An exact solution of transfer equations for interlocked multiplets

The transfer equations for non-coherent scattering arising from interlocking of principal lines without redistribution is exactly solved in a very simple way by Laplace tranform and Wiener-Hopf technique which are easily applied by the use of the new representation ofH-functions obtained recently by the author (1977). The emergent intensity in therth line is expressed in terms of anH-function and a Cauchy type integral admitting of closed form evaluation.     

Regularization and linearization of the equations of motion in central force-fields

Within the framework of linear and regular celestial mechanics, a wide class of central force field problems are considered. We take as potential function a polynomial whose variable is the reciprocal of the distance from the origin, and, as regularizing function the square root of a certain reciprocal polynomial, related to the potential function. The relations between the coefficients of both functions, in order to arrive to linear equations, are given. In particular, the case of a quintic polynomial is analyzed, and an application is made to artificial earth satellites considering harmonicsJ ₂,J ₃,J ₄.     

An exact solution of time-dependent equation of transfer of trapped radiation in a finite absorbing medium

Milne's time-dependent equation of transfer of trapped radiation in finite absorbing medium has been exactly solved by a combination of Das Gupta's modified form of the Wiener-Hopf technique and method of solving boundary value problems in the theory of heat conduction as adopted by Chandrasekhar (1950) to solve the same equation approximately in combination with his method of discrete ordinates. Milne himself had earlier obtained an approximate solution of his equation.     

Numerical solution of the time-dependent heat energy equations for the magnetosphere

A new solution of the magnetospheric heat equations capable of covering the whole region from 300 km along a field line to the equatorial plane has been achieved by adapting the searching procedure of Murphy (1974). It has been found that the protonospheric heat reservoir is sufficient to maintain T_e >T_n down to the height of the F2-peak electron density all through the night at mid-latitudes. Full solution of the equations has also shown that T_i >T_e in the protonosphere at night and the ions constitute a significant source of heat for the electrons.     

Coupling between the F-region and protonosphere: Numerical solution of the time-dependent equations

This paper describes a new method of solution of the time-dependent continuity and momentum equations for H⁺ and O⁺ in mid-latitude magnetic field tubes from the F-region to the equator. For each ion the equations are expressed as an integro-differential equation. This equation is treated as an ordinary differential equation and solved by a searching method. By means of this method, the distribution of H⁺ in the O⁺?H⁺ transition region and the protonosphere can be investigated and the influence of H⁺ fluxes on the F layer examined.As an example of application of the method a suggestion by Park (1971) about observed night-time enhancements of N_mF2 is examined. He suggested that lowering of the F layer some hours after a magnetic substorm may cause N_mF2 to increase because of increased ion influx from the protonosphere. In the present calculations the Flayer is maintained around a constant height for some time and then abruptly lowered. Under the conditions adopted the resulting increase in downward H⁺ flux is sufficient to maintain N_mF2 against the increased recombination but not to increase N_mF2 significantly. It is emphasised that these results are not conclusive.     

An exact analytical solution of Kepler's equation

Complex-variable analysis is used to develop an exact solution to Kepler's equation, for both elliptic and hyperbolic orbits. The method is based on basic properties of canonical solutions to appropriately posed Riemann problems, and the final results are expressed in terms of elementary quadratures.     

A new technique for exact and unique solution of transfer equations in finite media

In this paper we develop a new method, combined with Laplace transformation and Wiener-Hopf technique, to obtain unique solutions of transport equations in finite media. For this purpose we consider the simple transfer equation for diffuse reflection by a plane-parallel finite atmosphere scattering radiation with moderate anisotropy. It is transformed, by Laplace transformation, into two coupled linear integral equations which are then reduced to two uncoupled Fredholm integral equations admitting of unique solutions by the method of iteration for values of the breadth of the atmosphere greater than that specified, depending on the scattering process.     

An alpha theory of time-dependent warped accretion discs

The non-linear fluid dynamics of a warped accretion disc was investigated in an earlier paper by developing a theory of fully non-linear bending waves in a thin, viscous disc. That analysis is extended here to take proper account of thermal and radiative effects by solving an energy equation that includes viscous dissipation and radiative transport. The problem is reduced to simple one-dimensional evolutionary equations for mass and angular momentum, expressed in physical units and suitable for direct application. This result constitutes a logical generalization of the alpha theory of Shakura & Sunyaev to the case of a time-dependent warped accretion disc. The local thermal–viscous stability of such a disc is also investigated.     

