Some new exact solutions with finite central parameters and?uniform radial motion of sound

We present three new categories of exact and spherically symmetric Solutions with finite central parameters of the general relativistic field equations. Two well behaved solutions in curvature coordinates first category are being studied extensively. These solutions describe perfect fluid balls with positively finite central pressure, positively finite central density; their ratio is less than one and causality condition is obeyed at the centre. The outmarch of pressure, density, pressure-density ratio and the adiabatic speed of sound is monotonically decreasing for these solutions. Keeping in view of well behaved nature of these solutions, one of the solution (I₁) is studied extensively. The solution (I₁) gives us wide range of Schwarzschild parameter u (0.138≤u≤0.263), for which the solution is well behaved hence, suitable for modeling of Neutron star. For this solution the mass of Neutron star is maximized with all degree of suitability and by assuming the surface density ρ _b =2×10¹⁴ g/cm³. Corresponding to u=0.263, the maximum mass of Neutron star comes out to be 3.369 M _Θ with linear dimension 37.77 km and central and surface redshifts are 4.858 and 0.4524 respectively. We also study some well known regular solutions (T-4, D-1, D-2, H, A, P) of Einstein’s field equations in curvature coordinates with the feature of constant adiabatic sound speed. We have chosen those values of Schwarzschild parameter u for which, these solutions describe perfect fluid balls realistic equations of state. However, except (P) solution, all these solutions have monotonically non-decreasing feature of adiabatic sound speed. Hence (P) solution is having a well behaved model for uniform radial motion of sound. Keeping in view of well behaved nature of the solution for this feature and assuming the surface density; ρ _b =2×10¹⁴ g/cm³, the maximum mass of Neutron star comes out to be 1.34 M _Θ with linear dimension 28.74 km. Corresponding central and surface redshifts are 1.002 and 0.1752 respectively.     

Well behaved parametric class of relativistic charged fluid ball in?general relativity

The paper presents a class of interior solutions of Einstein–Maxwell field equations of general relativity for a static, spherically symmetric distribution of the charged fluid. This class of solutions describes well behaved charged fluid balls. The class of solutions gives us wide range of parameter K (0≤K≤42) for which the solution is well behaved hence, suitable for modeling of super dense star. For this solution the mass of a star is maximized with all degree of suitability and by assuming the surface density ρ _b =2×10¹⁴ g/cm³. Corresponding to K=2 and X=0.30, the maximum mass of the star comes out to be 4.96 M _Θ with linear dimension 34.16 km and central redshift and surface redshift 2.1033 and 0.683 respectively. In absence of the charge we are left behind with the well behaved fourth model of Durgapal (J. Phys., A, Math. Gen. 15:2637, 1982).     

Variety of Well behaved parametric classes of relativistic charged fluid spheres in general relativity

The paper presents a variety of classes of interior solutions of Einstein–Maxwell field equations of general relativity for a static, spherically symmetric distribution of the charged fluid with well behaved nature. These classes of solutions describe perfect fluid balls with positively finite central pressure, positively finite central density; their ratio is less than one and causality condition is obeyed at the center. The outmarch of pressure, density, pressure–density ratio and the adiabatic speed of sound is monotonically decreasing for these solutions. Keeping in view of well behaved nature of these solutions, two new classes of solutions are being studied extensively. Moreover, these classes of solutions give us wide range of constant K for which the solutions are well behaved hence, suitable for modeling of super dense star. For solution (I₁) the mass of a star is maximized with all degree of suitability and by assuming the surface density ρ _b =2×10¹⁴ g/cm³ corresponding to K=1.19 and X=0.20, the maximum mass of the star comes out to be 2.5M _Θ with linear dimension 25.29 Km and central redshift 0.2802. It has been observed that with the increase of charge parameter K, the mass of the star also increases. For n=4,5,6,7, the charged solutions are well behaved with their neutral counterparts however, for n=1,2,3, the charged solution are well behaved but their neutral counterparts are not well behaved.     

