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.