An exact solution of two-dimensional steady MGD flows

Steady-plane flow of an inviscid, electrically-conducting, compressible fluid with infinite electrical conductivity is considered and a single partial differential equation is obtained which involves two functions. Appropriate specialization of these functions generate new exact solutions of the orginal equations.     

On the physical parameters for Centaurus X-3 and Hercules X-1

Upper and lower limits on the physical parameters for Cen X-3 and Her X-1 have been computed from a simple assumption involving the mass function.     

An exact solution of the gamma ray burst arrival time analysis problem

An analytical solution of the GRB arrival time analysis is presented. The errors in the position of the GRB resulting from timing and position errors of different satellites are calculated. A simple method of cross-correlating gamma ray burst time-histories is discussed.     

An exact solution to the relativistic advance of perihelion: correcting the Einstein approximation

New calculations of the main term of the advance of perihelion for the asteroid Icarus and planet Mercury are discussed. With the help of this author’s previously published formula for the advance, results are then compared to the values given by Einstein’s approximation.     

An exact Bianchi type-V cosmological model in Saez-Ballester theory of gravitation

An exact Bianchi type-V cosmological model is obtained in a scalar-tensor theory of gravitation proposed by Saez and Ballester (Phys. Lett. A 113:467, 1986) in case of perfect fluid distribution. Some physical properties of the model are also discussed.     

Spectral and intensity variations in cygnus X-3 by the Astronomical Netherlands Satellite

Measurements obtained with the Utrecht (1–8 keV) and Cambridge (1–28 keV) instruments on board the Astronomical Netherlands Satellite are discussed. Particularly, the 4.8 hr period is investigated.Paper presented at the COSPAR Symposium on Fast Transients in X- and Gamma-Rays, held at Varna, Bulgaria, 29–31 May, 1975.     

Cyg X-3X光子场对γ射线的吸收效应

本文详细讨论了X射线双星Cyg X-3 的X光子场对γ射线的吸收效应.计算结果表明:当Cyg x-3 的X光子发射场处于高态时,从致密中子星附近发射的能量为10~2—10~4MeV的γ射线约有60％被其吸收,吸收过程产生的正负电子的逆Compton 散射会使出射能量10—70MeV的γ射线强度平均增加约50％.计算的γ射线能谱与实验观测结果基本相符.     

Cutoff in the hard X-ray spectra of the ultraluminous X-ray sources HoIX X-1 and M82 X-1

Using data from the XMM-Newton and INTEGRAL observatories, we have detected a cutoff at energies above 10 keV in the X-ray spectra of the ultraluminous X-ray sources HoIX X-1 and M82 X-1. The spectra obtained can be described by amodel of Comptonization of radiation in a gas cloud of moderate temperature (kT ～ 2–3 keV) and high optical depth (τ ～ 15–25). Such conditions can be fulfilled during supercritical accretion of matter onto a stellar-mass black hole accompanied by a strong gas outflow. The results of this work confirm the existence of a spectral state specific to ultraluminous X-ray sources, which is unlike any of the known spectral states in normal X-ray binaries.     

A type of second order linear ordinary differential equations with periodic coefficients for which the characteristic exponents have exact expressions

It is shown that the characteristic exponents can be exactly expressed for a type of second order linear ordinary differential equations with periodic coefficients (Hill's equation) which appear as the variational equations of certain periodic solutions of dynamical systems. Key points are the transformation of the equation to the Gauss' hypergeometric differential equation, and evaluation of the trace of monodormy matrix in the complex plane of the independent variable. Two simple examples are given for which the stability of periodic solutions is rigorously analyzed.     

An exact solution of the equation of transfer for coherent scattering in an exponential atmosphere

An exact solution of the transfer equation for coherent scattering in stellar atmospheres with Planck's function as a nonlinear function of optical depth, of the form $$B_v (T) = b_0 + b_1 {\text{ }}e^{ - \beta \tau } $$ is obtained by the method of the Laplace transform and Wiener-Hopf technique.     

An improved version of the implicit integral method to solving radiative transfer problems

Radiative transfer (RT) problems in which the source function includes a scattering-like integral are typical two-points boundary problems. Their solution via differential equations implies making hypotheses on the solution itself, namely the specific intensity I (τ; n) of the radiation field. On the contrary, integral methods require making hypotheses on the source function S(τ). It seems of course more reasonable to make hypotheses on the latter because one can expect that the run of S(τ) with depth is smoother than that of I (τ; n). In previous works we assumed a piecewise parabolic approximation for the source function, which warrants the continuity of S(τ) and its first derivative at each depth point. Here we impose the continuity of the second derivative S′′(τ). In other words, we adopt a cubic spline representation to the source function, which highly stabilizes the numerical processes.