J. L. Zdunik

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.

Maximum mass of neutron stars and strange neutron-star cores

Context. The recent measurement of mass of PSR J1614-2230 rules out most existing models of the equation of state (EOS) of dense matter with high-density softening due to hyperonization that were based on the recent hyperon-nucleon and hyperon-hyperon interactions, which leads to a “hyperon puzzle”. Aims. We study a specific solution of this hyperon puzzle that consists of replacing a too soft hyperon core by a sufficiently stiff quark core. In terms of the quark structure of the matter, one replaces a strangeness-carrying baryon phase of confined quark triplets, some of them involving s quarks, by a quark plasma of deconfined u, d, and s quarks. Methods. We constructed an analytic approximation that fits modern EOSs of the two flavor (2SC) and the color-flavor-locked (CFL) color-superconducting phases of quark matter very well. Then, we used it to generate a continuum of EOSs of quark matter. This allowed us to simulate continua of sequences of first-order phase transitions at prescribed pressures, from hadronic matter to the 2SC and then to the CFL state of color-superconducting quark matter. Results. We obtain constraints in the parameter space of the EOS of superconducting quark cores, EOS.Q, resulting from Mmax > 2 M� . These constraints depend on the assumed EOS of baryon phase, EOS.B. We also derive constraints that would

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.

The crust of rotating strange quark stars

Calculations of the properties of rotating strange stars with crusts are performed within the framework of general relativity. We employ an equation of state (EOS) of strange quark matter based on the MIT Bag Model with massive strange quarks and lowest order QCD interactions. The crust is described by the BPS equation of state. A signicant increase of the stellar radius is found close to the Keplerian (mass-shedding limit) conguration. This leads to the disappearance of the gap between the stellar surface and the innermost stable circular orbit (ISCO) at very high rotation rates, for a rather broad range of stellar masses. The Keplerian conguration for the strange star with crust corresponds to values of J, T=W, PISCO =1 =ISCO which are about 20% smaller than in the case of bare strange stars. Because the Keplerian conguration is achieved due to the increase of the stellar oblateness, the Keplerian frequency (of the rotation) remains almost unaltered. The lack of the gap close to the Keplerian rotation could imply a more stringent limit on ISCO, if the existence of such a gap is supported by observations, as in the source 4U 1820-30 with the upper QPO frequency 1.07 kHz. If such a constraint is taken into account (mandatory existence of a gap) the minimum ISCO is about 1 kHz even with the extreme ne tuning of strange quark matter parameters. The minimum ISCO is then obtained for the non-rotating conguration with maximum allowable mass. The maximum frequency in the stable circular orbit around the strange star with a crust is smaller by about 100 Hz than in the case of a bare strange star. During the spin-down of a magnetized strange quark star with crust, the crust matter is absorbed in the equatorial region by the strange matter core. The deconnement of absorbed crust matter is a strongly exothermic process, which would influence the cooling curve of this compact object.

Recycling strange stars to millisecond periods

Recycling strange stars to millisecond periods is studied within the framework of general relativity. We employ equations of state of strange quark matter based on the MIT Bag Model, with massive strange quarks and lowest order QCD interactions. The presence of the crust of normal matter is taken into account, with a bottom density assumed to be equal to the neutron-drip one. The calculations are performed by solving the exact 2-D equations for rigidly rotating stationary configurations in general relativity. Evolutionary tracks of accreting strange stars are computed, and their dependence on the initial strange star mass and on the fraction of the angular momentum transferred to the star from the infalling matter, is studied. The differences between recycling strange stars and neutron stars are pointed out.

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

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.

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

The effect of the hyperon softening of the equation of state (EOS) of dense matter on the spin evolution of isolated neutron stars is studied for a broad set of hyperonic EOSs. We use a multidomain 2-D code based on a spectral method, and show how important the precision of solving the equations of stationary motion is for the stability analysis. For some EOSs, the hyperon softening leads to spin-up by angular momentum loss, in the form of the back-bending phenomenon, for a rather broad range of stellar baryon mass. We show that large segments of the evolutionary tracks exhibiting the back-bending behaviour in the moment-of-inertia - rotation-frequency plane are unstable and therefore not astrophysically relevant. We show also that during the spin-up - angular-momentum-loss epoch, an isolated neutron star (e.g. a radio pulsar) can lose a sizable part of its initial angular momentum without significantly changing its rotation period. We propose also simple arguments and criteria allowing one to connect the presence of a back-bending epoch with the mass-radius relations and the stiffness and/or softness of the nucleon and hyperon EOSs of the neutron star core.

Compression of matter in the center of accreting neutron stars

Aims. To estimate the feasibility of dense-matter phase transition, we studied the evolution of the central density as well as the baryon chemical potential of accreting neutron stars. We compared the thin-disk accretion with and without the magnetic field torque with the spin-down scenario for a selection of recent equations of state. Methods. We compared the prevalent (in the recycled-pulsar context) Keplerian thin-disk model, in which the matter is accreted from the marginally-stable circular orbit, with the recent magnetic-torque model that takes into account the influence of stellar magnetic field on the effective inner boundary of the disk. Calculations were performed using a multi-domain spectral methods code in the framework of General Relativity. We considered three equations of state consistent with the recently measured mass of PSR J16142230, 1.97 ± 0.04 M� (one of them softened by the appearance of hyperons). Results. If there is no magnetic torque and efficient angular momentum transfer from the disk to the star, substantial central compression islimitedtothe region ofinitial stellarmasses close tothe maximum mass. Outsidethe maximum mass vicinity, accretion-induced central compression is significant only if the angular momentum transfer is inefficient. Accounting for the magnetic field effectively decreases the efficiency of angular momentum transfer and implies a significant central compression. Conclusions. An efficient angular momentum transfer from a thin disk onto a non-magnetized neutron star does not provide a good mechanism for the central compression and possible phase transition. Substantial central compression is possible for a broad range of masses of slowly-rotating initial configurations for magnetized neutron stars. Accretion-induced central compression is particularly strong for stiff equation of state with a high-density softening.