On the theory of X-ray pulsar radiation

The origin of hard X-ray spectrum (continuum and cyclotron lines) of pulsars in binary systems is discussed. A model of the polar region of a neutron star consisting of a hot spot in a dense plasma atmosphere with a quasi-homogeneous magnetic field and an extended accreting column in an inhomogeneous dipolar field is investigated. In the hot spot bremsstrahlung and Thomson scattering form continuum radiation, while bremsstrahlung and cyclotron scattering produce the absorption cyclotron lines. By the observed continuum intensity one can estimate the maximum distances to pulsars. Cyclotron scattering in gyro-resonant layers localized in the accreting column leads to a general attenuation of the radiation of a hot spot, but is unable to ensure the formation of cyclotron lines. For strong accretion the hot spot radiation becomes insignificant, the lines disappear and the pulsating component of an X-ray pulsar is produced by the accreting column bremsstrahlung transformed by Thomson scattering.     

The prominence radiation theory

The present work is a review of papers related to the theory of prominence radiation. Special attention is paid to stationary equations and the theory of radiation diffusion in the lines and continua of hydrogen, helium and metals.We conclude that prominences are low-temperature formations T _e 7000 K, of low density 10¹² particles per cm³, n _e 10¹¹ cm^–3, effective thickness 10⁹ cm, and that the chemical composition of prominences and that of the Sun's atmosphere are the same. The prominence radiation in the lines of hydrogen, helium and metals is due mainly to quasiresonance scattering of the photospheric radiation.     

On the theory of the generation of auroral radiation

The stability of the hot plasma located at the curvilinear geomagnetic field in relation to the generation of Alfvén oscillations is investigated. A general expression for the increment is obtained. The increments for the short wavelength disturbances and special energy distribution function in a parabolic magnetic field are presented. The obtained theoretical results are used in interpreting the oscillations of the “auroral radiation” type. The polarization relations in Alfvén waves are investigated.     

Hawking radiation in string theory

We review some of the progress in understanding the statistical basis of black hole thermodynamics in string theory. The emphasis is on the “derivation” of Hawking radiation from the unitary decay of near extremal D-brane states. We also review recent progress in understanding Schwarzschild black holes by relating them to D-brane black holes via “boosts” in M-theory.     

On the theory of radiation properties of an accelerated supersonic soliton

Taking into account the relativistic effect of a transverse high-frequency electromagnetic wave on the plasma electrons, the radiation properties of an accelerated supersonic soliton is studied, in the case when the acceleration of the soliton is due to an inhomogeneous density barrier of a wide range of applications. It is shown that the accelerated supersonic soliton radiates an ion-sound wave. The basic equations describing the dynamic behaviour of the high-frequency electromagnetic waves, as well as the emission of the ion-sound waves are formulated. The distribution of the perturbed concentration in the ion-sound wave is derived. The energy flux of the soliton + ion-sound system is estimated.     

Further notes on the associated alpha-functions and related integrals in the theory of the light changes of eclipsing variables

With a view to furthering the theory of the light changes of eclipsing variables, developed before systematically by Z. Kopal, this paper presents a number of new (and computable) expressions for the associated alpha-function _n ⁰ ,(r₁,r₂,) (and also for its partial derivatives), where _n ⁰ ,(r₁,r₂,) represents the fractional loss of light suffered by an eclipse of a circular disc of fractional radiusr ₁ (and darkened at the limb to thenth degree) by an opaque disc of radiusr ₂, with their centres separated by a fractional (projected) distance , provided that the transparency of the occulting disc increases with the angle of foreshortening in the same manner as the limb-darkening of the eclipsed star (that is, when the transparency functiong(, ) of the second aperture is given by Equation (4) below). Many of the explicit expressions derived here are valid for any type of eclipse, occultation or transit, regardless of whetherr ₁>r ₂ orr ₁<r ₂. and for any degreen of the adopted law of limb-darkening. It is also pointed out how some of the results obtained in this paper are related to the various representations given earlier in the literature for the case =0.     

On some approximations in Brown's lunar theory

A re-evaluation of Brown's Lunar Theory has long been awaited. While working on this problem a number of questions about the adequacy of Brown's approach have arisen, and some of these questions including that of the need for a literal solution of the main problem are discussed in this paper.     

The zeros of some transcendental functions of transport theory

The location of zeros of certain transcendental functions, which we usually come across in transport problems, is discussed.     

On the A-transform of the exponential integrals

In this paper, a technique of recursive analysis is developed for the integral transform A of the exponential integral functionsE _n which is denoted as _n (). The main result of this analysis enables us to establish a two-term recurrence formula for _n (0) and a three-term recurrence formula for _n (); 0. A computational algorithm based on these formulae is also constructed and its numerical results forn=2(1)25 are presented to 15-digit accuracy.     

On the theory of astronomical masers – II. Polarization of maser radiation

In this paper, we investigate the polarization property of the radiation amplified by astronomical masers in the presence of a strong magnetic field. Our model explicitly takes into account the broad-band nature of the radiation field and the interaction of the radiation with the maser transition   J = 1–0  . The amplification of different realizations of the background continuum radiation by the maser is directly simulated and the Stokes parameters of the radiation field are then obtained by averaging over the ensemble of emerging maser radiation. For isotropic pumping and partially saturated masers, we find that the maser radiation is linearly polarized in two representative cases where the magnetic field   B   makes an angle  θ= 30°  and  90°  to the maser axis. The linear polarization for maser radiation obtained in our simulations for both cases is in agreement with the results of the standard model. Furthermore, no instability during amplification is seen in our simulations. Therefore, we conclude that there is no problem with the previous numerical investigations of maser polarization in the unsaturated and partially saturated regime.     

Orbit determination with the two-body integrals

We investigate a method to compute a finite set of preliminary orbits for solar system bodies using the first integrals of the Kepler problem. This method is thought for the applications to the modern sets of astrometric observations, where often the information contained in the observations allows only to compute, by interpolation, two angular positions of the observed body and their time derivatives at a given epoch; we call this set of data attributable. Given two attributables of the same body at two different epochs we can use the energy and angular momentum integrals of the two-body problem to write a system of polynomial equations for the topocentric distance and the radial velocity at the two epochs. We define two different algorithms for the computation of the solutions, based on different ways to perform elimination of variables and obtain a univariate polynomial. Moreover we use the redundancy of the data to test the hypothesis that two attributables belong to the same body (linkage problem). It is also possible to compute a covariance matrix, describing the uncertainty of the preliminary orbits which results from the observation error statistics. The performance of this method has been investigated by using a large set of simulated observations of the Pan-STARRS project.