2014Ap&SS.353..223M
Title: Spectral signatures of dissipative standing shocks and mass outflow in presence of Comptonization around a black hole
Authors: Santanu Mondal & Sandip K. Chakrabarti & Dipak Debnath.
Key Findings: Accretion flows having positive specific energy are known to produce outflows and winds which escape to a large distance. According to Two Component Advective Flow (TCAF) model, centrifugal pressure dominated region of the flow just outside the black hole horizon, with or without shocks, acts as the base of this outflow. Electrons from this region are depleted due to the wind and consequently, energy transfer rate due to inverse Comptonization of low energy photons are affected. Specifically, it becomes easier to cool this region and emerging spectrum is softened. Our main goal is to show spectral softening due to mass outflow in presence of Compton cooling. To achieve this, we modify Rankine-Hugoniot relationships at the shock front when post-shock region suffers mass loss due to winds and energy loss due to inverse Comptonization. We solve two-temperature equations governing an accretion flow around a black hole which include Coulomb exchange between protons and electrons and other major radiative processes such as bremsstrahlung and thermal Comptonization. We then compute emitted spectrum from this post-shock flow. We also show how location of standing shock which forms outer boundary of centrifugal barrier changes with cooling. With an increase in disc accretion rate , cooling is enhanced and we find that the shock moves in towards the black hole. With cooling, thermal pressure is reduced, and as a result, outflow rate is decreased. We thus directly correlate outflow rate with spectral state of the disc.
=========================================================
2013MNRAS.436.2864K
Title: Effect of the flow composition
on outflow rates from accretion discs around black holes
Authors: Rajiv Kumar Singh, B. Chandra;
Indranil Chattopadhyay & Sandip K. Chakrabarti
Key Findings:
=========================================================
Title: Spectral properties of
two-component advective flows with standing shocks in the presence of
Comptonization
Author: Santanu Mondal & Sandip K.
Chakrabarti
Key findings:
=========================================================
2013ASInC...8...59M
(Recent Trends in
the Study of Compact Objects: Theory and Observation ASI Conference
Series, 2013)
(http://bulletin.astron-soc.in/asics_vol008/059_santanu.pdf)
Title: Spectral properties of two
component advective flows around black holes with standing shock in
presence of Comptonization
Authors: Santanu Mondal & Sandip K.
Chakrabarti
Key findings: We
study a self-consistent solution for the spectral properties of a
general class of steady state accretion disks in presence of
Comptonization. We couple both the hydrodynamics and the radiative
transfer process analytically to calculate the emitted spectrum. In
our work, we consider a two-component accretion flow, where one
component (Keplerian) supplies soft photons, which are reprocessed by
the electrons in the halo (sub-Keplerian). We show how the boundary
changes as the shock moves inward in presence of Compton cooling. Due
to the radiative loss,
some
energy is removed from the accreting matter and the shock moves
towards the black hole to maintain the pressure balance condition. We
solve the two-temperature equations with Coulomb energy exchange
between the protons and the electrons, and the radiative processes
such as the
bremsstrahlung
and Comptonization. We modify Rankine-Hugoniot relation to obtain the
shock-locations when the post-shock region suffers energy loss due to
Comptonization. We compute the radiated spectrum from the disk and
study the variation of the hydrodynamical and spectral proper-
ties
as functions of the accretion rates of the Keplerian and
sub-Keplerian components. Ours is the most self consistent transonic
solution of an inviscid flow around a black hole till now.
=========================================================
(http://mnras.oxfordjournals.org/content/421/2/1666.full.pdf+html)
Title: On the nature of the parameter
space in the presence of dissipative standing shocks in accretion
flows around black holes
Author: Singh, Chandra B.; Chakrabarti,
Sandip K.
Key findings: The spectral properties
of black hole candidates and outflow rates depend crucially on the
models of accretion flow, and thus they are interconnected. In a
model of transonic flow, the centrifugal barrier forms a shock wave
in the accretion disc at a few tens of Schwarzschild radii. The
post-shock region (i.e. the region between the shock and the
innermost critical point) can act as a Compton cloud as well a
reservoir of outgoing jets/outflows. In order to compute the
parameter space in which the outflow can form, we use a suitable Mach
number relation that can be satisfied at the shock derived in our
earlier work in the presence of dissipation and outflows. Assuming
three models of accretion flow (i.e. models of vertical equilibrium,
conical wedge shape and constant height), we examine the parameter
space of the specific energy and the specific angular momentum for
dissipative shock with mass loss. In the first two models, we find
that the parameter space is reduced as the cooling rate is increased.
