arXiv subjects

Tapas Kumar Das

Publications and source records attributed to Tapas Kumar Das.

At least 19 recordsLinked to original sources

arXiv2022

Effective sound speed in relativistic accretion discs around rotating black holes

For axially symmetric accretion maintained in the hydrostatic equilibrium along the vertical direction in the Kerr metric, the radial Mach number does not become unity at the critical point. The sonic points are, thus, formed at a radial distance different from that where the critical points are formed. We propose that a modified dynamical sound speed can be defined through the linear perturbation of the full space-time dependent equations describing the aforementioned accretion flow structure. The linear stability analysis of such fluid equations leads to the formation of an wave equation which describes the propagation of linear acoustic perturbation. The speed of propagation of such perturbation can be used as the effective sound speed which makes the value of the Mach number to be unity when evaluated at the critical points. This allows the critical points to coalesce with the sonic points. We study how the spin angular momentum of the black hole (the Kerr parameter) influences the value of the effective sound speed.

astro-ph.HE↗

arXiv2022

Multi-criticality and related bifurcation in accretion discs around non-rotating black holes -- an analytical study

Low angular momentum, general relativistic, axially symmetric accretion of hydrodynamic fluid onto Schwarzschild black holes may undergo more than one critical transition. To obtain the stationary integral solutions corresponding to such multi-critical accretion flow, one needs to employ numerical solutions of the corresponding fluid dynamics equations. In the present work, we develop a {\it{completely analytical}} solution scheme which may be used to find several trans-critical flow behaviours of aforementioned accretion, without explicitly solving the flow equations numerically. We study all possible geometric configurations of the flow profile, governed by all possible thermodynamic equations of state. We use Sturm's chain algorithm to find out how many physically acceptable critical points the accretion flow can have, and discuss the transition from the mono to the multi-critical flow profile, and related bifurcation phenomena. We thus illustrate, completely analytically, the application of certain aspects of the dynamical systems theory in the field of large scale astrophysical flow under the influence of strong gravity. Our work may possibly be generalized to calculate the maximal number of equilibrium points certain autonomous dynamical systems can have in general.

astro-ph.HE↗

arXiv2018

Linear perturbations of low angular momentum accretion flow in the Kerr metric and the corresponding emergent gravity phenomena

For certain geometric configuration of matter falling onto a rotating black hole, we develop a novel linear perturbation analysis scheme to perform the stability analysis of stationary integral accretion solutions corresponding to the steady state low angular momentum, inviscid, barotropic, irrotational, general relativistic accretion of hydrodynamic fluid. We demonstrate that such steady states remain stable under linear perturbation, and hence the stationary solutions are reliable to probe the black hole spacetime using the accretion phenomena.We report that a relativistic acoustic geometry emerges out as the consequence of such stability analysis procedure. We study various properties of that sonic geometry in detail. We construct the causal structures to establish the one to one correspondences of the sonic points with the acoustic black hole horizons, and the shock location with an acoustic white hole horizon. The influence of the spin of the rotating black holes on the emergence of such acoustic spacetime has been discussed.

astro-ph.HE↗

arXiv2018

Effective sound speed in relativistic accretion discs around Schwarzschild black holes

For low angular momentum axially symmetric accretion flow maintained in hydrostatic equilibrium along the vertical direction, the value of the Mach number at the critical points deviates from unity, resulting in the non-isomorphism of the critical and the sonic points. This introduces several undesirable complexities while analytically dealing with the stationary integral accretion solutions and the corresponding phase portraits. We propose that introduction of an effective dynamical sound speed may resolve the issue in an elegant way. We linear perturb the full spacetime-dependent general relativistic Euler and the continuity equations governing the structure and the dynamics of accretion disc in vertical equilibrium around Schwarzschild black holes and identify the sonic metric embedded within the stationary background flow. Such metric describes the propagation of the linear acoustic perturbation inside the accretion flow. We construct the wave equation corresponding to that acoustic perturbation and find the speed of propagation of such perturbation. We finally show that the ordinary thermodynamic sound speed should be substituted by the speed of propagation of the linear acoustic wave which has been obtained through the dynamical perturbation. Such substitution will make the value of Mach number at the critical point to be equal to unity. Use of the aforementioned effective sound speed will lead to a modified stationary disc structure where the critical and the sonic points will be identical.

