2007 (IPP)
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Item 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.Item 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.Item 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.Item 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.