However, in the case of the constant height model, the parameter
space initially increases with the cooling process, but starts to
decrease with a further increase in cooling. One common property in
all three accretion flow models is that, above a critical amount of
cooling, the parameter space disappears completely. This indicates
that the spectrally soft states might not have a significant amount
of outflows from the accretion disc.
=========================================================
(http://mnras.oxfordjournals.org/content/410/4/2414.full.pdf+html)
Title: Outflow rates in a black hole
environment in presence of a dissipative standing shock
Author: Singh, Chandra B. &
Chakrabarti, Sandip K.
Key findings: We find a self-consistent
solution for the outflow rate from an accretion disc around a black
hole. The centrifugal pressure dominated shock in a transonic
accretion flow can act as a Compton cloud by emitting radiation in
the form of hard X-rays. It is also the base of an outflow where
considerable matter is ejected. We modify the Rankine-Hugoniot
relationship in the accretion flow when the post-shock region suffers
energy as well mass-loss. After connecting the post-shock solution in
the disc with the sonic surface properties of the outflow, we obtain
the ratio of the outflow rate and inflow rate ? analytically. Our
conclusions are (i) the outflow rate is at the most a few per cent of
the inflow rate, (ii) the outflow is absent when the shock is
relatively weak (more precisely, the compression ratio is less than
about 2) and (iii) the outflow rate decreases with the increase of
the energy loss at the post-shock region. Thus spectrally soft states
will have lesser outflows.
=========================================================
(http://www.worldscientific.com/doi/abs/10.1142/S0218271811020482)
Title: Model Dependence of Outflow
Rates from AN Accretion Disk in Presence of a Dissipative Standing
Shock
Author: Singh, Chandra B. &
Chakrabarti, Sandip K.
Key findings: Solutions of black hole
accretion flows with axisymmetric shocks are obtained
self-consistently when the dissipation at the post-shock flow is
taken into account. The Rankine-Hugoniot relationships had to be
modified suitably to incorporate the energy loss as well as possible
matter loss due to outflows in the post-shock region. The outflow
rate from the post-shock region is also computed self-consistently.
This was done by considering the quantities in the subsonic
post-shock flow as the initial condition for the conical outflow. We
have several major results: we find the analytical expression of the
ratio of the outflow rate and the inflow rate Rṁ. We
find that Rṁ strongly depends on the model assumptions
which govern the flow geometry. It appears that, (a) the outflow rate
is at most a few percent of the inflow rate, (b) the outflow is
absent when the shock is relatively weak, (c) the outflow rate
decreases with the increase in the energy loss at the post-shock
region. These conclusions are very important as they have direct
bearings on the observational effects. Since spectrally soft states
are generally believed to be caused by the dominance of the soft
photons and almost total loss of thermal energy of the Compton cloud
by inverse Comptonization, a spectrally softer state should have less
outflows. The opposite is generally true: A spectrally harder state
will have a stronger outflow, but the result depends on the
compression ratio and the adopted model. The other major result is
that the model independence of the transonic properties of the flow
does not hold in presence of the loss of the energy (radiation) and
mass (outflow).
=========================================================
(http://www.worldscientific.com/doi/abs/10.1142/S0218271811019487)
Title: Effects of the Composition on
Transonic Properties of Accretion Flows around Black Holes
Author: Chattopadhyay, Indranil &
Chakrabarti, Sandip K.
Key findings: We study the properties
of a steady, multi-species, low angular momentum accretion flow
around a Schwarzschild black hole. Each species is described by a
relativistic equation of state. We find that the transonic properties
depend strongly on the composition of the flow. We find that an
electron-positron pair plasma is the least relativistic one. This
flow produces only one sonic point very close to the event horizon
and does not show multiple critical points for any angular momentum
or energy. When the baryons are present, the number of critical
points depend on the specific energy content. Since the number of
critical points decide whether the flow will have nonlinearities or
shock waves, our results imply that whether standing shocks will form
or not depends on the flow composition. Thus, for instance, a pure
electron-positron pair plasma will never undergo a shock transition,
while mixing it with some baryons (common in outflows and jets, for
example) as in a completely ionized gas, will have shocks. We study
in detail how the baryon loading affects the shock properties and
discuss the implications in astrophysical observations.
