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P♦s✐tr♦♥ ❆▼❙✲✵✷ ❆♥♦♠❛❧②✿ ❙✐♥❣❧❡ ❙◆❘ ❊①♣❧❛♥❛t✐♦♥ ✇✐t❤♦✉t ❉▼ ♦r P✉❧s❛r ❈♦♥tr✐❜✉t✐♦♥s

▼✐❦❤❛✐❧ ▼❛❧❦♦✈ P❛tr✐❝❦ ❉✐❛♠♦♥❞ ❯❈❙❉ ❘♦❛❧❞ ❙❛❣❞❡❡✈ ❯▼❉

❙✉♣♣♦rt❡❞ ❜② ◆❆❙❆ ❆str♦♣❤②s✐❝s ❚❤❡♦r② Pr♦❣r❛♠

✶ ✴ ✶✹

❖✉t❧✐♥❡

✶ Pr❡❧✐♠✐♥❛r② ■♥❢♦r♠❛t✐♦♥

❉❙❆ ✲ ❚❤❡ ❉✐✛✉s✐✈❡ ❙❤♦❝❦ ❆❝❝❡❧❡r❛t✐♦♥ ❉❙❆❅❙◆❘✿ ❚❡st P❛rt✐❝❧❡ ✈s ◆♦♥❧✐♥❡❛r

✷ ❉✐s❛❣r❡❡♠❡♥ts ✇✐t❤ t❤❡ st❛♥❞❛r❞ ❉❙❆

❆♥♦♠❛❧✐❡s ✐♥ ♣♦s✐tr♦♥ s♣❡❝tr✉♠ ❊❳■❙❚■◆● ❡①♣❧❛♥❛t✐♦♥s ❛♥❞ t❤❡✐r ✇❡❛❦♥❡ss❡s

✸ ◆❊❲✿ ▼✐♥✐♠✉♠ ❛ss✉♠♣t✐♦♥s✱ s✐♥❣❧❡ s♦✉r❝❡ ✭❙◆❘✮ s❝❡♥❛r✐♦

e± ❛s②♠♠❡tr② ♦❢ ❛❝❝❡❧❡r❛t✐♦♥✿ ▼♦❧❡❝✉❧❛r ❈❧✉♠♣s ▼✐♥✐♠✉♠ ✐♥ e+/ (e+ + e−) : ◆▲ ❉❙❆

✹ ❈♦♥❝❧✉s✐♦♥s✿ ♥♦ r♦♦♠ ✭❛❧♠♦st✮ ❢♦r ❉▼✴P✉❧s❛rs ❝♦♥tr✐❜✉t✐♦♥

✷ ✴ ✶✹

❊ss❡♥t✐❛❧ ❉❙❆ ✭❛❦❛ ❋❡r♠✐✲■ ♣r♦❝❡ss✱ ❊✳ ❋❡r♠✐✱ ⑦✶✾✺✵s✮

Down- stream x U(x) Upstream shock

Scaering Centers, frozen Into flow

Linear (TP) phase of acceleraon

❈❘ tr❛♣♣❡❞ ❜❡t✇❡❡♥ ❝♦♥✈❡r❣✐♥❣ ♠✐rr♦rs✿ p∆x ≈ const ❈❘ s♣❡❝tr✉♠ ❞❡♣❡♥❞s ♦♥ s❤♦❝❦ ❝♦♠♣r❡ss✐♦♥✱ r✿ f ∼ p−q, q = ✸r/ (r − ✶)✱ r = q = ✹ ✱ ▼❛❝❤ M → ∞

