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■♥tr♦❞✉❝t✐♦♥ Pr♦❥❡❝t ❙✉♠♠❛r② ■♥❞✐r❡❝t ❞❡t❡❝t✐♦♥ ✐♥ ▼✐❧❦② ❲❛② s❛t❡❧❧✐t❡s ❙❡❧❢✲❛♥♥✐❤✐❧❛t✐♥❣ ❉▼ ✐♥ ♣r❡s❡♥❝❡ ♦❢ ❧✐❣❤t ❢♦r❝❡ ♠❡❞✐❛t♦r ▼✐❤❛❡❧ P❡t❛↔ ■♥ ❝♦❧❧❛❜♦r❛t✐♦♥ ✇✐t❤ P✐❡r♦ ❯❧❧✐♦ ❛♥❞ ▼❛✉r♦ ❱❛❧❧✐ ❆str♦♣❛rt✐❝❧❡ ♣❤②s✐❝s ❣r♦✉♣ ❙■❙❙❆✱ ❚r✐❡st❡ ❏✉♥❡ ✶✸✱ ✷✵✶✽ ▼✐❤❛❡❧ P❡t❛↔ ■♥❞✐r❡❝t ❞❡t❡❝t✐♦♥ ✐♥ ▼✐❧❦② ❲❛② s❛t❡❧❧✐t❡s

■♥tr♦❞✉❝t✐♦♥ Pr♦❥❡❝t ❙✉♠♠❛r② ■♥❞✐r❡❝t ❞❡t❡❝t✐♦♥ ❙❡❛r❝❤ ❢♦r ❉▼ ❛♥♥✐❤✐❧❛t✐♦♥✴❞❡❝❛② s✐❣♥❛t✉r❡s ✐♥ t❤❡ s❦② ❯s❡ ❣❛❧❛①✐❡s ❛s ♣❛rt✐❝❧❡ ♣❤②s✐❝s ❧❛❜♦r❛t♦r✐❡s ❙tr♦♥❣ ❝♦♥str❛✐♥ts ♦♥ t❤❡r♠❛❧ r❡❧✐❝s ❘❛♣✐❞ ✐♠♣r♦✈❡♠❡♥ts ✐♥ ♦❜s❡r✈❛t✐♦♥❛❧ ❞❛t❛ ⇒ ◆❡❡❞ ❢♦r ❛❝❝✉r❛t❡ ♠♦❞❡❧✐♥❣ ♦❢ ❉▼ r❡❧❛t❡❞ s✐❣♥❛❧s ▼✐❤❛❡❧ P❡t❛↔ ■♥❞✐r❡❝t ❞❡t❡❝t✐♦♥ ✐♥ ▼✐❧❦② ❲❛② s❛t❡❧❧✐t❡s

■♥tr♦❞✉❝t✐♦♥ Pr♦❥❡❝t ❙✉♠♠❛r② ❈✉rr❡♥t ❝♦♥str❛✐♥ts DOI:1 0. 1 03 8/ NP HYS 4049 8 1 0 7 1 0 6 Icecube 201 6/ANTARES 201 5 1 0 5 1 0 ) 1 3 s − 4 1 0 26 cm 3 1 0 AMS 201 5 0 − 2 5 1 0 Planck 201 〉 ( × 1 HESS: 201 6 0 1 1 v 〈 σ 0 0 1 Ferm i-LAT 201 6 − 1 Galactic centre bulge em ission 0 Ferm i-LAT 201 5 1 Dwarf galaxies − 2 1 0 0 − 3 1 0 1 0 2 0 3 0 4 1 1 1 1 m DM (GeV) ❋✐❣✉r❡✿ ■♥❞✐r❡❝t ❞❡t❡❝t✐♦♥ ❝♦♥str❛✐♥ts ♦♥ ❉▼ ❛♥♥✐❤✐❧❛t✐♦♥ ❝r♦ss✲s❡❝t✐♦♥✳ ▼✐❤❛❡❧ P❡t❛↔ ■♥❞✐r❡❝t ❞❡t❡❝t✐♦♥ ✐♥ ▼✐❧❦② ❲❛② s❛t❡❧❧✐t❡s

