Realizability of stationary spherically symmetric transonic accretion

Ray, Arnab; Bhattacharjee, Jayanta K.

doi:10.1103/physreve.66.066303

Cited by 33 publications

(77 citation statements)

References 9 publications

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“…The separatrices of the saddle point with higher value ofṀ in the polytropic case (with lower value of C in isothermal case) form the homoclinic connection. Physically this is what it has to be, because it is the third critical point (saddle) which will allow the transonic flow solution from infinity to the event horizon, and here, following the line of argument in Ray & Bhattacharjee (2002), it can be stated that the stationary flow solution has to settle on the separatices of a saddle point only. That is why among the critical points, only the saddle points are termed as sonic points, and not the centre-type points, although for both the types of critical points the flow speed is equal to the sound speed, i.e.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…With respect to accretion studies in particular, this kind of parametrisation has been reported before (Ray & Bhattacharjee 2002;Afshordi & Paczyński 2003;Chaudhury et al 2006;Mandal et al 2007;Goswami et al 2007;Bhattacharjee et al 2009b). The critical points have been fixed in terms of the flow constants.…”

Section: Nature Of the Fixed Points : A Dynamical Systems Studymentioning

confidence: 99%

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The role of flow geometry in influencing the stability criteria for low angular momentum axisymmetric black hole accretion

et al. 2012

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Using mathematical formalism borrowed from dynamical systems theory, a complete analytical investigation of the critical behaviour of the stationary flow configuration for the low angular momentum axisymmetric black hole accretion provides valuable insights about the nature of the phase trajectories corresponding to the transonic accretion in the steady state, without taking recourse to the explicit numerical solution commonly performed in the literature to study the multi-transonic black hole accretion disc and related astrophysical phenomena. Investigation of the accretion flow around a non rotating black hole under the influence of various pseudo-Schwarzschild potentials and forming different geometric configurations of the flow structure manifests that the general profile of the parameter space divisions describing the multi-critical accretion is roughly equivalent for various flow geometries. However, a mere variation of the polytropic index of the flow cannot map a critical solution from one flow geometry to the another, since the numerical domain of the parameter space responsible to produce multi-critical accretion does not undergo a continuous transformation in multi-dimensional parameter space. The stationary configuration used to demonstrate the aforementioned findings is shown to be stable under linear perturbation for all kind of flow geometries, black hole potentials, and the corresponding equations of state used to obtain the critical transonic solutions. Finally, the structure of the acoustic metric corresponding to the propagation of the linear perturbation studied are discussed for various flow geometries used.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Nature Of the Fixed Points : A Dynamical Systems Studymentioning

confidence: 99%

The role of flow geometry in influencing the stability criteria for low angular momentum axisymmetric black hole accretion

et al. 2012

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“…The trouble with the transonic solution in the stationary regime is that its realizability is extremely vulnerable to even an infinitesimal deviation from the precisely needed boundary condition to generate the solution [7]. This difficulty may be overcome by considering the temporal evolution of global solutions towards the transonic state [7,8], but there is no analytical formulation to solve the nonlinear partial differential equations governing the temporal evolution of the flow.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…This difficulty may be overcome by considering the temporal evolution of global solutions towards the transonic state [7,8], but there is no analytical formulation to solve the nonlinear partial differential equations governing the temporal evolution of the flow. So, much of all time-dependent studies in spherically symmetric accretion is perturbative and linearized in character, although some non-perturbative studies are also known [7,8]. The commonly accepted view to have emerged from the linearized approach is that perturbations on the flow do not produce any linear mode with an amplitude that gets amplified in time [9], and that the perturbative method does not indicate the primacy of any particular class of solutions [10].…”

Section: Introductionmentioning

confidence: 99%

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Implications of nonlinearity for spherically symmetric accretion

Sen¹,

Ray²

2014

Phys. Rev. D

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We subject the steady solutions of a spherically symmetric accretion flow to a time-dependent radial perturbation. The equation of the perturbation includes nonlinearity up to any arbitrary order, and bears a form that is very similar to the metric equation of an analogue acoustic black hole. Casting the perturbation as a standing wave on subsonic solutions, and maintaining nonlinearity in it up to the second order, we get the timedependence of the perturbation in the form of a Liénard system. A dynamical systems analysis of the Liénard system reveals a saddle point in real time, with the implication that instabilities will develop in the accreting system when the perturbation is extended into the nonlinear regime. The instability of initial subsonic states also adversely affects the temporal evolution of the flow towards a final and stable transonic state.

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An analytical study on the multi-critical behaviour and related bifurcation phenomena for relativistic black hole accretion

et al. 2012

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We apply the theory of algebraic polynomials to analytically study the transonic properties of general relativistic hydrodynamic axisymmetric accretion onto non-rotating astrophysical black holes. For such accretion phenomena, the conserved specific energy of the flow, which turns out to be one of the two first integrals of motion in the system studied, can be expressed as a 8 th degree polynomial of the critical point of the flow configuration. We then construct the corresponding Sturm's chain algorithm to calculate the number of real roots lying within the astrophysically relevant domain of R. This allows, for the first time in literature, to analytically find out the maximum number of physically acceptable solution an accretion flow with certain geometric configuration, space-time metric, and equation of state can have, and thus to investigate its multi-critical properties completely analytically, for accretion flow in which the location of the critical points can not be computed without taking recourse to the numerical scheme. This work can further be generalized to analytically calculate the maximal number of equilibrium points certain autonomous dynamical system can have in general. We also demonstrate how the transition from a monocritical to multi-critical (or vice versa) flow configuration can be realized through the saddle-centre bifurcation phenomena using certain techniques of the catastrophe theory.

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Realizability of stationary spherically symmetric transonic accretion

Cited by 33 publications

References 9 publications

The role of flow geometry in influencing the stability criteria for low angular momentum axisymmetric black hole accretion

The role of flow geometry in influencing the stability criteria for low angular momentum axisymmetric black hole accretion

Implications of nonlinearity for spherically symmetric accretion

An analytical study on the multi-critical behaviour and related bifurcation phenomena for relativistic black hole accretion

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