astro-ph.HE↗

arXiv2018

Charged wormholes supported by 2-fluid immiscible matter particles

We provide a 2-fluid immiscible matter source that supplies fuel to construct wormhole spacetime. The exact wormhole solutions are found in the model having, besides real matter or ordinary matter, some quintessence matter along with charge distribution. We intend to derive a general metric of a charged wormhole under some density profiles of galaxies that is also consistent with the observational profile of rotation curve of galaxies. We have shown that the effective mass remains positive as well as the wormhole physics violate the null energy conditions. Some physical features are briefly discussed.

physics.gen-ph↗

arXiv2017

Influence of the geometric configuration of accretion flow on the black hole spin dependence of relativistic acoustic geometry

Linear perturbation of general relativistic accretion of low angular momentum hydrodynamic fluid onto a Kerr black hole leads to the formation of curved acoustic geometry embedded within the background flow. Characteristic features of such sonic geometry depend on the black hole spin. Such dependence can be probed by studying the correlation of the acoustic surface gravity $κ$ with the Kerr parameter $a$. The $κ- a$ relationship further gets influenced by the geometric configuration of the accretion flow structure. In this work, such influence has been studied for multitransonic shocked accretion where linear perturbation of general relativistic flow profile leads to the formation of two analogue black hole type horizons formed at the sonic points and one analogue white hole type horizon which is formed at the shock location producing divergent acoustic surface gravity. Dependence of the $κ- a$ relationship on the geometric configuration has also been studied for monotransonic accretion, over the entire span of the Kerr parameter including retrograde flow. For accreting astrophysical black holes, the present work thus investigates how the salient features of the embedded relativistic sonic geometry may be determined not only by the background space-time, but also by the flow configuration of the embedding matter.

gr-qc↗

arXiv2017

Influence of matter geometry on shocked flows-I: Accretion in the Schwarzschild metric

This work presents a comprehensive and extensive study to illustrate how the geometrical configurations of low angular momentum axially symmetric general relativistic matter flow in Schwarzschild metric may influence the formation of energy preserving shocks for adiabatic/polytropic accretion as well as of temperature preserving dissipative shocks for for the isothermal accretion onto non-rotating astrophysical black holes. The dynamical and thermodynamic states of post shock polytropic and isothermal flow have been studied extensively for three possible matter geometries, and it has been thoroughly discussed about how such states depend on the flow structure, even when the self gravity and the back reaction on the metric are not taken into account. Main purpose of this paper is thus to mathematically demonstrate that for non-self gravitating accretion, various matter geometry, in addition to the corresponding space-time geometry, controls the shock induced phenomena as observed within the black hole accretion discs. This work is expected to reveal how the shock generated phenomena (emergence of the outflows/flare or the behaviour of QPO of the associated light curves) observed at the close proximity of the horizon depends on the physical environment of the source harbouring a supermassive black hole.

gr-qc↗

arXiv2012

On Spin Dependence of Relativistic Acoustic Geometry

This work makes the first ever attempt to understand the influence of the black hole background space-time in determining the fundamental properties of the embedded relativistic acoustic geometry. To accomplish such task, the role of the spin angular momentum of the astrophysical black hole (the Kerr parameter $a$ -- a representative feature of the background black hole metric) in estimating the value of the acoustic surface gravity (the representative feature of the corresponding analogue space time) has been investigated for axially symmetric inflow of hydrodynamic fluid onto a rotating black hole. Since almost all astrophysical black holes are supposed to posses some degree of intrinsic rotation, the influence of the Kerr parameter on classical analogue models is very important to understand. For certain values of the initial boundary conditions describing the aforementioned flow, more than one acoustic horizons, namely two black hole type and one white hole type, may form, where the surface gravity may become formally infinite at the acoustic white hole. The connection between the corresponding analogue Hawking temperature with astrophysically relevant observables associated with the spectral signature has been discussed.

gr-qc↗

arXiv2011

Modeling the time-resolved quasi-periodic oscillations in AGNs

Observation of the bright Seyfert 1 galaxy RE J1034+396 is believed to demonstrate a drift of the central period of the Quasi Periodic Oscillation (QPO) linearly correlated with the temporary X-ray luminosity. We show, using a specific scenario of the oscillation mechanism in black hole accretion disc, that modeling such correlated trends puts very strong constraints on the nature of this oscillation and the characteristic features of the hot flow in Active Galactic Nuclei (AGN). In our model, QPO oscillations are due to the oscillations of the shock formed in the low angular momentum hot accretion flow, and the variation of the shock location corresponds to the observed changes in the QPO period and the X-ray flux. In this scenario, change in the shock location caused by perturbation of the flow angular momentum is compatible with the trends observed in RE J1034+396, whereas the perturbation of the specific flow energy results in too strong flux response to the change of the oscillation period. Using a complete general relativistic framework to study the accretion flow in the Kerr metric, we discuss the role of the black hole spin in the period drift. Future missions are expected to bring more active galaxies with time-resolved quasi-periodic oscillations so similar quantitative study for other QPO scenarios will be necessary.

