A new well behaved exact solution in general relativity for perfect fluid

We present a new spherically symmetric solution of the general relativistic field equations in isotropic coordinates. The solution is having positive finite central pressure and positive finite central density. The ratio of pressure and density is less than one and casualty condition is obeyed at the centre. Further, the outmarch of pressure, density and pressure-density ratio, and the ratio of sound speed to light is monotonically decreasing. The solution is well behaved for all the values of u lying in the range 0<u≤.186. The central red shift and surface red shift are positive and monotonically decreasing. Further, we have constructed a neutron star model with all degree of suitability and by assuming the surface density ρ _b =2×10¹⁴ g/cm³. The maximum mass of the Neutron star comes out to be M=1.591 M _Θ with radius R _b ≈12.685 km. The most striking feature of the solution is that the solution not only well behaved but also having one of the simplest expressions so far known well behaved solutions. Moreover, the good matching of our results for Vela pulsars show the robustness of our model.     

On the most general accurate solutions for Buchdahl's fluid spheres

The most general accurate solutions for the Buchdhal fluid sphere were obtained and matched with the Schwarzchild's exterior solution at the pressure free interface. Various parameters of the solutions were so adjusted that the energy density, pressure and temperature were positive and decreasing away from the centre, and the velocity of sound was less than unity throughout the spheroid model. Using this procedure, the maximum mass of the fluid sphere with a surface density of2 × 10¹⁴gm cm^-3 was determined to be 3.82MΘ and 4.57 MΘ for strong and weak energy conditions respectively. PACS number: 0402, 0402J, 0440D, 95301 This revised version was published online in July 2006 with corrections to the Cover Date.     

A class of well-behaved generalized charged analogues of Vaidya-Tikekar type fluid sphere in general relativity

In this paper first ever we have developed a class of well behaved charged fluid spheres expressed by a space time with its hypersurfaces $t = \operatorname {const}$ . as spheroid for the case 0<K<1 with surface density 2×10¹⁴ gm/cm³. The same utilized to construct a superdense star and seen that star satisfies all well behaved condition for 0<K≤0.038. The maximum mass occupied and the corresponding radius are found to be 4.830982M _Θ and 20.7612 km respectively. The redshift at the center and on the surface is given z ₀=0.425367 and z _a =0.240901.     

On the construction of a comprehensive general catalogue of star positions

The procedures that would lead to the construction of a comprehensive general catalogue of star positions are outlined and discussed. Attention is drawn to the problems faced by a definitive reduction of the Astrographic Catalogue. The importance and necessity of the repetition of the original work in this connection are stressed. This would provide at present—barring the development of revolutionary new and fast techniques—the only chance for the very desirable wholesale computation of the proper motions of all stars down to about 13 ^m .Presented at the Symposium Star Catalogues, Positional Astronomy and Celestial Mechanics, held in honor of Paul Herget at the U.S. Naval Observatory, Washington, November 30, 1978.     

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.     

The exact solution of Einstein's disc

In this Letter, Einstein's equations of gravitational field have been used to calculate the metric of Einstein's disc. The known result has been obtained, but its physical significance is made very clear.     

Report on the physical characteristics of Vaidya-Tikekar's exact relativistic model for a superdense star

We report here the results of our examination of the physical properties of Vaidya-Tikekar's model for a relativistic star. Full details will be published elsewhere. The analysis yields a strong indication that the model is stable with respect to infinitesimal radial oscillations. We find that the adiabatic speed of sound is smaller than the speed of light everywhere inside the fluid sphere if the radius of the sphere is larger than 1.46 times its Schwarzschild radius. We also find that the fluid must necessarily be supraluminal somewhere if the speed of sound is decreasing outwards close to the center. We further find that the strong energy condition is fulfilled everywhere if it is fulfilled at the center. Since the ratio of the pressure p and the density ⋅ is decreasing outwards, this indicates that the temperature gradient is negative. We also find that the relativistic adiabatic index is larger than two. Demanding the fluid to be causal, and taking the pressure and the density to be somewhere given by 7.4 ⋅ 10³³ dynes/cm³ and 5.1 ⋅ 10¹⁴ g/cm³, we calculate the maximum mass of the fluid sphere to be 3 solar masses.     

A 'super' star cluster grown old: the most massive star cluster in the Local Group

We independently redetermine the reddening and age of the globular cluster (GC) 037−B327 in M31 by comparing independently obtained multicolour photometry with theoretical stellar population synthesis models. 037−B327 has long been known to have a very large reddening value, which we confirm to be   E ( B − V ) = 1.360 ± 0.013  , in good agreement with the previous results. We redetermine its most likely age at  12.4 ± 3.2 Gyr  .
037−B327 is a prime example of an unusually bright early counterpart to the ubiquitous 'super' star clusters presently observed in most high-intensity star-forming regions in the local Universe. In order to have survived for a Hubble time, we conclude that its stellar initial mass function (IMF) cannot have been top-heavy. Using this constraint, and a variety of simple stellar population (SSP) models, we determine a photometric mass of     , somewhat depending on the SSP models used, the metallicity and age adopted and the IMF representation. This mass, and its relatively small uncertainties, makes this object the most massive star cluster of any age in the Local Group. Assuming that the photometric mass estimate thus derived is fairly close to its dynamical mass, we predict that this GC has a (one-dimensional) velocity dispersion of the order of  (72 ± 13) km s⁻¹  . As a surviving 'super' star cluster, this object is of prime importance for theories aimed at describing massive star cluster evolution.     

