Jacobi-like bar mode instability of relativistic rotating bodies

We perform some numerical study of the secular triaxial instability of rigidly rotating homogeneous fluid bodies in general relativity. In the Newtonian limit, this instability arises at the bifurcation point between the Maclaurin and Jacobi sequences. It can be driven in astrophysical systems by viscous dissipation. We locate the onset of instability along several constant baryon mass sequences of uniformly rotating axisymmetric bodies for compaction parameter $M/R = 0-0.275$. We find that general relativity weakens the Jacobi like bar mode instability, but the stabilizing effect is not very strong. According to our analysis the critical value of the ratio of the kinetic energy to the absolute value of the gravitational potential energy $(T/|W|)_{\rm crit}$ for compaction parameter as high as 0.275 is only 30% higher than the Newtonian value. The critical value of the eccentricity depends very weakly on the degree of relativity and for $M/R=0.275$ is only 2% larger than the Newtonian value at the onset for the secular bar mode instability. We compare our numerical results with recent analytical investigations based on the post-Newtonian expansion.Comment: 15 pages, 8 figures, submitted to Phys. Rev.

Dynamical stability of strange quark stars

We show that the mass-radius $(M-R)$ relation corresponding to the MIT bag models of strange quark matter (SQM) and the models obtained by Day et al (1998) do not provide the necessary and sufficient condition for dynamical stability for the equilibrium configurations, since such configurations can not even fulfill the necessary condition of hydrostatic equilibrium provided by the exterior Schwarzschild solution. These findings will remain unaltered and can be extended to any other sequence of pure SQM. This study explicitly show that although the strange quark matter might exist in the state of zero pressure and temperature, but the models of pure strange quark `stars' can not exist in the state of hydrostatic equilibrium on the basis of General Relativity Theory. This study can affect the results which are claiming that various objects like - RX J1856.5-3754, SAX J1808.4-3658, 4U 1728-34, PSR 0943+10 etc. might be strange stars.Comment: 7 pages (including 6 tables and 1 figure) in MNRAS styl

Last orbits of binary strange quark stars

We present the first relativistic calculations of the final phase of inspiral of a binary system consisting of two stars built predominantely of strange quark matter (strange quark stars). We study the precoalescing stage within the Isenberg-Wilson-Mathews approximation of general relativity using a multidomain spectral method. A hydrodynamical treatment is performed under the assumption that the flow is either rigidly rotating or irrotational, taking into account the finite density at the stellar surface -- a distinctive feature with respect to the neutron star case. The gravitational-radiation driven evolution of the binary system is approximated by a sequence of quasi-equilibrium configurations at fixed baryon number and decreasing separation. We find that the innermost stable circular orbit (ISCO) is given by an orbital instability both for synchronized and irrotational systems. This constrasts with neutron stars for which the ISCO is given by the mass-shedding limit in the irrotational case. The gravitational wave frequency at the ISCO, which marks the end of the inspiral phase, is found to be 1400 Hz for two irrotational 1.35 Msol strange stars and for the MIT bag model of strange matter with massless quarks and a bag constant B=60 MeV/fm^3. Detailed comparisons with binary neutrons star models, as well as with third order Post-Newtonian point-mass binaries are given.Comment: 11 pages, 10 figures, improved conclusion and figures, references added, accepted for publication in Phys. Rev.

Stability of strange stars (SS) derived from a realistic equation of state

A realistic equation of state (EOS) leads to realistic strange stars (ReSS) which are compact in the mass radius plot, close to the Schwarzchild limiting line (Dey et al 1998). Many of the observed stars fit in with this kind of compactness, irrespective of whether they are X-ray pulsars, bursters or soft $\gamma$ repeaters or even radio pulsars. We point out that a change in the radius of a star can be small or large, when its mass is increasing and this depends on the position of a particular star on the mass radius curve. We carry out a stability analysis against radial oscillations and compare with the EOS of other strange star (SS) models. We find that the ReSS is stable and an M-R region can be identified to that effect.Comment: 16 pages including 5 figures. Accepted for publication in MPL

Are rotating strange quark stars good sources of gravitational waves?

We study the viscosity driven (Jacobi-like) bar mode instability of rapidly rotating strange stars in general relativity. A triaxial, "bar shaped" compact star could be an efficient source of continuous wave gravitational radiation in the frequency range of the forthcoming interferometric detectors. We locate the secular instability point along several constant baryon mass sequences of uniformly rotating strange stars described by the MIT bag model. Contrary to neutron stars, strange stars with T/|W| (the ratio of the rotational kinetic energy to the absolute value of the gravitational potential energy) much lower than the corresponding value for the mass-shed limit can be secularly unstable to bar mode formation if shear viscosity is high enough to damp out any deviation from uniform rotation. The instability develops for a broad range of gravitational masses and rotational frequencies of strange quark stars. It imposes strong constraints on the lower limit of the frequency at the innermost stable circular orbit around rapidly rotating strange stars. The above results are robust for all linear self-bound equations of state assuming the growth time of the instability is faster than the damping timescale. We discuss astrophysical scenarios where triaxial instabilities (r-mode and viscosity driven instability) could be relevant in strange stars described by the standard MIT bag model of normal quark matter. Taking into account actual values of viscosities in strange quark matter and neglecting the magnetic field we show that Jacobi-like instability cannot develop in any astrophysicaly interesting temperature windows. The main result is that strange quark stars described by the MIT bag model can be accelerated to very high frequency in Low Mass X-ray binaries if the strange quark mass is ~ 200 MeV or higher.Comment: 15 pages, 10 figures, to appear in Astronomy and Astrophysic

