41 research outputs found
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
Dependence of acoustic surface gravity on disc thickness for accreting astrophysical black holes
For axially symmetric accretion maintained in hydrostatic equilibrium along
the vertical direction, we investigate how the characteristic features of the
embedded acoustic geometry depends on the background Kerr metric, and how such
dependence is governed by three different expressions of the thickness of the
matter flow. We first obtain the location of the sonic points and stationary
shock between the sonic points. We then linearly perturb the flow to obtain the
corresponding metric elements of the acoustic space-time. We thus construct the
causal structure to establish that the sonic points and the shocks are actually
the analogue black hole type and white hole type horizons, respectively. We
finally compute the value of the acoustic surface gravity as a function of the
spin angular momentum of the rotating black hole for three different flow
thicknesses considered in the present work. We find that for some flow models,
the intrinsic acoustic geometry, although in principle may be extended up to
the outer gravitational horizon of the astrophysical black hole, cannot be
constructed beyond a certain truncation radius as imposed by the expressions of
the thickness function of the corresponding flow.Comment: 22 pages, 9 figure
Carter-Penrose diagrams for emergent spacetime in axisymmetrically accreting black hole systems
For general relativistic, inviscid, axisymmetric flow around Kerr black hole
one may choose different flow thickness. The stationary flow equations can be
solved using methods of dynamical system to get transonic accretion flows ,
i.e, flow infalling in the blackhole that turns supersonic from subsonic with
decreasing radial distance, or vice versa. This transonic flows are obtained by
choosing the particular flow passing through critical points of phase portrait.
For certain flow thickness like the one maintaining conical shape, the sonic
point coincide with the critical point. But there are certain flows maintaining
hydrostatic equilibrium, such as the one described by Novikov-Thorne, where the
sonic point is not same as the critical point. We perturb the flow for both
kind of flow and study the behaviour of linear perturbation which behaves like
massless scalar field in some curved spacetime, known as, analogue space time.
We draw the compactified causal structure, i.e, Penrose Carter diagram for both
kind of analogue metric and prove that for both cases critical points are the
acoustic horizons, whereas in the case where sonic points do not coincide with
critical points, the sonic points are not the acoustic horizon, as one may
expect from the definition of sound speed.Comment: arXiv admin note: text overlap with arXiv:1811.0497