Relativistic temperature of gas raises the issue of the equation of state (EOS) in relativistic hydrodynamics. We study the EOS for numerical relativistic hydrodynamics, and propose a new EOS that is simple and yet approximates very closely the EOS of the single-component perfect gas in relativistic regime. We also discuss the calculation of primitive variables from conservative ones for the EOSs considered in the paper, and present the eigenstructure of relativistic hydrodynamics for a general EOS, in a way that they can be used to build numerical codes. Tests with a code based on the total variation diminishing (TVD) scheme are presented to highlight the differences induced by different EOSs.

Steady, spherically symmetric, adiabatic accretion and wind flows around non-rotating black holes were studied for fully ionized, multi-component fluids, which are described by a relativistic equation of state (EoS). We showed that the polytropic index depends on the temperature as well as on the composition of fluids, so the composition is important to the solutions of the flows. We demonstrated that fluids with different composition can produce dramatically different solutions, even if they have the same sonic point, or they start with the same specific energy or the same temperature. Then, we pointed that the Coulomb relaxation times can be longer than the dynamical time in the problem considered here, and discussed the implication.

We investigate the behaviour of low angular momentum viscous accretion flows around black holes using Smooth Particle Hydrodynamics (SPH) method. Earlier, it has been observed that in a significant part of the energy and angular momentum parameter space, rotating transonic accretion flow undergoes shock transition before entering in to the black hole and a part of the post-shock matter is ejected as bipolar outflows, which are supposed to be the precursor of relativistic jets. In this work, we simulate accretion flows having injection parameters from the inviscid shock parameter space, and study the response of viscosity on them. With the increase of viscosity, shock becomes time dependent and starts to oscillate when the viscosity parameter crosses its critical value. As a result, the in falling matter inside the post-shock region exhibits quasi-periodic variations and causes periodic ejection of matter from the inner disc as outflows. In addition, the same hot and dense post-shock matter emits high energy radiation and the emanating photon flux also modulates quasi-periodically. Assuming a ten solar mass black hole, the corresponding power density spectrum peaks at the fundamental frequency of few Hz followed by multiple harmonics. This feature is very common in several outbursting black hole candidates. We discuss the implications of such periodic variations.

Rotating transonic flows are long known to admit standing or oscillating shocks. The excess thermal energy in the post shock flow drives a part of the in falling matter as bipolar outflows. We compute mass loss from a viscous advective disc. We show that the mass outflow rate decreases with increasing viscosity of the accretion disc, since viscosity weakens the centrifugal barrier that generates the shock. We also show that the optical depth of the post-shock matter decreases due to mass loss which may soften the spectrum from such a mass losing disc.

Abstract. We self-consistently estimate the outflow rate from the accretion rates of an accretion disk around a black hole in which both the Keplerian and the sub-Keplerian matter flows simultaneously. While Keplerian matter supplies soft-photons, hot sub-Keplerian matter supplies thermal electrons. The temperature of the hot electrons is decided by the degree of inverse Comptonization of the soft photons. If we consider only thermallydriven flows from the centrifugal pressure-supported boundary layer around a black hole, we find that when the thermal electrons are cooled down, either because of the absence of the boundary layer (low compression ratio), or when the surface of the boundary layer is formed very far away, the outflow rate is negligible. For an intermediate size of this boundary layer the outflow rate is maximal. Since the temperature of the thermal electrons also decides the spectral state of a black hole, we predict that the outflow rate should be directly related to the spectral state.

We study viscous accretion disc around black holes, and all possible accretion solutions, including shocked as well as shock free accretion branches. Shock driven bipolar outflows from a viscous accretion disc around a black hole has been investigated. One can identify two critical viscosity parameters α cl and α cu , within which the stationary shocks may occur, for each set of boundary conditions. Adiabatic shock has been found for upto viscosity parameter α = 0.3, while in presence of dissipation and massloss we have found stationary shock upto α = 0.15. The mass outflow rate may increase or decrease with the change in disc parameters, and is usually around few to 10 % of the mass inflow rate. We show that for the same outer boundary condition, the shock front decreases to a smaller distance with the increase of α. We also show that the increase in dissipation reduces the thermal driving in the post-shock disc, and hence the mass outflow rate decreases upto a few %.

We compute locations of sonic points and standing shock waves in a thin, axisymmetric, adiabatic flow around a Schwarzschild black hole. We use completely analytical method to achieve our goal. Our results are compared with those obtained numerically and a good agreement is seen. Our results positively prove the existence of shocks in centrifugal pressure dominated flows. We indicate how our results could be used to obtain spectral properties and frequencies of shock oscillations which may be directly related to the quasi-periodic oscillations of hard X-rays.Comment: Astrophysical Journal (In press, August 20th, 2001 issue

We investigated the instability of advective accretion flow as a consequence of angular momentum transfer in one-dimensional, quasi-spherical transonic accretion flow around a non-rotating black hole. The code is designed to include the effects of viscosity; the hydrodynamics component preserves angular momentum strictly with Lagrangian and remap method in absence of viscosity, while the viscosity component updates viscous angular momentum transfer through the implicit method. We performed two tests to demonstrate the suitability of the code for accretion study. First, we simulated the inviscid, low angular momentum, transonic accretion flow with shocks around a black hole, and then the subsonic, self-similar ADAF solution around a Newtonian object. Both simulations fitted the corresponding analytical curves extremely well. We then simulated a rotating, viscous, transonic fluid with shocks. We showed that for low viscosity parameter, stable shocks at larger distance are possible. For higher viscosity parameter, more efficient angular momentum transfer in the post-shock disk makes the shock structure oscillatory. Moreover, as the shock drifts to larger distances, a secondary inner shock develops. We showed that the inner shock is the direct consequence of expansion of the outer shock, as well as creation of regions with ∂l/∂r < 0 due to more efficient angular momentum transfer near the inner sonic point. We showed that all disk parameters, including emissivity, oscillate with the same period as that of the shock oscillation. Our simulation may have implication for low frequency QPOs, e.g., GRO J1655-40 and XTE J1550-564.