Browsing by Author "Ray, Arnab K."

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Acoustic perturbations on steady spherical accretion in Schwarzschild geometry
(2007-06-10) Naskar, Tapan; Ray, Arnab K.
The stationary background ﬂow in the spherically symmetric infall of a compressible ﬂuid, coupled to the space-time deﬁned by the static chwarzschild metric, has been subjected to linearized acoustic perturbations. The perturbative procedure is based on the continuity condition and it shows that the coupling of the ﬂow with the geometry of space-time brings about greater stability for the ﬂow, to the extent that the amplitude of the perturbation, treated as a standing wave, decays in time, as opposed to the amplitude remaining constant in the Newtonian limit. In ualitative terms this situation simulates the effect of a dissipative mechanism in the classical Bondi accretion ﬂow, deﬁned in the Newtonian construct of space and time. As a result of this approach it becomes impossible to deﬁne an acoustic metric for a conserved spherically symmetric ﬂow, described within the framework of Schwarzschild geometry. In keeping with this view, the perturbation, considered eparately as a high-frequency travelling wave, also has its amplitude reduced.
Axisymmetric black hole accretion in the Kerr metric as an autonomous dynamical system
(2007-02-07) Goswami, Sanghamitra; Khan, Saba Nashreen; Ray, Arnab K.; et al.
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.
Critical properties and stability of stationary solutions in multi-transonic pseudo-schwarzschild accretion
(2006-09-13) Chaudhury, Soumini; Ray, Arnab K.; Das, Tapas K.
For inviscid, rotational accretion ows, 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 any pseudo-potential by which the ow may be driven on to a Schwarzschild black hole. This allows for a complete classi cation of the critical points for a wide range of ow parameters, and shows that the only possible critical points for this kind of ow 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 ows, is invariant under the choice of any particular pseudo-potential. Under generically true outer boundary conditions, the inviscid ow has been shown to be stable under an adiabatic and radially propagating perturbation. The perturbation equation has also served the dual purpose of enabling an understanding of the acoustic geometry for inviscid and rotationalows.
Critical properties of spherically symmetric accretion in a fractal medium
(2007-07-18) Roy, Nirupam; Ray, Arnab K.
Spherically symmetric transonic accretion of a fractal medium has been studied in both the stationary and the dynamic regimes. The stationary transonic solution is greatly sensitive to inﬁnitesimal deviations in the outer boundary condition, but the ﬂow becomes transonic and stable, when its evolution is followed through time. The evolution towards transonicity is more pronounced for a fractal medium than what is it for a continuum. The dynamic approach also shows that there is a remarkable closeness between an equation of motion for a perturbation in the ﬂow, and the metric of an analogue acoustic black hole. The stationary inﬂow solutions of a fractal medium are as much stable under the inﬂuence of linearised perturbations, as they are for the ﬂuid continuum.
Critical properties of spherically symmetric black hole accretion in Schwarzschild geometry
(2007-02-28) Mandal, Ipsita; Ray, Arnab K.; Das, Tapas K.
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.
Evolution of transonicity in an accretion disc
(2007-01-10) Ray, Arnab K.; Bhattacharjee, Jayanta K.
For inviscid, rotational accretion ows driven by a general pseudo Newtonian potential on to a Schwarzschild black hole, the only possible xed points are saddle points and centre-type points. For the speci c choice of the Newtonian potential, the ow has only two critical points, of which the outer one is a saddle point while the inner one is a centre-type point. A restrictive upper bound is imposed on the admissible range of values of the angular momentum of sub-Keplerian ows through a saddle point. These ows are very unstable to any deviation from a necessarily precise boundary condition. The di culties against the physical realisability of a solution passing through the saddle point have been addressed through a temporal evolution of the ow, which gives a non-perturbative mechanism for selecting a transonic solution passing through the saddle point. An equation of motion for a real-time perturbation about the stationary ows reveals a very close correspondence with the metric of an acoustic black hole, which is also an indication of the primacy of transonicity
Secular instability in quasi-viscous disc accretion
(2007-07-12) Bhattacharjee, Jayanta K.; Ray, Arnab K.
A ﬁrst-order correction in the -viscosity parameter of Shakura& Sunyaev has been introduced in the standard inviscid and thin accretion disc. A linearised time-dependent perturbative study of the stationary solutions of this “quasi-viscous” disc leads to the development of a secular instability on large spatial scales. This qualitative feature is equally manifest for two different types of perturbative treatment — a standing wave on subsonic scales, as well as a radially propagating wave. Stability of the ﬂow is restored when viscosity disappears.
Standing and travelling waves in the shallow-water circular hydraulic jump
(2007-08-20) Ray, Arnab K.; Bhattacharjee, Jayanta K.
A wave equation for a time-dependent perturbation about the steady shallow-water solution emulates the metric an acoustic white hole, even upon the incorporation of nonlinearity in the lowest order. A standing wave in the sub-critical region of the ﬂow is stabilised by viscosity, and the resulting time scale for the amplitude decay helps in providing a scaling argument for the formation of the hydraulic jump. A standing wave in the super-critical region, on the other hand, displays an unstable character, which, although somewhat mitigated by viscosity, needs nonlinear effects to be saturated. A travelling wave moving upstream from the sub-critical region, destabilises the ﬂow in the vicinity of the jump, for which experimental support has been given
Static & dynamic aspects of transonicity in bondi accretion
(2006-11-23) Ray, Arnab K.; Bhattacharjee, Jayanta K.
Transonicity in a spherically symmetric accreting system has been considered in both the stationary and the dynamic regimes. The stationary ﬂow, set up as a dynamical system, has been shown to be greatly unstable to even the minutest possible deviation in the boundary condition for transonicity. With the help of a simple analytical model, and some numerical modelling, it has then been argued that the ﬂow indeed becomes transonic and stable, when the evolution of the ﬂow is followed through time. The time-dependent approach also shows that there is a remarkable closeness between an equation of motion for a perturbation in the ﬂow, and the metric of an analog acoustic black hole.