Transcript Electron thermalization and emission from magnetized

Electron thermalization
and emission from
compact magnetized sources
Indrek Vurm and Juri Poutanen
University 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
Cygnus X-1
– Thermal
Comptonization
– Weak non-thermal tail
• Soft state
– Dominant disk
blackbody
– Non-thermal tail
extending to a few
MeV
keV
Zdziarski & Gierlinski 2004
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
• What is the
heated in HS, and
thermalization?
accelerated in SS (Poutanen
– Coulomb - not efficient
& Coppi 1998).
– synchrotron selfabsorption?
Cooling vs. escape
• Compton scattering:
t cool,Compton
V
1
  esc
t esc
c (1  )lrad
• Synchrotron radiation:
tcool,synch 3 Vesc
1

t esc
4 c (1  )lB
Luminosity
compactness:

 T Lrad
L
107 cm
lrad 
 26 37
3
me c R
10 erg/s R

Magnetic compactness:

lB 
T
me c
2
RUB
Cooling is always faster than escape if

lrad > 1 and/or
lB > 1
R
Vesc
Thermalization by Coulomb collisions
2
2
Ý
Ý
• Cooling Compton ( ) , synchrotron ( )
• Rate of energy exchange with
0
a low energy thermal pool of
Ý
Coulomb  
electrons by Coulomb

collisions:
• Thermalization happens only at

very low energies:
ÝCompton + 
Ýsynchrotron  
ÝCoulomb 


 T 
 th  ln 
  1
lB  lrad 

1/ 2
• In compact sources, Coulomb
thermalization is not efficient!
Synchrotron self-absorption
•
Assume power-law
distribution:
e–
Ne ( )   n
•
Ýh , 
Ýc )
log( 
Ýh

Electron heating in selfabsorption (SA) regime:

1. Nonrelativistic
limit
Ýh   0  const



2. Relativistic limit
•
•
2
Ý
h  ( )
Ýc ( )2

Katarzynski et al., 2006
Ýc ( )
Electron cooling 
log(  )
Ratio of heating and
cooling in SA relativistic
 3 is a solution?McCray 1967,
Ýh

5
regime:
"T urbulent plasma react or"
- Kaplan, T syt ovich

Ýc

2

n2
It is not a solution!
Rees 1967,Ghisellini et al. 1988

At low energies heating always dominates
Synchrotron self-absorption
Ýh

• Efficient thermalizing mechanism.
• Time-scale = synchrotron cooling time
Ghisellini, Haardt, Svensson 1998
Numerical simulations
• Synchrotron boiler (Ghisellini, Guilbert, Svensson 1988):
– synchrotron emission and thermalization by synchrotron selfabsorption (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; selfconsistent, but numerical problems because of SSA
Our code
• One-zone, isotropic particle distributions, tangled Bfield
• 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
inj  2
ELECTRONS
PHOTONS
3

4
4
3
L  1037 erg/s,  T  2, lB /linj  5, No ext ernal radiat ion
inj  2,
3,
kTe  12, 24,
4
36 keV
Variable luminosity
10
10
38
PHOTONS
ELECTRONS
10 38
10 37
37



inj  3.5, lB /linj  5, No external radiation
L  1036 , 1037 , 1038 erg/s
 T  0.2, 2,
20
kTe  140, 30,
1.3 keV
Variable luminosity
XTE J1550–564
PHOTONS
10 38
37
10
38
GRS
10 1915+105
10 37
Cyg X-3


GX 339-4


At L  1037 erg/s, power- law   1.7 
similar to the hard states of GBHs
At highL, Wien T  2 - 3 keV+ tail 
similar to the ultra
- soft, high stat es of GBHs
Role of magnetic field
PHOTONS
10
5
ELECTRONS
lB / linj  1

inj  3.5,  T  2,
B   c   Lsyn  
L  10 erg/s
mean electron energy 
37
No external radiat ion
 spectrum softens
Role of the external disk photons
ELECTRONS
Ldisk /Linj  10
0
PHOTONS
1 0.1
0

inj  3.5, T  2, L 1037 erg/s, lB /linj  5
Role of the external disk photons
Ldisk /Linj  10

0
Ldisk /Linj  
electrons: Te  , thermal  non- thermal
photon spectrum gets softer
similar to spectral transitions in GBHs
PHOTONS
1 0.1
0
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.