black holes as possible sources of uhecr

BLACK HOLES AS POSSIBLE SOURCES OFUHECR

K. Ptitsyna, S.Troitsky, O.Kalashev, A.Neronov

MSU, INR RAS, Moscow

K. Ptitsyna, S.Troitsky, O.Kalashev, A.Neronov BLACK HOLES AS POSSIBLE SOURCES OF UHECR

Plan

1 Task:

to determine a class of possible sources of the cosmic raysE > 1019эВ

2 Constrains on possible sources.

3 Answer:

Possible sourses - supermassive black holes in the centresof galaxies -discribe the observable cosmic ray spectrum

4 Development of the model

K. Ptitsyna, S.Troitsky, O.Kalashev, A.Neronov BLACK HOLES AS POSSIBLE SOURCES OF UHECR

Models of the sources

K. Ptitsyna, S.Troitsky, O.Kalashev, A.Neronov BLACK HOLES AS POSSIBLE SOURCES OF UHECR

Constrains on possible sources:

1 Spectrum (GZK) + isotropy −→ sources are extragalactic

2 Lack of clustering: a lot of sources (> 10−4 1Mpc3 , [Dubovsky])

3 Model of acceleration:1 geometric criterion: accelerated particle remains inside the

source during acceleration (Hillas criterion)2 energy losses for radiation should not exceed energy gain3 realistic source parametres4 The total gamma emission associated with particle

acceleration from all the sources should not exceed the valueof the diffuse gamma background.

4 Spectrum: a set of sources should describe cosmic rayspectrum

K. Ptitsyna, S.Troitsky, O.Kalashev, A.Neronov BLACK HOLES AS POSSIBLE SOURCES OF UHECR

Hillas criterion and constrains from the energy losses

Constrains:1 Hillas criterion: E ≤ qBR

2 Energy losses:dE−dt =

dE+dt

Models:1 inductive

1 curvature2 synchrotron

2 diffusive

Hillas diagram

[Ptitsyna, Troitsky, 2010]

K. Ptitsyna, S.Troitsky, O.Kalashev, A.Neronov BLACK HOLES AS POSSIBLE SOURCES OF UHECR

Model: black holes in the centres of galaxies

[Neronov, Semikoz, Tkachev, 2007]

rh = 0.5 · RSchw = GMBH

Particle energy

dE−dt

= −dE+

dt

dE−dt

= −23Z2e2E4

A4m4pR2

dE+

dt= EZe

Ecurv =

(32

A4m4pR2

SchwE

Zeχ2

)1/4

RSchw = 3 · 1013

(M

108M⊙)

sm

BEd = 104

(M

109M⊙)−1/2

G

Ecurv ≈ 28 · 1019 AZ 1/4

(M

109M⊙)3/8 ( χ

1◦)−1/2

κ1/4 eV

K. Ptitsyna, S.Troitsky, O.Kalashev, A.Neronov BLACK HOLES AS POSSIBLE SOURCES OF UHECR

Model

Model parametres:

1 energy of the accelerated particleE ← MBH ∈ (105M⊙ − 1010M⊙),

black hole mass distribution is known ← from the black holemass function [Li, 2011]

the total source concentration n ∼ 10−3 1Mpc3 .

2 luminosity of a single source in cosmic rays L ∝ Mα1

a part of “appropriate” black holes N ∝ Mα2 ← one parameterMα

α MBH

K. Ptitsyna, S.Troitsky, O.Kalashev, A.Neronov BLACK HOLES AS POSSIBLE SOURCES OF UHECR

Model: black hole in the center of galaxy

Results: cosmic ray spectrum

Auger

Hires

K. Ptitsyna, S.Troitsky, O.Kalashev, A.Neronov BLACK HOLES AS POSSIBLE SOURCES OF UHECR

Model

Checking constrains

1

Total radiation associated withaccelerationEγ ∼ TeV → GeV ⇒ shouldnot exceed diffuse gammabackground

2 Luminosity of a single source:

Lγ ≈ 1040(

M109M⊙

)1/8 ergs

<< LEd = 1047(

M109M⊙

)ergs

K. Ptitsyna, S.Troitsky, O.Kalashev, A.Neronov BLACK HOLES AS POSSIBLE SOURCES OF UHECR

Preliminary conclusions

1 formulation of the constrains on the possible UHECR sources.

