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 result from significantly higher measured masses. For 2.4 M⊙ the required stiffness of the CFL quark core is close to the causality limit while the density jump at the phase transition is very small. Conclusions. The condition Mmax > 2 M⊙ 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. The condition of thermodynamic stability of the quark phase results in a maximum mass of hybrid stars similar to that of purely baryon stars. This is due to the phase transition of quark matter back to the baryon phase (reconfinement) that we find for both EOS.B. Therefore, to obtain Mmax > 2 M⊙ for 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, we think that the high-density instability, which results in the reconfinement of quark matter, indicates actually the inadequacy of the point-particle model of baryons in dense matter at ρ ≳ 5 ÷ 8ρ0. We expect that reconfinement can be removed by a sufficient stiffening of the baryon phase, resulting from the repulsive finite size contribution for baryons to the EOS.
The uncertainties in neutron star (NS) radii and crust properties due to our limited knowledge of the equation of state (EOS) are quantitatively analysed. We first demonstrate the importance of a ...unified microscopic description for the different baryonic densities of the star. If the pressure functional is obtained matching a crust and a core EOS based on models with different properties at nuclear matter saturation, the uncertainties can be as large as $\sim 30\%$ for the crust thickness and $4\%$ for the radius. Necessary conditions for causal and thermodynamically consistent matchings between the core and the crust are formulated and their consequences examined. A large set of unified EOS for purely nucleonic matter is obtained based on 24 Skyrme interactions and 9 relativistic mean-field nuclear parametrizations. In addition, for relativistic models 17 EOS including a transition to hyperonic matter at high density are presented. All these EOS have in common the property of describing a $2\;M_\odot$ star and of being causal within stable NS. A span of $\sim 3$ km and $\sim 4$ km is obtained for the radius of, respectively, $1.0\;M_\odot$ and $2.0\;M_\odot$ star. Applying a set of nine further constraints from experiment and ab-initio calculations the uncertainty is reduced to $\sim 1$ km and $2$ km, respectively. These residual uncertainties reflect lack of constraints at large densities and insufficient information on the density dependence of the EOS near the nuclear matter saturation point. The most important parameter to be constrained is shown to be the symmetry energy slope $L$ which exhibits a linear correlation with the stellar radius, particularly for masses $\sim 1.0\;M_\odot$. Potential constraints on $L$, the NS radius and the EOS from observations of thermal states of NS are also discussed. Abriged
Context. Using parametric equations of state (relativistic polytropes and a simple quark bag model) to model dense-matter phase transitions, we study global, measurable astrophysical parameters of ...compact stars such as their allowed radii and tidal deformabilities. We also investigate the influence of stiffness of matter before the onset of the phase transitions on the parameters of the possible exotic dense phase. Aims. The aim of our study is to compare the parameter space of the dense matter equation of state permitting phase transitions to a sub-space compatible with current observational constraints such as the maximum observable mass, tidal deformabilities of neutron star mergers, radii of configurations before the onset of the phase transition, and to give predictions for future observations. Methods. We studied solutions of the Tolman-Oppenheimer-Volkoff equations for a flexible set of parametric equations of state, constructed using a realistic description of neutron-star crust (up to the nuclear saturation density), and relativistic polytropes connected by a density-jump phase transition to a simple bag model description of deconfined quark matter. Results. In order to be consistent with recent observations of massive neutron stars, a compact star with a strong high-mass phase transition cannot have a radius smaller than 12 km in the range of masses 1.2 − 1.6 M⊙. We also compare tidal deformabilities of stars with weak and strong phase transitions with the results of the GW170817 neutron star merger. Specifically, we study characteristic phase transition features in the Λ1 − Λ2 relation, and estimate the deviations of our results from the approximate formulæ for Λ∼ − R (M1) Λ ∼ − R ( M 1 ) $ \tilde{\Lambda}-R(M_1) $ and Λ-compactness proposed in the literature. We find constraints on the hybrid equations of state to produce stable neutron stars on the twin branch. For the exemplary equations of state most of the high-mass twins occur for the minimum values of the density jump λ = 1.33 − 1.54; corresponding values of the square of the speed of sound are α = 0.7 − 0.37. We compare results with observations of gravitational waves and with the theoretical causal limit and find that the minimum radius of a twin branch is between 9.5 and 10.5 km, and depends on the phase transition baryon density. For these solutions the phase transition occurs below 0.56 fm−3.