■♥tr♦❞✉❝t✐♦♥ Pr♦❥❡❝t ❙✉♠♠❛r② Pr♦❥❡❝t ♦✉t❧✐♥❡ ✲ ❛r❳✐✈✿✶✽✵✹✳✵✺✵✺✷ ▼♦t✐✈❛t✐♦♥✿ ●❡♥❡r✐❝ ❡♥❤❛♥❝❡♠❡♥t ♦❢ s✐❣♥❛❧ ✐♥ ♣r❡s❡♥❝❡ ♦❢ ❧✐❣❤t ♠❡❞✐❛t♦rs ✶ Pr♦❜❡ ❡✛❡❝t ♦❢ ❉▼ ✈❡❧♦❝✐t② ❛♥✐s♦tr♦♣② ♦♥ ❛♥♥✐❤✐❧❛t✐♦♥ s✐❣♥❛❧ ❊r❛ ♦❢ ❤✐❣❤ ♣r❡❝✐s✐♦♥ ❝♦s♠♦❧♦❣② ❛♥❞ ❛str♦♥♦♠② ✭❋❡r♠✐✲▲❆❚✱ ❛❝❝✉r❛t❡ ♠❡❛s✉r❡♠❡♥ts ♦❢ st❡❧❧❛r ❦✐♥❡♠❛t✐❝s✱ ✳✳✳✮ ❖✉t❧✐♥❡✿ ▼♦❞❡❧ t❤❡ ❉▼ ❤❛❧♦ ♣❤❛s❡✲s♣❛❝❡ ❞✐str✐❜✉t✐♦♥ ❙t✉❞② t❤❡ ❛♥♥✐❤✐❧❛t✐♦♥ r❛t❡s ✐♥ ♣r❡s❡♥❝❡ ♦❢ ❙♦♠♠❡r❢❡❧❞ ❡♥❤❛♥❝❡♠❡♥t ❆♣♣❧② t❤❡ ❛♥❛❧②s✐s t♦ ▼✐❧❦② ❲❛② s❛t❡❧❧✐t❡s ✶ ❇♦❞❞② ❡t ❛❧✳ ❛r❳✐✈✿✶✼✵✷✳✵✵✹✵✽✱ ❇❡r❣strö♠ ❡t ❛❧✳ ❛r❳✐✈✿✶✼✶✷✳✵✸✶✽✽ ▼✐❤❛❡❧ P❡t❛↔ ■♥❞✐r❡❝t ❞❡t❡❝t✐♦♥ ✐♥ ▼✐❧❦② ❲❛② s❛t❡❧❧✐t❡s

■♥tr♦❞✉❝t✐♦♥ Pr♦❥❡❝t ❙✉♠♠❛r② ■♥❞✐r❡❝t ❞❡t❡❝t✐♦♥ ❋♦❝✉s ♦♥ ❣❛♠♠❛ r❛②s ❢r♦♠ ❉▼ ❛♥♥✐❤✐❧❛t✐♦♥s✳ ❉✐✛❡r❡♥t✐❛❧ ♣❤♦t♦♥ ✢✉① ♣r♦❞✉❝❡❞ ❜② ❛♥♥✐❤✐❧❛t✐♦♥s✿ ❞ Φ = ✶ ❞ N � � � f ( � r , � v ✶ ) � f ( � r , � v ✷ ) ❞ ✸ v ✶ ❞ ✸ v ✷ ❞ Ω ❞ ℓ · ( σ v r❡❧ ) ❞ E γ ✽ π ❞ E γ m χ m χ ◆♦♥✲st❛♥❞❛r❞ ✐♥❣r❡❞✐❡♥ts✿ ❆♥♥✐❤✐❧❛t✐♦♥ ❝r♦ss✲s❡❝t✐♦♥ ❜♦♦st❡❞ ❜② r❡❧❛t✐✈❡ ✈❡❧♦❝✐t② ❞❡♣❡♥❞❡♥t ❢❛❝t♦r ✲ ❙♦♠♠❡r❢❡❧❞ ❡♥❤❛♥❝❡♠❡♥t ✿ � σ v r❡❧ � ✵ → � σ v r❡❧ � ✵ · S ( v r❡❧ ) ❈♦♠♣✉t❡ ♣❤❛s❡✲s♣❛❝❡ ❞✐str✐❜✉t✐♦♥ ❢♦r ✈❛r✐♦✉s ❉▼ ❞❡♥s✐t② ♣r♦✜❧❡s ✭◆❋❲✱ ❇✉r❦❡rt ❛♥❞ ♥♦♥✲♣❛r❛♠❡tr✐❝ ♣r♦✜❧❡✮ ▼✐❤❛❡❧ P❡t❛↔ ■♥❞✐r❡❝t ❞❡t❡❝t✐♦♥ ✐♥ ▼✐❧❦② ❲❛② s❛t❡❧❧✐t❡s