Upstream x U(x) Sub-shock Down- stream NL, with CR back-reacon NL-modified flow

■♥❞❡① q ❜❡❝♦♠❡s q (p)✿

s♦❢t ❛t ❧♦✇ p✿

q = ✸rs/ (rs − ✶) ∼ ✺

❤❛r❞ ❛t ❤✐❣❤ p : q → ✸.✺ ❢♦r M > ✶✵, Emax ✶ ❚❡❱ ❛❝❝❡❧❡r❛t✐♦♥ ♠✉st ❣♦ ♥♦♥❧✐♥❡❛r

✸ ✴ ✶✹

P♦s✐tr♦♥ ❆♥♦♠❛❧② ✭❡①❝❡ss✮

P♦s✐tr♦♥ ❡①❝❡ss ✭❆❝❝❛r❞♦ ❡t ❛❧ ✷✵✶✹✮ ❖❜s❡r✈❡❞ ❜② ❞✐✛❡r❡♥t ✐♥str✉♠❡♥ts ❢♦r s❡✈❡r❛❧ ②❡❛rs ❉r❛♠❛t✐❝❛❧❧② ✐♠♣r♦✈❡❞ st❛t✐st✐❝s ❜② ❆▼❙✲✵✷ ✭♣✉❜❧✐s❤❡❞ ✐♥ ✷✵✶✹✮ ❚❤✐♥❣s t♦ ♥♦t❡✿ ❘❡♠❛r❦❛❜❧❡ ♠✐♥ ❛t ≈ ✽ ●❡❱ ❯♥♣r❡❝❡❞❡♥t❡❞ ❛❝❝✉r❛❝② ✐♥ t❤❡ r❛♥❣❡ ✶✲✶✵✵ ●❡❱ ❙❛t✉r❛t✐♦♥ ✭s❧✐❣❤t ❞❡❝❧✐♥❡❄✮ tr❡♥❞ ❜❡②♦♥❞ ✷✵✵ ●❡❱ ❊❛❣❡r❧② ❛✇❛✐t✐♥❣ ♥❡①t ❞❛t❛ r❡❧❡❛s❡✦

✹ ✴ ✶✹

❙✉❣❣❡st❡❞ ❡①♣❧❛♥❛t✐♦♥s ♦❢ ♣♦s✐tr♦♥ ❡①❝❡ss

❢♦❝✉s ♦♥ t❤❡ r✐s✐♥❣ ❜r❛♥❝❤ ♦❢ e+/ (e+ + e−) ✐♥✈♦❦❡ s❡❝♦♥❞❛r② e+ ❢r♦♠ ❈❘ pp ✇✐t❤ t❤❡r♠❛❧ ❣❛s Pr♦❜❧❡♠s✿ ❚❡♥s✐♦♥s ✇✐t❤ ¯ p✿ s❡❝♦♥❞❛r✐❡s ✇✐t❤ ❞✐✛❡r✐♥❣ s♣❡❝tr❛ P♦♦r ✜ts✱ ❢r❡❡ ♣❛r❛♠❡t❡rs✱ ♥♦ ♣❤②s✐❝s ♦❢ ✽ ●❡❱ ✉♣t✉r♥✳✳✳ ❆❧t❡r♥❛t✐✈❡ s✉❣❣❡st✐♦♥s✿ P✉❧s❛rs ✭❧❛❝❦✐♥❣ ❛❝❝✉r❛t❡ ❛❝❝❡❧❡r❛t✐♦♥ ♠♦❞❡❧s✮ ❉❛r❦ ♠❛tt❡r ❝♦♥tr✐❜✉t✐♦♥ ❄❄ ❙t❛t✐♥❣ t❤❡ ❖❜✈✐♦✉s ✳✳✳✳ ❉❙❆❅❙◆❘✬ ♣r❡❞✐❝t✐✈❡ ❝❛♣❛❜✐❧✐t② ≫ P✉❧s❛r ♦r ❉▼ ♠♦❞❡❧s → ❉▼✴P✕ ♦♥❧② ✐❢ t❤❡ ❉❙❆❅❙◆❘ ❢❛✐❧s ❯♣s❤♦t ❙◆❘ ❝♦♥tr✐❜✉t✐♦♥ ❝♦♥str❛✐♥s ❉▼✴P✉❧s❛r ❝♦♥tr✐❜✉t✐♦♥s

✺ ✴ ✶✹

❚❤❡ ❲✐s❤❧✐st

❛❝❝♦✉♥t ❢♦r e+ ❢r❛❝t✐♦♥ ❜② ❛ s✐♥❣❧❡✲s♦✉r❝❡✱ ❛ ♥❡❛r❜② ❙◆❘ ❡①♣❧❛✐♥ ♣❤②s✐❝s ♦❢ ❞❡❝r❡❛s✐♥❣ ❛♥❞ ✐♥❝r❡❛s✐♥❣ ❜r❛♥❝❤❡s✱ ✽ ●❡❱ ♠✐♥

