Transcript Accretion modles for the flares of Sgr A*

Some issues on models of black
hole X-ray binaries
Feng Yuan
Shanghai Astronomical Observatory, Chinese Academy of Sciences
Outline

The accretion model for the hard state (XTE
J1550-564 as an example)
 Introduction to luminous hot accretion flows (LHAFs)
 Explaining the X-ray emission of the luminous hard
state of XTE J1550-564 with LHAFs
 On the contribution of jet in the X-ray radiation of the
hard state

The model for the quiescent state: jet-dominated?
ADAF and Its Critical Accretion Rate

The energy equation of ions in ADAFs:
dsi
Ti
 qadv,i  q   q  ( q   qie )
dr

.
.
For a typical ADAF (i.e., M  M Edd), we have:
q   qadv,i  q 

So advection is a cooling term
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):


q q

.
Self-similar solution of ADAF
 m1 
M1
.
M Edd
 0.4 2
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:
dsi
Ti
 qadv,i  q   qie
dr
since:
qadv  Ti
So we have:
dsi
d
  i  q c
dr
dr
d i

 q   q c  qie
dr
The dynamics of LHAFs:
Basic Physics (II)

An ADAF is hot because
.
.
when M  M 1 :
.
d i
 q   q c  qie  q   q c  0
dr
d i

 q   q c  qie  q c  0
dr
.
when M ~ M 1 :


so the flow remains hot if it starts out hot.
.
.
.
When M  M 1 , up to another critical rate M 2determined by

q  q  qie
c
We still have:
d i
note that 
 q c  q   qie  0,
d
dr
 i  q   q c  qie  0 
so advection is a heating term!
dr
So again the flow will be hot if it starts out hot,
i.e., a . new hot
.
accretion solution (LHAFs) exists between M 1 and M 2
Properties of LHAFs

Using the self-similar scaling law:
.
M1 :
.
M2:




.
.
q  q  M 1  0.4 M Edd


2
.
.
q  q  q  M 2   M Edd

c

2
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.
The thermal equilibrium curve of
accretion solutions: local analysis

Following the usual
approach, we adopt the
following two assumptions
  k


Qadv 
M P

2
2R 
we solve the algebraic
accretion equations, setting
ξto be positive (=1) and
negative (=-0.1, -1, -10) to
obtain different accretion
solutions.
Yuan 2003
Four Accretion Solutions
Yuan 2001
LHAFs: Two Types of Accretion
Geometry
.
.
.
.
.
When M 1  M  (3  5) M 1 : (M1  0.1 M Edd for   0.3)
Hot accretion flow
Type-I:
.
.
.
When (3 - 5) M 1  M  M Edd :
Collapse into a thin disk
See also Pringle, Rees &
Pacholczyk 1973;
Begelman, Sikora & Rees
1987
Type-II:
Strong magnetic dissipation?
Global Solutions of LHAFs: Dynamics
Yuan 2001


α=0.3; M BH  10M 
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)
Global Solutions of LHAFs:
Energetics
Yuan 2001

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)
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
For type-I solution
For type-II solution
Yuan 2003
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
obtain (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
6% LEdd
3%LEdd
1%LEdd
Yuan, Zdziarski, Xue & Wu 2007
LHAF
Yuan, Zdziarski, Xue & Wu 2007
Yuan, Zdziarski, Xue & Wu 2007
The three dots show the E-folding energy of the three X-ray
spectra shown in the previous figure.
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 twophase accretion flow may be formed (e.g., prominence in solar corona; multiphase ISM; Field 1965) .
Hot gas



Cold clumps
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?
The optical and X-ray light
curves of XTE J1550-564
during its 2000 outburst.
Secondary maxima
No maximum in the X-ray!
Jain et al. 2001, ApJ
Secondary Maximum: the contribution of the jet
Jet emission
Yuan, Zdziarski, Xue & Wu 2007
Observed radio---X-ray correlation
Radio/X-ray correlation of GX 339-4; from Corbel et al. 2003, A&A
Radio-X-ray correlation and the
quiescent state
The
optically-thin synchrotron emission
,. while the
2
Comptonization from the hot accretion flow M
With the decrease of accretion rate, the X-ray emission of
the system will be dominated by the jet
Thus 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
Radio-X-ray correlation in the larger
regime of luminosity
Yuan & Cui 2005, ApJ
The change of the radio—X-ray correlation from hard to quiescent states
Test the prediction
Wu, Yuan, & Cao 2007