kHz QPOs in LMXBs, relations between different frequencies and compactness of stars

We suggest that the mass of four compact stars SAX J1808.4-3658, KS 1731-260, SAX J1750.8-2900 and IGR J17191-2821 can be determined from the difference in the observed kiloHertz quasi periodic oscillations (kHz QPO-s) of these stars. The stellar radius is very close to the marginally stable orbit R_ms as predicted by Einstein’s general relativity. It may be noted that the first of these stars was suggested to be a strange star more than a decade back by Li et al. (1999a) from the unique millisecond X-ray pulsations with an accurate determination of its rotation period. It showed kHz QPO-s eight years back and so far it is the only set that has been observed. This is the first time we give an estimate of the mass of the star and of three other compact stars in low-mass X-ray binaries using their observed kHz QPO-s.     

Einstein–Maxwell Field Equation in Isotropic Coordinates: An Application to Modeling Superdense Star

We present a charged analogue of Pant et al. (2010, Astrophys. Space Sci., 330, 353) solution of the general relativistic field equations in isotropic coordinates by using simple form of electric intensity E that involve charge parameter K. Our solution is well behaved in all respects for all values of X lying in the range 0 <X≤ 0.11, K lying in the range 4 <K≤ 6.2 and Schwarzschild compactness parameter u lying in the range 0 <u≤ 0.247. Since our solution is well behaved for wide ranges of the parameters, we can model many different types of ultra-cold compact stars like quark stars and neutron stars. We have shown that corresponding to X = 0.077 and K = 6.13 for which u = 0.2051 and by assuming surface density ρ _b =4.6888×10¹⁴ g cm ^?3 the mass and radius are found to be 1.509M _⊙, 10.906 km respectively which match with the observed values of mass 1.51M _⊙ and radius 10.90 km of the quark star XTE J1739-217. The well behaved class of relativistic stellar models obtained in this work might have astrophysical significance in the study of more realistic internal structures of compact stars.     

Neutron stars in globular clusters: Formation and observational manifestations

Population synthesis is used to model the number of neutron stars in globular clusters that are observed as low-mass X-ray sources and millisecond radio pulsars. The dynamical interactions between binary and single stars in a cluster are assumed to take place only with a continuously replenished “background” of single stars whose properties keep track of the variations in parameters of the cluster as a whole and the evolution of single stars. We use the hypothesis that the neutron stars forming in binary systems from components with initial masses of ～8–12 M _⊙ during the collapse of degenerate O-Ne-Mg cores through electron captures do not acquire a high space velocity. The remaining neutron stars (from single stars with masses >8 M _⊙ or from binary components with masses >12 M _⊙) are assumed to be born with high space velocities. According to this hypothesis, a sizeable fraction of the forming neutron stars remain in globular clusters (about 1000 stars in a cluster with a mass of 5 × 10⁵ M _⊙). The number of millisecond radio pulsars forming in such a cluster in the case of accretion-driven spinup in binary systems is found to be ～10, in agreement with observations. Our modeling also reproduces the observed shape of the X-ray luminosity function for accreting neutron stars in binary systems with normal and degenerate components and the distribution of spin periods for millisecond pulsars.     

A well-behaved class of charged analogue of Durgapal solution

We present a well behaved class of charged analogue of M.C. Durgapal (J. Phys. A, Math. Gen. 15:2637, 1982) solution. This solution describes 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. This solution gives 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 this solution, one new class of solution is being studied extensively. Moreover, this class of solution gives us wide range of constant K (0≤K≤2.2) 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 solution 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 Capocaso, Nature 259:377, 1976), corresponding to K=0 with X=0..235, the resulting well behaved model has the mass M=4.03M _Θ , radius r _b =19.53 km and moment of inertia I=1.213×10⁴⁶ g?cm²; for K=1.5 with X=0.235, the resulting well behaved model has the mass M=4.43M _Θ , radius r _b =18.04 km and moment of inertia I=1.136×10⁴⁶ g?cm²; for K=2.2 with X=0.235, the resulting well behaved model has the mass M=4.56M _Θ , radius r _b =17.30 km and moment of inertia I=1.076×10⁴⁶ g?cm². These values of masses and moment of inertia are found to be consistent with the crab pulsars.     