→ ❧❡♥❞s ❝r❡❞❡♥❝❡ t♦ ❤✐❣❤ ❡♥❡r❣② ♣r❡❞✐❝t✐♦♥s

✉♥❞❡rst❛♥❞ ¯ p ✢❛t s♣❡❝tr✉♠ ❛s ✐♥tr✐♥s✐❝✱ ♥♦t ❝♦✐♥❝✐❞❡♥t❛❧✿

♠♦st ❧✐❦❡❧② ¯ p ❛❝❝❡❧❡r❛t❡❞ s✐♠✐❧❛r❧② t♦ ♣r♦t♦♥s✱ ✇❤❡♥❡✈❡r ✐♥❥❡❝t❡❞ ❇❯❚✿ ¯ p/p = e+/e− ✲ ❲❤② s♦❄

♣❧❛✉s✐❜❧❡ ❛♥s✇❡r✿ ❛❝❝❡❧❡r❛t✐♦♥✴✐♥❥❡❝t✐♦♥ ✐s ❝❤❛r❣❡✲s✐❣♥ ❛♥❞ ♠❛ss✴❝❤❛r❣❡ r❛t✐♦ ❞❡♣❡♥❞❡♥t ✉♥❞❡rst❛♥❞ t❤❡ ♣❤②s✐❝s ♦❢ ❝❤❛r❣❡✲s✐❣♥ s❡❧❡❝t✐✈✐t②

✻ ✴ ✶✹

❚❤❡ ❍✐♥ts

✭❑♦✉♥✐♥❡ ❍▲ t❛❧❦ ♦♥ ❙❛t✮

¯ p ❢r❛❝t✐♦♥ ✐s ✢❛t ♦♥ t❤❡ r✐s✐♥❣ e+ ❢r❛❝t✐♦♥ ❜r❛♥❝❤ E > ✽ ●❡❱ ❖♣♣♦s✐t❡ tr❡♥❞s ✐♥ e+/e− ❛♥❞ ¯ p/p s♣❡❝tr❛ ❛t E < ✽ ●❡❱ ❇♦t❤ ❛r❡ ❢r❛❝t✐♦♥s✱ t❤✉s ❡❧✐♠✐♥❛t✐♥❣ ❝❤❛r❣❡✲s✐❣♥ ✐♥❞❡♣❡♥❞❡♥t ❛s♣❡❝ts ♦❢ ♣r♦♣❛❣❛t✐♦♥ ❛♥❞ ❛❝❝❡❧❡r❛t✐♦♥ ✭st✐❧❧✱ ❍❙ ❡✛❡❝ts❄✮ ❙tr✐❦✐♥❣ s✐♠✐❧❛r✐t② ✇✐t❤ ◆▲ ❉❙❆ s♦❧✉t✐♦♥✱ ❛ss✉♠✐♥❣ ♠♦st ♦❢ e− ❛r❡ ❛❝❝❡❧❡r❛t❡❞ t♦ p−✹ ✭st❛♥❞❛r❞ ❉❙❆✮

✼ ✴ ✶✹

❚❤❡ ❆ss✉♠♣t✐♦♥s

❙◆❘ s❤♦❝❦ ♣r♦♣❛❣❛t❡s ✐♥ ✏❝❧✉♠♣②✑ ♠♦❧❡❝✉❧❛r ❣❛s ✭n❍ ✸✵❝♠−✸✱ ✜❧❧✐♥❣ ❢❛❝t♦r fV ∼ ✵.✵✶✮ ❍✐❣❤✲❡♥❡r❣② ♣r♦t♦♥s ❛r❡ ❛❧r❡❛❞② ❛❝❝❡❧❡r❛t❡❞ t♦ ✭❛t ❧❡❛st✮ E ∼ ✶✵✶✷eV t♦ ♠❛❦❡ ❛ str♦♥❣ ✐♠♣❛❝t ♦♥ t❤❡ s❤♦❝❦ str✉❝t✉r❡ ✭❈❘ ❜❛❝❦ r❡❛❝t✐♦♥✱ ◆▲ s❤♦❝❦ ♠♦❞✐✜❝❛t✐♦♥✮