=========================================================
(http://iopscience.iop.org/2041-8205/710/2/L147/pdf/apjl_710_2_147.pdf)
Title: On the Evolution of Accretion
Rates in Compact Outburst Sources
Author: Mandal, Samir &
Chakrabarti, Sandip K.
Key findings: Spectra in outburst
sources are found to become soft in viscous timescales before going
back to hard as in the pre-outburst phase. By using two component
accretion disks we show that major characteristics of the spectral
evolution can be reproduced. We find that the outburst is possibly
caused by a sudden rise in viscosity which gradually converts the
sub-Keplerian flow into a Keplerian flow. The decline of the
viscosity reduces the Keplerian accretion rate, and the system goes
back to hard states. We discuss the genesis of the characteristic
shape of the hardness-intensity diagram and reproduce this for the
well-known outburst source GRO J1655-40.
=========================================================
(http://mnras.oxfordjournals.org/content/401/3/2053.full.pdf+html)
Title: Studies of dissipative standing
shock waves around black holes
Author: Das, Santabrata; Chakrabarti,
Sandip K. & Mondal, Soumen
Key findings: We investigate the
dynamical structure of advective accretion flow around stationary as
well as rotating black holes. For a suitable choice of input
parameters, such as accretion rate and angular momentum (λ), a
global accretion solution may include a shock wave. The post-shock
flow is located at a few tens times the Schwarzchild radius and is
generally very hot and dense. This successfully mimics the so-called
Compton cloud, which is believed to be responsible for emitting hard
radiation. Owing to the radiative loss, significant energy is removed
from the accreting matter and the shock moves forward towards the
black hole in order to maintain the pressure balance across it. We
identify the effective area of parameter space that allows accretion
flows to have some energy dissipation at the shock . As the
dissipation is increased, the parameter space is reduced and finally
disappears when the dissipation reaches a critical value. The
dissipation has a profound effect on the dynamics of post-shock flow.
By moving forward, an unstable shock, the oscillation of which causes
quasi-periodic oscillations (QPOs) in the emitted radiation, will
produce oscillations of high frequency. Such an evolution of QPOs has
been observed in several black hole candidates during their
outbursts.
=========================================================
(http://mnras.oxfordjournals.org/content/396/2/1038.full.pdf+html)
Title: Studies of accretion flows
around rotating black holes - III. Shock oscillations and an
estimation of the spin parameter from QPO frequencies
Author: Mondal, S.; Basu, P.;
Chakrabarti, S. K.
Key
findings: In the present communication of our series of papers
dealing with the accretion flows in the pseudo-Kerr geometry, we
discuss the effects of viscosity on the accretion flow around a
rotating black hole. We find the solution topologies and give special
attention to the solutions containing shocks. We draw the parameter
space where standing shocks are possible and where the shocks could
be oscillating and could produce quasi-periodic oscillations (QPOs)
of X-rays observed from black hole candidates. In this model, the
extreme locations of the shocks give the upper limits of the QPO
frequencies (νQPO) which could be observed. We show that
both the viscosity of the flow and the spin of the black hole a
increase the QPO frequency while, as expected, the black hole mass
reduces the QPO frequencies. Our major conclusion is that the highest
observed frequency gives a strict lower limit of the spin. For
instance, a black hole exhibiting νQPO ~ 400 and 700Hz
must have the spin parameters of a > 0.25 and >0.75,
respectively, provided viscosity of the flow is small. We discuss the
implications of our results in the light of observations of QPOs from
black hole candidates.
=========================================================
(http://iopscience.iop.org/1538-4357/689/1/L17/pdf/595782.pdf)
Title:
Spectrum of Two-Component Flows around a Supermassive
Black Hole: An Application to M87
Author:
Mandal, Samir; Chakrabarti, Sandip K.