Probability distribution of terrestrial planets in habitable zones around host stars

With more and more exoplanets being detected, it is paid closer attention to whether there are lives outside solar system. We try to obtain habitable zones and the probability distribution of terrestrial planets in habitable zones around host stars. Using Eggleton’s code, we calculate the evolution of stars with masses less than 4.00 M _⊙. We also use the fitting formulae of stellar luminosity and radius, the boundary flux of habitable zones, the distribution of semimajor axis and mass of planets and the initial mass function of stars. We obtain the luminosity and radius of stars with masses from 0.08 to 4.00 M _⊙, and calculate the habitable zones of host stars, affected by stellar effective temperature. We achieve the probability distribution of terrestrial planets in habitable zones around host stars. We also calculate that the number of terrestrial planets in habitable zones of host stars is 45.5 billion, and the number of terrestrial planets in habitable zones around K type stars is the most, in the Milky Way.     

Main stages of evolution of matter in the universe. II

A possible scenario for the evolution of the universe following the big bang at t > 10^-5 sec is considered. The necessary conditions that must be present for the formation of stars and stellar systems to be possible are formulated. As a condition for the formation of stars we take kT_s≤ GM_sm_p(3R), and for stellar systems HR ? (GM/R)^1/2, where T_s is the temperature of the cosmic plasma, m_p is the mass of a proton, M_s is the mass of a star, M is the mass of a stellar cluster, R is the radius of these celestial bodies, and H is the bubble parameter for the corresponding time. In accordance with these criteria, we assume that in the course of cosmological expansion, neutron stars should have been formed first (times 2.10^-4 ? t ? 1 sec, densities 0.07 ? ρ_B? 2.10⁴ g/cm³) and then, in chronological order, appeared white dwarfs (t ≈ 10² sec, ρ_B ? 5.10^-3 g/cm³), ordinary stars (t ≈ 4.10⁶ sec, ?_B ≈ 10^-11 g/cm³), galactic nuclei (t ≈ 3.10¹¹ sec, ?_B ≈ 5.10^-19 g/cm³, globular clusters (t ≈ 10¹³ sec, ?_B ≈ 4.10^-21 g/cm³), and galaxies (t ≈ 10¹⁵ sec, ?_B ≈ 10^-24 g/cm³), where ?_B is the average density of ordinary (baryon) matter in the universe. It is shown that a galactic nucleus is a stellar system in statistical equilibrium and consists mainly of neutron stars and white dwarfs. The formation of some pulsars (neutron stars with angular rotation rates 1 < Ω < 200 sec^-1) may occur in a galactic nucleus. Observed pulsars should therefore contain some fraction of neutron stars from the nucleus of the Galaxy that were able to escape it over the relaxation time (the tail of the Maxwell distribution, with star velocities v > v₀, where v₀ is the velocity corresponding to the work function 2GMM_s/R, M being the mass and R the radius of the Galaxy’s nucleus.     

How asteroseismology can constrain the global parameters of solar-like star models

In the previous years, p-mode oscillations (pressure oscillations stochastically excited by convection) have been detected in several solar-like stars thanks to the ground-based spectroscopic and space spectroscopic and photometric observations. We study the importance of seismic constraints on stellar modeling and the impact of their accuracy on reducing the uncertainties of global stellar parameters (i.e. mass, age, etc.). We use the Singular Value Decomposition (SVD) method to analyze the sensitivity of stellar models to seismic constraints. In this context, we construct a grid of evolutionary sequences for solar-like stars with varying age and mass. Around each model of this grid, we evaluate the partial derivatives with respect to a large set of free parameters: mass ?, age τ, mixing-length parameter α, initial helium abundance Y ₀, and initial metallicity Z/X ₀. Masses between 0.9 and 1.55 M _⊙ and central hydrogen abundances from Xc=0.7 to 0.05 have been considered in this study.     

