An accretion disk-corona model for X-ray spectra of active galactic - - PowerPoint PPT Presentation

An accretion disk-corona model for X-ray spectra of active galactic nuclei

Xinwu Cao Shanghai Astronomical Observatory

Typical SED of AGN

X-ray observations as constraints on accretion disk-corona models

1. correlation between photon spectral index (2-10keV) and . 2. Anti-correlation between and . Γ

Edd bol / L

L

Edd bol / L

L

bol 10keV 2

/ L L −

Shemmer, Brandt, Netzer, Maiolino, & Kaspi, 2008, ApJ, 682, 81 Wang, Watarai, Mineshige, 2004, ApJ, 607, L107

• 3. Correlation between hard X-ray spectral index

and Compton reflection R

Γ

, where is the solid angle of the reflector ( for the reflection from a semi-infinite plane).

π 2 / Ω = R Ω 1 = Ω

Zdziarski A. A., Lubinski P., Smith D. A., 1999, MNRAS, 303, L11

Accretion disk-corona model

Growing loops around a sunspot. disk corona

Optical/UV flux

Taken from Galeev A. A., Rosner R., Vaiana G. S., 1979, ApJ, 229, 318.

In the disk-corona model, the magnetic fields generated in the cold disc are strongly buoyant, and a substantial fraction of magnetic energy is transported vertically to heat the corona above the disc with the reconnection of the fields (e.g., Di Matteo 1998). The key point for constructing a disk-corona model is: the strength of the magnetic fields, which determines the efficiency of the energy transportation from the disk to corona.

Magnetic fields in the disks

Possible options for magnetic stress tensor:

, 8

tot 2

p B

r

α π τ ϕ = = ) (

rad gas tot

p p p + =

a. is adopted in standard thin disk model (Shakura & Sunyaev 1973), which is thermal unstable.

gas 2

8 p B

r

α π τ ϕ = =

• b. , the modified alpha-viscosity, which is thermal stable.

tot gas 2

8 p p B

r

α π τ ϕ = =

• c. , which is initially suggested by Taam &Lin (1984)

based on the viscosity being proportional to the gas pressure while the size of turbulence being limited by the disk thickness (given by the total pressure). It’s thermal stable. is also supported by the analysis on the local dynamical instabilities in magnetized, radiation-pressure-supported accretion disks (Blaes & Socrates 2001).

tot gas 2

8 p p B

r

α π τ ϕ = =

The disk-corona model

A 2 p m cor

8 v B v p Q π ≈ =

+

The gravitational power released in the disk is (in unit surface area) The power transported from the cold disk to the corona is

⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − Ω =

+ 2 / 1 in 2 dissi

1 ) ( 8 3 R R R M Q

K

• π

The energy equation for the cold disk:

, 3 4 ) 1 ( 2 1

4 disk cor cor dissi

τ σT Q a Q Q = − + −

+ + +

where the reflection albedo , and is the optical depth of the cold disk.

2 . 1 . − = a τ

The equations describing the cold disk:

M R v R R RH

• =

− ) ( ) ( ) ( 4

R d

ρ π

Continuity: Equation of state: Angular momentum:

4 disk p disk rad gas tot

3 1 aT m kT p p p + = + = µ ρ

ϕ

τ π

r

H R R R M

d 2 / 1 in K

4 1 ) ( = ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + Ω

• The magnetic stress tensors:

⎪ ⎩ ⎪ ⎨ ⎧ = =

tot gas gas tot m

p p p p p

r

α α α τ ϕ

The ratio of the power radiated from the corona to the total (bolometric luminosity) for the disk-corona system is

∫ ∫

+ +

= R R Q R R Q f d 2 d 2

dissi cor

π π

red: green: blue:

tot

p

r

α τ ϕ =

gas

p

r

α τ ϕ =

tot gas p

p

r

α τ ϕ =

Ruled out!

Calculation of the spectrum of the corona

The equations of the corona: Equation of state:

m cor, p e e cor p i i cor cor

p m kT m kT p + + = µ ρ µ ρ

Energy equation:

,

cor cor ie cor cor − + +

= + = F Q Q Q δ

where the cooling rate , and is the energy transfer rate from the ions to electrons via Coulomb collisions.

− − − −

+ + =

Comp brem syn cor

F F F F ) , , (

cor e i ie cor

ρ T T Q

tot

p

r

α τ ϕ =

gas

p

r

α τ ϕ =

tot gas p

p

r

α τ ϕ =

red: green: blue:

tot

p

r

α τ ϕ =

gas

p

r

α τ ϕ =

tot gas p

p

r

α τ ϕ =

Ruled out! Ruled out!

Vasudevan R. V., Fabian A. C., 2007, MNRAS, 381, 1235

√ √

Summary

1. is roughly consistent with the X-ray

• bservations, while the other two are not.
• 2. decreases with increasing

. It means more soft photons supplied by the cold disk for high- cases, and the corona is therefore cooled down more efficiently, which leads to lower electron temperatures and then softer X- ray spectra.

• 3. Our spectral calculations show that the X-ray spectrum is too

softer when the accretion rate is as low as 0.01. We suggest that the ADAF+disk/corona model may resolve this issue, because the photon spectral index of an ADAF can be as low as ~1.5.

2 / 1

) (

tot gas r

p p α τ φ =

bol cor / L

L

Edd bol / L

L

Edd bol / L

L

• 4. The transition radius of the outer disk-corona to inner ADAF

increases with decreasing accretion rate, which also predicts a correlation between the Compton reflection and X-ray photon spectral index.

a

m

• Γ

R

It is still ongoing, and will be reported in

• ur future work.

Thank you!