On some transonic aspects of general relativistic spherical accretion on to Schwarzschild black holes

Abstract

ABSTRACT The equations governing general relativistic, spherically symmetric, hydrodynamicaccretion of polytropic fluid onto black holes are solved in Schwarzschild metric toinvestigate some of the transonic properties of the flow. Only stationary solutions arediscussed. For such accretion, it has been shown that real physical sonic points mayform even for flow with γ 53 . Behaviour of some flow variables inthe close vicinity of the event horizon are studied as a function of specific energy andpolytropic index of the flow.Key words: accretion, accretion discs – black hole physics – general relativity –hydrodynamics Published in the Monthly Notices of the Royal As-tronomical Society, 2002, Volume 330, Issue 3, pp.563-566.1 INTRODUCTIONInvestigation of accretion processes onto celestial objectswas initiated by Hoyle & Littleton (1939) by computing therate at which pressure-less matter would be captured by amoving star. Subsequently, theory of stationary, sphericallysymmetric and transonic hydrodynamic accretion of adia-batic fluid onto a gravitating astrophysical object at restwas formulated in a seminal paper by Bondi (1952) usingpurely Newtonian potential and by including the pressureeffect of the accreting material. Later on, Michel (1972)discussed fully general relativistic polytropic accretion onto a Schwarzschild black hole by formulating the govern-ing equations for steady spherical flow of perfect fluid inSchwarzschild metric. Following Michel’s relativistic gener-alization of Bondi’s treatment, Begelman (1978) discussedsome aspects of the critical points of the flow for such anaccretion. Spherical accretion and wind in general relativ-ity have also been considered using equations of state otherthan the polytropic one and by incorporating various ra-diative processes (Shapiro, 1973a,b, Blumenthal & Mathews1976, Brinkmann 1980). Recently Malec (1999) provided thesolution for general relativistic spherical accretion with andwithout back reaction and showed that relativistic effectsenhance mass accretion when back reaction is neglected.It is to be noted that one very important issue in under-standing the flow profile for accretion onto gravitating as-trophysical objects is the ‘transonicity’ of the flow. Let theinstantaneous dynamical velocity and the local acoustic ve-locity of a compressible fluid moving along a space curve pa-rameterized by rbe u(r) and a(r) respectively. Local Machnumber M(r) of the fluid can then be defined as the ra-tio of the dynamical flow velocity to its sound speed, i.e.,M(r) =