A model of low-mass neutron stars with a quark core

We consider an equation of state that leads to a first-order phase transition from the nucleon state to the quark state with a transition parameter λ>3/2 (λ=ρ_Q/(ρ_N+P₀/c²)) in superdense nuclear matter. Our calculations of integrated parameters for superdense stars using this equation of state show that on the stable branch of the dependence of stellar mass on central pressure dM/dP_c>0) in the range of low masses, a new local maximum with M_max=0.082_⊙ and R=1251 km appears after the formation of a toothlike kink (M=0.08M_⊙, R=205 km) attributable to quark production. For such a star, the mass and radius of the quark core are M_core=0.005M_⊙ and R_core=1.73 km, respectively. In the model under consideration, mass accretion can result in two successive transitions to a quark-core neutron star with energy release similar to a supernova explosion: initially, a low-mass star with a quark core is formed; the subsequent accretion leads to configurations with a radius of ～1000 km; and, finally, the second catastrophic restructuring gives rise to a star with a radius of ～100 km.     

A class of exact isotropic solutions of Einstein’s equations and relativistic stellar models in general relativity

In this paper we have studied a particular class of exact solutions of Einstein’s gravitational field equations for spherically symmetric and static perfect fluid distribution in isotropic coordinates. The Schwarzschild compactness parameter, GM/c ² R, can attain the maximum value 0.1956 up to which the solution satisfies the elementary tests of physical relevance. The solution also found to have monotonic decreasing adiabatic sound speed from the centre to the boundary of the fluid sphere. A wide range of fluid spheres of different mass and radius for a given compactness is possible. The maximum mass of the fluid distribution is calculated by using stellar surface density as parameter. The values of different physical variables obtained for some potential strange star candidates like Her X-1, 4U 1538–52, LMC X-4, SAX J1808.4?3658 given by our analytical model demonstrate the astrophysical significance of our class of relativistic stellar models in the study of internal structure of compact star such as self-bound strange quark star.     

Dynamical study of wide pairs of stars based on data from the WDS catalog

Using the method of apparent motion parameters, we have studied the relative motion of the components in 561 pairs of wide (ρ > 2″) and relatively nearby (Hipparcos parallaxes > 0.01″) visual double stars based on data from the WDS catalog. The minimum masses of the double stars have been calculated at given parallaxes. We have identified 358 optical pairs. For 11 stellar pairs, we have found the minimum mass to exceed the estimate corresponding to their spectral types and luminosities. This excess is 5–7 M _⊙ for two stars, ADS 7446 and 9701.     

Some static relativistic compact charged fluid spheres in general relativity

In this work a new family of relativistic models of electrically charged compact star has been obtained by solving Einstein–Maxwell field equations with preferred form of one of the metric potentials and a suitable form of electric charge distribution function. The resulting equation of state (EOS) has been calculated. The relativistic stellar structure for matter distribution obtained in this work may reasonably models an electrically charged compact star whose energy density associated with the electric fields is on the same order of magnitude as the energy density of fluid matter itself (e.g. electrically charged bare strange stars). Based on the analytic model developed in the present work, the values of the relevant physical quantities have been calculated by assuming the estimated masses and radii of some well known strange star candidates like X-ray pulsar Her X-1, millisecond X-ray pulsar SAX J 1808.4-3658, and 4U 1820-30.     

Comparison of the four catalogues by pairs,the Hipparcos,new Hipparcos,EOC‐2 and IL,by using μδ for the common 1120 stars

