arXiv subjects

J. L. Zdunik

Publications and source records attributed to J. L. Zdunik.

At least 19 recordsLinked to original sources

arXiv2026

Modelling mountains on accreting magnetized neutron stars

Continuous gravitational waves from accreting neutron stars in Low Mass X-ray Binaries are one of the main targets for current and next generation ground based detectors. In order to select the most promising astrophysical sources, however, reliable predictions for the signals are required, and it is therefore necessary to develop models that consistently account for the combined effects of magnetic stresses, accretion-induced heating, and the elastic response of the crust.}{We present a model for computing the quadrupolar deformation, incorporating for the first time the coupled effects of a poloidal magnetic field, deep crustal heating, and crustal elasticity. Perturbations to the star's structure driven by the Lorentz force density and by thermally-induced density variations are computed by solving a system of linearised deformation equations in the crust, for which we consider the full elastic response, while the ocean and core treated as barotropic fluids. We identify a threshold accretion rate whose value depends on crustal microphysics and the superfluid gaps in the core, above which magnetic stresses and asymmetric accretion drive deformations of opposite sign, while below this threshold their roles are reversed. The predicted eccentricities reach magnitudes up to $\varepsilon\sim 10^{-11}$, corresponding to characteristic gravitational-wave strains accessible to next-generation detectors such as the Einstein Telescope or Cosmic Explorer, but generally below the sensitivity of current LIGO, Virgo and KAGRA interferometers. These results are consistent with the non-detection of continuous gravitational waves from accreting neutron stars in Low Mass X-ray Binaries in recent observational campaigns, but highlight the need of reliable models to understand the impact of gravitational wave emission in these systems and select relevant targets for future searches.

astro-ph.HE↗

arXiv2022

Accreting neutron stars from the nuclear energy-density functional theory. II. Equation of state and global properties

The accretion of matter onto the surface of a neutron star in a low-mass X-ray binary triggers X-ray bursts, whose ashes are buried and further processed thus altering the composition and the properties of the stellar crust. In this second paper of a series, the impact of accretion on the equation of state and on the global properties of neutron stars is studied in the framework of the nuclear energy-density functional theory. Considering ashes made of $^{56}$Fe, we calculated the equations of state using the same Brussels-Montreal nuclear energy-density functionals BSk19, BSk20, and BSk21, as those already employed for determining the crustal heating in our previous study for the same ashes. All regions of accreting neutron stars were treated in a unified and thermodynamically consistent way. With these equations of state, we determined the mass, radius, moment of inertia, and tidal deformability of accreted neutron stars and compared with catalyzed neutron stars for which unified equations of state based on the same functionals are available. The equation of state of accreted neutron stars is found to be significantly stiffer than that of catalyzed matter, with an adiabatic index $Γ\approx 4/3$ throughout the crust. For this reason, accreting neutron stars have larger radii. However, their crustal moment of inertia and their tidal deformability are hardly changed provided density discontinuities at the interface between adjacent crustal layers are properly taken into account. The enhancement of the stiffness of the equation of state of accreting neutron stars is mainly a consequence of nuclear shell effects, thus confirming the importance of a quantum treatment as stressed in our first study. With our previous calculations of crustal heating using the same functionals, we have thus obtained consistent microscopic inputs for simulations of accreting neutron stars.

astro-ph.HE↗

arXiv2021

Magnetic fields in late-stage proto-neutron stars

We explore the thermal and magnetic-field structure of a late-stage proto-neutron star. We find the dominant contribution to the entropy in different regions of the star, from which we build a simplified equation of state for the hot neutron star. 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 equation of state 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 $10^{14}$ G have qualitatively similar equilibrium states in both hot and cold neutron stars, 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.

astro-ph.HE↗

arXiv2020

Redshift factor and diffusive equilibrium of unbound neutrons in the single nucleus model of accreting neutron star crust