2 Suggestion black holes in the centres of galaxies as a class ofthe possible sources and checking that this class of sourcessatisfies all the considered constrains.

3 this class of sources describes the observed cosmic rayspectrum, using only one free parameter (α)

K. Ptitsyna, S.Troitsky, O.Kalashev, A.Neronov BLACK HOLES AS POSSIBLE SOURCES OF UHECR

Development of the model

Er ∝ −aB0

a ↓↑ B0 a ↑↑ B0

ε = Efinal − Einitial ⇒ Q = 2B0J

K. Ptitsyna, S.Troitsky, O.Kalashev, A.Neronov BLACK HOLES AS POSSIBLE SOURCES OF UHECR

Development of the model

Charged black hole

K. Ptitsyna, S.Troitsky, O.Kalashev, A.Neronov BLACK HOLES AS POSSIBLE SOURCES OF UHECR

Development of the model

K. Ptitsyna, S.Troitsky, O.Kalashev, A.Neronov BLACK HOLES AS POSSIBLE SOURCES OF UHECR

Q = 0 a ↓↑ B0

K. Ptitsyna, S.Troitsky, O.Kalashev, A.Neronov BLACK HOLES AS POSSIBLE SOURCES OF UHECR

Q = max a ↑↑ B0

K. Ptitsyna, S.Troitsky, O.Kalashev, A.Neronov BLACK HOLES AS POSSIBLE SOURCES OF UHECR

Conclusions

1 black holes as possible UHECR sources

2 they describes a cosmic ray spectrum

3 development of the model

K. Ptitsyna, S.Troitsky, O.Kalashev, A.Neronov BLACK HOLES AS POSSIBLE SOURCES OF UHECR

Thank you for your attention!

K. Ptitsyna, S.Troitsky, O.Kalashev, A.Neronov BLACK HOLES AS POSSIBLE SOURCES OF UHECR

Модель

Поведение электрического и магнитного полей на оси симметрии

|E | ∼ |B0|

m

a ∼ (0, 8− 1)MBH

K. Ptitsyna, S.Troitsky, O.Kalashev, A.Neronov BLACK HOLES AS POSSIBLE SOURCES OF UHECR

Constraint: total radiation should not exceed diffuse gamma background

Curvature radiation

I (ω) ≈ 2√

3q2γω

ωc

∫ ∞2ω/ωc

K5/3(x)dx

Eγ =32E3curv

m3R

Eγ = 20A3

Z 3/4

(M

108M⊙)1/8 ( χ

1◦)−1/2

TeV

K. Ptitsyna, S.Troitsky, O.Kalashev, A.Neronov BLACK HOLES AS POSSIBLE SOURCES OF UHECR

K. Ptitsyna, S.Troitsky, O.Kalashev, A.Neronov BLACK HOLES AS POSSIBLE SOURCES OF UHECR

Thank you for your attention!

K. Ptitsyna, S.Troitsky, O.Kalashev, A.Neronov BLACK HOLES AS POSSIBLE SOURCES OF UHECR

Development of the model

[Neronov, Semikoz, Tkachev, 2007]

K. Ptitsyna, S.Troitsky, O.Kalashev, A.Neronov BLACK HOLES AS POSSIBLE SOURCES OF UHECR

Development of the model

F = 12B0

(dψ + 2J

M dη)

F = 12B0

[∂gµϕ∂xν + 2J

M∂gµt∂xν

]dxν ∧ dxµ

Fνµ = B0

[∂gµϕ∂xν + 2J

M∂gµt∂xν

] [Wald, 1974]

In the Locally non rotating frame:

FAB = Fµνeµ

AeνB

et =(

AΣ∆

)1/2∂∂t + 2Mar

(AΣ∆)1/2∂∂ϕ,

er =√

∆Σ∂∂r ,

eθ

= 1√Σ∂∂θ,

eθ

=√

Σ√Asinθ

∂∂ϕ,

FAB =

0 −Er −Eθ−Eϕ

Er 0 Bϕ −Bθ

Eθ−Bϕ 0 Br

Eϕ Bθ

−Br 0

∆ = r2 − 2Mr + a2, Σ = r2 + a2cos2θ, A = (r2 + a2)2 − a2∆sin2θ.

K. Ptitsyna, S.Troitsky, O.Kalashev, A.Neronov BLACK HOLES AS POSSIBLE SOURCES OF UHECR