Standing shocks in magnetized dissipative accretion flow around black holes

We explore the global structure of the accretion flow around a Schwarzschild black hole where the accretion disc is threaded by toroidal magnetic fields. The accretion flow is optically thin and advection dominated. The synchrotron radiation is considered to be the active cooling mechanism in the flow. With this, we obtain the global transonic accretion solutions and show that centrifugal barrier in the rotating magnetized accretion flow causes a discontinuous transition of the flow variables in the form of shock waves. The shock properties and the dynamics of the post-shock corona are affected by the flow parameters such as viscosity, cooling rate and strength of the magnetic fields. The shock properties are investigated against these flow parameters. We further show that for a given set of boundary parameters at the outer edge of the disc, accretion flow around a black hole admits shock when the flow parameters are tuned for a considerable range.     

A shock hodograph in collisionless plasma

In this paper, the shock hodograph (polar) for a collisionless transverse shock has been developed in the plane of the flow deflection angle and total pressure jump. The sonic point on the hodograph lies closer to the characteristic than to the point of maximum flow deflection for an attached shock. This hodograph is particularly useful in the analysis of three shock confluences and refraction of shock waves at gas interfaces. The first analysis is fully described in this paper. It is observed that the third shock wave is forward facing. It is pertinent to note that the limited region of supersonic flow also restricts the occurrences of three shock interactions.     

Flow behind an attached shock wave in a radiating gas

A simple method is used to determine the curvature of an attached shock wave and the flow variable gradients behind the shock curve at the tip of a straight-edged wedge placed symmetrically in a supersonic flow of a radiating gas near the optically thin limit. The shock curvature and the flow variable gradients along the wedge at the tip are computed for a wide range of upstream flow Mach numbers and wedge angles. Several interesting results are noted; in particular, it is found that the effect of an increase in the upstream flow Mach number or the radiative flux is to enhance the shock wave curvature which, however, decreases with an increase in the specific heat ratio or the wedge angle.     

Identification of a blue object with a newly detected X-ray source

An approximate analytical solution for self-similar flow behind a spherically-symmetric magnetogasdynamic strong shock wave is investigated using the method of Laumbach and Probstein (1969). The total energy of flow is taken to be dependent on the shock radius obeying a power law. The shock is propagating into a perfect gas at rest with non-uniform density and magnetic field.     

A universal vertical stellar density distribution law for the Galaxy

This article applies nonstandard analysis to derive jump conditions for one-dimensional, diverging, magnetogasdynamic shock waves emerging on the surface of a star. It is assumed that the shock thickness occurs on an infinitesimal interval and the jump functions for the flow parameters occur smoothly across this interval. Predistributions of the Heaviside function and the Dirac delta measure are used to model the flow variables across a shock wave. The equations of motion expressed in nonconservative form are then applied to derive unambiguous relationships between the jump functions for the flow parameters. It is shown here that the equations modeling a family of magnetogasdynamic shock waves yield products of generalized functions that may be analyzed consistently using nonstandard predistributions.     

A self-similar flow in Generalized Roche model with increasing energy

The self-similar flow of a gas, moving under the gravitational attraction of a central body of fixed mass behind a spherical shock wave driven out by a propelling contact surface into quiet solar wind region, is investigated. The total energy content between the inner expanding surface and the shock front increases with time. In the last section we briefly pose the self-similar isothermal flow of a gas behind a spherical shock wave.     

Dissipative accretion flows around a rotating black hole

We study the dynamical structure of a cooling dominated rotating accretion flow around a spinning black hole. We show that non-linear phenomena such as shock waves can be studied in terms of only three flow parameters, namely the specific energy     , the specific angular momentum (λ) and the accretion rate     of the flow. We present all possible accretion solutions. We find that a significant region of the parameter space in the     plane allows global accretion shock solutions. The effective area of the parameter space for which the Rankine–Hugoniot shocks are possible is maximum when the flow is dissipation-free. It decreases with the increase of cooling effects and finally disappears when the cooling is high enough. We show that shock forms further away when the black hole is rotating compared to the solution around a Schwarzschild black hole with identical flow parameters at a large distance. However, in a normalized sense, the flow parameters for which the shocks form around the rotating black holes are produced shocks closer to the black hole. The location of the shock is also dictated by the cooling efficiency in that higher the accretion rate     , the closer is the shock location. We believe that some of the high-frequency quasi-periodic oscillations may be due to the flows with higher accretion rate around the rotating black holes.     

Shock waves from point-sources in a heat-conducting gas

The shock wave produced by a point source has been studied in a heat-conducting gas medium. The shock is assumed to be strong enough to neglect the ambient gas pressure and the similarity method is used. The distribution of flow quantities behind the shock have been obtained by the numerical integration of a system of ordinary differential equations using the boundary conditions at the shock wave.     

Relativistic hydrodynamics of a free expansion and a shock wave in one-dimension

Dynamical evolution of a relativistic explosion resulting from a large amount of energy release in a homogenous medium is studied using the Khalatnikov equation describing relativistic, hydrodynamic, planar flow. The early phase of the explosion is idealized to two stages: a free expansion and a shock wave stage. By the hodograph transformation inverting the dependent and independent variables, the hydrodynamic equations for the relativistic flow are reduced to second-order linear equations in a velocity-enthalpy space and they are solved by the method of Laplace transformation. The propagation laws and flow structures of the relativistic expansion are obtained at each stage. In the free expansion stage, the flow with a sufficiently high sound velocity forms a thin shell of the energy density in the comoving frame at the front and accelerates the front. In the shock wave stage, the Lorentz factor of the shock front decreases logarithmically with time. The transition time from a free expansion to a shock wave stage suggests that the super-light expansion observed in extragalactic radio sources has no spherical geometry but must be confined to a narrow cone.     

