On transfer equation in a semi-infinite atmosphere with albedo ω>1

In this note we derive an exact solution of transfer equation in a plane-parallel semiinfinite atmosphere with albedo >1, by the method of Laplace transform and Wiener-Hopf technique. The emergent intensityI(0, ) is obtained in terms of theH ⁰-functionH ⁰() (Das Gupta, 1978) for which some good approximations are given. Intensity at any depth is also obtained.I(0, )/I(0, 0) is plotted in graphs against [0,1], and shows a maximum which drops and shifts towards the origin as increases.     

Computation of mass outflow rate from relativistic quasi-spherical accretion on to black holes

We compute the mass outflow rate R _m˙ from relativistic matter that is accreting quasi-spherically on to the Schwarzschild black holes. Taking the pair-plasma pressure-mediated shock surface as the effective boundary layer (of the black hole) from where the bulk of the outflow is assumed to be generated, computation of this rate is done using combinations of exact transonic inflow and outflow solutions. We find that R _m˙ depends on the initial parameters of the flow, the polytropic index of matter, the degree of compression of matter near the shock surface and the location of the shock surface itself. We thus not only study the variation of the mass outflow rate as a function of various physical parameters governing the problem, but also provide a sufficiently plausible estimation of this rate.     

Dynamical behavior of size-graded dust grains levitated in rotating magnetized astroplasmas

Our purpose is to examine the formation of different sheaths in rotating astroplasmas embedded in an ambient magnetic field. Sequel to our recent work (Das and Chakraborty in Astrophys. Space Sci., 2011) we remodeled our present study with the view to finding of robust sheath over the Earth’s Moon along with the formation of dust clouds therein. Based on using the pseudopotential analysis, a modified Sagdeev potential equation has been derived, which, in turns, quantifies the interaction of Coriolis force and magnetic field and to derive the different natures of sheath and dust atmosphere. The application of this result to the input numeric data of the lunar environment and dynamical behaviors of dust levitation has been studied. Our study finds that the dust particles having a spatial segregation within the sheath region form dust clouds in spaces.     

Exact solution of the problem of diffuse reflection and transmission by the method of Laplace transform and linear singular operators

The basic integro-differential equation is subjected to a one-sided finite Laplace transform to obtain linear integral equations of angular distribution of bounding faces. These linear integral equations have been transformed into linear singular integral equations which have been solved exactly to get the emergent distributions from the bounding faces by the theory of linear singular operators. Some solutions of linear singular integral equations have also been derived for future use in radiative transfer problems.     

A note on theH-functions of transfer problems in multiplying media

Some useful results and remodelled representations ofH-functions corresponding to the dispersion function $$T\left( z \right) = 1 - 2z^2 \sum\limits_1^n {\int_0^{\lambda r} {Y_r } \left( x \right){\text{d}}x/\left( {z^2 - x^2 } \right)} $$ are derived, suitable to the case of a multiplying medium characterized by $$\gamma _0 = \sum\limits_1^n {\int_0^{\lambda r} {Y_r } \left( x \right){\text{d}}x > \tfrac{1}{2} \Rightarrow \xi = 1 - 2\gamma _0< 0} $$      

Green's function of one group transport equation for a finite slab of passive and multiplying media by Wiener-Hopf technique

We have applied the method of Wiener-Hopf technique to obtain the Green's functions of one-group transport equations (with anisotropic unit plane source and with isotroic unit plane source) for a finite slab of passive and multiplying media.     

Laser radiation in active amplifying media treated as a transport problem: Transfer equation derived and exactly solved

The flow of laser radiation in a plane-parallel cylindrical slab of active amplifying medium with axial symmetry is treated as a problem in radiative transfer. The appropriate one-dimensional transfer equation describing the transfer of laser radiation has been derived by an appeal to Einstein'sA, B coefficients (describing the processes of stimulated line absorption, spontaneous line emission, and stimulated line emission sustained by population inversion in the medium) and considering the rate equations to completely establish the rational of the transfer equation obtained. The equation is then exactly solved and the angular distribution of the emergent laser beam intensity is obtained; its numerically computed values are given in tables and plotted in graphs showing the nature of peaks of the emerging laser beam intensity about the axis of the laser cylinder.     

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.     

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.