Using a Wigner-Seitz approximation with spherical cells, we re-analyze a widely used single nucleus model of accreting neutron star crust. We calculate beta disequilibrium within the crust, which is sizable, and implies that neutron and baryon chemical potentials, $μ_n$ and $μ_{\rm b}$, are not equal. We include also non-equilibrium reactions, driven by matter compression, and proceeding in the reaction layers. The constancy of $e^Φμ_n$, where the spacetime metric component $g_{00}=e^{2Φ}$, in the shells between the reaction layers is not applicable, because single electron captures are blocked, so that the neutron fraction is fixed, and therefore neutrons are not an independent component of the crust matter. The absence of neutron diffusion in the shells between the reaction layers, stems from the constancy of the neutron fraction (concentration) in these shells. In the reaction layers, the outward force resulting from neutron fraction gradient is balanced by the inward gravitational force acting on unbound neutrons. Neglecting the thickness of the reaction layers compared to the shell thickness, we obtain condition $e^{Φ(r)}f_Q(r)g(r)=$constant, where $g$ is Gibbs energy per nucleon, undergoing discontinuous drops on the reaction surfaces, and $f_Q(r)g(r)={\widetilde{g}}(r)$ is a continuous function, due to the factor $f_Q(r)$ canceling the discontinuities (drops) in $g(r)$. The function $f_Q(r)$ is calculated using the Tolman-Oppenheimer-Volkov equations from $f_Q(P)$ and $g(P)$ obtained from the equation of state (EOS) with discontinuites. The constancy of of $e^{Φ(r)}{\widetilde{g}}(r)$ is an extension of the standard relation $e^{Φ(r)}{μ}_{\rm b}(r)=$constant, valid in hydrostatic equilibrium for catalyzed crust.

astro-ph.HE↗

arXiv2018

Crustal heating in accreting neutron stars from the nuclear energy-density functional theory. I. Proton shell effects and neutron-matter constraint

Observations of soft X-ray transients in quiescence suggest the existence of heat sources in the crust of accreting neutron stars. Heat is thought to be released by electroweak and nuclear processes triggered by the burying of ashes of X-ray bursts. The heating is studied using a fully quantum approach taking consistently into account nuclear shell effects. We have followed the evolution of ashes made of $^{56}$Fe employing the nuclear energy-density functional theory. Both the outer and inner crusts are described using the same functional, thus ensuring a unified and thermodynamically consistent treatment. To assess the role of the neutron-matter constraint, we have employed the set of accurately calibrated Brussels-Montreal functionals BSk19, BSk20, and BSk21 and for comparison the SLy4 functional. Due to nuclear shell effects, the fully accreted crust is found to be much less stratified than in previous studies. In particular, large regions of the inner crust contain clusters with the magic number $Z=14$. The heat deposited in the outer crust is tightly constrained by experimental atomic mass data. The shallow heating we obtain does not exceed $0.2$~MeV and is therefore not enough to explain the cooling of some soft X-ray transients. The total heat released in the crust is very sensitive to details of the nuclear structure and is predicted to lie in the range from $1.5$~MeV to $1.7$~MeV. The evolution of an accreted matter element and therefore the location of heat sources are governed to a large extent by the existence of nuclear shell closures. Ignoring these effects in the inner crust, the total heat falls to $\sim 0.6$~MeV. The neutron-matter constraint is also found to play a key role. The large amount of heat obtained by Steiner et al. (2012) could thus be traced back to unrealistic neutron-matter equations of state.

astro-ph.HE↗

arXiv2018

Fundamental physics and the absence of sub-millisecond pulsars

Observations of the spin distribution of rapidly rotating neutron stars show evidence for a lack of stars spinning at frequencies larger than $f\approx 700$ 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. In this paper we aim to determine whether additional spin-down torques are necessary, or whether the observed limit of $f\approx 700$ Hz could correspond to the mass-shedding frequency for the observed systems and is simply a consequence of the, currently unknown, state of matter at high densities. Given our ignorance with regard to the true equation of state of matter above nuclear saturation densities, we make minimal physical assumption and only demand causality in the core. We then connect our causally-limited equation of state to a realistic microphysical crustal equation of state for densities below nuclear saturation density. This produces a limiting model that will give the lowest possible maximum frequency, which we compare to observational constraints on neutron star masses and frequencies. We also compare our findings with the constraints on the tidal deformability obtained in the observations of the GW170817 event. We find that the lack of pulsars spinning faster than $f\approx 700$ Hz is not compatible with our causal limited `minimal' equation of state, for which the breakup frequency cannot be lower than $f_{\rm max}\approx 1200$ Hz. A low frequency cutoff, around $f\approx 800$ Hz could only be possible if we assume that these systems do not contain neutron stars with masses above $M\approx 2 M_\odot$. This would have to be due either to selection effects, or possibly to a phase transition in the interior of the neutron star.

