arXiv subjects

Tapas K. Das

Publications and source records attributed to Tapas K. Das.

At least 37 records · Page 2Linked to original sources

arXiv2017

Relativistic sonic geometry for isothermal accretion in the Schwarzschild metric

In this work, we perform linear perturbation on general relativistic isothermal accretion onto a non-rotating astrophysical black hole to study the salient features of the corresponding emergent acoustic metric. For spherically symmetric accretion as well as for the axially symmetric matter flow for three different geometric configuration of matter, we perturb the velocity potential, the mass accretion rate, and the integral solution of the time independent part of the general relativistic Euler equation to obtain such acoustic geometry. We provide the procedure to locate the acoustic horizon and identify such horizon with the transonic surfaces of the accreting matter through the construction of the corresponding causal structures. We then discuss how one can compute the value of the acoustic surface gravity in terms of the accretion variable corresponding to the background flow solutions - i.e., stationary integral transonic accretion solutions for different matter geometries. We show that the salient features of the acoustic geometry is independent of the physical variable we perturb, but sensitively depends on the geometric configuration of the black hole accretion disc.

gr-qc↗

arXiv2017

Axially Symmetric Accretion of Fractal Medium onto Rotating Black Holes and the emergence of the Acoustic Manifold

For three different geometric configurations of matter and two different thermodynamic equations of state, low angular momentum, multi-transonic, axially symmetric accretion flow of matter having fractional dimension of mass distribution onto a rotating black hole has been studied by employing certain post-Newtonian pseudo-Kerr black hole potential. Such task has been accomplished mathematically by mapping the fractal nature of accreted medium onto its continuum counterpart. The difference between spin dependence of accretion dynamics of the fractal medium and the continuous medium has been highlighted. By employing a time dependent linear perturbation scheme, it has been demonstrated that accretion of matter with fractional dimension of density distribution can be considered as a natural example of classical analogue model. The corresponding acoustic surface gravity has been estimated in terms of accretion variables. The value of the surface gravity changes as the accreted matter makes a transition from its fractal nature to the corresponding continuum distribution.

astro-ph.HE↗

arXiv2015

Transonic behaviour and stability analysis of quasi-viscous black hole accretion

Analytical studies of black hole accretion usually presumes the stability of the stationary transonic configuration. Various authors in the past several decades demonstrated the validity of such an assumption for inviscid hydrodynamic flow. Inviscid approximation is a reasonable approach for low angular momentum advection dominated flow in connection to certain supermassive black holes at the centres of the galaxies (including our own) fed from a number of stellar donors. Introduction of a weak viscosity, as a first order linear correction involving the viscosity parameter, however, may sometimes provide a more detail understanding of the observed black hole spectra. The transonic behaviour of the stationary solutions have been studied for the aforementioned quasi-viscous accretion for all possible geometric configurations of axisymmetric flow. For a sufficiently low range of the viscosity parameter, transonic solutions containing one or three critical points have been found for allowed ranges in the astrophysical parameters under the post-Newtonian pseudo-Schwarzschild scheme. With the introduction of such viscosity parameter, the only feasible critical points are of saddle and spiral types in contrary to the inviscid case where centre type points were formed instead of spiral ones. Introduction of linear perturbations on stationary flow solutions and their time evolution in both standing and radially propagating wave forms have been examined (completely analytically) in detail. Our analysis shows that similar kind of secular instability exists in all the considered disk models at large distance in the asymptotic limit, however, the model itself is valid only within a certain length scale and the disks sustain within that length scale only for at least a considerable time scale.

astro-ph.HE↗

arXiv2015

Acoustic geometry through perturbation of mass accretion rate - radial flow in static spacetimes

In this work we present an alternative derivation of the general relativistic acoustic analogue geometry by perturbing the mass accretion rate or flux of an ideal fluid flowing radially in a general static and spherically symmetric spacetime. To the best of our knowledge, this has so far been done in non-relativistic scenario. The resulting causal structure of the two dimensional acoustic geometry is qualitatively similar to that one derives via the perturbation of the velocity potential. Using this, we then briefly discuss the stability issues by studying the wave configurations generated by the perturbation of the mass accretion rate, and formally demonstrate the stability of the accretion process. This is in qualitative agreement with earlier results on stability, established via study of wave configurations generated by the perturbation of velocity potential, by using the acoustic geometry associated with it. We further discuss explicit examples of the Schwarzschild and Rindler spacetimes.

astro-ph.HE↗

arXiv2014

Black Hole spin dependence of general relativistic multi-transonic accretion close to the horizon