Key
findings: We calculate the spectra of two-component
accretion flows around black holes of various masses, from quasars to
nanoquasars. Specifically, we fit the observational data of M87 very
satisfactorily using our model and find that the spectrum may be well
fitted by a sub-Keplerian component alone, and there is little need
of any Keplerian component. The nonthermal distribution of electrons
produced by their acceleration across the standing shock in the
sub-Keplerian component is enough to produce the observed flat
spectrum through the synchrotron radiation.
=========================================================
(http://mnras.oxfordjournals.org/content/389/1/371.full.pdf+html)
Title:
Dissipative accretion flows around a rotating black
hole
Author:
Das, Santabrata; Chakrabarti, Sandip K.
=========================================================
(http://link.springer.com/article/10.1007%2Fs10509-007-9398-7)
Title:
Spectral properties of shocked accretion flows— a
self-consistent study
Author:
Chakrabarti, Sandip K.; Mandal, Samir
Key findings: Magnetized accretion
flows around black holes which include standing or oscillating shock
waves can produce very realistic spectrum till a few MeV. These
shocks accelerate hot electrons which produce power-law spectrum. The
post-shock region intercepts soft-photons from an external source,
namely, a Keplerian disk and also from distributed sources such as
the synchrotron photons emitted from thermal and non-thermal
electrons originated in the pre-shock and post-shock flow. These
photons are inverse Comptonized by the thermal and the non-thermal
electrons present in the CENBOL region. Computations show that the
emitted radiation is extended till a few MeV. We include the bulk
motion Comptonization as well and discuss its importance vis-a-vis
the power-law spectrum produced by non-thermal electrons.
=========================================================
(http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?2007MNRAS.374..729D&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf)
Title:
Parameter space study of the magnetohydrodynamic
accretion flows around compact objects
Author:
Das, Santabrata; Chakrabarti, Sandip K.
Key
findings: We solve the magnetohydrodynamic (MHD)
equations governing axisymmetric flows around compact objects and
found all possible classes of solutions for non-relativistic
adiabatic accretion flows. We divide the parameter space in terms of
these classes. We study the possibility of the formation of the MHD
shock waves and show how the strength of the shocks depends on the
flow parameters. We also show regions of the parameter space where
the shock conditions are not satisfied and therefore the shocks may
oscillate. These solutions are astrophysically interesting as they
could give rise to quasi-periodic oscillations seen in hard X-rays.
=========================================================
(http://www.worldscientific.com/doi/abs/10.1142/S0218271807009279)
Title: Non-Linearities in Accretion and
Winds around Rotating Black Holes Using Pseudo-Kerr Geometry
Author: Mondal, Soumen; Chakrabarti,
Sandip K.
Key findings: Non-linearities such as
shock waves are common in accretion flows around compact objects.
Exact quantification of these non-linearities will help testing
time-dependent numerical codes. In this paper, we study the detailed
properties of these non-linear waves in a steady accretion or wind
flows around a rotating black hole. We use a pseudo-Kerr geometry for
this purpose. In the context of energy preserving standing shocks, we
find that there are two shock locations for a given pair of conserved
flow parameters, such as specific energy and angular momentum. We
also show that as the Kerr parameter is increased, the shock location
moves closer to the black hole. We discuss the astrophysical
implications of such solutions.
=========================================================
(http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?2006MNRAS.371.1418M&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf)
Title: Studies of accretion flows
around rotating black holes - II. Standing shocks in the pseudo-Kerr
geometry
Author: Mondal, Soumen;
Chakrabarti, Sandip K.
Key findings: Standing, propagating or
oscillating shock waves are common in accretion and winds around
compact objects. We study the topology of all possible solutions
using the pseudo-Kerr geometry. We present the parameter space
spanned by the specific energy and angular momentum and compare it
with that obtained from the full general relativity to show that the
potential can work satisfactorily in fluid dynamics also, provided
the polytropic index is suitably modified. We then divide the
parameter space depending on the nature of the solution topology. We
specifically study the nature of the standing Rankine-Hugoniot
shocks. We also show that as the Kerr parameter is increased, the
shock location generally moves closer to the black hole. In future,
these solutions can be used as guidelines to test numerical
simulations around compact objects.