Maximum mass of a cold compact star

We calculate the maximum mass of the class of compact stars described by Vaidya-Tikekar \cite{VT01} model. The model permits a simple method of systematically fixing bounds on the maximum possible mass of cold compact stars with a given value of radius or central density or surface density. The relevant equations of state are also determined. Although simple, the model is capable of describing the general features of the recently observed very compact stars. For the calculation, no prior knowledge of the equation of state (EOS) is required. This is in contrast to the earlier calculations for maximum mass which were done by choosing first the relevant EOSs and using those to solve the TOV equation with appropriate boundary conditions. The bounds obtained by us are comparable and, in some cases, more restrictive than the earlier results.Comment: 18 pages including 4 *.eps figures. Submitted for publicatio

The eccentricity distribution of compact binaries

The current gravitational wave detectors have reached their operational sensitivity and are nearing detection of compact object binaries. In the coming years, we expect that the Advanced LIGO/VIRGO will start taking data. At the same time, there are plans for third generation ground-based detectors such as the Einstein Telescope, and space detectors such as DECIGO. We discuss the eccentricity distribution of inspiral compact object binaries during they inspiral phase. We analyze the expected distributions of eccentricities at three frequencies that are characteristic of three future detectors: Advanced LIGO/VIRGO (30 Hz), Einstein Telescope (3 Hz), and DECIGO (0.3 Hz). We use the StarTrack binary population code to investigate the properties of the population of compact binaries in formation. We evolve their orbits until the point that they enter a given detector sensitivity window and analyze the eccentricity distribution at that time. We find that the eccentricities of BH-BH and BH-NS binaries are quite small when entering the Advanced LIGO/VIRGO detector window for all considered models of binary evolution. Even in the case of the DECIGO detector, the typical eccentricities of BH-BH binaries are below 10^{-4}, and the BH-NS eccentricities are smaller than 10^{-3}. Some fraction of NS-NS binaries may have significant eccentricities. Within the range of considered models, we found that a fraction of between 0.2% and 2% NS-NS binaries will have an eccentricity above 0.01 for the Advanced LIGO/VIRGO detectors. For the ET detector, this fraction is between 0.4% and 4%, and for the DECIGO detector it lies between 2% and 27%.Comment: 8 pages, 5 figures, accepted by A&

Population synthesis of double neutron stars

Using the StarTrack binary population synthesis code we model the population of double neutron stars in the Galaxy. We include a detailed treatment of the spin evolution of each pulsar due to processes such as spin-down and spin-up during accretion events as well as magnetic field decay. We also model the spatial distribution of double neutron stars by including their natal kicks and subsequent propagation in the Galactic gravitational potential. This synthetic pulsar population is compared to the observed sample of double neutron stars taking into account the selection effects of detection in the radio band, to determine the most likely evolutionary parameters. With these parameters we determine the properties of the double neutron star binaries detectable in gravitational waves by the high frequency interferometers LIGO and VIRGO. In particular, we discuss the distributions of chirp masses and mass ratios in samples selected by their radio or gravitational wave emission.Comment: 21 pages, 6 figures, accepted for publication in MNRA

A class of relativistic stars with a linear equation of state

By assuming a particular mass function we find new exact solutions to the Einstein field equations with an anisotropic matter distribution. The solutions are shown to be relevant for the description of compact stars. A distinguishing feature of this class of solutions is that they admit a linear equation of state which can be applied to strange stars with quark matter.Comment: 5 pages, 3 figures, to appear in Mon. Not. R. Astron. So

Lower limits on the maximum orbital frequency around rotating strange stars

Observations of kHz quasi-periodic oscillations (QPOs) in the X-ray fluxes of low-mass X-ray binaries (LMXBs) have been used in attempts to constrain the external metric of the compact members of these binaries, as well as their masses and the equation of state of matter at supranuclear denisties. We compute the maximum orbital frequency of stable circular motion around uniformly rotating strange stars described by the MIT bag model. The calculations are performed for both normal and supramassive constant baryon mass sequences of strange stars rotating at all possible rates. We find the lower limits on the maximum orbital frequency and discuss them for a range of masses and for all rotational frequencies allowed in the model considered. We show that for slowly and moderately rotating strange stars the maximum value of orbital frequency can be a good indicator of the mass of the compact object. However, for rapidly rotating strange stars the same value of orbital frequency in the innermost stable circular orbit is obtained for stars with masses ranging from that of a planetoid to about three solar masses. At sufficiently high rotation rates of the strange star, the rotational period alone constrains the stellar mass to a surprisingly narrow range.Comment: 9 pages, 5 figures, accepted by A&