Disk corona interaction: from X-ray binaries to AGN

In collaboration with F. Meyer, E. Meyer-Hofmeister and S. Mineshige

Bifang Liu Bifang Liu Yunnan Observatory, CASYunnan Observatory, CAS

Outline

The disk corona interaction: the evaporation

process

The disk corona evaporation model in X-ray

binaries

The magnetic reconnection-heated corona in

AGN

The disk corona evaporation model

First proposed by Meyer and Meyer-Hofmeister (1994) to int

erpret the UV delay in CVs

Developed to BHs by Meyer, Liu, Meyer-Hofmeister (2000)

Two-temperature model established by Liu, Mineshige, Mey

er et al. (2002)

Other approaches in the same frame:

• Rozanska & Czerny (2000), vertically approximated model

• Dullemond (1999), semi-analytical model

The disk corona interaction

• Interaction of the disk and the corona:

• Vertical heat conduction (Fc=-k0T5/2dT/dz)

• mass evaporation

• Steady accreting corona: Gas accretes to the BH, re-supplied by eva

porating gas from the disk

corona

BH/NS/WD

X-rays evaporation

disk

Conductive heat

Meyer & Meyer-Hofmeister 1994

Vertical structure of the corona

Continuity equation Momentum equation Energy equation Heat conduction (spitzer formula) Equation of state Boundary conditions (upper and lower)

Coronal structure (P,T,ρ,vz) determinedEvaporation rate: Means accretion flowing rate in the corona

zz

R

RvRdRvRM 2422

2

1

．

The radius-dependent evaporation rate

The maximal evaporation rate 0.02Eddington rate

The corresponding radius 300RS

Inclusion of magnetic field: maximal evaporation rate unchanged, corresponding radius shifted

Radial distribution of evaporation rate does not depend M

log

me

va

p

log r

.

0.02

Meyer, Liu, Meyer-Hofmeister,2000

2.5

Influence of magnetic field

Qian, Liu, wu 2006

Complete depletion of the inner disk by evaporation

m=6

Condition for inner disk depletion

M<Mevap(max)

M>Mevap(max), disk extends to ISCO

M<Mevap(max), inner disk depleted

Truncation radius: Mevap(rtr)=M

• •

• •

• •

• •

Disk evaporation: two basic accretion modes

Mass flow in the disk + corona

Mass flow in the outer cool disk

Accumulated in the outer disk Flow inwards:m

Evaporated into the corona Flow inwards through the disk

Wind loss from the corona Accreted through the corona to BH

Mass transferred from the companion star

.

m>m

evap

..

ADAF

Disk+corona

Black hole X-ray binaries: observations

Gilfanov et al 2000 Done et al 2004

Transition of spectral states

Well-known observational features

• X-ray transients

• Outburst: soft spectra

• Quiescence: hard spectra

• Persistent X-ray binaries

Accretion rate varying up and down

hard/soft spectral transition

• Spectral transition occurs at L~1037ergs/s (~0.01Ed

dington rate)

critmm critmm

•

• •

•

Interpreting the state transition

02.0(max) evapcrit mm• •

•

• m<0.02, RIAF-dominant accretion

Hard spectral state

m>0.02, Disk-dominant accretion

Soft spectral srtate

1 mrtr•

Transition rate:

Hysteresis in transition luminosity

Schematic light curve of an X-ray nova outburst

GX339-4

Observed light curve

Explanation by disk corona model

Different irradiation in hard and soft state leads to different evaporation rate and transition rate:

Meyer-Hofmeister, Liu, Meyer 2005

XTee

e Fncm

hvkTq

2

4

Hysteresis caused by irradiationsLiu, Meyer, Meyer-Hofmeister 2005

Accretion rates at hard/soft spectral transition

for various irradiation from the central black holeDependence of hysteresis on mean

photon energy of irradiation

XTee

e Fncm

hvkTq

2

4

Hysteresis in truncation radius

The intermediate stateLiu, Meyer, Meyer-Hofmeister 2006

log

me

va

p

log r

.