We present comparison results of our Independent Latitude (IL) catalogue of μ_δ determinations for 1120 bright stars with the Hipparcos, new Hipparcos and Earth Orientation Catalogue (EOC‐2) values. Also, we took into consideration the EOC3 and EOC4 (recent versions of EOC catalogues). Our μ_δ values are based on zenith telescope observations from seven Independent Latitude (IL) observatories. The IL measures are spanning a time baseline of up to 90 years which is the key advantage to the accurate determination of μ_δ. The short interval of the Hipparcos satellite observations is a disadvantage for a good accuracy of stellar proper motion, especially in the case of double and multiple stars. For this reason many astrometric catalogues have appeared after the publication of the Hipparcos including our IL catalogue. These catalogues are an appropriate combination of the Hipparcos satellite and ground‐based data which yields more accurate stellar coordinates and/or their proper motions. Among various types of ground‐based observations the latitude and universal time variations obtained from several million observations of stars reduced to the Hipparcos reference system were used for this purpose. These observations were obtained during almost the entire last century and were originally used to determine the Earth Orientation Parameters. It is also possible to use these data in the inverse task of checking the accuracy of stellar coordinates and/or their proper motions listed in the Hipparcos Catalogue. Such latitude and universal time variations data are the basis of the EOC and IL catalogues. In this paper, we computed the differences in μ_δ values between pairs of catalogues and analyzed the results to characterize the μ_δ errors for the four catalogues with a special focus on our IL catalogue. The standard errors of μ_δ for IL stars observed over more than 20 years are mostly smaller than or equal to the Hipparcos errors, and close to the accuracy level of the EOC‐2 (EOC‐3, EOC‐4) and the new Hipparcos. The resulting investigations of errors of differences of μ_δ, show that all four catalogues have relatively small random and systematic errors which are close to each other meaning that the corresponding μ_δ values have a high accuracy. Our sample also contains detected double and multiple stars for which the effects of the orbital and proper motions are difficult to separate. The differences of μ_δ values for these stars generally exceed those obtained for single stars. Also, these discrepancies could be attributed to effect of possible, still unrecognized, astrometric binaries. These investigations about the proper motions and double stars are in line with the activity of the IAU Working Group on Astrometry by Small Ground‐Based Telescopes. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Black holes in cosmic bodies

Possible manifestations of small mass black holes (M _BH<M ) in cosmic bodies (stars, millisecond pulsars, planets, etc.) are considered. The formation of millisecond pulsars in the early proposed pulsar's model goes onto a small black hole in the centre due to accretion of neutron star matter. Within the framework of a model under consideration, the following is predicted: millisecond pulsars withP _min=0.5 ms, single optical and X-ray pulsars with the negative derivative derivative of period. Small black holes can be applied to make models of anomalies in planetary bodies (gravitational, heat, etc.). The vulcan model with radiation of a microblack hole in a magnetic void (M _BH10¹⁵ g) as the source of energy is considered. At the Earth's surface, near a vulcan, the neutrino flow from a microblack hole is estimated.     

Mass-loss predictions for Subdwarf B stars

We present the results of Monte Carlo mass-loss computations for hot low-mass stars, specifically for subdwarf B (sdB) stars. It is shown that the mass-loss rates on the Horizontal Branch (HB) computed from radiative line-driven wind models are not high enough to create sdB stars. We argue, however, that mass loss plays a role in the chemical abundance patterns observed both in field sdB stars, as well as in cluster HB stars. The derived mass loss recipe for these (extremely) hot HB stars may also be applied to other groups of hot low-mass stars, such as post-HB (AGB-manqué, UV-bright) stars, over a range in effective temperatures between ?10 000 and 50 000 K. Finally, we present preliminary spectral synthesis on the more luminous sdB stars for which emission cores in Hα have been detected (Heber, U., et al.: 2003, in:Stellar Atmosphere Modeling, ASP Conference Proceedings, p. 251). We find that these line profiles can indeed be interpreted as the presence of a stellar wind with mass loss on the order of 10^?11?M _⊙ yr ^?1.     

On mass determination fromT eff,g, andM bol

The mass deduced, using photometrically determinedg, gives a lower limit to the mass. Furthermore, mass determination in giant and supergiant stars may be effected byg andT _eff being determined for different values of the stellar radius.On leave from the Tata Institute of Fundamental Research, Bombay, India.     

