Electron thermalization and emission from compact magnetized sources
description
Transcript of Electron thermalization and emission from compact magnetized sources
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.