Corona

Outer diskInner disk

Accretion rate

Intermediate states occur during the decay of an outburst

Spectral states of BHXBsMeyer, Liu, Meyer-Hofmeister 2006

Accretion rate

decreases

An inner disk below the ADAF

Vertical stratification of disk and corona Temperature distribution with height

2

3

232 )(1059.3

cm

kTTTnnq

e

eeiieie

Re-condensation from an ADAF into an inner disk

Fraction of ADAF flow condenses onto an inner disk as a function of distance

Summary: Disk corona model for X-ray binaries

Provides a physical mechanism to explain

• Truncation of the disk at low accretion rate

• Spectral transition between hard and soft states

• The hysteresis between the transitions of hard-to-soft and soft-to-hard states

• Occurrence of intermediate state

How about the disk corona in AGN?

Observational similarities between AGN and BHXBs

The fundamental plane for AGNs and BHXBs (Merloni et al. 2003)

log LR=0.6log LX+0.78log M+7.33

Falcke et al. 2004: Proposed unification scheme

Observational similarities between AGN and BHXBs

Similarities in spectral states

• Similarity between high-luminosity AGN and soft-state BHXBs (Maccarone et al. 2003)

• Similarity between low-luminosity AGN and hard-state BHXBs (Narayan 2004; Falcke et al. 2004)

• Similarity between NLS1s and very high state BHXBs?

• Timescale in AGN much longer than in BHXBs

Galactic sources: a laboratory for AGN?

Disk corona model in AGN

Theoretically, the disk corona mode does not depend on M.

It predicts spectral transition rate 0.02 Eddington rate for AGN

• Hard state: m<0.02

the Galactic Center, LLAGN, LINER, etc

• Soft state: m>0.02

e.g. quasars, some of the Seyferts

• An example of tentative spectral state transition

Seyfert-LINER transition galaxy NGC7589 (Yuan, Komossa, Xu et al. 2005)

Observations in AGN do show a critical accretion rate m0.02 (Maccarone et al 2003)

·

·

·

Importance of corona in luminous AGN

Luminous AGN and quasars (at soft state)

• SED (optical-UV, soft and hard X-ray, broad

fluorescent iron lines) indicates coexistence of

hot gas and cold gas close to BH, which are usu

ally thought to be the corona and thin disk.

• The high X-ray luminosity means a large fraction

of accretion energy released in the hot corona

UVoptX LL ~

Problem in disk corona model for luminous AGN

• The corona at high accretion rate is either over-cooled by inverse Compton scattering or blown away by radiation-driven winds.

• Additional heating is required to keep the corona

• The most promising heating mechanism:

Magnetic field transports accretion

energy to the corona, which is then

released by magnetic reconnection

The magnetic reconnection-heated corona

reconnection

Magnetic loops

Disk

Dynamo action in Dynamo action in disk: disk: Gravitational Gravitational energy to Benergy to B

Magnetic loops emerge Magnetic loops emerge above the disk andabove the disk and reconnect in the coronareconnect in the corona

Magnetic energy is Magnetic energy is transferred to thermal transferred to thermal energyenergy by reconnection by reconnection

The heat is radiated to X-rays The heat is radiated to X-rays

through Compton scatteringthrough Compton scattering

Liu, Mineshige, Shibata, 2002

The magnetic reconnection-heated corona

Interactions between the disk and corona Magnetic field transports accretion energy from the disk to the corona Disk radiations are Compton scattered in the c

orona Heat is conducted by electrons from corona to

chromosphere Evaporating gas supplies for the corona accreti

on

The disk with corona above

Shakura-Sunyaev (1973) disk

• Disk quantities determined by M, M and energy fraction

dissipated in the disk (1-f)

Pd=Pd (M,M, f), Td =Td (M,M, f)