❆❝❝❡❧❡r❛t✐♦♥ ♣r♦❝❡ss t❤✉s tr❛♥s✐t✐♦♥❡❞ ✐♥t♦ ❛♥ ❡✣❝✐❡♥t r❡❣✐♠❡ ✭✐♥ ❢❛❝t✱ r❡q✉✐r❡❞ t♦✱ ♦♥❝❡ E ✶ ❚❡❱✱ M ✶✵ − ✶✺ ❛♥❞ t❤❡ ❢r❛❝t✐♦♥ ♦❢ ❛❝❝❡❧❡r❛t❡❞ ♣r♦t♦♥s ∼ ✶✵−✹ − ✶✵−✸✮

❚❤❡ ❙◆❘ ✐s ♥♦t t♦♦ ❢❛r ❛✇❛②✱ ♣♦ss✐❜❧② ♠❛❣♥❡t✐❝❛❧❧② ❝♦♥♥❡❝t❡❞✱ t❤✉s ♠❛❦✐♥❣ s✐❣♥✐✜❝❛♥t ❝♦♥tr✐❜✉t✐♦♥ t♦ t❤❡ ❧♦❝❛❧ ❈❘ s♣❡❝tr✉♠ ❖t❤❡r ❙◆❘s ♦❢ t❤✐s ❦✐♥❞ ♠❛② ♦r ♠❛② ♥♦t ❝♦♥tr✐❜✉t❡

✽ ✴ ✶✹

■♥t❡r❛❝t✐♦♥ ♦❢ s❤♦❝❦✲❛❝❝✬❞ ❈❘s ✇✐t❤ ❣❛s ❝❧✉♠♣s ✭▼❈✮

❙❤♦❝❦✲❛❝❝✬❞ ❈❘s ❢♦r♠ ❛ ♣r❡❝✉rs♦r ✿ κ ✲ ❈❘ ❞✐✛✳ ❝♦❡✛✳✱ Lp ∼ κ/ush ❲✐t❤ s♦♠❡ ❤❡❧♣ ❢r♦♠ ♣❧❛s♠❛ t❡①t❜♦♦❦s✳✳✳ ▼❛①✐♠✉♠ ❡❧❡❝tr✐❝ ✜❡❧❞ ❞✉❡ t♦ e − i ❝♦❧❧✐s✐♦♥s E♠❛① ≃ me e ushνei n✵

CR

ni ♠❛①✐♠✉♠ ❊❙ ♣♦t❡♥t✐❛❧ ✐♥s✐❞❡ eφ♠❛① mpc✷ ∼ a ✶pc ush c nCR ✶cm−✸ ✶eV Te ✸/✷

✾ ✴ ✶✹

❊ ✐♥ ▼❈✿ ■♥❥❡❝t✐♦♥✴❛❝❝❡❧❡r❛t✐♦♥ ♦❢ e+ ❛♥❞ ¯

p ✐♥t♦ ❉❙❆

❡❧❡❝tr✐❝ ✜❡❧❞ tr❛♣s e− ❛♥❞ s♦♠❡ ¯ p ✐♥s✐❞❡ ▼❈ ❡❥❡❝ts s❡❝♦♥❞❛r② e+ →❝❤❛r❣❡✲s✐❣♥ ❛s②♠♠❡tr② e+❛r❡ ♦r❡✲❛❝❝❡❧❡r❛t❡❞ ✐♥ ❊ t♦ ✶ ●❡❱ ❛♥❞ r❡❛❞✐❧② ✐♥❥❡❝t❡❞ ✐♥t♦ ❉❙❆ ❛t Ee ❢❡✇ ●❡❱✱ e+ s♣❡❝tr✉♠ ✐s ❞♦♠✐♥❛t❡❞ ❜② t❤❡ s✉❜s❤♦❝❦ ❝♦♠♣r❡ss✐♦♥ r❛t✐♦✱ rs