astro-ph.HE↗

arXiv2010

The model constraints from the observed trends for the quasi-periodic oscillation in RE J1034+396

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 in the QPO frequency correlates with the change in the X-ray flux with a short time delay. The data specifically suggest a linear dependence between the QPO period and the flux, and this gives important constraints on the QPO models. In particular, it excludes explanation in terms of the orbiting hot spot model close to a black hole. Linear structures such as shocks, spiral waves, or very distant flares are favored.

astro-ph.GA↗

arXiv2007

Astrophysical Accretion as an Analogue Gravity Phenomena

In recent years, strong analogies have been established between the physics of acoustic perturbations in an inhomogeneous dynamical fluid system, and some kinematic features of space-time in general relativity. An effective metric, referred to as the `acoustic metric', which describes the geometry of the manifold in which acoustic perturbations propagate, can be constructed. This effective geometry can capture the properties of curved space-time in general relativity. Physical models constructed utilizing such analogies are called `analogue gravity models'. Classical analogue gravity effect may be observed when acoustic perturbations propagate through a inhomogeneous transonic classical fluid. The acoustic horizon, which resembles a black hole event horizon in many ways, is generated at the transonic point in the fluid flow. The acoustic horizon is essentially a null hyper surface, generators of which are the acoustic null geodesics, i.e. the phonons. The acoustic horizon emits acoustic radiation with quasi thermal phonon spectra, which is analogous to the actual Hawking radiation. The temperature of the radiation emitted from the acoustic horizon is referred to as the analogue Hawking temperature. It has been demonstrated that, in general, the transonic accretion in astrophysics can be considered as an example of the classical analogue gravity model naturally found in the Universe.

astro-ph↗

arXiv2007

Axisymmetric black hole accretion in the Kerr metric as an autonomous dynamical system

In a stationary, general relativistic, axisymmetric, inviscid and rotational accretion flow, described within the Kerr geometric framework, transonicity has been examined by setting up the governing equations of the flow as a first-order autonomous dynamical system. The consequent linearised analysis of the critical points of the flow leads to a comprehensive mathematical prescription for classifying these points, showing that the only possibilities are saddle points and centre-type points for all ranges of values of the fixed flow parameters. The spin parameter of the black hole influences the multitransonic character of the flow, as well as some of its specific critical properties. The special case of a flow in the space-time of a non-rotating black hole, characterised by the Schwarzschild metric, has also been studied for comparison and the conclusions are compatible with what has been seen for the Kerr geometric case.

astro-ph↗

arXiv2007

Critical properties of spherically symmetric black hole accretion in Schwarzschild geometry

The stationary spherically symmetric accretion flow in the Schwarzschild metric has been set up as an autonomous first-order dynamical system, and it has been studied completely analytically. Of the three possible critical points in the flow, the one that is physically realistic behaves like the saddle point of the standard Bondi accretion problem. One of the two remaining critical points exhibits the strange mathematical behaviour of being either a saddle point or a centre-type point, depending on the values of the flow parameters. The third critical point is always unphysical and behaves like a centre-type point. The treatment has been extended to pseudo-Schwarzschild flows for comparison with the general relativistic analysis.

astro-ph↗

arXiv2006

Critical properties and stability of stationary solutions in multi-transonic pseudo-Schwarzschild accretion

For inviscid, rotational accretion flows, both isothermal and polytropic, a simple dynamical systems analysis of the critical points has given a very accurate mathematical scheme to understand the nature of these points, for {\em any} pseudo-potential by which the flow may be driven on to a Schwarzschild black hole. This allows for a complete classification of the critical points for a wide range of flow parameters, and shows that the only possible critical points for this kind of flow are saddle points and centre-type points. A restrictive upper bound on the angular momentum of critical solutions has been established. A time-dependent perturbative study reveals that the form of the perturbation equation, for both isothermal and polytropic flows, is invariant under the choice of any particular pseudo-potential. Under generically true outer boundary conditions, the inviscid flow has been shown to be stable under an adiabatic and radially propagating perturbtion. The perturbation equation has also served the dual purpose of enabling an understanding of the acoustic geometry for inviscid and rotational flows.