■♥tr♦❞✉❝t✐♦♥ Pr♦❥❡❝t ❙✉♠♠❛r② ❙♦♠♠❡r❢❡❧❞ ❡♥❤❛♥❝❡♠❡♥t ●❡♥❡r✐❝ ❜♦♦st ♦❢ ❝r♦ss✲s❡❝t✐♦♥ ❢♦r ♥♦♥✲r❡❧❛t✐✈✐st✐❝ ♣❛rt✐❝❧❡s ❢♦r ✐♥t❡r❛❝t✐♦♥s ♠❡❞✐❛t❡❞ ❧✐❣❤t s❝❛❧❛r ♦r ✈❡❝t♦r ❢♦r❝❡ ♠❡❞✐❛t♦r φ ✭✐✳❡✳ r❡q✉✐r❡s E χ ≈ m χ ❛♥❞ m φ ≪ α χ m χ ✮✳ ❨✉❦❛✇❛ ❝♦✉♣❧✐♥❣ ❣✐✈❡s r✐s❡ t♦ t❤❡ ❢♦❧❧♦✇✐♥❣ ♣♦t❡♥t✐❛❧✿ V ( r ) = ∓ α χ r exp ( − m φ r ) ❙♦❧✈❡ ❙❝❤rö❞✐♥❣❡r ❡q✉❛t✐♦♥ t♦ ♦❜t❛✐♥ t❤❡ ✇❛✈❡ ❢✉♥❝t✐♦♥ ❞✐st♦rt✐♦♥ ❞✉❡ t♦ t❤❡ ♠❡❞✐❛t♦r ❡①❝❤❛♥❣❡✿ ✷ � v ✷ � � � χ ( ✵ ) ✶ χ ′′ ( x ) + r❡❧ � � + V ( x ) χ ( x ) = ✵ ⇒ S ( v r❡❧ ; ξ ) = ∝ � � v α α ✷ χ ( ∞ ) χ � � r❡❧ ▼✐❤❛❡❧ P❡t❛↔ ■♥❞✐r❡❝t ❞❡t❡❝t✐♦♥ ✐♥ ▼✐❧❦② ❲❛② s❛t❡❧❧✐t❡s

■♥tr♦❞✉❝t✐♦♥ Pr♦❥❡❝t ❙✉♠♠❛r② ❉▼ ♣❤❛s❡✲s♣❛❝❡ ❞✐str✐❜✉t✐♦♥ ❢✉♥❝t✐♦♥ ❉✐✛❡r❡♥t ✐s♦tr♦♣✐❝ ♠♦❞❡❧✐♥❣s ♣r❡s❡♥t ✐♥ ❧✐t❡r❛t✉r❡ ▼❛①✇❡❧❧✲❇♦❧t③♠❛♥♥ ❛♣♣r♦①✐♠❛t✐♦♥✿ v ✷ ρ ❉▼ ( r ) � � f ( r , v ) = ( ✷ πσ ✷ ( r )) ✸ / ✷ · ❡①♣ ✷ σ ✷ ( r ) ❊❞❞✐♥❣t♦♥✬s ✐♥✈❡rs✐♦♥ ✭❜❛s❡❞ ♦♥ s♣❤❡r✐❝❛❧ ❏❡❛♥s ❡q✉❛t✐♦♥✮✿ � E E = Ψ( r ) − v ✷ ✶ ❞ ❞ Ψ ❞ ρ f ( E ) = √ √ , ❞ E ❞ Ψ ✷ ✽ π ✷ E − Ψ ✵ ❊❞❞✐♥❣t♦♥✬s ✐♥✈❡rs✐♦♥ ❣✐✈❡s ✉♥✐q✉❡ s♦❧✉t✐♦♥ ❢♦r s♣❤❡r✐❝❛❧❧② s②♠♠❡tr✐❝ ❛♥❞ ❡r❣♦❞✐❝ ✭❤❡♥❝❡ ✐s♦tr♦♣✐❝✮ s②st❡♠✳ ▼✐❤❛❡❧ P❡t❛↔ ■♥❞✐r❡❝t ❞❡t❡❝t✐♦♥ ✐♥ ▼✐❧❦② ❲❛② s❛t❡❧❧✐t❡s

