Some issues on models of black holSome issues on models of black hole X-ray binariese X-ray binaries

Feng Yuan

Shanghai Astronomical Observatory, Chinese Academy of Sciences

Outline The accretion model for the hard state (XTE J155

0-564 as an example) Introduction to luminous hot accretion flows (LHAFs) Explaining the X-ray emission of the luminousluminous hard stat

e of XTE J1550-564 with LHAFs On the contribution of jet in the X-ray radiation of the har

d state The model for the quiescent state: jet-dominated?

ADAF and Its Critical Accretion Rate The energy equation of ions in ADAFs:

For a typical ADAF (i.e., ), we have:

Since q- increases faster than q+ and qadv with increasing accretion rate, there exists a critical accretion rate of ADAFs, determined by (Narayan, Mahadevan & Quataert 1998):

)(, ieiadvi

i qqqqqdrdsT

qqq iadv,

qq

EddMM..

2.

11

.4.0

EddM

MmSelf-similar solution of ADAF

So advection is a cooling term

The dynamics of LHAFs: Basic Physics (I)

What will happen above the critical rate of ADAF? Originally people think no hot solution exists; but this is not true

The energy equation of accretion flow:

ieiadvi

i qqqdrdsT

,

ciiiadv q

drd

drdsTq

ieci qqq

drd

since:

So we have:

The dynamics of LHAFs: Basic Physics (II)

An ADAF is hot because

so the flow remains hot if it starts out hot. When , up to another critical rate determined by

:~when .

1

.MM

0 cie

ci qqqqqdrd:when

.

1

.MM

0 cie

ci qqqqdrd

1

..MM

iec qqq

0 ie

ci qqqdrd

2

.M

We still have:

So again the flow will be hot if it starts out hot, i.e., a new hot accretion solution (LHAFs) exists between 2

.

1

. MandM

term! a isadvection so

,0 that note

heating

qqqdrd

ieci

Properties of LHAFs Using the self-similar scaling law:

LHAF is more luminous than ADAFs since it corresponds to higher accretion rates and efficiency.

The entropy decreases with the decreasing radii. It is the converted entropy together with the viscous dissipation that balance the radiation of the accretion flow.

Since the energy advection term is negative, it plays a heating role in the Euler point of view.

The dynamics of LHAFs is similar to the cooling flow and spherical accretion flow.

Eddc

Edd

MMqqqM

MMqqM.

22

.

2

.

.2

1

.

1

.

:

4.0 :

The thermal equilibrium curve of accretion solutions: local analysis

Following the usual approach, we adopt the following two assumptions

we solve the algebraic accretion equations, setting ξto be positive (=1) and negative (=-0.1, -1, -10) to obtain different accretion solutions.

k P

RMQadv 22

Yuan 2003

Four Accretion Solutions

Yuan 2001

LHAFs: Two Types of Accretion Geometry

:)53(When .

1

.

1

.MMM

:5)-(3When ..

1

.

EddMMM

)3.0for 1.0(..

1 EddMM

Hot accretion flow

Collapse into a thin disk

Strong magnetic dissipation?

Type-I:

Type-II:

See also Pringle, Rees & Pacholczyk 1973; Begelman, Sikora & Rees 1987

Global Solutions of LHAFs: Dynamics

α=0.3; Accretion rates are: 0.05(solid; ADAF); 0.1 (dotted; critical ADAF); 0.3 (dashed; type-I LH

AF) 0.5 (long-dashed; type-II LHAF)

MM BH 10

Yuan

2001

Global Solutions of LHAFs: Energetics

Accretion rates are: 0.05(solid; ADAF); 0.1 (dotted; critical ADAF); 0.3 (dashed; type-I LHAF) 0.5 (long-dashed; type-II LHAF)

Yuan

2001

Stability of LHAFs From the density profile, we know that LHAFs are viscousl

y stable. It is possibly convectively stable, since the entropy of the fl

ow decreases with decreasing radius. Outflow: the Bernoulli parameter is in general negative in L

HAF, so outflow may be very weak. LHAF is thermally unstable against local perturbations. Ho

wever, at most of the radii, the accretion timescale is found to be shorter than the timescale of the growth of perturbation, except at the ``collapse’’ radius.

The thermal stability of LHAFs

Yuan 2003

For type-I solution

For type-II solution

Application of LHAFs: the origin of X-ray emission in AGNs and black hole binaries X-ray Luminosity.

The maximum X-ray luminosity an ADAF can produce is (3-4)%LEdd

X-ray luminosities as high as ~20% Eddington have been observed for the hard state (XTE J1550+564; GX 339-4) & AGNs.

An LHAF can produce X-ray luminosities up to ~10%LEdd

Spectral parameters Assuming thermal Comptonization model for the X-ray emission, we can obt

ain (Te, τ) to describe the average spectrum of Seyfert galaxies

On the other side, we can solve the global solution for both ADAF and LHAF, to obtain the values of (Te, τ)

We find that an LHAF can produce better Te & τ than an ADAF (predicted Te too high compared to observation).

Modeling Luminous X-ray Sources: LHAFs better than ADAFs

Yuan & Zdziarski 2004

An example: the 2000 outburst of XTE J1550-564

Yuan, Zdziarski, Xue & Wu 2007

6% LEdd

3%LEdd

1%LEdd

Yuan, Zdziarski, Xue & Wu 2007

LHAF

The three dots show the E-folding energy of the three X-ray spectra shown in the previous figure.

Yuan, Zdziarski, X

ue & W

u 2007

Questions on LHAFs Questions on theoretical side

Type-II LHAF is strongly thermally unstable at the transition radius, thus is it applicable in nature?

The range between the critical ADAF and type-I LHAF seems to be rather small

Questions on applications It seems that an LHAF can only produce up to 10%LEdd

X-ray luminosity, but many X-ray sources are likely more luminous

How to explain the very high state? (may related with the above item)

In some relatively luminous hard state, iron Ka line seems to be detected (but…)

Speculations on the Above Questions the accretion flow is thermally unstable at the collapse radius. As a result, a two-p

hase accretion flow may be formed (e.g., prominence in solar corona; multi-phase ISM; Field 1965) .

The amount of clouds should be controlled by that the hot phase is in a ‘maximal’ LHAF regime

Such a two-phase configuration may correspond to a large range of rate; when the rate is higher, more matter will condense out.

when there are many clumps, they may form a thin disk. But photon bubble & clumping instabilities (Gammie 1998; Merloni et al. 2006) may make the disk clumpy again?

Cold clumpsHot gas

Jain et al. 2001, ApJ

The optical and X-ray light curves of XTE J1550-564 during its 2000 outburst.

Secondary maxima

No maximum in the X-ray!

Yuan, Zdziarski, Xue & Wu 2007

Secondary Maximum: the contribution of the jet

Jet emission

Radio/X-ray correlation of GX 339-4; from Corbel et al. 2003, A&A

Observed radio---X-ray correlation

Radio-X-ray correlation and the quiescent state

The optically-thin synchrotron emission , while the Comptonization from the hot accretion flow With the decrease of accretion rate, the X-ray emission of the system will be dominated by the jetThus a change of the radio---X-ray correlation is expected, from AB to CD. The critical luminosity is:

The X-ray emission of the quiescent state (below the above critical luminosity) should be dominated by jets

.2M

Radio-X-ray correlation in the larger regime of luminosity

The change of the radio—X-ray correlation from hard to quiescent states

Yuan &

Cui 2005,

ApJ

Test the predictionW

u, Yuan, &

Cao

2007