s♣❡❝tr❛❧ ✐♥❞❡① q = qs ≡ ✸rs/ (rs − ✶) ❛♥❞ t❤❡ s♣❡❝tr✉♠ fe+ ∝ p−qs✳

❛t ❤✐❣❤❡r ❡♥❡r❣✐❡s✱ ♣❛rt✐❝❧❡s ♣❡r❝❡✐✈❡ ❤✐❣❤❡r ✢♦✇ ❝♦♠♣r❡ss✐♦♥

P▲✲✐♥❞❡① ✐♥s✐❞❡ t❤❡ s♦✉r❝❡ q → ✸.✺

✶✵ ✴ ✶✹

P♦s✐tr♦♥ s♣❡❝tr❛ ❝♦♥t✬❞

e− ❛r❡ ❢r♦♠ t❤❡ ❚P ♣❤❛s❡ ✇✐t❤ p−✹ s♦✉r❝❡ s♣❡❝tr❛ ✭❛♥❞ ♦t❤❡r ❚P✲❙◆❘s✮ = ⇒ e+/ (e− + e+)✲s♣❡❝tr✉♠ ❂ p−s♣❡❝tr✉♠ ✐♥ p✹f (p) ❝✉st♦♠❛r② ♥♦r♠❛❧✐③❛t✐♦♥ r❛t✐♦ e+/ (e− + e+) ✐s ❞❡✲♣r♦♣❛❣❛t❡❞ ❛♥❞ ♣r♦❜❡s ❞✐r❡❝t❧② ✐♥t♦ t❤❡ ♣♦s✐tr♦♥ ❛❝❝❡❧❡r❛t♦r✦ ❜❡❢♦r❡ ❉▼✴♣✉❧s❛rs ❛r❡ ❞❡❝❧❛r❡❞ r❡s♣♦♥s✐❜❧❡ ❢♦r t❤❡ ❡①❝❡ss ❛❜♦✈❡ t❤❡ ❙◆❘ ✭❜❧✉❡ ❝✉r✈❡✮✱ t❤❡ ❢♦❧❧♦✇✐♥❣ ✭♣r♦s❛✐❝✮ ❛s♣❡❝ts ♠❛② ❜❡ ❝♦♥s✐❞❡r❡❞✿

✶ e+ r❡❧❡❛s❡ ❢r♦♠ ▼❈ ❢❛rt❤❡r

✉♣str❡❛♠ ✭❛❞❞✐t✐♦♥❛❧ s♣❡❝tr✉♠ ❤❛r❞❡♥✐♥❣✮

✷ s②♥❝❤r♦tr♦♥ ♣✐❧❡✲✉♣ ♥❡❛r t❤❡

❝✉t✲♦✛ ❡♥❡r❣②

✸ ❡❧❡❝tr♦st❛t✐❝ ❜r❡❛❦❞♦✇♥ ♦❢ ▼❈

✇✐t❤ ❡♥❤❛♥❝❡❞ e+ ❣❡♥❡r❛t✐♦♥

✶✶ ✴ ✶✹

❆♥t✐♣r♦t♦♥s

■❢ ♠♦st ♦❢ ¯ p ❛♥❞ p ❝♦♠❡ ❢r♦♠ t❤❡ s❛♠❡ s♦✉r❝❡ ❛s e+ ✭ ¯ p ❣❡♥❡r❛t❡❞ ✐♥ ▼❈s ❛❤❡❛❞ ♦❢ ❙◆❘ s❤♦❝❦✮✱ t❤❡ ¯ p ❛♥❞ e+ s♣❡❝tr❛ s❤♦✉❧❞ ❜❡ t❤❡ s❛♠❡ ❛s p ❛t E ✶✵ ●❡❱ ❙✐♠✐❧❛r❧②✱ ¯ p/p s❤♦✉❧❞ ❜❡ ✢❛t ✐❢ ¯ p ❛r❡ ❝♦✲✐♥❥❡❝t❡❞ ✭❛❧❜❡✐t ❛s s❡❝♦♥❞❛r✐❡s✮ ✐♥t♦ ❛♥② ❙◆❘✲❉❙❆ ♣r♦❝❡ss ❉❡❝❧✐♥❡ ♦❢ ¯ p ❛t ❧♦✇❡r ❡♥❡r❣✐❡s ✐s ❝♦♥s✐st❡♥t ✇✐t❤ ❡❧❡❝tr♦st❛t✐❝ r❡t❡♥t✐♦♥ ✐♥ ▼❈ ❙♦❧❛r ♠♦❞✉❧❛t✐♦♥ ♠❛② ❛❧s♦ ❝♦♥tr✐❜✉t❡ t♦ p − ¯ p ❞✐✛❡r❡♥❝❡ ❛t ❧♦✇❡r ❡♥❡r❣✐❡s ❋❧❛t ¯ p/p s❤♦✉❧❞ ❝♦♥t✐♥✉❡ ✉♣ t♦ p ∼ pmax ❛♥❞ ❞❡❝❧✐♥❡ ❛t p p♠❛① ✭s❡❝♦♥❞❛r✐❡s ✇✐t❤ ♥♦ ❛❝❝❡❧❡r❛t✐♦♥✮

