black holes as possible sources of uhecr
TRANSCRIPT
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