Context. Rapidly rotating neutron stars are an ideal laboratory to test models of matter at high densities. In particular, the maximum rotation frequency of a neutron star depends on the equation of ...state and can be used to test models of the interior. However, observations of the spin distribution of rapidly rotating neutron stars show evidence for a lack of stars spinning at frequencies higher than f ≈ 700 Hz, well below the predictions of theoretical equations of state. This has generally been taken as evidence of an additional spin-down torque operating in these systems, and it has been suggested that gravitational wave torques may be operating and be linked to a potentially observable signal. Aims. We aim to determine whether additional spin-down torques (possibly due to gravitational wave emission) are necessary, or if the observed limit of f ≈ 700 Hz could correspond to the Keplerian (mass-shedding) break-up frequency for the observed systems, and is simply a consequence of the currently unknown state of matter at high densities. Methods. Given our ignorance with regard to the true equation of state of matter above nuclear saturation densities, we make a minimal physical assumption and only demand causality, that is, that the speed of sound in the interior of the neutron star should be lower than or equal to the speed of light c. We then connected our causally limited equation of state to a realistic microphysical crustal equation of state for densities below nuclear saturation density. This produced a limiting model that gave the lowest possible maximum frequency, which we compared to observational constraints on neutron star masses and frequencies. We also compared our findings with the constraints on the tidal deformability obtained in the observations of the GW170817 event. Results. We rule out centrifugal breakup as the mechanism preventing pulsars from spinning faster than f ≈ 700 Hz, as the lowest breakup frequency allowed by our causal equation of state is f ≈ 1200 Hz. A low-frequency cutoff, around f ≈ 800 Hz could only be possible when we assume that these systems do not contain neutron stars with masses above M ≈ 2 M⊙. This would have to be due either to selection effects, or possibly to a phase transition in the interior of the neutron star that leads to softening at high densities and a collapse to either a black hole or a hybrid star above M ≈ 2 M⊙. Such a scenario would, however, require a somewhat unrealistically stiff equation of state for hadronic matter, in tension with recent constraints obtained from gravitational wave observations of a neutron star merger.
Aims.We calculate heating associated with non-equilibrium nuclear reactions in accreting neutron-star crusts, taking into account the suppression of neutrino losses demonstrated recently by Gupta ...et al. We consider two initial compositions of the nuclear-burning ashes, Ai = 56 and Ai = 106. We study the dependence of the integrated crustal heating on uncertainties plaguing pycnonuclear reaction models. Methods.We use one-component plasma approximation, with compressible liquid-drop model of Mackie and Baym to describe nuclei. We follow the evolution of a crust shell from 108 g cm-3 to 1013.6 g cm-3. Results.The integrated heating in the outer crust agrees nicely with results of self-consistent multicomponent plasma simulations: earlier results fall between our curves obtained for Ai = 56 and Ai = 106. The total crustal heat per one accreted nucleon ranges between 1.5 MeV/nucleon to 1.9 MeV/nucleon for Ai = 106 and Ai = 56, respectively. The value of Qtot weakly depends on the presence of pycnonuclear reactions at 1012-1013 g cm-3. The remarkable insensitivity of Qtot to the distribution of nuclear processes in accreted crust is explained.
ABSTRACT
We explore the thermal and magnetic field structure of a late-stage proto-neutron star (proto-NS). We find the dominant contribution to the entropy in different regions of the star, from ...which we build a simplified equation of state (EOS) for the hot neutron star (NS). With this, we numerically solve the stellar equilibrium equations to find a range of models, including magnetic fields and rotation up to Keplerian velocity. We approximate the EOS as a barotrope, and discuss the validity of this assumption. For fixed magnetic field strength, the induced ellipticity increases with temperature; we give quantitative formulae for this. The Keplerian velocity is considerably lower for hotter stars, which may set a de facto maximum rotation rate for non-recycled NSs well below 1 kHz. Magnetic fields stronger than around 1014 G have qualitatively similar equilibrium states in both hot and cold NSs, with large-scale simple structure and the poloidal field component dominating over the toroidal one; we argue this result may be universal. We show that truncating magnetic field solutions at low multipoles leads to serious inaccuracies, especially for models with rapid rotation or a strong toroidal-field component.