We introduce a novel formalism to investigate the role of the spin angular momentum of astrophysical black holes in influencing the behaviour of low angular momentum general relativistic accretion. We propose a metric independent analysis of axisymmetric general relativistic flow, and consequently formulate the space and time dependent equations describing the general relativistic hydrodynamic accretion flow in the Kerr metric. The associated stationary critical solutions for such flow equations are provided and the stability of the stationary transonic configuration is examined using an elegant linear perturbation technique. We examine the properties of infalling material for both prograde and retrograde accretion as a function of the Kerr parameter at extremely close proximity to the event horizon. Our formalism can be used to identify a new spectral signature of black hole spin, and has the potential of performing the black hole shadow imaging corresponding to the low angular momentum accretion flow.

astro-ph.HE↗

arXiv2014

On the realizability of relativistic acoustic geometry under a generalized perturbation scheme for axisymmetric matter flow onto black holes

We propose a novel linear perturbation scheme to study the stability properties of the stationary transonic integral solutions for axisymmetric matter flow around astrophysical black holes for the Schwarzschild as well as for rotating Rindler space time. We discuss the emergence of the relativistic acoustic geometry as a consequence of such stability analysis. Our work thus makes a crucial connection between two apparently non-overlapping fields of research - the accretion astrophysics and the analogue gravity phenomena.

astro-ph.HE↗

arXiv2014

Development of Secular Instability in Different Disc Models of Black Hole Accretion

Analytical treatment of black hole accretion generally presumes the stability of the stationary configuration. Various authors in the past several decades demonstrated the validity of such an assumption for inviscid hydrodynamic flow. Inviscid assumption is a reasonable approximation for low angular^M momentum advection dominated flow in connection to certain^M supermassive black holes at the^M centres of the galaxies (including our own) fed from a number of stellar donors.^M Introduction of a weak viscosity, however, may sometimes provide a more detail understanding of the observed spectrum. Recently it has been demonstrated that introduction of small amount of viscosity in the form of quasi-viscous flow makes a stationary accretion disc -- where the geometric configuration of matter is described by axisymmetric flow in hydrostatic equilibrium -- unstable. We perform similar analysis for other disc models (for all three possible geometric configurations of matter) for quasi-viscous models under the post-Newtonian scheme. We introduced perturbations on the stationary flow solution particularly in standing wave form and studied their time evolution to observe whether they grow with time. Our analysis shows that same sort of secular instability exists in other disc models too. We further argued that with sufficiently low value of viscosity in the realistic astrophysical perspective, the instability does not effectively jeopardize the stationary condition.

astro-ph.HE↗

arXiv2013

Multiple accretion events as a trigger for Sgr A* activity

Gas clouds are present in the Galactic centre, where they orbit around the supermassive black hole. Collisions between these clumps reduce their angular momentum, and as a result some of the clumps are set on a plunging trajectory. Constraints can be imposed on the nature of past accretion events based on the currently observed X-ray reflection from the molecular clouds. We discuss accretion of clouds in the context of enhanced activity of Sgr A* during the past few hundred years. We put forward a scenario according to which gas clouds bring material close to the horizon of the black hole on <~0.1 parsec scale. We have modelled the source intrinsic luminosity assuming that multiple events occur at various moments in time. These events are characterized by the amount of accreted material and the distribution of angular momentum. We parameterized the activity in the form of a sequence of discrete events, followed the viscous evolution, and calculated the luminosity of the system from the time-dependent accretion rate across the inner boundary. Accreting clumps settle near a circularization radius, spread there during the viscous time, and subsequently feed the black hole over a certain period. A significant enhancement (by factor of ten) of the luminosity is only expected if the viscous timescale of the inflow is very short. On the other hand, the increase in source activity is expected to be much less prominent if the latter timescale is longer and a considerable fraction of the material does not reach the centre. A solution is obtained under two additional assumptions: (i) the radiative efficiency is a decreasing function of the Eddington ratio; (ii) the viscous decay of the luminosity proceeds somewhat faster than the canonical L(t)~t^{-5/3} profile. We applied our scheme to the case of G2 cloud in the Galactic centre to obtain constraints on the core-less gaseous cloud model.

astro-ph.HE↗

arXiv2012

Mini-spiral as source of material for Sgr A* in bright state

The question of the origin of the gas supplying the accretion process is pertinent especially in the context of enhanced activity of Galactic Center during the past few hundred years, seen now as echo from the surrounding molecular clouds, and the currently observed new cloud approaching Sgr A*. We discuss the so-called Galactic Center mini-spiral as a possible source of material feeding the supermassive black hole on a 0.1 parsec scale. The collisions between individual clumps reduce their angular momentum. and set some of the clumps on a plunging trajectory. We conclude that the amount of material contained in the mini-spiral is sufficient to sustain the luminosity of Sgr A* at the required level. The accretion episodes of relatively dense gas from the mini-spiral passing through a transient ring mode at $\sim 10^4$ Rg provide a viable scenario for the bright phase of Galactic Center.