Self-similar solutions for the blast wave problem in radiative gasdynamics,I

Similarity solutions, describing the flow of a perfect gas behind spherical shock waves, are investigated including the radiation heat flux. The shock is assumed to be propagating in a medium at rest. Shock radius varies exponentially with time and density is inversely proportional to fifth power of the shock radius immediately ahead of the shock front.     

Impact cratering mechanics: Relationship between the shock wave and excavation flow

This paper describes the relationship between the shock wave produced by an impact and the excavation flow that opens the crater. The excavation flow velocity is shown to be a nearly constant fraction of the peak particle velocity in the wave. The existence of an excavation flow is due to thermodynamically irreversible processes in the shock. The excavation flow velocity is thus very sensitive to nonideal constitutive effects such as porosity, plastic yielding, and unreversed phase transformations. Cratering computations that do not model these effects correctly may produce misleading results.     

Unsteady isothermal flow of a gas behind an exponential shock in magnetogasdynamics

A self-similar flow of a perfect gas behind a strong shock driven out by a propelling contact discontinuity surface moving with time according to an exponential law in the presence of axial component of the magnetic field is investigated. The flow between the shock and the inner-expanding surface is assumed to be isothermal. The infinite electrically conductive and uniform medium has been taken into consideration.     

Strong point-explosions in media characterized by spheroidal symmetry with zero temperature gradient far behind the shock

Strong point-explosion in an axisymmetric medium whose density is decreasing exponentially and in which the flow field has zero temperature gradient sufficiently far behind the shock, is being studied. It is found that the shock velocity is the same as in the adiabatic case in the initial stages, but after a few seconds the shock moves much faster than it would if the flow field behind were adiabatic.     

Radiative decay behind strong M.H.D. shocks

The effect of radiation up on the state of gas behind strong M.H.D. shock front has been studied. The jump conditions for flow variables across the shock boundary have been obtained and temperature decay behind the shock front is determined for a optically-thin brehmsstrahlung radiation plasma. It has been found that, for a shock within strong magnetic field, the temperature decay is much quicker.     

A self-similar solution for spherically symmetric gravitational collapse

A model of gas-dynamical flow during gravitational collapse is analyzed mathematically by assuming its spherical symmetry and self-similarity. A shock wave diverging from the center emerges in this model. The physical requirements imposed on the post-shock flow at the center for the specified parameters at infinity unambiguously determine the shock front and the flow behind it.     

Propagation of a strong cylindrical shock wave in a rotational axisymmetric dusty gas with exponentially varying density

Non-similarity solutions are obtained for one-dimensional isothermal and adiabatic flow behind strong cylindrical shock wave propagation in a rotational axisymmetric dusty gas,which has a variable azimuthal and axial fluid velocity.The dusty gas is assumed to be a mixture of small solid particles and perfect gas.The equilibrium flow conditions are assumed to be maintained,and the density of the mixture is assumed to be varying and obeying an exponential law.The fluid velocities in the ambient medium are assumed to obey exponential laws.The shock wave moves with variable velocity.The effects of variation of the mass concentration of solid particles in the mixture,and the ratio of the density of solid particles to the initial density of the gas on the flow variables in the region behind the shock are investigated at given times.Also,a comparison between the solutions in the cases of isothermal and adiabatic flows is made.     

Self-similar model of magnetohydrodynamic radiative shock waves with increasing density

The magnetohydrodynamic model of shock waves has been discussed in an atmosphere with gravitation and radiation. The disturbance is headed by a strong shock of increasing density. The medium ahead of the shock is assumed to be inhomogeneous and at rest. Variation of magnetic field radiation flux, and other flow variables are given in tabular form.     

Study of magnetized accretion flow with cooling processes

We have studied shock in magnetized accretion flow/funnel flow in case of neutron star with bremsstrahlung cooling and cyclotron cooling. All accretion solutions terminate with a shock close to the neutron star surface, but at some regions of the parameter space, it also harbours a second shock away from the star surface. We have found that cyclotron cooling is necessary for correct accretion solutions which match the surface boundary conditions.     

Study of accretion disk dynamics in presence of cooling

We examine the behaviour of accretion flow around a rotating black hole in presence of cooling. We obtain global flow solutions for various accretion parameters that govern the accreting flow. We show that standing isothermal shock wave may develop in such an advective accretion flow in presence of cooling. This shocked solution has observational consequences as it successfully provides the possible explanations of energy spectra as well as generation of outflows/jets of various galactic and extra-galactic black hole candidates. We study the properties of isothermal shock wave and find that it strongly depends on the cooling efficiency. We identify the region in the parameter space spanned by the specific energy and specific angular momentum of the flow for standing isothermal shock as a function of cooling efficiencies and find that parameter space gradually shrinks with the increase of cooling rates. Our results imply that accretion flow ceases to contain isothermal shocks when cooling is beyond its critical value.     

Self-similar flows behind a spherical radiation-driven shock wave,II

Self-similar flows, behind a radiation-driven shock wave, have been investigated in non-uniform atmosphere. The total energy content of the flow behind the shock increases due to the absorption of radiation and it is assumed to be time-dependent.