Effective sound speed in relativistic accretion discs around Schwarzschild black holes

Shaikh, Arif; Maity, Susovan; Nag, Sankhasubhra; Das, Tapas K.

doi:10.1016/j.newast.2018.12.001

Cited by 8 publications

(4 citation statements)

References 75 publications

(87 reference statements)

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“…It has been recently proposed that accreting astrophysical systems may be considered as natural examples of classical analogue gravity models [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. In our present work, we shall consider such a model to manifest our formalism.…”

Section: Introductionmentioning

confidence: 99%

Emergent gravity through non-linear perturbation

Fernandes,

Maity,

Das

2020

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As of now, all analogue gravity models available in the literature deal with the emergence of an acoustic geometry through linear perturbations of transonic fluids only. It has never been investigated whether the analogue gravity phenomena is solely a consequence of linear perturbations, or rather a generic property of arbitrary perturbations of inhomogeneous, inviscid and irrotational fluids. In the present work, for the first time in the literature, we demonstrate that acoustic spacetimes may be formed through higher order non-linear perturbations, and thus establish that analogue gravity phenomena is rather more general than what was thought before. We consider spherically accreting astrophysical systems as a natural classical analogue gravity model, and develop a formalism to investigate non-linear perturbations of such accretion flows to arbitrary order. Our iterative approach involves a coupled set of equations for the mass accretion rate and the density of the fluid. In particular, we demonstrate that the wave equation for the mass accretion rate involves an acoustic metric which can be perturbatively constructed to all orders. We numerically solve the coupled equations about the leading transonic Bondi flow solution. This analysis uses boundary conditions set to the original unperturbed values, with the time dependence of the mass accretion rate perturbation taken to be exponentially damped. The perturbed solutions indicate that second order and higher perturbations of the metric generically cause the original acoustic horizon to oscillate and change in size. We explain this phenomenon in detail and its implications on non-linear perturbations of accretion flows in general.

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Section: Introductionmentioning

confidence: 99%

Emergent gravity through non-linear perturbation

Fernandes,

Maity,

Das

2020

Preprint

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“…The present work may also be useful in the context of analogue gravity phenomenon. It has been observed that a curved acoustic metric may be embedded within the accreting matter and such space-time may be generated through the perturbation of accretion flow ( [Ananda et al, 2015], [Bollimpalli et al, 2017], [Shaikh et al, 2017], , [Shaikh, 2018], [Datta et al, 2018], [Shaikh et al, 2019], [Datta and Das, 2019]). The present work will also lead to the understanding of how the flow thickness of axially symmetric accretion in the Kerr metric may influence the properties of the analogue surface gravity of the corresponding sonic space-time.…”

Section: Introductionmentioning

confidence: 99%

Influence of flow thickness on general relativistic low angular momentum accretion around spinning black holes

Tarafdar,

Maity,

Das

2020

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General relativistic, axisymmetric flow of low angular momentum accretion around a Kerr black hole can have certain geometric configuration where the flow is maintained in hydrostatic equilibrium along the vertical direction (direction orthogonal to the equatorial plane of the flow). The flow thickness for such accretion models becomes a function of the local radial distance measured from the black hole horizon. There are three types of functions defined in the literature which resemble the thickness of the flow for such a configuration. We formulate the equations governing the steady state astrophysical accretion characterized by both the polytropic as well as the isothermal equation of state in classical thermodynamics. We solve the equations within the framework of such geometric configuration for three different thickness functions, to obtain the multi-transonic, shocked, stationary integral accretion solutions. Such solutions enable us to study how flow thickness influences the dependence of the properties of post-shock flows on black hole spin angular momentum, i.e., the Kerr parameter. For temperature-preserving standings shocks, we find that the post-shock part of the disc can become luminous and considerable amount of gravitational energy carried by the accreting fluid can get liberated at the shock. We find which kind of thickness function produces the maximum liberated energy, making the disc most luminous.

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“…Owing to the fact that accretion of hydrodynamic fluid onto astrophysical black holes are usually transonic in nature ( [Liang and Thomson, 1980]), it has been recently proposed that accreting astrophysical systems may be considered as natural examples of classical analogue gravity models ( [Das, 2004], [Dasgupta et al, 2005], [Abraham et al, 2006], [Das et al, 2007], [Pu et al, 2012], [Bilić et al, 2014], [Tarafdar and Das, 2015], [Ananda et al, 2015], [Saha et al, 2016], [Bollimpalli et al, 2017], [Shaikh et al, 2017], [Tarafdar and Das, 2018], , [Shaikh, 2018], [Datta et al, 2018], [Shaikh et al, 2019], [Datta and Das, 2019]).…”

Section: Introductionmentioning

confidence: 99%

Dependence of acoustic surface gravity on disc thickness for accreting astrophysical black holes

Maity¹,

Tarafdar²,

Shaikh³

et al. 2020

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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.

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Effective sound speed in relativistic accretion discs around Schwarzschild black holes

Cited by 8 publications

References 75 publications

Emergent gravity through non-linear perturbation

Emergent gravity through non-linear perturbation

Influence of flow thickness on general relativistic low angular momentum accretion around spinning black holes

Dependence of acoustic surface gravity on disc thickness for accreting astrophysical black holes

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