Luminous Hot Accretion FlowsLuminous Hot Accretion Flows------extending ADAF beyond its critical accretion rate

Feng Yuan

Shanghai Astronomical Observatory, Chinese Academy of Science

Outline

The dynamics of luminous hot accretion flows (LHAFs)

Main features of LHAFs Stability Possible Applications (in AGNs & BH X-ray

Binaries) Questions & Speculations

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 qqqqqdr

dsT

qqq iadv,

qq

EddMM..

2.

11

.

4.0

EddM

MmSelf-similar solution of ADAF

So advection is a cooling term

The dynamics of LHAFs 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 qqqdr

dsT

,

ciiiadv q

dr

d

dr

dsTq

ieci qqq

dr

d

since:

So we have:

The dynamics of LHAFs 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 qqqqqdr

d:when .

1

.

MM

0 cie

ci qqqqdr

d

1

..

MM

iec qqq

0 ie

ci qqqdr

d

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

qqqdr

die

ci

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

R

MQadv 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 viscously stable.

It is possibly convectively stable, since the entropy of the flow decreases with decreasing radius.

Outflow: the Bernoulli parameter is in general negative in LHAF, so outflow may be very weak.

LHAF is thermally unstable against local perturbations. However, 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 ApJ

For type-I solution

For type-II solution

Application of LHAFs: the origin of X-ray emission of 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 that thermal Comptonization is the mechanism for the X-ray emis

sion of the sources, we can obtain the most suitable parameters (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 (T, τ)

We find that the most favored model is an LHAF (with parameterized energy equation), while ADAFs predicting too high T.

Modeling Luminous X-ray Sources: LHAFs better than ADAFs

Yuan & Zdziarski 2004

Modeling the 2000 outburst of XTE J1550-564

Yuan, Zdziarski, Xue & Wu 2007

6% LEdd

3%LEdd

1%LEdd

Yuan, Zdziarski, Xue, & Wu 2007

LHAF

Temperature profiles of the three solutions. The three dots show the E-folding energy of the three X-ray spectra shown in a previous figure.The theoretical predictions are in good agreement with observations.

Two phase accretion: Another possible consequence of the strong thermal instability

The accretion flow is thermally unstable at the collapse radius two-phase accretion flow? (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 configuration may hold for high accretion rates; when there are many clumps, they may form a thin disk. But photon bubble & clu

mping instabilities (Gammie 1998; Merloni et al. 2006) may make the disk clumpy again?

Cold clumpsHot gas

On the possible application of LHAFs: Questions from observations

1. The origin of X-ray emission in quasars & some BHXBs?

a) Lx >10% LEdd

b) The thin disk sandwiched between corona model does not work because the corona is too weak (Hirose, Krolik & Stone 2006)

c) One-phase LHAF can only explain Lx up to

~8% L

2. The accretion model for the very high state?

a)Both thermal & nonthermal (steep; no cut-off) spectral component are strong

b) strong QPOs

3. It is claimed that at some relatively luminous hard state, some broad iron Ka lines are detected (Miller et al. 2006; 2007)

Speculations on the above questions X-ray origin of quasars: accretion rate is high

The accretion rate in the hot phase: is decreasing with decreasing radii is in “maximal” value at each radius

Some hot gas gradually collapses into clouds by releasing their thermal energy

The very high state Accretion Geometry: truncated standard thin disk + two phase flow: QPO The thermal component is due to the blackbody or bremsstrahlung radiation from the clump

s The nonthermal component is due to Comptonization emission by the (thermal and nonther

mal) electrons in the hot phase

The presence of iron Ka line same line profile can be reproduced by two-phase flow and even better (Hartnoll & Blackm

an 2001) Puzzling low Inclination preferrance for some Seyfert 2 Reprocessed fraction too low & uncorrelated with line (Merloni et al. 2006)

The accretion flow of luminous hard state may also be two-phase