astro-ph.GA↗

arXiv2012

An Analytical Study on the Multi-critical Behaviour and Related Bifurcation Phenomena for Relativistic Black Hole Accretion

We apply the theory of algebraic polynomials to analytically study the transonic properties of general relativistic hydrodynamic axisymmetric accretion onto non-rotating astrophysical black holes. For such accretion phenomena, the conserved specific energy of the flow, which turns out to be one of the two first integrals of motion in the system studied, can be expressed as a 8$^{th}$ degree polynomial of the critical point of the flow configuration. We then construct the corresponding Sturm's chain algorithm to calculate the number of real roots lying within the astrophysically relevant domain of $\mathbb{R}$. This allows, for the first time in literature, to {\it analytically} find out the maximum number of physically acceptable solution an accretion flow with certain geometric configuration, space-time metric, and equation of state can have, and thus to investigate its multi-critical properties {\it completely analytically}, for accretion flow in which the location of the critical points can not be computed without taking recourse to the numerical scheme. This work can further be generalized to analytically calculate the maximal number of equilibrium points certain autonomous dynamical system can have in general. We also demonstrate how the transition from a mono-critical to multi-critical (or vice versa) flow configuration can be realized through the saddle-centre bifurcation phenomena using certain techniques of the catastrophe theory.

gr-qc↗

arXiv2012

Transonicity in black hole accretion -- A mathematical study using the generalized Sturm chains

By applying the theory of algebraic polynomials and the theory of dynamical systems, we construct the generalized Sturm sequences/chains to investigate the transonic properties of hydrodynamic accretion onto non-rotating astrophysical black holes, to demonstrate, completely analytically, how many critical point such an accretion flow can have. Our work is significantly important, because for the first time in the literature, we provide a purely analytical method, by applying certain powerful theorem of algebraic polynomials in pure mathematics, to check whether certain astrophysical hydrodynamic accretion may undergo more than one sonic transitions. Our work can be generalized to analytically calculate the maximal number of equilibrium points certain autonomous dynamical systems can have in general (Abridged).

astro-ph.HE↗

arXiv2012

QPO in RE J1034+396: model constraints from observed trends

We analyze the time variability of the X-ray emission of RE J1034+396, an active galactic nucleus with the first firm detection of a quasi-periodic oscillations (QPO). Based on the results of a wavelet analysis, we find a drift in the QPO central frequency. The change inthe QPO frequency correlates with the change in the X-ray flux with a short time delay. Linear structures such as shocks, spiral waves, orvery distant flares seem to be a favored explanation for this particular QPO event.

astro-ph.CO↗

arXiv2011

On the efficiency of the Blandford-Znajek mechanism for low angular momentum relativistic accretion

Blandford-Znajek (BZ) mechanism has usually been studied in the literature for accretion with considerably high angular momentum leading either to the formation of a cold Keplerian disc, or a hot and geometrically thick sub-Keplerian flow as described within the framework of ADAF/RIAF. However, in nearby elliptical galaxies, as well as for our own Galactic centre, accretion with very low angular momentum is prevalent. Such quasi-spherical strongly sub-Keplerian accretion has complex dynamical features and can accommodate stationary shocks. In this letter, we present our calculation for the maximum efficiency obtainable through the BZ mechanism for complete general relativistic weakly rotating axisymmetric flow in the Kerr metric. Both shocked and shock free flow has been studied in detail for rotating and counter rotating accretion. Such study has never been done in the literature before. We find that the energy extraction efficiency is low, about 0.1%, and increases by a factor 15 if the ram pressure is included. Such an efficiency is still much higher than the radiative efficiency of such optically thin flows. For BZ mechanism, shocked flow produces higher efficiency than the shock free solutions and retrograde flow provides a slightly larger value of the efficiency than that for the prograde flow.

astro-ph.HE↗

arXiv2010

The role of flow geometry in influencing the stability criteria for low angular momentum axisymmetric black hole accretion