=========================================================
(http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?2006MNRAS.369..976C&data_type=PDF_HIGH&whole_paper=YES&type=PRINTER&filetype=.pdf)
Title: Studies of accretion flows
around rotating black holes - I. Particle dynamics in a pseudo-Kerr
potential
Author: Chakrabarti, Sandip K.;
Mondal, Soumen
Key findings: In this series of papers,
we shall present a simplistic approach to the study of particle
dynamics, fluid dynamics and numerical simulations of accretion flows
and outflows around rotating black holes. We show that with a
suitably modified effective potential of the central gravitating
rotating object, one can carry out these studies very accurately. In
this approach, one need not use the full general relativistic
equations to obtain the salient features of the general relativistic
flows provided the Kerr parameter remains within -1 <= a <=
0.8. We present the equatorial and the non-equatorial particle
trajectories from our potential and compare salient properties in
Kerr and in pseudo-Kerr geometries. Our potential naturally produces
accurate results for motions around the Schwarzschild geometry when
the black hole angular momentum is set to zero.
=========================================================
(http://iopscience.iop.org/1538-4357/642/1/L49/pdf/20083.web.pdf)
Title: The Spectral Properties of
Shocked Two-Component Accretion Flows in the Presence of Synchrotron
Emission
Author: Chakrabarti, Sandip K.;
Mandal, Samir
Key findings: Two-component advective
flows have Keplerian accretion disks on the equatorial plane that is
surrounded by sub-Keplerian transonic flows. In this Letter, we study
the spectral properties of these flows when the shocks are present.
The shock acceleration produces nonthermal electrons in the postshock
region that in turn produce power-law synchrotron radiation. The soft
photons generated by the bremsstrahlung and synchrotron processes in
the sub-Keplerian flow, as well as the multicolor blackbody emission
from the Keplerian disk, are Comptonized by the thermal and
nonthermal electrons. By varying Keplerian and sub-Keplerian rates,
we are able to reproduce the observed soft and hard states as far as
the X-ray region is concerned and ``low γ-ray intensity'' and ``high
γ-ray intensity'' states as far as the soft γ-ray region is
concerned. We also find two pivotal points where the spectra
intersect, as is observed in, e.g., Cyg X-1.
=========================================================
(http://www.worldscientific.com/doi/abs/10.1142/9789812704030_0120)
Title : Spectral Properties of a Two
Component and Two Temperature Advective Flow
Author: Mandal, Samir;
Chakrabarti, Sandip K.
Key findings: Low angular momentum
accretion flows very often have centrifugal pressure supported
standing shock waves which can accelerate flow particles. The
accelerated particles in turn emit synchrotron radiation in presence
of magnetic fields. Efficient cooling of the electrons reduces its
temperature in comparison to the protons. In this paper, we assume
two temperature flows to explore this property of shocks and present
an example of the emitted radiation spectrum.
=========================================================
1995, Astrophysical Journal, 455, 623:
Spectral Properties of Galactic and Extragalactic Black Hole Candidates
Author: S. K. CHAKRABARTI and L. G. TITARCHUK
Extract:
Click Here to download the paper
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1996, Physics Reports, v.266, No 5 & 6, p 229-392:
Accretion Processes On Black Holes
Author: S. K. CHAKRABARTI
Extract:
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1996, Astrophys. J. 457, 805:
Resonance Oscillation of Radiative Shock Waves in Accretion Disks Around a Black Hole.
Author: D.
MOLTENI, H. SPONHOLZ and S. K. CHAKRABARTI
Extract:
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1996, Publ. Astron. Soc. Japan, v. 48 No. 1. 59:
On the spectral slopes of hard X-ray Emission from Black Hole Candidates
Author: K. EBISAWA, L. TITARCHUK & S. K. CHAKRABARTI
Extract:
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1996, Astrophys. J., 464, 664:
Grand Unification of Solutions of Accretions and Winds Around Black Holes and Neutron Stars
Author: S. K. CHAKRABARTI
Extract:
1996, Astron. & Astrophys. Suppl. Series, 120, 163-166
Observational Signatures of the Boundary layer of Black Holes
Author: S. K. CHAKRABARTI, L. G. TITARCHUK, D. KAZANAS & K. EBISAWA
Extract:
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