Variety of well behaved exact solutions of Einstein–Maxwell field equations: an application to Strange Quark stars, Neutron stars and Pulsars

We present a variety of well behaved classes of Charge Analogues of Tolman’s iv (1939). These solutions describe charged fluid balls with positively finite central pressure, positively finite central density; their ratio is less than one and causality condition is obeyed at the centre. The outmarch of pressure, density, pressure-density ratio and the adiabatic speed of sound is monotonically decreasing, however, the electric intensity is monotonically increasing in nature. These solutions give us wide range of parameter for every positive value of n for which the solution is well behaved hence, suitable for modeling of super dense stars. keeping in view of well behaved nature of these solutions, one new class of solutions is being studied extensively. Moreover, this class of solutions gives us wide range of constant K (0.3≤K≤0.91) for which the solution is well behaved hence, suitable for modeling of super dense stars like Strange Quark stars, Neutron stars and Pulsars. For this class of solutions the mass of a star is maximized with all degree of suitability, compatible with Quark stars, Neutron stars and Pulsars. By assuming the surface density ρ _b =2×10¹⁴ g/cm³ (like, Brecher and Caporaso in Nature 259:377, 1976), corresponding to K=0.30 with X=0.39, the resulting well behaved model has the mass M=2.12M _Θ, radius r _b ≈15.27 km and moment of inertia I=4.482×10⁴⁵ g cm²; for K=0.4 with X=0.31, the resulting well behaved model has the mass M=1.80M _Θ, radius r _b ≈14.65 km and moment of inertia I=3.454×10⁴⁵ g cm²; and corresponding to K=0.91 with X=0.135, the resulting well behaved model has the mass M=0.83M _Θ, radius r _b ≈11.84 km and moment of inertia I=0.991×10⁴⁵ g cm². For n=0 we rediscovered Pant et al. (in Astrophys. Space Sci. 333:161, 2011b) well behaved solution. These values of masses and moment of inertia are found to be consistent with other models of Neutron stars and Pulsars available in the literature and are applicable for the Crab and the Vela Pulsars.     

New class of Well behaved exact solutions of relativistic charged <Emphasis Type="Italic">white-dwarf</Emphasis> star with perfect fluid

The paper presents a class of interior solutions of Einstein-Maxwell field equations of general relativity for a static, spherically symmetric distribution of the charged fluid. This class of solutions describes well behaved charged fluid balls. The class of solutions gives us wide range of parameter K (0.3277≤K≤0.49), for which the solution is well behaved hence, suitable for modeling of super dense star. For this solution the mass of a star is maximized with all degree of suitability and by assuming the surface density ρ _b =2×10¹⁴ g/cm³. Corresponding to K=0.3277 with X=−0.15, the maximum mass of the star comes out to be M=0.92M _Θ with radius r _b ≈17.15 km and the surface red shift Z _b ≈0.087187. It has been observed that under well behaved conditions this class of solutions gives us the mass of super dense object within the range of white-dwarf.     

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.     

The evolution of BD+60°2522: with mass loss and overshooting

The ionizing star BD+60°2522 is known as the central star of Bubble Nebulae NGC 7635—wind-blown bubble created by the interaction of the stellar wind of BD+60°2522 (O6.5 IIIef, V=8.7 mag, mass loss rate 10^−5.76 M _⊙/year) with the ambient interstellar medium. From the evolutionary calculations for the star with mass loss and overshooting, we find that the initial mass of the star is 60M _⊙, its present age is 2.5×10⁶ years, and the present mass is 45M _⊙.     

Well behaved class of charge analogue of Heintzmann’s relativistic exact solution

We present a well behaved class of Charge Analogue of Heintzmann (Z. Phys. 228:489, 1969) solution. This solution describes charge fluid balls with positively finite central pressure and positively finite central density ; their ratio is less than one and causality condition is obeyed at the centre. The outmarch of pressure, density, pressure-density ratio and the adiabatic speed of sound is monotonically decreasing, however, the electric intensity is monotonically increasing in nature. The solution gives us wide range of constant K (1.25≤K≤15) for which the solution is well behaved and therefore, suitable for modeling of super dense star. For this solution the mass of a star is maximized with all degrees of suitability and by assuming the surface density ρ _b =2×10¹⁴ g/cm³. Corresponding to K=1.25 and X=0.42, the maximum mass of the star comes out to be 3.64M _Θ with linear dimension 24.31 km and central redshift 1.5316.     

A class of well behaved charged analogues of Vaidya–Tikekar type super-dense star

In the present article a model of well behaved charged superdense star with surface density 2×10¹⁴ gm/cm³ is constructed by considering a static spherically symmetric metric with t=const hypersurfaces as hyperboloid. So far well behaved model described by such metric could not be obtained. Maximum mass of the star is found to be 0.343457M _⊙ and the corresponding radius is 9.57459 km. The red shift at the centre and on the surface are given as 0.068887 and 0.031726 respectively.     

