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 L bol / L Γ index (2-10keV) and . Edd 2. Anti-correlation between L − / L L bol / L and . 2 10keV bol Edd 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 = Ω π Ω R / 2 , where is the solid angle of the reflector Ω = ( for the reflection from a semi-infinite plane). 1 Zdziarski A. A., Lubinski P., Smith D. A., 1999, MNRAS, 303, L11

Accretion disk-corona model corona Optical/UV flux disk Growing loops around a sunspot. 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: B 2 = + p p p τ ϕ = = α p ( ) a. , is adopted in standard thin disk model tot gas rad r π tot 8 (Shakura & Sunyaev 1973), which is thermal unstable. B 2 τ ϕ = = α p b. , the modified alpha-viscosity, which is thermal stable. r π gas 8 B 2 τ ϕ = = α p p c. , which is initially suggested by Taam &Lin (1984) r π gas tot 8 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. B 2 τ ϕ = = α p p is also supported by the analysis on the local r π gas tot 8 dynamical instabilities in magnetized, radiation-pressure-supported accretion disks (Blaes & Socrates 2001).

The disk-corona model The gravitational power released in the disk is (in unit surface area) ⎡ ⎤ 1 / 2 ⎛ ⎞ R 3 � + = Ω − ⎜ ⎟ Q M R ⎢ ⎥ 2 in ( ) 1 K π dissi ⎝ R ⎠ ⎢ ⎥ 8 ⎣ ⎦ The power transported from the cold disk to the corona is B 2 + = ≈ Q p v v π cor m p A 8 The energy equation for the cold disk: σ T 4 1 4 + − + + − + = Q Q a Q disk ( 1 ) , τ dissi cor cor 2 3 τ = − a where the reflection albedo , and is the optical depth of the 0 . 1 0 . 2 cold disk.

The equations describing the cold disk: � − π ρ = RH R R v R M 4 ( ) ( ) ( ) Continuity: d R ρ kT 1 aT = + = + p p p 4 disk Equation of state: µ tot gas rad m disk 3 p ⎡ ⎤ 1 / 2 ⎛ ⎞ R � Ω + = π τ ⎜ ⎟ M R ⎢ ⎥ H in ( ) 1 4 Angular momentum: ϕ r K d ⎝ R ⎠ ⎢ ⎥ ⎣ ⎦ The magnetic stress tensors: ⎧ α p ⎪ tot τ ϕ = = α p p ⎨ r m gas ⎪ α p p ⎩ gas tot The ratio of the power radiated from the corona to the total (bolometric luminosity) for the disk-corona system is ∫ + π Q R R 2 d = cor f ∫ + π Q R R 2 d dissi

Ruled out! τ ϕ = α p red: r tot τ ϕ = α p green: r gas τ ϕ = α p gas p blue: r tot

Calculation of the spectrum of the corona The equations of the corona: ρ ρ kT kT = + + p p cor i cor e Equation of state: µ µ cor cor, m m m i p e p + = + δ + = − Q Q Q F ie , Energy equation: cor cor cor cor − = − + − + − ρ Q T T F F F F ie ( , , ) where the cooling rate , and cor i e cor cor syn brem Comp is the energy transfer rate from the ions to electrons via Coulomb collisions.

τ ϕ = α p r tot τ ϕ = α p r gas τ ϕ = α p gas p r tot

√ √ Vasudevan R. V., Fabian A. C., 2007, MNRAS, 381, 1235 Ruled out! τ ϕ = α p red: r tot Ruled out! τ ϕ = α p green: r gas τ ϕ = α p gas p blue: r tot

Summary τ φ = α p p 1 / 2 1. ( ) is roughly consistent with the X-ray r gas tot observations, while the other two are not. L bol / L L cor / L 2. decreases with increasing . It means more Edd bol L bol / L soft photons supplied by the cold disk for high- cases, Edd 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.

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 Γ � R m It is still ongoing, and will be reported in our future work.

Thank you!