Formation scenarios and mass-radius relation for neutron stars

Neutron star crust, formed via accretion of matter from a companion in a low-mass X-ray binary (LMXB), has an equation of state (EOS) stiffer than that of catalyzed matter. At a given neutron star mass, M, the radius of a star with an accreted crust is therefore larger, by DR(M), than for usually considered star built of catalyzed matter. Using a compressible liquid drop model of nuclei, we calculate, within the one-component plasma approximation, the EOSs corresponding to different nuclear compositions of ashes of X-ray bursts in LMXB. These EOSs are then applied for studying the effect of different formation scenarios on the neutron-star mass-radius relation. Assuming the SLy EOS for neutron star's liquid core, derived by Douchin & Haensel (2001), we find that at M=1.4 M_sun the star with accreted crust has a radius more than 100 m larger that for the crust of catalyzed matter. Using smallness of the crust mass compared to M, we derive a formula that relates DR(M) to the difference in the crust EOS. This very precise formula gives also analytic dependence of DR on M and R of the reference star built of catalyzed matter. The formula is valid for any EOS of the liquid core. Rotation of neutron star makes DR(M) larger. We derive an approximate but very precise formula that gives difference in equatorial radii, DR_eq(M), as a function of stellar rotation frequency.Comment: 6 pages, 4 figures. Accepted for publication in Astronomy and Astrophysic

Maximum mass of neutron stars and strange neutron-star cores

Recent measurement of mass of PSR J1614-2230 rules out most of existing models of equation of state (EOS) of dense matter with high-density softening due to hyperonization, based on the recent hyperon-nucleon and hyperon-hyperon interactions, leading to a "hyperon puzzle". We study a specific solution of "hyperon puzzle", consisting in replacing a too soft hyperon core by a sufficiently stiff quark core. We construct an analytic approximation fitting very well modern EOSs of 2SC and CFL color superconducting phases of quark matter. This allows us for simulating continua of sequences of first-order phase transitions from hadronic matter to the 2SC, and then to the CFL state of color superconducting quark matter. We obtain constraints in the parameter space of the EOS of superconducting quark cores, resulting from M_max> 2 M_sol. We also derive constraints that would result from significantly higher measured masses. For 2.4 M_sol required stiffness of the CFL quark core should have been close to the causality limit, the density jump at the phase transition being very small. Condition M_max > 2 M_sol puts strong constraints on the EOSs of the 2SC and CFL phases of quark matter. Density jumps at the phase transitions have to be sufficiently small and sound speeds in quark matter - sufficiently large. A strict condition of thermodynamic stability of quark phase results in the maximum mass of hybrid stars similar to that of purely baryon stars. Therefore, to get M_max>2 M_sol for stable hybrid stars, both sufficiently strong additional hyperon repulsion at high density baryon matter and a sufficiently stiff EOS of quark matter would be needed. However, it is likely that the high density instability of quark matter (reconfinement) indicates actually the inadequacy of the point-particle model of baryons in dense matter at very high densities.Comment: 8 pages, 10 figures, submitted to A&

Spin-Down of Neutron Stars and Compositional Transitions in the Cold Crustal Matter

Transitions of nuclear compositions in the crust of a neutron star induced by stellar spin-down are evaluated at zero temperature. We construct a compressible liquid-drop model for the energy of nuclei immersed in a neutron gas, including pairing and shell correction terms, in reference to the known properties of the ground state of matter above neutron drip density, $4.3 \times 10^{11} g cm^{-3}$. Recent experimental values and extrapolations of nuclear masses are used for a description of matter at densities below neutron drip. Changes in the pressure of matter in the crust due to the stellar spin-down are calculated by taking into account the structure of the crust of a slowly and uniformly rotating relativistic neutron star. If the initial rotation period is $\sim$ ms, these changes cause nuclei, initially being in the ground-state matter above a mass density of about $3 \times 10^{13} g cm^{-3}$, to absorb neutrons in the equatorial region where the matter undergoes compression, and to emit them in the vicinity of the rotation axis where the matter undergoes decompression. Heat generation by these processes is found to have significant effects on the thermal evolution of old neutron stars with low magnetic fields; the surface emission predicted from this heating is compared with the $ROSAT$ observations of X-ray emission from millisecond pulsars and is shown to be insufficient to explain the observed X-ray luminosities.Comment: 32 pages, LaTeX, 11 Postscript figures. Accepted for publication in Ap

Superbursts from Strange Stars

Recent models of carbon ignition on accreting neutron stars predict superburst ignition depths that are an order of magnitude larger than observed. We explore a possible solution to this problem, that the compact stars in low mass X-ray binaries that have shown superbursts are in fact strange stars with a crust of normal matter. We calculate the properties of superbursts on strange stars, and the resulting constraints on the properties of strange quark matter. We show that the observed ignition conditions exclude fast neutrino emission in the quark core, for example by the direct Urca process, which implies that strange quark matter at stellar densities should be in a color superconducting state. For slow neutrino emission in the quark matter core, we find that reproducing superburst properties requires a definite relation between three poorly constrained properties of strange quark matter: its thermal conductivity, its slow neutrino emissivity and the energy released by converting a nucleon into strange quark matter.Comment: 4 pages, submitted to Ap. J. Let

Energy release associated with a first-order phase transition in a rotating neutron star core

We calculate energy release associated with a first order phase transition at the center of a rotating neutron star. The results are based on precise numerical 2-D calculations, in which both the polytropic equations of state (EOS) as well as realistic EOS of the normal phase are used. Presented results are obtained for a broad range of metastability of initial configuration and size of the new superdense phase core in the final configuration. For small radii of the superdense phase core analytical expressions for the energy release are obtained. For a fixed "overpressure" dP (the relative excess of central pressure of collapsing metastable star over the pressure of equilibrium first-order phase transition) the energy release remarkably does not depend on the stellar angular momentum and coincides with that for nonrotating stars with the same dP. The energy release is proportional to dP^2.5 for small dPs, when sufficiently precise brute force 2-D numerical calculations are out of question. For higher dPs, results of 1-D calculations of energy release for non-rotating stars are shown to reproduce, with very high precision, the exact 2-D results for rotating stars.Comment: 8 pages, 8 figures, submitted to A&

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