M. Bejger

Hyperons in neutron-star cores and a 2 M⊙ pulsar

Context. A recent measurement of the mass of PSR J1614-2230 rules out most existing models of the equation of state (EOS) of dense matter that is subjected to the high-density softening caused by either hyperonization or a phase transition to either quark matter or a boson condensate. Aims. We attempt to resolve the apparent differences between the predictions derived from up-to-date hypernuclear data, which in- clude the appearance of hyperons at about three nuclear densities and the existence of a M = 2.0 Mneutron star. Methods. We consider a non-linear relativistic mean field (RMF) model involving the baryon octet coupled to meson fields. An effective Lagrangian includes quartic terms in the meson fields. The values of the model parameters are obtained by fitting the semi- empirical parameters of nuclear matter at the saturation point, as well as potential wells for hyperons in nuclear matter and the strength of the Λ − Λ attraction in double-Λ hypernuclei. Results. We propose a non-linear RMF model that is consistent with up-to-date semi-empirical nuclear and hypernuclear data and allows for neutron stars with hyperon cores and M > 2 M� . The model involves hidden-strangeness scalar and vector mesons, coupled only to hyperons, and quartic terms involving vector meson fields. Conclusions. Our EOS involving hyperons is stiffer than the corresponding nucleonic EOS (in which hyperons are artificially sup- pressed) above five nuclear densities. The required stiffening is generated by the quartic terms involving the hidden-strangeness vector meson.

Neutron stars with hyperon cores: stellar radii and equation of state near nuclear density

Context. The existence of 2 Mpulsars 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. Aims. 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. Methods. We consider a set of 14 theoretical EOS of dense matter, based on the relativistic mean-field approximation, allowing for the presence of hyperons in NSs. We also discuss a recent EOS based on non-relativistic G-matrix theory yielding NSs with hyperonic cores and M > 2 M� . We seek correlations between R(M) and the stiffness of the EOS below the hyperon threshold needed to pass the 2 Mtest. Results. For NS masses 1.0 13 km, because of a very stiff pre-hyperon segment of the EOS. At nuclear density (n0 = 0.16 fm −3 ), the pressure is significantly higher than a robust upper bound obtained recently using chiral effective field theory. Conclusions. If massive NSs do have a sizable hyperon core, then according to current models the radii for M = 1.0−1.6 Mare necessarily >13 km. If, on the contrary, a NS with a radius R (obs) 2 Myield a pressure at nuclear density that is too high relative to up-to-date microscopic calculations of this quantity.

Keplerian frequency of uniformly rotating neutron stars and strange stars

Aims. We calculate Keplerian (mass shedding) configurations of rigidly rotating neutron stars and strange stars with crusts. We check the validity of the empirical formula for Keplerian frequency, f K , proposed by Lattimer & Prakash, f K (M) = C (M/M ⊙ ) 1/2 (R/10 km) -3/2 , where M is the (gravitational) mass of the Keplerian configuration, R is the (circumferential) radius of the non-rotating configuration of the same gravitational mass, and C = 1.04 kHz. Methods. Numerical calculations are performed using precise 2D codes based on the multi-domain spectral methods. We use a representative set of equations of state (EOSs) of neutron stars and quark stars. Results. We show that the empirical formula for f K (M) holds within a few percent for neutron stars with realistic EOSs, provided 0.5 M ⊙ < M < 0.9 M stat max , where M stat max ) is the maximum allowable mass of non-rotating neutron stars for an EOS, and C = C NS = 1.08 kHz. Similar precision is obtained for strange stars with 0.5 M ⊙ < M < 0.9 M stat max . For maximal crust masses we obtain C ss = 1.15 kHz, and the value of C ss is not very sensitive to the crust mass. All our Cs are significantly larger than the analytic value from the relativistic Roche model, C Roche = 1.00 kHz. For 0.5 M ⊙ < M < 0.9 M stat max , the equatorial radius of the Keplerian configuration of mass M, R K (M), is, to a very good approximation, proportional to the radius of the non-rotating star of the same mass, R K (M) = a R(M), with α NS ≈ α ss ≈ 1.44. The value of α ss is very weakly dependent on the mass of the crust of the strange star. Both a values are smaller than the analytic value α Roche = 1.5 from the relativistic Roche model.

Phase transitions in rotating neutron stars cores: back bending, stability, corequakes, and pulsar timing

Aims. We analyze potentially observable phenomena during spin evolution of isolated pulsars, such as back bending and corequakes resulting from instabilities, which could result from phase transitions in neutron star cores. Methods. We study these aspects of spin evolution of isolated compact stars by means of analytical models of equations of state, for both constant-pressure phase transitions and the transitions through the mixed-phase region. We use high-precision 2-D multi-domain spectral code LORENE for the calculation of the evolutionary sequences of rotating neutron stars. This allows us to search the parameter space for possible instability regions, and possible changes in the stability character of rotating stars with phase transitions in their cores. Results. We determine the conditions on the density jump in constant-pressure phase transitions which leads to the back bending phenomena or to the existence of the unstable segments in the evolutionary sequences of spinning down isolated normal neutron stars. We formulate the conjectures concerning the existence of two disjoint families of non-rotating and rotating stationary configurations of neutron stars. To clarify the effect of rotation on the stability of neutron star we present the particular case of EOSs leading to marginal instability of static and rotating configurations: marginal instability point in non-rotating configurations continues to exist in all evolutionary spin-down tracks. We discuss the fate of rotating stars entering the region of instability calculating the change in radius, energy release, and spin-up associated with the corequake in rotating neutron star, triggered by the instability. The energy release is found to be very weakly dependent on the angular momentum of collapsing star.

Constraints on the dense matter equation of state from the measurements of PSR J0737-3039A moment of inertia and PSR J0751+1807 mass

The moment of inertia of the pulsar A in the neutron star binary J0737−3039 will soon be measurable through detailed measurements of the periastron advance. We present the calculation of the moment of inertia of neutron stars with the masses of the components of the binary J0737−3039 for a broad range of equations of state of dense matter, and we discuss the implications of such measurement for constraining the equation of state. An observational determination of the moment of inertia of the pulsar A in J0737−3039 with the accuracy of 10 per cent will narrow down considerably the range of viable equations of state. We also show that limits on the maximal mass of a neutron star provide a complementary set of constraints on the properties of dense nuclear matter.

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 to the 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 of ~

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

7~M_{\odot}

Mixed-phase induced core-quakes and the changes in neutron-star parameters

the results obtained within our model are not in conflict with the modern stiff equations of state of dense matter.

Hyperon softening of the EOS of dense matter and the spin evolution of isolated neutron stars

Abstract.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 (716Hz) and the maximum measured mass ( 2M⊙ . The 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.

Compression of matter in the center of accreting neutron stars

We present approximate formulae describing the changes in neutron-star parameters caused by the first-order phase transition to an exotic state (pion or kaon condensate, quark matter) resulting in formation of a mixed-phase core. The analytical formulae for the changes in radius, moment of inertia and the amount of energy released during the core-quake are derived using the theory of linear response of stellar structure to the core transformation. Numerical coefficients in these formulae are obtained for two realistic equations of state (EOSs) of dense matter. The problem of nucleation of the exotic phase as well as possible astrophysical scenarios leading to a core-quake phenomenon are also discussed.