Using mathematical formalism borrowed from dynamical systems theory, a complete analytical investigation of the critical behaviour of the stationary flow configuration for the low angular momentum axisymmetric black hole accretion provides valuable insights about the nature of the phase trajectories corresponding to the transonic accretion in the steady state, without taking recourse to the explicit numerical solution commonly performed in the literature to study the multi-transonic black hole accretion disc and related astrophysical phenomena. Investigation of the accretion flow around a non rotating black hole under the influence of various pseudo-Schwarzschild potentials and forming different geometric configurations of the flow structure manifests that the general profile of the parameter space divisions describing the multi-critical accretion is roughly equivalent for various flow geometries. However, a mere variation of the polytropic index of the flow cannot map a critical solution from one flow geometry to the another, since the numerical domain of the parameter space responsible to produce multi-critical accretion does not undergo a continuous transformation in multi-dimensional parameter space. The stationary configuration used to demonstrate the aforementioned findings is shown to be stable under linear perturbation for all kind of flow geometries, black hole potentials, and the corresponding equations of state used to obtain the critical transonic solutions. Finally, the structure of the acoustic metric corresponding to the propagation of the linear perturbation studied are discussed for various flow geometries used.

astro-ph.HE↗

arXiv2008

Quasi-viscous accretion flow -- I: Equilibrium conditions and asymptotic behaviour

In a novel approach to studying viscous accretion flows, viscosity has been introduced as a perturbative effect, involving a first-order correction in the $α$-viscosity parameter. This method reduces the problem of solving a second-order nonlinear differential equation (Navier-Stokes equation) to that of an effective first-order equation. Viscosity breaks down the invariance of the equilibrium conditions for stationary inflow and outflow solutions, and distinguishes accretion from wind. Under a dynamical systems classification, the only feasible critical points of this "quasi-viscous" flow are saddle points and spirals. A linearised and radially propagating time-dependent perturbation gives rise to secular instability on large spatial scales of the disc. Further, on these same length scales, the velocity evolution equation of the quasi-viscous flow has been transformed to bear a formal closeness with Schrödinger's equation with a repulsive potential. Compatible with the transport of angular momentum to the outer regions of the disc, a viscosity-limited length scale has been defined for the full spatial extent over which the accretion process would be viable.

astro-ph↗

arXiv2006

The pattern of accretion flow onto Sgr A*

The material accreting onto Sgr A* most probably comes from the nearby stars. We analyze the pattern of this flow at distances of a fraction of a parsec and we argue that the net angular momentum of this material is low but non-negligible, and the initially supersonic disk accretion changes into subsonic flow with constant angular momentum. Next we estimate the flow parameters at a distance $R_{BHL}$ from the black hole and we argue that for the plausible parameter range the accretion flow is non-stationary. The inflow becomes supersonic at distance of $\sim 10^4 R_g$ but the solution does not continue below the horizon and the material piles up forming a torus, or a ring, at a distance of a few up to tens of Schwarzchild radii. Such a torus is known to be unstable and may explain strong variability of the flow in Sgr A*. Our considerations show that the temporary formation of such a torus seems to be unavoidable. Our best fitting model predicts a rather large accretion rate of around $4 \cdot 10^{-6} M_{\odot}/yr$ directly on Sgr A*. We argue that magnetic fields in the flow are tangled and this allows our model to overcome the disagreement with the Faraday rotation limits.

astro-ph↗

arXiv2006

Acoustic horizons in axially symmetric relativistic accretion

Transonic accretion onto astrophysical objects is a unique example of analogue black hole realized in nature. In the framework of acoustic geometry we study axially symmetric accretion and wind of a rotating astrophysical black hole or of a neutron star assuming isentropic flow of a fluid described by a polytropic equation of state. In particular we analyze the causal structure of multitransonic configurations with two sonic points and a shock. Retarded and advanced null curves clearly demonstrate the presence of the acoustic black hole at regular sonic points and of the white hole at the shock. We calculate the analogue surface gravity and the Hawking temperature for the inner and the outer acoustic horizons.

gr-qc↗

arXiv2005

Pseudo-Schwarzschild Spherical Accretion as a Classical Black Hole Analogue

We demonstrate that a spherical accretion onto astrophysical black holes, under the influence of Newtonian or various post-Newtonian pseudo-Schwarzschild gravitational potentials, may constitute a concrete example of classical analogue gravity naturally found in the Universe. We analytically calculate the corresponding analogue Hawking temperature as a function of the minimum number of physical parameters governing the accretion flow. We study both the polytropic and the isothermal accretion. We show that unlike in a general relativistic spherical accretion, analogue white hole solutions can never be obtained in such post-Newtonian systems. We also show that an isothermal spherical accretion is a remarkably simple example in which the only one information--the temperature of the fluid, is sufficient to completely describe an analogue gravity system. For both types of accretion, the analogue Hawking temperature may become higher than the usual Hawking temperature. However, the analogue Hawking temperature for accreting astrophysical black holes is considerably lower compared with the temperature of the accreting fluid.

astro-ph↗