❡ ♠❡❞✐♦ ✭λ✮ ❡♥tr❡ ♣❛rtí❝✉❧❛s✳ ❙❡ ❝♦♥s✐❞❡r❛♥ ❧♦s s✐❣✉✐❡♥t❡s ❝❛s♦s✿ ❛✮ ❝♦❧✐✲ s✐♦♥❡s ❡♥tr❡ ✐♦♥❡s ② ♥❡✉tr♦s✱ ❜✮ ❝♦❧✐s✐♦♥❡s ❡♥tr❡ ♥❡✉tr♦s✱ ② ❝✮ ❝♦❧✐s✐♦♥❡s ❡♥tr❡ ✐♦♥❡s✳ ❘❡❝✉ér❞❡s❡ q✉❡ ❡❧ ❝❛♠✐♥♦ ❧✐❜r❡ ♠❡❞✐♦ ❡stá ❞❛❞♦ ♣♦r✿ λ= 1 nσ = 1 ❞♦♥❞❡ n(4 π r 2 ) n ❡s ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✸✳✶✳ ▼♦❞❡❧♦ ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ♣❛r❛ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ✺✹ ❧❛ ❞❡♥s✐❞❛❞ ♦❜s❡r✈❛❞❛ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ② σ ❡s ❧❛ s❡❝❝✐ó♥ ❡✜❝❛③ ❞❡ ❧❛ ✐♥t❡r❛❝❝✐ó♥✳ P❛r❛ ❡❧ ♣r✐♠❡r ❝❛s♦ s❡ ❡♠♣❧❡❛ ❡❧ r❛❞✐♦ ✐ó♥✐❝♦ r✱ ❡♥ ❡❧ s❡❣✉♥❞♦ ❝❛s♦ s❡ ✉t✐❧✐③❛ ❡❧ r❛❞✐♦ ❛tó♠✐❝♦ r ② ❡♥ ❡❧ t❡r❝❡r ❝❛s♦ s❡ ❡st✐♠❛ ❡❧ ♣❛rá♠❡tr♦ ❞❡ ✐♠♣❛❝t♦ b✱ ❞❛❞♦ ♣♦r✿ b= Ze2 4 π ε0 K cot θ 2  ❞♦♥❞❡ Z ❡s ❡❧ ♥ú♠❡r♦ ❛tó♠✐❝♦✱ e ❡s ❧❛ ❝❛r❣❛ ❢✉♥❞❛♠❡♥t❛❧✱ ε0 ❡s ❧❛ ❝♦♥st❛♥t❡ ❞❡ ♣❡r♠✐t✐✈✐❞❛❞ ❡♥ ❡❧ ✈❛❝í♦✱ K ❡s ❧❛ ❡♥❡r❣í❛ ❞❡ ❧❛ ♣❛rtí❝✉❧❛ ② θ ❡s ❡❧ á♥❣✉❧♦ ❞❡ ❞✐s♣❡rs✐ó♥ ❞❡❜✐❞♦ ❛ ❧❛s ✐♥t❡r❛❝❝✐♦♥❡s ❈♦✉❧♦♠❜✐❛♥❛s✳ ❙✐ ❡❧ ✈❛❧♦r ❞❡❧ ❝❛♠✐♥♦ ❧✐❜r❡ ♠❡❞✐♦ ❡s ♠❛②♦r ✭♦ ❞❡❧ ♦r❞❡♥ ❞❡ ♠❛❣♥✐t✉❞✮ q✉❡ ❡❧ r❛❞✐♦ ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ s✐♠✉❧❛❞❛ s❡ ❝♦♥❝❧✉②❡ q✉❡ ❡❧ ♣❧❛s♠❛ ❞❡♥tr♦ ❞❡ ❡s❛ r❡❣✐ó♥ ❡s ♥♦✲ ❝♦❧✐s✐♦♥❛❧ ② ♣♦r ❧♦ t❛♥t♦ ♥♦ s❡ ✐♥❝❧✉②❡ ❡s❛ ✐♥t❡r❛❝❝✐ó♥ ❡♥ ❧❛ ❡❝✉❛❝✐ó♥ ❞❡ ♠♦✈✐♠✐❡♥t♦ ✭✸✳✶✮✳ ✸✳✶✳✷✳ ▲❛ ❡♥❡r❣í❛ ✜♥❛❧ ② ❧❛ ✈❡❧♦❝✐❞❛❞ ✜♥❛❧ ♣❛r❛ ❧❛ ❞✐str✐❜✉❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ❊♥ ❧❛ ❊❝✳ ✭✸✳✶✮ s❡ ❡stá ❝♦♥s✐❞❡r❛♥❞♦ ❧❛ ❢✉❡r③❛ t♦t❛❧ q✉❡ ❛❝tú❛ s♦❜r❡ ❝❛❞❛ ✉♥❛ ❞❡ ❧❛s ♣❛rtí❝✉❧❛s ❧♦❝❛❧✐③❛❞❛s ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ♦ ❡♥ ❡❧ s✐st❡♠❛ ❞❡ ❛♥✐❧❧♦s✳ ❉❡ ❡st❛ ♠❛♥❡r❛ s❡ ❡♠♣❧❡❛ ❡❧ ❚❡♦r❡♠❛ ❞❡ tr❛❜❛❥♦✲❡♥❡r❣í❛ ♣❛r❛ ❡st❛❜❧❡❝❡r ❧♦ s✐❣✉✐❡♥t❡✿ ∆W = F · ∆r = Fx ∆x + Fy ∆y + Fz ∆z = ∆K ✭✸✳✾✮ ❊♥ ❧❛ ❊❝✳ ✭✸✳✾✮ s❡ ❝❛❧❝✉❧❛ ❧❛ ❣❛♥❛♥❝✐❛ ✭♦ ♣ér❞✐❞❛✮ ❞❡ ❡♥❡r❣í❛ ❝✐♥ét✐❝❛ ❞❡s♣✉és ❞❡ ❝❛❞❛ ✐♥t❡r❛❝❝✐ó♥ ❝♦♥ ❧❛ ❢✉❡r③❛ t♦t❛❧ F ✭❡st♦❝ást✐❝❛✱ ▲♦r❡♥t③✱ ❣r❛✈✐t❛❝✐♦♥❛❧ ② ♣r❡s✐ó♥ ❞❡ r❛❞✐❛❝✐ó♥✮ ♣❛r❛ ❝❛❞❛ ♣❛rtí❝✉❧❛ ❡♥ ❡❧ ❡s♣❛❝✐♦✳ ❊st❡ ✐♥❝r❡♠❡♥t♦ ✭♦ ❞❡❝r❡♠❡♥t♦✮ ❞❡ ❡♥❡r❣í❛ s❡ ❞❡❜❡ ❛ ❧❛ ❛❝❝✐ó♥ ❞❡❧ ❝❛♠♣♦ ❞❡ ❢✉❡r③❛s ❡st♦❝ást✐❝♦✱ ♣♦r ❧♦ q✉❡ ❛ ∆K s❡ ❧❡ ❞❡♥♦♠✐♥❛ ❣❛♥❛♥❝✐❛ ✭♦ ♣ér❞✐❞❛✮ ❞❡ ❡♥❡r❣í❛ ❡st♦❝ást✐❝❛✳ ❊❧ ✈❛❧♦r q✉❡ s❡ ❛s✐❣♥❡ ❛❧ ♣❛s♦ ♥✉♠ér✐❝♦ ❡♥ ❝❛❞❛ ❞✐r❡❝❝✐ó♥ ✭❞❡♥♦t❛❞♦ ♣♦r ∆x✱ ∆y ② ∆z ✮ ❞❡❜❡ ❛s❡❣✉r❛r q✉❡ ❡❧ ❡rr♦r ❝♦♠♣✉t❛❝✐♦♥❛❧ s❡❛ ♠❡♥♦r ❡♥ ❝❛❞❛ ✐t❡r❛❝✐ó♥ ② q✉❡ ❧❛ ♣❛rtí❝✉❧❛ ✐♥t❡r❛❝tú❡ s✉✜❝✐❡♥t❡s ✈❡❝❡s ❝♦♥ ❡❧ ❝❛♠♣♦ ❞❡ ❢✉❡r③❛s ❡st♦❝ást✐❝♦✳ P❛r❛ ❡❧ ❝❛s♦ ❞❡ ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ✭♣r♦t♦♥❡s ② ✐♦♥❡s ♣❡s❛❞♦s✮ s❡ t♦♠❛ ✉♥❛ ❢r❛❝❝✐ó♥ ❞❡❧ r❛❞✐♦ ❞❡ ❣✐r♦ ♠í♥✐♠♦ ② ♣❛r❛ ❧♦s ❣r❛♥♦s ❞❡ ♣♦❧✈♦ ❝❛r❣❛❞♦s s❡ ❝♦♥s✐❞❡r❛ ✉♥❛ ❢r❛❝❝✐ó♥ ❞❡ ❧❛ ❞✐st❛♥❝✐❛ ♠í♥✐♠❛ ❡♥tr❡ ♣❛rtí❝✉❧❛s✳ P♦r ♦tr♦ ❧❛❞♦✱ ❡s ✐♠♣♦rt❛♥t❡ r❡s❛❧t❛r q✉❡ ❝❛❞❛ ❞✐r❡❝❝✐ó♥ ❡s♣❛❝✐❛❧ ❝♦♥tr✐❜✉②❡ ❛ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✸✳✶✳ ▼♦❞❡❧♦ ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ♣❛r❛ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ✺✺ ❡st❛ ❣❛♥❛♥❝✐❛ ✭♦ ♣ér❞✐❞❛✮ ❞❡ ❡♥❡r❣í❛ ❡st♦❝ást✐❝❛✳ P❛rt✐❡♥❞♦ ❞❡ ❧❛ ❡①♣r❡s✐ó♥ ❝❧ás✐❝❛ ♣❛r❛ ❡❧ ❝á❧❝✉❧♦ ❞❡ ❧❛ ❡♥❡r❣í❛ ❝✐♥ét✐❝❛ ❧❛ ❞❡♠♦str❛❝✐ó♥ ❡s ❝♦♠♦ s✐❣✉❡✿   1  ∆K = K2 − K1 = m v22 x + v22 y + v22 z − v12 x + v12 y + v12 z 2    1  = m v22 x − v12 x + v22 y − v12 y + v22 z − v12 z 2  1  = m ∆vx2 + ∆vy2 + ∆vz2 2 = ∆Kx + ∆Ky + ∆Kz ✭✸✳✶✵✮ ▲❛ ❡♥❡r❣í❛ ❝✐♥ét✐❝❛ ✜♥❛❧ ♣❛r❛ ✉♥❛ ♣❛rtí❝✉❧❛ ❞❡s♣✉és ❞❡ ❝❛❞❛ ✐♥t❡r❛❝❝✐ó♥ ❝♦♥ ❧❛ ❢✉❡r③❛ t♦t❛❧ s❡ ♦❜t✐❡♥❡ ♠❡❞✐❛♥t❡ ❧❛ ❡①♣r❡s✐ó♥✿ K2 = K1 + ∆K − Kr ✭✸✳✶✶✮ ❞♦♥❞❡ Kr ❡s ❧❛ ♣ér❞✐❞❛ ❞❡ ❡♥❡r❣í❛ ♣♦r r❛❞✐❛❝✐ó♥ ❡❧❡❝tr♦♠❛❣♥ét✐❝❛ ❞❡❜✐❞❛ ❛ ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s✳ ▲❛ ❡♠✐s✐ó♥ ❞❡ r❛❞✐❛❝✐ó♥ ❡❧❡❝tr♦♠❛❣♥ét✐❝❛ ❡s t✐♣♦ ❧✐❜r❡✲❧✐❜r❡ ② s❡ ❝❛❧❝✉❧❛ ❝♦♠♦ ❬❏❛❝❦s♦♥✱ ✶✾✾✾❪✿ Kr = q2 a2 ∆t 6 π ε 0 c3 ✭✸✳✶✷✮ ❞♦♥❞❡ q ❡s ❧❛ ❝❛r❣❛ ❡❧é❝tr✐❝❛ ❞❡ ❧❛ ♣❛rtí❝✉❧❛✱ ε0 ❡s ❧❛ ❝♦♥st❛♥t❡ ❞❡ ♣❡r♠✐t✐✈✐❞❛❞ ❡♥ ❡❧ ✈❛❝í♦✱ c ❡s ❧❛ ✈❡❧♦❝✐❞❛❞ ❞❡ ❧❛ ❧✉③ ❡♥ ❡❧ ✈❛❝í♦✱ a ❡s ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ❞❡ ❧❛ ♣❛rtí❝✉❧❛ ② ∆t ❡s ❡❧ t✐❡♠♣♦ q✉❡ t❛r❞❛ ❧❛ ♣❛rtí❝✉❧❛ ❡♥ s❡r ❛❝❡❧❡r❛❞❛✳ ❊s ✐♠♣♦rt❛♥t❡ ♠❡♥❝✐♦♥❛r q✉❡ s❡ ❝♦♥s✐❞❡r❛ ❧❛ ♣ér❞✐❞❛ ❞❡ ❡♥❡r❣í❛ ♣♦r r❛❞✐❛❝✐ó♥ ❡♥ ❝❛❞❛ ❞✐r❡❝❝✐ó♥ ❡s♣❛❝✐❛❧✳ ❊❧ r❛③♦♥❛♠✐❡♥t♦ ❞❡ ❡st❡ ❤❡❝❤♦ ❡s s✐♠✐❧❛r ❛ ❧❛ ❊❝✳ ✭✸✳✶✵✮✳ ▲❛ ✈❡❧♦❝✐❞❛❞ ✜♥❛❧ ❛❧❝❛♥③❛❞❛ ♣♦r ✉♥❛ ♣❛rtí❝✉❧❛ s❡ ❝❛❧❝✉❧❛ s✐♠♣❧❡♠❡♥t❡ ❛ tr❛✈és ❞❡ ❧❛ ❡♥❡r❣í❛ ❝✐♥ét✐❝❛ ✜♥❛❧✱ ❡st♦ ❡s✿ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✸✳✶✳ ▼♦❞❡❧♦ ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ♣❛r❛ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s r v2 = ± 2 K2 m ✺✻ ✭✸✳✶✸✮ ❊♥ ❧❛ ❊❝✳ ✭✸✳✶✸✮✱ ❡❧ s✐❣♥♦ ❡s ❛s✐❣♥❛❞♦ ❛ tr❛✈és ❞❡❧ ❛❧❣♦r✐t♠♦ ♥✉♠ér✐❝♦ t♦♠❛♥❞♦ ❡♥ ❝✉❡♥t❛ ❧❛ ✈❡❧♦❝✐❞❛❞ ✐♥✐❝✐❛❧✱ ❧❛ ♠❛❣♥✐t✉❞ ❞❡ ❧❛ ❢✉❡r③❛ t♦t❛❧ ② ❧❛ ❣❛♥❛♥❝✐❛ ✭♦ ♣ér❞✐❞❛✮ ❞❡ ❡♥❡r❣í❛✳ ▲❛ ♣♦s✐❝✐ó♥ ✜♥❛❧ ❡♥ ❧❛ ❞✐r❡❝❝✐ó♥ r❛❞✐❛❧ ❛❧❝❛♥③❛❞❛ ♣♦r ✉♥❛ ♣❛rtí❝✉❧❛ ❞❡s♣✉és ❞❡ ❝❛❞❛ ✐♥t❡r❛❝❝✐ó♥ ❡stá ❞❛❞❛ ♣♦r✿ ✭✸✳✶✹✮ r2 = r1 + ∆r ❊♥ ❧❛ ❊❝✳ ✭✸✳✶✹✮ ❧❛ ♣♦s✐❝✐ó♥ ✐♥✐❝✐❛❧ ❡s ❡❧ ❧✉❣❛r ♦❝✉♣❛❞♦ ♣♦r ❧❛ ♣❛rtí❝✉❧❛ ❛❧ ✜♥❛❧ ❞❡ ❧❛ ✐♥t❡r❛❝❝✐ó♥ ♣r❡✈✐❛ ❝♦♥ ❡❧ ❝❛♠♣♦ ❞❡ ❢✉❡r③❛s ❡st♦❝ást✐❝♦ ② ∆r ❝♦rr❡s♣♦♥❞❡ ❛❧ ♣❛s♦ ♥✉♠ér✐❝♦ ♣r❡✈✐❛♠❡♥t❡ ❞❡t❡r♠✐♥❛❞♦✳ ▲❛ ❊❝✳ ✭✸✳✶✹✮ s❡ ❛♣❧✐❝❛ ❡♥ ❝❛❞❛ ❞✐r❡❝❝✐ó♥ ❡s♣❛❝✐❛❧✳ ▲❛s ❊❝s✳ ✭✸✳✶✶✮✱ ✭✸✳✶✸✮ ② ✭✸✳✶✹✮ s♦♥ ❝❛❧❝✉❧❛❞❛s ♣❛r❛ ✉♥❛ ♣❛rtí❝✉❧❛ ❞❛❞❛ ❞❡s♣✉és ❞❡ ❝❛❞❛ ✐♥t❡r❛❝❝✐ó♥ ❝♦♥ ❧❛ ❢✉❡r③❛ t♦t❛❧✳ ❊s ✐♠♣♦rt❛♥t❡ ❛❝❧❛r❛r q✉❡ ❡st♦s ✈❛❧♦r❡s ✜♥❛❧❡s s❡ ❝♦♥✈✐❡rt❡♥ ❡♥ ❧♦s ✈❛❧♦r❡s ✐♥✐❝✐❛❧❡s ♣❛r❛ ❧❛ s✐❣✉✐❡♥t❡ ✐♥t❡r❛❝❝✐ó♥✳ ❯♥❛ ✈❡③ q✉❡ ❧❛ ♣❛rtí❝✉❧❛ s❡❧❡❝❝✐♦♥❛❞❛ ✐♥t❡r❛❝❝✐♦♥❛ ❝♦♥ ❡❧ ❝❛♠♣♦ ❞❡ ❢✉❡r③❛s ❡st♦✲ ❝ást✐❝♦ ❡❧ ♥ú♠❡r♦ ❞❡ ✈❡❝❡s ♣r❡❞❡t❡r♠✐♥❛❞♦✱ ♦tr❛ ♣❛rtí❝✉❧❛ ❡s ✐♥②❡❝t❛❞❛ ❛ ❧❛ ♠❛❣♥❡✲ tós❢❡r❛ ♦ ❛❧ s✐st❡♠❛ ❞❡ ❛♥✐❧❧♦s✳ ❊st❡ ♣r♦❝❡s♦ t❡r♠✐♥❛ ❝✉❛♥❞♦ ❧❛ ♠✉❡str❛ ❞❡ ♣❛rtí❝✉❧❛s ❡s s♦♠❡t✐❞❛ ❛❧ ♠✐s♠♦ ♥ú♠❡r♦ ❞❡ ✐♥t❡r❛❝❝✐♦♥❡s✳ ❋✐♥❛❧♠❡♥t❡ ♣❛r❛ ❛s❡❣✉r❛r q✉❡ ❧❛s ♣❛r✲ tí❝✉❧❛s ♣❡r♠❛♥❡❝❡♥ ❞❡♥tr♦ ❞❡ ❧❛ r❡❣✐ó♥ ♠❛❣♥❡t♦s❢ér✐❝❛ ✭✐♥t❡r♥❛ ♦ ❡①t❡r♥❛✮ ♦ ❞❡♥tr♦ ❞❡❧ ❛♥✐❧❧♦ s❡ ❡st❛❜❧❡❝❡ ❧❛ ❝♦♥❞✐❝✐ó♥ ❞❡ ❝♦rt❡ ❝♦rr❡s♣♦♥❞✐❡♥t❡✿ 1 RP < r < RIN T , magnetosfera interna ✭✸✳✶✺✮ r ≥ RIN T , magnetosfera externa ✭✸✳✶✻✮ BIN T < r < BEXT , anillo ✭✸✳✶✼✮ ❊♥ ❧❛s r❡❧❛❝✐♦♥❡s ❛♥t❡r✐♦r❡s r ❡s ❧❛ ♣♦s✐❝✐ó♥ ✜♥❛❧ q✉❡ ❛❧❝❛♥③❛ ❧❛ ♠✉❡str❛ ❞❡ ♣❛rtí❝✉❧❛s✱ ❡st♦ ❡s✱ r = p x22 + y22 + z22 ❞♦♥❞❡ x2 ✱ y2 ✱ z2 s❡ ♦❜t✐❡♥❡♥ ❛ ♣❛rt✐r ❞❡ ❧❛ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✸✳✷✳ ▼♦❞❡❧♦ ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ♣❛r❛ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ♥❡✉tr❛s ✺✼ ❊❝✳ ✭✸✳✶✹✮✳ ❊♥ ❧❛s ♠❛❣♥❡tós❢❡r❛s ♣❧❛♥❡t❛r✐❛s ❧❛ r❡❣✐ó♥ ✐♥t❡r♥❛ ❡♠♣✐❡③❛ ❞❡s❞❡ 1 RP ✭RP ❡s ❡❧ r❛❞✐♦ ♣❧❛♥❡t❛r✐♦✮ ② t❡r♠✐♥❛ ❞♦♥❞❡ ❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❞❡❥❛ ❞❡ t❡♥❡r ❧❛ ❝♦♥✜❣✉r❛❝✐ó♥ ❞✐♣♦❧❛r ✭RIN T ✮❀ ❧❛ ❢r♦♥t❡r❛ ❞❡ ❧❛ r❡❣✐ó♥ ❡①t❡r♥❛ s❡ ❡①t✐❡♥❞❡ ❤❛st❛ ❧❛ ♠❛❣♥❡t♦❝♦❧❛ ② ❧❛s ♣❛rtí❝✉❧❛s ❞❡ ♣♦❧✈♦ ❡♥ ❧♦s ❛♥✐❧❧♦s s❡ ❡♥❝✉❡♥tr❛♥ ❝♦♥✜♥❛❞❛s ❛ ❧♦s ❜♦r❞❡s ✐♥t❡r♥♦ ✭BIN T ✮ ② ❡①t❡r♥♦ ✭BEXT ✮ ❞❡ ❧♦s ♠✐s♠♦s✳ ❈✉❛♥❞♦ r t♦♠❛ ✉♥ ✈❛❧♦r ❢✉❡r❛ ❞❡ ❡st♦s ✐♥t❡r✈❛❧♦s✱ ❧❛ ♣❛rtí❝✉❧❛ ❡s ❝♦♥s✐❞❡r❛❞❛ ❝♦♠♦ ♣❡r❞✐❞❛✳ ✸✳✷✳ ▼♦❞❡❧♦ ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ♣❛r❛ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛r✲ tí❝✉❧❛s ♥❡✉tr❛s ▲❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ♥❡✉tr❛s ❥✉❡❣❛ ✉♥ ♣❛♣❡❧ ✐♠♣♦rt❛♥t❡ ❡♥ ❧❛s ♠❛❣♥❡tós✲ ❢❡r❛s ♣❧❛♥❡t❛r✐❛s ❝♦♠♦ s❡ ♠❡♥❝✐♦♥ó ❡♥ ❡❧ ❈❛♣ít✉❧♦ ✷✳ ❊s ❞❡ ❡s♣❡❝✐❛❧ ✐♥t❡rés ❡❧ ❡st✉❞✐♦ ❞❡ ❧❛ ❞✐♥á♠✐❝❛ ❞❡ ❧❛s ♣❛rtí❝✉❧❛s ❞❡ ♣♦❧✈♦ q✉❡ s❡ ❡♥❝✉❡♥tr❛♥ ❡♥ ❧♦s ❛♥✐❧❧♦s ♣❧❛♥❡t❛r✐♦s ♣✉❡s s♦♥ ✉♥❛ ❢✉❡♥t❡ ♣♦t❡♥❝✐❛❧ ❞❡ ♣❛rtí❝✉❧❛s✳ ✸✳✷✳✶✳ ▲❛ ❡❝✉❛❝✐ó♥ ❞❡ ♠♦✈✐♠✐❡♥t♦ ♣❛r❛ ✉♥❛ ♣❛rtí❝✉❧❛ ❞❡ ♣♦❧✈♦ ♥❡✉tr❛ ❊♥ ❡❧ ❝❛s♦ ❞❡ ❧♦s ❣r❛♥♦s ❞❡ ♣♦❧✈♦ ♥❡✉tr♦s✱ ❧❛ ❡❝✉❛❝✐ó♥ ❞❡ ♠♦✈✐♠✐❡♥t♦ ✭✸✳✶✮ ✐♥✲ ❝❧✉✐rá ❛ ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ♣r♦❞✉❝✐❞❛ ♣♦r ❧❛ ❢✉❡r③❛ ❞❡ ❛tr❛❝❝✐ó♥ ❣r❛✈✐t❛❝✐♦♥❛❧ ❡♥tr❡ ❡❧ ♣❧❛♥❡t❛ ② ❧❛ ♣❛rtí❝✉❧❛✱ ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ❡st♦❝ást✐❝❛ ♣r♦❞✉❝✐❞❛ ♣♦r ❧❛ ❢✉❡r③❛ ❞❡ ❛tr❛❝✲ ❝✐ó♥ ❣r❛✈✐t❛❝✐♦♥❛❧ ❡♥tr❡ ❞♦s ♣❛rtí❝✉❧❛s ❞❡ ♣♦❧✈♦ ♣❡rt❡♥❡❝✐❡♥t❡s ❛❧ ♠✐s♠♦ ❛♥✐❧❧♦ ② ❧❛ ❢✉❡r③❛ ❞❡ ♣r❡s✐ó♥ ❞❡ r❛❞✐❛❝✐ó♥ ❡①♣❧✐❝❛❞❛ ❛♥t❡r✐♦r♠❡♥t❡✳ ❊st♦ ❡s✿ d2 r MP mstoc 1 Qpr A r̂stoc − J = G 3 r̂ + G 2 2 3 dt |r | | rstoc | m c rhelio ✭✸✳✶✽✮ ❊♥ ❡❧ ❧❛❞♦ ❞❡r❡❝❤♦ ❞❡ ❧❛ ❊❝✳ ✭✸✳✶✽✮✱ ❡❧ ♣r✐♠❡r tér♠✐♥♦ s❡ r❡✜❡r❡ ❛ ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ❣r❛✈✐t❛❝✐♦♥❛❧ ♣r♦❞✉❝✐❞❛ ♣♦r ❡❧ ♣❧❛♥❡t❛ ❞❡ ♠❛s❛ MP ✱ ❡❧ s❡❣✉♥❞♦ tér♠✐♥♦ r❡♣r❡s❡♥t❛ ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ❣r❛✈✐t❛❝✐♦♥❛❧ ❡st♦❝ást✐❝❛ ❡♥tr❡ ❣r❛♥♦s ❞❡ ♣♦❧✈♦ ❞♦♥❞❡ mstoc ❡s ❧❛ ♠❛s❛ ❞❡❧ ❣r❛♥♦ q✉❡ ♣r♦❞✉❝❡ ❡st❛ ❛❝❡❧❡r❛❝✐ó♥ s♦❜r❡ ❡❧ ❣r❛♥♦ ❞❡ ♠❛s❛ m ② ❡stá s❡♣❛r❛❞❛ ❛ ✉♥❛ ❞✐st❛♥❝✐❛ ❛❧❡❛t♦r✐❛ rstoc ✱ ❡❧ t❡r❝❡r tér♠✐♥♦ ❡s ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ♣r♦❞✉❝✐❞❛ ♣♦r ❧❛ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✸✳✷✳ ▼♦❞❡❧♦ ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ♣❛r❛ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ♥❡✉tr❛s ✺✽ ❢✉❡r③❛ ❞❡ ♣r❡s✐ó♥ ❞❡ r❛❞✐❛❝✐ó♥ ❞♦♥❞❡ Qpr ❡s ❡❧ ❝♦❡✜❝✐❡♥t❡ ❞❡ ♣r❡s✐ó♥ ❞❡ r❛❞✐❛❝✐ó♥✱ A ❡s ❧❛ s❡❝❝✐ó♥ tr❛♥s✈❡rs❛❧ ❞❡ ❧❛ ♣❛rtí❝✉❧❛✱ c ❡s ❧❛ ✈❡❧♦❝✐❞❛❞ ❞❡ ❧❛ ❧✉③ ❡♥ ❡❧ ✈❛❝í♦✱ rhelio ❡s ❧❛ ❞✐st❛♥❝✐❛ ❤❡❧✐♦❝é♥tr✐❝❛ ♠❡❞✐❞❛ ❡♥ ✉♥✐❞❛❞❡s ❛str♦♥ó♠✐❝❛s ② J ❡s ❡❧ ✈❡❝t♦r ❞❡ ✢✉❥♦ ❞❡ ❡♥❡r❣í❛ ❞❡❜✐❞♦ ❛ ❧❛ r❛❞✐❛❝✐ó♥ s♦❧❛r✳ ✸✳✷✳✶✳✶✳ ▲❛ ❛❝❡❧❡r❛❝✐ó♥ ❣r❛✈✐t❛❝✐♦♥❛❧ ❱é❛s❡ ❧❛ ❙❡❝❝✐ó♥ ✸✳✶✳✶✳✸ ✸✳✷✳✶✳✷✳ ▲❛ ❛❝❡❧❡r❛❝✐ó♥ ❣r❛✈✐t❛❝✐♦♥❛❧ ❡st♦❝ást✐❝❛ ❡♥tr❡ ❣r❛♥♦s ❞❡ ♣♦❧✈♦ ❙❡ ♣r♦♣♦♥❡ q✉❡ ❧❛ ❢✉❡r③❛ ❞❡ ❛tr❛❝❝✐ó♥ ❣r❛✈✐t❛❝✐♦♥❛❧ ❡♥tr❡ ♣❛rtí❝✉❧❛s ❞❡ ♣♦❧✈♦ ♥❡✉tr♦ ❡♥ ✉♥ ❛♥✐❧❧♦ t✐❡♥❡ ❝❛rá❝t❡r ❡st♦❝ást✐❝♦ ♣♦r ❧♦ q✉❡ ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ♣r♦❞✉❝✐❞❛ t❛♠❜✐é♥ ❧♦ ❡s✳ P❛r❛ ❣❡♥❡r❛r ❡st❛ ❢✉❡r③❛ s❡ r❡q✉✐❡r❡ q✉❡ ✉♥❛ ♣❛rtí❝✉❧❛ ♣r♦✈❡♥✐❡♥t❡ ❞❡ ✉♥❛ ❞✐str✐❜✉❝✐ó♥ ❞❡ ♠❛s❛ ❛❧❡❛t♦r✐❛ ② ✉♥❛ ♣❛rtí❝✉❧❛ ❞❡ ♠❛s❛ ♠í♥✐♠❛ ❧♦❝❛❧✐③❛❞❛s ❡♥ ✉♥ ❛♥✐❧❧♦ ❡♥ ♣❛rt✐❝✉❧❛r ② s❡♣❛r❛❞❛s ♣♦r ✉♥❛ ❞✐st❛♥❝✐❛ t❛♠❜✐é♥ ❛❧❡❛t♦r✐❛ s❡❛♥ ❛tr❛í❞❛s ♠✉t✉❛♠❡♥t❡✳ ❚❛♥t♦ ❧❛ ❞✐str✐❜✉❝✐ó♥ ❞❡ ♠❛s❛s ❝♦♠♦ ❧❛ ❞❡ ❞✐st❛♥❝✐❛s s❡ s✐♠✉❧❛♥ ❛ tr❛✈és ❞❡ ✉♥ ♠ét♦❞♦ ❞❡ ▼♦♥t❡ ❈❛r❧♦✳ ❙✉♣♦♥✐❡♥❞♦ q✉❡ ❧♦s ❣r❛♥♦s ❞❡ ♣♦❧✈♦ s♦♥ ❡s❢ér✐❝♦s ② q✉❡ ♥♦ ❤❛② ♣r♦❝❡s♦s ❞❡ ❡✈❛♣♦r❛❝✐ó♥ ♦ ❝♦❧✐s✐♦♥❡s q✉❡ ❧♦s ♣✉❡❞❛♥ r♦♠♣❡r ♦ ❞❡❢♦r♠❛r✱ ❧❛ ❞✐str✐❜✉❝✐ó♥ ❞❡ ♠❛s❛s ♣❛r❛ ✉♥ ❛♥✐❧❧♦ s❡ ❣❡♥❡r❛ ❛ ♣❛rt✐r ❞❡ ❧❛ ❡①♣r❡s✐ó♥✿ mstoc = ρm Vstoc = ρm  4 3 πa 3 stoc  ✭✸✳✶✾✮ ❊♥ ❧❛ ❊❝✳ ✭✸✳✶✾✮ ❧❛ ❞❡♥s✐❞❛❞ ❡stá ❞❛❞❛ ♣♦r ρm ✭kg m−3 ✮ ② ❡❧ r❛❞✐♦ ❞❡ ❧❛ ♣❛rtí❝✉❧❛ ❡s astoc ✭m✮✳ ▲❛s ♣❛rtí❝✉❧❛s ❡♥ ❧♦s ❛♥✐❧❧♦s ❡stá♥ ❝❛r❛❝t❡r✐③❛❞❛s ♣♦r ✉♥❛ ❞✐str✐❜✉❝✐ó♥ ❞❡ t❛♠❛ñ♦s ② ❛ ❡s♦ s❡ ❞❡❜❡ ❡❧ ❝❛rá❝t❡r ❡st♦❝ást✐❝♦ ❞❡❧ r❛❞✐♦ ② ❡♥ ❝♦♥s❡❝✉❡♥❝✐❛ ❞❡❧ ✈♦❧✉♠❡♥✳ ❉❛❞♦ q✉❡ ❧❛s ♣❛rtí❝✉❧❛s ❡stá♥ ❡♥ ♠♦✈✐♠✐❡♥t♦ t♦❞♦ ❡❧ t✐❡♠♣♦ r❡s✉❧t❛ ♥❛t✉r❛❧ ♣❡♥s❛r q✉❡ ❧❛ ❞✐st❛♥❝✐❛ q✉❡ s❡♣❛r❛ ❛ ést❛s ❞❡ ❧❛ ♣❛rtí❝✉❧❛ ♠í♥✐♠❛ ❡s ✈❛r✐❛❜❧❡ ② ❛❧❡❛t♦r✐❛✳ P❛r❛ ♦❜t❡♥❡r ❡st❛ ❞✐str✐❜✉❝✐ó♥ s❡ ♣✉❡❞❡ ♣r♦❝❡❞❡r ❞❡ ❞♦s ♠❛♥❡r❛s✿ ✶✮ ❛ ♣❛rt✐r ❞❡❧ ❛♥á❧✐s✐s ❞❡ ❞❛t♦s ♦❜s❡r✈❛❝✐♦♥❛❧❡s ✭✐♥ s✐t✉ ♦ ❞❡s❞❡ ❧❛ ❚✐❡rr❛✮ ❀ ✷✮ s✉♣♦♥❡r q✉❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ ❡s ✉♥✐❢♦r♠❡✱ ❡st♦ ❡s✱ ✈❛ ❞❡ ✉♥ ✈❛❧♦r ♠í♥✐♠♦ ❛ ✉♥ ✈❛❧♦r ♠á①✐♠♦✳ P❛r❛ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✸✳✷✳ ▼♦❞❡❧♦ ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ♣❛r❛ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ♥❡✉tr❛s ✺✾ ❡❧ s❡❣✉♥❞♦ ❝❛s♦ s❡rá ♥❡❝❡s❛r✐♦ ❤❛❝❡r ✉♥❛ s❡r✐❡ ❞❡ ❡st✐♠❛❝✐♦♥❡s ❜❛s❛❞♦s ❡♥ ❛❧❣✉♥♦s ♣❛rá♠❡tr♦s ❝♦♠♦ ❧❛ ♠❛s❛ ❞❡ ❝❛❞❛ ❛♥✐❧❧♦✱ ❡❧ ❡s♣❡s♦r ❞❡ ❝❛❞❛ ❛♥✐❧❧♦✱ ❧❛ ♣r♦❢✉♥❞✐❞❛❞ ó♣t✐❝❛✱ ❡t❝ét❡r❛✳ ✸✳✷✳✶✳✸✳ ▲❛ ❛❝❡❧❡r❛❝✐ó♥ ❞❡❜✐❞❛ ❛ ❧❛ ❢✉❡r③❛ ❞❡ ♣r❡s✐ó♥ ❞❡ r❛❞✐❛❝✐ó♥ ❱é❛s❡ ❙❡❝❝✐ó♥ ✸✳✶✳✶ ✸✳✷✳✷✳ ▲❛ ❡♥❡r❣í❛ ✜♥❛❧ ② ❧❛ ✈❡❧♦❝✐❞❛❞ ✜♥❛❧ ♣❛r❛ ❧❛ ❞✐str✐❜✉❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❞❡ ♣♦❧✈♦ ♥❡✉tr❛s ▲❛ ❡♥❡r❣í❛ ❝✐♥ét✐❝❛ ✜♥❛❧ s❡ ♦❜t✐❡♥❡ ♠❡❞✐❛♥t❡ ❧❛ ❡①♣r❡s✐ó♥✿ K2 = K1 + ∆K ✭✸✳✷✵✮ ▲❛ ✈❡❧♦❝✐❞❛❞ ② ❧❛ ♣♦s✐❝✐ó♥ ✜♥❛❧❡s ❛❧❝❛♥③❛❞❛ ♣♦r ✉♥❛ ♣❛rtí❝✉❧❛ s❡ ❝❛❧❝✉❧❛ ❝♦♥ ❧❛ ❊❝✳ ✭✸✳✶✸✮ ② ❝♦♥ ❧❛ ❊❝✳ ✭✸✳✶✹✮ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ P❛r❛ ❧♦s ❞❡t❛❧❧❡s r❡✜ér❛s❡ ❛ ❧❛ ❙❡❝❝✐ó♥ ✸✳✶✳✷✳ ❊♥ ❡st❡ ❝❛s♦✱ ❡❧ ♣❛s♦ ♥✉♠ér✐❝♦ ❡♥ ❝❛❞❛ ❞✐r❡❝❝✐ó♥ ❡stá ❞❛❞♦ ♣♦r ✉♥❛ ❢r❛❝❝✐ó♥ ❞❡ ❧❛ ❞✐st❛♥❝✐❛ ❛❧❡❛t♦r✐❛ ❡♥tr❡ ❣r❛♥♦s ❞❡ ♣♦❧✈♦✳ ❊♥ ❡st❡ ❈❛♣ít✉❧♦ s❡ ❡①♣✉s♦ ② ❞❡s❛rr♦❧❧ó ❡❧ ♠♦❞❡❧♦ ❞❡ ❡♥❡r❣✐③❛❝✐ó♥✱ q✉❡ s❡ ❜❛s❛ ❡♥ ❧❛s ✢✉❝t✉❛❝✐♦♥❡s ❛❧❡❛t♦r✐❛s ❞❡ ✉♥ ❝❛♠♣♦ ❞❡ ❢✉❡r③❛s✱ ♣❛r❛ ❧❛s ♣❛rtí❝✉❧❛s q✉❡ s❡ ❡♥❝✉❡♥tr❛♥ ❡♥ ✉♥❛ ♠❛❣♥❡tós❢❡r❛ ♣❧❛♥❡t❛r✐❛✳ ❉♦s ❛♣❧✐❝❛❝✐♦♥❡s ✐♥t❡r❡s❛♥t❡s s❡ ❞❡s❛rr♦✲ ❧❧❛♥ ❡♥ ❡❧ s✐❣✉✐❡♥t❡ ❈❛♣ít✉❧♦✳ ❯♥❛ s❡ r❡✜❡r❡ ❛❧ ❡st✉❞✐♦ ❞❡ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❡♥❡r❣ét✐❝❛s ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦ ② ❧❛ ♦tr❛ ❡s ✉♥❛ ♣r♦♣✉❡st❛ ♣❛r❛ ❡①♣❧✐❝❛r ♣❛rt❡ ❞❡ ❧❛ ❞✐♥á♠✐❝❛ ❞❡ ❧♦s ❣r❛♥♦s ❞❡ ♣♦❧✈♦ ❡♥ ❡❧ s✐st❡♠❛ ❞❡ ❛♥✐❧❧♦s ❞❡ ❙❛t✉r♥♦✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❈❛♣ít✉❧♦ ✹ ❆♣❧✐❝❛❝✐ó♥ ❞❡❧ ♠♦❞❡❧♦ ❛ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦ P♦s✐❜❧❡s ❡①♣❧✐❝❛❝✐♦♥❡s ❛ ❧❛ ♣♦❜❧❛❝✐ó♥ ♦❜s❡r✈❛❞❛ ❞❡ ♣❛rtí❝✉❧❛s ❡♥❡r❣ét✐❝❛s ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦ ✐♥✈♦❧✉❝r❛♥ ❧❛ ❧✐❜❡r❛❝✐ó♥ ❞❡ ❡♥❡r❣í❛ ♠❛❣♥ét✐❝❛ q✉❡ ❝❛❧✐❡♥t❛ ❛ ❧❛ ❝♦♠♣♦♥❡♥t❡ ✐ó♥✐❝❛ ❞❡❧ ♣❧❛s♠❛ ② ❡♥t♦♥❝❡s ❛❝❡❧❡r❛ ❛ ❧♦s ❡❧❡❝tr♦♥❡s ❛ ❡♥❡r❣í❛s ❞❡❧ ♦r❞❡♥ ❞❡ ✷ ▼❡❱ ❬❙❝❤❛r❞t ❡t ❛❧✳✱ ✶✾✽✺❪✳ ❖tr❛ ♣♦s✐❜✐❧✐❞❛❞ s♦♥ ❧♦s ❝❛♠❜✐♦s ❡♥ ❧❛ ❝♦♥✜❣✉r❛❝✐ó♥ ❞❡ ❧❛ ♠❛❣♥❡t♦❝♦❧❛ ✐♥❞✉❝✐❞♦s ♣♦r ❧❛s ♣❡rt✉r❜❛❝✐♦♥❡s ❡♥ ❡❧ ♠❡❞✐♦ ✐♥t❡r♣❧❛♥❡t❛r✐♦ q✉❡ ♣✉❡❞❡♥ ❧❧❡✈❛r ❛ ❧❛ ❛❝❡❧❡r❛❝✐ó♥ t❛♥t♦ ❞❡ ✐♦♥❡s ❝♦♠♦ ❞❡ ❡❧❡❝tr♦♥❡s ❛ ✈❛r✐♦s ❝✐❡♥t♦s ❞❡ ❦❡❱ ❬❑r✐♠✐❣✐s ❡t ❛❧✳✱ ✶✾✽✶❀ ✶✾✽✷❪✳ P❛r❛ ❡①♣❧✐❝❛r ❧❛ ❝♦♠♣♦♥❡♥t❡ ❝❛❧✐❡♥t❡ ❞❡❧ ♣❧❛s♠❛ s❡ ❛♣❧✐❝❛ ❡❧ ♠♦❞❡❧♦ ❞❡s❝r✐t♦ ❡♥ ❡❧ ❈❛♣ít✉❧♦ ✸ ❛ ❧❛ ♠❛❣♥❡tós❢❡r❛ ✭✐♥t❡r♥❛ ② ❡①t❡r♥❛✮ ❞❡ ❙❛t✉r♥♦✳ ❯♥ ♠❡❝❛♥✐s♠♦ ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❡st♦❝ást✐❝♦ s✐♠✐❧❛r ❛❧ ♣r♦♣✉❡st♦ ❡♥ ❡st❡ tr❛❜❛❥♦ ❢✉❡ ❞❡s❛rr♦❧❧❛❞♦ ♣♦r ❇❛r❜♦s❛ ❬✶✾✾✹❪ ♣❛r❛ ❞❛r ✉♥❛ ❡①♣❧✐❝❛❝✐ó♥ ❝✉❛♥t✐t❛t✐✈❛ ② ❞❡✜♥✐t✐✈❛ ❞❡ ❧❛ ❝♦♠♣♦♥❡♥t❡ ✐ó♥✐❝❛ ❞❡ ❛❧t❛ ❡♥❡r❣í❛ ♣r❡s❡♥t❡ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❏♦✈✐❛♥❛✳ ❊♥ s✉ tr❛❜❛❥♦ ❞❡r✐✈ó ✉♥❛ ❡❝✉❛❝✐ó♥ q✉❡ ✐♥❝❧✉②❡ ❛ ❧❛ ❞✐❢✉s✐ó♥ r❛❞✐❛❧ ② ❛ ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ❡st♦❝ást✐❝❛ ❞❡ ✢✉✲ ❥♦s ❞❡ ✐♦♥❡s s✉♣❡r ❆❧❢✈é♥✐❝♦s ♣♦r ❧❛ ❛❝❝✐ó♥ ❞❡ ♦♥❞❛s ♠❛❣♥❡t♦❤✐❞r♦❞✐♥á♠✐❝❛s ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ ❏♦✈✐❛♥❛✳ P❛r❛ ❡❧❧♦✱ s✉♣✉s♦ q✉❡ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❏♦✈✐❛♥❛ s❡ ♣r♦♣❛❣❛♥ ❝✐❡rt♦ t✐♣♦ ❞❡ ♦♥❞❛s q✉❡ ❡♥tr❛♥ ❡♥ r❡s♦♥❛♥❝✐❛ ❝♦♥ ❧❛s ♣❛rtí❝✉❧❛s ② ❡st♦ s❡ ✈❡ r❡✢❡❥❛❞♦ ❡♥ ❡❧ ❝♦❡✜❝✐❡♥t❡ ❞❡ ❞✐❢✉s✐ó♥ ❡♥ ❧❛ ❡❝✉❛❝✐ó♥ ❞❡ ❋♦❦❦❡r✲P❧❛♥❝❦✳ ✻✵ ✹✳✶✳ P❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ✭♣r♦t♦♥❡s✱ ✐♦♥❡s ♣❡s❛❞♦s ② ❣r❛♥♦s ❞❡ ♣♦❧✈♦✮ ✻✶ ❊st❡ ❈❛♣ít✉❧♦ s❡ ❞❡❞✐❝❛ ❛ ❧❛ ❛♣❧✐❝❛❝✐ó♥ ❞❡❧ ♠♦❞❡❧♦ ❡①♣✉❡st♦ ♣r❡✈✐❛♠❡♥t❡ ❛ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦✳ ❘❡❝✉ér❞❡s❡ q✉❡ ❡❧ ♠♦❞❡❧♦ s❡ ❜❛s❛ ❡♥ ❧❛s ✢✉❝t✉❛❝✐♦♥❡s ❛❧❡❛t♦r✐❛s ❞❡❧ ❝❛♠♣♦ ❞❡ ❢✉❡r③❛s✳ ❊♥ ❡❧ ❝❛s♦ ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦ s❡ ❝♦♥✲ s✐❞❡r❛♥ ❧❛s ✢✉❝t✉❛❝✐♦♥❡s ♠❛❣♥ét✐❝❛s ♠❡❞✐❞❛s ❞❡♥tr♦ ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ✭♣❛r❛ ❡❧ ♠♦❞❡❧♦ ❞❡ ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s✮ ② ❡♥ ❧❛s ✢✉❝t✉❛❝✐♦♥❡s ❣r❛✈✐t❛❝✐♦♥❛❧❡s ✐♥❢❡r✐❞❛s ♣❛r❛ ❣r❛♥♦s ❞❡ ♣♦❧✈♦ ✭♣❛r❛ ❡❧ ♠♦❞❡❧♦ ❞❡ ♣❛rtí❝✉❧❛s ♥❡✉tr❛s✮✳ ▲❛s ♣❛rtí❝✉❧❛s ✐♥t❡r❛❝tú❛♥ ❝♦♥ ❞✐❢❡r❡♥t❡s ♣♦❜❧❛❝✐♦♥❡s✱ q✉❡ ✈❛♥ ❞❡s❞❡ ❧♦s ♣r♦t♦♥❡s ❤❛st❛ ♣r♦❞✉❝t♦s ❞❡r✐✈❛❞♦s ❞❡❧ ❛❣✉❛✳ ✹✳✶✳ P❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ✭♣r♦t♦♥❡s✱ ✐♦♥❡s ♣❡s❛❞♦s ② ❣r❛♥♦s ❞❡ ♣♦❧✈♦✮ ▲❛ ❡❝✉❛❝✐ó♥ ❞❡ ♠♦✈✐♠✐❡♥t♦ q✉❡ ♦❜❡❞❡❝❡♥ ❧❛s ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ❡stá ❞❛❞❛ ♣♦r ❧❛ ❊❝✳ ✭✸✳✶✮✳ ❊♥ ❡❧ ♣r✐♠❡r tér♠✐♥♦ s❡ ❝❛❧❝✉❧❛ ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ❞❡❜✐❞❛ ❛ ❧❛ ❢✉❡r③❛ ❞❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❡st♦❝ást✐❝♦✳ ❊♥ ❧❛ s✐❣✉✐❡♥t❡ s❡❝❝✐ó♥ s❡ ❡①♣❧✐❝❛ ❧❛ ♦❜t❡♥❝✐ó♥ ❞❡ ❡st❡ ❝❛♠♣♦ ❞❡♥tr♦ ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦✳ ✹✳✶✳✶✳ ❊❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❡st♦❝ást✐❝♦ P❛r❛ ❡st❡ tr❛❜❛❥♦ s❡ ❡♠♣❧❡❛♥ ❧♦s ❞❛t♦s ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ♠❡❞✐❞♦s ♣♦r ❡❧ ♠❛❣♥❡tó♠❡tr♦ tr✐❛①✐❛❧ ❛ ❜♦r❞♦ ❞❡ ❧❛ ♥❛✈❡ ❱♦②❛❣❡r ✶ ② ❱♦②❛❣❡r ✷ ❡♥ ❡❧ s✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s ❙❙❖ ✭❙❛t✉r♥ ❙♦❧❛r ❖r❜✐t ✮✳ ❇ás✐❝❛♠❡♥t❡ ❡❧ s✐st❡♠❛ ❙❙❖ ❡s ❛♥á❧♦❣♦ ❛❧ s✐st❡♠❛ ❝♦♦r❞❡♥❛❞♦ ✉t✐❧✐③❛❞♦ ♣❛r❛ ❧❛ ❚✐❡rr❛✱ ❡st♦ ❡s✱ ❡❧ ●❙❊ ✭●❡♦❝❡♥tr✐❝ ❊❝❧✐♣t✐❝ ✮ ❙♦❧❛r ❡♥ ❞♦♥❞❡ ❧❛ ❞✐r❡❝❝✐ó♥ ✏①✑ ♣❛rt❡ ❞❡❧ ❝❡♥tr♦ ❞❡ ♠❛s❛ ✐♥st❛♥tá♥❡♦ ❞❡ ❙❛t✉r♥♦ ② ❛♣✉♥t❛ ♣♦s✐t✐✈❛♠❡♥t❡ ❤❛❝✐❛ ❡❧ ❙♦❧❀ ✏③✑ ❡s ❧❛ ♥♦r♠❛❧ ❛❧ ♣❧❛♥♦ ♦r❜✐t❛❧ ❞❡ ❙❛t✉r♥♦ ② ❛♣✉♥t❛ ♣♦s✐t✐✈❛♠❡♥t❡ ❤❛❝✐❛ ❛rr✐❜❛ ✭s❡ ❡♥❝✉❡♥tr❛ t♦♠❛♥❞♦ ❡❧ ♣r♦❞✉❝t♦ ✈❡❝t♦r✐❛❧ ❛♣r♦♣✐❛❞♦ ❡♥tr❡ ❧♦s ✈❡❝t♦r❡s ♣♦s✐❝✐ó♥ ② ✈❡❧♦❝✐❞❛❞ ❞❡❧ ♣❧❛♥❡t❛✮❀ ② ✏②✑ ❝♦♠♣❧❡t❛ ❡st❡ s✐st❡♠❛ ♦rt♦❣♦♥❛❧ s✐❡♥❞♦ ♣♦s✐t✐✈♦ ❤❛❝✐❛ ❡❧ ❧❛❞♦ ❛t❛r❞❡❝❡r✳ ❆ú♥ ❝✉❛♥❞♦ ❡❧ ❡❥❡ ❞✐♣♦❧❛r ❞❡ ❙❛t✉r♥♦ ❡stá ✐♥❝❧✐♥❛❞♦ ✷✻✳✼✸⋄ ❝♦♥ r❡s♣❡❝t♦ ❛❧ ❡❥❡ ③ ❞❡❧ s✐st❡♠❛ ❙❙❖✱ ❡❧ ♠♦❞❡❧♦ ❡♥ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✹✳✶✳ P❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ✭♣r♦t♦♥❡s✱ ✐♦♥❡s ♣❡s❛❞♦s ② ❣r❛♥♦s ❞❡ ♣♦❧✈♦✮ ✻✷ s✉ t♦t❛❧✐❞❛❞ ❡stá ❞❡s❛rr♦❧❧❛❞♦ ❡♥ ✉♥ s✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s r❡❝t❛♥❣✉❧❛r ❝✉②♦ ❡❥❡ ③ s❡ ❡♥❝✉❡♥tr❛ ❡♥ ❧❛ ♠✐s♠❛ ❞✐r❡❝❝✐ó♥ q✉❡ ❡❧ ❡❥❡ ❞❡❧ ❞✐♣♦❧♦✳ ▲❛ r❡s♦❧✉❝✐ó♥ t❡♠♣♦r❛❧ ❞❡ ❧♦s ❞❛t♦s ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ♣❛r❛ ❛♠❜❛s ♥❛✈❡s ❡s ❞❡ ✶✳✾✷ s❡❣✉♥❞♦s ❞✉r❛♥t❡ s✉s r❡s♣❡❝t✐✈♦s ❡♥❝✉❡♥tr♦s ❝♦♥ ❙❛t✉r♥♦✳ ❊❧ ❱♦②❛❣❡r ✶ s❡ ♠♦✈✐ó ❞❡♥tr♦ ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡❧ ✶✷ ❞❡ ◆♦✈✐❡♠❜r❡ ❞❡ ✶✾✽✵ ❛ ❧❛s ✵✶✿✺✹ ❯❚ ❤❛st❛ ❡❧ ✶✹ ❞❡ ◆♦✈✐❡♠❜r❡ ❞❡ ✶✾✽✵ ❛ ❧❛s ✷✶✿✹✵ ❯❚✱ ♠✐❡♥tr❛s q✉❡ ❡❧ ❱♦②❛❣❡r ✷ ❧♦ ❤✐③♦ ❞❡s❞❡ ❡❧ ✷✺ ❞❡ ❛❣♦st♦ ❞❡ ✶✾✽✶ ❛ ❧❛s ✵✼✿✵✶ ❯❚ ❤❛st❛ ❡❧ ✷✽ ❞❡ ❛❣♦st♦ ❞❡ ✶✾✽✶ ❛ ❧❛s ✷✵✿✸✼ ❯❚✳ ❙❡ ❡stá ❝♦♥s✐❞❡r❛♥❞♦ ❡❧ ♣r✐♠❡r ❝r✉❝❡ ❞❡ ❧❛ ❡♥tr❛❞❛ ② ❡❧ q✉✐♥t♦ ❝r✉❝❡ ❞❡ s❛❧✐❞❛ ♣♦r ❧❛ ♠❛❣♥❡t♦♣❛✉s❛ ❝♦♠♦ ❧í♠✐t❡s ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❬❇r✐❞❣❡ ❡t ❛❧✳✱ ✶✾✽✶❀ ◆❡ss ❡t ❛❧✳✱ ✶✾✽✷❪✳ ▲❛ ❋✐❣✉r❛ ✹✳✶ ♠✉❡str❛ ❧❛s tr❛②❡❝t♦r✐❛s s❡❣✉✐❞❛s ♣♦r ❧❛s ♥❛✈❡s ❡♥ s✉s r❡s♣❡❝t✐✈♦s ❡♥❝✉❡♥tr♦s ❝♦♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦✳ P❛r❛ s✉ ❡st✉❞✐♦ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦ s❡ ❞✐✈✐❞❡ ❡♥ ❞♦s r❡❣✐♦♥❡s ❞❡ ❛❝✉❡r❞♦ ❝♦♥ ❧❛ ❝♦♥✜❣✉r❛❝✐ó♥ ❞❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦✱ ❡st♦ ❡s✱ ❧❛ r❡❣✐ó♥ ✐♥t❡r♥❛ ❡stá ❝❛r❛❝t❡r✐③❛✲ ❞❛ ♣♦r ✉♥ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ q✉❡ ♥♦ ❡s ❝♦♠♣❧❡t❛♠❡♥t❡ ❞✐♣♦❧❛r ♣✉❡s ❧❛s ❝♦♠♣♦♥❡♥t❡s ♠✉❧t✐♣♦❧❛r❡s ♥♦ s♦♥ ❞❡s♣r❡❝✐❛❜❧❡s ✭❡st♦ ♦❝✉rr❡ ❛ ❞✐st❛♥❝✐❛s < ✶✵ RS ✮ ② ❧❛ r❡❣✐ó♥ ❡①t❡r♥❛ ❡s ❛q✉❡❧❧❛ ❞♦♥❞❡ ❡❧ ❝❛♠♣♦ ❡s ♣rá❝t✐❝❛♠❡♥t❡ ❞✐♣♦❧❛r ✭> ✶✵ RS ✮✳ ❊♥ ❧❛ ♠❛❣✲ ♥❡tós❢❡r❛ ❡①t❡r♥❛ s❡ ❝♦♥s✐❞❡r❛♥ ❧❛s tr❛②❡❝t♦r✐❛s ❞❡ ❡♥tr❛❞❛ ② ❞❡ s❛❧✐❞❛ ♣♦r s❡♣❛r❛❞♦✱ ❡st♦ ❡s✱ ♣❛r❛ ❛♥❛❧✐③❛r ♣♦s✐❜❧❡s ✢✉❝t✉❛❝✐♦♥❡s ❞❡❜✐❞❛s ❛❧ ❝r✉❝❡ ♣♦r ❧❛ ♠❛❣♥❡t♦❝♦❧❛✳ ❊❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ♦❜s❡r✈❛❞♦ ♣♦r ❛♠❜❛s ♥❛✈❡s t✐❡♥❡ ❞♦s ❝♦♠♣♦♥❡♥t❡s✿ ❡s♣❛❝✐❛❧ ② t❡♠♣♦r❛❧✳ ❙✐ s❡ ❛s✉♠❡ q✉❡ ❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❡s♣❛❝✐❛❧ ❞❡ ❙❛t✉r♥♦ ❡stá ❜✐❡♥ r❡♣r❡s❡♥t❛❞♦ ♣♦r ✉♥ ❞✐♣♦❧♦ ❞❡ ♠♦♠❡♥t♦ ✵✳✷✶ ± ✵✳✵✺ Gauss R3S ✶ ✭✸✳✺✵✷✺x1018 T m3 ✱ ✺✳✻✾✶✻x1018 T m3 ✮ ❬◆❡ss ❡t ❛❧✳✱ ✶✾✽✶❪✱ s❡ ❝❛❧❝✉❧❛ ❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ r❡s✐❞✉❛❧✱ BR ✱ ❡♥ ✉♥ ♣✉♥t♦ ♣❛rt✐❝✉❧❛r ❞❡ ❧❛ tr❛②❡❝t♦r✐❛ ❞❡ ❧❛s ♣❛rtí❝✉❧❛s ✭❋✐❣✉r❛ ✹✳✷ ② ❋✐❣✉r❛ ✹✳✸✮✿ ✭✹✳✶✮ BR = BO − BD ❉♦♥❞❡ BO ❡s ❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ♦❜s❡r✈❛❞♦ ② BD ❡s ❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❞✐♣♦❧❛r✳ P❛r❛ ♦❜t❡♥❡r ❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❞✐♣♦❧❛r s❡ ❝♦♥s✐❞❡r❛♥ ❧❛s ❡①♣r❡s✐♦♥❡s ❞❡r✐✈❛❞❛s ♣♦r ❑✐✈❡❧s♦♥ ② ❘✉ss❡❧❧ ❬✶✾✾✼❪ ② ♣❛r❛ ❙❛t✉r♥♦ s❡ ❡st✐♠❛ ❡❧ ✈❛❧♦r ❞❡❧ ♠♦♠❡♥t♦ ❞✐♣♦❧❛r ✶ ❙❡ ❝♦♥s✐❞❡r❛ q✉❡ Gauss cm −3 1 RS =✻✳✵✷✻✽x109 cm ♣❛r❛ t❡♥❡r ✉♥✐❞❛❞❡s ❡♥ ❡❧ s✐st❡♠❛ ❈●❙✱ ❡st♦ ❡s✱ ✳ ❊♥ ❡st❡ tr❛❜❛❥♦ s❡ ✉t✐❧✐③❛ ❡❧ s✐st❡♠❛ ▼❑❙✱ ♣♦r ❧♦ q✉❡ s❡rá ♥❡❝❡s❛r✐♦ ✭❛❞❡♠ás ❞❡ q✉❡ ❡❧ r❛❞✐♦ ❞❡❜❡ ❡st❛r ❡♥ ♠❡tr♦s✮ ♠✉❧t✐♣❧✐❝❛r ♣♦r ✉♥ ❢❛❝t♦r ❞❡ 10−4 ♣❛r❛ t❡♥❡r T m3 ✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✹✳✶✳ P❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ✭♣r♦t♦♥❡s✱ ✐♦♥❡s ♣❡s❛❞♦s ② ❣r❛♥♦s ❞❡ ♣♦❧✈♦✮ ✻✸ ❋✐❣✉r❛ ✹✳✶✿ ❱✐st❛ ❡❝✉❛t♦r✐❛❧ ❞❡ ❧❛ tr❛②❡❝t♦r✐❛ ❞❡ ❧❛s ♥❛✈❡s ❱♦②❛❣❡r ❡♥ s✉ ❡♥❝✉❡♥tr♦ ❝♦♥ ❙❛t✉r♥♦✳ ❙♦❜r❡ ❧❛s tr❛②❡❝t♦r✐❛s ❧♦s ♣✉♥t♦s ♥❡❣r♦s ♠❛r❝❛❞♦s ❝♦♠♦ ❙ ✐♥❞✐❝❛♥ ❧♦s ❝r✉❝❡s ♣♦r ❡❧ ❢r❡♥t❡ ❞❡ ❝❤♦q✉❡ ② ❧♦s r❡❝tá♥❣✉❧♦s ♥❡❣r♦s ♠❛r❝❛❞♦s ❝♦♠♦ ▼ ✐♥❞✐❝❛♥ ❧♦s ❝r✉❝❡s ♣♦r ❧❛ ♠❛❣♥❡t♦♣❛✉s❛✳ ▲❛ ❞✐r❡❝❝✐ó♥ ❤❛❝✐❛ ❡❧ ❙♦❧ ❡s ♣♦s✐t✐✈❛✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✹✳✶✳ P❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ✭♣r♦t♦♥❡s✱ ✐♦♥❡s ♣❡s❛❞♦s ② ❣r❛♥♦s ❞❡ ♣♦❧✈♦✮ 0 50000 VO YA G ER 1 100000 150000 Campo magnético residual (nT) 1600 INTERNA (< 10 Rs) 1400 EXTERNA ENTRADA (>= 10 Rs) 1200 1000 ✻✹ 200000 1600 1400 EXTERNA SALIDA (>= 10 Rs) 1200 1000 800 800 600 600 400 400 200 200 0 0 -200 0 50000 100000 150000 -200 200000 T iem po (seg) ❋✐❣✉r❛ ✹✳✷✿ ❈❛♠♣♦ ♠❛❣♥ét✐❝♦ r❡s✐❞✉❛❧ ♦❜t❡♥✐❞♦ ♣❛r❛ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦ ❜❛s❛❞♦ ❡♥ ❧❛s ♦❜s❡r✈❛❝✐♦♥❡s ❞❡❧ ❱♦②❛❣❡r ✶✳ ❝♦♠♦✿ MS = ✸✳✾✻✷✺x1018 T m3 ✭❱♦②❛❣❡r ✶✮ ② MS = ✺✳✵✻✺✼x1018 T m3 ✭❱♦②❛❣❡r ✷✮✳ ❊♥ ❡st❡ ❡st✉❞✐♦ ❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ r❡s✐❞✉❛❧ t✐❡♥❡ s♦❧❛♠❡♥t❡ ✈❛r✐❛❝✐♦♥❡s t❡♠✲ ♣♦r❛❧❡s ♣✉❡s ést❛s s♦♥ ♠❛②♦r❡s q✉❡ ❧❛s ❡s♣❛❝✐❛❧❡s✳ ❊♥ ❧❛ ❋✐❣✉r❛ ✹✳✹ s❡ ♠✉❡str❛ ✉♥❛ ❝♦♠♣❛r❛❝✐ó♥ ❡♥tr❡ ❧❛s ✈❛r✐❛❝✐♦♥❡s t❡♠♣♦r❛❧❡s ② ❡s♣❛❝✐❛❧❡s ♦❜t❡♥✐❞❛s ♣❛r❛ ❧❛s ♠❡✲ ❞✐❝✐♦♥❡s ❞❡❧ ❱♦②❛❣❡r ✶ ❞❡♥tr♦ ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦ ✭❛♥á❧♦❣❛♠❡♥t❡ ♣❛r❛ ❡❧ ❱♦②❛❣❡r ✷✮✳ ❉❡♥tr♦ ❞❡❧ ♣♦❧í❣♦♥♦ s❡ ❡♥❝✉❡♥tr❛♥ ✈❛r✐❛❝✐♦♥❡s t❡♠♣♦r❛❧❡s ❤❛st❛ ✹ ór❞❡♥❡s ❞❡ ♠❛❣♥✐t✉❞ ♠❛②♦r❡s q✉❡ ❧❛s ✈❛r✐❛❝✐♦♥❡s ❡s♣❛❝✐❛❧❡s✳ ❊♥t♦♥❝❡s ❧❛s ✢✉❝t✉❛❝✐♦♥❡s ❞❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦✱ ∆B✱ s♦♥ ❝❛❧❝✉❧❛❞❛s t♦♠❛♥❞♦ ❡♥ ❝✉❡♥t❛ ❧❛ ❞✐❢❡r❡♥❝✐❛ ❡♥tr❡ ♣✉♥t♦s ❛❞②❛❝❡♥t❡s ❞❡ ❧♦s r❡s✐❞✉❛❧❡s✳ ▲❛ ❋✐❣✉r❛ ✹✳✺ ✐❧✉str❛ ❧❛s ✢✉❝t✉❛❝✐♦♥❡s t❡♠♣♦r❛❧❡s ❞❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛ ❞❡ ❙❛t✉r♥♦ ② ❧❛s ❋✐❣✉r❛s ✹✳✻ ② ✹✳✼ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ ✭tr❛②❡❝t♦r✐❛ ❞❡ ❡♥tr❛❞❛ ② s❛❧✐❞❛✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✮ ❜❛s❛❞❛s ❡♥ ❧❛s ♠❡❞✐❝✐♦♥❡s ❞❡❧ ❱♦②❛❣❡r ✷✳ ❆♥á❧♦❣❛♠❡♥t❡ s✉❝❡❞❡ ♣❛r❛ ❧❛s ♠❡❞✐❝✐♦♥❡s ❞❡❧ ❱♦②❛❣❡r ✶✳ ❉❡ ❧❛s ❣rá✜❝❛s ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✹✳✶✳ P❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ✭♣r♦t♦♥❡s✱ ✐♦♥❡s ♣❡s❛❞♦s ② ❣r❛♥♦s ❞❡ ♣♦❧✈♦✮ 0 50000 Campo magnético residual (nT) 200 EXTERNA ENTRADA (>= 10 Rs) 100 VOYAGER 2 100000 150000 INTERNA (< 10 Rs) EXTERNA SALIDA (>= 10 Rs) ✻✺ 200000 200 100 0 0 -100 -100 -200 0 50000 100000 150000 -200 200000 Tiem po (seg) ❋✐❣✉r❛ ✹✳✸✿ ❈❛♠♣♦ ♠❛❣♥ét✐❝♦ r❡s✐❞✉❛❧ ♦❜t❡♥✐❞♦ ♣❛r❛ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦ ❜❛s❛❞♦ ❡♥ ❧❛s ♦❜s❡r✈❛❝✐♦♥❡s ❞❡❧ ❱♦②❛❣❡r ✷✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✹✳✶✳ P❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ✭♣r♦t♦♥❡s✱ ✐♦♥❡s ♣❡s❛❞♦s ② ❣r❛♥♦s ❞❡ ♣♦❧✈♦✮ 1E-14 10 -7 1E-13 1E-12 1E-11 1E-10 1E-9 ✻✻ 1E-8 -7 10 Fluctuaciones temporales (nT) VOYAGER 1 10 -8 10 -8 10 -9 10 -9 -10 10 -10 -11 10 -11 -12 10 -12 10 10 10 10 -14 10 -13 -12 10 10 -11 10 -10 10 -9 10 -8 Fluctuaciones espaciales (nT) ❋✐❣✉r❛ ✹✳✹✿ ❈♦♠♣❛r❛❝✐ó♥ ❡♥tr❡ ❧❛s ✢✉❝t✉❛❝✐♦♥❡s t❡♠♣♦r❛❧❡s ② ❧❛s ✢✉❝t✉❛❝✐♦♥❡s ❡s✲ ♣❛❝✐❛❧❡s ♦❜t❡♥✐❞❛s ♣❛r❛ ❧❛s ♠❡❞✐❝✐♦♥❡s ❞❡❧ ❱♦②❛❣❡r ✶ ❞❡♥tr♦ ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✹✳✶✳ P❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ✭♣r♦t♦♥❡s✱ ✐♦♥❡s ♣❡s❛❞♦s ② ❣r❛♥♦s ❞❡ ♣♦❧✈♦✮ ✻✼ M A G N E T O S F E R A IN T E R N A (< 10 R s) Fluctuaciones del campo magnético (nT) 10 V O Y AG E R 2 1 60000 70000 80000 90000 100000 T ie m p o (s ) ❋✐❣✉r❛ ✹✳✺✿ ❋❧✉❝t✉❛❝✐♦♥❡s t❡♠♣♦r❛❧❡s ❞❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ✐♥✲ t❡r♥❛ ❞❡ ❙❛t✉r♥♦ ♦❜t❡♥✐❞❛s ♠❡❞✐❛♥t❡ ❧❛s ♠❡❞✐❝✐♦♥❡s ❞❡❧ ❱♦②❛❣❡r ✷✳ s❡ ♦❜s❡r✈❛ q✉❡ ❤❛② ♠ás ✢✉❝t✉❛❝✐♦♥❡s ✐♥t❡♥s❛s ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ ✭s❛❧✐❞❛✮ q✉❡ ❡♥ ❧❛ ✐♥t❡r♥❛✱ ♣❡r♦ ♥♦ ❡①❝❡❞❡♥ ❧♦s ✶✵ ♥❚✳ ❉❡ ❧❛s ❡❝✉❛❝✐♦♥❡s ❞❡ ▼❛①✇❡❧❧ s❡ ♦❜t✐❡♥❡ ❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❛s♦❝✐❛❞♦ ❡♥ ❝❛❞❛ ❞✐r❡❝❝✐ó♥ ❡s♣❛❝✐❛❧✳ ❆s✉♠✐❡♥❞♦ ❝✉❛s✐♥❡✉tr❛❧✐❞❛❞✱ ❡st♦ ❡s✱ ρ = 0 ② q✉❡ ❧♦s ❝❛♠❜✐♦s ❞❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❛ tr❛✈és ❞❡ ❧❛ tr❛②❡❝t♦r✐❛ ❞❡ ❧❛ ♥❛✈❡ s♦♥ ❧♦ s✉✜❝✐❡♥t❡♠❡♥t❡ ♣❡q✉❡ñ♦s ✭∆ ≈ δ ✮✱ ❡st❛s ❡❝✉❛❝✐♦♥❡s s❡ r❡s✉❡❧✈❡♥ ♣❛r❛ ❧❧❡❣❛r ❛✿ ∆Ex = ∆Bz ∆t  1 ∆xT ∆xT ∆yT ∆xT ∆yT (∆zT )2 + + ∆xT   1 (∆yT )2 + + ∆Bx ∆yT ∆t ∆zT 1 (∆zT )2  ✭✹✳✷✮ ∆Ey = ∆xT  ∆Ex ∆Bz − ∆yT ∆t  ✭✹✳✸✮ ∆Ez = ∆xT  ∆Ex ∆By + ∆zT ∆t  ✭✹✳✹✮ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✹✳✶✳ P❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ✭♣r♦t♦♥❡s✱ ✐♦♥❡s ♣❡s❛❞♦s ② ❣r❛♥♦s ❞❡ ♣♦❧✈♦✮ ✻✽ M A G N E T O S F E R A E X T E R N A (> = 10 R s) Fluctuaciones del campo magnético (nT) 10 V O Y AG E R 2 (E N T R AD A) 1 0 .1 0 .0 1 0 5000 10000 15000 20000 25000 30000 35000 T ie m p o (s ) ❋✐❣✉r❛ ✹✳✻✿ ❋❧✉❝t✉❛❝✐♦♥❡s t❡♠♣♦r❛❧❡s ❞❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①✲ t❡r♥❛ ❞❡ ❙❛t✉r♥♦ ♦❜t❡♥✐❞❛s ♠❡❞✐❛♥t❡ ❧❛s ♠❡❞✐❝✐♦♥❡s ❞❡❧ ❱♦②❛❣❡r ✷ ❡♥ s✉ tr❛②❡❝t♦r✐❛ ❞❡ ❡♥tr❛❞❛✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✹✳✶✳ P❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ✭♣r♦t♦♥❡s✱ ✐♦♥❡s ♣❡s❛❞♦s ② ❣r❛♥♦s ❞❡ ♣♦❧✈♦✮ ✻✾ Fluctuaciones del campo magnético (nT) M A G N E T O S F E R A E X T E R N A (> = 10 R s) V O Y AG E R 2 (S AL ID A) 10 1 0 .1 100000 150000 200000 250000 300000 T ie m p o (s ) ❋✐❣✉r❛ ✹✳✼✿ ❋❧✉❝t✉❛❝✐♦♥❡s t❡♠♣♦r❛❧❡s ❞❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①✲ t❡r♥❛ ❞❡ ❙❛t✉r♥♦ ♦❜t❡♥✐❞❛s ♠❡❞✐❛♥t❡ ❧❛s ♠❡❞✐❝✐♦♥❡s ❞❡❧ ❱♦②❛❣❡r ✷ ❡♥ s✉ tr❛②❡❝t♦r✐❛ ❞❡ s❛❧✐❞❛✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✹✳✶✳ P❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ✭♣r♦t♦♥❡s✱ ✐♦♥❡s ♣❡s❛❞♦s ② ❣r❛♥♦s ❞❡ ♣♦❧✈♦✮ ✼✵ ❊♥ ❧❛s ❊❝s✳ ✭✹✳✷✱ ✹✳✸ ② ✹✳✹✮ ❧❛s ❞✐❢❡r❡♥❝✐❛s ❡♥tr❡ r❡s✐❞✉❛❧❡s ♦❜t❡♥✐❞❛s ❛ tr❛✈és ❞❡ ❧❛ ❊❝✳ ✭✹✳✶✮ ❡stá♥ r❡♣r❡s❡♥t❛❞❛s ♣♦r ∆Bx ✱ ∆By ② ∆Bz ✳ ▲❛ ❞✐❢❡r❡♥❝✐❛✱ ❡♥ ❝❛❞❛ ❞✐r❡❝❝✐ó♥✱ ❡♥tr❡ ♣♦s✐❝✐♦♥❡s ❛❞②❛❝❡♥t❡s ❞❡ ❧❛ tr❛②❡❝t♦r✐❛ ❞❡ ❧❛ ♥❛✈❡ ❡stá ❞❛❞❛ ♣♦r ∆xT ✱ ∆yT ② ∆zT ✳ ◆ót❡s❡ q✉❡ ❤❛② s✐♥❣✉❧❛r✐❞❛❞❡s ❝✉❛♥❞♦ ∆xT = ∆yT = ∆zT = 0✱ ❡♥ ❡s♦s ❝❛s♦s ❡❧ ✈❛❧♦r ❞❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ♥♦ ❡s ❝♦♥s✐❞❡r❛❞♦✳ ❊s ✐♠♣♦rt❛♥t❡ s❡ñ❛❧❛r q✉❡ ❡st♦s ❝❛s♦s ♥♦ ❛❢❡❝t❛♥ ❧❛ ❞✐str✐❜✉❝✐ó♥ t❡♠♣♦r❛❧ ❞❡ ❧♦s ❞❛t♦s ②❛ q✉❡ ❡stá♥ ♠✉❡str❡❛❞❛s ❝♦♥ ❧❛ ♠✐s♠❛ r❡s♦❧✉❝✐ó♥ ❞❡ ✶✳✾✷ s❡❣✉♥❞♦s✳ ❉❡ ❛❝✉❡r❞♦ ❝♦♥ ❧♦ ❡①♣✉❡st♦ ❡♥ ❡❧ ❈❛♣ít✉❧♦ ✸✱ ❡❧ ❝❛rá❝t❡r ❡st♦❝ást✐❝♦ ❞❡❧ ❝❛♠♣♦ ♦❜t❡♥✐❞♦ ❡♥ ❧❛s ❡❝✉❛❝✐♦♥❡s ❛♥t❡r✐♦r❡s ❡s s✐♠✉❧❛❞♦ ❛ tr❛✈és ❞❡ ✉♥ ♠ét♦❞♦ ❞❡ ▼♦♥t❡ ❈❛r❧♦✿ ✶✳ Pr✐♠❡r♦ ❡s ♥❡❝❡s❛r✐♦ ❝♦♥♦❝❡r ❧❛ ❢✉♥❝✐ó♥ ❞❡ ❞❡♥s✐❞❛❞ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞ ✭♣❞❢✮ q✉❡ ♠❡❥♦r s❡ ❛❥✉st❛ ❛ ❧♦s r❡s✉❧t❛❞♦s ② ♣❛r❛ ❡♥❝♦♥tr❛r❧❛ s❡ r❡❛❧✐③❛♥ ♣r✉❡❜❛s ❞❡ ❤✐✲ ♣ót❡s✐s ❞❡ ❜♦♥❞❛❞ ❞❡ ❛❥✉st❡ ✭❆♣é♥❞✐❝❡ ❆✮ ❡♠♣❧❡❛♥❞♦ ❡❧ ✈❛❧♦r ❞❡❧ ❡st❛❞íst✐❝♦ ❆♥❞❡rs♦♥✲❉❛r❧✐♥❣ ❛❧ ✾✺ ✪ ❞❡ s✐❣♥✐✜❝❛♥❝✐❛ ❬❙t❡♣❤❡♥s✱ ✶✾✼✹❪✳ ▲❛s ❢✉♥❝✐♦♥❡s ♣r✉❡✲ ❜❛ ❝♦rr❡s♣♦♥❞❡♥ ❛ ❧❛ ❞✐str✐❜✉❝✐ó♥ ♥♦r♠❛❧✱ ❡①♣♦♥❡♥❝✐❛❧✱ ❧♦❣íst✐❝❛✱ ❧♦❣♥♦r♠❛❧✱ ❲❡✐❜✉❧❧✱ ✉♥✐❢♦r♠❡ ② ❞❡ ✈❛❧♦r ❡①tr❡♠♦✳ ▲❛ r❡❣❧❛ ❞❡ ❞❡❝✐s✐ó♥ ♣❛r❛ ❡st❛ ♣r✉❡❜❛ ❞❡ ❤✐♣ót❡s✐s ❡st❛❜❧❡❝❡ q✉❡ ✉♥ ✈❛❧♦r ♣❡q✉❡ñ♦ ❞❡❧ ❡st❛❞íst✐❝♦ ❡❧❡❣✐❞♦ ✐♥❞✐❝❛ q✉❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ ♣r✉❡❜❛ s❡ ❛❥✉st❛ ❜✐❡♥ ❛ ❧♦s ❞❛t♦s✳ P❛r❛ ❝❛❞❛ ❝♦♠♣♦♥❡♥t❡ ❞❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ∆E s❡ ❡♥❝✉❡♥tr❛ q✉❡ ❧❛ ❢✉♥❝✐ó♥ ❧♦❣íst✐❝❛ ❬❇❛❧❛❦r✐s❤♥❛♥✱ ✶✾✾✷❪ ❡s ❧❛ ❢✉♥❝✐ó♥ ❞❡ ❞✐str✐❜✉❝✐ó♥ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞ ♠ás ❛❞❡❝✉❛❞❛ ✭❆♣é♥❞✐❝❡ ❇✮✱ ♣❡✲ r♦ ♥♦ ♥❡❝❡s❛r✐❛♠❡♥t❡ ❡s ❧❛ q✉❡ ♠❡❥♦r s❡ ❛❥✉st❛✳ ❈♦♠♦ ❡❥❡♠♣❧♦ s❡ ♠✉❡str❛ ❧❛ ❋✐❣✉r❛ ✹✳✽ ❞♦♥❞❡ s❡ ❣r❛✜❝❛ ❡❧ ❤✐st♦❣r❛♠❛ ❞❡ ❢r❡❝✉❡♥❝✐❛s ♣❛r❛ ❧❛ ❝♦♠♣♦♥❡♥t❡ ✏①✑ ❞❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ♦❜s❡r✈❛❞♦ ② s✉ ❝✉r✈❛ ❞❡ ❛❥✉st❡ ✭❢✉♥❝✐ó♥ ❧♦❣íst✐❝❛✮✳ ❙❡ ♦❜s❡r✈❛ q✉❡ ❡st❛ ❢✉♥❝✐ó♥ ♥♦ ❡s ❡①❛❝t❛♠❡♥t❡ ❧❛ q✉❡ s❡ ❛❥✉st❛ ❛ ❧❛ ❞✐str✐❜✉❝✐ó♥ ❞❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ♦❜s❡r✈❛❞♦✱ ♣❡r♦ ❡s ❧♦ q✉❡ ✐♥❞✐❝❛ ❡❧ ✈❛❧♦r ❞❡❧ ❡st❛❞íst✐❝♦ ❞❡ ♣r✉❡❜❛✳ ✷✳ ❊❧ ❣❡♥❡r❛❞♦r ❞❡ ♥ú♠❡r♦s ❛❧❡❛t♦r✐♦s q✉❡ s❡ ✉t✐❧✐③❛ ❡♥ ❡st❡ tr❛❜❛❥♦ ❡s ❧❛ ❢✉♥❝✐ó♥ ❘❆◆❉❖▼ ❞❡✜♥✐❞❛ ❝♦♠♦✿ ❘❆◆ ✭◆❙❊❊❉✮ ❞♦♥❞❡ ◆❙❊❊❉ ❡s ❧❛ s❡♠✐❧❧❛ q✉❡ ❣❡♥❡r❛ ❧❛ s❡❝✉❡♥❝✐❛ ❞❡ ♥ú♠❡r♦s ❛❧❡❛t♦r✐♦s✳ ❙✐ s❡ r❡q✉✐❡r❡ t❡♥❡r ✉♥❛ s❡❝✉❡♥❝✐❛ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✹✳✶✳ P❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ✭♣r♦t♦♥❡s✱ ✐♦♥❡s ♣❡s❛❞♦s ② ❣r❛♥♦s ❞❡ ♣♦❧✈♦✮ ✼✶ ❞✐st✐♥t❛ ❡♥ ❝❛❞❛ ✐t❡r❛❝✐ó♥ ❡♥t♦♥❝❡s ❡❧ ✈❛❧♦r ❞❡ ❧❛ s❡♠✐❧❧❛ ❞❡❜❡ ✈❛r✐❛r✱ ❡s ❞❡❝✐r✱ ♣✉❡❞❡ s❡r ✉♥ ♥ú♠❡r♦ q✉❡ ❞❡♣❡♥❞❛ ❞❡❧ r❡❧♦❥ ❞❡❧ s✐st❡♠❛ ♦ ❜✐❡♥ ❞❡ ❧❛ ❢❡❝❤❛✳ ✸✳ ▲❛ r❡❣❧❛ ❞❡ ♠✉❡str❡♦ q✉❡ s❡ ✉t✐❧✐③❛ ❡♥ ❡st❡ tr❛❜❛❥♦ ❡s ❡❧ ♠ét♦❞♦ ❞❡ tr❛♥s❢♦r♠❛✲ ❝✐ó♥ ✐♥✈❡rs❛✳ P❛r❛ q✉❡ ❡st❡ ♠ét♦❞♦ s❡❛ ❛♣❧✐❝❛❜❧❡ ❡s ♥❡❝❡s❛r✐♦ q✉❡ ❧❛ ✈❛r✐❛❜❧❡ ❛❧❡❛t♦r✐❛ ∆E ② s✉ ❢✉♥❝✐ó♥ ❞❡ ❞✐str✐❜✉❝✐ó♥ ❛❝✉♠✉❧❛❞❛ F (∆E) s❡❛♥ ✉♥♦✲❛✲✉♥♦✳ ❉❡ ❡st❛ ♠❛♥❡r❛ ❡s ♣♦s✐❜❧❡ ♦❜t❡♥❡r ✉♥❛ ♠✉❡str❛ ❛ ♣❛rt✐r ❞❡ ξ = F (∆E) ② ❛sí ❝❛❧❝✉❧❛r ❧❛ ❢✉♥❝✐ó♥ ✐♥✈❡rs❛ ∆E (ξ) = F −1 (ξ) ✳ ❖❜sér✈❡s❡ q✉❡ ξ ❡stá ✉♥✐❢♦r♠❡✲ ♠❡♥t❡ ❞✐str✐❜✉✐❞❛ ❡♥ ❡❧ ✐♥t❡r✈❛❧♦ [0, 1] ② q✉❡ ❧❛ ❢✉♥❝✐ó♥ ✐♥✈❡rs❛ s❡ ❡♥❝✉❡♥tr❛ ❛♥❛❧ít✐❝❛♠❡♥t❡✳ ❊♥t♦♥❝❡s ❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❡st♦❝ást✐❝♦ ❡stá ❞❛❞♦ ♣♦r ❧❛ ❡①♣r❡s✐ó♥ ✭❆♣é♥❞✐❝❡ ❇✮✿ ∆E (ξ) = α + β loge ❊♥ ❧❛ ❊❝✳ ✭✹✳✺✮✱ α ❡s ❧❛ ♠❡❞✐❛ ② β = q σ2 3,29  ξ 1−ξ  ✭✹✳✺✮ ❞♦♥❞❡ σ 2 ❡s ❧❛ ✈❛r✐❛♥③❛ ❞❡ ❧❛ s❡r✐❡ ❞❡ ❞❛t♦s q✉❡ ❝♦rr❡s♣♦♥❞❡♥ ❛ ∆E ✳ ❊♥ ❡❧ ❈✉❛❞r♦ ✹✳✶ s❡ ♠✉❡str❛♥ ❧♦s ✈❛❧♦r❡s ❞❡ ❡st♦s ♣❛rá♠❡tr♦s ♦❜t❡♥✐❞♦s ♣❛r❛ ❝❛❞❛ ✉♥❛ ❞❡ ❧❛s ♥❛✈❡s ❡♥ s✉s ❡♥❝✉❡♥tr♦s ❝♦♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛ ② ❡①t❡r♥❛ ❞❡ ❙❛t✉r♥♦✳ ❆♣❧✐❝❛♥❞♦ ❧❛ ❊❝✳ ✭✹✳✺✮ ② ❧♦s ✈❛❧♦r❡s ❞❡❧ ❈✉❛❞r♦ ✹✳✶ s❡ ♦❜t✐❡♥❡♥ ❧❛s ❞✐str✐❜✉❝✐♦♥❡s ❞❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❡st♦❝ást✐❝♦ q✉❡ s♦♥ ❞✐❢❡r❡♥t❡s ♣❛r❛ ❝❛❞❛ r❡❣✐ó♥ ❞❡ ❧❛ ♠❛❣♥❡tós❢❡✲ r❛ ✭❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❡s ♠ás ✐♥t❡♥s♦ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛ q✉❡ ❡♥ ❧❛ ❡①t❡r♥❛✮✳ ❈♦♠♦ ❡❥❡♠♣❧♦s s❡ ♠✉❡str❛♥ ❧❛ ❋✐❣✉r❛ ✹✳✾ ❞♦♥❞❡ s❡ ❝♦♥s✐❞❡r❛♥ ❧❛s ♠❡❞✐❝✐♦♥❡s ❤❡❝❤❛s ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛ ♣♦r ❡❧ ❱♦②❛❣❡r ✶ ② ❧❛ ❋✐❣✉r❛ ✹✳✶✵ ♣❛r❛ ❡❧ ❝❛s♦ ❞❡❧ ❱♦②❛❣❡r ✷ ❡♥ s✉ tr❛②❡❝t♦r✐❛ ❞❡ s❛❧✐❞❛ ♣♦r ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛✳ ❆❧ ❛♣❧✐❝❛r ❧❛ ❊❝✳ ✭✹✳✺✮ s❡ ❡stá ❝♦♥s✐❞❡r❛♥❞♦ q✉❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ ❞❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❡st♦❝ást✐❝♦ ❡s ❡❧ ♠✐s♠♦ ♣❛r❛ t♦❞❛s ❧❛s ❧❛t✐t✉❞❡s ② t✐❡♠♣♦s ❧♦❝❛❧❡s ❡♥ ❧❛s ❞♦s r❡❣✐♦♥❡s ♠❛❣♥❡t♦s❢ér✐❝❛s✳ ❉❡ ❧♦s ❞❛t♦s ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ♥♦ ❡s ♣♦s✐❜❧❡ ❞❡t❡r♠✐♥❛r ✉♥❛ ❞❡♣❡♥❞❡♥❝✐❛ ❧❛t✐t✉❞✐♥❛❧ ②✴♦ ❡♥ t✐❡♠♣♦s ❧♦❝❛❧❡s ♣❛r❛ ❡❧ ❡s♣❡❝tr♦ ❞❡ ✢✉❝t✉❛❝✐♦♥❡s q✉❡ ❞❛ ♦r✐❣❡♥ ❛❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❡st♦❝ást✐❝♦✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✹✳✶✳ P❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ✭♣r♦t♦♥❡s✱ ✐♦♥❡s ♣❡s❛❞♦s ② ❣r❛♥♦s ❞❡ ♣♦❧✈♦✮ ✼✷ 1800 1600 Observado 1400 Frecuencia 1200 1000 800 600 400 200 0 -3.0x10 -6 -2.0x10 -6 -1.0x10 -6 0.0 1.0x10 -6 2.0x10 -6 3.0x10 -6 -1 ∆Ex (V m ) 1800 1600 1400 Función de distribución ajustada (logística) f (∆Ex) 1200 1000 800 600 400 200 0 -3.0x10 -3 -2.0x10 -3 -1.0x10 -3 0.0 1.0x10 -3 2.0x10 -3 3.0x10 -3 -1 ∆Ex (V m ) ❋✐❣✉r❛ ✹✳✽✿ ❍✐st♦❣r❛♠❛ ❞❡ ❢r❡❝✉❡♥❝✐❛s ♣❛r❛ ❧❛ ❞✐str✐❜✉❝✐ó♥ ❞❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❡♥ ❧❛ ❝♦♠♣♦♥❡♥t❡ ✏①✑ ② s✉ ❝✉r✈❛ ❞❡ ❛❥✉st❡ ✭❢✉♥❝✐ó♥ ❧♦❣íst✐❝❛✮✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✹✳✶✳ P❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ✭♣r♦t♦♥❡s✱ ✐♦♥❡s ♣❡s❛❞♦s ② ❣r❛♥♦s ❞❡ ♣♦❧✈♦✮ ❈✉❛❞r♦ ✹✳✶✿ ❱❛❧♦r❡s ❞❡ α ② β ✼✸ ♦❜t❡♥✐❞♦s ♣❛r❛ ❡❧ ❱♦②❛❣❡r ✶ ② ❱♦②❛❣❡r ✷ ❡♥ s✉s ❡♥❝✉❡♥tr♦s ❝♦♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛ ② ❡①t❡r♥❛ ❞❡ ❙❛t✉r♥♦✳ Componente del campo eléctrico ∆E (V m-1) Magnetosfera interna VOYAGER 1 VOYAGER 2 α β α β ∆Ex 6.35x10-7 6.05x10-4 1.05x10-7 4.26x10-5 ∆Ey 2.31 x10-6 4.22x10-4 -1.27 x10-8 1.45 x10-6 ∆Ez -6.84 x10-5 3.81 x10-3 -2.03 x10-6 1.24 x10-3 Componente del campo eléctrico ∆E (V m-1) Magnetosfera externa (entrada) VOYAGER 1 VOYAGER 2 α β α β ∆Ex -4.39x10-8 2.37x10-6 -6.89x10-9 1.46x10-7 ∆Ey 2.93 x10-9 2.39x10-7 -2.64 x10-11 1.26 x10-8 ∆Ez 1.04 x10-6 7.27 x10-5 Componente del campo eléctrico ∆E (V m-1) 3.46 x10-6 6.22 x10-5 Magnetosfera externa (salida) VOYAGER 1 VOYAGER 2 α β α β ∆Ex 2.70x10-7 3.81x10-5 5.13x10-8 3.65x10-6 ∆Ey 2.93 x10-7 4.96x10-5 1.86 x10-8 1.20 x10-6 ∆Ez -8.79 x10-7 1.08 x10-4 6.74 x10-8 4.42 x10-6 ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✹✳✶✳ P❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ✭♣r♦t♦♥❡s✱ ✐♦♥❡s ♣❡s❛❞♦s ② ❣r❛♥♦s ❞❡ ♣♦❧✈♦✮ 0.000 200 0.005 0.010 0.015 0.020 0.025 VOYAGER 1 160 Frecuencia 0.030 200 180 180 160 140 140 120 120 100 100 80 80 60 60 40 40 20 20 0 0.000 ✼✹ 0.005 0.010 0.015 0.020 0.025 0 0.030 -1 C am po eléctrico estocástico ∆ E (V m ) ❋✐❣✉r❛ ✹✳✾✿ ❉✐str✐❜✉❝✐ó♥ ❞❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❡st♦❝ást✐❝♦ ❜❛s❛❞♦ ❡♥ ❧❛s ♦❜s❡r✈❛❝✐♦♥❡s ❞❡❧ ❱♦②❛❣❡r ✶ ❡♥ s✉ ♣❛s♦ ♣♦r ❧❛ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛ ❞❡ ❙❛t✉r♥♦✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✹✳✶✳ P❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ✭♣r♦t♦♥❡s✱ ✐♦♥❡s ♣❡s❛❞♦s ② ❣r❛♥♦s ❞❡ ♣♦❧✈♦✮ 0.0 5.0x10 -6 1.0x10 -5 1.5x10 -5 -5 2.5x10 -5 -5 200 3.0x10 200 180 180 VOYAGER 2 160 Frecuencia 2.0x10 ✼✺ 160 140 140 120 120 