An exact analytic solution for axially-symmetric explosion in a spheroid

The BK Theory as modified by Sachdev and Kogure and Osaki, is applied to a point explosion in a spheroid with exponentially decreasing density distribution. Similar results to those of Sakashita are obtained but without the assumption of the mass concentration at the shock surface.     

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.     

Spectroscopic solution of the star QX Cas

High-resolution spectroscopic observations around the Hα line of the binary star QX Cas covering the whole orbital period are presented. Our radial velocity solution, the first ever determined, requires an eccentric orbit with the following orbital parameters: eccentricity,   e = 0.22 ± 0.01  ; longitude of periastron,  ω= 45°± 5°  ; semi-amplitudes of the radial velocity curves of the primary and secondary stars,   K ₁ sin  i = 125.8 ± 0.9 km s⁻¹  and   K ₂ sin  i = 144.8 ± 1.1 km s⁻¹  ; gamma velocity,   V ₀= 65.1 ± 0.5 km s⁻¹  ; and mass ratio,   q = 0.869 ± 0.013  . The corresponding lower limits of the masses of the components and their separation are         , and   a sin  i = 31.34 ± 0.48 R_⊙  .     

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.     

An exact analytical solution in radiation gas dynamics

The Brinkley-Kirkwood theory, as modified by Bhatnagar and Kushwaha for the inclusion of radiation pressure, is applied to obtain an exact analytical solution for radiation pressure, shock velocity, etc., when a strong explosion takes place in a cold undisturbed gas obeying an exponential density distribution. Cases involving spherical symmetry, axial symmetry or spheroidal symmetry are also considered.     

Some physical properties and stability of an exact model of a relativistic star

An exact solution of Einstein's field equations for an isentropic fluid sphere is examined. It turns out that the crucial factor for the physical properties and the stability of this model is the degree of incompressibility. Necessary and sufficient conditions are given for the weak and the strong energy conditions to be fulfilled and for the speed of sound to be less than the speed of light. The speed of sound always has a minimum at the center of the fluid sphere. But two possibilities exist: either the speed of sound is increasing all the way outwards to the surface of the sphere, or the speed of sound is first increasing, then reaching a maximum when still inside the fluid sphere, and thereafter decreasing outwards to the surface. The adiabatic index is investigated and is found to be increasing outwards for the actual degrees of compressibility. This adiabatic index is always greater than unity, and the temperature is thus decreasing throughout the sphere. The necessary and sufficient condition for the adiabatic index to be greater than 4/3 is also given. (This is a necessary condition for the fluid sphere to be stable.) Chandrasekhar's pulsation equation with boundary conditions is investigated, and the fluid sphere is found to bestable if and only if the degree of incompressibility is greater than a certain value.Dedicated to the memory of the late Bronislaw Kuchowicz.     

A new method for exact solution of transfer equations in finite media

In this paper we develop a new exact method combined with finite Laplace transform and theory of linear singular operators to obtain a solution of transport equation in finite plane-parallel steady-state scattering atmosphere both for angular distribution of radiation from the bounding faces of the atmosphere and for intensity of radiation at any depth of the atmosphere. The emergent intensity of radiation from the bounding faces are determined from simultaneous linear integral equations of the emergent intensity of radiation in terms ofX andY equations of Chandrasekhar. The intensity of radiation at any optical depth for a positive and negative direction parameter is derived by inversion of the Laplace transform in terms of intergrals of the emergent intensity of radiation. A new expression of theX andY equation is also derived for easy numerical computation. This is a new and exact method applicable to all problems in finite plane parallel steady scattering atmosphere.     

An exact solution to determination of an open orbit

We present an exact solution of the equations for orbit determination of a two body system in a hyperbolic or parabolic motion. In solving this problem, we extend the method employed by Asada, Akasaka and Kasai (AAK) for a binary system in an elliptic orbit. The solutions applicable to each of elliptic, hyperbolic and parabolic orbits are obtained by the new approach, and they are all expressed in an explicit form, remarkably, only in terms of elementary functions. We show also that the solutions for an open orbit are recovered by making a suitable transformation of the AAK solution for an elliptic case.     

The photometric solution of W UMa-type star BW draconis

The photometric solutions of W UMa-type binary BW Dra have been determined by applying the Wilson and Devinney Code toUBV observations of Rucinski and Kaluzny.It is shown that BW Dra is corresponding to a system with an overcontact configuration and smaller mass ratioq=0.392 andUBV light curves give the converging solutions with non-zero third light.It is proved that the components of BW Dra are older stars (the spectral types are G0 and G3, respectively). They could come into contact later stage of evolution. The photometric solution is similar to the results of Kaluzny and Rucinski. According to the photometric solution and spectroscopic results of Batten and Lu, the absolute parameters are presented too.