Context. The existence of 2 M⊙ 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. 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> 2M⊙. We seek correlations between R(M) and the stiffness of the EOS below the hyperon threshold needed to pass the 2 M⊙ test. Results. For NS masses 1.0 <M/M⊙< 1.6, we get R> 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 M⊙ are necessarily >13 km. If, on the contrary, a NS with a radius R(obs)< 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 Mmax> 2 M⊙ yield a pressure at nuclear density that is too high relative to up-to-date microscopic calculations of this quantity.
Context. Few unified equations of state for neutron star matter, in which core and crust are described using the same nuclear model, are available. However the use of non-unified equations of state ...with simplified matching between the crust and core has been shown to introduce uncertainties in the radius determination, which can be larger than the expected precision of the next generation of X-ray satellites. Aims. We aim to eliminate the dependence of the radius and mass of neutron stars on the detailed model for the crust and on the crust-core matching procedure. Methods. We solved the approximate equations of the hydrostatic equilibrium for the crust of neutron stars and obtained a precise formula for the radius that only depends on the core mass and radius, the baryon chemical potential at the core-crust interface, and at the crust surface. For a fully accreted crust one needs, additionally, the value of the total deep crustal heating per one accreted nucleon. Results. For typical neutron star masses, the approximate approach allows us to determine the neutron star radius with an error ~0.1% (~10 m, equivalent to a 1% inaccuracy in the crust thickness). The formalism applies to neutron stars with a catalyzed or a fully accreted crust. The difference in the neutron star radius between the two models is proportional to the total energy release due to deep crustal heating. Conclusions. For a given model of dense matter describing the neutron star core, the radius of a neutron star can be accurately determined independent of the crust model with a precision much better than the ~5% precision expected from the next generation of X-ray satellites. This allows us to circumvent the problem of the radius uncertainty that may arise when non-unified equations of state for the crust and core are used.
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, ...fK, proposed by Lattimer & Prakash, $f_{\rm K}(M)=C\; (M/M_\odot)^{1/2}(R/10~{\rm km})^{-3/2}$, 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 $f_{\rm K}(M)$ holds within a few percent for neutron stars with realistic EOSs, provided $0.5~M_\odot<M<0.9~M_{\rm max}^{\rm stat}$, where $M_{\rm max}^{\rm stat}$ is the maximum allowable mass of non-rotating neutron stars for an EOS, and $C=C_{\rm NS}=1.08~$kHz. Similar precision is obtained for strange stars with $0.5~M_\odot<M<0.9~M_{\rm max}^{\rm stat}$. For maximal crust masses we obtain $C_{\rm SS}=1.15$ kHz, and the value of CSS is not very sensitive to the crust mass. All our Cs are significantly larger than the analytic value from the relativistic Roche model, $C_{\rm Roche}=1.00$ kHz. For $0.5~M_\odot<M<0.9~M_{\rm max}^{\rm stat}$, the equatorial radius of the Keplerian configuration of mass M, $R_{\rm K}(M)$, is, to a very good approximation, proportional to the radius of the non-rotating star of the same mass, $R_{\rm K}(M)=a\;R(M)$, with $a_{\rm NS}\approx a_{\rm SS} \approx 1.44$. The value of aSS is very weakly dependent on the mass of the crust of the strange star. Both a values are smaller than the analytic value $a_{\rm Roche}=1.5$ from the relativistic Roche model.
Context. The recent mass measurements of two binary millisecond pulsars, PSR J1614−2230 and PSR J0751+1807 with a mass M = 1.97 ± 0.04 M⊙ and M = 1.26 ± 0.14 M⊙, 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. Aims. 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. Methods. 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 analyse 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. Results. The estimated birth mass of the neutron stars PSR J0751+1807 and PSR J1614−2230 could be as low as 1.0 M⊙ and as high as 1.9 M⊙, respectively. These values depend weakly on the equation of state and the assumed model for the magnetic field and its accretion-induced decay. Conclusions. The masses of progenitor neutron stars of recycled pulsars span a broad interval from 1.0 M⊙ to 1.9 M⊙. 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 supernovæ should account for this wide range of mass.
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