■♥tr♦❞✉❝t✐♦♥ Pr♦❥❡❝t ❙✉♠♠❛r② ❆♥✐s♦tr♦♣✐❝ ❉▼ ♣❤❛s❡✲s♣❛❝❡ ❞✐str✐❜✉t✐♦♥ ❢✉♥❝t✐♦♥ ❱❡❧♦❝✐t② ❛♥✐s♦tr♦♣② ❝❤❛r❛❝t❡r✐③❡❞ ❜②✿ β ( r ) ≡ ✶ − σ ✷ t ✷ σ ✷ r ❙❧♦♣❡✲❛♥✐s♦tr♦♣② ✐♥❡q✉❛❧✐t② ✷ ✿ ✲ d ❧♥ ρ d ❧♥ r ≥ ✷ β ❲❡ ❝♦♥s✐❞❡r t❤❡ ❢♦❧❧♦✇✐♥❣ ♣♦ss✐❜❧❡ ❝❤♦✐❝❡s✿ r ✷ ❖s✐♣❦♦✈✲▼❡rr✐tt ♠♦❞❡❧ ✿ β ( r ) = r ✷ + r ✷ a E → Q = E − L ✷ ✶ + r ✷ � � , ρ ( r ) → ρ ( r ) · ✷ r ✷ r ✷ a a ❈♦♥st❛♥t ♦r❜✐t❛❧ ❛♥✐s♦tr♦♣②✿ β ( r ) = β c f ( E , L ) = L − ✷ β c · f β c ( E ) ✷ ❆♥✫❊✈❛♥s ❛r❳✐✈✿❛str♦✲♣❤✴✵✺✶✶✻✽✻✈✹✱ ❈✐♦tt✐✫▼♦r❣❛♥t✐ ❛r❳✐✈✿✶✵✵✻✳✷✸✹✹ ▼✐❤❛❡❧ P❡t❛↔ ■♥❞✐r❡❝t ❞❡t❡❝t✐♦♥ ✐♥ ▼✐❧❦② ❲❛② s❛t❡❧❧✐t❡s

■♥tr♦❞✉❝t✐♦♥ Pr♦❥❡❝t ❙✉♠♠❛r② ❉▼ ✈❡❧♦❝✐t② ❞✐str✐❜✉t✐♦♥ Eddington Eddington 4 M.B. M.B. 3.0 O.M. ( r a /r s = 1) O.M. ( r a /r s = 1) β DM = − 1 / 2 β DM = − 1 / 2 2.5 3 2.0 P( v ) P( v ) 2 1.5 1.0 1 0.5 0.0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 v/v esc v/v esc ❋✐❣✉r❡✿ ❱❡❧♦❝✐t② ❞✐str✐❜✉t✐♦♥s ❝♦♠♣✉t❡❞ ✉♥❞❡r ❞✐✛❡r❡♥t ❛ss✉♠♣t✐♦♥s ❢♦r ◆❋❲ ✭❧❡❢t✮ ❛♥❞ ❇✉r❦❡rt ✭r✐❣❤t✮ ❞❡♥s✐t② ♣r♦✜❧❡s✳ ▼✐❤❛❡❧ P❡t❛↔ ■♥❞✐r❡❝t ❞❡t❡❝t✐♦♥ ✐♥ ▼✐❧❦② ❲❛② s❛t❡❧❧✐t❡s