Late stages of the evolution of close binaries

Close binaries can evolve through various ways of interaction into compact objects (white dwarfs, neutron stars, black holes). Massive binary systems (mass of the primaryM ₁ larger than 14 to 15M ₀) are expected to leave, after the first stage of mass transfer a compact component orbiting a massive star. These systems evolve during subsequent stages into massive X-ray binaries. Systems with initial large periode evolve into Be X-ray binaries.Low mass X-ray sources are probably descendants of lower mass stars, and various channels for their production are indicated. The evolution of massive close binaries is examined in detail and different X-ray stages are discussed. It is argued that a first X-ray stage is followed by a reverse extensive mass transfer, leading to systems like SS 433, Cir X1. During further evolution these systems would become Wolf-Rayet runaways. Due to spiral in these system would then further evolve into ultra short X-ray binaries like Cyg X-3.Finally the explosion of the secondary will in most cases disrupt the system. In an exceptional case the system remains bound, leading to binary pulsars like PSR 1913+16. In such systems the orbit will shrink due to gravitational radiation and finally the two neutron stars will coalesce. It is argued that the millisecond pulsar PSR 1937+214 could be formed in this way.A complete scheme starting from two massive ZAMS stars, ending with a millisecond pulsar is presented.Paper presented at the Lembang-Bamberg IAU Colloquium No. 80 on Double Stars: Physical Properties and Generic Relations, held at Bandung, Indonesia 3–7 June, 1983.     

Stochastic excitation of gravity modes in massive main-sequence stars

We investigate the possibility that gravity modes can be stochastically excited by turbulent convection in massive main-sequence (MS) stars. We build stellar models of MS stars with masses M=10?M _⊙,15?M _⊙, and 20?M _⊙. For each model, we then compute the power supplied to the modes by turbulent eddies in the convective core (CC) and the outer convective zones (OCZ). We found that, for asymptotic gravity modes, the major part of the driving occurs within the outer iron convective zone, while the excitation of low n order modes mainly occurs within the CC. We compute the mode lifetimes and deduce the expected mode amplitudes. We finally discuss the possibility of detecting such stochastically-excited gravity modes with the CoRoT space-based mission.     

On the nature of compact galactic nuclei

Spherically symmetric stellar clusters (compact galactic nuclei and globular clusters), far advanced toward the state of complete statistical equilibrium in the course of evolution, are investigated. The equation of state of such systems (a polytrope with an index k = 0.5) is derived and their main characteristics are calculated. It is shown that compact galactic nuclei must consist mainly of rapidly rotating neutron stars and white dwarfs. It is demonstrated that pulsars may be created by the evaporation of neutron stars from the nucleus of our Galaxy. The number of such pulsars is ~3.10⁶. Translated from Astrofizika, Vol. 41, No. 1, pp. 41–50, January-March, 1998.     

A family of exact solutions of Einstein-Maxwell field equations in isotropic coordinates: an application to optimization of quark star mass

In the present paper, we have obtained a class of charged super dense star models, starting with a static spherically symmetric metric in isotropic coordinates for perfect fluid by considering Hajj-Boutros (in J. Math. Phys. 27:1363, 1986) type metric potential and a specific choice of electrical intensity which involves a parameter K. The resulting solutions represent charged fluid spheres joining smoothly with the Reissner-Nordstrom metric at the pressure free interface. The solutions so obtained are utilized to construct the models for super-dense star like neutron stars (ρ _b =2 and 2.7×10¹⁴ g/cm³) and Quark stars (ρ _b =4.6888×10¹⁴ g/cm³). Our solution is well behaved for all values of n satisfying the inequalities \(4 < n \le4(4 + \sqrt{2} )\) and K satisfying the inequalities 0≤K≤0.24988, depending upon the value of n. Corresponding to n=4.001 and K=0.24988, we observe that the maximum mass of quark star M=2.335M _⊙ and radius R=10.04 km. Further, this maximum mass limit of quark star is in the order of maximum mass of stable Strange Quark Star established by Dong et al. (in arXiv:1207.0429v3, 2013). The robustness of our results is that the models are alike with the recent discoveries.