• Equipartition between the magnetic energy and gas thermal

energy in the disk: Pd=B2/8π

B=B(M, M, f)

•

•

•

•

The corona above a disk

Energy balance

reconnection heating = Compton cooling in corona

conduction heating = evaporation cooling in chromosphere

　　　　　⇒ T (M, M, f), n (M, M, f)

,radTe

A LcUncm

kTV

Bσ

4

4 2

2

2127

γ

γ/

H

/

1

m

kTnkT

L

KT

••

Determination of energy fraction dissipated in corona

Equation concerning f for given M and M

),,(8

34 3

2

fMMFR

GMMVBf A

Calculate the disk variablesCalculate the corona T, n, τfor given M and M

Solve the equation for f

•

•

•

•

Two solutions for disk-corona model

Gas pressure-dominated (disk) solutionExists for accretion rate>0.02

• Most of the accretion energy is transferred to the

corona, f ~ 1

• Corona is strong with T ～ 109 K, n ～ 109 cm-3

and Compton radiation is large

• Disk is cool with temperature T~ a few 104K

• Backward Compton radiation is reprocessed as

seed soft photons, little intrinsic disk contribution

Two solutions for disk-corona model

Radiation pressure-dominated (disk) solution

Exists for high accretion rate

• Most of the accretion energy is dissipated in disk, f « 1

• Disk is like a usual one with temperature T~105—T~107K

• Corona is weak with T ～ 108 K, n ～ 108 cm-3 and

Compton radiation is low

• The emission is dominated by disk multi-color

blackbody emission

Emission from disk and corona Disk emission: multi-color blackbody Emergent emissions—disk photons coming out of

the corona

• Part of them come out without scattering (disk

component): Observed UV and soft X-rays

• Part of them are Compton upscattered in corona

• Coming out upwards: the observed X-rays

• Going out backwards: processed as seed photons

Spectra from Monte Carlo Simulations

Spectra from disk+corona

Two types of spectrum

• Hard spectrum: Multi-color blackbody

+ Power law X-rays

• Soft spectrum: Multi-color blackbody

• Hard spectrum can occur for both high m and low m (m>0.02)

• Soft spectrum occurs only for high m

· ·

·

Liu, Mineshige, Ohsuga 2003

·

Spectra emerging from the corona

Hard spectrum: Power Law, α~ 1.1--1.2 (Γ ~ 2.1--2.2 )Occurrence at accretion rate>0.02 Eddington rateSpectra similar to that of Haardt & Maraschi 1991,1993

L=0.35LEdd

L=0.7LEdd

L=0.07LEd

d

M=108Msun

Spectra emerging from the corona

Soft spectrum: Occurrence only in luminous system

M=108

Msun

L=0.7LE

dd

What’s new in our model? Propose a mechanism for transferring accretion energy to the corona

Establish a self-consistent disk+corona model

Interpret strong X-ray radiation in AGN

Interpret the very high state in BHXBs (the spetrem seems too flat)?

Disk and corona variables and spectra are solely determined by m and mdot

Modeling observations without free parameters

Summary: B-heated corona

• for a relatively low-luminosity system

(<0.02<L/LEdd<0.2)

Hard spectrum: Power law, ≈1.1

comparable with Seyfert galaxies: ≈0.9-1.0

• for a high-luminosity system (L>0.2LEdd)

either hard spectrum ≈1.1

or soft spectrum (disk dominated MCD)

• BH mass independent, applicable to stellar-mass

black hole

Liu, Mineshige, Ohsuga 2003

Conclusion

The disk corona interaction leads to

• depletion of the inner disk at low accretion rate

• Triggering the spectral state transition

• Formation of a weak interior disk: the intermediate state

• Hysteresis observed in X-ray binaries

• Magnetic reconnection heated corona in AGN: the strong X-ray radiations

• Magnetic reconnection heated corona in BHXBs: the very high state?