Transcript Accretion modles for the flares of Sgr A*

Luminous 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:
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

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

An ADAF is hot because
.

.
when M  M 1 :
.
d i

 q   q c  qie  q c  0
dr
.
when M ~ M 1 :

d i
 q   q c  qie  q   q c  0
dr
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  q   q c  qie  0
dr

d i
note that 
 q c  q   qie  0,
dr
so advection is a heating term!
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 ApJ
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
emission 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
6% LEdd
3%LEdd
1%LEdd
Yuan, Zdziarski, Xue & Wu 2007
LHAF
Yuan, Zdziarski, Xue, & Wu 2007
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) .
Hot gas



Cold clumps
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 &
clumping instabilities (Gammie 1998; Merloni et al. 2006) may make the disk
clumpy again?
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
clumps
 The nonthermal component is due to Comptonization emission by the (thermal and
nonthermal) 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 &
Blackman 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