A class of charged analogues of Durgapal and Fuloria superdense star

We obtain a new class of charged super-dense star models after prescribing particular forms of the metric potential g ₄₄ and electric intensity. The metric describing the superdense stars joins smoothly with the Reissner-Nordstrom metric at the pressure free boundary. The interior of the stars possess there energy density, pressure, pressure-density ratio and velocity of sound to be monotonically decreasing towards the pressure free interface. In view of the surface density 2×10¹⁴ g/cm³, the heaviest star occupies a mass 5.6996 M _⊙ with its radius 17.0960 km. The red shift at the centre and boundary are found to be 3.5120 and 1.1268 respectively. In absence of the charge we are left behind with the regular and well behaved fifth model of Durgapal (J. Phys. A 15:2637, 1982).     

A red giant with a strange star as its core. Principal similarities to and differences from Thorne-Zytkow objects

A model red giant with a mass of 5 M_⊙ a luminosity of 41,740 L_⊙, and a radius of 960 R_⊙ and with a strange quark star as its core is constructed, and it is compared with a Thorne-Zytkow object having similar integrated parameters. The difference in internal structure is manifested right at the dense core: matter above the core is held off only by γ rays from the strange star, and convection is maintained down to the strange star. The lifetime of a red giant containing a strange star turns out to be almost 500 times shorter than that of a Thorne-Zytkow object — on the order of 10⁵ years. Translated from Astrofizika, Vol. 41. No. 4, pp. 533–544, October–December, 1998.     

BVRI photometry and light curve analysis of VW CEP

Synthetic light curve solutions for the W UMa-system VW Cep have been determined by applying the most new version of Wilson (1998)approach to B-observations of 1996 and VRI-observations of 1999. From a consideration of the possible evolution of this system, it is found that the system is a partial eclipsing contact one, and its primary to be a nearly Main-Sequence F5 star of mass 0.85 M _⊙ and the secondary to be a dwarf of spectral type G0 of mass 0.34 M _⊙. This revised version was published online in July 2006 with corrections to the Cover Date.     

Absolute parameters of the close binary BW Boo with a superasynchronous A2m primary component

Based on two high-dispersion spectra of the close binary BW Boo, we have detected lines of the secondary component whose contribution to the combined spectrum does not exceed 2%. We have determined the rotation velocities of the components and spectroscopic orbital elements. Numerous lines of neutral and ionized iron have been used to determine the effective temperature and surface gravity for the primary component. The photometric light curves for this binary have been solved for the first time. Its primary component is an A2Vm star with a mass of 2 ± 0.1M _⊙ and a radius of 1.9 ± 0.4R _⊙. Its rotation velocity is 2 km s⁻¹, which is a factor of 18 lower than the pseudo-synchronous velocity for this component. The G6 secondary component, a T Tau star, has a rotation velocity of 17 km s⁻¹, amass of 1.1M _⊙, and a radius of 1 R _⊙. The age of the binary has been estimated to be 10⁷ yr.     

A model of the Algol type close binary TT hydrae

UBV photometric observations and elements of TT Hydrae obtained by Kulkarni and Abhyankar (1980) are combined with the radial velocity curve of Popper (1979, personal communication) to derive the absolute dimensions and. a model of this important Algol system. While the photometric ratios of radii inV andB are in agreement givingk = 0.3812 for a limb darkening coefficient ofx = 0.6, application of Irwin’s (1947) method givesx = 0.4 forU. The primary is found to be a main sequence Al V star of mass 2.61M _⊙ and radius 2.01 R_⊙, and the secondary is classified as a Kl III star of mass 0.70M _⊙ and radius 5.33R _⊙. The observed Fourier coefficients for the light outside the eclipse agree with those calculated from theory for the reflection and ellipticity effects. The system shows an ultraviolet excess of 0.5 to 0.6 magnitudes during primary eclipse, which is attributed to an asymmetric circumstellar distribution of matter around the primary. The evolutionary status of the secondary, which does not appear to fill its Roche lobe completely, is discussed.     

Aq Psc – Analysis of New Light Curves

New BV light curves of the A-type W UMa star AQ Psc (P = 0.476d) have been observed and are described. A few times of minimum light are obtained and the ephemeris is improved. The light curves are analyzed for the binary parameters with a light curve synthesis method. Combining the results with Lu and Rucinski’s spectroscopic mass ratio we determined the masses and radii of the components: M ₁ = 1.69M _⊙, M ₂ = 0.38M _⊙, R ₁ = 1.77R _⊙, and R ₂ = 0.89R _⊙.     