✶✷ ✴ ✶✹

❈♦♥❝❧✉s✐♦♥s

s❡❝♦♥❞❛r② ♣♦s✐tr♦♥s ♣r♦❞✉❝❡❞ ✐♥ pp ❝♦❧❧✐s✐♦♥s ✐♥s✐❞❡ ▼❈s ❛❤❡❛❞ ♦❢ ❙◆❘ s❤♦❝❦s ❛♥❞ ❡①♣❡❧❧❡❞ ✐♥t♦ s❤♦❝❦ ♣r❡❝✉rs♦r ♠❛❦❡ ❛ s❡❡❞ ♣♦♣✉❧❛t✐♦♥ ❢♦r t❤❡ ❉❙❆ s❤♦❝❦✲❛❝❝❡❧❡r❛t❡❞ ♣♦s✐tr♦♥s ❞❡✈❡❧♦♣ ❛ ❝♦♥❝❛✈❡ s♣❡❝tr✉♠✱ ❝❤❛r❛❝t❡r✐st✐❝ ❢♦r t❤❡ ◆▲ ❉❙❆✳ ♠♦st ♦❢ t❤❡ ♥❡❣❛t✐✈❡❧② ❝❤❛r❣❡❞ ❧✐❣❤t s❡❝♦♥❞❛r✐❡s ✭e−)✱ ❛♥❞ t♦ s♦♠❡ ❡①t❡♥t✱ ¯ p✱ ❛❧♦♥❣ ✇✐t❤ t❤❡ ♣r✐♠❛r② ❡❧❡❝tr♦♥s✱ r❡♠❛✐♥ ✐♥s✐❞❡ ▼❈s ❛♥❞ ♠❛❦❡ ❧❡ss ❝♦♥tr✐❜✉t✐♦♥s t♦ t❤❡ ♦✈❡r❛❧❧ s♣❡❝tr✉♠ ❞✉❡ t♦ t❤❡ ◆▲ s✉❜s❤♦❝❦ r❡❞✉❝t✐♦♥✱ t❤❡ ▼❈ r❡♠❛✐♥s ✉♥s❤♦❝❦❡❞✱ s♦ t❤❛t s❡❝♦♥❞❛r② ¯ p ❛♥❞✱ ✐♥ ♣❛rt✱ ❤❡❛✈✐❡r ♥✉❝❧❡✐ ❛❝❝✉♠✉❧❛t❡❞ ✐♥ ✐ts ✐♥t❡r✐♦r ❧❛r❣❡❧② ❡✈❛❞❡ s❤♦❝❦ ❛❝❝❡❧❡r❛t✐♦♥ t❤❡ ❆▼❙✲✵✷ ♣♦s✐tr♦♥ ❡①❝❡ss ✐s ♥♦t ❢✉❧❧② ❛❝❝♦✉♥t❡❞ ❢♦r ♦♥❧② ✐♥ t❤❡ r❛♥❣❡ ∼ ✷✵✵ − ✹✵✵●❡❱✱ ❇❯❚✿ ♣❤②s✐❝❛❧ ♣❤❡♥♦♠❡♥❛ t♦ ❜❡ ✐♥❝❧✉❞❡❞ ✐♥ t❤❡ ♥❡①t✲st❡♣ ♠♦❞❡❧ ✭e+/e− r✉♥✲❛✇❛② ❜r❡❛❦❞♦✇♥✱ ❙②♥✳ ♣✐❧❡✲✉♣✱ ❡t❝✳✮ ❛r❡ ❧✐❦❡❧② t♦ s✉✣❝❡ ❢♦r ❛ ❝♦♥✈❡♥t✐♦♥❛❧ ❡①♣❧❛♥❛t✐♦♥ ♦❢ t❤❡ r❡s✐❞✉❛❧ ❡①❝❡ss

✶✸ ✴ ✶✹

▼❡ss❛❣❡ t♦ t❤❡ ❖❜s❡r✈❡rs

◆♦t ❡✈❡r② ❜✉♠♣ ✐♥ t❤❡ ❞❛t❛ ✐s ❢r♦♠ ❉▼

✶✹ ✴ ✶✹