astro-ph.HE↗

arXiv2017

Thermal states of neutron stars with a consistent model of interior

We model the thermal states of both isolated neutron stars and accreting neutron stars in X-ray transients in quiescence and confront them with observations. We use an equation of state and superfluid baryon gaps, which are consistently calculated. We conclude that the direct Urca process is required to be consistent with low-luminous accreting neutron stars. In addition, proton superfluidity and sufficiently weak neutron superfluidity are necessary to explain the cooling of middle-aged neutron stars and to obtain a realistic distribution of neutron star masses.

astro-ph.HE↗

arXiv2017

Neutrino luminosities and heat capacities of neutron stars in analytic form

We derive analytic approximations for the neutrino luminosities and the heat capacities of neutron stars with isothernal nucleon cores as functions of the mass and radius of stars. The neutrino luminosities are approximated for the three basic neutrino emission mechanisms, and the heat capacities for the five basic combinations of the partial heat capacities. The approximations are valid for for a wide class of equations of state of dense nucleonmatter. The results significantly simplify the theoretical interpretation of observations of cooling neutron stars as well as of quasistationary thermal states of neutron stars in X-ray transients. For illustration, we present an analysis of the neutrino cooling functions of nine isolated neutron stars taking into account the effects of their magnetic fields and of the presence of light elements in their heat blanketing envelopes. These results allow one to investigate the superfluid properties of neutron star cores.

astro-ph.HE↗

arXiv2017

Consequences of a strong phase transition in the dense matter equation of state for the rotational evolution of neutron stars

We explore the implications of a strong first-order phase transition region in the dense matter equation of state in the interiors of rotating neutron stars, and the resulting creation of two disjoint families of neutron-star configurations (the so-called high-mass twins). We numerically obtained rotating, axisymmetric, and stationary stellar configurations in the framework of general relativity, and studied their global parameters and stability. The instability induced by the equation of state divides stable neutron star configurations into two disjoint families: neutron stars (second family) and hybrid stars (third family), with an overlapping region in mass, the high-mass twin-star region. These two regions are divided by an instability strip. Its existence has interesting astrophysical consequences for rotating neutron stars. We note that it provides a natural explanation for the rotational frequency cutoff in the observed distribution of neutron star spins, and for the apparent lack of back-bending in pulsar timing. It also straightforwardly enables a substantial energy release in a mini-collapse to another neutron-star configuration (core quake), or to a black hole.

astro-ph.HE↗

arXiv2016

Analytic approximations of neutrino luminosities and heat capacities of neutron stars with nucleon cores

We derive analytic approximations of neutrino luminosities and heat capacities of neutron stars with nucleon cores valid for a wide class of equations of state of dense nucleon matter. The neutrino luminosities are approximated for the three cases in which they are produced by (i) direct Urca or (ii) modified Urca processes in non-superfluid matter, or (iii) neutrino-pair bremsstrahlung in neutron-neutron collisions (when other neutrino reactions are suppressed by strong proton superfluidity). The heat capacity is approximated for the two cases of (i) non-superfluid cores and (ii) the cores with strong proton superfluidity. The results can greatly simplify numerical simulations of cooling neutron stars with isothermal interiors at the neutrino and photon cooling stages as well as simulations of quasi-stationary internal thermal states of neutron stars in X-ray transients. For illustration, a model-independent analysis of thermal states of the latter sources is outlined.