Astrometric masses of 21 asteroids, and an integrated asteroid ephemeris

We apply the technique of astrometric mass determination to measure the masses of 21 main-belt asteroids; the masses of 9 Metis (1.03 ± 0.24 × 10^-11 M_⊙), 17 Thetis (6.17 ± 0.64 × 10^-13 M_⊙), 19 Fortuna (5.41 ± 0.76 × 10^-12 M_⊙), and 189 Phthia (1.87 ± 0.64 × 10^-14 M_⊙) appear to be new. The resulting bulk porosities of 11 Parthenope (12±4%) and 16 Psyche (46±16%) are smaller than previously-reported values. Empirical expressions modeling bulk density as a function of mean radius are presented for the C and S taxonomic classes. To accurately model the forces on these asteroids during the mass determination process, we created an integrated ephemeris of the 300 large asteroids used in preparing the DE-405 planetary ephemeris; this new BC-405 integrated asteroid ephemeris also appears useful in other high-accuracy applications.     

The bolometric light curve of SN 1993J and the nature of its progenitor

We have constructed the bolometric light curve of SN 1993J based on UBVRI(JHK) photometric data obtained from various sources and assumingA _V = 0 and a distance modulus of 27.6. Effective temperatures and photosphere radius at various times have been obtained from detailed blackbody fits. The bolometric light curve shows two maxima. The short rise time to the second maximum, and the luminosities at the minimum and the second maximum are used to constrain the properties of the progenitor star. The total mass of the hydrogen envelope M_H, in the star is found to be ≲ 0.2 M_⊙ at the time of explosion, and the explosion ejected about 0.05 M_⊙ of Ni⁵⁶. Thin hydrogen envelope combined with a sufficient presupernova luminosity suggest that the exploding star was in a binary with a probable period range of 5yr ≤P _orb ≤ 11yr.     

Radial Velocity and Light Curves Analysis of the Contact Binary V1073 Cygni

In this study complete BV light curves of the W Ursae Majoris binary V1073 Cygni obtained in 2005 are presented. We have used the spectroscopic data of V1073 Cyg obtained by Ahn et al. (1992) for analysis. The analysis of radial velocity and light curves was made with Wilson} program (1998) and the geometric and physical elements} of the system were derived. By searching the simultaneous} solutions of the system, we have determined the masses and radii of the components: 1.64M_⊙, 2.275R_⊙ for the primary component and 0.55M_⊙, 1.397R_⊙ for the secondary component respectively. The effective temperature of 6494 ± 53 K for the secondary component was also estimated.     

Investigation of the new cataclysmic variable 1RXS J180834.7+101041

We present the results of our photometric and spectroscopic studies of the new eclipsing cataclysmic variable star 1RXS J180834.7+101041. Its spectrum exhibits double-peaked hydrogen and helium emission lines. The Doppler maps constructed from hydrogen lines show a nonuniform distribution of emission in the disk similar to that observed in IP Peg. This suggests that the object can be a cataclysmic variable with tidal density waves in the disk. We have determined the component masses (M _WD = 0.8 ± 0.22M _⊙ and M _RD = 0.14 ± 0.02M _⊙) and the binary inclination (i = 78° ± 1.5°) based on well-known relations between parameters for cataclysmic variable stars. We have modeled the binary light curves and showed that the model of a disk with two spots is capable of explaining the main observed features of the light curves.     

Gamma-Ray Bursts and magnetar-forming Supernovae

The connection between long Gamma Ray Bursts (GRBs) and Supernovae (SNe) have been established through the well observed cases. These events can be explained as the prompt collapse to a black hole (BH) of the core of a massive star (M≳40M _⊙). The energies of these GRB-SNe were much larger than those of typical SNe, thus these SNe are called Hypernovae (HNe). The case of SN 2006aj/GRB060218 appears different: the GRB was weak and soft, being called an X-Ray Flash (XRF); the SN is dimmer and has very weak oxygen lines. The explosion energy of SN 2006aj was smaller, as was the ejected mass. In our model, the progenitor star had a smaller mass than other GRB-SNe (M∼20M _⊙), suggesting that a neutron star (NS) rather than a BH was formed. If the nascent NS was strongly magnetized as a magnetar and rapidly spinning, it may launch a weak GRB or an XRF. The peculiar light curve of Type Ib SN 2005bf may also be powered by a magnetar. The blue-shifted nebular emission lines of 2005bf indicate the unipolar explosion possibly related to standing accretion shock instability (SASI) associated with a newly born NS.