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

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

Neutron stars with hyperon cores: stellar radii and EOS near nuclear density

The existence of 2 Msun pulsars puts very strong constraints on the equation of state (EOS) of neutron stars (NSs) with hyperon cores, which can be satisfied only by special models of hadronic matter. The radius-mass relation for these models is sufficiently specific that it could be subjected to an observational test with future X-ray observatories. We want to study the impact of the presence of hyperon cores on the radius-mass relation for NS. We aim to find out how, and for which particular stellar mass range, a specific relation R(M), where M is the gravitational mass, and R is the circumferential radius, is associated with the presence of a hyperon core. We consider a set of 14 theoretical EOS of dense matter, based on the relativistic mean-field (RMF) approximation, allowing for the presence of hyperons in NSs. We seek correlations between R(M) and the stiffness of the EOS below the hyperon threshold needed to pass the 2 Msun test. For NS masses 1.013km, because of a very stiff pre-hyperon segment of the EOS. At nuclear density, the pressure is significantly higher than a robust upper bound obtained recently using chiral effective field theory. If massive NSs do have a sizable hyperon core, then according to current models the radii for M=1.0-1.6 Msun are necessarily >13km. If, on the contrary, a NS with a radius R<12 km is observed in this mass domain, then sizable hyperon cores in NSs, as we model them now, are ruled out. Future X-ray missions with <5% precision for a simultaneous M and R measurement will have the potential to solve the problem with observations of NSs. Irrespective of this observational test, present EOS allowing for hyperons that fulfill condition M_max>2 Msun yield a pressure at nuclear density that is too high relative to up-to-date microscopic calculations of this quantity.Comment: 10 pages, 10 figures, published in A&

EOS of dense matter and fast rotation of neutron stars

Recent observations of XTE J1739-285 suggest that it contains a neutron star rotating at 1122 Hz. Such rotational frequency would be the first for which the effects of rotation are significant. We study the consequences of very fast rotating neutron stars for the potentially observable quantities as stellar mass and pulsar period.Comment: 8 pages, 5 eps figures, proceedings of the International Symposium on Exotic States of Nuclear Matter, EXOCT07, to be published by World Scientific Publishing C

The energy release--stellar angular momentum independence in rotating compact stars undergoing first-order phase transitions

We present the general relativistic calculation of the energy release associated with a first order phase transition (PT) at the center of a rotating neutron star (NS). The energy release, E_rel, is equal to the difference in mass-energies between the initial (normal) phase configuration and the final configuration containing a superdense matter core, assuming constant total baryon number and the angular momentum. The calculations are performed with the use of precise pseudo-spectral 2-D numerical code; the polytropic equations of state (EOS) as well as realistic EOSs (Skyrme interactions, Mean Field Theory kaon condensate) are used. The 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 a fixed ``overpressure'', dP, defined as the relative excess of central pressure of a collapsing metastable star over the pressure of the equilibrium first-order PT, the energy release up to numerical accuracy does not depend on the stellar angular momentum and coincides with that for nonrotating stars with the same dP. When the equatorial radius of the superdense phase core is much smaller than the equatorial radius of the star, analytical expressions for the E_rel can be obtained: E_rel is proportional to dP^2.5 for small dP. At higher dP, the results of 1-D calculations of E_rel(dP) for non-rotating stars reproduce with very high precision exact 2-D results for fast-rotating stars. The energy release-angular momentum independence for a given overpressure holds also for the so-called ``strong'' PTs (that destabilise the star against the axi-symmetric perturbations), as well as for PTs with ``jumping'' over the energy barrier.Comment: 4 pages, 2 figures, proceedings of the International Symposium on Exotic States of Nuclear Matter, EXOCT07, to be published by World Scientific Publishing C