100 100 80 80 60 60 40 40 20 20 0 0 0.0 5.0x10 -6 1.0x10 -5 1.5x10 -5 2.0x10 -5 2.5x10 -5 3.0x10 -5 -1 C am po eléctrico estocástico ∆ E (V m ) ❋✐❣✉r❛ ✹✳✶✵✿ ❉✐str✐❜✉❝✐ó♥ ❞❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❡st♦❝ást✐❝♦ ❜❛s❛❞♦ ❡♥ ❧❛s ♦❜s❡r✈❛❝✐♦♥❡s ❞❡❧ ❱♦②❛❣❡r ✷ ❡♥ s✉ ♣❛s♦ ♣♦r ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ ❞❡ ❙❛t✉r♥♦ ✭tr❛②❡❝t♦r✐❛ ❞❡ s❛❧✐❞❛✮✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✹✳✶✳ P❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ✭♣r♦t♦♥❡s✱ ✐♦♥❡s ♣❡s❛❞♦s ② ❣r❛♥♦s ❞❡ ♣♦❧✈♦✮ ✹✳✶✳✷✳ ✼✻ ❈❛r❛❝t❡ríst✐❝❛s ❞❡ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❊♥ ❡st❛ s❡❝❝✐ó♥ s❡ ❤❛❜❧❛rá ❞❡ ❧❛s ♣r♦♣✐❡❞❛❞❡s ❞❡ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s q✉❡ s❡ ❡♥❝✉❡♥tr❛ ❡♥ ❝❛❞❛ r❡❣✐ó♥✳ ❊♥ ❡❧ ❈❛♣ít✉❧♦ ✸ s❡ ♠❡♥❝✐♦♥ó q✉❡ ❡♥ ❧❛s ❞♦s r❡❣✐♦♥❡s ♠❛❣♥❡t♦s❢ér✐❝❛s ❧❛s ♣❛rtí❝✉❧❛s ❡stá♥ ❝❛r❛❝t❡r✐③❛❞❛s ♣♦r ✉♥❛ ❞❡t❡r♠✐♥❛❞❛ ❞✐str✐❜✉✲ ❝✐ó♥ ❞❡ ✈❡❧♦❝✐❞❛❞❡s✳ ❙✐ ❧❛s ♣❛rtí❝✉❧❛s ♣r♦✈✐❡♥❡♥ ❞❡ ❧❛s ❛t♠ós❢❡r❛s ♣❧❛♥❡t❛r✐❛s ♦ ❞❡ ❧❛s ✐♦♥ós❢❡r❛s s❡ ♣✉❡❞❡ ❛s✉♠✐r q✉❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ ❞❡ ✈❡❧♦❝✐❞❛❞❡s s✐❣✉❡ ✉♥ ♣❡r✜❧ ▼❛①✲ ✇❡❧❧✐❛♥♦✳ P❡r♦✱ s✐ ❧❛s ♣❛rtí❝✉❧❛s s❡ ♦r✐❣✐♥❛♥ ❡♥ ❧❛ s✉♣❡r✜❝✐❡ ❞❡ ❧♦s s❛té❧✐t❡s ❞❡ ❤✐❡❧♦ ❧❛ ❞✐str✐❜✉❝✐ó♥ ♣✉❡❞❡ s❡r ♠ás ❡①ót✐❝❛ ✭♣♦r ❡❥❡♠♣❧♦✱ ✉♥❛ ❜✐✲▼❛①✇❡❧❧✐❛♥❛✱ ▲♦r❡♥t③✐❛✲ ♥❛ ♦ ❑❛♣♣❛✮✳ ❙✐♥ ♣ér❞✐❞❛ ❞❡ ❣❡♥❡r❛❧✐❞❛❞✱ ❡♥ ❡st❡ tr❛❜❛❥♦ s❡ ❝♦♥s✐❞❡r❛ q✉❡ ❡♥ ❝❛❞❛ ❞✐r❡❝❝✐ó♥ ❡s♣❛❝✐❛❧ ❧❛ ✈❡❧♦❝✐❞❛❞ ❡stá ❞❛❞❛ ♣♦r ✉♥❛ ❞✐str✐❜✉❝✐ó♥ ▼❛①✇❡❧❧✐❛♥❛✳ ❙❡ ❛♣❧✐❝❛ ♥✉❡✈❛♠❡♥t❡ ▼♦♥t❡ ❈❛r❧♦ ♣❛r❛ s❡❧❡❝❝✐♦♥❛r ❛❧❡❛t♦r✐❛♠❡♥t❡ ✉♥❛ ♣❛rtí❝✉❧❛ q✉❡ ♣r♦✈❡♥❣❛ ❞❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ ▼❛①✇❡❧❧✐❛♥❛✳ P❛r❛ ❡st❡ ❝❛s♦ ❡♥ ♣❛rt✐❝✉❧❛r s❡ ❤❛❝❡ ✉♥❛ ✐♠♣❧❡♠❡♥t❛❝✐ó♥ ❞❡❧ ♠ét♦❞♦ ❞❡ ❇♦①✲▼ü❧❧❡r ❬✶✾✺✽❪ ❛ ♣❛rt✐r ❞❡❧ ❝✉❛❧ s❡ ❧❧❡❣❛ ❛ ❧❛ s✐❣✉✐❡♥t❡ ❡①♣r❡s✐ó♥ ✭❆♣é♥❞✐❝❡ ❈✮✿ vM 1 (χ1 , χ2 ) = ❉♦♥❞❡ ✐♥t❡r✈❛❧♦ ② m χ1 ② χ2 [0, 1]✱ kB r p kB T cos (2 π χ1 ) −2 log (χ2 ) m ✭✹✳✻✮ s♦♥ ♥ú♠❡r♦s ❛❧❡❛t♦r✐♦s ② ❡st❛❞íst✐❝❛♠❡♥t❡ ✐♥❞❡♣❡♥❞✐❡♥t❡s ❡♥ ❡❧ ❡s ❧❛ ❝♦♥st❛♥t❡ ❞❡ ❇♦❧t③♠❛♥♥✱ T ❡s ❧❛ t❡♠♣❡r❛t✉r❛ ❞❡ ❧❛ ❢✉❡♥t❡✱ ❡s ❧❛ ♠❛s❛ ❞❡ ❧❛ ♣❛rtí❝✉❧❛✳ ✹✳✶✳✷✳✶✳ ▼❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛ ▲❛s ♣r✐♥❝✐♣❛❧❡s ❢✉❡♥t❡s ❞❡ ♣❧❛s♠❛ ② ❞❡ ♣❛rtí❝✉❧❛s ♥❡✉tr❛s ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛ s♦♥ ❧♦s ❝✐♥❝♦ s❛té❧✐t❡s ✭▼✐♠❛s✱ ❊♥❝❡❧❛❞♦✱ ❚❡t✐s✱ ❉✐♦♥❡ ② ❘❡❛✮ ❧♦❝❛❧✐③❛❞♦s ❡♥tr❡ ✸ RS ② ✾ RS ❧♦s ❛♥✐❧❧♦s ❧♦❝❛❧✐③❛❞♦s ❡♥tr❡ ✶✳✵✾ RS ② ✽ RS ② ❧❛ ✐♦♥ós❢❡r❛ ❞❡ ❙❛t✉r♥♦✳ ▲♦s s❛té❧✐t❡s ❞❡ ❤✐❡❧♦ ❡stá♥ s✐❡♥❞♦ ❝♦♥t✐♥✉❛♠❡♥t❡ ❜♦♠❜❛r❞❡❛❞♦s ♣♦r ♣❛rtí❝✉❧❛s ❡♥❡r❣ét✐❝❛s✱ ♣♦r ❡❧ ♣❧❛s♠❛ ❝♦rr♦t❛♥t❡ ② ♣♦r ❧❛ r❛❞✐❛❝✐ó♥ s♦❧❛r q✉❡ ♣r♦✈♦❝❛♥ ❧❛ ✏s❛❧✲ ♣✐❝❛❞✉r❛✑ ❞❡ ❝❛♥t✐❞❛❞❡s s✐❣♥✐✜❝❛t✐✈❛s ❞❡ ❛❣✉❛ ❞❡ s✉s s✉♣❡r✜❝✐❡s ❢♦r♠❛♥❞♦ ✉♥❛ ♥✉❜❡ ❡♥ ❡❧ ♣❧❛♥♦ ❡❝✉❛t♦r✐❛❧ ❝♦♠♣✉❡st❛ ♣♦r ♣r♦❞✉❝t♦s ❞❡ ❧❛ ❞✐s♦❝✐❛❝✐ó♥ ❞❡❧ ❛❣✉❛ ❬❏♦❤♥s♦♥ ❡t ❛❧✳✱ ✶✾✽✾❀ ❘✐❝❤❛r❞s♦♥✱ ✶✾✾✽❪✳ ▲❛ ♣♦st❡r✐♦r ✐♦♥✐③❛❝✐ó♥ ❞❡ ❡st♦s ♥❡✉tr♦s ♣r♦✈❡❡ ❡❧ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✹✳✶✳ P❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ✭♣r♦t♦♥❡s✱ ✐♦♥❡s ♣❡s❛❞♦s ② ❣r❛♥♦s ❞❡ ♣♦❧✈♦✮ ✼✼ cm−3 ✱ ✉♥❛ ♣❧❛s♠❛ ♦❜s❡r✈❛❞♦ ❡♥tr❡ ✹ RS ② ✽ RS q✉❡ t✐❡♥❡ ✉♥❛ ❞❡♥s✐❞❛❞ ❞❡ ♣♦❝♦s t❡♠♣❡r❛t✉r❛ ❞❡ ❛❧❣✉♥❛s ❞❡❝❡♥❛s ❞❡ ❡❱ ② ❛♣r♦①✐♠❛❞❛♠❡♥t❡ ❡❧ 20 % s♦♥ ✐♦♥❡s ❧✐❣❡✲ r♦s ② ❡❧ r❡st❛♥t❡ s♦♥ ✐♦♥❡s ♣❡s❛❞♦s ❬❘✐❝❤❛r❞s♦♥✱ ✶✾✽✻❪✳ ▲❛s ♣❛rtí❝✉❧❛s ❞❡ ❧♦s ❛♥✐❧❧♦s ❡stá♥ ❝♦♠♣✉❡st❛s ♣r❡❞♦♠✐♥❛♥t❡♠❡♥t❡ ♣♦r ❤✐❡❧♦ ❞❡ ❛❣✉❛✳ ▲❛ ✏s❛❧♣✐❝❛❞✉r❛✑ ♣♦r ✐♠✲ ♣❛❝t♦s ❝♦♥ ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ② ♣♦r ❜♦♠❜❛r❞❡♦ ♠❡t❡♦rít✐❝♦ ✐♥②❡❝t❛ ♠❛t❡r✐❛❧ ❛ ❧❛ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛✳ ❆✉♥q✉❡ ❧♦s s❛té❧✐t❡s ② ❧♦s ❛♥✐❧❧♦s ❛❝tú❛♥ ❝♦♠♦ ❢✉❡♥t❡s ❞❡ ♣❛rtí❝✉❧❛s t❛♠❜✐é♥ ♣✉❡❞❡♥ ❛❜s♦r❜❡r❧❛s✳ ❉❡ ❤❡❝❤♦ ❛❧ r❡✈✐s❛r ❧♦s ❞❛t♦s ❞❡ ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ❞❡ ❧♦s ❱♦②❛❣❡r s❡ ♦❜s❡r✈❛♥ ❝❧❛r❛♠❡♥t❡ ✜r♠❛s ❞❡ ❛❜s♦r❝✐ó♥ ❡♥ ❧❛ ✈❡❝✐♥❞❛❞ ❞❡ ✉♥ s❛té❧✐t❡ ❬❙✐♠♣s♦♥ ❡t ❛❧✳✱ ✶✾✽✵❀ ❙❛♥t♦s✲❈♦st❛ ❡t ❛❧✱ ✷✵✵✸❪✳ P❛r❛ ♣r♦♣ós✐t♦s ❝♦♠♣✉t❛❝✐♦♥❛❧❡s ② ❞❡ ❛❝✉❡r❞♦ ❝♦♥ ❧❛s ♠❡❞✐❝✐♦♥❡s ♠ás r❡❝✐❡♥t❡s r❡❛❧✐③❛❞❛s ♣♦r ❧❛ ♥❛✈❡ ❈❛ss✐♥✐ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦ ❬❨♦✉♥❣ ❡t ❛❧✳✱ ✷✵✵✺❪ s❡ ❝♦♥s✐❞❡r❛♥ ❞✐st✐♥t❛s ♠✉❡str❛s ❞❡ ♣❛rtí❝✉❧❛s q✉❡ ♣r♦✈✐❡♥❡♥ ❞❡ ❧❛s ❢✉❡♥t❡s ♠ás ✐♠♣♦r✲ t❛♥t❡s ✭❈✉❛❞r♦ ✹✳✷✮✳ ❊♥ ❧❛ ♣r✐♠❡r❛ ❝♦❧✉♠♥❛ ❡stá ✐♥❞✐❝❛❞❛ ❧❛ ❢✉❡♥t❡ ❞❡ ♣❛rtí❝✉❧❛s✱ ❧❛ ♣♦s✐❝✐ó♥ ✐♥✐❝✐❛❧ ❞❡ ❧❛ ❝✉❛❧ ♣❛rt❡♥ ❡stá s❡ñ❛❧❛❞❛ ❡♥ ❧❛ s❡❣✉♥❞❛ ❝♦❧✉♠♥❛ ✭♣❛r❛ ❡✈✐✲ t❛r ❛❜s♦r❝✐ó♥ ❡♥ ❧❛ r❡❣✐ó♥ ❞❡ ❧♦s ❛♥✐❧❧♦s ❧❛s ♣❛rtí❝✉❧❛s ❡stá♥ ❧♦❝❛❧✐③❛❞❛s ❡♥❝✐♠❛ ❞❡❧ ♣❧❛♥♦ q✉❡ ❧♦s ❝♦♥t✐❡♥❡ ❡♥ ❧❛ ❞✐r❡❝❝✐ó♥ ✏③✑ ❀ ♠✐❡♥tr❛s q✉❡ ❡♥ ❧❛ ❞✐r❡❝❝✐ó♥ ✏①✑ ❡♥ ❡❧ ❝❡♥tr♦ ❞❡❧ ❛♥✐❧❧♦✮ ✱ ❡♥ ❧❛ t❡r❝❡r❛ ❝♦❧✉♠♥❛ ❡stá♥ ❧❛s ❡s♣❡❝✐❡s ✐ó♥✐❝❛s ❞♦♠✐♥❛♥t❡s✱ ❡♥ ❧❛ ❝✉❛rt❛ ❝♦❧✉♠♥❛ ❧❛ ♠❛s❛✱ ❡♥ ❧❛ q✉✐♥t❛ ❧❛ t❡♠♣❡r❛t✉r❛ ❞❡ ❧❛ ❢✉❡♥t❡ ② ❡♥ ❧❛ ú❧t✐♠❛ ✷ ❡stá♥ ❧❛s ✈❡❧♦❝✐❞❛❞❡s ❞❡ ❝♦rr♦t❛❝✐ó♥ ✳ ▲❛s ✈❡❧♦❝✐❞❛❞❡s ❞❡ ❝♦rr♦t❛❝✐ó♥ ❡stá♥ ❜❛s❛❞❛s RS < r < ✻✳✹✾ RS RS ✭C = 1✮ ② ✾ RS ❡♥ ❡❧ ♠♦❞❡❧♦ ❞❡ ❊✈✐❛t❛r ❛♥❞ ❘✐❝❤❛r❞s♦♥ ❬✶✾✽✻❪ ② ✈❛rí❛♥ ❝♦♠♦✿ ✶ ✭C = 1✮❀ ✻✳✺ RS < r < < r ✵✳✵✻ ▼❡❱✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✺✳✶✳ ▼❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛ 10.4 160 10.6 10.7 REA (r = 9.6 Rs) 10.8 10.9 11.0 11.1 11.2 11.3 11.4 160 140 140 120 120 100 Frecuencia 10.5 ✶✵✻ 100 Logística 80 80 Exponencial 60 60 40 40 20 20 0 10.4 10.5 10.6 10.7 10.8 10.9 11.0 11.1 11.2 11.3 0 11.4 E nergía cinética final (eV ) ❋✐❣✉r❛ ✺✳✶✷✿ ❍✐st♦❣r❛♠❛ ❞❡ ❢r❡❝✉❡♥❝✐❛s ♣❛r❛ ❧❛ ❡♥❡r❣í❛ ❝✐♥ét✐❝❛ ✜♥❛❧ ❛❧❝❛♥③❛❞❛ ♣♦r ✉♥❛ ♠✉❡str❛ ❞❡ ♣r♦t♦♥❡s ❞❡s♣✉és ❞❡ 5x107 ✐♥t❡r❛❝❝✐♦♥❡s ② s✉ ❢✉♥❝✐ó♥ ❞❡ ❛❥✉st❡ ❡♥ ❘❡❛✳ ❊❧ ❡s♣❡❝tr♦ ❞❡ ❡♥❡r❣í❛ q✉❡❞❛ ❜✐❡♥ ❞❡s❝r✐t♦ ♣♦r ❞♦s ❢✉♥❝✐♦♥❡s ❞❡ ❞✐str✐❜✉❝✐ó♥✱ ❡st♦ ❡s✱ ♣❛r❛ E 11 eV ✉♥❛ ❢✉♥❝✐ó♥ ❡①♣♦✲ ♥❡♥❝✐❛❧ ❞❡❝r❡❝✐❡♥t❡ s♦♥ ❧❛s ♠ás ❛❞❡❝✉❛❞❛s✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✺✳✷✳ ▼❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ ✶✵✼ ❊st♦s r❡s✉❧t❛❞♦s ♥♦ ❝♦♥tr❛❞✐❝❡♥ ❛❧ ❤❡❝❤♦ ❞❡ q✉❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ ✜♥❛❧ ❞❡ ✈❡❧♦❝✐❞❛✲ ❞❡s ❝♦♥s❡r✈❡ s✉ ♣❡r✜❧ ▼❛①✇❡❧❧✐❛♥♦ ✭② ❞❡ ❛❧❧í q✉❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ ❞❡ ❡♥❡r❣í❛s t❛♠❜✐é♥ ❧♦ ♠❛♥t❡♥❣❛✮✳ ▲♦ q✉❡ s✉❝❡❞❡ ❡s q✉❡ ❧❛s ♣r✉❡❜❛s ❡st❛❞íst✐❝❛s ❞❡ ❜♦♥❞❛❞ ❞❡ ❛❥✉st❡ ❡s✲ t❛❜❧❡❝❡♥ ✉♥❛ ❝♦♠♣❛r❛❝✐ó♥ ❡♥tr❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ ▼❛①✇❡❧❧✐❛♥❛ ② ❝✉❛❧q✉✐❡r ♦tr❛ ❢✉♥❝✐ó♥ ❞❡ ❞✐str✐❜✉❝✐ó♥✳ ❨✱ ♣♦r ♦tr♦ ❧❛❞♦✱ ❡❧ ✈❛❧♦r ❞❡❧ ❡st❛❞íst✐❝♦ ✐♥❞✐❝❛ q✉❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ ▼❛①✇❡❧❧✐❛♥❛ ❡s ❧❛ ✏♠❡❥♦r✑ ❡♥tr❡ t♦❞❛s ❧❛s ❝♦♥s✐❞❡r❛❞❛s ❝♦♠♦ ❢✉♥❝✐ó♥ ♣r✉❡❜❛✱ ♣❡r♦ ♥♦ ♥❡❝❡s❛r✐❛♠❡♥t❡ ❡s ❧❛ q✉❡ s❡ ❛❥✉st❛✳ ▲❛ ❝♦♠♣♦♥❡♥t❡ ❞❡ ❧❛ ✈❡❧♦❝✐❞❛❞ ✜♥❛❧ ❡♥ ❧❛ ❞✐r❡❝❝✐ó♥ ✏②✑ ✱ ♠✉❡str❛ ✉♥❛ ❝❛r❛❝t❡✲ ríst✐❝❛ ❜✐♠♦❞❛❧ ♣❛r❛ ♣❛rtí❝✉❧❛s ❧♦❝❛❧✐③❛❞❛s ❡♥ ❡❧ ♣♦❧♦ ♥♦rt❡✳ ❊st❛ ❡str✉❝t✉r❛ ♣✉❡❞❡ s❡r ❡①♣❧✐❝❛❞❛ ❡♥ tér♠✐♥♦s ❞❡ ❧♦s ❡st✉❞✐♦s r❡❛❧✐③❛❞♦s ♣♦r ❉✉r❛♥❞✲▼❛♥t❡r♦❧❛ ❬✷✵✵✸❪✳ ❊❧ ❛✉t♦r ❡st❛❜❧❡❝❡ q✉❡ ❧❛ ♣r♦❜❛❜✐❧✐❞❛❞ ♣❛r❛ ❣❛♥❛r ❡♥❡r❣í❛ ❡s s✐❡♠♣r❡ ♠❛②♦r q✉❡ ❧❛ ♣r♦❜❛❜✐❧✐❞❛❞ ♣❛r❛ ♣❡r❞❡r ❡♥❡r❣í❛✳ ❊♥t♦♥❝❡s✱ ❞✉r❛♥t❡ ❡❧ ♣r♦❝❡s♦ ❞❡ ❛❝❡❧❡r❛❝✐ó♥✱ ❧❛s ♣❛rtí❝✉❧❛s ❝♦♥ ♠♦♠❡♥t♦ ❧✐♥❡❛❧ ✐♥✐❝✐❛❧ ♠❡♥♦r ✭♣♦❧♦ ♥♦rt❡✮ ❡stá♥ s✐❡♥❞♦ ❜♦♠❜❡❛❞❛s ❞❡❧ ❝❡♥tr♦ ❞❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ ❤❛❝✐❛ ✈❡❧♦❝✐❞❛❞❡s ❛❧t❛s ❝♦♠♦ r❡s✉❧t❛❞♦ ❞❡ s✉ ♣r♦♣✐❛ ❛❝❡❧❡r❛❝✐ó♥✱ ❡♥ ❝♦♥tr❛st❡✱ ❧❛s ♣❛rtí❝✉❧❛s ❝♦♥ ♠♦♠❡♥t♦ ❧✐♥❡❛❧ ✐♥✐❝✐❛❧ ♠❛②♦r ✭❘❡❛✮ ♥♦ ♠✉❡str❛♥ t❛❧ ❝❛r❛❝t❡ríst✐❝❛ ❜✐♠♦❞❛❧ ✭❋✐❣✉r❛ ✺✳✶✸✮✳ ✺✳✷✳ ▼❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ ❊st❛ r❡❣✐ó♥ ❡stá ♣♦❜❧❛❞❛ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♣♦r ♣r♦t♦♥❡s ② ❛❧❣✉♥♦s ✐♦♥❡s ♣❡s❛❞♦s ❝❡r❝❛ ❞❡ ❧❛ ór❜✐t❛ ❞❡ ❚✐tá♥✳ ❊♥ ❡❧ ♣r❡s❡♥t❡ ❛♥á❧✐s✐s s❡ ❡st✉❞✐❛ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣r♦t♦✲ ♥❡s q✉❡ ♣r♦✈✐❡♥❡ ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛ ② s❡ ❧❡ ❞❛ ✉♥ ♣♦st❡r✐♦r s❡❣✉✐♠✐❡♥t♦ ❛ ❧♦ ❧❛r❣♦ ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛✳ P♦r ♦tr❛ ♣❛rt❡✱ ❚✐tá♥ ② s✉ ❞❡♥s❛ ❛t♠ós❢❡r❛ ❝♦♥tr✐✲ + + ❜✉②❡♥ ❝♦♥ ✐♦♥❡s ♣❡s❛❞♦s ❝♦♠♦ ♠❡t❛♥♦ ✭CH4 ✮ ✱ ♥✐tró❣❡♥♦ ❛tó♠✐❝♦ ✭N ✮ ② ♥✐tró❣❡♥♦ + ♠♦❧❡❝✉❧❛r ✭N2 ✮✳ ❱❡r ❈✉❛❞r♦ ✹✳✸✳ P❛r❛ s✉ ❡st✉❞✐♦ s❡ ❝♦♥s✐❞❡r❛♥ ❧❛s tr❛②❡❝t♦r✐❛s ❞❡ ❡♥tr❛❞❛ ② s❛❧✐❞❛ ♣❛r❛ ❝❛❞❛ ♥❛✈❡ ♣♦r s❡♣❛r❛❞♦✳ ❊st♦ s❡ ❤❛❝❡ ❝♦♥ ❡❧ ♦❜❥❡t♦ ❞❡ ✐♥✈❡st✐❣❛r ❡❧ ❡❢❡❝t♦ q✉❡ t✐❡♥❡♥ ❧❛s ✢✉❝t✉❛❝✐♦♥❡s ❞❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❡♥ ❧❛ ♠❛❣♥❡t♦❝♦❧❛ ✭s❛❧✐❞❛✮ ② s✉ ❝♦rr❡s♣♦♥❞✐❡♥t❡ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❡st♦❝ást✐❝♦ s♦❜r❡ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s✳ ❊♥ ❧❛ ❋✐❣✉r❛ ✭✹✳✾✮ s❡ ♠✉❡str❛ ❡❧ ♣❡r✜❧ ❝❛r❛❝t❡ríst✐❝♦ ❞❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❡st♦✲ ❝ást✐❝♦ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛✳ ❊♥ ❡s❡ ❝❛s♦✱ ❡♥ ♣❛rt✐❝✉❧❛r✱ ❡stá r❡❢❡r✐❞♦ ❛ ❧❛ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✺✳✷✳ ▼❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ Frecuencia -10 ✶✵✽ IONOSFERA DE SATURNO (r = 1.2 Rs) -5 0 5 10 80 80 70 70 60 60 50 50 40 40 30 30 20 20 10 10 0 0 -10 -5 0 5 10 -1 C om ponente y de la velocidad final (km s ) 3.5 4.0 4.5 REA (r = 9.6 Rs) 5.0 5.5 6.0 6.5 7.0 Frecuencia 100 7.5 100 80 80 60 60 40 40 20 20 0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 0 7.5 -1 Componente y de la velocidad final (km s ) ❋✐❣✉r❛ ✺✳✶✸✿ ❍✐st♦❣r❛♠❛ ❞❡ ❢r❡❝✉❡♥❝✐❛s ♣❛r❛ ❧❛ ❞✐str✐❜✉❝✐ó♥ ❞❡ ❧❛ ❝♦♠♣♦♥❡♥t❡ ✏②✑ ❞❡ ❧❛ ✈❡❧♦❝✐❞❛❞ ✜♥❛❧ ❛s♦❝✐❛❞❛ ❛ ❧♦s ♣r♦t♦♥❡s q✉❡ ♣r♦✈✐❡♥❡♥ ❞❡ ❧❛ ✐♦♥ós❢❡r❛ ❞❡ ❙❛t✉r♥♦ ② ❞❡ ❧❛ s✉♣❡r✜❝✐❡ ❞❡ ❘❡❛✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ Ganancia de energía (∆K/Kmin) ✺✳✷✳ ▼❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ 10 6 10 5 10 4 10 3 10 2 10 1 10 10 -4 ✶✵✾ MAGNE N A E N T R0A D A (> = 11 0 R s ) -3 T O S F E R-2A E X T E R-1 10 10 10 11 11 12 12 10 10 10 -1 10 -2 13 13 14 14 10 -4 10 10 Rs R s (e xtra p o la c ió n ) Rs R s (e xtra p o la c ió n ) Rs R s (e xtra p o la c ió n ) 0 10 10 -3 10 -2 10 -1 Rs R s (e xtra p o la c ió n ) Rs R s (e xtra p o la c ió n ) 10 0 10 1 10 2 10 6 10 5 10 4 10 3 10 2 10 1 10 0 10 -1 10 -2 2 T ie m p o (s e g ) ❋✐❣✉r❛ ✺✳✶✹✿ ●❛♥❛♥❝✐❛ ❡st♦❝ást✐❝❛ ❞❡ ❡♥❡r❣í❛ ♣r♦♠❡❞✐❛❞❛ s♦❜r❡ t♦❞❛ ❧❛ ❞✐str✐❜✉❝✐ó♥ ✈s✳ ❡❧ t✐❡♠♣♦ ♣❛r❛ ✉♥❛ ♠✉❡str❛ ❞❡ ♣r♦t♦♥❡s ❧♦❝❛❧✐③❛❞♦s ❡♥ ❞✐❢❡r❡♥t❡s ♣♦s✐❝✐♦♥❡s ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛✳ ❘❡s✉❧t❛❞♦s ❜❛s❛❞♦s ❡♥ ❧❛s ♠❡❞✐❝✐♦♥❡s ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ r❡❛❧✐③❛❞♦s ♣♦r ❡❧ ❱♦②❛❣❡r ✶ ❡♥ ❧❛ tr❛②❡❝t♦r✐❛ ❞❡ ❡♥tr❛❞❛✳ tr❛②❡❝t♦r✐❛ ❞❡ s❛❧✐❞❛ ❞❡❧ ❱♦②❛❣❡r ✷✳ ▲❛s ❣rá✜❝❛s q✉❡ s❡ ♣r❡s❡♥t❛♥ ❡stá♥ ❜❛s❛❞❛s ❡♥ ❧♦s r❡s✉❧t❛❞♦s ♦❜t❡♥✐❞♦s ♣❛r❛ ❧❛ tr❛②❡❝t♦r✐❛ ❞❡ ❡♥tr❛❞❛ ❞❡❧ ❱♦②❛❣❡r ✶ ② ♣❛r❛ ❧❛ tr❛②❡❝t♦r✐❛ ❞❡ s❛❧✐❞❛ ❞❡❧ ❱♦②❛❣❡r ✷✳ ❘❡s✉❧t❛❞♦s s✐♠✐❧❛r❡s s❡ ♦❜t✐❡♥❡♥ ♣❛r❛ ❡❧ r❡st♦ ❞❡ ❧♦s ❝❛s♦s✳ ❉❡s♣✉és ❞❡ q✉❡ ❧❛ ♠✉❡str❛ ❞❡ ♣❛rtí❝✉❧❛s ✐♥t❡r❛❝tú❛ ❝♦♥ ❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❡st♦✲ ❝ást✐❝♦✱ ❡♥ ♣r♦♠❡❞✐♦ t✐❡♥❞❡♥ ❛ ❣❛♥❛r ❡♥❡r❣í❛ ❝✐♥ét✐❝❛ ❞❡s♣✉és ❞❡ ❛❧❣✉♥♦s s❡❣✉♥❞♦s✱ ❝♦♠♦ s❡ ♣✉❡❞❡ ✈❡r ❡♥ ❧❛s ❋✐❣✉r❛s ✺✳✶✹ ❤❛st❛ ✺✳✶✾✳ ▲❛s ❣❛♥❛♥❝✐❛s ❞❡ ❡♥❡r❣í❛ ❝✐♥ét✐❝❛ ♦❜t❡♥✐❞❛s ♣❛r❛ ❧♦s ♣r♦t♦♥❡s ② ❧♦s ✐♦♥❡s ❞❡ ♥✐tró❣❡♥♦ ✭N+ ✮ s❡ ❝❛❧❝✉❧❛♥ ❞❡ ❛❝✉❡r❞♦ ❛ ❧❛ ❊❝✳ ✭✺✳✶✮✱ ✉t✐❧✐③❛♥❞♦ ❧♦s ✈❛❧♦r❡s ❞❡❧ ❈✉❛❞r♦ ✺✳✶✳ ❊♥ ❡st❡ ❝❛s♦✱ ❧♦s ✐♦♥❡s ♣❡s❛❞♦s + ❝♦♠♦ ❡❧ ♠❡t❛♥♦ ✭CH+ 4 ✮ ② ❡❧ ♥✐tró❣❡♥♦ ♠♦❧❡❝✉❧❛r ✭N2 ✮ só❧♦ s❡ ❡♥❝✉❡♥tr❛♥ ❡♥ ❧❛ r❡❣✐ó♥ ❡①t❡r♥❛✱ ❞❡ ❛❧❧í q✉❡ ❡♥ ❧❛ ❊❝✳ ✭✺✳✶✮ s❡ ✉t✐❧✐❝❡ ❡❧ ✈❛❧♦r ❞❡ ❧❛ ❡♥❡r❣í❛ ❝✐♥ét✐❝❛ ♠í♥✐♠❛ q✉❡ t✐❡♥❡♥ ❡s♦s ✐♦♥❡s ❡♥ ❚✐tá♥✳ P♦r ❡st❛ r❛③ó♥ ♥♦ ❡stá♥ ❣r❛✜❝❛❞♦s ❡♥ ❧❛ ❋✐❣✉r❛ ✺✳✶✻ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ Ganancia de energía (∆K/Kmin) ✺✳✷✳ ▼❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ 10 5 10 4 10 3 10 2 10 10 10 -4 ✶✶✵ -3 T O S F E R-2A E X T E R-1 0 1 2 M A G 1N0E 10 1 0 N A E N T1R 0 A D A (> 1=0 1 0 R s ) 1 0 10 5 10 4 10 3 10 2 1 10 1 0 10 0 10 -1 10 -2 10 -3 10 -1 10 -2 10 -3 15 15 16 16 17 17 Rs R s (e x tra p o la c ió n ) Rs R s (e x tra p o la c ió n ) Rs R s (e x tra p o la c ió n ) 18 18 19 19 10 -4 10 -3 10 -2 10 -1 Rs R s (e x tra p o la c ió n ) Rs R s (e x tra p o la c ió n ) 10 0 10 1 10 2 T ie m p o (s e g ) ❋✐❣✉r❛ ✺✳✶✺✿ ●❛♥❛♥❝✐❛ ❡st♦❝ást✐❝❛ ❞❡ ❡♥❡r❣í❛ ♣r♦♠❡❞✐❛❞❛ s♦❜r❡ t♦❞❛ ❧❛ ❞✐str✐❜✉❝✐ó♥ ✈s✳ ❡❧ t✐❡♠♣♦ ♣❛r❛ ✉♥❛ ♠✉❡str❛ ❞❡ ♣r♦t♦♥❡s ❧♦❝❛❧✐③❛❞♦s ❡♥ ❞✐❢❡r❡♥t❡s ♣♦s✐❝✐♦♥❡s ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛✳ ❘❡s✉❧t❛❞♦s ❜❛s❛❞♦s ❡♥ ❧❛s ♠❡❞✐❝✐♦♥❡s ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ r❡❛❧✐③❛❞♦s ♣♦r ❡❧ ❱♦②❛❣❡r ✶ ❡♥ ❧❛ tr❛②❡❝t♦r✐❛ ❞❡ ❡♥tr❛❞❛✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ Ganancia de energía (∆K/Kmin) ✺✳✷✳ ▼❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ 10 5 10 4 10 3 10 2 10 10 10 -4 ✶✶✶ 10ATM Ó SFERA 10 -3 -2 -1 0 1 DE 10 TITÁN (r =1020.27 Rs) 10 10 2 10 5 10 4 10 3 10 2 1 10 1 0 10 0 10 -1 10 -1 10 -2 10 -2 10 -3 10 -3 10 -4 10 -4 10 -5 10 -5 + H + H (extrapolación) + N + N (extrapolación) 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 Tiem po (seg) ❋✐❣✉r❛ ✺✳✶✻✿ ●❛♥❛♥❝✐❛ ❡st♦❝ást✐❝❛ ❞❡ ❡♥❡r❣í❛ ♣r♦♠❡❞✐❛❞❛ s♦❜r❡ t♦❞❛ ❧❛ ❞✐str✐❜✉❝✐ó♥ ✈s✳ ❡❧ t✐❡♠♣♦ ♣❛r❛ ✉♥❛ ♠✉❡str❛ ❞❡ ♣r♦t♦♥❡s ② ❞❡ ♥✐tró❣❡♥♦ ❛tó♠✐❝♦ ✐♦♥✐③❛❞♦ ✭N+ ✮ ❧♦❝❛❧✐③❛❞♦s ❡♥ ❧❛ ❛t♠ós❢❡r❛ s✉♣❡r✐♦r ❞❡ ❚✐tá♥✳ ❘❡s✉❧t❛❞♦s ❜❛s❛❞♦s ❡♥ ❧❛s ♠❡❞✐❝✐♦♥❡s ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ r❡❛❧✐③❛❞♦s ♣♦r ❡❧ ❱♦②❛❣❡r ✶ ❡♥ ❧❛ tr❛②❡❝t♦r✐❛ ❞❡ ❡♥tr❛❞❛✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ Ganancia de energía (∆K/Kmin) ✺✳✷✳ ▼❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ 10 -4 ✶✶✷ MAGNE -3 TO S FER-2A E X TE R-1N A S A LID 0 A (>= 10 1R s) 10 10 10 10 10 10 2 10 6 10 5 10 4 10 3 2 10 2 10 1 10 1 10 0 10 0 10 -1 10 -2 10 -3 10 6 10 5 10 4 10 3 10 10 -1 10 -2 10 -3 10 10 11 11 12 12 Rs R s (extrapolación) Rs R s (extrapolación) Rs R s (extrapolación) 13 13 14 14 10 -4 10 -3 10 -2 10 -1 10 Rs R s (extrapolación) Rs R s (extrapolación) 0 10 1 10 2 T iem p o (se g ) ❋✐❣✉r❛ ✺✳✶✼✿ ●❛♥❛♥❝✐❛ ❡st♦❝ást✐❝❛ ❞❡ ❡♥❡r❣í❛ ♣r♦♠❡❞✐❛❞❛ s♦❜r❡ t♦❞❛ ❧❛ ❞✐str✐❜✉❝✐ó♥ ✈s✳ ❡❧ t✐❡♠♣♦ ♣❛r❛ ✉♥❛ ♠✉❡str❛ ❞❡ ♣r♦t♦♥❡s ❧♦❝❛❧✐③❛❞♦s ❡♥ ❞✐❢❡r❡♥t❡s ♣♦s✐❝✐♦♥❡s ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛✳ ❘❡s✉❧t❛❞♦s ❜❛s❛❞♦s ❡♥ ❧❛s ♠❡❞✐❝✐♦♥❡s ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ r❡❛❧✐③❛❞♦s ♣♦r ❡❧ ❱♦②❛❣❡r ✷ ❡♥ ❧❛ tr❛②❡❝t♦r✐❛ ❞❡ s❛❧✐❞❛✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ Ganancia de energía (∆K/Kmin) ✺✳✷✳ ▼❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ 10 -4 ✶✶✸ -3 T O S F E R-2A E X T E R-1 0 1 M A G 1N0E 10 1 0 N A S A L1ID 0 A (> = 1100 R s ) 10 2 10 5 10 4 10 3 10 2 1 10 1 0 10 0 10 -1 10 -2 10 -3 10 5 10 4 10 3 10 2 10 10 10 -1 10 -2 10 -3 15 15 16 16 17 17 Rs R s (e x tra p o la c ió n ) Rs R s (e x tra p o la c ió n ) Rs R s (e x tra p o la c ió n ) 18 18 19 19 10 -4 10 -3 10 -2 10 -1 Rs R s (e x tra p o la c ió n ) Rs R s (e x tra p o la c ió n ) 10 0 10 1 10 2 T ie m p o (s e g ) ❋✐❣✉r❛ ✺✳✶✽✿ ●❛♥❛♥❝✐❛ ❡st♦❝ást✐❝❛ ❞❡ ❡♥❡r❣í❛ ♣r♦♠❡❞✐❛❞❛ s♦❜r❡ t♦❞❛ ❧❛ ❞✐str✐❜✉❝✐ó♥ ✈s✳ ❡❧ t✐❡♠♣♦ ♣❛r❛ ✉♥❛ ♠✉❡str❛ ❞❡ ♣r♦t♦♥❡s ❧♦❝❛❧✐③❛❞♦s ❡♥ ❞✐❢❡r❡♥t❡s ♣♦s✐❝✐♦♥❡s ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛✳ ❘❡s✉❧t❛❞♦s ❜❛s❛❞♦s ❡♥ ❧❛s ♠❡❞✐❝✐♦♥❡s ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ r❡❛❧✐③❛❞♦s ♣♦r ❡❧ ❱♦②❛❣❡r ✷ ❡♥ ❧❛ tr❛②❡❝t♦r✐❛ ❞❡ s❛❧✐❞❛✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ Ganancia de energía (∆K/Kmin) ✺✳✷✳ ▼❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ 10 5 10 4 10 3 10 2 10 10 10 -4 ✶✶✹ A TM Ó S FE R A S U P E R IO R-1D E TITÁ N0 (r = 20.27 R s) -3 -2 1 10 10 10 10 10 10 2 10 5 10 4 10 3 10 2 1 10 1 0 10 0 10 -1 10 -1 10 -2 10 -2 10 -3 10 -3 10 -4 10 -4 10 -5 10 -5 + H + H (extrapolación) + N + N (extrapolación) 10 -4 10 -3 10 -2 10 -1 10 0 10 1 10 2 T ie m p o (se g ) ❋✐❣✉r❛ ✺✳✶✾✿ ●❛♥❛♥❝✐❛ ❡st♦❝ást✐❝❛ ❞❡ ❡♥❡r❣í❛ ♣r♦♠❡❞✐❛❞❛ s♦❜r❡ t♦❞❛ ❧❛ ❞✐str✐❜✉❝✐ó♥ ✈s✳ ❡❧ t✐❡♠♣♦ ♣❛r❛ ✉♥❛ ♠✉❡str❛ ❞❡ ♣r♦t♦♥❡s ② ❞❡ ♥✐tró❣❡♥♦ ❛tó♠✐❝♦ ✐♦♥✐③❛❞♦ ✭N+ ✮ ❧♦❝❛❧✐③❛❞♦s ❡♥ ❧❛ ❛t♠ós❢❡r❛ s✉♣❡r✐♦r ❞❡ ❚✐tá♥✳ ❘❡s✉❧t❛❞♦s ❜❛s❛❞♦s ❡♥ ❧❛s ♠❡❞✐❝✐♦♥❡s ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ r❡❛❧✐③❛❞♦s ♣♦r ❡❧ ❱♦②❛❣❡r ✷ ❡♥ ❧❛ tr❛②❡❝t♦r✐❛ ❞❡ s❛❧✐❞❛✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✺✳✷✳ ▼❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ ✶✶✺ ② ✺✳✶✾✳ ❆❞❡♠ás ❞❡ ❧♦s ✈❛❧♦r❡s ♦❜t❡♥✐❞♦s ❞✐r❡❝t❛♠❡♥t❡ ❞❡ ❧❛ s✐♠✉❧❛❝✐ó♥ ♥✉♠ér✐❝❛ s❡ ♠✉❡s✲ tr❛♥ ❧♦s ❝♦rr❡s♣♦♥❞✐❡♥t❡s ❛ ✉♥❛ ❡①tr❛♣♦❧❛❝✐ó♥ ❤❛st❛ ✸✵ s❡❣✉♥❞♦s✳ ❊♥ ❛♥❛❧♦❣í❛ ❝♦♥ ❧♦ r❡❛❧✐③❛❞♦ ♣❛r❛ ❡❧ ❝❛s♦ ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛✱ s❡ ❡❢❡❝tú❛♥ ♣r✉❡❜❛s ❞❡ ❤✐♣ót❡s✐s ❞❡ ❜♦♥❞❛❞ ❞❡ ❛❥✉st❡ ❛❧ ✾✺ ✪ ❞❡ s✐❣♥✐✜❝❛♥❝✐❛✳ ❊♥ t♦❞♦s ❧♦s ❝❛s♦s ❡s ♣♦s✐❜❧❡ ❡st❛❜❧❡❝❡r q✉❡ ❧❛ ❢✉♥❝✐ó♥ ❞❡ ❧❡② ❞❡ ♣♦t❡♥❝✐❛s ❡s ❧❛ q✉❡ ♠❡❥♦r s❡ ❛❥✉st❛ ❛ ❧❛s ❝✉r✈❛s ❞❡ ❣❛✲ ♥❛♥❝✐❛ ♠♦str❛❞❛s ❛♥t❡r✐♦r♠❡♥t❡✳ ◆♦ ♦❜st❛♥t❡✱ ❡s ✐♠♣♦rt❛♥t❡ ❛❝❧❛r❛r q✉❡ ❡♥ ❛❧❣✉♥❛s r❡❣✐♦♥❡s ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ ❝❛❜❡ ❧❛ ♣♦s✐❜✐❧✐❞❛❞ ❞❡ ❛❥✉st❛r ♦tr❛ ❢✉♥❝✐ó♥✱ ♣♦r ❡❥❡♠♣❧♦ ✉♥❛ ❧♦❣íst✐❝❛✱ s✐♥ ❡♠❜❛r❣♦ ❞❡s❞❡ ❡❧ ♣✉♥t♦ ❞❡ ✈✐st❛ ❢ís✐❝♦ ❡st♦ ú❧t✐♠♦ ♥♦ ❡s ♣❧❛✉s✐❜❧❡ ②❛ q✉❡ ✲s✐♥ ❧❛ ❛❝❝✐ó♥ ❞❡❧ ❝❛♠♣♦ ❡st♦❝ást✐❝♦✲ ❞❡s❞❡ ❡❧ ✐♥✐❝✐♦ s❡ r❡♣♦rt❛ ✉♥❛ ❣❛♥❛♥❝✐❛ ✭♦ ♣ér❞✐❞❛✮✳ ❙❡ ❝♦♥s✐❞❡r❛ q✉❡ ✐♥✐❝✐❛❧♠❡♥t❡ ❧♦s ♣r♦t♦♥❡s ✈✐❡♥❡♥ ❞❡ ❘❡❛ ② s♦♥ ✐♥②❡❝t❛❞♦s ❡♥ ❡❧ ❜♦r❞❡ ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ ✭10 RS ✮✳ ❉❡s♣✉és ❞❡ ✵✳✶ s❡❣✉♥❞♦s ❞❡ ✐♥t❡r❛❝t✉❛r ❝♦♥ ❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❡st♦❝ást✐❝♦ ✭❋✐❣✉r❛ ✹✳✾✮✱ ❧♦s ♣r♦t♦♥❡s s✉♣❡r❛♥ ❡♥ ∼ 100 ✈❡❝❡s ❡❧ ✈❛❧♦r ❞❡ s✉ ❡♥❡r❣í❛ ♠í♥✐♠❛✳ ❊st♦s ♣r♦t♦♥❡s s♦♥ ✐♥②❡❝t❛❞♦s ❛ 11 RS ❞♦♥❞❡ ❞❡s♣✉és ❞❡ ✵✳✶ s❡❣✉♥❞♦s s✉♣❡r❛♥ ❡♥ ∼ 50 ✈❡❝❡s ❡❧ ✈❛❧♦r ❞❡ s✉ ❡♥❡r❣í❛ ♠í♥✐♠❛✳ ❙❡ ✐♥②❡❝t❛♥ ❝♦♥t✐♥✉❛♠❡♥t❡ ❡♥ ✈❛r✐❛s ♣♦s✐❝✐♦♥❡s ② ✜♥❛❧♠❡♥t❡ ❡♥ 19 RS ✲❞❡s♣✉és ❞❡ ✵✳✶ s❡❣✉♥❞♦s✲ ❧♦s ♣r♦t♦♥❡s só❧♦ ❛❧❝❛♥③❛♥ ∼ 5 ✈❡❝❡s ❡❧ ✈❛❧♦r ❞❡ s✉ ❡♥❡r❣í❛ ♠í♥✐♠❛✳ ❊♥t♦♥❝❡s✱ ❡♥ ♣r♦♠❡❞✐♦✱ ❧♦s ♣r♦t♦♥❡s ✈❛♥ ❣❛♥❛♥❞♦ ♠❡♥♦s ❡♥❡r❣í❛ ❝♦♥❢♦r♠❡ s❡ ❛❧❡❥❛♥ ❞❡❧ ♣❧❛♥❡t❛ ✭❋✐❣✉r❛ ✺✳✷✵✮✳ ❊♥ ❡❧ ❝❛s♦ ❞❡ ❚✐tá♥ ❡s ❡✈✐❞❡♥t❡ q✉❡ ❧♦s ♣r♦t♦♥❡s ❡stá♥ s✐❡♥❞♦ ♠ás ❛❝❡❧❡r❛❞♦s q✉❡ ❡❧ ✐ó♥ ♣❡s❛❞♦✳ ❊st♦ ❡s✱ ❧♦s ♣r♦t♦♥❡s ❡♥ ❡st❡ ❧✉❣❛r s♦♥ ♠ás ❡♥❡r❣ét✐❝♦s q✉❡ ❧♦s ♣r♦t♦♥❡s ❧♦❝❛❧✐③❛❞♦s ❡♥ ❡❧ ♣♦❧♦ ♥♦rt❡ ♣♦r ✉♥ ❢❛❝t♦r ❞❡ ∼ 104 ✱ ❡♥ ❝❛♠❜✐♦✱ ❡❧ ♥✐tró❣❡♥♦ ❛tó♠✐❝♦ ✐♦♥✐③❛❞♦ ✭N+ ✮ ❡s ∼ 102 ✈❡❝❡s ♠ás ❡♥❡r❣ét✐❝♦ q✉❡ ❧♦s q✉❡ s❡ ❡♥❝✉❡♥tr❛♥ ❡♥ ❡❧ ❛♥✐❧❧♦ ❈✳ ❊♥ ❧❛ ❋✐❣✉r❛ ✺✳✷✵ s❡ ✐❧✉str❛ q✉❡ ❧❛ ❣❛♥❛♥❝✐❛ ❞❡❜✐❞❛ ❛❧ ♠❡❝❛♥✐s♠♦ ❡st♦❝ást✐❝♦ ✭❊❝✳ ✺✳✶✮ ❡s ♠❛②♦r ❝♦♥ ❧❛ ❞✐st❛♥❝✐❛ ② ❡♥ ❝❛♠❜✐♦ ❧❛ ❣❛♥❛♥❝✐❛ ❝♦♠❜✐♥❛❞❛ ❞❡ ❧♦s ❞♦s ❡❢❡❝t♦s ✭❞✐str✐❜✉❝✐ó♥ ✰ ❝♦rr♦t❛❝✐ó♥✮ ❝♦♥tr✐❜✉②❡ ❝❛❞❛ ✈❡③ ♠❡♥♦s ❛ ❧❛ ❣❛♥❛♥❝✐❛ ❡st♦❝ást✐❝❛✳ ❉❡ ❧❛ ❋✐❣✉r❛ ✺✳✷✵ t❛♠❜✐é♥ ❡s ❝❧❛r♦ q✉❡ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ ♥♦ ❡s ♣♦s✐❜❧❡ ❞✐st✐♥❣✉✐r ❡♥tr❡ ❞✐❢❡r❡♥t❡s r❡❣✐♦♥❡s ❞❡ ❡♥❡r❣✐③❛❝✐ó♥ ❝♦♠♦ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛✳ P❛r❛ ❧♦s r❡s✉❧t❛❞♦s ♦❜t❡♥✐❞♦s ❞✐r❡❝t❛♠❡♥t❡ ❞❡ ❧❛ s✐♠✉❧❛❝✐ó♥ ♥✉♠ér✐❝❛ s❡ ♦❜s❡r✈❛ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✺✳✷✳ ▼❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ 9 10 11 ✶✶✻ MAGNETOSFERA EXTERNA 12 13 14 16 17 18 19 20 300 250 250 Ganancia estocástica Ganancia combinada Ganancia de la distribución 200 Ganancia de energía (∆K/Kmin) 15 300 150 200 150 100 100 50 50 0 0 -50 -50 -100 -100 -150 -150 -200 -200 -250 -250 -300 -300 9 10 11 12 13 14 15 16 17 18 19 20 Distancia a Saturno (Rs) ❋✐❣✉r❛ ✺✳✷✵✿ ●❛♥❛♥❝✐❛ ❞❡ ❡♥❡r❣í❛ ❝✐♥ét✐❝❛ ❞❡ ❧♦s ♣r♦t♦♥❡s ✈s✳ ❧❛ ❞✐st❛♥❝✐❛ ❛❧ ♣❧❛♥❡t❛ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛✳ ❙❡ ♠✉❡str❛ ❧❛ ❣❛♥❛♥❝✐❛ ❞❡ ❡♥❡r❣í❛ ❡st♦❝ást✐❝❛✱ ❧❛ ❣❛♥❛♥✲ ❝✐❛ ❞❡ ❡♥❡r❣í❛ ❞❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ ② ❧❛ ❣❛♥❛♥❝✐❛ ❞❡ ❡♥❡r❣í❛ ❞❡❜✐❞❛ ❛❧ ❡❢❡❝t♦ ❝♦♠❜✐♥❛❞♦ ❞❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ ✰ ❝♦rr♦t❛❝✐ó♥✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✺✳✷✳ ▼❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ 0 ✶✶✼ M20A G N E TO S FE R A 80 E X TE100 R N A , 120 salida140 (r = 19 R s) 180 40 60 160 100 100 H + 80 Frecuencia 80 sigm oidal 60 60 40 40 sigm oidal 20 20 0 0 0 20 40 60 80 100 120 140 160 180 -1 V e lo cid a d fin a l (km s ) ❋✐❣✉r❛ ✺✳✷✶✿ ❍✐st♦❣r❛♠❛ ❞❡ ❢r❡❝✉❡♥❝✐❛s ♣❛r❛ ❧❛ ❞✐str✐❜✉❝✐ó♥ ✜♥❛❧ ❞❡ ✈❡❧♦❝✐❞❛❞❡s ❛s♦❝✐❛❞❛ ❛ ❧♦s ♣r♦t♦♥❡s ❧♦❝❛❧✐③❛❞♦s ❝❡r❝❛ ❞❡ ❧❛ ór❜✐t❛ ❞❡ ❚✐tá♥ ✭tr❛②❡❝t♦r✐❛ ❞❡ s❛❧✐❞❛✮✳ q✉❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ ❞❡ ✈❡❧♦❝✐❞❛❞❡s ▼❛①✇❡❧❧✐❛♥❛ ♠❛♥t✐❡♥❡ s✉ ♣❡r✜❧ ❞❡s♣✉és ❞❡❧ ♣r♦✲ ❝❡s♦ ❞❡ ❛❝❡❧❡r❛❝✐ó♥✳ ❙✐♥ ❡♠❜❛r❣♦✱ ♣❛r❛ ❧❛ tr❛②❡❝t♦r✐❛s ❞❡ ❡♥tr❛❞❛ ② s❛❧✐❞❛ ❡st♦ ♥♦ ❡s ❞❡❧ t♦❞♦ ❝✐❡rt♦✳ P♦r ❡❥❡♠♣❧♦✱ ❡♥ ❧❛ ❋✐❣✉r❛ ✺✳✷✶ s❡ ♠✉❡str❛ ❧❛ ❞✐str✐❜✉❝✐ó♥ ✜♥❛❧ ❞❡ ✈❡❧♦❝✐❞❛❞❡s ♣❛r❛ ♣r♦t♦♥❡s ❧♦❝❛❧✐③❛❞♦s ❝❡r❝❛ ❞❡ ❧❛ ór❜✐t❛ ❞❡ ❚✐tá♥ ✭19 RS ✮ ❡♥ ❞♦♥❞❡ ❞❡s♣✉és ❞❡ 5x107 ✐♥t❡r❛❝❝✐♦♥❡s✱ ♦ ❜✐❡♥✱ ✵✳✵✻ s❡❣✉♥❞♦s s❡ ❝♦♠✐❡♥③❛ ❛ ❞❡s❛rr♦❧❧❛r ✉♥❛ ❝♦❧❛ ② ❡❧ ❛❥✉st❡ ❝♦rr❡s♣♦♥❞✐❡♥t❡ ❛ ❧❛ ❞✐str✐❜✉❝✐ó♥ ② ❛ ❧❛ ❝♦❧❛✳ ❊♥ t♦❞♦s ❧♦s ❝❛s♦s ❡st✉❞✐❛❞♦s✱ ❡❧ ❛❥✉st❡ ❛ ❧❛s ❞✐str✐❜✉❝✐♦♥❡s ✜♥❛❧❡s s❡ ❞❡♠✉❡str❛ ❛ tr❛✈és ❞❡ ✉♥❛ ♣r✉❡❜❛ ❞❡ ❜♦♥❞❛❞ ❞❡ ❛❥✉st❡ ② s❡ ❝♦♥s✐❞❡r❛ ❡❧ ❡st❛❞íst✐❝♦ ❏❛rq✉❡✲❇❡r❛ ❝♦♥ ❡❧ ✾✺ ✪ ❞❡ ♥✐✈❡❧ ❞❡ ❝♦♥✜❛♥③❛✳ ❊❧ ❡s♣❡❝tr♦ ❞❡ ❡♥❡r❣í❛s ♣❛r❛ ❧♦s ♣r♦t♦♥❡s ❧♦❝❛❧✐③❛❞♦s ❛ 10 RS ✭❋✐❣✉r❛ ✺✳✷✷✮✱ 15 RS ✭❋✐❣✉r❛ ✺✳✷✸ ✮ ② ❡♥ ❚✐tá♥ ✭❋✐❣✉r❛ ✺✳✷✹✮ ♠✉❡str❛ q✉❡ ❡♥ ❡❧ ♣r✐♠❡r ❝❛s♦ ♣❛r❛ ♣❛rtí❝✉✲ ❧❛s ❝♦♥ ❡♥❡r❣í❛s ❡♥ ❡❧ ✐♥t❡r✈❛❧♦ ✸✻✳✺ ❡❱< E < 40 eV ✱ ❡❧ ❡s♣❡❝tr♦ s✐❣✉❡ ✉♥❛ ❢✉♥❝✐ó♥ ●❛✉ss✐❛♥❛✱ ❡♥ ❡❧ s❡❣✉♥❞♦ ❝❛s♦ ❡❧ ❡s♣❡❝tr♦ ✭E > 100 eV✮ ❡stá ❞❡s❝r✐t♦ ♣♦r ✉♥❛ ❢✉♥✲ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✺✳✷✳ ▼❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ ✶✶✽ M A G N E TO S FE R A E X TE R N A , salida (r = 10 R s) 36.0 180 36.5 37.0 37.5 38.0 38.5 39.5 40.0 180 160 160 140 140 120 Frecuencia 39.0 120 gaussiana 100 100 80 80 60 60 40 40 20 20 0 36.0 36.5 37.0 37.5 38.0 38.5 39.0 39.5 0 40.0 E n e rg ía cin é tica fin a l (e V ) ❋✐❣✉r❛ ✺✳✷✷✿ ❍✐st♦❣r❛♠❛ ❞❡ ❢r❡❝✉❡♥❝✐❛s ♣❛r❛ ❧❛ ❡♥❡r❣í❛ ❝✐♥ét✐❝❛ ✜♥❛❧ ❛❧❝❛♥③❛❞❛ ♣♦r ✉♥❛ ♠✉❡str❛ ❞❡ ♣r♦t♦♥❡s ❞❡s♣✉és ❞❡ 5x107 ✐♥t❡r❛❝❝✐♦♥❡s ② s✉ ❢✉♥❝✐ó♥ ❞❡ ❛❥✉st❡ ❡♥ 10 RS ✭tr❛②❡❝t♦r✐❛ ❞❡ s❛❧✐❞❛✮✳ ❊❧ ❡s♣❡❝tr♦ ❞❡ ❡♥❡r❣í❛ q✉❡❞❛ ❜✐❡♥ ❞❡s❝r✐t♦ ♣♦r ✉♥❛ ●❛✉ss✐❛♥❛✳ ❝✐ó♥ ❡①♣♦♥❡♥❝✐❛❧ ❞❡❝r❡❝✐❡♥t❡ ② ♣❛r❛ ❡❧ t❡r❝❡r ❝❛s♦ s❡ ❡♥❝✉❡♥tr❛♥ ❞♦s ❞✐str✐❜✉❝✐♦♥❡s ▲♦r❡♥t③✐❛♥❛s ❡♥ ✭E < 117 eV✮ ② ✭E > 122 eV✮✳ ▲♦ ❛♥t❡r✐♦r ♥♦ ❝♦♥tr❛❞✐❝❡ ❛❧ ❤❡❝❤♦ ❞❡ q✉❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ ✜♥❛❧ ❞❡ ✈❡❧♦❝✐❞❛❞❡s s❡❛ ▼❛①✇❡❧❧✐❛♥❛ ✭✈❡r ❡①♣❧✐❝❛❝✐ó♥ ❡♥ ❙❡❝❝✐ó♥ ✺✳✶✮✳ ■♥✈❛r✐❛♥t❡s ❛❞✐❛❜át✐❝♦s ❊♥ ❝❛♠♣♦s q✉❡ ✈❛rí❛♥ ❧❡♥t❛♠❡♥t❡✱ ❡❧ ❝♦♥❝❡♣t♦ ❞❡ ✐♥✈❛r✐❛♥t❡s ❛❞✐❛❜át✐❝♦s ♣r♦♣♦r✲ ❝✐♦♥❛ ✉♥❛ ❤❡rr❛♠✐❡♥t❛ út✐❧ ♣❛r❛ ❞❡s❝r✐❜✐r ❧♦s ♠♦✈✐♠✐❡♥t♦s ♣❡r✐ó❞✐❝♦s ❞❡ ❧❛s ♣❛rtí❝✉✲ ❧❛s✳ ▲♦s ✐♥✈❛r✐❛♥t❡s ❛❞✐❛❜át✐❝♦s r❡q✉✐❡r❡♥ q✉❡ ❧♦s ❝❛♠❜✐♦s t❡♠♣♦r❛❧❡s ✭② ❡s♣❛❝✐❛❧❡s✮ ❞❡ ✉♥❛ ❝♦♥✜❣✉r❛❝✐ó♥ s❡❛♥ ❧❡♥t♦s ❡♥ ❝♦♠♣❛r❛❝✐ó♥ ❝♦♥ ❡❧ ♣❡r✐♦❞♦ ❛s♦❝✐❛❞♦ ❝♦♥ ❡❧ ✐♥✈❛r✐❛♥t❡✳ ▲❛ r❡❧❛❝✐ó♥ ωg > ωb > ωd ✭❞♦♥❞❡ ωg ❡s ❧❛ ❣✐r♦❢r❡❝✉❡♥❝✐❛✱ ωb ❡s ❧❛ ❢r❡❝✉❡♥✲ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✺✳✷✳ ▼❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ Frecuencia 0 ✶✶✾ M A G N E T O S F E R A E X T E R N A , salid a (r = 15 R s) 160 50 100 150 20 0 250 30 0 160 140 140 120 120 100 100 exponencial decreciente 80 80 60 60 40 40 20 20 0 0 50 100 150 20 0 250 0 30 0 E n e rg ía cin é tica fin a l (e V ) ❋✐❣✉r❛ ✺✳✷✸✿ ❍✐st♦❣r❛♠❛ ❞❡ ❢r❡❝✉❡♥❝✐❛s ♣❛r❛ ❧❛ ❡♥❡r❣í❛ ❝✐♥ét✐❝❛ ✜♥❛❧ ❛❧❝❛♥③❛❞❛ ♣♦r ✉♥❛ ♠✉❡str❛ ❞❡ ♣r♦t♦♥❡s ❞❡s♣✉és ❞❡ 5x107 ✐♥t❡r❛❝❝✐♦♥❡s ② s✉ ❢✉♥❝✐ó♥ ❞❡ ❛❥✉st❡ ❡♥ 15 RS ✭tr❛②❡❝t♦r✐❛ ❞❡ s❛❧✐❞❛✮✳ ❊❧ ❡s♣❡❝tr♦ ❞❡ ❡♥❡r❣í❛ q✉❡❞❛ ❜✐❡♥ ❞❡s❝r✐t♦ ♣♦r ✉♥❛ ❢✉♥❝✐ó♥ ❡①♣♦♥❡♥❝✐❛❧ ❞❡❝r❡❝✐❡♥t❡ ♣❛r❛ E > 100 eV ✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✺✳✷✳ ▼❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ Frecuencia 114 ✶✷✵ A T M Ó S F E R A S U P E R IO R D E T IT Á N (r = 20.27 R s) 116 118 120 122 12 4 140 140 120 120 100 100 80 80 60 60 40 Lorentziana Lorentziana 20 40 20 0 0 114 116 118 120 122 12 4 E n e rg ía c in é tic a fin a l (e V ) ❋✐❣✉r❛ ✺✳✷✹✿ ❍✐st♦❣r❛♠❛ ❞❡ ❢r❡❝✉❡♥❝✐❛s ♣❛r❛ ❧❛ ❡♥❡r❣í❛ ❝✐♥ét✐❝❛ ✜♥❛❧ ❛❧❝❛♥③❛❞❛ ♣♦r ✉♥❛ ♠✉❡str❛ ❞❡ ♣r♦t♦♥❡s ❞❡s♣✉és ❞❡ 5x107 ✐♥t❡r❛❝❝✐♦♥❡s ② s✉ ❢✉♥❝✐ó♥ ❞❡ ❛❥✉st❡ ❡♥ ❚✐tá♥ ✭tr❛②❡❝t♦r✐❛ ❞❡ s❛❧✐❞❛✮✳ ❊❧ ❡s♣❡❝tr♦ ❞❡ ❡♥❡r❣í❛ q✉❡❞❛ ❜✐❡♥ ❞❡s❝r✐t♦ ♣♦r ❞♦s ❢✉♥❝✐♦♥❡s ▲♦r❡♥t③✐❛♥❛s ❡♥ E < 117 eV ② E > 122 eV✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✺✳✷✳ ▼❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ ✶✷✶ ❝✐❛ ❞❡❧ ♠♦✈✐♠✐❡♥t♦ ❡♥tr❡ ❧♦s ♣✉♥t♦s ❡s♣❡❥♦ ② ωd ❡s ❧❛ ❢r❡❝✉❡♥❝✐❛ ❞❡❧ ♠♦✈✐♠✐❡♥t♦ ❞❡ ❛rr❛str❡✮ ❡st❛❜❧❡❝❡ ✉♥❛ ❥❡r❛rq✉í❛✿ ❝❛♠❜✐♦s ❡♥ ❧❛ ❝♦♥✜❣✉r❛❝✐ó♥ ❝♦♥ τ ≈ 1 ωd ❞❡str✉✐rá♥ ❡❧ t❡r❝❡r ✐♥✈❛r✐❛♥t❡ ♠✐❡♥tr❛s q✉❡ ❧♦s ♣r✐♠❡r♦s ❞♦s s❡ ❝♦♥s❡r✈❛♥❀ ❝❛♠❜✐♦s ❞❡❧ ♦r❞❡♥ ❞❡ τ ≈ 1 ωb ❞❡str✉✐rá♥ ❛❧ s❡❣✉♥❞♦ ② t❡r❝❡r ✐♥✈❛r✐❛♥t❡s ❛❞✐❛❜át✐❝♦s✱ ❞❡❥❛♥❞♦ q✉❡ ❡❧ ♣r✐♠❡r♦ s❡ ❝♦♥s❡r✈❡✳ ❙✐ ❧♦s ❝❛♠❜✐♦s ♦❝✉rr❡♥ ❡♥ ✉♥❛ ❡s❝❛❧❛ ❞❡ ✉♥ ❣✐r♦♣❡r✐♦❞♦✱ t♦❞♦s ❧♦s ✐♥✈❛r✐❛♥t❡s s❡rá♥ ❞❡str✉✐❞♦s✳ P♦r ❡❥❡♠♣❧♦✱ ❧❛s ♣❛rtí❝✉❧❛s ❡♥ ❧♦s ❛♥✐❧❧♦s ❞❡ r❛❞✐❛✲ ❝✐ó♥ ♣❡r♠❛♥❡❝❡♥ ❛tr❛♣❛❞♦s ♣♦rq✉❡ ❧♦s tr❡s ✐♥✈❛r✐❛♥t❡s ❛❞✐❛❜át✐❝♦s s♦♥ ❝♦♥s❡r✈❛❞♦s✱ s✐♥ ❡♠❜❛r❣♦ s✐ ❧❛s ♦♥❞❛s ❝❛✉s❛♥ q✉❡ ❧♦s ✐♥✈❛r✐❛♥t❡s s❡❛♥ ✈✐♦❧❛❞♦s✱ ❧❛s ♣❛rtí❝✉❧❛s s❡ ❞✐❢✉♥❞✐rá♥ ❡♥ ❡❧ ❡s♣❛❝✐♦ ♣♦s✐❜❧❡♠❡♥t❡ ❛❧❡❥á♥❞♦s❡ ♦ ❛❝❡r❝á♥❞♦s❡ ❞❡❧ ♣❧❛♥❡t❛✳ ❊s ✐♠♣♦rt❛♥t❡ s❡ñ❛❧❛r q✉❡ ❡❧ ♣r✐♠❡r ✐♥✈❛r✐❛♥t❡ ❛❞✐❛❜át✐❝♦ ✐♥✈♦❧✉❝r❛ s♦❧❛♠❡♥t❡ ✈❛❧♦r❡s ❧♦❝❛❧❡s✱ ♠✐❡♥tr❛s q✉❡ ❧♦s ♦tr♦s r❡q✉✐❡r❡♥ ❞❡❧ ❝♦♥♦❝✐♠✐❡♥t♦ ❞❡ ❧❛s ♣r♦♣✐❡❞❛❞❡s ❞❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❡♥ ✉♥ ❣r❛♥ ✈♦❧✉♠❡♥ ❞❡❧ ❡s♣❛❝✐♦✱ ❛❞❡♠ás ❞❡ ❧❛s ♣r♦♣✐❡❞❛❞❡s ❞❡ ❧❛s ♣❛rtí❝✉❧❛s ② ❞❡❧ ❝❛♠♣♦ ❡♥ ❧❛ ♣♦s✐❝✐ó♥ ❞♦♥❞❡ s❡ ❡♥❝✉❡♥tr❛ ❧❛ ♥❛✈❡✳ ❊♥ ✉♥❛ ♠❛❣♥❡tós❢❡r❛✱ ♥♦ s❡ ❡s♣❡r❛ q✉❡ ❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ✈❛rí❡ ❧❡♥t❛♠❡♥t❡ ❞❛❞❛ ❧❛ ✈❛r✐❡❞❛❞ ❞❡ ❢❡♥ó♠❡♥♦s q✉❡ ❛❧❧í ♦❝✉rr❡♥ ✭♣♦r ❡❥❡♠♣❧♦✱ ♦♥❞❛s ❞❡ ❞✐st✐♥t❛ ❢r❡❝✉❡♥❝✐❛✱ ❧❛ ❞❡❢♦r♠❛❝✐ó♥ r❡♣❡♥t✐♥❛ ❞❡ ❧❛ ❝♦♥✜❣✉r❛❝✐ó♥ ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦✱ ❧❛ t✉r❜✉❧❡♥❝✐❛ ❞❡❧ ♣❧❛s♠❛✱ ❡♥tr❡ ♦tr♦s✮✳ ▲❛ ❋✐❣✉r❛ ✹✳✹ ♠✉❡str❛ q✉❡ ❧❛s ✈❛r✐❛❝✐♦♥❡s t❡♠♣♦r❛❧❡s s♦♥ ❛❧ ♠❡♥♦s ❞❡❧ ♠✐s♠♦ ♦r❞❡♥ ❞❡ ♠❛❣♥✐t✉❞ q✉❡ ❧❛s ✢✉❝t✉❛❝✐♦♥❡s ❡s♣❛❝✐❛❧❡s ❬▼❛rtí♥❡③✲ ●ó♠❡③ ❡t ❛❧✳✱ ✷✵✵✼❜❪✳ ❊st♦ s✐❣♥✐✜❝❛ q✉❡ ❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ✈❛rí❛ rá♣✐❞❛♠❡♥t❡ ② ❝♦♠♦ ✉♥❛ ❝♦♥s❡❝✉❡♥❝✐❛ ❧♦s ✐♥✈❛r✐❛♥t❡s ❛❞✐❛❜át✐❝♦s ♥♦ ♣✉❡❞❡♥ s❡r ❝♦♥s❡r✈❛❞♦s✳ ❊❧ ♣r✐♠❡r ✐♥✈❛r✐❛♥t❡✱ ❡❧ ♠♦♠❡♥t♦ ♠❛❣♥ét✐❝♦✱ ♥♦ ♣✉❡❞❡ s❡r ❝♦♥st❛♥t❡ ❡♥ ✉♥ ❣✐r♦r❛❞✐♦ ❞❡❜✐❞♦ ❛❧ ❝❛♠❜✐♦ rá♣✐❞♦ ❡♥ ❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❡♥ ❝♦♠♣❛r❛❝✐ó♥ ❝♦♥ ❧❛ ❣✐r♦❢r❡❝✉❡♥❝✐❛ ❞❡ ❧❛ ♣❛rtí❝✉❧❛✳ ❊❧ s❡❣✉♥❞♦ ✐♥✈❛r✐❛♥t❡ ❞❡♣❡♥❞❡ ❞❡❧ ♣r♦♠❡❞✐♦ ❞❡ ❧❛ ✈❡❧♦❝✐❞❛❞ ♣❛r❛❧❡❧❛ ② ♥♦ ♥❡❝❡s❛r✐❛♠❡♥t❡ ❞❡❜❡ t❡♥❡r ❡❧ ♠✐s♠♦ ✈❛❧♦r ❡♥ ❝❛❞❛ ♣❛s♦ ❛❧❡❛t♦r✐♦✳ ▼ás ❛ú♥✱ ♥♦ s❡ ❝♦♥s❡r✈❛ ❜❛❥♦ ❧❛ ❛❝❝✐ó♥ ❞❡ ❢✉❡r③❛s ❛❞✐❝✐♦♥❛❧❡s ❝♦♠♦ ❧❛s ❢✉❡r③❛s ❞❡ ♣ér❞✐❞❛ ❞❡ r❛❞✐❛❝✐ó♥✳ ❊❧ t❡r❝❡r ✐♥✈❛r✐❛♥t❡✱ ♣♦r ♦tr♦ ❧❛❞♦✱ ♥♦ ♣✉❡❞❡ ❝♦♥s❡r✈❛rs❡ ②❛ q✉❡ ❧❛s ♣❛rtí❝✉❧❛s ❡stá♥ s✐❡♥❞♦ tr❛♥s♣♦rt❛❞❛s ❤❛❝✐❛ ❡❧ ♣❧❛♥❡t❛✱ ❣❛♥❛♥❞♦ ❡♥❡r❣í❛✳ ❉❡ ❧❛ ❞✐s❝✉s✐ó♥ ❛♥t❡r✐♦r✱ ♥♦ s❡ ❡s♣❡r❛ q✉❡ ❧♦s ✐♥✈❛r✐❛♥t❡s ❛❞✐❛❜át✐❝♦s ♣✉❡❞❛♥ ❝♦♥s❡r✈❛rs❡ ❡♥ ❡❧ ♠♦❞❡❧♦ ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❡st♦❝ást✐❝❛ ♣r❡s❡♥t❛❞♦✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✺✳✸✳ ❙✐st❡♠❛ ❞❡ ❛♥✐❧❧♦s ✺✳✸✳ ✶✷✷ ❙✐st❡♠❛ ❞❡ ❛♥✐❧❧♦s ❙❡ ❡st✉❞✐❛♥ ❧♦s ❡❢❡❝t♦s q✉❡ ♣r♦✈♦❝❛ ❧❛ ❛❝❝✐ó♥ ❞❡ ✉♥ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❡st♦❝ást✐❝♦ ② ✉♥ ❝❛♠♣♦ ❣r❛✈✐t❛❝✐♦♥❛❧ ❡st♦❝ást✐❝♦ s♦❜r❡ ❧❛s ♣❛rtí❝✉❧❛s ❞❡ ♣♦❧✈♦ ❝❛r❣❛❞❛s ② ♥❡✉tr❛s✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✳ ▲❛s ❣❛♥❛♥❝✐❛s ❞❡ ❡♥❡r❣í❛ ❝✐♥ét✐❝❛ r❡♣♦rt❛❞❛s ❡♥ ❛♠❜♦s ❝❛s♦s s❡ ❝❛❧❝✉❧❛♥ ❛ tr❛✈és ❞❡ ❧❛ ❊❝✳ ✭✺✳✶✮ ✉s❛♥❞♦ ❡❧ ✈❛❧♦r ❞❡ ❧❛ ❡♥❡r❣í❛ ♠í♥✐♠❛ q✉❡ ♣✉❡❞❡ t❡♥❡r ✉♥ ❣r❛♥♦ ❞❡ ♣♦❧✈♦ ❡♥ ❝❛❞❛ ❛♥✐❧❧♦✳ ✺✳✸✳✶✳ P♦❧✈♦ ❝❛r❣❛❞♦ ▲♦s ❣r❛♥♦s ❞❡ ♣♦❧✈♦ ❝❛r❣❛❞♦ ✐♥t❡r❛❝tú❛♥ ❝♦♥ ❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❡st♦❝ást✐❝♦ ❝♦rr❡s✲ ♣♦♥❞✐❡♥t❡ ❛ ❧❛ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛ ✭❋✐❣✉r❛ ✹✳✽✮✳ ❈♦♠♦ ②❛ s❡ ❡①♣❧✐❝ó ❡♥ ❡❧ ❈❛♣ít✉❧♦ ✹✱ só❧♦ s❡ ❛♥❛❧✐③❛ ❡❧ ❝❛s♦ ❞❡ ♣♦❧✈♦ ❝❛r❣❛❞♦ ❡♥ ❡❧ ❛♥✐❧❧♦ ❊ q✉❡ ❤❛ s✐❞♦ ❞✐✈✐❞✐❞♦ ❡♥ tr❡s r❡❣✐♦♥❡s✳ ▲♦s r❡s✉❧t❛❞♦s ♦❜t❡♥✐❞♦s s❡ ♠✉❡str❛♥ ❡♥ ❧❛ ❋✐❣✉r❛ ✺✳✷✺ ❞♦♥❞❡ ❧❛ ❡♥❡r❣í❛ ♠í♥✐♠❛ ❡s ❞❡ ✶✳✸✽x109 eV✳ ❉❡❜✐❞♦ ❛ ❧❛ ❢♦r♠❛ ❞❡ ❧❛s ❝✉r✈❛s ❞❡ ❣❛♥❛♥❝✐❛ ♥♦ ❡s ♣♦s✐❜❧❡ r❡♣♦rt❛r ❧♦s ✈❛❧♦r❡s ❞❡ ❡①tr❛♣♦❧❛❝✐ó♥ ✭❞✉r❛♥t❡ ❧♦s ♣r✐♠❡r♦s s❡❣✉♥❞♦s ❧♦s ❣r❛♥♦s ❣❛♥❛♥ ❡♥❡r❣í❛✱ ❧✉❡❣♦ s❡ ❡st❛❜✐❧✐③❛♥ ② ❡♥s❡❣✉✐❞❛ ✈✉❡❧✈❡♥ ❛ ❣❛♥❛r✮✳ ❖❜sér✈❡s❡ q✉❡ ❧♦s ❣r❛♥♦s ❞❡ ♣♦❧✈♦ ❧♦❝❛❧✐③❛❞♦s ❡♥ ❡❧ ❜♦r❞❡ ❡①t❡r♥♦ ❞❡❧ ❛♥✐❧❧♦ t✐❡♥❞❡♥ ❛ ♣❡r❞❡r ❡♥❡r❣í❛✱ ❡♥ ❝♦♥tr❛st❡ ❝♦♥ ❧♦s q✉❡ s❡ ❡♥❝✉❡♥tr❛♥ ❡♥ ❡❧ ❜♦r❞❡ ✐♥t❡r♥♦ ② ❡♥ ❧❛ ♣❛rt❡ ♠❡❞✐❛✳ ▼ás ❛ú♥✱ ❧♦s ❣r❛♥♦s q✉❡ ❡stá♥ ❡♥ ❡❧ ❜♦r❞❡ ✐♥t❡r♥♦ t✐❡♥❞❡♥ ❛ ❣❛♥❛r ♠ás ❡♥❡r❣í❛ ✭ ∼ 10−4 ✮ ❡♥ ✵✳✷✺ s❡❣✉♥❞♦s✳ ❊❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❡st♦❝ást✐❝♦ ❡s ❝❛♣❛③ ❞❡ ❡♥❡r❣✐③❛r ❛ ❧♦s ❣r❛♥♦s ❞❡ ♣♦❧✈♦ ❝❛r❣❛✲ ❞♦s ♣❡r♦ ❡s ❧❡♥t♦ ❡♥ ❝♦♠♣❛r❛❝✐ó♥ ❝♦♥ ❧♦ ❞❡s❝r✐t♦ ♣❛r❛ ❧♦s ✐♦♥❡s✳ ✺✳✸✳✷✳ P♦❧✈♦ ♥❡✉tr♦ ▲♦s ❣r❛♥♦s ❞❡ ♣♦❧✈♦ ♥❡✉tr♦ ✐♥t❡r❛❝tú❛♥ ❝♦♥ ❡❧ ❝❛♠♣♦ ❣r❛✈✐t❛❝✐♦♥❛❧ ❡st♦❝ást✐❝♦ ❝♦rr❡s♣♦♥❞✐❡♥t❡ ❛ ❝❛❞❛ ❛♥✐❧❧♦ ✭♣♦r ❡❥❡♠♣❧♦✱ ✈é❛s❡ ❧❛ ❋✐❣✉r❛ ✹✳✶✷✮✳ ▲♦s r❡s✉❧t❛❞♦s ♦❜✲ t❡♥✐❞♦s s❡ ♠✉❡str❛♥ ❡♥ ❧❛ ❋✐❣✉r❛ ✺✳✷✻ ❞♦♥❞❡ ❧❛s ❡♥❡r❣í❛s ♠í♥✐♠❛s s♦♥✿ ✽✳✺✾x1024 eV ✭❛♥✐❧❧♦ ❈✮✱ ✻✳✽✸x1024 eV✭❛♥✐❧❧♦ ❇✮✱ ✻x1024 eV✭❉✐✈✐s✐ó♥ ❞❡ ❈❛ss✐♥✐✮✱ ✺✳✺✷x1024 eV ✭❛♥✐✲ ❧❧♦ ❆✮ ② ✶✳✸✽x109 eV ✭❛♥✐❧❧♦ ❊✮✳ ❚❛♠❜✐é♥ s❡ ♠✉❡str❛♥ ❧♦s ✈❛❧♦r❡s ❞❡ ❧❛ ❡①tr❛♣♦❧❛❝✐ó♥ ❝♦rr❡s♣♦♥❞✐❡♥t❡s ❤❛st❛ ∼ 16 ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✺✳✸✳ ❙✐st❡♠❛ ❞❡ ❛♥✐❧❧♦s Ganancia de energía (∆K/Kmin) 0.00 1.4x10 -4 1.2x10 -4 1.0x10 -4 8.0x10 ✶✷✸ POLVO CARGADO EN EL ANILLO E 0.05 0.10 0.15 0.20 0.25 0.30 -4 1.4x10 1.2x10 -4 1.0x10 -4 -5 8.0x10 -5 6.0x10 -5 6.0x10 -5 4.0x10 -5 4.0x10 -5 2.0x10 -5 2.0x10 -5 3.5 Rs 6.5 Rs 8 Rs 0.0 -2.0x10 0.0 -5 0.00 0.05 0.10 0.15 0.20 0.25 -2.0x10 0.30 -5 Tiempo (seg) ❋✐❣✉r❛ ✺✳✷✺✿ ●❛♥❛♥❝✐❛ ❡st♦❝ást✐❝❛ ❞❡ ❡♥❡r❣í❛ ♣❛r❛ ❧♦s ❣r❛♥♦s ❞❡ ♣♦❧✈♦ ❝❛r❣❛❞♦s ❡♥ ❡❧ ❛♥✐❧❧♦ ❊ ❛ ❞✐❢❡r❡♥t❡s ❞✐st❛♥❝✐❛s✳ ❘❡s✉❧t❛❞♦s ❜❛s❛❞♦s ❡♥ ❧❛s ♠❡❞✐❝✐♦♥❡s ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❞❡❧ ❱♦②❛❣❡r ✶ ❡♥ s✉ ♣❛s♦ ♣♦r ❧❛ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✺✳✸✳ ❙✐st❡♠❛ ❞❡ ❛♥✐❧❧♦s Ganancia de energía (∆K/Kmin) 10 -4 10 -2 ✶✷✹ P O L V O -1N E U T R O E N E L S IS T E 1M A D E A N IL LOS 0 2 10 A n illo A n illo A n illo A n illo 10 C C B B 10 10 10 (r = 1 .3 8 R s ) (e xtra p o la c ió n ) (r = 1 .7 4 R s ) (e xtra p o la c ió n ) 3 10 -4 10 -5 10 -5 10 -6 10 -6 10 -7 10 -7 10 -8 10 -9 10 -8 10 -9 D iv is ió n d e C a s s in i (r = 1 .9 9 R s ) D iv is ió n d e C a s s in i (e xtra p o la c ió n ) A n illo A (r = 2 .5 1 R s ) A n illo A (e xtra p o la c ió n ) A n illo E (r = 5 .5 1 R s ) A n illo E (e xtra p o la c ió n ) 10 -2 10 -1 10 0 10 1 10 2 10 3 T ie m p o (s e g ) ❋✐❣✉r❛ ✺✳✷✻✿ ●❛♥❛♥❝✐❛ ❡st♦❝ást✐❝❛ ❞❡ ❡♥❡r❣í❛ ♣❛r❛ ❧♦s ❣r❛♥♦s ❞❡ ♣♦❧✈♦ ♥❡✉tr♦s ❡♥ ❡❧ s✐st❡♠❛ ❞❡ ❛♥✐❧❧♦s ❞❡ ❙❛t✉r♥♦✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✺✳✸✳ ❙✐st❡♠❛ ❞❡ ❛♥✐❧❧♦s ✶✷✺ ♠✐♥✉t♦s✳ ❉❡ ♠❛♥❡r❛ ❣❡♥❡r❛❧ s❡ ♦❜s❡r✈❛ q✉❡ ❧♦s ❣r❛♥♦s ❞❡ ♣♦❧✈♦ t✐❡♥❞❡♥ ❛ ❣❛♥❛r ❡♥❡r❣í❛ ❝♦♥ ❡❧ t✐❡♠♣♦✳ ■♥❝❧✉s✐✈❡✱ ❡st❛ ❣❛♥❛♥❝✐❛ ❡s ❞❡❜✐❞❛ ú♥✐❝❛♠❡♥t❡ ❛ ❧❛ ❛❝❝✐ó♥ ❞❡❧ ❝❛♠♣♦ ❣r❛✈✐t❛❝✐♦♥❛❧ ❡st♦❝ást✐❝♦ ✭✈❡r ❊❝✳ ✺✳✶✮✳ ❙❡ ✐❞❡♥t✐✜❝❛♥ tr❡s r❡❣✐♦♥❡s ❞❡ ❡♥❡r❣✐③❛❝✐ó♥ ❞❡♥tr♦ ❞❡❧ s✐st❡♠❛ ❞❡ ❛♥✐❧❧♦s✳ ✶✳ ❆❧t❛ ❡♥❡r❣✐③❛❝✐ó♥✿ ▲♦s ❣r❛♥♦s ❞❡ ♣♦❧✈♦ ♠ás ❣r❛♥❞❡s ✭❉✐✈✐s✐ó♥ ❞❡ ❈❛ss✐♥✐ ② ❛♥✐❧❧♦ ❆✮ t❛r❞❛♥ ♠ás t✐❡♠♣♦ ❡♥ r❡s♣♦♥❞❡r ❛ ❧❛ ❛❝❝✐ó♥ ❞❡❧ ❝❛♠♣♦ ❣r❛✈✐t❛❝✐♦♥❛❧ ❡st♦❝ást✐❝♦✱ s✐♥ ❡♠❜❛r❣♦✱ ❧✉❡❣♦ ❞❡ ✶✺ ♠✐♥✉t♦s ❛❞q✉✐❡r❡♥ ✉♥❛ ❡♥❡r❣í❛ q✉❡ ❡s ∼ 10−4 ✈❡❝❡s ♠❛②♦r q✉❡ s✉ ❡♥❡r❣í❛ ♠í♥✐♠❛✳ ✷✳ ❇❛❥❛ ❡♥❡r❣✐③❛❝✐ó♥✿ ▲♦s ❣r❛♥♦s ❞❡ ♣♦❧✈♦ ❞❡❧ ❛♥✐❧❧♦ ❇ ② ❞❡❧ ❛♥✐❧❧♦ ❊ s♦♥ ❧♦s q✉❡ ♠ás rá♣✐❞♦ r❡s♣♦♥❞❡♥ ❛ ❧❛ ❛❝❝✐ó♥ ❞❡❧ ❝❛♠♣♦ ❣r❛✈✐t❛❝✐♦♥❛❧ ❡st♦❝ást✐❝♦✱ ♣❡r♦ t❛♠❜✐é♥ s♦♥ ❧♦ q✉❡ ♠❡♥♦s s❡ ❡♥❡r❣✐③❛♥ ✭❞❡s♣✉és ❞❡ ✶✺ ♠✐♥✉t♦s ❛♣❡♥❛s s✉♣❡r❛♥ ❛ s✉ ❡♥❡r❣í❛ ♠í♥✐♠❛ ❡♥ ∼ 10−5 ✮✳ ✸✳ ❡♥❡r❣✐③❛❝✐ó♥ ✐♥t❡r♠❡❞✐❛✿ ❊♥ ❡❧ ❛♥✐❧❧♦ ❈ ❧♦s ❣r❛♥♦s ❞❡ ♣♦❧✈♦ r❡s♣♦♥❞❡♥ ♠ás rá♣✐❞♦ ② ❛ ❧❛ ✈❡③ ❛❧❝❛♥③❛♥ ✲❛♣r♦①✐♠❛❞❛♠❡♥t❡✲ ❧❛ ♠✐s♠❛ ❡♥❡r❣í❛ q✉❡ ❧♦s ❣r❛♥♦s ❞❡❧ ❛♥✐❧❧♦ ❆ ② ❧♦s ❞❡ ❧❛ ❉✐✈✐s✐ó♥ ❞❡ ❈❛ss✐♥✐✳ ❚❛♥t♦ ❧♦s ❣r❛♥♦s ❞❡ ♣♦❧✈♦ ♥❡✉tr♦ ❝♦♠♦ ❝❛r❣❛❞♦ ♥♦ ♣✉❡❞❡♥ ❣❛♥❛r ✭♦ ♣❡r❞❡r✮ ❡♥❡r❣í❛ ♣♦r s✐❡♠♣r❡✳ ▲❛ r❛③ó♥ ❛ ❧❛ ❝✉❛❧ s❡ ✐♥❝r❡♠❡♥t❛ ❡❧ ✈❛❧♦r ❞❡ s✉ ❡♥❡r❣í❛ ❞❡♣❡♥❞❡ ❞❡ ❧❛ ❡♥❡r❣í❛ t♦t❛❧ ✭❝✐♥ét✐❝❛ ② ♣♦t❡♥❝✐❛❧✮ ❞✐s♣♦♥✐❜❧❡ ❡♥ ❝❛❞❛ ❛♥✐❧❧♦✱ ❡st♦ ❡s✱ G S MR 1 2 + ET = K + U = MR vK 2 r ✭✺✳✸✮ ❊♥ ❧❛ ❊❝✳ ✭✺✳✸✮ ❧❛ ♠❛s❛ ❞❡❧ ❛♥✐❧❧♦ ❡s MR ✱ ❧❛ ✈❡❧♦❝✐❞❛❞ ❑❡♣❧❡r✐❛♥❛ vK s❡ ❝❛❧❝✉❧❛ ❡♥ ❧❛ ❊❝✳ ✭✸✳✽✮✱ ❧❛ ♠❛s❛ ❞❡ ❙❛t✉r♥♦ ❡s MS =✺✳✻✽x1026 kg ② ❧❛ ❞✐st❛♥❝✐❛ ❛❧ ♣❧❛♥❡t❛ ❡s r✳ ▲♦s ✈❛❧♦r❡s ❞❡ ❧❛ ♠❛s❛ ❞❡❧ ❛♥✐❧❧♦ ② ❞❡ ❧❛ ❞✐st❛♥❝✐❛ ❛❧ ♣❧❛♥❡t❛ s❡ ❡♥❝✉❡♥tr❛♥ ❡♥ ❡❧ ❈✉❛❞r♦ ✹✳✹✳ ▲❛ ❡♥❡r❣í❛ t♦t❛❧ ❞✐s♣♦♥✐❜❧❡ ❡♥ ❝❛❞❛ ❛♥✐❧❧♦ ❡s✿ ∼✹✳✷✼x1045 eV ✭❛♥✐❧❧♦ ❈✮ ∼✶✳✵✷x1047 eV ✭❛♥✐❧❧♦ ❇✮ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✺✳✸✳ ❙✐st❡♠❛ ❞❡ ❛♥✐❧❧♦s ✶✷✻ ∼✶✳✹✽x1045 eV ✭❉✐✈✐s✐ó♥ ❞❡ ❈❛ss✐♥✐✮ ∼✶✳✻✹x1046 eV ✭❛♥✐❧❧♦ ❆✮ ∼✼✳✹✾x1035 eV ✭❛♥✐❧❧♦ ❊✮ ❊❢❡❝t♦s ❞❡❧ ♣❡r✜❧ ❞❡ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ s♦❜r❡ ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ❞❡ ❧❛s ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ❋✐♥❛❧♠❡♥t❡ ♣❛r❛ ❡st✉❞✐❛r ❧♦s ❡❢❡❝t♦s q✉❡ ♣r♦❞✉❝❡ ❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ s♦❜r❡ ❧❛ ❛❝❡✲ ❧❡r❛❝✐ó♥ ② ❧❛ ❞✐str✐❜✉❝✐ó♥ ✜♥❛❧ ❞❡ ✈❡❧♦❝✐❞❛❞❡s ❞❡ ❧❛s ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s✱ s❡ ♣r♦♣♦♥❡♥ ❞♦s ♣❡r✜❧❡s ❤✐♣♦tét✐❝♦s ♣❛r❛ ❧❛s ✢✉❝t✉❛❝✐♦♥❡s✿ ❜❛❥❛s✲ ♦❝✉rr❡♥ s✐♥ ♣r❡❢❡r❡♥❝✐❛ ❛❧❣✉♥❛✮ ② ✉♥✐❢♦r♠❡ ❧✐♥❡❛❧ ✭❧❛s ✐♥t❡♥s✐❞❛❞❡s ✲❛❧t❛s ② ✭❧❛s ✐♥t❡♥s✐❞❛❞❡s ❛❧t❛s s♦♥ ❧❛s ♠ás ❢❛✈♦r❛❜❧❡s✮✳ ❊❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❡st♦❝ást✐❝♦ ❧✐♥❡❛❧ ❤❛❝❡ q✉❡ ❧❛s ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ✭♣r♦t♦♥❡s✱ ✐♦♥❡s ♣❡s❛❞♦s ② ❣r❛♥♦s ❞❡ ♣♦❧✈♦✮ ❛❧❝❛♥❝❡♥ ❡♥❡r❣í❛s ♠✉② ❛❧t❛s ✭✐♥❝❧✉s♦ ❞❡❧ ♦r❞❡♥ ❞❡ ▼❡❱✮ ❡♥ ♠✉② ♣♦❝♦ t✐❡♠♣♦✳ ❊st❡ ❤❡❝❤♦ t❛♠❜✐é♥ s❡ ✈❡ r❡✢❡❥❛❞♦ ❡♥ ❧❛ ❞✐str✐❜✉❝✐ó♥ ✜♥❛❧ ❞❡ ✈❡❧♦❝✐❞❛❞❡s q✉❡ t✐❡♥❡ ✉♥ ❞❡s♣❧❛③❛♠✐❡♥t♦ ❤❛❝✐❛ ✈❛❧♦r❡s ♠❛②♦r❡s ② ❡♥ ❧❛ ♥♦ ❢♦r♠❛❝✐ó♥ ❞❡ ❝♦❧❛s s✉♣r❛t❡r♠❛❧❡s✳ ❈♦♠♦ ❡❥❡♠♣❧♦ ✈é❛s❡ ❧❛ ❋✐❣✉r❛ ✺✳✷✼ ❞♦♥❞❡ ❧❛s ❝✉r✈❛s ❞❡ ❣❛♥❛♥❝✐❛ s♦♥ ♦❜t❡♥✐❞❛s ♣❛r❛ ✉♥❛ ♠✉❡str❛ ❞❡ ♣r♦t♦♥❡s ✭H+ ✮ ② ♣❛r❛ ✉♥❛ ♠✉❡str❛ ❞❡ ✐♦♥❡s ♣❡s❛❞♦s ❝♦♠♦ ❡❧ ❛❣✉❛ ✭H2 O+ ✮ ❧♦❝❛❧✐③❛❞❛s s♦❜r❡ ❡❧ ❛♥✐❧❧♦ ❊✳ ❈✉❛♥❞♦ ❛❝tú❛ ✉♥ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❡st♦❝ást✐❝♦ ✉♥✐❢♦r♠❡✱ ❧❛s ♣❛rtí❝✉❧❛s ❛❧❝❛♥③❛♥ ❡♥❡r❣í❛s ♠❡♥♦r❡s ❛ ❧❛s ♦❜t❡♥✐❞❛s ❡♥ ❡❧ ❝❛s♦ ❧♦❣íst✐❝♦ ② ❛❞❡♠ás s❡ ♦❜s❡r✈❛ q✉❡ ❧❛ ❡str✉❝t✉r❛ ❞❡ ❝♦❧❛ ❡♥ ❧❛ ❞✐str✐❜✉❝✐ó♥ ✜♥❛❧ ❞❡ ✈❡❧♦❝✐❞❛❞❡s ♣✉❡❞❡ ❛♣❛r❡❝❡r ♦ ♥♦✳ ❊♥ ❧❛ ❋✐❣✉r❛ ✺✳✷✽ s❡ ♠✉❡str❛♥ ❧❛s ❝✉r✈❛s ❞❡ ❣❛♥❛♥❝✐❛ ♦❜t❡♥✐❞❛s ♣❛r❛ ❧♦s ♣r♦t♦♥❡s ✭H+ ✮ ❧♦❝❛❧✐③❛❞♦s ❡♥ ❞✐❢❡r❡♥t❡s ♣♦s✐❝✐♦♥❡s ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ ❞✉r❛♥t❡ ❧❛ tr❛②❡❝t♦✲ r✐❛ ❞❡ s❛❧✐❞❛✳ ❚♦❞♦s ❧♦s r❡s✉❧t❛❞♦s ❡stá♥ ❜❛s❛❞♦s ❡♥ ❧♦s ❞❛t♦s ❞❡ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ♠❡❞✐❞♦s ♣♦r ❧❛s ♥❛✈❡s ❱♦②❛❣❡r ❝♦♥ ✉♥❛ r❡s♦❧✉❝✐ó♥ t❡♠♣♦r❛❧ ✭♦ t✐❡♠♣♦ ❞❡ ♠✉❡str❡♦ ♣r♦♠❡❞✐♦✮ ❞❡ ✶✳✾✷ s❡❣✉♥❞♦s✳ ▲♦s ♠ás s♦❜r❡s❛❧✐❡♥t❡s✱ ❧✉❡❣♦ ❞❡ ❛♣❧✐❝❛r ❡❧ ♠♦❞❡❧♦ ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❡st♦❝ást✐❝❛ ❛ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦✱ s♦♥✿ ✶✮ ▲❛s ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✺✳✸✳ ❙✐st❡♠❛ ❞❡ ❛♥✐❧❧♦s 1E-5 10 ✶✷✼ 1E-4 ANILLO E (r = 7.6 Rs) 1E-3 0.01 0.1 1 15 10 15 10 13 10 11 Ganancia de energía (∆K/Kmin) + 10 13 H + H (extrapolación) + H 2O 10 11 H 2 O (extrapolación) + 10 9 10 9 10 7 10 7 10 5 10 5 10 3 10 3 10 1 10 1 10 -5 10 -4 10 -3 10 -2 10 -1 10 0 Tiempo (seg) ❋✐❣✉r❛ ✺✳✷✼✿ ●❛♥❛♥❝✐❛ ❡st♦❝ást✐❝❛ ❞❡ ❡♥❡r❣í❛ ♣r♦♠❡❞✐❛❞❛ s♦❜r❡ t♦❞❛ ❧❛ ❞✐str✐❜✉❝✐ó♥ ✈s✳ ❡❧ t✐❡♠♣♦ ♣❛r❛ ✉♥❛ ♠✉❡str❛ ❞❡ ♣r♦t♦♥❡s ② ✉♥❛ ❞❡ ✐♦♥❡s ♣❡s❛❞♦s ❧♦❝❛❧✐③❛❞♦s s♦❜r❡ ❡❧ ❛♥✐❧❧♦ ❊✳ ▲❛s ✢✉❝t✉❛❝✐♦♥❡s ❞❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ t✐❡♥❡♥ ✉♥ ♣❡r✜❧ ❧✐♥❡❛❧✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ Ganancia de energía (∆K/Kmin) ✺✳✸✳ ❙✐st❡♠❛ ❞❡ ❛♥✐❧❧♦s 10 1 10 0 10 -4 ✶✷✽ M A G N E T-3O S F E R A E-2X T E R N A S A R s) -1 L ID A (> = 10 0 10 10 10 12 12 14 14 10 10 10 10 Rs R s (e xtra p o la ció n ) Rs R s (e xtra p o la ció n ) Rs R s (e xtra p o la ció n ) 1 10 1 10 0 10 -1 10 -1 10 -2 10 -2 10 -3 10 -3 10 -4 10 -4 10 -5 10 -5 10 -6 10 -6 16 16 18 18 10 -4 10 -3 10 -2 Rs R s (e xtra p o la ció n ) Rs R s (e xtra p o la ció n ) 10 -1 10 0 T ie m p o (s e g ) ❋✐❣✉r❛ ✺✳✷✽✿ ●❛♥❛♥❝✐❛ ❡st♦❝ást✐❝❛ ❞❡ ❡♥❡r❣í❛ ♣r♦♠❡❞✐❛❞❛ s♦❜r❡ t♦❞❛ ❧❛ ❞✐str✐❜✉❝✐ó♥ ✈s✳ ❡❧ t✐❡♠♣♦ ♣❛r❛ ✉♥❛ ♠✉❡str❛ ❞❡ ♣r♦t♦♥❡s ❧♦❝❛❧✐③❛❞♦s ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ ❞✉r❛♥t❡ ❧❛ tr❛②❡❝t♦r✐❛ ❞❡ s❛❧✐❞❛✳ ▲❛s ✢✉❝t✉❛❝✐♦♥❡s ❞❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ t✐❡♥❡♥ ✉♥ ♣❡r✜❧ ✉♥✐❢♦r♠❡✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✺✳✸✳ ❙✐st❡♠❛ ❞❡ ❛♥✐❧❧♦s ✶✷✾ ♣❛rtí❝✉❧❛s ❡♥ ♣r♦♠❡❞✐♦ t✐❡♥❞❡♥ ❛ ❣❛♥❛r ❡♥❡r❣í❛✱ ✷✮ ❊❧ ♠❡❝❛♥✐s♠♦ ❡s ♠ás ❡✜❝✐❡♥t❡ ♣❛r❛ ♣❛rtí❝✉❧❛s ❝♦♥ ❡♥❡r❣í❛s ✐♥✐❝✐❛❧♠❡♥t❡ ❜❛❥❛s✱ ✸✮ ❊♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛ s❡ ✐❞❡♥t✐✜❝❛♥ ❞✐❢❡r❡♥t❡s r❡❣✐♦♥❡s ❞❡ ❡♥❡r❣✐③❛❝✐ó♥✱ ✹✮ ❊♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛ ♥♦ s❡ ❡♥❝✉❡♥tr❛♥ ❞✐❢❡r❡♥❝✐❛s ♥♦t❛❜❧❡s ❡♥ ❧❛ ❡♥❡r❣✐③❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s✱ ✺✮ ❊❧ ♠❡❝❛♥✐s♠♦ ❛❝❡❧❡r❛ ❡♥ ♣♦❝♦s s❡❣✉♥❞♦s✱ ✻✮ ❊❧ ♣❡r✜❧ ❞❡ ✈❡❧♦❝✐❞❛❞❡s s❡ ♠❛♥t✐❡♥❡ ❡♥ ❝❛s✐ t♦❞♦s ❧♦s ❝❛s♦s ❡st✉❞✐❛❞♦s✱ ✼✮ ❊♥ ❡❧ ❝❛s♦ ❞❡ ❣r❛♥♦s ❞❡ ♣♦❧✈♦✱ ❡❧ ♠❡❝❛♥✐s♠♦ ❡s ❧❡♥t♦✳ ❆❧ ❝♦♥s✐❞❡r❛r ✉♥ t✐❡♠♣♦ ❞❡ ♠✉❡str❡♦ ❞✐st✐♥t♦ ✭♣♦r ❡❥❡♠♣❧♦✱ ✸✶ s❡❣✉♥❞♦s✮ ❝♦♥ ❡❧ ♣r♦♣ós✐t♦ ❞❡ ❡st✉❞✐❛r ❧♦s ♣♦s✐❜❧❡s ❡❢❡❝t♦s ❞❡ ❡st❡ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❡st♦❝ást✐❝♦ s♦❜r❡ ❧❛ ❡♥❡r❣✐③❛❝✐ó♥ ❞❡ ❧❛s ♣❛rtí❝✉❧❛s✱ s❡ ❡♥❝✉❡♥tr❛✿ ❛✮ ❡❧ ♠✐s♠♦ ♣❡r✜❧ ❞❡ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❡♥ ❝❛❞❛ ❞✐r❡❝❝✐ó♥ ❡s♣❛❝✐❛❧✱ ❡st♦ ❡s✱ ❧❛s ✢✉❝t✉❛❝✐♦♥❡s s✐❣✉❡♥ ✉♥❛ ❞✐str✐❜✉❝✐ó♥ ❧♦❣íst✐❝❛❀ ❜✮ ❧❛s ♣❛rtí❝✉❧❛s t✐❡♥❞❡♥ ❛ ❛✉♠❡♥t❛r ❡❧ ✈❛❧♦r ✐♥✐❝✐❛❧ ❞❡ s✉ ❡♥❡r❣í❛ ❝✐♥ét✐❝❛❀ ❝✮ ❧❛ ❝❛♥t✐❞❛❞ ❞❡ ♣❛rtí❝✉❧❛s ❞❡ ❛❧t❛s ❡♥❡r❣í❛s ❞✐s♠✐♥✉②❡ ②❛ q✉❡ ❤❛② ♠❡♥♦s ✢✉❝t✉❛❝✐♦♥❡s ❝❛♣❛❝❡s ❞❡ ❛❝❡❧❡r❛r❧❛s❀ ❞✮ ❧❛ ❞✐str✐❜✉❝✐ó♥ ✜♥❛❧ ❞❡ ✈❡❧♦❝✐❞❛❞❡s ♣r❡s❡r✈❛ ❡❧ ♣❡r✜❧ ▼❛①✇❡❧❧✐❛♥♦ ②✱ ❡✮ ♥♦ ❤❛② ✐♦♥❡s s✉♣r❛t❡r♠❛❧❡s✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❈❛♣ít✉❧♦ ✻ ❈♦♥❝❧✉s✐♦♥❡s ❙❡ ❤❛ ❞❡s❛rr♦❧❧❛❞♦ ✉♥ ♠♦❞❡❧♦ ♣❛r❛ ❡①♣❧✐❝❛r ❧❛ ❡♥❡r❣✐③❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❡♥ ❧❛s ♠❛❣♥❡tós❢❡r❛s ♣❧❛♥❡t❛r✐❛s✳ ❊♥ ♣❛rt✐❝✉❧❛r✱ s❡ ❤❛ ❡st✉❞✐❛❞♦ ❡♥ ❞❡t❛❧❧❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦ ♣❛r❛ ❧♦ ❝✉❛❧ s❡ ❤❛♥ ❝♦♥s✐❞❡r❛❞♦ ❞✐st✐♥t❛s ♣♦❜❧❛❝✐♦♥❡s ❞❡ ✐♦♥❡s✿ ♠❡t❛♥♦ + + + ✭CH+ 4 ✮✱ ❤✐❞ró❣❡♥♦ ♠♦❧❡❝✉❧❛r ✭H2 ✮✱ ❛❣✉❛ ✭H2 O ✮✱ ♥✐tró❣❡♥♦ ❛tó♠✐❝♦ ✭N ✮✱ ♥✐tró❣❡♥♦ + + ♠♦❧❡❝✉❧❛r ✭N+ 2 ✮✱ ♦①í❣❡♥♦ ❛tó♠✐❝♦ ✭O ✮ ❡ ❤✐❞ró①✐❞♦ ✭OH ✮ ✱ ❞❡ ♣r♦t♦♥❡s ② ❞❡ ❣r❛♥♦s ❞❡ ♣♦❧✈♦ ✭❢♦r♠❛❞♦s ♣♦r ❤✐❡❧♦ ❞❡ ❛❣✉❛ ② ♣♦r ✉♥❛ ♠❡③❝❧❛ ❞❡ ❤✐❡❧♦✲s✐❧✐❝❛t♦s✮ ❧♦❝❛❧✐③❛❞♦s t❛♥t♦ ❡♥ ❧❛ r❡❣✐ó♥ ✐♥t❡r♥❛ ✭✐♥❝❧✉②❡♥❞♦ ❛❧ s✐st❡♠❛ ❞❡ ❛♥✐❧❧♦s✮ ❝♦♠♦ ❡♥ ❧❛ ❡①t❡r♥❛✳ ❊♥ ❧♦s ❣r❛♥♦s ❞❡ ♣♦❧✈♦ s❡ ❛♥❛❧✐③ó t❛♠❜✐é♥ ❡❧ ❝❛s♦ ♥❡✉tr♦✳ ❇ás✐❝❛♠❡♥t❡ ❡❧ ♠♦❞❡❧♦ ❝♦♥s✐❞❡r❛ q✉❡ ❧❛ ❛❝❝✐ó♥ ❞❡ ✉♥ ❝❛♠♣♦ ❞❡ ❢✉❡r③❛s ❡st♦❝ás✲ t✐❝♦ ✭❡❧é❝tr✐❝♦ ♦ ❣r❛✈✐t❛❝✐♦♥❛❧✮ ❡s ✉♥♦ ❞❡ ❧♦s r❡s♣♦♥s❛❜❧❡s ❞❡ ❧❛ ❡♥❡r❣✐③❛❝✐ó♥ ❞❡ ❧❛s ♣❛rtí❝✉❧❛s ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛✳ ❊❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❡st♦❝ást✐❝♦ ❡s ♦❜t❡♥✐❞♦ ❛ tr❛✈és ❞❡ ❧❛ ❛♣❧✐❝❛❝✐ó♥ ❞❡ ❧❛s ❡❝✉❛❝✐♦♥❡s ❞❡ ▼❛①✇❡❧❧ ❛ ❧❛s ✢✉❝t✉❛❝✐♦♥❡s ❞❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ♦❜s❡r✈❛❞❛s ♣♦r ❧❛s ♥❛✈❡s ❡s♣❛❝✐❛❧❡s✱ ♠✐❡♥tr❛s q✉❡ ❡❧ ❝❛♠♣♦ ❣r❛✈✐t❛❝✐♦♥❛❧ ❡st♦❝ás✲ t✐❝♦ ❡s ❝❛❧❝✉❧❛❞♦ ❝♦♥ ❧❛ ▲❡② ❞❡ ❧❛ ●r❛✈✐t❛❝✐ó♥ ❯♥✐✈❡rs❛❧ ❞❡ ◆❡✇t♦♥ ❛♣❧✐❝❛❞❛ ❛ ❧❛ ❞✐str✐❜✉❝✐ó♥ ❞❡ ♠❛s❛s ❞❡ ❧♦s ❣r❛♥♦s ❞❡ ♣♦❧✈♦ ❡♥ ❝❛❞❛ ❛♥✐❧❧♦✳ ▲❛ ♠❛❣♥❡tós❢❡r❛ ✭✐♥t❡r♥❛ ② ❡①t❡r♥❛✮ ❞❡ ❙❛t✉r♥♦ ❡s s✐♠✉❧❛❞❛ t♦♠❛♥❞♦ ❡♥ ❝✉❡♥t❛ s✉ s✐♠❡trí❛ ② ❡❧ ❝♦♠♣♦rt❛♠✐❡♥t♦ ♥♦✲❝♦❧✐s✐♦♥❛❧ ❞❡❧ ♣❧❛s♠❛✳ ❙✐♥ ♣ér❞✐❞❛ ❞❡ ❣❡♥❡r❛❧✐❞❛❞✱ ❧❛s ♣❛rtí❝✉❧❛s ❡stá♥ ❝❛r❛❝t❡r✐③❛❞❛s ✐♥✐❝✐❛❧♠❡♥t❡ ♣♦r ✉♥❛ ❞✐str✐❜✉❝✐ó♥ ❞❡ ✈❡❧♦❝✐❞❛❞❡s ▼❛①✇❡❧❧✐❛♥❛ ✲❡①❝❡♣t♦ ❧♦s ❣r❛♥♦s ❞❡ ♣♦❧✈♦ q✉❡ s✐❣✉❡♥ ✈❡❧♦❝✐❞❛❞❡s ❑❡♣❧❡r✐❛♥❛s✲ ② s✉ ❝♦rr❡s♣♦♥❞✐❡♥t❡ ❞✐str✐❜✉❝✐ó♥ ❞❡ ❡♥❡r❣í❛✳ ❊♥ ❡❧ ♣r❡s❡♥t❡ ❈❛♣ít✉❧♦ s❡ r❡s✉♠❡♥ ❧♦s ❡❢❡❝t♦s ♣r♦❞✉❝✐❞♦s ♣♦r ❧❛ ❛❝❝✐ó♥ ❞❡❧ ❝❛♠♣♦ ✶✸✵ ✻✳✶✳ P❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ✭❈❛♠♣♦ ❊❧é❝tr✐❝♦ ❊st♦❝ást✐❝♦✮ ✶✸✶ ❞❡ ❢✉❡r③❛s ❡st♦❝ást✐❝♦ ✭❡❧é❝tr✐❝♦ ♦ ❣r❛✈✐t❛❝✐♦♥❛❧✮ s♦❜r❡ ✉♥❛ ♠✉❡str❛ ❞❡ ♣❛rtí❝✉❧❛s ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦✳ ▲♦s r❡s✉❧t❛❞♦s ♦❜t❡♥✐❞♦s ❡stá♥ ❜❛s❛❞♦s ❡♥ ❡❧ ú♥✐❝♦ ❝r✉❝❡ q✉❡ r❡❛❧✐③❛r♦♥ ❧❛s ♥❛✈❡s ❱♦②❛❣❡r ♣♦r ❧❛ ♠❛❣♥❡tós❢❡r❛✳ ❊♥ ❣❡♥❡r❛❧✱ ❧❛ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛ ❡s ♠ás ❞✐♥á♠✐❝❛ q✉❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛✳ ❊st♦ s❡ ❞❡❜❡✱ q✉✐③á✱ ❛ ❧❛ ♣r❡s❡♥❝✐❛ ❞❡ ♥✉♠❡r♦s❛s ❢✉❡♥t❡s ❞❡ ♣❛rtí❝✉❧❛s q✉❡ ❛❧t❡r❛♥ ❧❛ ✈❡❧♦❝✐❞❛❞ ❞❡ ❝♦rr♦t❛❝✐ó♥ ❞❡❧ ♣❧❛s♠❛✱ ②❛ q✉❡ ❧❛ ✐♥t❡♥s✐❞❛❞ ❞❡ ❧❛s ✢✉❝t✉❛❝✐♦♥❡s ❞❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❡s ♠❡♥♦r ❡♥ ❧❛ r❡❣✐ó♥ ✐♥t❡r♥❛✳ ❉❡♥tr♦ ❞❡❧ s✐st❡♠❛ ❞❡ ❛♥✐❧❧♦s✱ ❡❧ ♠❡❝❛♥✐s♠♦ ❡st♦❝ást✐❝♦ ❤❛❝❡ q✉❡ ❧♦s ❣r❛♥♦s ❞❡ ♣♦❧✈♦ s❡❛♥ ❡♥❡r❣✐③❛❞♦s ❛ ✉♥❛ t❛s❛ t❛❧✱ q✉❡ ❧❡s ♣❡r♠✐t❡ ♣❡r♠❛♥❡❝❡r ♣♦r ♠ás t✐❡♠♣♦ ❡♥ ❧❛ r❡❣✐ó♥ ❛♥t❡s ❞❡ ❛❧❝❛♥③❛r ❧❛ ❡♥❡r❣í❛ ❞❡ ❡s❝❛♣❡✳ ❊st❡ ♠❡❝❛♥✐s♠♦ ❡s ✉♥ ❜✉❡♥ ❝❛♥❞✐❞❛t♦ ♣❛r❛ ❡①♣❧✐❝❛r ❧❛ ♣r❡s❡♥❝✐❛ ❞❡ ❧❛ ✐♦♥ós❢❡r❛ s♦❜r❡ ❧♦s ❛♥✐❧❧♦s s✐♥ ❝♦♥s✐❞❡r❛r ❛ ❧❛s ❝♦❧✐s✐♦♥❡s ❡♥tr❡ ♣❛rtí❝✉❧❛s✳ ✻✳✶✳ P❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ✭❈❛♠♣♦ ❊❧é❝tr✐❝♦ ❊st♦❝ás✲ t✐❝♦✮ ▲❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ✭✐♦♥❡s ② ❣r❛♥♦s ❞❡ ♣♦❧✈♦✮ ❡s ❡♥❡r❣✐③❛❞❛✱ ❞❡ ♠❛♥❡r❛ ❞✐st✐♥t❛✱ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❞❡ ❙❛t✉r♥♦✳ ❆ ❝♦♥t✐♥✉❛❝✐ó♥ s❡ ❡♥✉♥❝✐❛♥ ❧♦s r❡s✉❧t❛❞♦s ♠ás s♦❜r❡s❛❧✐❡♥t❡s ♣❛r❛ ❝❛❞❛ r❡❣✐ó♥✳ ✻✳✶✳✶✳ ▼❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛ ✶✳ ▲❛s ♣❛rtí❝✉❧❛s ❡①♣❡r✐♠❡♥t❛♥ ✲❡♥ ♣r♦♠❡❞✐♦✲ ✉♥❛ ❣❛♥❛♥❝✐❛ ❞❡ ❡♥❡r❣í❛ ❝♦♥ ❡❧ t✐❡♠♣♦✳ ❨❛ q✉❡ ❧❛s ♣ér❞✐❞❛s ❞❡ ❡♥❡r❣í❛ ♣♦r r❛❞✐❛❝✐ó♥ ❡❧❡❝tr♦♠❛❣♥ét✐❝❛✱ ❝❛❧❝✉✲ ❧❛❞❛s ❝♦♥ ❧❛ ❊❝✳ ✭✸✳✶✷✮✱ s♦♥ ♣❡q✉❡ñ❛s ✭< 10−27 eV✮ ❝✉❛♥❞♦ s❡ ❧❡ ❝♦♠♣❛r❛ ❝♦♥ ❧❛ ❣❛♥❛♥❝✐❛ ❞❡ ❡♥❡r❣í❛ t♦t❛❧✱ ❡st❡ ❡❢❡❝t♦ ❡s ❞❡❜✐❞♦ ♠❡r❛♠❡♥t❡ ❛❧ ♠❡❝❛♥✐s♠♦ ❡st♦❝ást✐❝♦✳ ❊st♦ ❡s ♠♦str❛❞♦ ❛ tr❛✈és ❞❡ ✉♥ ✐♥❝r❡♠❡♥t♦ ❡♥ ❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧ ♣❧❛s♠❛ ✭❝❛❧❡♥t❛♠✐❡♥t♦ ❡st♦❝ást✐❝♦✮ ② ❡♥ ✉♥ ✐♥❝r❡♠❡♥t♦ ❡♥ ❧❛ ✈❡❧♦❝✐❞❛❞ ♠❡❞✐❛ ✭❛❝❡❧❡r❛❝✐ó♥ ❡st♦❝ást✐❝❛✮✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✻✳✶✳ P❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ✭❈❛♠♣♦ ❊❧é❝tr✐❝♦ ❊st♦❝ást✐❝♦✮ ✶✸✷ ✷✳ ❊♥ ❣❡♥❡r❛❧✱ ② s❡❣ú♥ ❧❛s ♣r✉❡❜❛s ❞❡ ✐♥❢❡r❡♥❝✐❛ ❡st❛❞íst✐❝❛✱ ❧❛ ❞✐str✐❜✉❝✐ó♥ ✐♥✐❝✐❛❧ ❞❡ ✈❡❧♦❝✐❞❛❞❡s ❝♦♥ ♣❡r✜❧ ▼❛①✇❡❧❧✐❛♥♦ ♠❛♥t✐❡♥❡ s✉ ❢♦r♠❛ ❞❡s♣ú❡s ❞❡ q✉❡ ❧❛ ♠✉❡str❛ ❞❡ ♣❛rtí❝✉❧❛s ❤❛ ✐♥t❡r❛❝t✉❛❞♦ ❝♦♥ ❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❡st♦❝ást✐❝♦✳ ▲❛s ❡①❝❡♣❝✐♦♥❡s s♦♥ ❧❛ ❞✐str✐❜✉❝✐ó♥ ❞❡ ✈❡❧♦❝✐❞❛❞❡s ♣❛r❛ ❧♦s ♣r♦t♦♥❡s ② ♣❛r❛ ❧♦s ✐♦♥❡s ♣❡s❛❞♦s ❧♦❝❛❧✐③❛❞♦s ❝❡r❝❛ ❞❡❧ ❛♥✐❧❧♦ ❈ ② ❧❛ ❞✐str✐❜✉❝✐ó♥ ❞❡ ✈❡❧♦❝✐❞❛❞❡s ♣❛r❛ ❧♦s ♣r♦t♦♥❡s q✉❡ ✈✐❡♥❡♥ ❞❡ ❊♥❝❡❧❛❞♦❀ ❡♥ ❡st♦s ❝❛s♦s ❧❛s ❞✐str✐❜✉❝✐♦♥❡s s❡ ✈✉❡❧✈❡♥ ✐♥❡st❛❜❧❡s✳ ✸✳ ▲❛ ❝❛r❛❝t❡ríst✐❝❛ ❜✐♠♦❞❛❧ ♦❜s❡r✈❛❞❛ ❡♥ ❧❛ ❝♦♠♣♦♥❡♥t❡ ✏②✑ ❞❡ ❧❛ ✈❡❧♦❝✐❞❛❞ ✜♥❛❧ ❞❡♣❡♥❞❡ ❞❡❧ ✈❛❧♦r ❞❡❧ ♠♦♠❡♥t♦ ❧✐♥❡❛❧ ✐♥✐❝✐❛❧ ✭✈❛ ❞❡s❞❡ ✻✳✽✺x10−24 kg m s−1 ❤❛st❛ ✷✳✷✺x10−21 kg m s−1 ✮ ❛❞q✉✐r✐❞❛ ♣♦r ❧❛ ♠✉❡str❛ ❞❡ ♣❛rtí❝✉❧❛s✳ ❊st♦ ❡s✱ ♣❛r❛ ♣❛rtí❝✉❧❛s ❧♦❝❛❧✐③❛❞❛s ❝❡r❝❛ ❞❡❧ ♣❧❛♥❡t❛ ❡❧ ♠♦♠❡♥t♦ ❧✐♥❡❛❧ ❡s ♠❡♥♦r q✉❡ ♣❛r❛ ❧❛s ♣❛rtí❝✉❧❛s ❧♦❝❛❧✐③❛❞❛s ❧❡❥♦s ②✱ ❝♦♠♣❛rá♥❞♦❧♦ ❝♦♥ ❡❧ ✐♠♣✉❧s♦ ❞❛❞♦ ♣♦r ❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ✭✺✳✺✺x10−21 kg m s−1 ✮✱ ❧❛ ♣r♦❜❛❜✐❧✐❞❛❞ ❞❡ s❡r ❛❝❡❧❡r❛❞♦ ❡s ♠❛②♦r ✶ ✳ ✹✳ ▲❛ ❡❢❡❝t✐✈✐❞❛❞ ❞❡❧ ♠❡❝❛♥✐s♠♦ ❞❡♣❡♥❞❡ ❢✉❡rt❡♠❡♥t❡ ❞❡ ❧♦s tr❡s tér♠✐♥♦s q✉❡ ❛♣❛r❡❝❡♥ ❡♥ ❧❛ ❡❝✉❛❝✐ó♥ ♣❛r❛ ❧❛ ❡♥❡r❣í❛ r❡s✉❧t❛♥t❡✳ ❊❧ ♣r✐♠❡r tér♠✐♥♦ ❡stá r❡❧❛❝✐♦♥❛❞♦ ❝♦♥ ❧❛ ❡♥❡r❣í❛ ❞❡ ❧❛ ❞✐str✐❜✉❝✐ó♥✱ ❡❧ s❡❣✉♥❞♦ tér♠✐♥♦ ❡s ❞❡❜✐❞♦ ❛ ❧❛ ❡♥❡r❣í❛ ❝♦rr♦t❛❝✐♦♥❛❧ ② ❡❧ t❡r❝❡r tér♠✐♥♦ ❡s ✉♥❛ ❝♦♠❜✐♥❛❝✐ó♥ ❞❡ ❧❛s ❡♥❡r❣í❛s ❞❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ ② ❝♦rr♦t❛❝✐♦♥❛❧✳ ❊st❡ ú❧t✐♠♦ tér♠✐♥♦ ❡s ❛❧t❛♠❡♥t❡ ✈❛r✐❛❜❧❡ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛✳ ✺✳ ❈♦♠♦ ✉♥❛ ❝♦♥s❡❝✉❡♥❝✐❛ ❞❡ ❧♦ ❞❡s❝r✐t♦ ❡♥ ❡❧ ♣✉♥t♦ ❛♥t❡r✐♦r s❡ ♣✉❡❞❡♥ ❞✐st✐♥✲ ✶ ▲❛ ♣r♦❜❛❜✐❧✐❞❛❞ ❞❡ ❣❛♥❛♥❝✐❛ ✭P ✮ ② ❧❛ ♣r♦❜❛❜✐❧✐❞❛❞ ❞❡ ♣ér❞✐❞❛ ✭P ✮ ❞❡ ❡♥❡r❣í❛ ♣❛r❛ ✉♥❛ G P ♣❛rtí❝✉❧❛ q✉❡ ❡stá s♦♠❡t✐❞❛ ❛ ❧❛ ❛❝❝✐ó♥ ❞❡ ✉♥ ❝❛♠♣♦ ❞❡ ❢✉❡r③❛s ❡st♦❝ást✐❝♦✱ s❡ ❝❛❧❝✉❧❛♥ ❛ ♣❛rt✐r ❞❡ ❧❛s ❡①♣r❡s✐♦♥❡s ❬❉✉r❛♥❞✲▼❛♥t❡r♦❧❛✱ ✷✵✵✸❪✿ 1 PG = 2  I 1+ 20  1 2  I 20  PP = ❞♦♥❞❡ I 1− ❡s ❡❧ ✐♠♣✉❧s♦ ❞❛❞♦ ♣♦r ❡❧ ❝❛♠♣♦ ❞❡ ❢✉❡r③❛s ❡♥ ❝❛❞❛ ✐♥t❡r❛❝❝✐ó♥ ② P0 ❡s ❡❧ ♠♦♠❡♥t♦ ❧✐♥❡❛❧ ❞❡ ❧❛ ♣❛rtí❝✉❧❛ ❛♥t❡s ❞❡ ❝❛❞❛ ✐♥t❡r❛❝❝✐ó♥✳ ❊st❛s ❡❝✉❛❝✐♦♥❡s s♦♥ ✈á❧✐❞❛s ❝✉❛♥❞♦ ❧❛ ❞❡s✐❣✉❛❧❞❛❞ 0≤ I 2 P0 ≤ 1 s❡ ♠❛♥t✐❡♥❡✳ ❈✉❛♥❞♦ I 2 P0 > 1 s❡ t✐❡♥❡ q✉❡ PG = 1 ② PP = 0✳ ▲❛s ❡❝✉❛❝✐♦♥❡s ❛♥t❡r✐♦r❡s ♠✉❡str❛♥ q✉❡ ❧❛ ♣r♦❜❛❜✐❧✐❞❛❞ ❞❡ ❣❛♥❛♥❝✐❛ ❡s s✐❡♠♣r❡ ♠❛②♦r q✉❡ ❧❛ ♣r♦❜❛❜✐❧✐❞❛❞ ❞❡ ♣ér❞✐❞❛✱ ❡①❝❡♣t♦ I ❡♥ ❡❧ ❝❛s♦ ❞♦♥❞❡ 2 P 0 = 0 ✭PG = PP ❂ ✵✳✺ ✮✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✻✳✶✳ P❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ✭❈❛♠♣♦ ❊❧é❝tr✐❝♦ ❊st♦❝ást✐❝♦✮ ✶✸✸ ❣✉✐r ❞✐❢❡r❡♥t❡s r❡❣✐♦♥❡s ❞❡ ❡♥❡r❣✐③❛❝✐ó♥ ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛✿ ✶✮ r❡❣✐ó♥ ❞❡ ❜❛❥❛ ❡♥❡r❣✐③❛❝✐ó♥ ✭♣♦❧♦ ♥♦rt❡ ❞❡ ❙❛t✉r♥♦✱ ❊♥❝❡❧❛❞♦ ② ❘❡❛✮❀ ✷✮ r❡❣✐ó♥ ❞❡ ✐♥❡st❛❜✐❧✐❞❛❞ ✭❆♥✐❧❧♦ ❈✮❀ ✸✮ r❡❣✐ó♥ ❞❡ ❡♥❡r❣✐③❛❝✐ó♥ ✐♥t❡r♠❡❞✐❛ ✭❉✐♦♥❡✮❀ ② ✹✮ r❡❣✐ó♥ ❞❡ ❛❧t❛ ❡♥❡r❣✐③❛❝✐ó♥ ✭❆♥✐❧❧♦ ❊✮✳ ✻✳ ❙❡ ❡♥❝✉❡♥tr❛♥ ❞✐❢❡r❡♥t❡s t✐♣♦s ❞❡ ❡s♣❡❝tr♦s ❞❡ ❡♥❡r❣í❛✿ ♣❛r❛ ♣❛rtí❝✉❧❛s ❝♦♥ ❡♥❡r❣í❛s ❡♥ ❡❧ ✐♥t❡r✈❛❧♦ ✵✳✹ ❡❱< E 122 eV✮ s❡ ❡♥❝✉❡♥tr❛♥ ❞♦s ❞✐str✐❜✉❝✐♦♥❡s ▲♦r❡♥t③✐❛♥❛s✳ ▲♦ ❛♥t❡r✐♦r ♥♦ ❝♦♥tr❛❞✐❝❡ ❧♦ ❡①✲ ♣✉❡st♦ ❡♥ ❡❧ ♣✉♥t♦ ✹✱ ♣✉❡s ❧❛s ♣r✉❡❜❛s ❡st❛❞íst✐❝❛s ❝♦♠♣❛r❛♥ ✉♥❛ ❞✐str✐❜✉❝✐ó♥ ▼❛①✇❡❧❧✐❛♥❛ ❝♦♥ ❝✉❛❧q✉✐❡r ♦tr❛ ❞✐str✐❜✉❝✐ó♥✳ ◆♦ ♥❡❝❡s❛r✐❛♠❡♥t❡ t✐❡♥❡ q✉❡ s❡r ❧❛ q✉❡ r❡❛❧♠❡♥t❡ s❡ ❛❥✉st❛ ②❛ q✉❡ ❡st♦ s❡ ✈❡ r❡✢❡❥❛❞♦ ❡♥ ❧♦s ❞✐❢❡r❡♥t❡s t✐♣♦s ❞❡ ❡s♣❡❝tr♦s ❞❡ ❡♥❡r❣í❛ ❡♥❝♦♥tr❛❞♦s ② q✉❡ ♥♦ ❝♦rr❡s♣♦♥❞❡♥ ❛❧ ❞❡ ✉♥❛ ❞✐str✐❜✉❝✐ó♥ ❞❡ ✈❡❧♦❝✐❞❛❞❡s ▼❛①✇❡❧❧✐❛♥❛✳ ✽✳ ❊s ♣♦s✐❜❧❡ r❡❞✉❝✐r ❧❛ ❣❡♥❡r❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s s✉♣r❛t❡r♠❛❧❡s ♠❡❞✐❛♥t❡ ❧❛ ❛♣❧✐✲ ❝❛❝✐ó♥ ❞❡ ✉♥ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❡st♦❝ást✐❝♦ ❝♦♥ ♣❡r✜❧ ❛❞❡❝✉❛❞♦✳ ✾✳ ❆❧ ♠♦❞✐✜❝❛r ❡❧ t✐❡♠♣♦ ❞❡ ♠✉❡str❡♦ ❡♥ ❧❛s ♠❡❞✐❝✐♦♥❡s ❞❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦✱ ❡❧ ♣❡r✜❧ ❞❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ s✐❣✉❡ s✐❡♥❞♦ ❞❡s❝r✐t♦ ♣♦r ✉♥❛ ❢✉♥❝✐ó♥ ❞❡ ❞✐str✐❜✉❝✐ó♥ ❧♦❣íst✐❝❛ ♣❡r♦ ❧❛ ❝❛♥t✐❞❛❞ ❞❡ ♣❛rtí❝✉❧❛s ❞❡ ❛❧t❛s ❡♥❡r❣í❛s ❞✐s♠✐♥✉②❡ ❝♦♥s✐❞❡r❛✲ ❜❧❡♠❡♥t❡ ② ❧❛ ♣♦s✐❜✐❧✐❞❛❞ ❞❡ ❢♦r♠❛❝✐ó♥ ❞❡ ❝♦❧❛s s✉♣r❛t❡r♠❛❧❡s ❡s ♥✉❧❛✳ ✻✳✶✳✸✳ ❙✐st❡♠❛ ❞❡ ❛♥✐❧❧♦s ✶✳ ❙ó❧♦ s❡ ♣✉❡❞❡ ♣❡♥s❛r ❡♥ ❧♦s ❣r❛♥♦s ❞❡ ♣♦❧✈♦ ❧♦❝❛❧✐③❛❞♦s ❡♥ ❡❧ ❛♥✐❧❧♦ ❊✳ ❊♥ ❧♦s ❞❡♠ás ❛♥✐❧❧♦s ♣✉❡❞❡♥ ❡①✐st✐r ♣❛rtí❝✉❧❛s ❝❛r❣❛❞❛s ♣❡r♦ ♣r♦❜❛❜❧❡♠❡♥t❡ s❡❛♥ ❝❛r❣❛❞❛s ② ❞❡s❝❛r❣❛❞❛s ❝♦♥st❛♥t❡♠❡♥t❡✳ ✷✳ ❙❡ ✐❞❡♥t✐✜❝❛♥ ❜ás✐❝❛♠❡♥t❡ ❞♦s r❡❣✐♦♥❡s✿ ❡♥ ❡❧ ❜♦r❞❡ ❡①t❡r♥♦ ❞❡❧ ❛♥✐❧❧♦ ❧♦s ❣r❛♥♦s ❞❡ ♣♦❧✈♦ t✐❡♥❞❡♥ ❛ ♣❡r❞❡r ❡♥❡r❣í❛ ② ❡♥ ❡❧ ❜♦r❞❡ ✐♥t❡r♥♦ t✐❡♥❞❡♥ ❛ ❣❛♥❛r ♠ás ❡♥❡r❣í❛ ❡♥ ❛❧❣✉♥♦s s❡❣✉♥❞♦s✳ ✸✳ ❊❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❡st♦❝ást✐❝♦ ❡s ❝❛♣❛③ ❞❡ ❡♥❡r❣✐③❛r ❛ ❧♦s ❣r❛♥♦s ❞❡ ♣♦❧✈♦ ❞❡❧ ❛♥✐❧❧♦ ❊ s✉❥❡t♦ ❛ ❧❛ ❡♥❡r❣í❛ ❞✐s♣♦♥✐❜❧❡ q✉❡ ❤❛② ❡♥ é❧✳ ✹✳ ❊s ✉♥ ♠❡❝❛♥✐s♠♦ ❧❡♥t♦ ❡♥ ❝♦♠♣❛r❛❝✐ó♥ ❝♦♥ ❧❛ ❡♥❡r❣✐③❛❝✐ó♥ ❞❡ ✐♦♥❡s ② ♣♦❞rí❛ s❡r ❝♦♥s✐❞❡r❛❞♦ ✉♥ ♠❡❝❛♥✐s♠♦ ♣♦r ❡❧ ❝✉❛❧ ❧❛s ♣❛rtí❝✉❧❛s ❞❡ ♣♦❧✈♦ ❡✈❡♥t✉❛❧♠❡♥t❡ ❡s❝❛♣❛♥ ❞❡❧ ❛♥✐❧❧♦✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✻✳✷✳ P❛rtí❝✉❧❛s ♥❡✉tr❛s ✭❈❛♠♣♦ ●r❛✈✐t❛❝✐♦♥❛❧ ❊st♦❝ást✐❝♦✮ ✻✳✷✳ ✶✸✻ P❛rtí❝✉❧❛s ♥❡✉tr❛s ✭❈❛♠♣♦ ●r❛✈✐t❛❝✐♦♥❛❧ ❊s✲ t♦❝ást✐❝♦✮ ❙❡ ❝♦♥s✐❞❡r❛ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ❣r❛♥♦s ❞❡ ♣♦❧✈♦ ♥❡✉tr♦ ♣r❡s❡♥t❡ ❡♥ ❝❛❞❛ ✉♥♦ ❞❡ ❧♦s ❛♥✐❧❧♦s ❞❡ ❙❛t✉r♥♦✳ P♦r ❡st❛ r❛③ó♥✱ ❧❛ ú♥✐❝❛ ❢✉❡r③❛ ❡st♦❝ást✐❝❛ q✉❡ ❛❝tú❛ ❡♥tr❡ ❧♦s ❣r❛♥♦s ❞❡ ♣♦❧✈♦ ❡s ❧❛ ❣r❛✈✐t❛❝✐♦♥❛❧✳ ✻✳✷✳✶✳ ❙✐st❡♠❛ ❞❡ ❛♥✐❧❧♦s ✶✳ ❉❡ ♠❛♥❡r❛ ❣❡♥❡r❛❧ s❡ ♦❜s❡r✈❛ q✉❡ ❧♦s ❣r❛♥♦s ❞❡ ♣♦❧✈♦ t✐❡♥❞❡♥ ❛ ❣❛♥❛r ❡♥❡r❣í❛ ❝♦♥ ❡❧ t✐❡♠♣♦ ❛ ❡①♣❡♥s❛s ú♥✐❝❛♠❡♥t❡ ❞❡❧ ❝❛♠♣♦ ❣r❛✈✐t❛❝✐♦♥❛❧ ❡st♦❝ást✐❝♦✳ ✷✳ ❙❡ ✐❞❡♥t✐✜❝❛♥ tr❡s r❡❣✐♦♥❡s ❞❡ ❡♥❡r❣✐③❛❝✐ó♥ ❞❡♥tr♦ ❞❡❧ s✐st❡♠❛ ❞❡ ❛♥✐❧❧♦s✿ ❛✮ ❆❧t❛ ❡♥❡r❣✐③❛❝✐ó♥ ✭❉✐✈✐s✐ó♥ ❞❡ ❈❛ss✐♥✐ ② ❛♥✐❧❧♦ ❆✮❀ ❜✮ ❇❛❥❛ ❡♥❡r❣✐③❛❝✐ó♥ ✭❛♥✐❧❧♦ ❇ ② ❛♥✐❧❧♦ ❊ ✮✱ ② ❝✮ ❡♥❡r❣✐③❛❝✐ó♥ ✐♥t❡r♠❡❞✐❛ ✭❛♥✐❧❧♦ ❈✮✳ ✸✳ ❊s ✉♥ ♠❡❝❛♥✐s♠♦ ❧❡♥t♦ ❡♥ ❝♦♠♣❛r❛❝✐ó♥ ❝♦♥ ❧♦ ❞❡s❝r✐t♦ ♣❛r❛ ❧♦s ✐♦♥❡s✱ s✐♥ ❡♠✲ ❜❛r❣♦ ❡s ✉♥ ❜✉❡♥ ❝❛♥❞✐❞❛t♦ ♣❛r❛ s❡r ✉♥ ♠❡❝❛♥✐s♠♦ ❞❡ ♣ér❞✐❞❛ ❞❡ ♣❛rtí❝✉❧❛s✳ ❙✐ ❡s❝❛♣❛r❛♥ rá♣✐❞❛♠❡♥t❡ ❡♥t♦♥❝❡s ❧❛ ❡str✉❝t✉r❛ ❞❡ ❧♦s ❛♥✐❧❧♦s ♥♦ s❡rí❛ t❛♥ ❡st❛❜❧❡ ❝♦♠♦ ❧♦ ✐♥❞✐❝❛♥ ❧❛s ♦❜s❡r✈❛❝✐♦♥❡s✳ ❊❧ ♠♦❞❡❧♦ ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❡st♦❝ást✐❝❛ ♣r❡s❡♥t❛❞♦ ❡♥ ❡st❡ tr❛❜❛❥♦ t✐❡♥❡ ✈❡♥t❛❥❛s ❝♦♥✲ ❝❡♣t✉❛❧❡s ② ♠❡t♦❞♦❧ó❣✐❝❛s✳ ❈♦♥❝❡♣t✉❛❧❡s✿ ❚❛❧ ② ❝♦♠♦ s❡ ♠❡♥❝✐♦♥ó ❡♥ ❡❧ ❈❛♣ít✉❧♦ ✶✱ ❧♦s r❡q✉✐s✐t♦s ♣r✐♥❝✐✲ ♣❛❧❡s ♣❛r❛ q✉❡ ✉♥ ♠❡❝❛♥✐s♠♦ ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ❡st♦❝ást✐❝❛ ❡sté ❛❝t✉❛♥❞♦ s♦❜r❡ ❧❛ ♣♦❜❧❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s s♦♥✿ ✶✮ ✐♥t❡r❛❝❝✐♦♥❡s ❡❧❡♠❡♥t❛❧❡s q✉❡ ❝❛✉s❛♥ ✉♥ ❝❛♠❜✐♦ ❡♥ ❧❛ ❡♥❡r❣í❛ ❞❡ ❧❛ ♣❛rtí❝✉❧❛✱ ✷✮ ❞✐s♣❡rs✐ó♥ ❡❢❡❝t✐✈❛ ❛tr✐❜✉✐❞❛ ❛ ❧❛s ✐♥✲ t❡r❛❝❝✐♦♥❡s ♦♥❞❛✲♣❛rtí❝✉❧❛✱ ② ✸✮ ✉♥ ♣r♦❝❡s♦ ❛❧❡❛t♦r✐♦ ✭tr❛t❛♠✐❡♥t♦ ❡st❛❞íst✐❝♦✮✳ ❙✐ ❧❛s ♦♥❞❛s q✉❡ ♣r♦❞✉❝❡♥ ❧❛ ❛❝❡❧❡r❛❝✐ó♥ ❞❡ ♣❛rtí❝✉❧❛s s♦♥ ❧♦ s✉✜❝✐❡♥t❡♠❡♥t❡ ❛❧❡❛t♦r✐❛s ✭❡st♦ ❡s✱ ♦♥❞❛s ❝♦♥ ❢❛s❡ ❛❧❡❛t♦r✐❛✮✱ ❡♥t♦♥❝❡s ♦❝✉rr❡ ❡❧ ♣r♦❝❡s♦ ❞❡ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✻✳✷✳ P❛rtí❝✉❧❛s ♥❡✉tr❛s ✭❈❛♠♣♦ ●r❛✈✐t❛❝✐♦♥❛❧ ❊st♦❝ást✐❝♦✮ ✶✸✼ ❞✐❢✉s✐ó♥ ❡♥ ❡❧ ❡s♣❛❝✐♦ ❞❡ ✈❡❧♦❝✐❞❛❞❡s ② ❡❧ ❢❡♥ó♠❡♥♦ ❡s ❝♦♥♦❝✐❞♦ ❝♦♠♦ ❞✐❢✉✲ s✐ó♥ ❝✉❛s✐✲❧✐♥❡❛❧✳ ❊st❡ ❡❢❡❝t♦ ❡s tr❛t❛❞♦ ❝♦♠♦ ✉♥ ♦♣❡r❛❞♦r ❞❡ ❞✐❢✉s✐ó♥ ❡♥ ❧❛ ❡❝✉❛❝✐ó♥ ❞❡ ❋♦❦❦❡r✲P❧❛♥❝❦✱ ❧❛ ❝✉❛❧ ♣✉❡❞❡ s❡r r❡❡♠♣❧❛③❛❞❛ ♣♦r ✉♥ ❝♦♥❥✉♥t♦ ❞❡ ❡❝✉❛❝✐♦♥❡s ❞✐❢❡r❡♥❝✐❛❧❡s ❡st♦❝ást✐❝❛s✳ ❊♥ ❡❧ ♠♦❞❡❧♦ ♣r❡s❡♥t❛❞♦ ♥♦ s❡ ❝♦♥s✐❞❡r❛ ✉♥ ❡s♣❡❝tr♦ ❞❡ ♦♥❞❛ ❡♥ ♣❛rt✐❝✉❧❛r s✐♥♦ ❡❧ ❡s♣❡❝tr♦ ❞❡ ✢✉❝t✉❛❝✐♦♥❡s ❞❡ ❝❛♠♣♦ ✭♠❛❣♥ét✐❝♦ ♦ ❣r❛✈✐t❛❝✐♦♥❛❧✮ ❝❛r❛❝t❡ríst✐❝♦ ❞❡ ❧❛ r❡❣✐ó♥ ❡♥ ❡st✉❞✐♦✳ ❆❞❡♠ás ♥♦ ❡s ♥❡❝❡s❛r✐♦ ❝♦♥♦❝❡r ❧♦s ✈❛❧♦r❡s ♣r♦♠❡❞✐♦ ♣❛r❛ ❧❛ ✈❡❧♦❝✐❞❛❞✱ ♣❛r❛ ❧❛ ❞❡♥s✐❞❛❞ ② ♣❛r❛ ❧❛ t❡♠♣❡r❛t✉r❛✱ q✉❡ ♣✉❡❞❡♥ ♦❜t❡♥❡rs❡ ❛ ♣❛rt✐r ❞❡ ❧❛s ♠❡❞✐❝✐♦♥❡s ♦ ❝❛❧✲ ❝✉❧❛❞♦s t❡ór✐❝❛♠❡♥t❡❀ ❡♥ ❡st❡ ♠♦❞❡❧♦ s❡ r❡q✉✐❡r❡ ❧❛ ❢✉♥❝✐ó♥ ❞❡ ❞✐str✐❜✉❝✐ó♥ ❞❡ ✈❡❧♦❝✐❞❛❞❡s ♣❛r❛ ❧❛s ❞✐st✐♥t❛s ♣♦❜❧❛❝✐♦♥❡s✳ ▼❡t♦❞♦❧ó❣✐❝❛s ✿ ❊❧ ♠ét♦❞♦ ❡st❛❞íst✐❝♦ ✉t✐❧✐③❛❞♦ ❡♥ ❡st❡ tr❛❜❛❥♦ ✲❛ tr❛✈és ❞❡ ✉♥❛ s✐♠✉❧❛❝✐ó♥ ▼♦♥t❡ ❈❛r❧♦✲ ❡s ✈❡♥t❛❥♦s♦ ❡♥ ❝♦♠♣❛r❛❝✐ó♥ ❝♦♥ ❧♦s ♠ét♦❞♦s ♥✉♠ér✐❝♦s ❝♦♥✈❡♥❝✐♦♥❛❧❡s q✉❡ ♣✉❡❞❡♥ ✈♦❧✈❡rs❡ ♠✉② ❝♦♠♣❧✐❝❛❞♦s ❝♦♥❢♦r♠❡ ❡❧ ♥ú♠❡r♦ ❞❡ ❡❝✉❛❝✐♦♥❡s ❡ ✐♥❝ó❣♥✐t❛s ❛✉♠❡♥t❛✳ ❊♥ ✉♥ ♠ét♦❞♦ ❞❡ ▼♦♥t❡ ❈❛r❧♦ ❜❛st❛ ❝♦♥ ❝♦♥♦❝❡r ❧❛s ❢✉♥❝✐♦♥❡s ❞❡ ❞✐str✐❜✉❝✐ó♥ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞ q✉❡ ♠❡❥♦r ❞❡s❝r✐❜❡♥ ❛❧ s✐st❡♠❛ q✉❡ s❡ ❡stá ❡st✉❞✐❛♥❞♦ s✐♥ ✐♠♣♦rt❛r ❡❧ ♥ú♠❡r♦ ❞❡ ✈❛r✐❛❜❧❡s ✐♥✈♦❧✉❝r❛❞❛s✳ ❉❡ ❡st❛ ♠❛♥❡r❛✱ s❡ r❡s✉❡❧✈❡ ❧❛ ♠✐s♠❛ ❡❝✉❛❝✐ó♥ ❞❡ ♠♦✈✐♠✐❡♥t♦ ♣❛r❛ ❝❛❞❛ ♣❛rtí❝✉❧❛ ❡♥ ❧✉❣❛r ❞❡ ✉♥ ❝♦♥❥✉♥t♦ ❞❡ ✏♥✑ ❡❝✉❛❝✐♦♥❡s✳ ❊st❡ ♠❡❝❛♥✐s♠♦ ♣✉❡❞❡ s❡r ❝♦♥s✐❞❡r❛❞♦ ❝♦♠♦ ✉♥ ♣r♦❝❡s♦ ❞❡ ❛❝❡❧❡r❛❝✐ó♥ ♣r✐♠❛r✐♦ ❞♦♥❞❡ ❧♦s ♣r♦t♦♥❡s ✲q✉❡ s♦♥ ♠ás s✉s❝❡♣t✐❜❧❡s ❞❡ s❡r ❛❝❡❧❡r❛❞♦s✲ ❣❛♥❛♥ ❡♥❡r❣í❛ ❝♦✲ ♠♦ ❝♦♥s❡❝✉❡♥❝✐❛ ❞❡ ❧❛ ❛❝❝✐ó♥ ❞❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❡st♦❝ást✐❝♦✳ ❊st♦s ♣r♦t♦♥❡s s❡rá♥ ❝❛♣❛❝❡s ❞❡ tr❛♥s❢❡r✐r ❡♥❡r❣í❛ ❛ ❧❛s ❞✐st✐♥t❛s ♣♦❜❧❛❝✐♦♥❡s ❞❡ ✐♦♥❡s ♣r❡s❡♥t❡s ❡♥ ❧❛ ♠❛❣♥❡tós❢❡r❛✱ q✉❡ ❛❞❡♠ás✱ ❡stá♥ ❣❛♥❛♥❞♦ ❡♥❡r❣í❛ ♣♦r ❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❡st♦❝ást✐❝♦ ❞❡ ❢♦♥❞♦✳ ❊✈❡♥t✉❛❧♠❡♥t❡ s❡ ❡s♣❡r❛ q✉❡ ❡❧ ♣❧❛s♠❛ s❡ ✈❛②❛ ❡♥❡r❣✐③❛♥❞♦ ♣❛r❛ ❛❧❝❛♥✲ ③❛r ❧❛ ❡♥❡r❣í❛ ♦❜s❡r✈❛❞❛ ♣♦r ❧❛s ♥❛✈❡s✳ ❉❡ ❛❝✉❡r❞♦ ❝♦♥ ❧♦s r❡s✉❧t❛❞♦s ♦❜t❡♥✐❞♦s✱ ❧❛ ♠❛❣♥❡tós❢❡r❛ ✐♥t❡r♥❛ ❡s ♠ás ❞✐♥á♠✐❝❛ q✉❡ ❧❛ ♠❛❣♥❡tós❢❡r❛ ❡①t❡r♥❛✱ ♣♦r ❧♦ q✉❡ ❧♦s ❡❢❡❝t♦s ❞❡s❝r✐t♦s ❛♥t❡r✐♦r♠❡♥t❡ s❡ ♣r❡s❡♥t❛♥ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ❡♥ ❡st❛ r❡❣✐ó♥✳ ❙✐ ❛❞❡♠ás ❞❡ ❧❛ ❛❝❝✐ó♥ ❞❡❧ ❝❛♠♣♦ ❡❧é❝tr✐❝♦ ❡st♦❝ást✐❝♦ s❡ ❝♦♥s✐❞❡r❛ ❛❧ ❝❛♠♣♦ ❣r❛✈✐t❛❝✐♦♥❛❧ ❡st♦❝ást✐❝♦✱ ❡❧ ♣♦s✐❜❧❡ ❡❢❡❝t♦ ❞❡ ❧❛ ❝♦♠❜✐♥❛❝✐ó♥ ❞❡ ❛♠❜♦s r❡s✉❧t❛rí❛ ❡♥ ❢❡♥ó♠❡♥♦s ❞❡ ✐♥❡st❛❜✐❧✐❞❛❞ ❡♥ ❡❧ ♣❧❛s♠❛ q✉❡ ♣♦❞rí❛♥ ❝♦♥❞✉❝✐r ❛ ❧❛ ❡♥❡r❣✐③❛❝✐ó♥ ❞❡ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ✻✳✷✳ P❛rtí❝✉❧❛s ♥❡✉tr❛s ✭❈❛♠♣♦ ●r❛✈✐t❛❝✐♦♥❛❧ ❊st♦❝ást✐❝♦✮ ✶✸✽ ♣❛rtí❝✉❧❛s ❞❡♥tr♦ ❞❡ ❧❛ ♠❛❣♥❡tós❢❡r❛✳ ▲♦s r❡s✉❧t❛❞♦s ♠♦str❛❞♦s ❡♥ ❡st❡ tr❛❜❛❥♦ ♣✉❡❞❡♥ s❡r ♣r♦❜❛❞♦s ♦ ✈❛❧✐❞❛❞♦s t♦✲ ♠❛♥❞♦ ❡♥ ❝✉❡♥t❛ ❧❛s ♠❡❞✐❝✐♦♥❡s ❤❡❝❤❛s ♣♦r ❡❧ ✐♥str✉♠❡♥t♦ ❞❡ ♣❧❛s♠❛ ❛ ❜♦r❞♦ ❞❡ ❈❛ss✐♥✐✳ ❊♥ ❡s❡ s❡♥t✐❞♦✱ s❡ ❡s♣❡r❛ q✉❡ ❧❛ ❞❡♥s✐❞❛❞ ♦❜s❡r✈❛❞❛ ❞❡ ✐♦♥❡s✴♥❡✉tr♦s ♠✉❡s✲ tr❡♥ ✉♥ ♠á①✐♠♦ ❡♥ s✉ ❞✐str✐❜✉❝✐ó♥ ❡♥ ❧♦s ❧✉❣❛r❡s ❞♦♥❞❡ ❡❧ ♠❡❝❛♥✐s♠♦ ❡st♦❝ást✐❝♦ ❡s ♠❡♥♦s ❡❢❡❝t✐✈♦ ✭∼✶✳✸ RS ✱ ∼✻✳✺ RS ② ∼✾✳✻ RS ✮ ②❛ q✉❡ ❧❛s ♣❛rtí❝✉❧❛s ♥♦ ❤❛♥ ❛❧❝❛♥③❛❞♦ ❧❛ ❡♥❡r❣í❛ s✉✜❝✐❡♥t❡ ♣❛r❛ ❛❜❛♥❞♦♥❛r ❧❛ r❡❣✐ó♥ ②✱ ♣♦r ❧♦ t❛♥t♦✱ ♣✉❡❞❡♥ ♣❡r♠❛♥❡❝❡r ❡♥ ❡❧ ♠✐s♠♦ ❧✉❣❛r ♣♦r ♠ás t✐❡♠♣♦✳ ❆❞❡♠ás ❞❡ ❧❛ ❞❡♥s✐❞❛❞✱ ❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧ ♣❧❛s♠❛ ♣♦❞rí❛ ♠♦str❛r ✉♥ ✈❛❧♦r ♠í♥✐♠♦ ❞❡❜✐❞♦ ❛ ❧❛ ❜❛❥❛ ❡♥❡r❣✐③❛❝✐ó♥✳ P♦r ❡❧ ❝♦♥tr❛r✐♦✱ ❡♥ ❧♦s ❧✉❣❛r❡s ❞♦♥❞❡ ❡❧ ♠❡❝❛♥✐s♠♦ ❡st♦❝ást✐❝♦ ❡s ♠ás ❡✜❝✐❡♥t❡ ✭∼✸✳✺ RS ② ∼✼✳✻ RS ✮✱ s❡ ❡s♣❡r❛ q✉❡ ❧❛ ❞❡♥s✐❞❛❞ ❞❡ ✐♦♥❡s✴♥❡✉tr♦s s❡❛ ♠í♥✐♠❛ ② ❧❛ t❡♠♣❡r❛t✉r❛ ❞❡❧ ♣❧❛s♠❛ s❡❛ ❡❧❡✈❛❞❛✳ P♦r ♦tr♦ ❧❛❞♦✱ ❡♥ ❡st❡ ♠♦❞❡❧♦ ♥♦ s❡ t✐❡♥❡ ✉♥ ❢❡♥ó♠❡♥♦ ❞❡ r❡s♦♥❛♥❝✐❛ ❡✈✐❞❡♥t❡ ♣♦rq✉❡✿ ❛✮ ▲❛s ✢✉❝t✉❛❝✐♦♥❡s ❞❡❧ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ s♦♥ ❡❧ r❡s✉❧t❛❞♦ ❞❡ ❧❛ s✉♣❡r♣♦✲ s✐❝✐ó♥ ❞❡ ✉♥ ❣r❛♥ ♥ú♠❡r♦ ❞❡ ♦♥❞❛s ❝♦♥ ❞✐❢❡r❡♥t❡s ❢r❡❝✉❡♥❝✐❛s✱ ❜✮ ❈✉❛♥❞♦ ❧❛ ♥❛✈❡ ❝r✉③❛ ✉♥❛ ♠❛❣♥❡t♦s❢❡r❛ ♣❧❛♥❡t❛r✐❛✱ s❡ ❡stá♥ ♣r♦♣❛❣❛♥❞♦ ♠✉❝❤❛s ♦♥❞❛s ❡♥ ❧❛ r❡❣✐ó♥❀ ❡♥t♦♥❝❡s✱ ❧❛ ♥❛✈❡ ♠✐❞❡ ❞✐✈❡rs♦s ♠♦❞♦s ❞❡ ♣r♦♣❛❣❛❝✐ó♥ ❡♥ ❡❧ ♠✐s♠♦ ✐♥st❛♥t❡✱ ❝✮ ▲❛ ♣❛rtí❝✉❧❛ ❆ ❡stá ❡♥ r❡s♦♥❛♥❝✐❛ ❝♦♥ ❧❛ ♦♥❞❛ ❞❡ ❢r❡❝✉❡♥❝✐❛ ❆✱ ♠✐❡♥tr❛s q✉❡ ❧❛ ♣❛rtí❝✉❧❛ ❇ ❡stá ❡♥ r❡s♦♥❛♥❝✐❛ ❝♦♥ ❧❛ ♦♥❞❛ ❞❡ ❢r❡❝✉❡♥❝✐❛ ❇✳ ❉❡ ❛q✉í✱ q✉❡ ❡♥ ❡st❛ s✐t✉❛❝✐ó♥✱ ❡❧ ❢❡♥ó♠❡♥♦ ❞❡ r❡s♦♥❛♥❝✐❛ ♥♦ s❡❛ ❡✈✐❞❡♥t❡ ✭❡♥ ♦tr❛s ♣❛❧❛❜r❛s✱ ❡s ✏✐♥✈✐s✐❜❧❡✑ ❞❛❞❛ ❧❛ ✈❛r✐❡❞❛❞ ❞❡ r❡s♦♥❛♥❝✐❛s q✉❡ t✐❡♥❡♥ ❧✉❣❛r✮✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❇✐❜❧✐♦❣r❛❢í❛ ❬❆❜❡ ❛♥❞ ◆✐s❤✐❞❛✱ ✶✾✽✻❪ ❆❜❡✱ ❚✳ ❛♥❞ ❆✳ ◆✐s❤✐❞❛ ✭✶✾✽✻✮✱ ❆♥♦♠❛❧♦✉s ♦✉t✇❛r❞ ❞✐✛✉s✐♦♥ ❛♥❞ ❛ss♦❝✐❛t❡❞ ❤❡❛t✐♥❣ ♦❢ ■♦✲ ❣❡♥✐❝ ✐♦♥s ✐♥ t❤❡ ❏♦✈✐❛♥ ♠❛❣♥❡t♦s♣❤❡r❡✱ ❏✳ ●❡♦♣❤②s✳ ❘❡s✳ ✾✶✱ ✶✵✵✵✸✳ ❬❆❝✉ñ❛ ❛♥❞ ◆❡ss✱ ✶✾✽✵❪ ❆❝✉ñ❛✱ ▼✳ ❛♥❞ ◆✳ ❋✳ ◆❡ss ✭✶✾✽✵✮✱ ❚❤❡ ♠❛❣♥❡✲ t✐❝ ✜❡❧❞ ♦❢ ❙❛t✉r♥ ✲ P✐♦♥❡❡r ✶✶ ♦❜s❡r✈❛t✐♦♥s✱ ❙❝✐❡♥❝❡ ✷✵✼✱ ✹✹✹✳ ❬❆tr❡②❛ ❡t ❛❧✳✱ ✶✾✽✻❪ ❆tr❡②❛✱ ❙✳ ❑✳✱ ❏✳ ❍✳ ❲❤✐t❡ ❏r✳✱ ❚✳ ▼✳ ❉♦♥❛❤✉❡ ❡t✳ ❛❧✳ ✭✶✾✽✻✮✱ ❚❤❡♦r②✱ ♠❡❛s✉r❡♠❡♥ts✱ ❛♥❞ ♠♦✲ ❞❡❧s ♦❢ t❤❡ ✉♣♣❡r ❛t♠♦s♣❤❡r❡ ❛♥❞ ✐♦♥♦s♣❤❡r❡ ♦❢ ❙❛t✉r♥✱ ✐♥ ❙❛t✉r♥✱ ❡❞✐t❡❞ ❜② ❚✳ ●❡❤r❡❧s ❛♥❞ ▼✳ ❙✳ ▼❛tt❤❡✇s✱ ✷✸✾✳ ❬❇❛❧❛❦r✐s❤♥❛♥✱ ✶✾✾✷❪ ❇❛❧❛❦r✐s❤♥❛♥✱ ◆✳✱ ❍❛♥❞❜♦♦❦ ♦❢ t❤❡ ▲♦❣✐s✲ t✐❝ ❉✐str✐❜✉t✐♦♥ ✭▼❛r❝❡❧ ❉❡❦❦❡r✱ ◆❡✇ ❨♦r❦✱ ✶✾✾✷✮✳ ❬❇❛r❜♦s❛ ❡t ❛❧✳✱ ✶✾✽✹❪ ❇❛r❜♦s❛✱ ❉✳ ❉✳✱ ❆✳ ❊✈✐❛t❛r ❛♥❞ ●✳ ▲✳ ❙✐s❝♦❡ ✭✶✾✽✹✮✱ ❖♥ t❤❡ ❛❝❝❡❧❡r❛t✐♦♥ ♦❢ ❡♥❡r❣❡t✐❝ ✐♦♥s ✐♥ ❏✉♣✐t❡r✬s ♠❛❣♥❡t♦s♣❤❡r❡✱ ❏✳ ●❡♦♣❤②s✳ ❘❡s✳ ✽✾✱ ✸✼✽✾✳ ❬❇❛r❜♦s❛✱ ✶✾✽✻❪ ❇❛r❜♦s❛✱ ❉✳ ❉✳ ✭✶✾✽✻✮✱ ▼❡❞✐✉♠✲❡♥❡r❣② ❡❧❡❝tr♦♥s ❛♥❞ ❤❡❛✈② ✐♦♥s ✐♥ ❏✉♣✐t❡r✬s ♠❛❣♥❡t♦s♣❤❡r❡✲❊✛❡❝ts ✶✸✾ ♦❢ ❧♦✇❡r ❤②❜r✐❞ ❇✐❜❧✐♦❣r❛❢í❛ ✶✹✵ ✇❛✈❡✲♣❛rt✐❝❧❡ ✐♥t❡r❛❝t✐♦♥s✱ ❏✳ ●❡♦♣❤②s✳ ❘❡s✳ ✾✶✱ ✺✻✵✺✳ ❬❇❛r❜♦s❛✱ ✶✾✾✹❪ ❇❛r❜♦s❛✱ ❉✳ ❉✳ ✭✶✾✾✹✮✱ ❙t♦❝❤❛st✐❝ ❛❝❝❡❧❡r❛t✐♦♥ ✱ ♦❢ ❡♥❡r❣❡t✐❝ ✐♦♥s ✐♥ ❏✉♣✐t❡r✬s ♠❛❣♥❡t♦s♣❤❡r❡ ❏✳ ●❡♦♣❤②s✳ ❘❡s✳✱ ✾✾✭❆✼✮✱ ✶✸✺✵✾✳ ❬❇❡r❦s♦♥✱ ✶✾✺✵❪ ❇❡r❦s♦♥✱ ❏✳ ✭✶✾✺✵✮✱ ❆r❡ t❤❡r❡ t✇♦ r❡❣r❡ss✐♦♥s❄✱ ❏✳ ❆♠✳ ❙t❛t✳ ❆ss♦❝✳ ✹✺✱ ✶✻✹✳ ❬❇❧❛♥❝ ❡t ❛❧✳✱ ✷✵✵✷❪ ❇❧❛♥❝✱ ▼✳✱ ❙✳ ❇♦❧t♦♥✱ ❏✳ ❇r❛❞❧❡② ❡t ❛❧✳ ✭✷✵✵✷✮✱ ▼❛❣♥❡t♦s♣❤❡r✐❝ ❛♥❞ P❧❛s♠❛ ❙❝✐❡♥❝❡ ✇✐t❤ ❈❛ss✐♥✐✲❍✉②❣❡♥s✱ ❙♣❛❝❡ ❙❝✐❡♥❝❡ ❘❡✈✐❡✇s ✶✵✹✭✶✮✱ ✷✺✸✳ ❬❇♦① ❛♥❞ ▼ü❧❧❡r✱ ✶✾✺✽❪ ❇♦①✱ ●✳ ❊✳ P ❛♥❞ ▼✳ ❊✳ ▼ü❧❧❡r ✭✶✾✺✽✮✱ ❆ ♥♦t❡ ✱ ♦♥ t❤❡ ❣❡♥❡r❛t✐♦♥ ♦❢ r❛♥❞♦♠ ♥♦r♠❛❧ ❞❡✈✐❛t❡s ❆♥♥❛❧s ▼❛t❤✳ ❙t❛t✳ ✷✾✱ ✻✶✵✳ ❬❇r✐❞❣❡ ❡t ❛❧✳✱ ✶✾✽✶❪ ❇r✐❞❣❡✱ ❍✳ ❙✳✱ ❏✳ ❲✳ ❇❡❧❝❤❡r✱ ❆✳ ❏✳ ▲❛③❛r✉s ❡t✳ ❛❧✳ ✭✶✾✽✶✮✱ P❧❛s♠❛ ♦❜s❡r✈❛t✐♦♥s ♥❡❛r ❙❛✲ ✱ ❙❝✐❡♥❝❡ t✉r♥✿ ■♥✐t✐❛❧ r❡s✉❧ts ❢r♦♠ ❱♦②❛❣❡r ✶ ✷✶✷✭✶✵✮✱ ✷✶✼✳ ❬❇r✐❞❣❡ ❡t ❛❧✳✱ ✶✾✽✷❪ ❇r✐❞❣❡✱ ❍✳ ❙✳✱ ❋✳ ❇❛❣❡♥❛❧✱ ❏✳ ❲✳ ❇❡❧❝❤❡r ❡t✳ ❛❧✳ ✭✶✾✽✷✮✱ P❧❛s♠❛ ♦❜s❡r✈❛t✐♦♥s ♥❡❛r ❙❛t✉r♥✿ ✱ ❙❝✐❡♥❝❡ ✷✶✺✱ ■♥✐t✐❛❧ r❡s✉❧ts ❢r♦♠ ❱♦②❛❣❡r ✷ ✺✻✸✳ ❬❇✉r♥s ❡t ❛❧✳✱ ✶✾✼✾❪ ❇✉r♥s✱ ❏✳✱ P✳ ▲✳ ▲❛♠② ❛♥❞ ❙✳ ❙♦t❡r ✭✶✾✼✾✮✱ ❘❛❞✐❛t✐♦♥ ❢♦r❝❡s ♦♥ s♠❛❧❧ ♣❛rt✐❝❧❡s ✐♥ t❤❡ s♦❧❛r s②st❡♠ ❬❇✉r♥s ❡t ❛❧✳✱ ✶✾✽✹❪ ✱ ■❝❛r✉s ✹✵✱ ✶✳ ❇✉r♥s✱ ❏✳ ❆✳✱ ▼✳ ❘✳ ❙❤♦✇❛❧t❡r ❛♥❞ ●✳ ❊✳ ▼♦r✲ ✜❧❧ ✭✶✾✽✹✮✱ ❚❤❡ ❡t❤❡r❡❛❧ r✐♥❣s ♦❢ ❏✉♣✐t❡r ❛♥❞ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❇✐❜❧✐♦❣r❛❢í❛ ✶✹✶ ❙❛t✉r♥✱ ✐♥ P❧❛♥❡t❛r② ❘✐♥❣s✱ ✭❡❞s✳ ❘✳ ●r❡❡♥✲ ❜❡r❣ ❛♥❞ ❆✳ ❇r❛❤✐❝✮✱ ❯♥✐✈❡rs✐t② ♦❢ ❆r✐③♦♥❛ Pr❡ss✱ ✷✵✵✳ ❬❈❤❡✇ ❡t ❛❧✳✱ ✶✾✻✾❪ ❈❤❡✇✱ ●✳ ❋✳✱ ▼✳ ▲✳ ●♦❧❞❜❡r❣❡r ❛♥❞ ❋✳ ❊✳ ▲♦✇ ✭✶✾✻✾✮✱ ❆♥ ■♥t❡❣r❛❧ ❊q✉❛t✐♦♥ ❢♦r ❙❝❛tt❡r✐♥❣ ❆♠♣❧✐t✉❞❡s✱ P❤②s✳ ❘❡✈✳ ▲❡tt✳ ✷✷✭✺✮✱ ✷✵✽✳ ❬❈❤r✐st✐❛♥s❡♥ ❛♥❞ ❍❛♠❜❧✐♥✱ ✶✾✾✺❪ ❈❤r✐st✐❛♥s❡♥ ❊✳ ❍✳✱ ❛♥❞ ❲✳ ❑ ❍❛♠❜❧✐♥✱ ❊①✲ ♣❧♦r✐♥❣ t❤❡ ♣❧❛♥❡ts ✭Pr❡♥t✐❝❡ ❍❛❧❧✱ ❯❙❆✱ ✶✾✾✺✮✳ ❬❈❧❛❞✐s✱ ✶✾✽✻❪ ❈❧❛❞✐s✱ ❏✳ ❇✳ ✭✶✾✽✻✮✱ P❛r❛❧❧❡❧ ❛❝❝❡❧❡r❛t✐♦♥ ❛♥❞ tr❛♥s♣♦rt ♦❢ ✐♦♥s ❢r♦♠ ♣♦❧❛r ✐♦♥♦s♣❤❡r❡ t♦ ♣❧❛s♠❛ s❤❡❡t✱ ●❡♦♣❤②s✳ ❘❡s✳ ▲❡tt✳ ✶✸✱ ✽✾✸✳ ❬❈❧❛r❦✱ ✶✾✽✵❪ ❈❧❛r❦✱ ❘✳ ◆✳ ✭✶✾✽✵✮✱ ●❛♥②♠❡❞❡✱ ❊✉r♦♣❛✱ ❈❛✲ ❧❧✐st♦✱ ❛♥❞ ❙❛t✉r♥✬s r✐♥❣s ✲ ❈♦♠♣♦s✐t✐♦♥❛❧ ❛♥❛❧②s✐s ❢r♦♠ r❡✢❡❝t❛♥❝❡ s♣❡❝tr♦s❝♦♣②✱ ■❝❛r✉s ✹✹✱ ✸✽✽✳ ❬❈r✉✐❦s❤❛♥❦ ❡t ❛❧✳✱ ✶✾✽✹❪ ❈r✉✐❦s❤❛♥❦✱ ❉✳ P✳✱ ❏✳ ❱❡✈❡r❦❛ ❛♥❞ ▲✳ ❆✳ ▲❡✲ ❜♦❢s❦② ✭✶✾✽✹✮✱ ❙❛t❡❧❧✐t❡s ♦❢ ❙❛t✉r♥✿ ❖♣t✐❝❛❧ Pr♦♣❡rt✐❡s✱ ✐♥ ❙❛t✉r♥✱ ❡❞s✳ ❚✳ ●❡❤r❡❧s ❛♥❞ ▼✳ ❙✳ ▼❛tt❤❡✇s✱ ❯♥✐✈❡rs✐t② ♦❢ ❆r✐③♦♥❛ Pr❡ss✱ ✻✹✵✳ ❬❈✉③③✐✱ ✶✾✽✸❪ ❈✉③③✐✱ ❏✳ ◆✳ ✭✶✾✽✸✮✱ P❧❛♥❡t❛r② r✐♥❣ s②st❡♠s✱ ❘❡✈✳ ●❡♦♣❤②s✳ ❛♥❞ ❙♣❛❝❡ P❤②s✳ ✷✶✱ ✶✼✸✳ ❬❈✉③③✐ ❡t✳ ❛❧✳✱ ✶✾✽✹❪ ❈✉③③✐✱ ❏✳ ◆✳✱ ❏✳ ❏✳ ▲✐ss❛✉❡r ❛♥❞ ▲✳ ❲✳ ❊s♣♦s✐✲ t♦ ✭✶✾✽✹✮✱ ❙❛t✉r♥✬s r✐♥❣s✲❙tr✉❝t✉r❡✱ ❞②♥❛♠✐❝s✱ ❛♥❞ ♣❛rt✐❝❧❡ ♣r♦♣❡rt✐❡s✱ ✐♥ P❧❛♥❡t❛r② ❘✐♥❣s ✭❡❞s✳ ❘✳ ●r❡❡♥❜❡r❣ ❛♥❞ ❆✳ ❇r❛❤✐❝✮✱ ❯♥✐✈❡rs✐t② ♦❢ ❆r✐③♦♥❛ Pr❡ss✱ ✹✻✸✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❇✐❜❧✐♦❣r❛❢í❛ ❬❉❡❧✐ts❦② ❛♥❞ ▲❛♥❡✱ ✷✵✵✷❪ ✶✹✷ ❉❡❧✐ts❦②✱ ▼✳ ▲✳ ❛♥❞ ❆✳ ▲✳ ▲❛♥❡ ✭✷✵✵✷✮✱ ❙❛t✉r♥✬s ✐♥♥❡r s❛t❡❧❧✐t❡s✿ ■❝❡ ❝❤❡♠✐str② ❛♥❞ ♠❛❣♥❡t♦s♣❤❡r❡ ❡✛❡❝ts✱ ❏✳ ❘❡s✳✭P❧❛♥❡ts✮✱ ❈✐t❡■❉ ✶✵✼✭❊✶✶✮✱ ✸✱ ●❡♦♣❤②s✳ ✺✵✾✸✱ ❞♦✐✿✶✵✳✶✵✷✾✴✷✵✵✷❏❊✵✵✶✽✺✺✳ ❬❉❡ P❛t❡r ❛♥❞ ▲✐ss❛✉❡r✱ ✷✵✵✶❪ ❉❡ P❛t❡r✱ ■✳ ❛♥❞ ❏✳ ▲✳ ▲✐ss❛✉❡r ✭✷✵✵✶✮✱ P❧❛♥❡✲ t❛r② ❙❝✐❡♥❝❡s✱ ❈❛♠❜r✐❞❣❡ ❯♥✐✈❡rs✐t② Pr❡ss✱ ❯❑✱ ✭❈❤❛♣t❡r ✶✶✮✳ ❬❉✉♥❣❡②✱ ✶✾✺✵❪ ❉✉♥❣❡②✱ ❏✳ ❲✳ ✭✶✾✺✵✮✱ ❚❤❡ ♠♦t✐♦♥ ♦❢ ♠❛❣♥❡✲ t✐❝ ✜❡❧❞s✱ ▼♦♥✳ ◆♦t✐❝❡s ❘♦②✳ ❆str♦♥✳ ❙♦❝✳ ✶✶✸✱ ✻✼✾✳ ❬❉✉r❛♥❞✲▼❛♥t❡r♦❧❛✱ ✷✵✵✸❪ ❉✉r❛♥❞✲▼❛♥t❡r♦❧❛✱ ❍✳ ✭✷✵✵✸✮✱ ❆❝❝❡❧❡r❛t✐♦♥ ♦❢ ♣❛rt✐❝❧❡s ✐♥ ❛ r❛♥❞♦♠ ❢♦r❝❡ ✜❡❧❞✱ ✐♥ ■❳ ▼❡❡✲ t✐♥❣ ♦❢ t❤❡ ❉②♥❛♠✐❝ ❋❧✉✐❞s ❉✐✈✐s✐♦♥ Pr♦✲ ❝❡❡❞✐♥❣s✱ ❙♦❝✐❡❞❛❞ ▼❡①✐❝❛♥❛ ❞❡ ❋ís✐❝❛✱ ▼é✲ ①✐❝♦ ❉✳❋✳✱ ▼é①✐❝♦✱ ✶✼✲✶✾ ◆♦✈❡♠❜❡r ✷✵✵✸✳ ❬❊r❛❦❡r ❛♥❞ ❙✐♠♣s♦♥✱ ✶✾✽✻❪ ❊r❛❦❡r✱ ❏✳ ❍✳✱ ❛♥❞ ❏✳ ❆✳ ❙✐♠♣s♦♥ ✭✶✾✽✻✮✱ ❆❝❝❡✲ ❧❡r❛t✐♦♥ ♦❢ ❝❤❛r❣❡❞ ♣❛rt✐❝❧❡s ✐♥ ▼❡r❝✉r②✬s ♠❛❣✲ ♥❡t♦s♣❤❡r❡✱ ❏✳ ●❡♦♣❤②s✳ ❘❡s✳ ✾✶✱ ✾✾✼✸✳ ❬❊s♣♦s✐t♦ ❡t ❛❧✳✱ ✶✾✽✹❪ ❊s♣♦s✐t♦✱ ▲✳ ❲✳✱ ❏✳ ◆✳ ❈✉③③✐✱ ❏✳ ❇✳ ❍♦❧❜❡r❣ ❡t✳ ❛❧✳ ✭✶✾✽✹✮✱ ❙❛t✉r♥✬s ❘✐♥❣s✿ str✉❝t✉r❡✱ ❞②♥❛♠✐❝s ❛♥❞ ♣❛rt✐❝❧❡ ♣r♦♣❡rt✐❡s✱ ✐♥ ❙❛t✉r♥✱ ❡❞✐t❡❞ ❜② ❚✳ ●❡❤r❡❧s ❛♥❞ ▼✳❙✳ ▼❛tt❤❡✇s✱ ✹✻✸ ❬❊s♣♦s✐t♦✱ ✶✾✽✻❪ ❊s♣♦s✐t♦✱ ▲✳ ❲✳ ✭✶✾✽✻✮✱ ❙tr✉❝t✉r❡ ❛♥❞ ❡✈♦❧✉✲ t✐♦♥ ♦❢ ❙❛t✉r♥✬s r✐♥❣s✱ ■❝❛r✉s ✻✼✱ ✸✹✺✳ ❬❊str❛❞❛ ❛♥❞ ❈✉③③✐✱ ✷✵✵✷❪ ❊str❛❞❛✱ P✳ ❘✳ ❛♥❞ ❏✳ ◆✳ ❈✉③③✐ ✭✶✾✾✻✮✱ ❱♦②❛❣❡r ❖❜s❡r✈❛t✐♦♥s ♦❢ t❤❡ ❈♦❧♦r ♦❢ ❙❛t✉r♥✬s ❘✐♥❣s✱ ■❝❛r✉s ✶✷✷✱ ✷✺✶✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❇✐❜❧✐♦❣r❛❢í❛ ❬❊✈✐❛t❛r ❡t ❛❧✳✱ ✶✾✽✷❪ ✶✹✸ ❊✈✐❛t❛r✱ ❆✳✱ ●✳ ▲✳ ❙✐s❝♦❡✱ ❏✳ ❉✳ ❙❝✉❞❞❡r ❡t✳ ❛❧✳ ✭✶✾✽✷✮✱ ❚❤❡ ♣❧✉♠❡s ♦❢ ❚✐t❛♥✱ ❏✳ ●❡♦♣❤②s✳ ❘❡s✳ ✽✼✱ ✽✵✾✶✳ ❬❊✈✐❛t❛r✱ ✶✾✽✸❪ ❊✈✐❛t❛r✱ ❆✳✱ ❘✳ ▲✳ ▼❝◆✉tt ❏r✳✱ ●✳ ▲✳ ❙✐s❝♦❡ ❡t✳ ❛❧✳ ✭✶✾✽✸✮✱ ❍❡❛✈② ✐♦♥s ✐♥ t❤❡ ♦✉t❡r ❑r♦♥✐❛♥ ♠❛❣♥❡t♦s♣❤❡r❡✱ ❬❊✈✐❛t❛r✱ ✶✾✽✹❪ ❊✈✐❛t❛r✱ ❆✳ ✭✶✾✽✹✮✱ ♥❡t♦s♣❤❡r❡✱ ❬❊✈✐❛t❛r ❛♥❞ ❘✐❝❤❛r❞s♦♥✱ ✶✾✽✻❪ ❏✳ ●❡♦♣❤②s✳ ❘❡s✳ ✽✽✱ ✽✷✸✳ P❧❛s♠❛ ✐♥ ❙❛t✉r♥✬s ♠❛❣✲ ❏✳ ●❡♦♣❤②s✳ ❘❡s✳ ✽✾✱ ✸✽✷✶✳ ❊✈✐❛t❛r✱ ❆✳ ❛♥❞ ❏✳ ❉✳ ❘✐❝❤❛r❞s♦♥ ✭✶✾✽✻✮✱ ❈♦r♦t❛t✐♦♥ ♦❢ t❤❡ ❑r♦♥✐❛♥ ♠❛❣♥❡t♦s♣❤❡r❡✱ ●❡♦♣❤②s✳ ❘❡s✳ ❬❊✈✐❛t❛r ❛♥❞ ❘✐❝❤❛r❞s♦♥✱ ✶✾✾✷❪ ❏✳ ✾✶✱ ✸✷✾✾✳ ❊✈✐❛t❛r✱ ❆✳ ❛♥❞ ❏✳ ❉✳ ❘✐❝❤❛r❞s♦♥ ✭✶✾✾✷✮✱ ❚❤❡r♠❛❧ ♣❧❛s♠❛ ✐♥ t❤❡ ✐♥♥❡r ❦r♦♥✐❛♥ ♠❛❣♥❡✲ t♦s♣❤❡r❡✱ ❬❋❡r♠✐✱ ✶✾✹✾❪ ❆♥♥✳ ●❡♦♣❤②s✳ ❋❡r♠✐✱ ❊✳ ✭✶✾✹✾✮✱ r❛❞✐❛t✐♦♥✱ ❬❋❡r♠✐✱ ✶✾✺✹❪ ✶✵✱ ✺✶✶✳ ❖♥ t❤❡ ♦r✐❣✐♥ ♦❢ t❤❡ ❝♦s♠✐❝ P❤②s✳ ❘❡✈✳ ❋❡r♠✐✱ ❊✳ ✭✶✾✺✹✮✱ ✼✺✭✽✮✱ ✶✶✻✾✳ ●❛❧❛❝t✐❝ ▼❛❣♥❡t✐❝ ❋✐❡❧❞s ❛♥❞ t❤❡ ❖r✐❣✐♥ ♦❢ ❈♦s♠✐❝ ❘❛❞✐❛t✐♦♥✱ ❆♣❏✳ ✶✶✾✱ ✶✳ ❬❋✐❧❧✐✉s ❡t ❛❧✳✱ ✶✾✽✵❪ ❋✐❧❧✐✉s✱ ❲✳✱ ❲✳ ❍✳ ■♣ ❛♥❞ ❈✳ ❊✳ ▼❝■❧✇❛✐♥ ✭✶✾✽✵✮✱ ❚r❛♣♣❡❞ ❧♦♦❦✱ ❬❋r❛♥❦✱ ✶✾✽✵❪ ❙❝✐❡♥❝❡ ✷✵✼✱ ✹✷✺✳ ❋r❛♥❦✱ ▲✳ ❆✳✱ ❇✳ ●✳ ❇✉r❡❦✱ ❑✳ ▲✳ ❆❝❦❡rs♦♥ ❡t✳ ❛❧✳ ✭✶✾✽✵✮✱ r❡✱ ❬●❛❧❧❛❣❤❡r ❡t ❛❧✳✱ ✷✵✵✺❪ r❛❞✐❛t✐♦♥ ❜❡❧ts ♦❢ ❙❛t✉r♥✿ ❋✐rst P❧❛s♠❛s ✐♥ ❙❛t✉r♥✬s ♠❛❣♥❡t♦s♣❤❡✲ ❏✳ ●❡♦♣❤②s✳ ❘❡s✳ ✽✺✱ ✺✻✾✺✳ ●❛❧❧❛❣❤❡r✱ ❉✳ ▲✳✱ ❏✳ ▲✳ ❍♦r✇✐t③✱ ❏✳ ❉✳ P❡r❡③ ❡t✳ ❛❧✳ ✭✷✵✵✺✮✱ ■♥tr♦❞✉❝t✐♦♥ t♦ P❛rt✐❝❧❡ ❆❝❝❡❧❡✲ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❇✐❜❧✐♦❣r❛❢í❛ ✶✹✹ r❛t✐♦♥ ✐♥ t❤❡ ❈♦s♠♦s✱ ✐♥ P❛rt✐❝❧❡ ❆❝❝❡❧❡r❛✲ t✐♦♥ ✐♥ ❆str♦♣❤②s✐❝❛❧ P❧❛s♠❛s✱ ❝❛❧ ▼♦♥♦❣r❛♣❤ ❙❡r✐❡s ❬●✐♦✈❛♥❡❧❧✐✱ ✶✾✹✼❪ ✶✺✻✱ ●❡♦♣❤②s✐✲ ✶✳ ●✐♦✈❛♥❡❧❧✐✱ ❘✳ ●✳ ✭✶✾✹✼✮✱ ▼❛❣♥❡t✐❝ ❛♥❞ ❡❧❡❝tr✐❝ ♣❤❡♥♦♠❡♥❛ ✐♥ t❤❡ ❙✉♥✬s ❛t♠♦s♣❤❡r❡ ❛ss♦❝✐❛t❡❞ ✇✐t❤ s✉♥s♣♦ts✱ ▼♦♥✳ ◆♦t✐❝❡s ❘♦②✳ ❆str♦♥✳ ❙♦❝✳ ✶✵✼✱ ❬●❧❛❞st♦♥❡ ❡t ❛❧✳✱ ✷✵✵✷❪ ✸✸✽✳ ●❧❛❞st♦♥❡✱ ●✳ ❘✳✱ ❏✳ ❍✳ ❲❛✐t❡✱ ❉✳ ●r♦❞❡♥t ❡t✳ ❛❧✳ ✭✷✵✵✷✮✱ ❆ ♣✉❧s❛t✐♥❣ ❛✉r♦r❛❧ ❳✲r❛② ❤♦t s♣♦t ♦♥ ❏✉♣✐t❡r✱ ◆❛t✉r❡ ❬●r❛♣s ❛♥❞ ●rü♥✱ ✷✵✵✷❪ ✹✶✺✭✻✽✼✺✮✱ ✶✵✵✵✳ ●r❛♣s✱ ❆✳ ▲✳ ❛♥❞ ❊✳ ●rü♥ ✭✷✵✵✷✮✱ ❈❤❛r❣✐♥❣ Pr♦❝❡ss❡s ❢♦r ❉✉st P❛rt✐❝❧❡s ✐♥ ❙❛t✉r♥✬s ▼❛❣✲ ♥❡t♦s♣❤❡r❡✱ ✐♥ ❉✉st ✐♥ t❤❡ s♦❧❛r s②st❡♠ ❛♥❞ ♦t❤❡r ♣❧❛♥❡t❛r② s②st❡♠s✱ ❈❖❙P❆❘ ❈♦❧❧♦q✉✐❛ ❙❡r✐❡s ✶✺✱ ✭❡❞s✳ ❙✳ ❋✳ ●r❡❡♥✱ ■✳ P✳ ❲✐❧❧✐❛♠s✱ ❏✳ ❆✳ ▼✳ ▼❝❉♦♥♥❡❧❧✱ ❛♥❞ ◆✳ ▼❝❇r✐❞❡✮✱ ✶✻✽✳ ❬●r✐❣♦r♦✈ ❡t ❛❧✳✱ ✶✾✾✶❪ ●r✐❣♦r♦✈✱ ◆✳ ▲✱ ▼✳ ❆✳ ❑♦♥❞r❛t✬❡✈❛✱ ▼✳ ■✳ P❛✲ ♥❛s✐✉❦ ❡t✳ ❛❧✳ ✭✶✾✾✶✮✱ ❊✈✐❞❡♥❝❡ ❢♦r tr❛♣♣❡❞ ❛♥♦✲ ♠❛❧♦✉s ❝♦s♠✐❝ r❛② ♦①②❣❡♥ ✐♦♥s ✐♥ t❤❡ ✐♥♥❡r ♠❛❣♥❡t♦s♣❤❡r❡✱ ●❡♦♣❤②s✳ ❘❡s✳ ▲❡tt✳ ❬●r♦❞❡♥t ❡t ❛❧✳✱ ✷✵✵✹❪ ✶✽✱ ✶✾✺✾✳ ●r♦❞❡♥t✱ ❉✳✱ ❏✳ ❈✳ ●❡r❛r❞✱ ❏✳ ❚✳ ❈❧❛r❦❡ ❡t✳ ❛❧✳ ✭✷✵✵✹✮✱ ❆ ♣♦ss✐❜❧❡ ❛✉r♦r❛❧ s✐❣♥❛t✉r❡ ♦❢ ❛ ♠❛❣♥❡t♦t❛✐❧ r❡❝♦♥♥❡❝t✐♦♥ ♣r♦❝❡ss ♦♥ ❏✉♣✐✲ t❡r✱ ❏✳ ●❡♦♣❤②s✳ ❘❡s✳ ✶✵✾✱ ❆✵✺✷✵✶✱ ✶✵✳✶✵✷✾✴ ✷✵✵✸❏❆✵✶✵✸✹✶✳ ❬●r♦❞❡♥t✱ ✷✵✵✹❪ ●r♦❞❡♥t✱ ❊❛rt❤✱ ❉✳ ❏✉♣✐t❡r ✭✷✵✵✹✮✱ ❛♥❞ ❆✉r♦r❛❧ ❙❛t✉r♥✱ ✐♥✿ ♣r♦❝❡ss❡s ❊♦s ❛t ❚r❛♥s✳ ❆●❯ ✽✺✭✶✼✮✱ ❏♦✐♥t ❆ss❡♠❜❧② ❙✉♣♣❧✳✱ ❆❜str❛❝t ❙▼✶✷❆✲✵✹✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❇✐❜❧✐♦❣r❛❢í❛ ❬●✉r♥❡tt ❡t ❛❧✳✱ ✷✵✵✺❪ ✶✹✺ ●✉r♥❡tt✱ ❉✳ ❆✳✱ ❲✳ ❙✳ ❑✉rt❤✱ ●✳ ❇✳ ❍♦s♣♦✲ ❞❛rs❦② ❡t✳ ❛❧✳ ✭✷✵✵✺✮✱ ❘❛❞✐♦ ❛♥❞ P❧❛s♠❛ ❲❛✲ ✈❡ ❖❜s❡r✈❛t✐♦♥s ❛t ❙❛t✉r♥ ❢r♦♠ ❈❛ss✐♥✐✬s ❆♣✲ ♣r♦❛❝❤ ❛♥❞ ❋✐rst ❖r❜✐t✱ ❙❝✐❡♥❝❡ ✸✵✼✱✶✷✺✺✳ ❬❍❛♠✐❧t♦♥ ❡t ❛❧✳✱ ✶✾✽✸❪ ❍❛♠✐❧t♦♥✱ ❉✳ ❈✳✱ ❉✳ ❈✳ ❇r♦✇♥✱ ●✳ ●❧♦❡❝❦❧❡r ❡t✳ ❛❧✳ ✭✶✾✽✸✮✱ ❊♥❡r❣❡t✐❝ ❆t♦♠✐❝ ❛♥❞ ▼♦❧❡❝✉❧❛r ■♦♥s ✐♥ ❙❛t✉r♥✬s ♠❛❣♥❡t♦s♣❤❡r❡✱ ❏✳ ●❡♦♣❤②s✳ ❘❡s✳ ✽✽✭❆✶✶✮✱ ✽✾✵✺✳ ❬❍❛♠♠❡rs❧❡② ❛♥❞ ❍❛♥❞s❝♦♠❜✱ ✶✾✻✹❪ ❍❛♠♠❡rs❧❡②✱ ❏✳ ▼✳ ❛♥❞ ❉✳ ❈✳ ❍❛♥❞s❝♦♠❜✱ ▼♦♥t❡ ❈❛r❧♦ ▼❡t❤♦❞s ✭▼♦♥♦❣r❛♣❤s ♦♥ ❆♣♣❧✐❡❞ Pr♦❜❛❜✐❧✐t② ❛♥❞ ❙t❛t✐st✐❝s✱ ❡❞✐t❡❞ ❜② ▼✳ ❙✳ ❇❛rt❧❡tt ❛♥❞ ❉✳ ❘✳ ❈♦①✱ ▲♦♥❞♦♥ ❈❤❛♣✲ ♠❛♥ ❛♥❞ ❍❛❧❧✱ ❯❙❆✱ ✶✾✻✹✮✳ ❬❍❛rtq✉✐st ❡t ❛❧✳✱ ✷✵✵✸❪ ❍❛rtq✉✐st✱ ❚✳ ❲✳✱ ❖✳ ❍❛✈♥❡s ❛♥❞ ●✳ ❊✳ ▼♦r✜❧❧ ✭✷✵✵✸✮✱ ❚❤❡ ❡✛❡❝ts ♦❢ ❝❤❛r❣❡❞ ❞✉st ✐♥ ❙❛t✉r♥✬s r✐♥❣s✱ ❆str♦♥✳ ❛♥❞ ●❡♦♣❤②s✳ ✹✹✱ ✷✻✳ ❬❍❡ss✱ ✶✾✻✽❪ ❍❡ss✱ ❲✳ ◆✳ ✭✶✾✻✽✮✱ ❚❤❡ r❛❞✐❛t✐♦♥ ❜❡❧t ❛♥❞ ♠❛❣♥❡t♦s♣❤❡r❡✱ ✐♥ ■♥tr♦❞✉❝t✐♦♥ t♦ ❙♣❛❝❡ ❙❝✐❡♥❝❡✱ ❡❞✐t❡❞ ❜② ❲✳ ◆✳ ❍❡ss ❛♥❞ ●✳ ❉✳ ▼❡❛❞ ✭◆❡✇ ❨♦r❦✱ ●♦r❞♦♥ ❛♥❞ ❇r❡❛❝❤✮✳ ❬❍♦r❛♥②✐ ❡t ❛❧✳✱ ✶✾✾✷❪ ❍♦r❛♥②✐✱ ▼✳✱ ❏✳ ❆✳ ❇✉r♥s ❛♥❞ ❉✳ P✳ ❍❛♠✐❧✲ t♦♥ ✭✶✾✾✷✮✱ ❚❤❡ ❞②♥❛♠✐❝s ♦❢ ❙❛t✉r♥✬s ❊ r✐♥❣ ♣❛rt✐❝❧❡s✱ ■❝❛r✉s ✾✼✱ ✷✹✽✳ ❬❍♦r❛♥②✐✱ ✶✾✾✻❪ ❍♦r❛♥②✐✱ ▼✳ ✭✶✾✾✻✮✱ ❈❤❛r❣❡❞ ❞✉st ❞②♥❛♠✐❝s ✐♥ t❤❡ ❙♦❧❛r ❙②st❡♠✱ ❆♥♥✉✳ ❘❡✈✳ ❆str♦♥✳ ❆s✲ tr♦♣❤②s✳ ✸✹✱ ✸✽✸✳ ❬❍♦r✇✐t③ ❡t ❛❧✳✱ ✶✾✾✹❪ ❍♦r✇✐t③✱ ❏✳ ▲✳✱ ❈✳ ❲✳ ❍♦✱ ❍✳ ❉✳ ❙❝❛r❜r♦ ❡t✳ ❛❧✳ ✭✶✾✾✹✮✱ ❈❡♥tr✐❢✉❣❛❧ ❛❝❝❡❧❡r❛t✐♦♥ ♦❢ t❤❡ ♣♦❧❛r ✇✐♥❞✱ ❏✳ ●❡♦♣❤②s✳ ❘❡s✳ ✾✾✱ ✺✵✺✶✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❇✐❜❧✐♦❣r❛❢í❛ ❬❍♦✇❛r❞ ❡t ❛❧✳✱ ✶✾✾✾❪ ✶✹✻ ❍♦✇❛r❞✱ ❏✳ ❊✳✱ ▼✳ ❍♦rá♥②✐ ❛♥❞ ●✳ ❘✳ ❙t❡✇❛rt ✭✶✾✾✾✮✱ ✱ P❤②s✳ ❘❡✈✳ ▲❡tt✳ ✽✸ ✭✷✵✮✱ ✸✾✾✸✳ ●❧♦❜❛❧ ❞②♥❛♠✐❝s ♦❢ ❝❤❛r❣❡❞ ❞✉st ♣❛rt✐✲ ❝❧❡s ✐♥ P❧❛♥❡t❛r② ▼❛❣♥❡t♦s♣❤❡r❡s ❬■♣✱ ✶✾✾✷❪ ■♣✱ ❲✳✲❍✳ ✭✶✾✾✷✮✱ ✱ ❆❞✈✳ ❙♣❛❝❡ ❘❡s✳ ✶✷✭✽✮✱ ✼✸✳ ❚❤❡ ◆✐tr♦❣❡♥ ❚♦r✐ ♦❢ ❚✐t❛♥ ❛♥❞ ❚r✐t♦♥ ❬■♣✱ ✶✾✾✺❪ ■♣✱ ❲✳ ❍✳ ✭✶✾✾✺✮✱ ✱ ■❝❛r✉s ✶✶✺✱ ✷✾✺✳ ❚❤❡ ❡①♦s♣❤❡r✐❝ s②st❡♠s ♦❢ ❙❛t✉r♥✬s r✐♥❣s ❬■♣✱ ✶✾✾✻❪ ■♣✱ ❲✳✲❍✳ ✭✶✾✾✻✮✱ ❚❤❡ ❆s②♠♠❡tr✐❝ ❉✐str✐❜✉✲ t✐♦♥ ♦❢ ❚✐t❛♥✬s ❆t♦♠✐❝ ❍②❞r♦❣❡♥ ❈❧♦✉❞ ❛s ❛ ✱ ❆♣❏✳ ✹✺✼✱ ✾✷✷✳ ❋✉♥❝t✐♦♥ ♦❢ ▲♦❝❛❧ ❚✐♠❡ ❬■♣✱ ✷✵✵✵❪ ■♣✱ ❲✳❍✳ ✭✷✵✵✵✮✱ ❚❤❡r♠❛❧ ♣❧❛s♠❛ ❝♦♠♣♦s✐✲ ✱ P❧❛♥❡t❛r② ❛♥❞ t✐♦♥ ✐♥ ❙❛t✉r♥✬s ♠❛❣♥❡t♦s♣❤❡r❡ ❙♣❛❝❡ ❙❝✐❡♥❝❡ ✹✽✱ ✼✼✺✳ ❬❏❛❝❦s♦♥✱ ✶✾✾✾❪ ❏❛❝❦s♦♥✱ ❏✳ ❉✳ ✭✶✾✾✾✮✱ ❈❧❛ss✐❝❛❧ ❊❧❡❝tr♦❞②✲ ♥❛♠✐❝s ✭❏♦❤♥ ❲✐❧❡② ✫ ❙♦♥s✱ ❯❙❆✮✳ ❬❏❛r❞✐♥❡ ❛♥❞ ❆❧❧❡♥✱ ✶✾✾✻❪ ❏❛r❞✐♥❡✱ ▼✳ ❛♥❞ ❍✳ ❘✳ ❆❧❧❡♥ ✭✶✾✾✻✮✱ P❛r✲ t✐❝❧❡ ❆❝❝❡❧❡r❛t✐♦♥ ❛♥❞ ▼❛❣♥❡t✐❝ ❆♥♥✐❤✐❧❛t✐♦♥ ✐♥ ❈✉rr❡♥t ❙❤❡❡ts✱ ▼❛❣♥❡t✐❝ ❘❡❝♦♥♥❡❝t✐♦♥ ✐♥ ✱ ❆❙P ❈♦♥❢❡r❡♥❝❡ ❙❡r✐❡s✱ ❱♦❧✳ ✶✶✶✱ ❘✳ ❉✳ ❇❡♥t❧❡② ❛♥❞ ❏✳ ❚✳ ▼❛r✐s❦❛ ✭❡❞s✳✮✱ ✸✵✵✳ t❤❡ ❙♦❧❛r ❆t♠♦s♣❤❡r❡ ❬❏♦❤♥s♦♥ ❡t ❛❧✳✱ ✶✾✽✾❪ ❏♦❤♥s♦♥✱ ❘✳ ❊✳✱ ▼✳ ❑✳ P♦s♣✐❡s③❛❧s❦❛✱ ❊✳ ❈✳ ❙✐tt❧❡r ❡t✳ ❛❧✳ ✭✶✾✽✾✮✱ ✱ ■❝❛r✉s ✼✼✱ ✸✶✶✳ ❚❤❡ ♥❡✉tr❛❧ ❝❧♦✉❞ ❛♥❞ ❤❡❛✈② ✐♦♥ ✐♥♥❡r t♦r✉s ❛t ❙❛t✉r♥ ❬❏♦❤♥s♦♥ ❡t ❛❧✳✱ ✷✵✵✸❪ ❏♦❤♥s♦♥✱ ❘✳ ❊✳✱ ❚✳ ■✳ ◗✉✐❝❦❡♥❞❡♥✱ P✳ ❉✳ ❈♦♦♣❡r ❡t✳ ❛❧✳ ✭✷✵✵✸✮✱ ❚❤❡ Pr♦❞✉❝t✐♦♥ ♦❢ ❖①✐✲ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❇✐❜❧✐♦❣r❛❢í❛ ✶✹✼ ❞❛♥ts ✐♥ ❊✉r♦♣❛✬s ❙✉r❢❛❝❡✱ ❆str♦❜✐♦❧♦❣② ✸✱ ✽✷✸✳ ❬❏♦❦✐♣✐✐✱ ✶✾✼✾❪ ❏♦❦✐♣✐✐✱ ❏✳ ❘✳ ✭✶✾✼✾✮✱ ■♥tr♦❞✉❝t♦r② ❧❡❝t✉r❡✱ ✐♥ ❆■P ❈♦♥❢❡r❡♥❝❡ Pr♦❝❡❡❞✐♥❣s ✺✻✿ P❛r✲ t✐❝❧❡ ❛❝❝❡❧❡r❛t✐♦♥ ♠❡❝❤❛♥✐s♠s ✐♥ ❆s✲ tr♦♣❤②s✐❝s✱ ❡❞✐t❡❞ ❜② ❏✳ ❆r♦♥s✱ ▼✳ ❈❧❛✐r❡ ❛♥❞ ❈✳ ▼❝❑❡❡✱ ✶✳ ❬❏♦❦✐♣✐✐ ❡t ❛❧✳✱ ✷✵✵✶❪ ❏♦❦✐♣✐✐✱ ❏✳ ❘✳✱ ❏✳ ❑♦t❛ ❛♥❞ ❏✳ ●✐❛❝❛❧♦♥❡ ✭✷✵✵✶✮✱ ❈♦♠♣r❡ss✐✈❡✲❉✐✛✉s✐✈❡ ❆❝❝❡❧❡r❛t✐♦♥ ♦❢ ❊♥❡r✲ ❣❡t✐❝ ❈❤❛r❣❡❞ P❛rt✐❝❧❡s✱ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ✷✼t❤ ■♥t❡r♥❛t✐♦♥❛❧ ❈♦s♠✐❝ ❘❛② ❈♦♥❢❡r❡♥❝❡✱ ✼✲ ✶✺ ❆✉❣✉st✱ ✷✵✵✶✱ ❍❛♠❜✉r❣✱ ●❡r♠❛♥②✳ ❯♥❞❡r t❤❡ ❛✉s♣✐❝❡s ♦❢ t❤❡ ■♥t❡r♥❛t✐♦♥❛❧ ❯♥✐♦♥ ♦❢ P✉✲ r❡ ❛♥❞ ❆♣♣❧✐❡❞ P❤②s✐❝s ✭■❯P❆P✮✱ ✸✺✽✶✳ ❬❏♦♥❡s✱ ✶✾✾✹❪ ❏♦♥❡s✱ ❋✳ ❈✳ ✭✶✾✾✹✮✱ ❆ t❤❡♦r❡t✐❝❛❧ r❡✈✐❡✇ ♦❢ ❞✐❢✲ ❢✉s✐✈❡ s❤♦❝❦ ❛❝❝❡❧❡r❛t✐♦♥✱ ❆str♦♣❤②s✳ ❏✳ ❙✉♣♣❧✳ ❙❡r✐❡s ✾✵✭✷✮✱ ✺✻✶✳ ❬❏✉r❛❝ ❡t ❛❧✳✱ ✷✵✵✶❪ ❏✉r❛❝✱ ❙✳✱ ❘✳ ❊✳ ❏♦❤♥s♦♥✱ ❏✳ ❉✳ ❘✐❝❤❛r❞s♦♥ ❡t✳ ❛❧✳ ✭✷✵✵✶✮✱ ❙❛t❡❧❧✐t❡ s♣✉tt❡r✐♥❣ ✐♥ ❙❛t✉r♥✬s ♠❛❣♥❡t♦s♣❤❡r❡✱ P❧❛♥❡t❛r② ❛♥❞ ❙♣❛❝❡ ❙❝✐❡♥❝❡ ✹✾✭✸✲✹✮✱ ✸✶✾✳ ❬❏✉r❛❝ ❡t ❛❧✳✱ ✷✵✵✷❪ ❏✉r❛❝✱ ❙✳✱ ▼✳ ❆✳ ▼❝●r❛t❤✱ ❘✳ ❊✳ ❏♦❤♥s♦♥ ❡t✳ ❛❧✳ ✭✷✵✵✷✮✱ ❙❡❛r❝❤ ❢♦r ❛ ♠✐ss✐♥❣ ✇❛t❡r s♦✉r❝❡✱ ●❡♦♣❤②s✳ ❘❡s✳ ▲❡tt✳ ✷✾✭✷✹✮✱ ✷✺✲✶✱ ❈✐t❡■❉ ✷✶✼✷✱ ❞♦✐✿ ✶✵✳✶✵✷✾✴✷✵✵✷●▲✵✶✺✽✺✺✳ ❬❑❛r❣❡❧ ❛♥❞ P♦③❧♦✱ ✶✾✾✻❪ ❑❛r❣❡❧✱ ❏✳ ❙✳ ❛♥❞ ❙✳ P♦③❧♦ ✭✶✾✾✻✮✱ ❚❤❡ ❱♦❧❝❛✲ ♥✐❝ ❛♥❞ ❚❡❝t♦♥✐❝ ❍✐st♦r② ♦❢ ❊♥❝❡❧❛❞✉s✱ ■❝❛r✉s ✶✶✾✱ ✸✽✺✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❇✐❜❧✐♦❣r❛❢í❛ ❬❑✐♠✉r❛ ❛♥❞ ▼❛♥♥✱ ✶✾✾✽❪ ✶✹✽ ❑✐♠✉r❛✱ ❍✳ ❛♥❞ ■✳ ▼❛♥♥ ✭✶✾✾✽✮✱ ❚❤❡ ❊❧❡❝tr✐❝ ❈❤❛r❣✐♥❣ ♦❢ ■♥t❡rst❡❧❧❛r ❉✉st ✐♥ t❤❡ ❙♦❧❛r ❙②s✲ t❡♠ ❛♥❞ ❈♦♥s❡q✉❡♥❝❡s ❢♦r ✐ts ❉②♥❛♠✐❝s✱ ❆♣❏✳ ✹✾✾✱ ✹✺✹✳ ❬❑✐✈❡❧s♦♥ ❛♥❞ ❘✉ss❡❧❧✱ ✶✾✾✼❪ ❑✐✈❡❧s♦♥✱ ▼✳ ●✳ ❛♥❞ ❈✳ ❚✳ ❘✉ss❡❧❧✱ ■♥tr♦❞✉❝✲ t✐♦♥ t♦ ❙♣❛❝❡ P❤②s✐❝s ✭❈❛♠❜r✐❞❣❡ ❯♥✐✈❡r✲ s✐t② Pr❡ss✱ ❯❙❆✱ ✶✾✾✼✮✳ ❬❑✐✈❡❧s♦♥✱ ✷✵✵✺❪ ❑✐✈❡❧s♦♥✱ ▼✳ ●✳ ✭✷✵✵✺✮✱ ❚r❛♥s♣♦rt ❛♥❞ ❛❝❝❡✲ ❧❡r❛t✐♦♥ ♦❢ ♣❧❛s♠❛ ✐♥ t❤❡ ♠❛❣♥❡t♦s♣❤❡r❡s ♦❢ ❊❛rt❤ ❛♥❞ ❏✉♣✐t❡r ❛♥❞ ❡①♣❡❝t❛t✐♦♥s ❢♦r ❙❛t✉r♥✱ ❆❞✈✳ ❙♣❛❝❡ ❘❡s✳ ✸✻✱ ✷✵✼✼✳ ❬❑❧❡✐♥❜❛✉♠✱ ✷✵✵✺❪ ❑❧❡✐♥❜❛✉♠✱ ❉✳ ●✳ ❛♥❞ ▼✳ ❑❧❡✐♥✱ ▲♦❣✐st✐❝ r❡✲ ❣r❡ss✐♦♥ ✭❙♣r✐♥❣❡r ❱❡r❧❛❣✱ ❯❙❆✱ ✷✵✵✺✮✳ ❬❑r✐♠✐❣✐s ❡t ❛❧✳✱ ✶✾✽✶❪ ❑r✐♠✐❣✐s✱ ❙✳ ▼✳✱ ❚✳ P✳ ❆r♠str♦♥❣✱ ❲✳ ■✳ ❆①❢♦r❞ ❡t✳ ❛❧✳ ✭✶✾✽✶✮✱ ▲♦✇✲❊♥❡r❣② ❝❤❛r❣❡❞ ♣❛rt✐❝❧❡s ✐♥ ❙❛t✉r♥✬s ♠❛❣♥❡t♦s♣❤❡r❡✿ ❘❡s✉❧ts ❢r♦♠ ❱♦②❛❣❡r ✶✱ ❬❑r✐♠✐❣✐s ❡t ❛❧✳✱ ✶✾✽✷❪ ❙❝✐❡♥❝❡ ✷✶✷✭✶✵✮✱ ✷✷✺✳ ❑r✐♠✐❣✐s✱ ❙✳ ▼✳✱ ❚✳ P✳ ❆r♠str♦♥❣✱ ❲✳ ■✳ ❆①✲ ❢♦r❞ ❡t✳ ❛❧✳ ✭✶✾✽✷✮✱ ▲♦✇✲❊♥❡r❣② ❤♦t ♣❧❛s♠❛ ❛♥❞ ♣❛rt✐❝❧❡s ✐♥ ❙❛t✉r♥✬s ♠❛❣♥❡t♦s♣❤❡r❡✱ ❙❝✐❡♥❝❡ ✷✶✺✭✷✾✮✱ ✺✼✶✳ ❬❑r✐♠✐❣✐s ❛♥❞ ❆r♠str♦♥❣✱ ✶✾✽✷❪ ❑r✐♠✐❣✐s✱ ❙✳ ▼✳ ❛♥❞ ❚✳ P✳ ❆r♠str♦♥❣ ✭✶✾✽✷✮✱ ❚✇♦✲❝♦♠♣♦♥❡♥t ♣r♦t♦♥ s♣❡❝tr❛ ✐♥ t❤❡ ✐♥♥❡r ❙❛t✉r♥✐❛♥ ♠❛❣♥❡t♦s♣❤❡r❡✱ ●❡♦♣❤②s✳ ❘❡s✳ ▲❡tt✳ ✾✱ ✶✶✹✸✳ ❬❑r✐♠✐❣✐s✱ ✶✾✽✷❪ ❑r✐♠✐❣✐s✱ ❙✳ ▼✳ ✭✶✾✽✷✮✱ ❆ ♣♦st✲❱♦②❛❣❡r ✈✐❡✇ ♦❢ ❙❛t✉r♥✬s ❡♥✈✐r♦♥♠❡♥t✱ ❏♦❤♥s ❍♦♣❦✐♥s ❆P▲ ❚❡❝❤♥✐❝❛❧ ❉✐❣❡st✱ ❱♦❧✳ ✸✱ ✶✽✵✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❇✐❜❧✐♦❣r❛❢í❛ ❬❑r✐♠✐❣✐s ❡t ❛❧✳✱ ✶✾✽✸❪ ✶✹✾ ❑r✐♠✐❣✐s✱ ❙✳ ▼✳✱ ❏✳ ❋✳ ❈❛r❜❛r②✱ ❊✳ P✳ ❑❡❛t❤ ❡t✳ ❛❧✳ ✭✶✾✽✸✮✱ ●❡♥❡r❛❧ ❝❤❛r❛❝t❡r✐st✐❝s ♦❢ ❤♦t ♣❧❛s♠❛ ❛♥❞ ❡♥❡r❣❡t✐❝ ♣❛rt✐❝❧❡s ✐♥ t❤❡ ❙❛t✉r✲ ♥✐❛♥ ♠❛❣♥❡t♦s♣❤❡r❡✲❘❡s✉❧ts ❢r♦♠ t❤❡ ❱♦②❛❣❡r s♣❛❝❡❝r❛❢t✱ ❏✳ ●❡♦♣❤②s✳ ❘❡s✳ ✽✽✱ ✽✽✼✶✳ ❬❑r✐♠✐❣✐s ❡t ❛❧✳✱ ✷✵✵✺❪ ❑r✐♠✐❣✐s✱ ❙✳ ▼✳✱ ❉✳ ●✳ ▼✐t❝❤❡❧❧✱ ❉✳ ❈✳ ❍❛♠✐❧✲ t♦♥ ❡t✳ ❛❧✳ ✭✷✵✵✺✮✱ ❉②♥❛♠✐❝s ♦❢ ❙❛t✉r♥✬s ▼❛❣✲ ♥❡t♦s♣❤❡r❡ ❢r♦♠ ▼■▼■ ❉✉r✐♥❣ ❈❛ss✐♥✐✬s ❖r❜✐✲ t❛❧ ■♥s❡rt✐♦♥✱ ❙❝✐✳ ✸✵✼✱ ✶✷✼✵✳ ❬❑r✉♣♣✱ ✷✵✵✺❪ ❑r✉♣♣✱ ◆✳ ✭✷✵✵✺✮✱ ❊♥❡r❣❡t✐❝ P❛rt✐❝❧❡s ✐♥ t❤❡ ▼❛❣♥❡t♦s♣❤❡r❡ ♦❢ ❙❛t✉r♥ ❛♥❞ ❛ ❈♦♠♣❛r✐s♦♥ ✇✐t❤ ❏✉♣✐t❡r✱ ❙♣❛❝❡ ❙❝✐✳ ❘❡✈✳ ✶✶✻✱ ✸✹✺✳ ❬▲❛✈✐♥❡ ❛♥❞ ❱❡tt❡✱ ✶✾✼✵❪ ▲❛✈✐♥❡✱ ❏✳ P✳ ❛♥❞ ❏✳ ■✳ ❱❡tt❡ ✭✶✾✼✵✮✱ ▼♦❞❡❧s ♦❢ t❤❡ tr❛♣♣❡❞ r❛❞✐❛t✐♦♥ ❡♥✈✐r♦♥♠❡♥t✱ ❱♦❧✳ ✻✿ ❍✐❣❤ ❡♥❡r❣② ♣r♦t♦♥s ✭◆❆❙❆✲❙P ✸✵✷✹✮✳ ❬▲❛③❛r✉s ❡t ❛❧✳✱ ✶✾✽✸❪ ▲❛③❛r✉s✱ ❆✳ ❏✳✱ ❚✳ ❍❛s❡❣❛✇❛✱ ❚✳ ❛♥❞ ❋✳ ❇❛✲ ❣❡♥❛❧ ✭✶✾✽✸✮✱ ▲♦♥❣✲❧✐✈❡❞ ♣❛rt✐❝✉❧❛t❡ ♦r ❣❛✲ s❡♦✉s str✉❝t✉r❡ ✐♥ ❙❛t✉r♥✬s ♦✉t❡r ♠❛❣♥❡t♦s♣✲ ❤❡r❡✱ ◆❛t✉r❡ ✸✵✷✱ ✷✸✵✳ ❬▲❛③❛r✉s ❛♥❞ ▼❝◆✉tt✱ ✶✾✽✸❪ ▲❛③❛r✉s✱ ❆✳ ❏✳ ❛♥❞ ❘✳ ▲✳ ▼❝◆✉tt ❏r✳✭✶✾✽✸✮✱ ▲♦✇ ❡♥❡r❣② ♣❧❛s♠❛ ✐♦♥ ♦❜s❡r✈❛t✐♦♥s ✐♥ ❙❛✲ t✉r♥✬s ♠❛❣♥❡t♦s♣❤❡r❡✱ ❏✳ ●❡♦♣❤②s✳ ❘❡s✳ ✽✽✱ ✽✽✸✶✳ ❬▲❡❜♦❢s❦② ❡t ❛❧✳✱ ✶✾✼✵❪ ▲❡❜♦❢s❦②✱ ▲✳ ❆✳✱ ❚✳ ❱✳ ❏♦❤♥s♦♥✱ ❛♥❞ ❚✳ ❇✳ ▼❝✲ ❈♦r❞ ✭✶✾✼✵✮✱ ❙❛t✉r♥✬s r✐♥❣s✿ ❙♣❡❝tr❛❧ r❡✢❡❝t✐✲ ✈✐t② ❛♥❞ ❝♦♠♣♦s✐t✐♦♥❛❧ ✐♠♣❧✐❝❛t✐♦♥s✱ ■❝❛r✉s ✶✸✱ ✷✷✻✳ ❬▲❡❜♦❢s❦② ❛♥❞ ❋❡❣❧❡②✱ ✶✾✼✻❪ ▲❡❜♦❢s❦②✱ ▲✳ ❆✳✱ ▼✳ ❇✳ ❋❡❣❧❡② ❏r✳ ✭✶✾✼✻✮✱ ▲❛❜♦✲ r❛t♦r② r❡✢❡❝t✐♦♥ s♣❡❝tr❛ ❢♦r t❤❡ ❞❡t❡r♠✐♥❛t✐♦♥ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❇✐❜❧✐♦❣r❛❢í❛ ✶✺✵ ♦❢ ❝❤❡♠✐❝❛❧ ❝♦♠♣♦s✐t✐♦♥ ♦❢ ✐❝❡ ❜♦❞✐❡s✱ ■❝❛r✉s ✷✽✱ ✸✼✾✳ ❬▼❛rtí♥❡③✲●ó♠❡③ ❡t ❛❧✳✱ ✷✵✵✻❪ ▼❛rtí♥❡③✲●ó♠❡③✱ ❊✳✱ ❍✳ ❏✳ ❉✉r❛♥❞✲▼❛♥t❡r♦❧❛ ❛♥❞ ❍✳ Pér❡③ ❞❡ ❚❡❥❛❞❛ ✭✷✵✵✻✮✱ ❙t♦❝❤❛st✐❝ ❆❝✲ ❝❡❧❡r❛t✐♦♥ ♦❢ ❊♥❡r❣❡t✐❝ P❛rt✐❝❧❡s ✐♥ t❤❡ ▼❛❣♥❡✲ t♦s♣❤❡r❡ ♦❢ ❙❛t✉r♥✱ ❆str♦♣❤②s✳ ❛♥❞ ❙♣❛❝❡ ❙❝✐✳ ✸✵✻✭✹✮✱ ✷✺✾✱ ❞♦✐ ✶✵✳✶✵✵✼✴s✶✵✺✵✾✲✵✵✻✲✾✷✼✶✲✵✳ ❬▼❛rtí♥❡③✲●ó♠❡③ ❡t ❛❧✳✱ ✷✵✵✼❛❪ ▼❛rtí♥❡③✲●ó♠❡③✱ ❊✳✱ ❍✳ ❏✳ ❉✉r❛♥❞✲▼❛♥t❡r♦❧❛ ❛♥❞ ❍✳ Pér❡③ ❞❡ ❚❡❥❛❞❛ ✭✷✵✵✼✮✱ ❊♥❡r❣✐③❛t✐♦♥ ♦❢ ♣❛rt✐❝❧❡s ✐♥ ❙❛t✉r♥✬s ✐♥♥❡r ♠❛❣♥❡t♦s♣❤❡r❡✿ ▼♦♥t❡ ❈❛r❧♦ s✐♠✉❧❛t✐♦♥ ♦❢ st♦❝❤❛st✐❝ ❡❧❡❝tr✐❝ ✜❡❧❞ ❡✛❡❝ts✱ ❆str♦♥✳ ❛♥❞ ❆str♦♣❤②s✳ ✭❡♥ ♣r❡♥✲ s❛✮✳ ❬▼❛rtí♥❡③✲●ó♠❡③ ❡t ❛❧✳✱ ✷✵✵✼❜❪ ▼❛rtí♥❡③✲●ó♠❡③✱ ❊✳✱ ❍✳ ❏✳ ❉✉r❛♥❞✲▼❛♥t❡r♦❧❛ ❛♥❞ ❍✳ Pér❡③ ❞❡ ❚❡❥❛❞❛ ✭✷✵✵✼✮✱ ❊♥❡r❣✐③❛t✐♦♥ ♦❢ ❝❤❛r❣❡❞ ♣❛rt✐❝❧❡s ✐♥ ♣❧❛♥❡t❛r② ♠❛❣♥❡t♦s♣❤❡r❡s✱ ❆str♦♣❤②s✳ ❛♥❞ ❙♣❛❝❡ ❙❝✐✳ ✭❡♥ ♣r❡♥s❛✮✳ ❬▼❛✉❦ ❛♥❞ ▼❡♥❣✱ ✶✾✽✸❪ ▼❛✉❦✱ ❇✳ ❍✳ ❛♥❞ ❈✳ ▲✳ ▼❡♥❣ ✭✶✾✽✸✮✱ ❉②♥❛♠✐✲ ❝❛❧ ✐♥❥❡❝t✐♦♥s ❛s t❤❡ s♦✉r❝❡ ♦❢ ♥❡❛r ❣❡♦st❛t✐♦✲ ♥❛r② q✉✐❡t t✐♠❡ ♣❛rt✐❝❧❡ s♣❛t✐❛❧ ❜♦✉♥❞❛r✐❡s✱ ❏✳ ●❡♦♣❤②s✳ ❘❡s✳ ❬▼❛✉❦ ❡t ❛❧✳✱ ✶✾✾✼❪ ✽✽✱ ✶✵✵✶✶✳ ▼❛✉❦✱ ❇✳ ❍✳✱ ❉✳ ❏✳ ❲✐❧❧✐❛♠s ❛♥❞ ❘✳ ❲✳ ▼❝❊♥✲ t✐r❡ ✭✶✾✾✼✮✱ ❊♥❡r❣②✲t✐♠❡ ❞✐s♣❡rs❡❞ ❝❤❛r❣❡❞ ♣❛r✲ t✐❝❧❡ s✐❣♥❛t✉r❡s ♦❢ ❞②♥❛♠✐❝ ✐♥❥❡❝t✐♦♥s ✐♥ ❏✉✲ ♣✐t❡r✬s ✐♥♥❡r ♠❛❣♥❡t♦s♣❤❡r❡✱ ▲❡tt✳ ❬▼❝❉♦♥❛❧❞ ❡t ❛❧✳✱ ✶✾✽✵❪ ●❡♦♣❤②s✳ ❘❡s✳ ✷✹✱ ✷✾✹✾✳ ▼❝❉♦♥❛❧❞✱ ❋✳ ❇✳✱ ❆✳ ❲✳ ❙❝❤❛r❞t ❛♥❞ ❏✳ ❍✳ ❚r❛✐♥♦r ✭✶✾✽✵✮✱ ■❢ ②♦✉✬✈❡ s❡❡♥ ♦♥❡ ♠❛❣♥❡t♦s♣✲ ❤❡r❡ ②♦✉ ❤❛✈❡♥✬t s❡❡♥ t❤❡♠ ❛❧❧✿ ❊♥❡r❣❡t✐❝ ♣❛r✲ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❇✐❜❧✐♦❣r❛❢í❛ ✶✺✶ t✐❝❧❡ ♦❜s❡r✈❛t✐♦♥s ✐♥ t❤❡ ❙❛t✉r♥✐❛♥ ♠❛❣♥❡t♦s♣✲ ❤❡r❡✱ ❬▼ö❜✐✉s✱ ✶✾✾✹❪ ❏✳ ●❡♦♣❤②s✳ ❘❡s✳ ✽✺✱ ✺✽✶✸✳ ▼ö❜✐✉s✱ ❊✳ ✭✶✾✾✹✮✱ ❙♦✉r❝❡s ❛♥❞ ❛❝❝❡❧❡r❛t✐♦♥ ♦❢ ❡♥❡r❣❡t✐❝ ♣❛rt✐❝❧❡s ✐♥ ♣❧❛♥❡t❛r② ♠❛❣♥❡t♦s♣❤❡✲ r❡s✱ ❬▼♦rr✐s♦♥ ❡t ❛❧✳✱ ✶✾✽✻❪ ❆str♦♣❤②s✳ ❏✳ ❙✉♣♣❧✳ ❙❡r✐❡s ✾✵✱ ✺✷✶✳ ▼♦rr✐s♦♥✱ ❉✳✱ ❚✳ ❖✇❡♥ ❛♥❞ ▲ ❆✳ ❙♦❞❡r❜❧♦♠ ✭✶✾✽✻✮✱ ❚❤❡ s❛t❡❧❧✐t❡s ♦❢ ❙❛t✉r♥✳ ■♥ ❙❛t❡❧❧✐t❡s✱ ❡❞✐t❡❞ ❜② ❏✳ ❆✳ ❇✉r♥s ❛♥❞ ▼✳ ❙✳ ▼❛tt❤❡✇s✱ ✼✻✹✳ ❬▼♦t❡③ ❡t ❛❧✳✱ ✷✵✵✶❪ ▼♦tt❡③✱ ✭✷✵✵✹✮✱ ❋✳✱ ❱✳ ◆✉♠❡r✐❝❛❧ ●é♥♦t ❛♥❞ s✐♠✉❧❛t✐♦♥ P✳ ♦❢ ▲♦✉❛r♥ t✉r❜✉❧❡♥❝❡ ❛♥❞ ❛❝❝❡❧❡r❛t✐♦♥ ✐♥ t❤❡ ♠❛❣♥❡t♦s♣❤❡r✐❝ ❛✉✲ r♦r❛❧ ③♦♥❡s✱ ✐♥ ❙❋✷❆✲✷✵✵✹✿ ❙❡♠❛✐♥❡ ❞❡ ❧✬❆str♦♣❤②s✐q✉❡ ❋r❛♥❝❛✐s❡✱ P❛r✐s✱ ❋r❛♥❝❡✱ ❊❞✐t❡❞ ❜② ❋✳ ❈♦♠❜❡s✱ ❉✳ ❇❛rr❡t✱ ❚✳ ❈♦♥t✐✲ ♥✐✱ ❋✳ ▼❡②♥❛❞✐❡r ❛♥❞ ▲✳ P❛❣❛♥✐✱ ❊❞P✲❙❝✐❡♥❝❡s✱ ❈♦♥❢❡r❡♥❝❡ ❙❡r✐❡s✱ ✶✹✲✶✽ ❏✉♥❡ ✷✵✵✹✳ ❬▼✉r❞✐♥✱ ✷✵✵✶❪ ▼✉r❞✐♥✱ P✳ ✭✷✵✵✶✮✱ ❊♥❝②❝❧♦♣❡❞✐❛ ♦❢ ❆str♦✲ ♥♦♠② ❛♥❞ ❆str♦♣❤②s✐❝s✱ P✳ ▼✉r❞✐♥ ✭❡❞✳✮✱ ❛rt✐✲ ❝❧❡ ✹✹✸✾✳ ❬▼✉rr❛② ❛♥❞ ❉❡r♠♦tt✱ ✶✾✾✾❪ ▼✉rr❛②✱ ❈✳ ❉✳ ❛♥❞ ❙✳ ❋✳ ❉❡r♠♦tt ✭✶✾✾✾✮✱ ❙♦✲ ❧❛r ❙②st❡♠ ❉②♥❛♠✐❝s✱ ❈❛♠❜r✐❞❣❡ ❯♥✐✈❡r✲ s✐t② Pr❡ss✳ ❬◆❡✉❜❛✉❡r ❡t ❛❧✳✱ ✶✾✽✹❪ ◆❡✉❜❛✉❡r✱ ❋✳ ▼✳✱ ❉✳ ●✉r♥❡tt✱ ❏✳ ❙❝✉❞❞❡r ❡t✳ ❛❧✳ ✭✶✾✽✹✮✱ ❚✐t❛♥✬s ♠❛❣♥❡t♦s♣❤❡r✐❝ ✐♥t❡r❛❝t✐♦♥✱ ✐♥ ❙❛t✉r♥✱ ❡❞s✳ ❚✳ ●❡❤r❡❧s ❛♥❞ ▼✳ ❙✳ ▼❛tt✲ ❤❡✇s✱ ✼✻✵✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❇✐❜❧✐♦❣r❛❢í❛ ✶✺✷ ❬◆❡ss ❡t ❛❧✳✱ ✶✾✽✶❪ ◆❡ss✱ ◆✳ ❋✳✱ ▼✳ ❍✳ ❆❝✉ñ❛✱ ❘✳ P✳ ▲❡♣♣✐♥❣ ❡t✳ ❛❧✳ ✭✶✾✽✶✮✱ ▼❛❣♥❡t✐❝ ✜❡❧❞ st✉❞✐❡s ❜② ❱♦②❛✲ ❣❡r ✶✿ ♣r❡❧✐♠✐♥❛r② r❡s✉❧ts ❛t ❙❛t✉r♥✱ ❙❝✐❡♥❝❡ ✷✶✷✭✶✵✮✱ ✷✶✶✳ ❬◆❡ss ❡t ❛❧✳✱ ✶✾✽✷❪ ◆❡ss✱ ❋✳✱ ▼✳ ❍✳ ❆❝✉ñ❛✱ ❑✳ ❲✳ ❇❡❤❛♥♥♦♥ ❡t✳ ❛❧✳ ✭✶✾✽✷✮✱ ▼❛❣♥❡t✐❝ ✜❡❧❞ st✉❞✐❡s ❜② ❱♦②❛❣❡r ✷ ✲ Pr❡❧✐♠✐♥❛r② r❡s✉❧ts ❛t ❙❛t✉r♥✱ ❙❝✐❡♥❝❡ ✷✶✺✱ ✺✺✽✳ ❬◆✐❝❤♦❧s♦♥ ❛♥❞ ❋r❡♥❝❤✱ ✶✾✾✽❪ ◆✐❝❤♦❧s♦♥✱ P✳ ❉✳ ❛♥❞ ❘✳ ●✳ ❋r❡♥❝❤ ✭✶✾✾✽✮✱ P❛r✲ t✐❝❧❡ s✐③❡s ✐♥ ❙❛t✉r♥✬s r✐♥❣s ❞❡r✐✈❡❞ ❢r♦♠ st❡✲ ❧❧❛r ♦❝❝✉❧t❛t✐♦♥ ❞❛t❛✱ ❆♠❡r✐❝❛♥ ❆str♦♥♦♠✐❝❛❧ ❙♦❝✐❡t②✱ ❉P❙ ♠❡❡t✐♥❣ ★✸✵✱ ★✶✼✳✵✸❀ ❇✉❧❧❡t✐♥ ♦❢ t❤❡ ❆♠❡r✐❝❛♥ ❆str♦♥♦♠✐❝❛❧ ❙♦❝✐❡t② ✸✵✱ ✶✵✹✸✳ ❬◆✐s❤✐❞❛✱ ✶✾✼✻❪ ◆✐s❤✐❞❛✱ ❆✳ ✭✶✾✼✻✮✱ ❖✉t✇❛r❞ ❞✐✛✉s✐♦♥ ♦❢ ❡♥❡r✲ ❣❡t✐❝ ♣❛rt✐❝❧❡s ❢r♦♠ t❤❡ ❏♦✈✐❛♥ r❛❞✐❛t✐♦♥ ❜❡❧t✱ ❏✳ ●❡♦♣❤②s✳ ❘❡s✳ ✽✶✱ ✶✼✼✶✳ ❬❖str♦✇s❦✐ ❛♥❞ ❙❝❤❧✐❝❦❡✐s❡r✱ ✶✾✾✸❪ ❖str♦✇s❦✐✱ ▼✳✱ ❛♥❞ ❘✳ ❙❝❤❧✐❝❦❡✐s❡r ✭✶✾✾✸✮✱ ❉✐❢✲ ❢✉s✐✈❡ ✜rst ❛♥❞ s❡❝♦♥❞ ♦r❞❡r ❋❡r♠✐ ❛❝❝❡❧❡r❛✲ t✐♦♥ ❛t ♣❛r❛❧❧❡❧ s❤♦❝❦ ✇❛✈❡s✱ tr♦♣❤②s✳ ✷✻✽✭✷✮✱ ✽✶✷✳ ❆str♦♥✳ ❛♥❞ ❆s✲ ❬P❛r❛♥✐❝❛s ❡t ❛❧✳✱ ✷✵✵✺❪ P❛r❛♥✐❝❛s✱ ❈✳✱ ❉✳ ●✳ ▼✐t❝❤❡❧❧✱ ❙✳ ▲✐✈✐ ❡t✳ ❛❧✳ ✭✷✵✵✺✮✱ ❊✈✐❞❡♥❝❡ ♦❢ ❊♥❝❡❧❛❞✉s ❛♥❞ ❚❡t❤②s ♠✐✲ ❝r♦s✐❣♥❛t✉r❡s✱ ●❡♦♣❤②s✳ ❘❡s✳ ▲❡tt✳ ✸✷✭✷✵✮✱ ❈✐✲ t❡■❉ ▲✷✵✶✵✶✳ ❬P❛r❦ ❛♥❞ P❡tr♦s✐❛♥✱ ✶✾✽✻❪ P❛r❦✱ ❇✳ ❚✳ ❛♥❞ ❱✳ P❡tr♦s✐❛♥ ✭✶✾✾✻✮✱ ❋♦❦❦❡r✲ P❧❛♥❝❦ ❡q✉❛t✐♦♥s ♦❢ st♦❝❤❛st✐❝ ❛❝❝❡❧❡r❛t✐♦♥✿ ❛ st✉❞② ♦❢ ♥✉♠❡r✐❝❛❧ ♠❡t❤♦❞s✱ ❙✉♣♣❧✳ ❙❡r✳ ✶✵✸✱ ✷✺✺✳ ❆str♦♣❤②s✳ ❏✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❇✐❜❧✐♦❣r❛❢í❛ ❬Pér❡③ ❞❡ ❚❡❥❛❞❛ ❡t ❛❧✳✱ ✶✾✾✺❪ ✶✺✸ Pér❡③ ❞❡ ❚❡❥❛❞❛✱ ❍✳✱ ❉✳ ❙✳ ■♥tr✐❧✐❣❛t♦r ❛♥❞ ❘✳ ❏✳ ❙tr❛♥❣❡✇❛② ✭✶✾✾✺✮✱ ■♥t❡r♠❡❞✐❛t❡ tr❛♥s✐✲ t✐♦♥ ✐♥ t❤❡ ❱❡♥✉s ✐♦♥♦s❤❡❛t❤✱ ❏✳ ●❡♦♣❤②s✳ ❘❡s✳ ✶✵✵✭❆✽✮✱ ✶✹✺✷✸✳ ❬P❡r❦✐♥s✱ ✶✾✻✽❪ P❡r❦✐♥s✱ ❋✳ ❲✳ ✭✶✾✻✽✮✱ P❧❛s♠❛✲✇❛✈❡ ✐♥st❛❜✐✲ ❧✐t✐❡s ✐♥ t❤❡ ✐♦♥♦s♣❤❡r❡ ♦✈❡r t❤❡ ❛✉r♦r❛✱ ●❡♦♣❤②s✳ ❘❡s✳ ❬P♦♥t✐✉s ❡t ❛❧✳✱ ✶✾✽✻❪ ❏✳ ✼✸✱ ✻✻✸✶✳ P♦♥t✐✉s✱ ❉✳ ❍✳✱ ❏r✳✱ ❚✳ ❲✳ ❍✐❧❧ ❛♥❞ ▼✳ ❊✳ ❘❛ss❜❛❝❤✱ ✭✶✾✽✻✮✱ ❙t❡❛❞② st❛t❡ ♣❧❛s♠❛ tr❛♥s✲ ♣♦rt ✐♥ ❛ ❝♦r♦t❛t✐♦♥✲❞♦♠✐♥❛t❡❞ ♠❛❣♥❡t♦s♣❤❡✲ r❡✱ ❬P♦r❝♦ ❡t ❛❧✳✱ ✷✵✵✻❪ ●❡♦♣❤②s✳ ❘❡s✳ ▲❡tt✳ P♦r❝♦✱ ❈✳❈✳✱ P✳ ❍❡❧❢❡♥st❡✐♥✱ P✳ ❈✳ ❚❤♦♠❛s ❡t✳ ❛❧✳ ✭✷✵✵✻✮✱ ❈❛ss✐♥✐ ❖❜s❡r✈❡s t❤❡ ❆❝t✐✈❡ ❙♦✉t❤ P♦❧❡ ♦❢ ❊♥❝❡❧❛❞✉s✱ ❬P♦s♣✐❡s③❛❧s❦❛ ❛♥❞ ❏♦❤♥s♦♥✱ ✶✾✾✶❪ ✶✸✱ ✶✵✾✼✳ ✸✶✶✱ ✶✸✾✸✳ ❙❝✐❡♥❝❡ P♦s♣✐❡s③❛❧s❦❛✱ ▼✳ ❑✳ ❛♥❞ ❘✳ ❊✳ ❏♦❤♥s♦♥ ✭✶✾✾✶✮✱ ▼✐❝r♦♠❡t❡♦r✐t❡ ❊r♦s✐♦♥ ♦❢ t❤❡ ▼❛✐♥ ❘✐♥❣s ❛s ❛ ❙♦✉r❝❡ ♦❢ P❧❛s♠❛ ✐♥ t❤❡ ■♥♥❡r ❙❛✲ t✉r♥✐❛♥ P❧❛s♠❛ ❚♦r✉s✱ ❬P♦✉❧❡t ❛♥❞ ❈✉③③✐✱ ✷✵✵✷❪ ■❝❛r✉s P♦✉❧❡t✱ ❋✳ ❛♥❞ ❏✳ ◆✳ ❈✉③③✐ ✭✷✵✵✷✮✱ ♣♦s✐t✐♦♥ ♦❢ ❙❛t✉r♥✬s r✐♥❣s✱ ❬❘✐❝❤❛r❞s♦♥✱ ✶✾✽✻❪ ✾✸✱ ✹✺✳ ■❝❛r✉s ❘✐❝❤❛r❞s♦♥✱ ❏✳ ❉✳ ✭✶✾✽✻✮✱ ❚❤❡ ❝♦♠✲ ✶✻✵✱ ✸✺✵✳ ❚❤❡r♠❛❧ ✐♦♥s ❛t ❙❛t✉r♥✿ P❧❛s♠❛ ♣❛r❛♠❡t❡rs ❛♥❞ ✐♠♣❧✐❝❛t✐♦♥s✱ ❏✳●❡♦♣❤②s✳ ❘❡s✳ ❬❘✐❝❤❛r❞s♦♥ ❛♥❞ ❊✈✐❛t❛r✱ ✶✾✽✽❪ ✾✶✱ ✶✸✽✶✳ ❘✐❝❤❛r❞s♦♥✱ ❏✳ ❉✳ ❛♥❞ ❆✳ ❊✈✐❛t❛r ✭✶✾✽✽✮✱ ❖❜s❡r✈❛t✐♦♥❛❧ ❛♥✐s♦tr♦♣✐❡s ❛♥❞ ✐♥ ●❡♦♣❤②s✳ ❘❡s✳ t❤❡♦r❡t✐❝❛❧ ❙❛t✉r♥✬s ❡✈✐❞❡♥❝❡ ♠❛❣♥❡t♦s♣❤❡r❡✱ ❢♦r ❏✳ ✾✸✱ ✼✷✾✼✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❇✐❜❧✐♦❣r❛❢í❛ ❬❘✐❝❤❛r❞s♦♥✱ ✶✾✾✽❪ ✶✺✹ ❘✐❝❤❛r❞s♦♥✱ ❏✳ ❉✳ ✭✶✾✾✽✮✱ ❚❤❡r♠❛❧ ♣❧❛s♠❛ ❛♥❞ ✱ ❘❡✈✳ ♥❡✉tr❛❧ ❣❛s ✐♥ ❙❛t✉r♥✬s ♠❛❣♥❡t♦s♣❤❡r❡ ●❡♦♣❤②s✳ ✸✻✭✹✮✱ ✺✵✶✳ ❬❘♦❤❛t❣✐ ✷✵✵✸❪ ❘♦❤❛t❣✐✱ ❱✳ ❑✳✱ ❙t❛t✐st✐❝❛❧ ✐♥❢❡r❡♥❝❡ ✭❉♦✈❡r ❇♦♦❦s ♦♥ ▼❛t❤❡♠❛t✐❝s✱ ❉♦✈❡r P✉❜❧✐❝❛t✐♦♥s✱ ■♥❝✳✱ ❯♥✐t❡❞ ❙t❛t❡s✱ ✷✵✵✸✮✳ ❬❘♦s❡♥✱ ✶✾✽✾❪ ❘♦s❡♥✱ P✳ ❆✳ ✭✶✾✽✾✮✱ ❲❛✈❡s ✐♥ ❙❛t✉r♥✬s r✐♥❣s ✱ P❤❉ ❚❤❡s✐s ❙t❛♥✲ ♣r♦❜❡❞ ❜② r❛❞✐♦ ♦❝❝✉❧t❛t✐♦♥ ❢♦r❞ ❯♥✐✈❡rs✐t②✳ ❬❘♦s❡♥ ❡t ❛❧✳✱ ✶✾✾✶❪ ❘♦s❡♥✱ P✳ ❆✳✱ ●✳ ▲✳ ❚②❧❡r✱ ❊✳ ❆✳ ▼❛r♦✉❢ ❡t✳ ❛❧✳ ✭✶✾✾✶✮✱ ❘❡s♦♥❛♥❝❡ str✉❝t✉r❡s ✐♥ ❙❛t✉r♥✬s r✐♥❣s ♣r♦❜❡❞ ❜② r❛❞✐♦ ♦❝❝✉❧t❛t✐♦♥ ■■✿ r❡s✉❧ts ❛♥❞ ✐♥✲ ✱ ■❝❛r✉s ✾✸✱ ✷✺✳ t❡r♣r❡t❛t✐♦♥ ❬❘♦✉ss♦s ❡t ❛❧✳✱ ✷✵✵✺❪ ❘♦✉ss♦s✱ ❊✳✱ ◆✳ ❑r✉♣♣✱ ❏✳ ❲♦❝❤ ❡t✳ ❛❧✳ ✭✷✵✵✺✮✱ ▲♦✇ ❡♥❡r❣② ❡❧❡❝tr♦♥ ♠✐❝r♦s✐❣♥❛t✉r❡s ❛t t❤❡ ♦r❜✐t ♦❢ ❚❡t❤②s✿ ❈❛ss✐♥✐ ▼■▼■✴▲❊▼▼❙ ♦❜✲ ✱ ●❡♦♣❤②s✳ ❘❡s✳ ▲❡tt✳ ❞♦✐✿✶✵✳✶✵✷✾✴✷✵✵✺●▲✵✷✹✵✽✹✳ s❡r✈❛t✐♦♥s ❬❘✉❜✐♥st❡✐♥✱ ✶✾✽✶❪ ❘✉❜✐♥st❡✐♥✱ ❘✳ ❨✳✱ ✸✷✱ ▲✷✹✶✵✼✱ ❙✐♠✉❧❛t✐♦♥ ❛♥❞ t❤❡ ▼♦♥t❡ ❈❛r❧♦ ▼❡t❤♦❞ ✭❲✐❧❡② ❙❡r✐❡s ✐♥ Pr♦✲ ❜❛❜✐❧✐t② ❛♥❞ ▼❛t❤❡♠❛t✐❝❛❧ ❙t❛t✐st✐❝s✱ ❏♦❤♥ ❲✐❧❡② ✫ ❙♦♥s✱ ■♥❝✳✱ ❯♥✐t❡❞ ❙t❛t❡s✱ ✶✾✽✶✮✳ ❬❙❛❧♦✱ ✶✾✾✷❪ ❙❛❧♦✱ ❍✳ ✭✶✾✾✷✮✱ ✱ ◆❛t✉r❡ ✸✺✾✱ ✻✶✾✳ ●r❛✈✐t❛t✐♦♥❛❧ ✇❛❦❡s ✐♥ ❙❛✲ t✉r♥✬s r✐♥❣s ❬❙❛♥❞❡❧ ❡t ❛❧✳✱ ✶✾✽✷❪ ❙❛♥❞❡❧✱ ❇✳ ❘✳✱ ❉✳ ❊✳ ❙❤❡♠❛♥s❦②✱ ❆✳ ▲✳ ❇r♦❛❞✲ ❢♦♦t ❡t✳ ❛❧✳ ✭✶✾✽✷✮✱ ✱ ❙❝✐❡♥❝❡ ✷✶✺✱ ✺✹✽✳ ❊①tr❡♠❡ ✉❧tr❛✈✐♦❧❡t ♦❜s❡r✈❛✲ t✐♦♥s ❢r♦♠ ❱♦②❛❣❡r ✷ ❡♥❝♦✉♥t❡r ✇✐t❤ ❙❛t✉r♥ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❇✐❜❧✐♦❣r❛❢í❛ ❬❙❛♥t♦s✲❈♦st❛ ❡t ❛❧✳✱ ✷✵✵✸❪ ✶✺✺ ❙❛♥t♦s✲❈♦st❛✱ ❉✳✱ ❇❧❛♥❝✱ ▼✳✱ ▼❛✉r✐❝❡ ❡t✳ ❛❧✳ ✭✷✵✵✸✮✱ ▼♦❞❡❧✐♥❣ t❤❡ ❡❧❡❝tr♦♥ ❛♥❞ ♣r♦t♦♥ r❛✲ ❞✐❛t✐♦♥ ❜❡❧ts ♦❢ ❙❛t✉r♥✱ ●❡♦♣❤②s✳ ❘❡s✳ ▲❡tt✳ ✸✵✱ ✻✱ ✶✵✳✶✵✷✾✴✷✵✵✸●▲✵✶✼✾✼✷✳ ❬❙❛✉r ❡t ❛❧✳✱ ✷✵✵✹❪ ❙❛✉r✱ ❏✳✱ ❇✳ ▼❛✉❦✱ ❆✳ ❑❛ÿ♥❡r ❡t✳ ❛❧✳ ✭✷✵✵✹✮✱ ❆ ♠♦❞❡❧ ❢♦r t❤❡ ❛③✐♠✉t❤❛❧ ♣❧❛s♠❛ ✈❡❧♦❝✐t② ✐♥ ❙❛t✉r♥✬s ♠❛❣♥❡t♦s♣❤❡r❡✱ ❏✳ ●❡♦♣❤②s✳ ❘❡s✳ ✶✵✾✭❆✺✮✱ ❈✐t❡■❉ ❆✵✺✷✶✼✳ ❬❙❝❛r❢ ❡t ❛❧✳✱ ✶✾✽✹❪ ❙❝❛r❢✱ ❋✳ ▲✳✱ ▲✳ ❆✳ ❋r❛♥❦✱ ❉✳ ❆✳ ●✉r♥❡tt ❡t✳ ❛❧✳ ✭✶✾✽✹✮✱ ▼❡❛s✉r❡♠❡♥ts ♦❢ P❧❛s♠❛✱ ♣❧❛s♠❛ ✇❛✲ ✈❡s✱ ❛♥❞ s✉♣r❛t❤❡r♠❛❧ ❝❤❛r❣❡❞ ♣❛rt✐❝❧❡s ✐♥ ❙❛✲ t✉r♥✬s ✐♥♥❡r ♠❛❣♥❡t♦s♣❤❡r❡✱ ✐♥ ❙❛t✉r♥✱ ❡❞s✳ ❚✳ ●❡❤r❡❧s ❛♥❞ ▼✳ ❙✳ ▼❛tt❤❡✇s✱ ✸✶✽✱ ❯♥✐✈❡r✲ s✐t② ♦❢ ❆r✐③♦♥❛ Pr❡ss✱ ❚✉❝s♦♥✳ ❬❙❝❤❛r❞t ❛♥❞ ▼❝❉♦♥❛❧❞✱ ✶✾✽✸❪ ❙❝❤❛r❞t✱ ❆✳ ❲✳✱ ❛♥❞ ❋✳ ❇✳ ▼❝❉♦♥❛❧❞ ✭✶✾✽✸✮✱ ❚❤❡ ✢✉① ❛♥❞ s♦✉r❝❡ ♦❢ ❡♥❡r❣❡t✐❝ ♣r♦t♦♥s ✐♥ ❙❛✲ t✉r♥✬s ✐♥♥❡r ♠❛❣♥❡t♦s♣❤❡r❡✱ ❏✳ ●❡♦♣❤②s✳ ❘❡s✳ ✽✽✱ ✽✾✷✸✳ ❬❙❝❤❛r❞t ❡t ❛❧✳✱ ✶✾✽✹❪ ❙❝❤❛r❞t✱ ❆✳ ❲✳✱ ❑✳ ❲✳ ❇❡❤❛♥♥♦♥✱ ❘✳ P✳ ▲❡♣✲ ♣✐♥❣ ❡t✳ ❛❧✳ ✭✶✾✽✹✮✱ ✐♥ ❙❛t✉r♥✱ ❚❤❡ ❖✉t❡r ▼❛❣♥❡t♦s♣❤❡r❡✱ ❡❞s✳ ❚✳ ●❡❤r❡❧s ❛♥❞ ▼✳ ❙✳ ▼❛tt✲ ❤❡✇s✱ ✹✶✻✱ ❯♥✐✈❡rs✐t② ♦❢ ❆r✐③♦♥❛ Pr❡ss✳ ❬❙❝❤❛r❞t ❡t ❛❧✳✱ ✶✾✽✺❪ ❙❝❤❛r❞t✱ ❆✳ ❲✳✱ ❲✳ ❙✱ ❑✉rt❤✱ ❘✳ P✳ ▲❡♣♣✐♥❣ ❡t✳ ❛❧✳ ✭✶✾✽✺✮✱ P❛rt✐❝❧❡ ❛❝❝❡❧❡r❛t✐♦♥ ✐♥ ❙❛t✉r♥✬s ♦✉✲ t❡r ♠❛❣♥❡t♦s♣❤❡r❡✱ ❏✳ ●❡♦♣❤②s✳ ❘❡s✳✱ ✾✵✭❆✾✮✱ ✽✺✸✾✳ ❬❙❝❤❛t③♠❛♥♥✱ ✶✾✻✸❪ ❙❝❤❛t③♠❛♥♥✱ ❊✳ ✭✶✾✻✸✮✱ ❖♥ t❤❡ ❛❝❝❡❧❡r❛t✐♦♥ ♦❢ ♣❛rt✐❝❧❡s ✐♥ s❤♦❝❦ ❢r♦♥ts✱ ❆♥♥✳ ❆str♦♣❤②✳ ✷✻✱ ✷✸✹✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❇✐❜❧✐♦❣r❛❢í❛ ❬❙❝❤❧✐❝❦❡✐s❡r✱ ✶✾✽✾❪ ✶✺✻ ❙❝❤❧✐❝❦❡✐s❡r✱ ❘✳ ✭✶✾✽✾✮✱ ❘❡♠❛r❦s ❛❜♦✉t ❞✐✛✉s✐✲ ✈❡ s❤♦❝❦ ✇❛✈❡ ❛❝❝❡❧❡r❛t✐♦♥✱ ✐♥✿ ❍♦t s♣♦ts ✐♥ ❡①tr❛❣❛❧❛❝t✐❝ r❛❞✐♦ s♦✉r❝❡s❀ Pr♦❝❡❡❞✐♥❣s ♦❢ t❤❡ ❲♦r❦s❤♦♣✱ ❚❡❣❡r♥s❡❡✱ ❋❡❞❡r❛❧ ❘❡♣✉❜❧✐❝ ♦❢ ●❡r♠❛♥②✱ ❋❡❜✳ ✽✲✶✷ ✶✾✽✽✱ ✷✻✺✳ ❬❙❡❧❦♦✇✐t③ ❛♥❞ ❇❧❛❝❦♠❛♥✱ ✷✵✵✹❪ ❙❡❧❦♦✇✐t③✱ ❘✳✱ ❛♥❞ ❊✳ ●✳ ❇❧❛❝❦♠❛♥ ✭✷✵✵✹✮✱ ❙t♦❝❤❛st✐❝ ❋❡r♠✐ ❛❝❝❡❧❡r❛t✐♦♥ ♦❢ s✉❜r❡❧❛t✐✈✐st✐❝ ❡❧❡❝tr♦♥s ❛♥❞ ✐ts r♦❧❡ ✐♥ ✐♠♣✉❧s✐✈❡ s♦❧❛r ✢❛r❡s✱ ▼♦♥✳ ◆♦t✐❝❡s ❘♦②✳ ❆str♦♥✳ ❙♦❝✳ ❬❙❤❡♥✱ ✶✾✻✺❪ ✸✺✹✭✸✷✼✮✱ ✽✼✵✳ ❙❤❡♥✱ ❈✳ ❙✳ ✭✶✾✻✺✮✱ ❚r❛♥s✐t ❆❝❝❡❧❡r❛t✐♦♥ ♦❢ ❈❤❛r❣❡❞ P❛rt✐❝❧❡s ✐♥ ❛♥ ■♥❤♦♠♦❣❡♥❡♦✉s ❊❧❡❝✲ tr♦♠❛❣♥❡t✐❝ ❋✐❡❧❞✱ ❆♣❏ ❬❙❤❡♠❛♥s❦② ❛♥❞ ❙♠✐t❤✱ ✶✾✽✸❪ ✶✹✶✱ ✶✵✾✶✳ ❙❤❡♠❛♥s❦②✱ ❉✳ ❛♥❞ ●✳ ❘✳ ❙♠✐t❤ ✭✶✾✽✸✮✱ ❲❤❡♥✲ ❝❡ ❝♦♠❡s t❤❡ ✏❚✐t❛♥✑ t♦r✉s✳ ❊♦s✿ ❚r❛♥s✳ ❆●❯ ✻✸✱ ✶✵✶✾✳ ❬❙❤❡♠❛♥s❦② ❛♥❞ ❍❛❧❧✱ ✶✾✾✷❪ ❙❤❡♠❛♥s❦②✱ ❉✳ ❊✳ ❛♥❞ ❉✳ ❚✳ ❍❛❧❧ ✭✶✾✾✷✮✱ ❚❤❡ ❞✐str✐❜✉t✐♦♥ ♦❢ ❛t♦♠✐❝ ❤②❞r♦❣❡♥ ✐♥ t❤❡ ♠❛❣♥❡✲ t♦s♣❤❡r❡ ♦❢ ❙❛t✉r♥✱ ❏✳ ●❡♦♣❤②s✳ ❘❡s✳ ❬❙❤❡♠❛♥s❦② ❡t ❛❧✳✱ ✶✾✾✸❪ ✾✼✱ ✹✶✹✸✳ ❙❤❡♠❛♥s❦②✱ ❉✳ ❊✳✱ P✳ ▼❛t❤❡s♦♥✱ ❉✳ ❚✳ ❍❛❧❧ ❡t✳ ❛❧✳ ✭✶✾✾✸✮✱ ❉❡t❡❝t✐♦♥ ♦❢ t❤❡ ❤②❞r♦①②❧ r❛❞✐❝❛❧ ✐♥ t❤❡ ❙❛t✉r♥ ♠❛❣♥❡t♦s♣❤❡r❡✱ ◆❛t✉r❡ ✸✻✸✭✻✹✷✼✮✱ ✸✷✾✳ ❬❙❤❡♣♣❛r❞✱ ✷✵✵✼❪ ❙❤❡♣♣❛r❞✱ ❙✳ ❙✳ ✭✷✵✵✼✮✱ ❤tt♣✿✴✴✇✇✇✳✐❢❛✳❤❛✇❛✐✐✳❡❞✉✴⑦s❤❡♣♣❛r❞✴s❛t❡❧❧✐t❡s✳ ❬❙❤✐ ❡t ❛❧✳✱ ✶✾✾✺❪ ❙❤✐✱ ▼✳✱ ❘✳ ❆✳ ❇❛r❛❣✐♦❧❛✱ ❉✳ ❊✳ ●r♦s❥❡❛♥ ❡t✳ ❛❧✳ ✭✶✾✾✺✮✱ ❙♣✉tt❡r✐♥❣ ♦❢ ✇❛t❡r ✐❝❡ s✉r❢❛❝❡s ❛♥❞ t❤❡ ♣r♦❞✉❝t✐♦♥ ♦❢ ❡①t❡♥❞❡❞ ♥❡✉tr❛❧ ❛t♠♦s♣❤❡✲ r❡s✱ ❏✳ ●❡♦♣❤②s✳ ❘❡s✳ ✶✵✵✱ ✷✻✸✽✼✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❇✐❜❧✐♦❣r❛❢í❛ ❬❙✐❝❛r❞②✱ ✷✵✵✺❪ ✶✺✼ ❙✐❝❛r❞②✱ ❇✳ ✭✷✵✵✺✮✱ ❉②♥❛♠✐❝s ❛♥❞ ❝♦♠♣♦s✐t✐♦♥ ✱ ❙♣❛❝❡ ❙❝✐❡♥❝❡ ❘❡✈✐❡✇s ✶✶✻✱ ✹✺✼✳ ♦❢ r✐♥❣s ❬❙✐♠♣s♦♥ ❡t ❛❧✳✱ ✶✾✽✵❪ ❙✐♠♣s♦♥✱ ❏✳❆✳✱ ❚✳ ❙✳ ❇❛st✐❛♥✱ ❉✳ ▲✳ ❈❤❡♥❡tt❡ ❡t✳ ❛❧✳ ✭✶✾✽✵✮✱ ❚❤❡ tr❛♣♣❡❞ r❛❞✐❛t✐♦♥s ♦❢ ❙❛t✉r♥ ✱ ❏✳ ❛♥❞ t❤❡✐r ❛❜s♦r♣t✐♦♥ ❜② s❛t❡❧❧✐t❡s ❛♥❞ r✐♥❣s ●❡♦♣❤②s✳ ❘❡s✳ ✽✺✱ ✺✼✸✶✳ ❬❙✐tt❧❡r ❡t ❛❧✳✱ ✶✾✽✸❪ ❙✐tt❧❡r ❏r✳✱ ❊✳ ❈✳✱ ❑✳ ❲✳ ❖❣✐❧✈✐❡ ❛♥❞ ❏✳ ❉✳ ❙❝✉❞❞❡r ✭✶✾✽✸✮✱ ❙✉r✈❡② ♦❢ ❧♦✇✲❡♥❡r❣② ♣❧❛s♠❛ ❡❧❡❝tr♦♥s ✐♥ ❙❛t✉r♥✬s ♠❛❣♥❡t♦s♣❤❡r❡ ✲ ❱♦②❛✲ ✱ ❏✳ ●❡♦♣❤②s✳ ❘❡s✳ ✽✽✱ ✽✽✹✼✳ ❣❡rs ✶ ❛♥❞ ✷ ❬❙✐tt❧❡r ❡t ❛❧✳✱ ✷✵✵✺❪ ❙✐tt❧❡r ❏r✳✱ ❊✳ ❈✳✱ ❘✳ ❊✳ ❍❛rt❧❡✱ ❆✳ ❋✳ ❱✐✲ ñ❛s ❡t✳ ❛❧✳ ✭✷✵✵✺✮✱ ❙❛t✉r♥✬s ❚✐t❛♥ ♠❛❣♥❡t♦s♣❤❡r❡✿ ✐♥t❡r❛❝t✐♦♥ ❱♦②❛❣❡r ✶ ✇✐t❤ r❡s✉❧ts ❏✳ ●❡♦♣❤②s✳ ❘❡s✳ ✶✶✵✱ ❆✵✾✸✵✷✱ r❡✈✐s✐t❡❞✱ ❞♦✐✿✶✵✳✶✵✷✾✴✷✵✵✹❏❆✵✶✵✼✺✾✳ ❬❙✐tt❧❡r ❡t ❛❧✳✱ ✷✵✵✻❪ ❙✐tt❧❡r ❏r✳✱ ❊✳ ❈✳✱ ❘✳ ❊✳ ❏♦❤♥s♦♥✱ ❍✳ ❚✳ ❙♠✐t❤ ❡t✳ ❛❧✳ ✭✷✵✵✻✮✱ ❣❡♥ ♦❢ ✐♦♥s ✇✐t❤✐♥ t❤❡ ❊♥❡r❣❡t✐❝ ✐♥♥❡r ♥✐tr♦✲ ♠❛❣♥❡t♦s♣❤❡r❡ ✱ ❏✳ ●❡♦♣❤②s✳ ❘❡s✳ ✶✶✶✱ ❆✵✾✷✷✸✱ ❙❛t✉r♥ ❞♦✐✿✶✵✳✶✵✷✾✴✷✵✵✹❏❆✵✶✵✺✵✾✳ ❬❙♠✐t❤ ❡t ❛❧✳✱ ✷✵✵✹❪ ❙♠✐t❤✱ ❍✳ ❚✳✱ ❘✳ ❊✳ ❏♦❤♥s♦♥ ❛♥❞ ❱✳ ▲✳ ❙❤❡♠❛✲ t♦✈✐❝❤ ✭✷✵✵✹✮✱ ❚✐t❛♥✬s ❛t♦♠✐❝ ❛♥❞ ♠♦❧❡❝✉❧❛r ✱ ●❡♦♣❤②s✳ ❘❡s✳ ▲❡tt✳ ✸✶✱ ▲✶✻✽✵✹✳ ♥✐tr♦❣❡♥ t♦r✐ ❬❙♦❞❡r❜❧♦♠ ❛♥❞ ❏♦❤♥s♦♥✱ ✶✾✽✷❪ ❙♦❞❡r❜❧♦♠✱ ▲✳ ❆✳ ❛♥❞ ❚✳ ❱✳ ❏♦❤♥s♦♥ ✭✶✾✽✷✮✱ ❚❤❡ ♠♦♦♥s ♦❢ ✱ ❙❝✐❡♥t✐✜❝ ❆♠❡r✐❝❛♥ ❙❛t✉r♥ ✷✹✻✱ ✶✵✶✳ ❬❙♣❛❤♥ ❡t ❛❧✳✱ ✷✵✵✻❪ ❙♣❛❤♥✱ ❋✳✱ ❏✳ ❙❝❤♠✐❞t✱ ◆✳ ❆❧❜❡rs ❡t✳ ❛❧✳ ✭✷✵✵✻✮✱ ❈❛ss✐♥✐ ❉✉st ▼❡❛s✉r❡♠❡♥ts ❛t ❊♥❝❡❧❛❞✉s ❛♥❞ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❇✐❜❧✐♦❣r❛❢í❛ ✶✺✽ ■♠♣❧✐❝❛t✐♦♥s ❢♦r t❤❡ ❖r✐❣✐♥ ♦❢ t❤❡ ❊ ❘✐♥❣✱ ❙❝✐❡♥❝❡ ❬❙♣❡✐s❡r✱ ✶✾✻✺❪ ✸✶✶✱ ✶✹✶✻✳ ❙♣❡✐s❡r✱ ❚✳ ❲✳ ✭✶✾✻✺✮✱ P❛rt✐❝❧❡ ❚r❛❥❡❝t♦r✐❡s ✐♥ ❛ ▼♦❞❡❧ ❈✉rr❡♥t ❙❤❡❡t✱ ❇❛s❡❞ ♦♥ t❤❡ ❖♣❡♥ ▼♦❞❡❧ ♦❢ t❤❡ ▼❛❣♥❡t♦s♣❤❡r❡✱ ✇✐t❤ ❆♣♣❧✐❝❛t✐♦♥s t♦ ❆✉r♦r❛❧ P❛rt✐❝❧❡s✱ ❏✳ ●❡♦♣❤②s✳ ❘❡s✳ ✼✵✱ ✶✼✶✼✳ ❬❙♣❡♥❝❡r ❡t✳ ❛❧✳✱ ✷✵✵✻❪ ❙♣❡♥❝❡r✱ ❏✳ ❘✳✱ ❏✳ ❈✳ P❡❛r❧✱ ▼✳ ❙❡❣✉r❛ ❡t✳ ❛❧✳ ✭✷✵✵✻✮✱ ❈❛ss✐♥✐ ❊♥❝♦✉♥t❡rs ❊♥❝❡❧❛❞✉s✿ ❇❛❝❦✲ ❣r♦✉♥❞ ❛♥❞ t❤❡ ❉✐s❝♦✈❡r② ♦❢ ❛ ❙♦✉t❤ P♦❧❛r ❍♦t ❙♣♦t✱ ❙❝✐❡♥❝❡ ✸✶✶✱ ✶✹✵✶✳ ❬❙♣✐❧❦❡r ❡t✳ ❛❧✳✱ ✷✵✵✻❪ ❙♣✐❧❦❡r✱ ▲✳ ❏✳✱ ❙✳ ❍✳ P✐❧♦r③✱ ❈✳ ❋❡rr❛r✐ ❡t✳ ❛❧✳ ✭✷✵✵✻✮✱ ❈❛ss✐♥✐ ❈■❘❙ ♦❜s❡r✈❛t✐♦♥s ♦❢ t❤❡r♠❛❧ ❞✐✛❡r❡♥❝❡s ✐♥ ❙❛t✉r♥✬s ♠❛✐♥ r✐♥❣s ✇✐t❤ ✐♥❝r❡❛✲ s✐♥❣ ♣❤❛s❡ ❛♥❣❧❡✳ P❛♣❡r ♣r❡s❡♥t❡❞ ❛t t❤❡ ✸✼t❤ ▲✉♥❛r ❛♥❞ P❧❛♥❡t❛r② ❙❝✐❡♥❝❡✱ ▲❡❛❣✉❡ ❈✐t②✱ ❚❡✲ ①❛s✱ ✶✸✲✶✼ ▼❛r❝❤ ✷✵✵✻✳ ❬❙t❡♣❤❡♥s✱ ✶✾✼✹❪ ❙t❡♣❤❡♥s✱ ▼✳ ❆✳ ✭✶✾✼✹✮✱ ❊❉❋ ❙t❛t✐st✐❝s ❢♦r ●♦♦❞♥❡ss ♦❢ ❋✐t ❛♥❞ ❙♦♠❡ ❈♦♠♣❛r✐s♦♥s✱ ❏♦✉r✲ ♥❛❧ ♦❢ t❤❡ ❆♠❡r✐❝❛♥ ❙t❛t✐st✐❝❛❧ ❆ss♦❝✐❛t✐♦♥ ✻✾✱ ✼✸✵✳ ❬❙✉♠♠❡rs ❛♥❞ ❈❤✉♥✲②✉✱ ✷✵✵✵❪ ❙✉♠♠❡rs✱ ❉✳ ❛♥❞ ▼✳ ❈❤✉♥✲②✉ ✭✷✵✵✵✮✱ ❘❛♣✐❞ ❛❝❝❡❧❡r❛t✐♦♥ ♦❢ ❡❧❡❝tr♦♥s ✐♥ t❤❡ ♠❛❣♥❡t♦s♣❤❡r❡ ❜② ❢❛st✲♠♦❞❡ ▼❍❉ ✇❛✈❡s✱ ❏✳ ●❡♦♣❤②s✳ ❘❡s✳ ✶✵✺ ✭❆✼✮✱ ✶✺✽✽✼✳ ❬❙✇❛♥♥✱ ✶✾✸✸❪ ❙✇❛♥♥✱ ❲✳ ❋✳ ●✳ ✭✶✾✸✸✮✱ ❆♣♣❧✐❝❛t✐♦♥ ♦❢ ▲✐♦✉✲ ✈✐❧❧❡✬s ❚❤❡♦r❡♠ t♦ ❊❧❡❝tr♦♥ ❖r❜✐ts ✐♥ t❤❡ ❊❛rt❤✬s ▼❛❣♥❡t✐❝ ❋✐❡❧❞✱ P❤②s✳ ❘❡✈✳ ✹✹✭✸✮✱ ✷✷✹✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❇✐❜❧✐♦❣r❛❢í❛ ❬❱❛♥ ❆❧❧❡♥✱ ✶✾✽✹❪ ✶✺✾ ❱❛♥ ❆❧❧❡♥✱ ❏✳ ❆✳ ✭✶✾✽✹✮✱ ❊♥❡r❣❡t✐❝ ♣❛rt✐❝❧❡s ✐♥ t❤❡ ✐♥♥❡r ♠❛❣♥❡t♦s♣❤❡r❡ ♦❢ ❙❛t✉r♥✱ ✐♥ ❙❛✲ t✉r♥✱ ❡❞✐t❡❞ ❜② ❚✳ ●❡❤r❡❧s ❛♥❞ ▼✳❙✳ ▼❛tt✲ ❤❡✇s✱ ✷✽✶✳ ❬❱❛♥ ❆❧❧❡♥✱ ✶✾✽✻❪ ❱❛♥ ❆❧❧❡♥✱ ❏✳ ❆✳ ✭✶✾✽✻✮✱ ❆♥ ✉♣♣❡r ❧✐♠✐t ♦♥ s❤❡♣❤❡r❞✐♥❣ s❛t❡❧❧✐t❡s ❛t ❙❛t✉r♥✬s ❘✐♥❣ ●✱ Pr♦✲ ❣r❡ss ❘❡♣♦rt ■♦✇❛ ❯♥✐✈✳✱ ■♦✇❛ ❈✐t②✳ ❉❡♣t✳ ♦❢ P❤②s✐❝s ❛♥❞ ❆str♦♥♦♠②✳ ❬❱❛s✉♥❞❤❛r❛ ❡t ❛❧✳✱ ✶✾✽✹❪ ❱❛s✉♥❞❤❛r❛✱ ❘✳✱ P✳ ❙❛♥t❤❛♥❛♠ ❛♥❞ ▼✳ ❘♦③❛✲ r✐♦ ✭✶✾✽✹✮✱ P♦ss✐❜❧❡ ❖❝❝✉❧t❛t✐♦♥ ❜② ❙❛t✉r♥✐❛♥ ▼❛❣♥❡t♦s♣❤❡r✐❝ ❘✐♥❣✱ ■❆❯ ❈✐r❝✳ ◆♦✳ ✸✾✹✶✱ ✸✾✹✺✳ ❬❱♦❣t ❡t ❛❧✳✱ ✶✾✽✷❪ ❱♦❣t✱ ❘✳ ❊✳✱ ❉✳ ▲✳ ❈❤❡♥❡tt❡✱ ❆✳ ❈✳ ❈✉♠♠✐♥❣s ❡t✳ ❛❧✳ ✭✶✾✽✷✮✱ ❊♥❡r❣❡t✐❝ ❝❤❛r❣❡❞ ♣❛rt✐❝❧❡s ✐♥ ❙❛t✉r♥✬s ♠❛❣♥❡t♦s♣❤❡r❡ ✲ ❱♦②❛❣❡r ✷ r❡s✉❧ts✱ ❙❝✐❡♥❝❡ ✷✶✺✱ ✺✼✼✳ ❬❲❛❤❧✉♥❞ ❡t ❛❧✳✱ ✷✵✵✺❪ ❲❛❤❧✉♥❞✱ ❏✳ ❊✳✱ ❘✳ ❇♦strö♠✱ ●✳ ●✉st❛❢ss♦♥ ❡t✳ ❛❧✳ ✭✷✵✵✺✮✱ ❚❤❡ ✐♥♥❡r ♠❛❣♥❡t♦s♣❤❡r❡ ♦❢ ❙❛✲ t✉r♥✿ ❈❛ss✐♥✐ ❘P❲❙ ❝♦❧❞ ♣❧❛s♠❛ r❡s✉❧ts ❢r♦♠ t❤❡ ✜rst ❡♥❝♦✉♥t❡r✱ ●❡♦♣❤②s✳ ❘❡s✳ ▲❡tt✳ ✸✷✱ ▲✷✵❙✵✾✱ ❞♦✐✿✶✵✳✶✵✷✾✴✷✵✵✺●▲✵✷✷✻✾✾✳ ❬❲❡✐❞❡♥s❝❤✐❧❧✐♥❣ ❡t ❛❧✳✱ ✶✾✽✹❪ ❲❡✐❞❡♥s❝❤✐❧❧✐♥❣✱ ❙✳ ❏✳✱ ❈✳ ❘✳ ❈❤❛♣♠❛♥✱ ❉✳ ❘✳ ❉❛✈✐s ❡t✳ ❛❧✳ ✭✶✾✽✹✮✱ ❘✐♥❣ ♣❛rt✐❝❧❡s✿ ❝♦❧❧✐s✐♦✲ ♥❛❧ ✐♥t❡r❛❝t✐♦♥s ❛♥❞ ♣❤②s✐❝❛❧ ♥❛t✉r❡✱ ✐♥ P❧❛✲ ♥❡t❛r② ❘✐♥❣s✱ ✭❡❞s✳ ❘✳ ●r❡❡♥❜❡r❣ ❛♥❞ ❆✳ ❇r❛❤✐❝✮✱ ❯♥✐✈❡rs✐t② ♦❢ ❆r✐③♦♥❛ Pr❡ss✱ ✸✻✼✳ ❬❨❡❧❧❡ ❡t ❛❧✳✱ ✷✵✵✻❪ ❨❡❧❧❡✱ ❘✳ ❱✳✱ ◆✳ ❇♦r❣❣r❡♥✱ ❱✳ ❞❡ ❧❛ ❍❛②❡ ❡t✳ ❛❧✳ ✭✷✵✵✻✮✱ ❚❤❡ ✈❡rt✐❝❛❧ str✉❝t✉r❡ ♦❢ ❚✐t❛♥✬s ✉♣✲ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❇✐❜❧✐♦❣r❛❢í❛ ✶✻✵ ♣❡r ❛t♠♦s♣❤❡r❡ ❢r♦♠ ❈❛ss✐♥✐ ■♦♥ ◆❡✉tr❛❧ ▼❛ss ❙♣❡❝tr♦♠❡t❡r ♠❡❛s✉r❡♠❡♥ts✱ ❬❨♦✉♥❣ ❡t ❛❧✳✱ ✷✵✵✺❪ ✶✽✷✱ ✺✻✼✳ ❨♦✉♥❣✱ ❉✳ ❚✳✱ ❏✳ ❏✳ ❇❡rt❤❡❧✐❡r✱ ▼✳ ❇❧❛♥❝ ❡t✳❛❧✳ ✭✷✵✵✺✮✱ ❈♦♠♣♦s✐t✐♦♥ ❛♥❞ ❉②♥❛♠✐❝s ♦❢ P❧❛s♠❛ ✐♥ ❙❛t✉r♥✬s ▼❛❣♥❡t♦s♣❤❡r❡✱ ❬❩❡❜❦❡r ❛♥❞ ❚②❧❡r✱ ✶✾✽✹❪ ■❝❛r✉s ❙❝✐❡♥❝❡ ✸✵✼✱ ✶✷✻✷✳ ❩❡❜❦❡r✱ ❍✳ ❆✳ ❛♥❞ ●✳ ▲✳ ❚②❧❡r ✭✶✾✽✹✮✱ ❚❤✐❝❦✲ ♥❡ss ♦❢ ❙❛t✉r♥✬s r✐♥❣s ✐♥❢❡rr❡❞ ❢r♦♠ ❱♦②❛❣❡r ✶ ♦❜s❡r✈❛t✐♦♥s ♦❢ ♠✐❝r♦✇❛✈❡ s❝❛tt❡r✱ ❙❝✐❡♥❝❡ ✷✷✸✱ ✸✾✻✳ ❬❩❡❜❦❡r ❡t ❛❧✳✱ ✶✾✽✺❪ ❩❡❜❦❡r✱ ❍✳ ❆✳✱ ❊✳ ❆✳ ▼❛r♦✉❢ ❛♥❞ ●✳ ▲✳ ❚②✲ ❧❡r ✭✶✾✽✺✮✱ ❙❛t✉r♥✬s r✐♥❣s✲P❛rt✐❝❧❡ s✐③❡ ❞✐str✐✲ ❜✉t✐♦♥s ❢♦r t❤✐♥ ❧❛②❡r ♠♦❞❡❧✱ ■❝❛r✉s ✻✹✱ ✺✸✶✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❆♣é♥❞✐❝❡ ❆ Pr✉❡❜❛s ❞❡ ❤✐♣ót❡s✐s ❞❡ ❜♦♥❞❛❞ ❞❡ ❛❥✉st❡ ❯♥❛ ❤✐♣ót❡s✐s ❡st❛❞íst✐❝❛ s❡ ❞❡✜♥❡ ❝♦♠♦ ✉♥❛ ❛✜r♠❛❝✐ó♥ ♦ ❝♦♥❥❡t✉r❛ ❛❝❡r❝❛ ❞❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ f (x, θ) ❞❡ ✉♥❛ ♦ ♠ás ✈❛r✐❛❜❧❡s ❛❧❡❛t♦r✐❛s✳ ❊st❛ ❞✐str✐❜✉❝✐ó♥ ♣✉❡❞❡ t❡♥❡r ✉♥♦ ♦ ♠ás ♣❛rá♠❡tr♦s ❞❡s❝♦♥♦❝✐❞♦s✱ ❞❡♥♦t❛❞♦s ♣♦r θ ② ❧❛ ❤✐♣ót❡s✐s s❡ r❡❧❛❝✐♦♥❛ ❝♦♥ ❡st❡ ♣❛rá♠❡tr♦ ♦ ❝♦♥❥✉♥t♦ ❞❡ ♣❛rá♠❡tr♦s✳ ❊♥ ♦tr♦s ❝❛s♦s✱ s❡ ❞❡s❝♦♥♦❝❡ ♣♦r ❝♦♠♣❧❡t♦ ❧❛ ❢♦r♠❛ ❞❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ ② ❧❛ ❤✐♣ót❡s✐s ❡♥t♦♥❝❡s s❡ r❡❧❛❝✐♦♥❛ ❝♦♥ ✉♥❛ ❞✐str✐❜✉❝✐ó♥ ❡s♣❡❝í✜❝❛ f (x, θ) q✉❡ ♣✉❡❞❡ s❡r ❛s✐❣♥❛❞❛ ❛❧ ❝♦♥❥✉♥t♦ ❞❡ ❞❛t♦s ❞❡ ❧❛ ♠✉❡str❛✳ ❊♥ ❡st❡ tr❛❜❛❥♦ ❡❧ ♣r♦❜❧❡♠❛ ❡s ✈❡r✐✜❝❛r s✐ ❡❧ ❝♦♥❥✉♥t♦ ❞❡ ❞❛t♦s s❡ ♣✉❡❞❡ ❛❥✉st❛r ♦ ❛✜r♠❛r q✉❡ ♣r♦✈✐❡♥❡ ❞❡ ✉♥❛ ❞❡t❡r♠✐♥❛❞❛ ❞✐str✐❜✉❝✐ó♥✳ ▲❛s ♣r✉❡❜❛s ❡st❛❞íst✐❝❛s q✉❡ tr❛t❛♥ ❡st❡ ♣r♦❜❧❡♠❛ r❡❝✐❜❡♥ ❡❧ ♥♦♠❜r❡ ❣❡♥❡r❛❧ ❞❡ ✏Pr✉❡❜❛s ❞❡ ❇♦♥❞❛❞ ❞❡ ❆❥✉st❡✑✳ ❙❡ ❛♥❛❧✐③❛rá♥ ❞♦s ♣r✉❡❜❛s ❜ás✐❝❛s q✉❡ ♣✉❡❞❡♥ ❛♣❧✐❝❛rs❡✿ ❧❛ ♣r✉❡❜❛ χ2 ② ❧❛ ♣r✉❡❜❛ ❞❡ ❑♦❧♠♦❣♦r♦✈✲❙♠✐r♥♦✈✳ ❆♠❜❛s ♣r✉❡❜❛s ❡stá♥ ❜❛s❛❞❛s ❡♥ ❧❛ ❤✐♣ót❡s✐s ♥✉❧❛ ❞❡ q✉❡ ♥♦ ❤❛② ❞✐❢❡r❡♥❝✐❛s s✐❣♥✐✜❝❛t✐✈❛s ❡♥tr❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ ♠✉❡str❛❧ ② ❧❛ t❡ór✐❝❛✿ H0 : f (x, θ) = f0 (x, θ) H1 : f (x, θ) 6= f0 (x, θ) ❞♦♥❞❡ f0 (x, θ) ❡s ❧❛ ❞✐str✐❜✉❝✐ó♥ q✉❡ s❡ s✉♣♦♥❡ s✐❣✉❡ ❧❛ ♠✉❡str❛ ❛❧❡❛t♦r✐❛✳ ▲❛ ❤✐♣ót❡s✐s ❛❧t❡r♥❛t✐✈❛ s✐❡♠♣r❡ s❡ ❡♥✉♥❝✐❛ ❝♦♠♦ q✉❡ ❧♦s ❞❛t♦s ♥♦ s✐❣✉❡♥ ❧❛ ❞✐str✐❜✉❝✐ó♥ ✶✻✶ ❆♣é♥❞✐❝❡ ❆✳ Pr✉❡❜❛s ❞❡ ❤✐♣ót❡s✐s ❞❡ ❜♦♥❞❛❞ ❞❡ ❛❥✉st❡ ✶✻✷ s✉♣✉❡st❛✳ ❙✐ s❡ ❞❡s❡❛ ❡①❛♠✐♥❛r ♦tr❛ ❞✐str✐❜✉❝✐ó♥ ❡s♣❡❝í✜❝❛✱ ❞❡❜❡rá r❡❛❧✐③❛rs❡ ❞❡ ♥✉❡✈♦ ❧❛ ♦tr❛ ♣r✉❡❜❛ s✉♣♦♥✐❡♥❞♦ q✉❡ ❧❛ ❤✐♣ót❡s✐s ♥✉❧❛ ❡s ❡st❛ ♥✉❡✈❛ ❞✐str✐❜✉❝✐ó♥✳ ❆❧ ❡s♣❡❝✐✜❝❛r ❧❛ ❤✐♣ót❡s✐s ♥✉❧❛✱ ❡❧ ❝♦♥❥✉♥t♦ ❞❡ ♣❛rá♠❡tr♦s ❞❡✜♥✐❞♦s ♣♦r θ ♣✉❡❞❡ s❡r ❝♦♥♦❝✐❞♦ ♦ ❞❡s❝♦♥♦❝✐❞♦✳ ❊♥ ❝❛s♦ ❞❡ q✉❡ ❧♦s ♣❛rá♠❡tr♦s s❡❛♥ ❞❡s❝♦♥♦❝✐❞♦s✱ ❡s ♥❡❝❡s❛r✐♦ ❡st✐♠❛r❧♦s✳ P❛r❛ ❢♦r♠✉❧❛r ❧❛ ❤✐♣ót❡s✐s ♥✉❧❛ ❞❡❜❡rá♥ t❡♥❡rs❡ ❡♥ ❝✉❡♥t❛ ❧♦s s✐❣✉✐❡♥t❡s ❛s♣❡❝t♦s ♦ ❝r✐t❡r✐♦s✿ ✶✳ ▲❛ ♥❛t✉r❛❧❡③❛ ❞❡ ❧♦s ❞❛t♦s ❛ ❛♥❛❧✐③❛r✳ P♦r ❡❥❡♠♣❧♦✱ s✐ s❡ ❞❡s❡❛ ✐♥✈❡st✐❣❛r ❧❛ ❞✐str✐❜✉❝✐ó♥ q✉❡ s✐❣✉❡♥ ❧♦s t✐❡♠♣♦s ❞❡ ❢❛❧❧❛ ❞❡ ✉♥♦s ❝♦♠♣♦♥❡♥t❡s✱ ❡s ♣♦s✐✲ ❜❧❡ ♣❡♥s❛r ❡♥ ✉♥❛ ❞✐str✐❜✉❝✐ó♥ ❡①♣♦♥❡♥❝✐❛❧✱ ♦ ✉♥❛ ❞✐str✐❜✉❝✐ó♥ ❣❛♠❛ ♦ ✉♥❛ ❞✐str✐❜✉❝✐ó♥ ❲❡✐❜✉❧❧✱ ♣❡r♦ ♥♦ ✉♥❛ ❞✐str✐❜✉❝✐ó♥ ♥♦r♠❛❧✳ ✷✳ ❍✐st♦❣r❛♠❛✳ ▲❛ ❢♦r♠❛ q✉❡ t♦♠❡ ❡❧ ❤✐st♦❣r❛♠❛ ❞❡ ❢r❡❝✉❡♥❝✐❛ ❡s q✉✐③ás ❧❛ ♠❡❥♦r ✐♥❞✐❝❛❝✐ó♥ ❞❡❧ t✐♣♦ ❞❡ ❞✐str✐❜✉❝✐ó♥ ❛ ❝♦♥s✐❞❡r❛r✳ ❆✳✵✳✷✳ Pr✉❡❜❛ χ2 ▲❛ ♣r✉❡❜❛ χ2 s❡ ❜❛s❛ ❡♥ ❧❛ ❝♦♠♣❛r❛❝✐ó♥ ❡♥tr❡ ❧❛ ❢r❡❝✉❡♥❝✐❛ ♦❜s❡r✈❛❞❛ ❡♥ ✉♥ ✐♥t❡r✈❛❧♦ ❞❡ ❝❧❛s❡ ② ❧❛ ❢r❡❝✉❡♥❝✐❛ ❡s♣❡r❛❞❛ ❡♥ ❞✐❝❤♦ ✐♥t❡r✈❛❧♦✱ ❝❛❧❝✉❧❛❞❛ ❞❡ ❛❝✉❡r❞♦ ❝♦♥ ❧❛ ❤✐♣ót❡s✐s ♥✉❧❛ ❢♦r♠✉❧❛❞❛✳ ❊s ❞❡❝✐r✱ s❡ q✉✐❡r❡ ❞❡t❡r♠✐♥❛r s✐ ❧❛s ❢r❡❝✉❡♥❝✐❛s ♦❜s❡r✈❛❞❛s ❡♥ ❧❛ ♠✉❡str❛ ❡stá♥ ❧♦ s✉✜❝✐❡♥t❡♠❡♥t❡ ❝❡r❝❛ ❞❡ ❧❛s ❢r❡❝✉❡♥❝✐❛s ❡s♣❡r❛❞❛s ❜❛❥♦ ❧❛ ❤✐♣ót❡s✐s ♥✉❧❛✳ P❛r❛ ❡st❛ ♣r✉❡❜❛ ❡s ♥❡❝❡s❛r✐♦ ❛❣r✉♣❛r ♦ ❞✐str✐❜✉✐r ❧❛s ♦❜s❡r✈❛❝✐♦♥❡s ❞❡ ❧❛ ♠✉❡str❛ ❡♥ ✐♥t❡r✈❛❧♦s ❞❡ ❝❧❛s❡✱ ♣r❡❢❡r✐❜❧❡♠❡♥t❡ ❞❡❧ ♠✐s♠♦ t❛♠❛ñ♦✳ ❊❧ ❡st❛❞íst✐❝♦ ❞❡ ♣r✉❡❜❛ ❡stá ❞❡✜♥✐❞♦ ❝♦♠♦✿ χ2 = k X (Oi − Ei )2 i=1 Ei ❞♦♥❞❡✿ Oi ❡s ❡❧ t♦t❛❧ ❞❡ ✈❛❧♦r❡s q✉❡ ❝❛❡♥ ❡♥ ❡❧ ✐♥t❡r✈❛❧♦ ✐ ❀ Ei ❡s ❡❧ ♥ú♠❡r♦ ❡s♣❡r❛❞♦ ❞❡ ✈❛❧♦r❡s ❡♥ ❡❧ ✐♥t❡r✈❛❧♦ ✐✱ ❦ ❡s ❡❧ ♥ú♠❡r♦ ❞❡ ✐♥t❡r✈❛❧♦s ❞❡ ❝❧❛s❡ ❡♥ q✉❡ s❡ ❞✐str✐❜✉②❡♥ ❧❛s ♦❜s❡r✈❛❝✐♦♥❡s✳ ❈❛❜❡ ♠❡♥❝✐♦♥❛r q✉❡ ❧❛s ❝❧❛s❡s ② ❧❛s ❢r❡❝✉❡♥❝✐❛s ♦❜s❡r✈❛❞❛s s❡ ♦❜t✐❡♥❡♥ ❞✐r❡❝t❛♠❡♥t❡ ❞❡ ❝✉❛❧q✉✐❡r ♣❛q✉❡t❡ ❡st❛❞íst✐❝♦✳ ❙✐ ❧♦s ❧í♠✐t❡s ❞❡❧ ✐♥t❡r✈❛❧♦ ❞❡ ❝❧❛s❡ ✐ ❡stá♥ ❞❛❞♦s ♣♦r xi−1 ② xi ✱ ❡❧ ♥ú♠❡r♦ ❡s♣❡r❛❞♦ ❞❡ ♦❜s❡r✈❛❝✐♦♥❡s ♣❛r❛ ❡s❡ ✐♥t❡r✈❛❧♦ ❡stá ❞❛❞♦ ♣♦r✿ Ei = nPi ❞♦♥❞❡ Pi r❡♣r❡s❡♥t❛ ❧❛ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❆♣é♥❞✐❝❡ ❆✳ Pr✉❡❜❛s ❞❡ ❤✐♣ót❡s✐s ❞❡ ❜♦♥❞❛❞ ❞❡ ❛❥✉st❡ ✶✻✸ ♣r♦❜❛❜✐❧✐❞❛❞ ❞❡ q✉❡ ✉♥❛ ♦❜s❡r✈❛❝✐ó♥ q✉❡❞❡ ❡♥ ❡❧ ✐♥t❡r✈❛❧♦ ✐✱ ❞❡ ❛❝✉❡r❞♦ ❝♦♥ ❢✉♥❝✐ó♥ ❞❡ ❞❡♥s✐❞❛❞ q✉❡ s❡ ❡sté ❛♥❛❧✐③❛♥❞♦✱ ② ♥ ❡s ❡❧ ♥ú♠❡r♦ t♦t❛❧ ❞❡ ♦❜s❡r✈❛❝✐♦♥❡s✳ ▲❛ ♣r♦❜❛❜✐❧✐❞❛❞ ❞❡ q✉❡ ✉♥❛ ♦❜s❡r✈❛❝✐ó♥ ❝❛✐❣❛ ❡♥ ❡❧ ✐♥t❡r✈❛❧♦ ✐ ❡stá ❞❛❞❛ ♣♦r✿ Pi = P (xi−1 ≤ x < xi ) = xi Z f0 (x, θ) dx xi−1 s✐❡♥❞♦ f0 (x, θ) ❧❛ ❢✉♥❝✐ó♥ ❞❡ ❞❡♥s✐❞❛❞ ❞❡ ❧❛ ✈❛r✐❛❜❧❡ ❛❧❡❛t♦r✐❛ ❳ ❜❛❥♦ ❧❛ ❤✐♣ót❡s✐s ♥✉❧❛✳ ❊♥ ❡st❛ ♣r✉❡❜❛ ❞❡ ❤✐♣ót❡s✐s s❡ ❛❝❡♣t❛ ❧❛ ❤✐♣ót❡s✐s ♥✉❧❛ s✐ χ2 ≤ χ2k−1−p,α ✱ ❞♦♥❞❡ ❡❧ ✈❛❧♦r χ2k−1−p,α r❡♣r❡s❡♥t❛ ❡❧ ✈❛❧♦r ❞❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ χ2 ❝♦♥ ❦✲✶✲♣ ❣r❛❞♦s ❞❡ ❧✐❜❡rt❛❞ ② ✉♥ ♥✐✈❡❧ ❞❡ s✐❣♥✐✜❝❛♥❝✐❛ α ✳ ❆✳✵✳✸✳ Pr✉❡❜❛ ❞❡ ❑♦❧♠♦❣♦r♦✈✲❙♠✐r♥♦✈ ❊♥ ❡st❛ ♣r✉❡❜❛ ✭♣❡rt❡♥❡❝✐❡♥t❡ ❛ ❧❛ ❊st❛❞íst✐❝❛ ◆♦ P❛r❛♠étr✐❝❛✮ t❛♠❜✐é♥ s❡ ❡stá ✐♥t❡r❡s❛❞♦ ❡♥ ❡❧ ❣r❛❞♦ ❞❡ ❝♦♥❝♦r❞❛♥❝✐❛ ❡♥tr❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ ❞❡ ❢r❡❝✉❡♥❝✐❛ ♠✉❡str❛❧ ② ❧❛ ❞✐str✐❜✉❝✐ó♥ ❞❡ ❢r❡❝✉❡♥❝✐❛ t❡ór✐❝❛✱ ❜❛❥♦ ❧❛ ❤✐♣ót❡s✐s ♥✉❧❛ ❞❡ q✉❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ ❞❡ ❧❛ ♠✉❡str❛ ❡s f0 (x, θ) ② ♣r♦❜❛r q✉❡ ♥♦ ❡①✐st❡ ❞✐❢❡r❡♥❝✐❛ s✐❣♥✐✜❝❛t✐✈❛✳ ▲❛ ♣r✉❡❜❛ tr❛❜❛❥❛ ❝♦♥ ❧❛ ❢✉♥❝✐ó♥ ❞❡ ❞✐str✐❜✉❝✐ó♥ ✭❞✐str✐❜✉❝✐ó♥ ❞❡ ❢r❡❝✉❡♥❝✐❛ ❛❝✉♠✉❧❛t✐✈❛✮✳ ❙❡❛ F0 (x) ❧❛ ❢✉♥❝✐ó♥ ❞❡ ❞✐str✐❜✉❝✐ó♥ t❡ór✐❝❛ ♣❛r❛ ❧❛ ✈❛r✐❛❜❧❡ ❛❧❡❛t♦r✐❛ ❳✱ ② r❡♣r❡✲ s❡♥t❛ ❧❛ ♣r♦❜❛❜✐❧✐❞❛❞ ❞❡ q✉❡ ❧❛ ✈❛r✐❛❜❧❡ ❛❧❡❛t♦r✐❛ ❳ t♦♠❡ ✉♥ ✈❛❧♦r ♠❡♥♦r ♦ ✐❣✉❛❧ ❛ ① ✭t❛♠❜✐é♥ s❡ ✐♥t❡r♣r❡t❛ ❝♦♠♦ ❧❛ ♣r♦♣♦r❝✐ó♥ ❡s♣❡r❛❞❛ ❞❡ ♦❜s❡r✈❛❝✐♦♥❡s q✉❡ t❡♥❣❛♥ ✉♥ ✈❛❧♦r ♠❡♥♦r ♦ ✐❣✉❛❧ ❛ ①✮✳ ❊s ❞❡❝✐r✿ F0 (x) = P (X < x) = Z x f0 (x, θ) dx ∞ ❙❡❛ Sn (x) ❧❛ ❢✉♥❝✐ó♥ ❞❡ ❞✐str✐❜✉❝✐ó♥ ❡♠♣ír✐❝❛✱ ❝❛❧❝✉❧❛❞❛ ❛ ♣❛rt✐r ❞❡ ❧♦s ✈❛❧♦r❡s ♦❜s❡r✈❛❞♦s ❞❡ ❧❛ ♠✉❡str❛ ❞❡ ♥ ♦❜s❡r✈❛❝✐♦♥❡s✳ Sn (x) r❡♣r❡s❡♥t❛ ❧❛ ♣r♦♣♦r❝✐ó♥ ❞❡ ✈❛❧♦r❡s ♦❜s❡r✈❛❞♦s q✉❡ s♦♥ ♠❡♥♦r❡s ♦ ✐❣✉❛❧❡s ❛ ①✱ ② ❡stá ❞❡✜♥✐❞❛ ❝♦♠♦✿ Sn (x) = P (X < x| resultados muestrales) = m n ❞♦♥❞❡ ♠ ❡s ❡❧ ♥ú♠❡r♦ ❞❡ ✈❛❧♦r❡s ♦❜s❡r✈❛❞♦s q✉❡ s♦♥ ♠❡♥♦r❡s ♦ ✐❣✉❛❧❡s ❛ ①✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❆♣é♥❞✐❝❡ ❆✳ Pr✉❡❜❛s ❞❡ ❤✐♣ót❡s✐s ❞❡ ❜♦♥❞❛❞ ❞❡ ❛❥✉st❡ ✶✻✹ ❊♥ ❧❛ ♣r✉❡❜❛ ❞❡ ❑♦❧♠♦❣♦r♦✈✲❙♠✐r♥♦✈ s❡ ❡stá ✐♥t❡r❡s❛❞♦ ❡♥ ❧❛ ♠❛②♦r ❞❡s✈✐❛❝✐ó♥ ❡♥tr❡ ❧❛ ❢✉♥❝✐ó♥ ❞❡ ❞✐str✐❜✉❝✐ó♥ t❡ór✐❝❛ ② ❧❛ ❡♠♣ír✐❝❛✱ ❡s ❞❡❝✐r ❡♥tr❡ F0 (x) ② Sn (x)✱ ♣❛r❛ t♦❞♦ ❡❧ r❛♥❣♦ ❞❡ ✈❛❧♦r❡s ❞❡ ①✳ ❇❛❥♦ ❧❛ ❤✐♣ót❡s✐s ♥✉❧❛ s❡ ❡s♣❡r❛ q✉❡ ❡st❛s ❞❡s✲ ✈✐❛❝✐♦♥❡s s❡❛♥ ♣❡q✉❡ñ❛s ② ❡sté♥ ❞❡♥tr♦ ❞❡ ❧♦s ❧í♠✐t❡s ❞❡ ❡rr♦r❡s ❛❧❡❛t♦r✐♦s✳ P♦r ❧♦ t❛♥t♦✱ ❡♥ ❧❛ ♣r✉❡❜❛ ❑✲❙ s❡ ❝❛❧❝✉❧❛ ❧❛ ♠❛②♦r ❞❡s✈✐❛❝✐ó♥ ❡①✐st❡♥t❡ ❡♥tr❡ F0 (x) ② Sn (x)✱ ❞❡♥♦t❛❞❛ ♣♦r Dmax (x) ② ❡stá ❞❛❞❛ ♣♦r✿ Dmax (x) = M ax |F0 (x) − Sn (x)| ▲❛ ❞✐str✐❜✉❝✐ó♥ ❞❡ Dmax (x) ❡s ❝♦♥♦❝✐❞❛ ② ❞❡♣❡♥❞❡ ❞❡❧ ♥ú♠❡r♦ ❞❡ ♦❜s❡r✈❛❝✐♦♥❡s ♥✳ ❙❡ ❛❝❡♣t❛ ❧❛ ❤✐♣ót❡s✐s ♥✉❧❛ ❞❡ q✉❡ ♥♦ ❡①✐st❡ ❞✐❢❡r❡♥❝✐❛ s✐❣♥✐✜❝❛t✐✈❛ ❡♥tr❡ ❧❛s ❞✐str✐❜✉❝✐♦♥❡s t❡ór✐❝❛s ② ❡♠♣ír✐❝❛s s✐ ❡❧ ✈❛❧♦r ❞❡ Dmax (x) ❡s ♠❡♥♦r ♦ ✐❣✉❛❧ q✉❡ ❡❧ ✈❛❧♦r ❝rít✐❝♦ Dmaxp (α, n)✳ ▲❛s ♣r♦♣✐❡❞❛❞❡s ♠ás s♦❜r❡s❛❧✐❡♥t❡s ❞❡ ❡st❛ ♣r✉❡❜❛ s♦♥✿ ▲❛ ♣r✉❡❜❛ ❑✲❙ ♣✉❡❞❡ ❛♣❧✐❝❛rs❡ ♣❛r❛ t❛♠❛ñ♦s ❞❡ ♠✉❡str❛ ♣❡q✉❡ñ♦s✱ ❧♦ q✉❡ ♥♦ s✉❝❡❞❡ ❝♦♥ ❧❛ χ2 ✳ ❆❞❡♠ás✱ ❧❛ ♣r✉❡❜❛ ❑✲❙ ❡s ♠ás ♣♦❞❡r♦s❛ q✉❡ ❧❛ χ2 ✱ ❡s ❞❡❝✐r✱ ❝✉❛♥❞♦ s❡ r❡❝❤❛③❛ ❧❛ ❤✐♣ót❡s✐s ♥✉❧❛✱ s❡ t✐❡♥❡ ✉♥❛ ♠❛②♦r ❝♦♥✜❛❜✐❧✐❞❛❞ ❡♥ ❞✐❝❤♦ r❡s✉❧t❛❞♦✳ ▲❛ ♣r✉❡❜❛ ❑✲❙ ❞❡❜❡ ✉s❛rs❡ ❝✉❛♥❞♦ ❧❛ ✈❛r✐❛❜❧❡ ❞❡ ❛♥á❧✐s✐s ❡s ❝♦♥t✐♥✉❛✳ ❙✐♥ ❡♠✲ ❜❛r❣♦✱ s✐ ❧❛ ♣r✉❡❜❛ s❡ ✉s❛ ❝✉❛♥❞♦ ❧❛ ❞✐str✐❜✉❝✐ó♥ ❞❡ ❧❛ ♣♦❜❧❛❝✐ó♥ ♥♦ ❡s ❝♦♥t✐♥✉❛✱ ❡❧ ❡rr♦r q✉❡ ♦❝✉rr❡ ❡♥ ❧❛ ♣r♦❜❛❜✐❧✐❞❛❞ r❡s✉❧t❛♥t❡ ❡stá ❡♥ ❧❛ ❞✐r❡❝❝✐ó♥ s❡❣✉r❛✳ ❊s ❞❡❝✐r✱ ❝✉❛♥❞♦ s❡ r❡❝❤❛③❛ ❧❛ ❤✐♣ót❡s✐s ♥✉❧❛✱ t❡♥❡♠♦s ✈❡r❞❛❞❡r❛ ❝♦♥✜❛♥③❛ ❡♥ ❧❛ ❞❡❝✐s✐ó♥✳ ❊①✐st❡♥ ♦tr❛s ♣r✉❡❜❛s ❡st❛❞íst✐❝❛s ♣❡r♦ ❜ás✐❝❛♠❡♥t❡ ❡stá♥ ❞✐s❡ñ❛❞❛s ♣❛r❛ ❞❡♠♦str❛r ♥♦r♠❛❧✐❞❛❞ ❡♥ ✉♥❛ ❞✐str✐❜✉❝✐ó♥ ❞❡ ❞❛t♦s ♠✉❡str❛❧❡s✳ ❊♥tr❡ ❡❧❧❛s ❡stá♥ ❧❛s ❣rá✜❝❛s ❞❡ ♥♦r♠❛❧✐❞❛❞ ❞✐s♣♦♥✐❜❧❡s ❡♥ ❝✉❛❧q✉✐❡r ♣❛q✉❡t❡ ❡st❛❞íst✐❝♦✱ ❧❛ ♣r✉❡❜❛ ❞❡ ❏❛rq✉❡✲❇❡r❛✱ ❧❛ ♣r✉❡❜❛ ❞❡ ❙❤❛♣✐r♦✲❲✐❧❦ ② ♦tr❛s✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❆♣é♥❞✐❝❡ ❇ ❋✉♥❝✐ó♥ ❞❡ ❞✐str✐❜✉❝✐ó♥ ❧♦❣íst✐❝❛ ❊♥ t❡♦rí❛ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞ ② ❡st❛❞íst✐❝❛✱ ❧❛ ❞✐str✐❜✉❝✐ó♥ ❧♦❣íst✐❝❛ ❡s ✉♥❛ ❢✉♥❝✐ó♥ ❞❡ ❞❡♥s✐❞❛❞ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞ ❝♦♥t✐♥✉❛✱ s✐♠étr✐❝❛ ② ✉♥✐♠♦❞❛❧✳ ❙❡ ❞❡r✐✈❛ ❞❡❧ tr❛❜❛❥♦ ❞❡ P✐❡rr❡ ❋✳ ❱❡r❤✉❧st s♦❜r❡ ❡❧ ♠♦❞❡❧♦ ❞❡ ❝r❡❝✐♠✐❡♥t♦ ❞❡ ❧❛ ♣♦❜❧❛❝✐ó♥ ❡♥ ❇é❧❣✐❝❛ ❛ ♣r✐♥❝✐♣✐♦s ❞❡ ✶✽✵✵✳ ▲❛ ❞❡s❝r✐♣❝✐ó♥ ❞❡ ❱❡r❤✉❧st s✐❣✉❡ ❧❛ ❢✉♥❝✐ó♥ ❞❡ ❞✐str✐❜✉❝✐ó♥ ❛❝✉♠✉❧❛❞❛ ❞❡ ❧❛ ❢✉♥❝✐ó♥ ❧♦❣íst✐❝❛ ✭t❛♠❜✐é♥ ❝♦♥♦❝✐❞❛ ❝♦♠♦ ✏♦❥✐✈❛ ❧♦❣íst✐❝❛✑✮✳ ❆ ❝♦♥✲ t✐♥✉❛❝✐ó♥ s❡ ❞❡✜♥❡ ♠❛t❡♠át✐❝❛♠❡♥t❡ ❡st❛ ❢✉♥❝✐ó♥ ② s❡ ❡♥✉♥❝✐❛♥ s✉s ♣r♦♣✐❡❞❛❞❡s ♠ás ✐♠♣♦rt❛♥t❡s✳ ❇✳✵✳✹✳ ❉❡✜♥✐❝✐ó♥ ♠❛t❡♠át✐❝❛✳ ▲❛ ❢✉♥❝✐ó♥ ❞❡ ❞❡♥s✐❞❛❞ ❞❡ ♣r♦✲ ❜❛❜✐❧✐❞❛❞ ② ❧❛ ❢✉♥❝✐ó♥ ❞❡ ❞✐str✐❜✉❝✐ó♥ ❛❝✉♠✉❧❛❞❛ ❊st❛ ❢✉♥❝✐ó♥ ❡stá ❝❛r❛❝t❡r✐③❛❞❛ ♣r✐♥❝✐♣❛❧♠❡♥t❡ ♣♦r ❞♦s ♣❛rá♠❡tr♦s✿ ❧♦❝❛❧✐③❛❝✐ó♥ ✭α✮ ② ❡s❝❛❧❛ ✭β ✮✳ ▲❛ ❢✉♥❝✐ó♥ ❞❡ ❞❡♥s✐❞❛❞ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞ ✭♣❞❢ ✮ ❡stá ❞❛❞❛ ♣♦r✿ f (X) = ❞♦♥❞❡ e− (X−α) β ✭❇✳✵✳✶✮   (X−α) 2 β 1 + e− β −∞ < X < ∞✱ −∞ < α < ∞ ② β > 0✳ ❙✐ ❡q✉✐✈❛❧❡♥t❡♠❡♥t❡ s❡ ❝♦♥s✐❞❡r❛ ❧❛ ❞✐str✐❜✉❝✐ó♥ ❞❡ ❧❛ ✈❛r✐❛❜❧❡ α = 0 Y ② β = 1✱ ❞❡✜♥✐❞❛ ❝♦♠♦ ♦ s✐ Y = X−α ✱ ❞❡ ❧❛ ❊❝✳ ✭❇✳✵✳✶✮ s❡ ♦❜t✐❡♥❡ ❧❛ ❢♦r♠❛ ❡st❛♥❞❛r✐③❛❞❛✿ β f (Y ) = e−Y [1 + e−Y ]2 ✶✻✺ ✭❇✳✵✳✷✮ ❆♣é♥❞✐❝❡ ❇✳ ❋✉♥❝✐ó♥ ❞❡ ❞✐str✐❜✉❝✐ó♥ ❧♦❣íst✐❝❛ ✶✻✻ ▲❛ ❢✉♥❝✐ó♥ ❞❡ ❞✐str✐❜✉❝✐ó♥ ❛❝✉♠✉❧❛❞❛ ✭❝❞❢ ✮ s❡ ♦❜t✐❡♥❡ ❛❧ ✐♥t❡❣r❛r ❧❛ ❊❝✳ ✭❇✳✵✳✶✮✿ FX (x) = 1 1 + e− ✭❇✳✵✳✸✮ (X−α) β ♦ ❜✐❡♥✱ FY (y) = ❇✳✵✳✺✳ 1 1 + e−Y ✭❇✳✵✳✹✮ Pr♦♣✐❡❞❛❞❡s ❆❞❡♠ás ❞❡ s❡r ✉t✐❧✐③❛❞❛ ♣❛r❛ ❧♦s ♠♦❞❡❧♦s ❞❡ ❝r❡❝✐♠✐❡♥t♦ ✲❞♦♥❞❡ x r❡♣r❡s❡♥t❛ ❛❧ t✐❡♠♣♦✲ ❡st❛ ❞✐str✐❜✉❝✐ó♥ ❡s ❡♠♣❧❡❛❞❛ ❡♥ ✉♥ t✐♣♦ ❞❡ r❡❣r❡s✐ó♥ ❝♦♥♦❝✐❞❛ ❝♦♠♦ r❡❣r❡s✐ó♥ ❧♦❣íst✐❝❛ ❬❑❧❡✐♥❜❛✉♠ ❡t ❛❧✳✱ ✷✵✵✺❪✳ ❚❛♠❜✐é♥ t✐❡♥❡ ❛♣❧✐❝❛❝✐♦♥❡s ❡♥ ❧♦s ♠♦❞❡❧♦s ❞❡ ✏t✐❡♠♣♦s ❞❡ ✈✐❞❛✑✳ ❆❧❣✉♥♦s ❝♦♥s✐❞❡r❛♥ q✉❡ ❡s ✐♥❛♣r♦♣✐❛❞♦ ✉s❛r❧❛ ❡♥ ❡st♦s ❝❛s♦s ②❛ q✉❡ ❡❧ ❧í♠✐t❡ ♣♦r ❧❛ ✐③q✉✐❡r❞❛ ❞❡ ❡st❛ ❢✉♥❝✐ó♥ t✐❡♥❞❡ ❛ −∞✱ ❧♦ ❝✉❛❧ ♣♦❞rí❛ r❡s✉❧t❛r ❡♥ ♠♦❞❡❧❛r t✐❡♠♣♦s ♥❡❣❛t✐✈♦s✳ ❙✐♥ ❡♠❜❛r❣♦✱ ❞❛❞♦ q✉❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ t✐❡♥❡ ✉♥❛ ♠❡❞✐❛ r❡❧❛t✐✈❛♠❡♥t❡ ❛❧t❛ ② ✉♥ ♣❛rá♠❡tr♦ ❞❡ ❧♦❝❛❧✐③❛❝✐ó♥ ♣❡q✉❡ñ♦✱ ❡❧ ❤❡❝❤♦ ❞❡ t❡♥❡r t✐❡♠♣♦s ♥❡❣❛t✐✈♦s ♥♦ r❡♣r❡s❡♥t❛ ✉♥ ♣r♦❜❧❡♠❛ s✐❣♥✐✜❝❛t✐✈♦✳ ▲❛ ❢♦r♠❛ ❞❡ ❡st❛ ❞✐str✐❜✉❝✐ó♥ ❡s s✐♠✐❧❛r ❛ ❧❛ ❞❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ ♥♦r♠❛❧ ② ❡♥ ❧❛ ♣rá❝t✐❝❛ ❡st❛s ❞♦s ❞✐str✐❜✉❝✐♦♥❡s ♥♦ ♣✉❡❞❡♥ ❞✐st✐♥❣✉✐rs❡ ❡♥tr❡ sí✳ ❊st❛ ❞✐str✐✲ ❜✉❝✐ó♥ t✐❡♥❡ ❝♦❧❛s ♠ás ❧❛r❣❛s q✉❡ ❧❛s ❞❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ ♥♦r♠❛❧ ② ✉♥ ❝♦❡✜❝✐❡♥t❡ ❞❡ ❝✉rt♦s✐s ❞❡ ✹✳✷ ✭❧❛ ❞✐str✐❜✉❝✐ó♥ ♥♦r♠❛❧ t✐❡♥❡ ✉♥ ❝♦❡✜❝✐❡♥t❡ ❞❡ ❝✉rt♦s✐s ❞❡ ✸✮✳ ❊st♦ ♣✉❡❞❡ t❡♥❡r ✉♥ ❣r❛♥ ❡❢❡❝t♦ s♦❜r❡ ❡❧ ✈❛❧♦r ❞❡❧ ❝✉❛rt♦ ♠♦♠❡♥t♦ ❝❡♥tr❛❧✱ ♣❡r♦ ♥♦ ❡♥ ❧❛ ❢✉♥❝✐ó♥ ❞❡ ❞✐str✐❜✉❝✐ó♥ ❛❝✉♠✉❧❛❞❛✳ ▲❛ ❞✐str✐❜✉❝✐ó♥ ❧♦❣íst✐❝❛ ❝♦♥ ✈❛❧♦r ❡s♣❡r❛❞♦ ✐❣✉❛❧ ❛ ❝❡r♦ ✭α❂ ✵✮ ② ✈❛r✐❛♥③❛ ✐❣✉❛❧ ❛ ❧❛ ✉♥✐❞❛❞ ✭β ❂ ✵✳✺✺✶✸✷✾✮✱ ❡s s✐♠étr✐❝❛ ❛❧r❡❞❡❞♦r ❞❡ α ❝♦♥ ♣✉♥t♦s ❞❡ √ √  3 loge 2 + 3 ❂ ±✵✳✼✷✻✵✼✼❀ ♠✐❡♥tr❛s q✉❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ ✐♥✢❡①✐ó♥ ❡♥✿ x = ± π ♥♦r♠❛❧ ❡st❛♥❞❛r✐③❛❞❛ t✐❡♥❡ ❧♦s ♣✉♥t♦s ❞❡ ✐♥✢❡①✐ó♥ ❡♥ x = ±1✳ ▲❛ ❞✐str✐❜✉❝✐ó♥ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞ ❧♦❣íst✐❝❛ ❡stá ❝❛r❛❝t❡r✐③❛❞❛ ♣♦r✿ f (Y ) = F (y) [1 − F (y)] ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❆♣é♥❞✐❝❡ ❇✳ ❋✉♥❝✐ó♥ ❞❡ ❞✐str✐❜✉❝✐ó♥ ❧♦❣íst✐❝❛ ✶✻✼ ② y = loge ▲❛ s✐♠♣❧❡ r❡❧❛❝✐ó♥ ❡①♣❧í❝✐t❛ ❡♥tr❡  F (y) 1 − F (y) y ✱ F (y)✱ f (Y )  ❤❛❝❡ q✉❡ ❣r❛♥ ♣❛rt❡ ❞❡❧ ❛♥á❧✐s✐s ❞❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ ❧♦❣íst✐❝❛ s❡❛ s✐♠♣❧❡✳ ❊❧ ❤❡❝❤♦ ❞❡ q✉❡ ❡❧ ♣❡r✜❧ ❞❡ ❡st❛ ❞✐str✐❜✉❝✐ó♥ s❡❛ s✐♠✐❧❛r ❛❧ ❞❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ ♥♦r♠❛❧ ❤❛❝❡ ♣♦s✐❜❧❡✱ ❡♥ ♦❝❛s✐♦♥❡s✱ r❡❡♠♣❧❛③❛r ❧❛ ♥♦r♠❛❧ ♣♦r ❧❛ ❧♦❣íst✐❝❛ ❝♦♥ ❡❧ ♣r♦♣ós✐t♦ ❞❡ s✐♠♣❧✐✜❝❛r ❡❧ ❛♥á❧✐s✐s s✐♥ t❡♥❡r ❣r❛♥❞❡s ❞✐s❝r❡♣❛♥❝✐❛s ❝♦♥ ❧❛ t❡♦rí❛✳ ❙✐ s❡ ✉s❛ ✉♥❛ ❞✐str✐❜✉❝✐ó♥ ❞❡ ♣r♦❜❛❜✐❧✐❞❛❞ ❧♦❣íst✐❝❛ ❡♥ ❧✉❣❛r ❞❡ ✉♥❛ ♥♦r♠❛❧✱ ❡❧ ❛♥á❧✐s✐s s❡ ❧❧❡✈❛ ❛ ❝❛❜♦ ❡♥ tér♠✐♥♦s ❞❡ ✏❧♦❣✐ts✑ ❬❇❡r❦s♦♥✱ ✶✾✺✵❪✳ ▲❛ ❢✉♥❝✐ó♥ ✏❧♦❣✐t✑ ❡s ❡❧ ✐♥✈❡rs♦ ❞❡ ❧❛ ❢✉♥❝✐ó♥ ❧♦❣íst✐❝❛✳ ❇✳✵✳✻✳ ▼♦♠❡♥t♦s ❇✳✵✳✻✳✶✳ ❋✉♥❝✐ó♥ ❣❡♥❡r❛❞♦r❛ ❞❡ ♠♦♠❡♥t♦s ❙❡❛ X ✉♥❛ ✈❛r✐❛❜❧❡ ❛❧❡❛t♦r✐❛ q✉❡ s✐❣✉❡ ✉♥❛ ❢✉♥❝✐ó♥ ❞❡ ❞✐str✐❜✉❝✐ó♥ ❧♦❣íst✐❝❛✳ ❊❧ ♠♦♠❡♥t♦ ❞❡ X ✭❛❧r❡❞❡❞♦r ❞❡ t✮ s❡ ❝❛❧❝✉❧❛ ❛ tr❛✈és ❞❡ ❧❛ ❢✉♥❝✐ó♥ ❣❡♥❡r❛❞♦r❛ ❞❡ ♠♦♠❡♥t♦s ❞❛❞❛ ♣♦r✿ MX (t) = eαt Γ [1 − β t] Γ [1 + β t] ❞♦♥❞❡ − β1 < t < ✭❇✳✵✳✺✮ 1 ✳ ❆❧ ❞❡r✐✈❛r ❧❛ ❡①♣r❡s✐ó♥ ❛♥t❡r✐♦r s❡ ♦❜t✐❡♥❡♥ ❝❛❞❛ ✉♥♦ ❞❡ ❧♦s β ♠♦♠❡♥t♦s q✉❡ s❡ ♠❡♥❝✐♦♥❛♥ ❛ ❝♦♥t✐♥✉❛❝✐ó♥✳ Pr✐♠❡r ♠♦♠❡♥t♦✿ ✈❛❧♦r ❡s♣❡r❛❞♦ ♦ ♠❡❞✐❛ ❊❧ ♣r✐♠❡r ♠♦♠❡♥t♦ ❛❧r❡❞❡❞♦r ❞❡❧ ♦r✐❣❡♥ ✭t = 0✮ ❝♦rr❡s♣♦♥❞❡ ❛❧ ✈❛❧♦r ❡s♣❡r❛❞♦ ✭♦ ♠❡❞✐❛✮ ② ❡s ✐❣✉❛❧ ❛❧ ✈❛❧♦r ❞❡❧ ♣❛rá♠❡tr♦ ❞❡ ❧♦❝❛❧✐③❛❝✐ó♥✱ E [X ] = α α✿ ✭❇✳✵✳✻✮ ❉❛❞♦ q✉❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ ❡s s✐♠étr✐❝❛✱ ❧❛ ♠❡❞✐❛♥❛ ② ❧❛ ♠♦❞❛ t❛♠❜✐é♥ s♦♥ ✐❣✉❛❧❡s ❛ α✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❆♣é♥❞✐❝❡ ❇✳ ❋✉♥❝✐ó♥ ❞❡ ❞✐str✐❜✉❝✐ó♥ ❧♦❣íst✐❝❛ ✶✻✽ ❙❡❣✉♥❞♦ ♠♦♠❡♥t♦ ❝❡♥tr❛❧✿ ✈❛r✐❛♥③❛ ▲❛ ✈❛r✐❛♥③❛ ❞❡ ❡st❛ ❞✐str✐❜✉❝✐ó♥ ❡s✿ V ar ( X ) = 1 (π β)2 = σ 2 3 ✭❇✳✵✳✼✮ P♦r ❧♦ t❛♥t♦ ❞❡ ❧❛ ❊❝✳ ✭❇✳✵✳✼✮ s❡ ❞❡❞✉❝❡ q✉❡✿ β ❂ ✵✳✺✺✶✸✷✾ σ ✳ ❉♦♥❞❡ σ ❡s ❧❛ ❞❡s✈✐❛❝✐ó♥ ❡stá♥❞❛r ❛s♦❝✐❛❞❛ ❛ ❧❛ ❞✐str✐❜✉❝✐ó♥✳ ❆❧ ❝♦♠♣❛r❛r ❧❛ ✈❛r✐❛♥③❛ ❞❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ ♥♦r♠❛❧ ❝♦♥ ❧❛ ❞❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ ❧♦✲ ❣íst✐❝❛ s❡ ♦❜s❡r✈❛ q✉❡ ❡st❛ ú❧t✐♠❛ ❡s ❞✐❢❡r❡♥t❡ ♣♦r ✉♥ ❢❛❝t♦r ❞❡ ❡s❝❛❧❛ ❞❡ π2 3 ✳ ❚❡r❝❡r ♠♦♠❡♥t♦ ❝❡♥tr❛❧✿ s❡s❣♦ ❊❧ s❡s❣♦ ❞❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ ❧♦❣íst✐❝❛ ❡s ❝❡r♦✱ r❡✢❡❥❛♥❞♦ s✉ s✐♠❡trí❛✳ ❈✉❛rt♦ ♠♦♠❡♥t♦ ❝❡♥tr❛❧✿ ❝✉rt♦s✐s ▲❛ ❝✉rt♦s✐s ❞❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ ❧♦❣íst✐❝❛ ❡s ❞❡ ✹✳✷✱ ❧♦ ❝✉❛❧ s✐❣♥✐✜❝❛ q✉❡ ❧❛ ❧♦❣íst✐❝❛ ❡s ✉♥❛ ❞✐str✐❜✉❝✐ó♥ ❧❡♣t♦❝úrt✐❝❛✱ ❡s ❞❡❝✐r✱ ❡s ♠ás ♣✐❝✉❞❛ q✉❡ ❧❛ ❞✐str✐❜✉❝✐ó♥ ♥♦r♠❛❧✳ ❇✳✵✳✼✳ ●❡♥❡r❛❝✐ó♥ ❞❡ ♥ú♠❡r♦s ❛❧❡❛t♦r✐♦s ▲❛ ❣❡♥❡r❛❝✐ó♥ ❞❡ ♥ú♠❡r♦s ❛❧❡❛t♦r✐♦s X ❝♦♥ ❞✐str✐❜✉❝✐ó♥ ❧♦❣íst✐❝❛ ❡stá ❜❛s❛❞❛ ❡♥ ❡❧ ♠ét♦❞♦ ❞❡ ❧❛ tr❛♥s❢♦r♠❛❝✐ó♥ ✐♥✈❡rs❛ ❬❘✉❜✐♥st❡✐♥✱ ✶✾✽✶❪✳ ❙❡❛♥ X ✉♥❛ ✈❛r✐❛❜❧❡ ❛❧❡❛t♦r✐❛ ❝♦♥ ✉♥❛ ❢✉♥❝✐ó♥ ❞❡ ❞✐str✐❜✉❝✐ó♥ ❛❝✉♠✉❧❛❞❛ ✭❝❞❢✮ ❞❛❞❛ ♣♦r ❧❛ ❊❝✳ ✭❇✳✵✳✸✮ ② ξ ✉♥ ♥ú♠❡r♦ q✉❡ ❡stá ✉♥✐❢♦r♠❡♠❡♥t❡ ❞✐str✐❜✉✐❞♦ ❡♥ ❡❧ ✐♥t❡r✈❛❧♦ [0, 1]✳ ❊♥t♦♥❝❡s s❡ ❝✉♠♣❧❡ q✉❡✱ X = FX−1 (ξ) ② q✉❡ ❛❞❡♠ás t✐❡♥❡ ✉♥❛ ❢✉♥❝✐ó♥ ❞❡ ❞✐str✐❜✉❝✐ó♥ ❛❝✉♠✉❧❛❞❛ ❞❛❞❛ ♣♦r FX (x)✳ P♦r ❧♦ t❛♥t♦✿ 1 + e− e X = β loge  (X−α) β (X−α) β = U (0, 1) 1 − U (0, 1) = 1 U (0, 1) U (0, 1) 1 − U (0, 1)  + α = β loge  ξ 1−ξ  +α ✭❇✳✵✳✽✮ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❆♣é♥❞✐❝❡ ❇✳ ❋✉♥❝✐ó♥ ❞❡ ❞✐str✐❜✉❝✐ó♥ ❧♦❣íst✐❝❛ ▲❛ ❊❝✳ ✭❇✳✵✳✽✮ tr❛♥s❢♦r♠❛ ❛ ❧♦s ♥ú♠❡r♦s [0, 1] ❡♥ ♥ú♠❡r♦s ❛❧❡❛t♦r✐♦s X ξ ✶✻✾ q✉❡ ❡stá♥ ❞✐str✐❜✉✐❞♦s ❡♥ ❡❧ ✐♥t❡r✈❛❧♦ ❝♦♥ ❞✐str✐❜✉❝✐ó♥ ❧♦❣íst✐❝❛✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼ ❆♣é♥❞✐❝❡ ❈ ▼ét♦❞♦ ❞❡ ❇♦①✲▼ü❧❧❡r ♣❛r❛ ❣❡♥❡r❛r ♥ú♠❡r♦s ❛❧❡❛t♦r✐♦s ❝♦♥ ❞✐str✐❜✉❝✐ó♥ ♥♦r♠❛❧ ▲❛ tr❛♥s❢♦r♠❛❝✐ó♥ ❞❡ ❇♦①✲▼ü❧❧❡r ❡s ✉♥ ♠ét♦❞♦ ♣❛r❛ ❣❡♥❡r❛r ♣❛r❡s ❞❡ ♥ú♠❡✲ r♦s ❛❧❡❛t♦r✐♦s ❡ ✐♥❞❡♣❡♥❞✐❡♥t❡s ♥♦r♠❛❧♠❡♥t❡ ❞✐str✐❜✉✐❞♦s✳ ❍❛② ❞♦s ♠❛♥❡r❛s ♣❛r❛ ❣❡♥❡r❛r❧♦s✿ ❉❛❞♦s r ② ϕ ❞✐str✐❜✉✐❞♦s ✉♥✐❢♦r♠❡♠❡♥t❡ ❡ ✐♥❞❡♣❡♥❞✐❡♥t❡s ❡♥ ❡❧ ✐♥t❡r✈❛❧♦ (0, 1] s❡ ❝❛❧❝✉❧❛✿ z0 = cos (2 π ϕ) z1 = sen (2 π ϕ) p −2 log r p −2 log r ✭❈✳✵✳✶✮ ✭❈✳✵✳✷✮ ❆❧ ❣❡♥❡r❛r ❧♦s ♥ú♠❡r♦s ❞❡ ❡st❛ ♠❛♥❡r❛✱ s❡ ❛s❡❣✉r❛ q✉❡ ést♦s s❡ ❞✐str✐❜✉②❡♥ ❞❡♥tr♦ ❞❡ ✉♥ ❝ír❝✉❧♦ ✉♥✐t❛r✐♦ ❝♦♥ ❧❛s ❝♦♦r❞❡♥❛❞❛s ♣♦❧❛r❡s (r, 2 π ϕ)✳ ❉❛❞♦s ① ❡ ② ❞✐str✐❜✉✐❞♦s ✉♥✐❢♦r♠❡♠❡♥t❡ ❡ ✐♥❞❡♣❡♥❞✐❡♥t❡s ❡♥ ❡❧ ✐♥t❡r✈❛❧♦ [−1, 1] q✉❡ ❝✉♠♣❧❡♥ ❝♦♥ ❧❛ r❡❧❛❝✐ó♥ R = x2 + y 2 ✳ ❙✐ R = 0 ó R > 1✱ s❡ ❞❡s❡❝❤❛♥ ② s❡ ❜✉s❝❛ ♦tr❛ ♣❛r❡❥❛ (x, y)✳ ❊♥t♦♥❝❡s ♣❛r❛ ❡s♦s ♣✉♥t♦s ✜❧tr❛❞♦s s❡ ❝❛❧❝✉❧❛✿ z0 = x r −2 log R R ✶✼✵ ✭❈✳✵✳✸✮ ❆♣é♥❞✐❝❡ ❈✳ ▼ét♦❞♦ ❞❡ ❇♦①✲▼ü❧❧❡r ♣❛r❛ ❣❡♥❡r❛r ♥ú♠❡r♦s ❛❧❡❛t♦r✐♦s ❝♦♥ ❞✐str✐❜✉❝✐ó♥ ♥♦r♠❛❧ ✶✼✶ z1 = y r −2 log R R ✭❈✳✵✳✹✮ ❚♦❞♦s ❧♦s ♣✉♥t♦s q✉❡ ❤❛♥ q✉❡❞❛❞♦ ❞❡s♣✉és ❞❡ ❤❛❜❡r s✐❞♦ ✜❧tr❛❞♦s ❡st❛rá♥ ❞✐str✐✲ ❜✉✐❞♦s ✉♥✐❢♦r♠❡♠❡♥t❡ ❞❡♥tr♦ ❞❡ ✉♥ ❝ír❝✉❧♦ ❝♦♥ ❧❛s ❝♦♦r❞❡♥❛❞❛s ❝❛rt❡s✐❛♥❛s (x, y) ② ❝♦♥ R q✉❡ ❞❡✜♥❡ ❧❛ ❞✐st❛♥❝✐❛ ❛❧ ♦r✐❣❡♥✳ ❊st❡ ♣r♦❝❡❞✐♠✐❡♥t♦ r❡s✉❧t❛ s❡r ❡❧ ♠ás rá♣✐❞♦ ♣♦rq✉❡ só❧♦ ❡♠♣❧❡❛ ✉♥❛ ❢✉♥❝✐ó♥ tr❛s❝❡♥❞❡♥t❛❧✱ ❛ú♥ ❝✉❛♥❞♦ ❞❡s❡❝❤❛ 4 π − 1 ≈ ✵✳✷✼✸✷ ❞❡ ❧♦s ♥ú♠❡r♦s ❛❧❡❛t♦r✐♦s ❞✐str✐❜✉✐❞♦s ✉♥✐❢♦r♠❡♠❡♥t❡ ♣♦r ❝❛❞❛ ♣❛r ❞❡ ♥ú♠❡r♦s ❛❧❡❛✲ t♦r✐♦s ❝♦♥ ❞✐str✐❜✉❝✐ó♥ ❣❛✉ss✐❛♥❛✳ ●❡♥❡r❛❝✐ó♥ ❞❡ ♥ú♠❡r♦s ❛❧❡❛t♦r✐♦s ❝♦♥ ❞✐str✐❜✉❝✐ó♥ ▼❛①✇❡❧❧✐❛♥❛ P❛r❛ ❣❡♥❡r❛r ♥ú♠❡r♦s ❛❧❡❛t♦r✐♦s ❝♦♥ ❞✐str✐❜✉❝✐ó♥ ▼❛①✇❡❧❧✐❛♥❛✱ ❜❛st❛ ❝♦♥ ♠✉❧✲ t✐♣❧✐❝❛r ❧♦s ♥ú♠❡r♦s z0 ② z1 ❝❛❧❝✉❧❛❞♦s ❡♥ ❧❛s ❊❝s✳ ✭❈✳✵✶✮ ② ✭❈✳✵✳✷✮ ♣♦r ✉♥ ❢❛❝t♦r ❛❞❡❝✉❛❞♦✳ ❊st❡ ❢❛❝t♦r s❡ ❞❡t❡r♠✐♥❛ ❛ ♣❛rt✐r ❞❡ ❧❛ ❡q✉✐✈❛❧❡♥❝✐❛ ❡♥tr❡ ❧❛s ❞✐str✐❜✉❝✐♦♥❡s ▼❛①✇❡❧❧✐❛♥❛ ② ●❛✉ss✐❛♥❛✳ ▲❛ ❢✉♥❝✐ó♥ ❞❡ ❞✐str✐❜✉❝✐ó♥ ▼❛①✇❡❧❧✐❛♥❛ ❡♥ ✶❉ ❡stá ❞❛❞❛ ♣♦r ❧❛ ❡①♣r❡s✐ó♥✿ 1 f (v) = 2π r ❤ m e kB T 2 v − 2m k T B ✐ ✭❈✳✵✳✺✮ ▲❛ ❢✉♥❝✐ó♥ ❞❡ ❞✐str✐❜✉❝✐ó♥ ♥♦r♠❛❧ ♦ ●❛✉ss✐❛♥❛ ❡s✿ ✔ 1 g (x) = √ e σ 2π − (x−µ)2 2 σ2 ✕ ✭❈✳✵✳✻✮ P❛r❛ q✉❡ ❧❛s ❊❝s✳ ✭❈✳✵✳✺✮ ② ✭❈✳✵✳✻✮ s❡❛♥ ✐❣✉❛❧❡s✱ s❡ ❞❡❜❡ ❞❡ ❝✉♠♣❧✐r q✉❡ µ = 0 ② σ= q kB T m ✳ P♦r ❧♦ t❛♥t♦✱ ❧❛ ❢✉♥❝✐ó♥ ❞❡ ❞✐str✐❜✉❝✐ó♥ ▼❛①✇❡❧❧✐❛♥❛ ❡s ✉♥❛ ❢✉♥❝✐ó♥ ❞❡ ❞✐str✐❜✉✲ ❝✐ó♥ ●❛✉ss✐❛♥❛ ❝♦♥ ♣❛rá♠❡tr♦s µ = 0 ② σ = q kB T m ✳ ✶ ❞❡ ♠❛②♦ ❞❡ ✷✵✵✼
Analisis de las fuerzas estocasticas que actuan sobre la poblacion de particulas en la magnetosfera de Saturno Analisis De Las Fuerzas Estocasticas Que Actuan Sobre La Poblacion De Particulas En La Magnetosfera De Saturno

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Unido : 2017-01-23

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Analisis de las fuerzas estocasticas que actuan sobre la poblacion de particulas en la magnetosfera de Saturno

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