astro-ph↗

arXiv2006

Black-Hole Accretion Disc as an Analogue Gravity Model

We formulate and solve the equations governing the transonic behaviour of a general relativistic black-hole accretion disc with non-zero advection velocity. We demonstrate that a relativistic Rankine-Hugoniot shock may form leading to the formation of accretion powered outflow. We show that the critical points of transonic discs generally do not coincide with the corresponding sonic points. The collection of such sonic points forms an axisymmetric hypersurface, generators of which are the acoustic null geodesics, i.e. the phonon trajectories. Such a surface is shown to be identical with an acoustic event horizon. The acoustic surface gravity and the corresponding analogue horizon temperature $T_{AH}$ at the acoustic horizon are then computed in terms of fundamental accretion parameters. Physically, the analogue temperature is associated with the thermal phonon radiation analogous to the Hawking radiation of the black-hole horizon.Thus, an axisymmetric black-hole accretion disc is established as a natural example of the classical analogue gravity model, for which two kinds of horizon exist simultaneously. We have shown that for some values of astrophysically relevant accretion parameters, the analogue temperature exceeds the corresponding Hawking temperature. We point out that acoustic {\it white holes} can also be generated for a multi-transonic black-hole accretion with a shock. Such a white hole, produced at the shock, is always flanked by two acoustic black holes generated at the inner and the outer sonic points. Finally, we discuss possible applications of our work to other astrophysical events which may exhibit analogue effects.

astro-ph↗

arXiv2004

Transonic Black Hole Accretion as Analogue System

Classical black hole analogues (alternatively, the analogue systems) are fluid dynamical analogue of general relativistic black holes. Such analogue effects may be observed when acoustic perturbations (sound waves) propagate through a classical dissipation-less tran-sonic fluid. The acoustic horizon, which resembles the actual black hole event horizon in many ways, may be generated at the transonic point in the fluid flow. Acoustic horizon emits quasi thermal phonon spectra, which is analogous to the actual Hawking radiation, and possesses the temperature referred as the analogue Hawking temperature, or simply, the analogue temperature. Transonic accretion onto astrophysical black holes is a very interesting example of classical analogue system found naturally in the Universe. An accreting black holes system as a classical analogue is unique in the sense that only for such a system, both kind of horizons, the electromagnetic and the acoustic (generated due to transonicity of accreting fluid) are simultaneously present in the same system. Hence an accreting astrophysical black hole is the ideal-most candidate to theoretically study and to compare the properties of these two different kind of horizons. Also such system is unique in the aspect that general relativistic spherical accretion onto the Schwarzschild black hole represents the only classical analogue system found in the nature so far, where the analogue Hawking temperature may be higher than the actual Hawking temperature.

gr-qc↗

arXiv2004

Dependence of General Relativistic Accretion on Black Hole Spin

We propose a novel approach to the investigation of how black hole spin influences the behavior of astrophysical accretion. We examine the terminal behavior of general relativistic, multi-transonic, hydrodynamic advective accretion in the Kerr metric, by analyzing various dynamical as well as thermodynamic properties of accreting matter extremely close to the event horizon, as a function of Kerr parameter $a$. The examination of the transonic properties of such flows can be useful in self-consistently discriminating between prograde and retrograde relativistic accretion, and in studying the spectral signatures of black hole rotation.

astro-ph↗

arXiv2004

Analogous Hawking Radiation from Astrophysical Black Hole Accretion

For the first time in literature, we provide an exact analytical scheme for calculating the analogous Hawking temperature and surface gravity for general relativistic accretion onto astrophysical black holes. Our calculation may bridge the gap between the theory of transonic astrophysical accretion and the theory of analogous Hawking radiation, and may allow one to compare the properties of the two types of horizons, electromagnetic and acoustic, in connection to the black hole physics. We show that the domination of the analogous Hawking radiation over the actual Hawking radiation may be a real astrophysical phenomena. We also discuss the possibilities of the emergence of analogous white holes around astrophysical black holes. Our calculation is general enough to accommodate accreting black holes with any mass.

astro-ph↗