MHD of rotating compact stars with spectral methods: description of the algorithm and tests

A flexible spectral code for the study of general relativistic magnetohydrodynamics is presented. Aiming at investigating the physics of slowly rotating magnetized compact stars, this new code makes use of various physically motivated approximations. Among them, the relativistic anelastic approximation is a key ingredient of the current version of the code. In this article, we mainly outline the method, putting emphasis on algorithmic techniques that enable to benefit as much as possible of the non-dissipative character of spectral methods, showing also a potential astrophysical application and providing a few illustrative tests.Comment: 15 pages, 4 figures (new figure added, misprints corrected) Article accepted for publication in a special issue of Classical and Quantum Gravity "New Frontiers in Numerical Relativity

Rotating neutron stars with exotic cores: masses, radii, stability

A set of theoretical mass-radius relations for rigidly rotating neutron stars with exotic cores, obtained in various theories of dense matter, is reviewed. Two basic observational constraints are used: the largest measured rotation frequency (716 Hz) and the maximum measured mass ($2\;M_\odot$). Present status of measuring the radii of neutron stars is described. The theory of rigidly rotating stars in general relativity is reviewed and limitations of the slow rotation approximation are pointed out. Mass-radius relations for rotating neutron stars with hyperon and quark cores are illustrated using several models. Problems related to the non-uniqueness of the crust-core matching are mentioned. Limits on rigid rotation resulting from the mass-shedding instability and the instability with respect to the axisymmetric perturbations are summarized. The problem of instabilities and of the back-bending phenomenon are discussed in detail. Metastability and instability of a neutron star core in the case of a first-order phase transition, both between pure phases, and into a mixed-phase state, are reviewed. The case of two disjoint families (branches) of rotating neutron stars is discussed and generic features of neutron-star families and of core-quakes triggered by the instabilities are considered.Comment: Matches published version. Minor modifications and reference adde

Accelerated expansion of the Crab Nebula and evaluation of its neutron-star parameters

A model of an accelerated expansion of the Crab Nebula powered by the spinning-down Crab pulsar is proposed, in which time dependence of the acceleration is connected with evolution of pulsar luminosity. Using recent observational data, we derive estimates of the Crab neutron-star moment of inertia. Correlations between the neutron star moment of inertia and its mass and radius allow for rough estimates of the Crab neutron-star radius and mass. In contrast to the previously used constant-acceleration approximation, even for the expanding nebula mass ~7 M_sun results obtained within our model do not stay in conflict with the modern stiff equations of state of dense matter.Comment: to be submitted to Astronomy & Astrophysic

Moments of inertia for neutron and strange stars: limits derived for the Crab pulsar

Recent estimates of the properties of the Crab nebula are used to derive constraints on the moment of inertia, mass and radius of the pulsar. To this purpose, we employ an approximate formula combining these three parameters. Our "empirical formula" I = a(x)MR^2, where x = (M/M_sun)(km/R), is based on numerical results obtained for thirty theoretical equations of state of dense matter. The functions a(x) for neutron stars and strange stars are qualitatively different. For neutron stars a_NS(x) = x/(0.1+2x) for x 0.2 M_sun) and a_NS(x) = (2/9)(1+5x) for x > 0.1. For strange stars a_SS(x) = (2/5)(1+x) (not valid for strange stars with crust and M 1.4 M_sun and R_Crab = 10-14 km. Setting the most recent evaluation ("central value") M_neb = 4.6 M_sun rules out most of the existing equations of state, leaving only the stiffest ones: M_Crab > 2 M_sun, R_Crab = 14-15 km

Progenitor neutron stars of the lightest and heaviest millisecond pulsars

The recent mass measurements of two binary millisecond pulsars, PSR J1614-2230 and PSR J0751+1807 with a mass M=1.97+/-0.04 Msun and M= 1.26 +/- 0.14 Msun, respectively, indicate a wide range of masses for such objects and possibly also a broad spectrum of masses of neutron stars born in core-collapse supernovae. Starting from the zero-age main sequence binary stage, we aim at inferring the birth masses of PSR J1614-2230 and PSR J0751+1807 by taking the differences in the evolutionary stages preceding their formation into account. Using simulations for the evolution of binary stars, we reconstruct the evolutionary tracks leading to the formation of PSR J1614-2230 and PSR J0751+1807. We analyze in detail the spin evolution due to the accretion of matter from a disk in the intermediate-mass/low-mass X-ray binary. We consider two equations of state of dense matter, one for purely nucleonic matter and the other one including a high-density softening due to the appearance of hyperons. Stationary and axisymmetric stellar configurations in general relativity are used, together with a recent magnetic torque model and observationally-motivated laws for the decay of magnetic field. The estimated birth mass of the neutron stars PSR J0751+1807 and PSR J1614-2230 could be as low as 1.0 Msun and as high as 1.9 Msun, respectively. These values depend weakly on the equation of state and the assumed model for the magnetic field and its accretion-induced decay. The masses of progenitor neutron stars of recycled pulsars span a broad interval from 1.0 Msun to 1.9 Msun. Including the effect of a slow Roche-lobe detachment phase, which could be relevant for PSR J0751+1807, would make the lower mass limit even lower. A realistic theory for core-collapse supernovae should account for this wide range of mass.Comment: 13 pages, 10 figures, accepted in A&

Correlations in the properties of static and rapidly rotating compact stars

Correlations in the properties of the static compact stars (CSs) and the ones rotating with the highest observed frequency of 1122Hz are studied using a large set of equations of state (EOSs). These EOSs span various approaches and their chemical composition vary from the nucleons to hyperons and quarks in $\beta$-equilibrium. It is found that the properties of static CS, like, the maximum gravitational mass $M_{\rm max}^{\rm stat}$ and radius $R_{1.4}^{\rm stat}$ corresponding to t he canonical mass and supramassive or non-supramassive nature of the CS rotating at 1122 Hz are strongly correlated. In particular, only those EOSs yield the CS rotating at 1122Hz to be non-supramassive for which \left (\frac{M_{\rm max}^{\rm stat}}{M_\odot}\right )^{1/2} \left (\frac{10{\rm km}}{R_{1.4}^{\rm stat}})^{3/2} is greater than unity. Suitable parametric form which can be used to split the $M_{\rm max}^{\rm stat}$ $-$ $R_{1.4}^{\rm stat}$ plane into the regions of different supramassive nature of the CS rotating at 1122Hz is presented. Currently measured maximum gravitational mass 1.76$M_\odot$ of PSR J0437-4715 suggests that the CS rotating at 1122Hz can be non-supramassive provided $R_{1.4}^{\rm stat} \leqslant 12.4$ km.Comment: 13 pages, 4 figures, Appearing in Phys. Rev.

Formation of millisecond pulsars - NS initial mass and EOS constraints

Recent measurement of a high millisecond pulsar mass (PSR J1614-2230, 1.97+-0.04 Msun) compared with the low mass of PSR J0751+1807 (1.26+-0.14 Msun) indicates a large span of masses of recycled pulsars and suggests a broad range of neutron stars masses at birth. We aim at reconstructing the pre-accretion masses for these pulsars while taking into account interaction of the magnetic field with a thin accretion disk, magnetic field decay and relativistic 2D solutions for stellar configurations for a set of equations of state. We briefly discuss the evolutionary scenarios leading to the formation of these neutron stars and study the influence of the equation of state.Comment: 4 pages, 2 figures; proceedings of IAUS 290 "Feeding Compact Objects: Accretion on All Scales", C. M. Zhang, T. Belloni, M. Mendez & S. N. Zhang (eds.