electron thermalization and emission from compact magnetized sources
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Electron thermalizationand emission from
compact magnetized sources
Indrek Vurm and Juri PoutanenUniversity of Oulu, Finland
Spectra of accreting black holes
• Hard state– Thermal
Comptonization– Weak non-thermal tail
• Soft state– Dominant disk
blackbody– Non-thermal tail
extending to a few MeV Zdziarski et al. 2002
Spectra of accreting black holes
• Hard state– Thermal
Comptonization– Weak non-thermal tail
• Soft state– Dominant disk
blackbody– Non-thermal tail
extending to a few MeV
Zdziarski & Gierlinski 2004
Cygnus X-1
keV
Electron distribution• Why electrons are (mostly)
thermal in the hard state? • Why electrons are (mostly)
non-thermal in the soft state?
• Spectral transitions can be explained if electrons are heated in HS, and accelerated in SS (Poutanen & Coppi 1998).
• What is the thermalization? – Coulomb - not efficient – synchrotron self-
absorption?
Cooling vs. escape• Compton scattering:
• Synchrotron radiation:
Luminosity compactness:
Magnetic compactness:
Cooling is always faster than escape if lrad > 1 and/or lB > 1€
lB =σ T
mec2
RUB
€
lrad =σ T
mec3
Lrad
R= 26
L
1037erg/s
107cm
R
€
tcool ,Compton
tesc
= πVesc
c
1
(1+ γ)lrad
€
tcool ,synch
tesc
=3
4
Vesc
c
1
(1+ γ)lB
R
Vesc
Thermalization by Coulomb collisions• Cooling• Rate of energy exchange with
a low energy thermal pool of electrons by Coulomb collisions:
• Thermalization happens only at very low energies:
• In compact sources, Coulomb thermalization is not efficient!
€
˙ γ Coulomb ∝ γ 0
€
˙ γ Compton ∝ (γβ )2, ˙ γ synchrotron ∝ (γβ )2
€
˙ γ Compton + ˙ γ synchrotron < ˙ γ Coulomb ⇒
γβ( )th< lnΛ
τ T
lB + lrad
⎡
⎣ ⎢
⎤
⎦ ⎥
1/ 2
≈1
€
log(γβ )
€
log( ˙ γ h, ˙ γ c )
€
˙ γ h
€
˙ γ c ∝ (γβ )2
Katarzynski et al., 2006
Synchrotron self-absorption• Assume power-law e–
distribution:
• Electron heating in self-absorption (SA) regime: 1. Nonrelativistic limit
2. Relativistic limit
• Electron cooling• Ratio of heating and
cooling in SA relativistic regime:
At low energies heating always dominates
€
Ne (γ)∝ γ −n
€
˙ γ h ∝ γ 0 = const
€
˙ γ h ∝ (γβ )2
€
˙ γ h˙ γ c
=5
n + 2€
˙ γ c ∝ (γβ )2
€
γ−3 is a solution? McCray 1967,
"Turbulent plasma reactor"- Kaplan, Tsytovich
It is not a solution! Rees 1967, Ghisellini et al. 1988
Synchrotron self-absorption
• Efficient thermalizing mechanism. • Time-scale = synchrotron cooling time
Ghisellini, Haardt, Svensson 1998
€
˙ γ h
Numerical simulations• Synchrotron boiler (Ghisellini, Guilbert, Svensson 1988):
– synchrotron emission and thermalization by synchrotron self-absorption (SSA), electron equation only, self-consistent
• Ghisellini, Haardt, Svensson (1998)– synchrotron and Compton cooling, SSA thermalization– not fully self-consistent (only electron equation solved)
• EQPAIR (Coppi):– Compton scattering, pair production, bremsstrahlung, Coulomb
thermalization; self-consistent, but electron thermal pool at low energies
• Large Particle Monte Carlo (Stern): – Compton scattering, pair production, SSA thermalization; self-
consistent, but numerical problems because of SSA
Our code• One-zone, isotropic particle distributions, tangled B-
field• Processes:
– Compton scattering: • exact Klein-Nishina scattering cross-sections for all particles• diffusion limit at low energies
– synchrotron radiation: exact emissivity/absorption for photons and heating/cooling (thermalization) for pairs.
– pair-production, exact rates• Time-dependent, coupled kinetic equations for electrons,
positrons and photons.• Contain both integral and differential terms• Discretized on energy and time grids and solved iteratively as a
set of coupled systems of linear algebraic equations• Exact energy conservation.
Variable injection slope
€
L = 1037 erg/s, τ T = 2, lB / linj = 5, No external radiation
Γinj = 2, 3, 4
kTe = 12, 24, 36 keV
34
inj=
2ELECTRONS
€
inj = 2
3
4
PHOTONS
Variable luminosity
€
inj = 3.5, lB / linj = 5, No external radiation
L =1036, 1037, 1038 erg/s
τ T = 0.2, 2, 20
kTe =140, 30, 1.3 keV
ELECTRONS
€
1037
€
1038L=
1036 er
g/s
€
1037
€
1038PHOTONS
L=1036 erg/s
€
1037
€
1038PHOTONS
L=1036 erg/s
Variable luminosity
€
1038
€
1037
GX 339-4
GRS 1915+105
XTE J1550–564
Cyg X-3
€
At L ≈1037erg/s, power - law Γ ≈1.7 →
similar to the hard states of GBHs
At high L, Wien T ≈ 2 - 3 keV + tail →
similar to the ultra - soft, high states of GBHs
Role of magnetic fieldELECTRONS
€
inj = 3.5, τ T = 2,
L =1037erg/s
No external radiation
PHOTONS
€
lB / linj =1
510
€
B↑ ⇒ ν c ↑ ⇒ Lsyn ↑ ⇒
mean electron energy γ ↓
⇒ spectrum softens Γ ↑
Role of the external disk photons
€
inj = 3.5, τ T = 2, L =1037erg/s, lB / linj = 5
€
Ldisk /Linj =10 PHOTONS
0.110
ELECTRONS0
L disk
/L inj=
10
Role of the external disk photons
0€
Ldisk /Linj =10 PHOTONS
0.110
€
Ldisk /Linj ↑ ⇒
electrons : Te ↓ , thermal → non - thermal
photon spectrum gets softer -
similar to spectral transitions in GBHs
Conclusions• Hard injection produces too soft spectra (due to strong
synchrotron emission) inconsistent with hard state of GBHs.
• Hard state spectra of GBHs = synchrotron self-Compton, no feedback or contribution from the disk is needed.
• At high L, the spectrum is close to saturated Comptonization peaking at ~5 keV, similar to thermal bump in the very high state.
• Spectral state transitions can be a result of variation of the ratio of disk luminosity and power dissipated in the hot flow. Our self-consistent simulations show that the electron distribution in this case changes from nearly thermal in the hard state to nearly non-thermal in the soft state.
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