astro-ph.HE↗

arXiv2016

Neutron star properties and the equation of state for its core

Few unified equations of state for neutron star matter where core and crust are described using the same nuclear model are available. However the use of non-unified equations of state with a simplified matching between the crust and the 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. We aim at eliminating the dependence of the radius and mass of neutron staron the detailed model for the crust and on the crust-core matching procedure. We solve the approximate equations of the hydrostatic equilibrium for the crust of neutron stars obtaining a precise formula for the radius which depends only on the core mass and radius, and on the baryon chemical potential at the core-crust interface and on the crust surface. For a fully accreted crust one needs additionally the value of the total deep crustal heating per one accreted nucleon. For typical neutron star masses the approximate approach allows 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. For a given model of dense matter describing the neutron star core, the radius of a neutron star can be accurately determined independently of the crust model with a precision much better than the ~5% one expected from the next generation of X-ray satellites. This allows to circumvent the problem of the radius uncertainty which may arise when non-unified equations of state for the crust and the core are used.

astro-ph.HE↗

arXiv2016

Cooling of neutron stars with diffusive envelopes

We study the effects of heat blanketing envelopes of neutron stars on their cooling. To this aim, we perform cooling simulations using newly constructed models of the envelopes composed of binary ion mixtures (H--He, He--C, C--Fe) varying the mass of lighter ions (H, He or C) in the envelope. The results are compared with those calculated using the standard models of the envelopes which contain the layers of lighter (accreted) elements (H, He and C) on top of the Fe layer, varying the mass of accreted elements. The main effect is that the chemical composition of the envelopes influences their thermal conductivity and, hence, thermal insulation of the star. For illustration, we apply these results to estimate the internal temperature of the Vela pulsar and to study the cooling of neutron stars of ages of 0.1 - 1 Myr at the photon cooling stage. The uncertainties of the cooling models associated with our poor knowledge of chemical composition of the heat insulating envelopes strongly complicate theoretical reconstruction of the internal structure of cooling neutron stars from observations of their thermal surface emission.

astro-ph.HE↗

arXiv2016

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.

astro-ph.HE↗

arXiv2015

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.

astro-ph.SR↗

arXiv2015

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 1.0 13km, 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.

astro-ph.SR↗

arXiv2015

Neutron drip transition in accreting and nonaccreting neutron star crusts

The neutron-drip transition in the dense matter constituting the interior of neutron stars generally refers to the appearance of unbound neutrons as the matter density reaches some threshold density $ρ_\textrm{drip}$. This transition has been mainly studied under the cold catalyzed matter hypothesis. However, this assumption is unrealistic for accreting neutron stars. After examining the physical processes that are thought to be allowed in both accreting and nonaccreting neutron stars, suitable conditions for the onset of neutron drip are derived and general analytical expressions for the neutron drip density and pressure are obtained. Moreover, we show that the neutron-drip transition occurs at lower density and pressure than those predicted within the mean-nucleus approximation. This transition is studied numerically for various initial composition of the ashes from X-ray bursts and superbursts using microscopic nuclear mass models.

astro-ph.HE↗

arXiv2013

On the Maximum Mass of Neutron Stars

One of the most intringuing questions about neutron stars concerns their maximum mass. The answer is intimately related to the properties of matter at densities far beyond that found in heavy atomic nuclei. The current view on the internal constitution of neutron stars and on their maximum mass, both from theoretical and observational studies, are briefly reviewed.

astro-ph.HE↗

arXiv2012

Maximum mass of neutron stars and strange neutron-star cores

Recent measurement of mass of PSR J1614-2230 rules out most of existing models of equation of state (EOS) of dense matter with high-density softening due to hyperonization, based on the recent hyperon-nucleon and hyperon-hyperon interactions, leading to a "hyperon puzzle". We study a specific solution of "hyperon puzzle", consisting in replacing a too soft hyperon core by a sufficiently stiff quark core. We construct an analytic approximation fitting very well modern EOSs of 2SC and CFL color superconducting phases of quark matter. This allows us for simulating continua of sequences of first-order phase transitions from hadronic matter to the 2SC, and then to the CFL state of color superconducting quark matter. We obtain constraints in the parameter space of the EOS of superconducting quark cores, resulting from M_max> 2 M_sol. We also derive constraints that would result from significantly higher measured masses. For 2.4 M_sol required stiffness of the CFL quark core should have been close to the causality limit, the density jump at the phase transition being very small. Condition M_max > 2 M_sol 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. A strict condition of thermodynamic stability of quark phase results in the maximum mass of hybrid stars similar to that of purely baryon stars. Therefore, to get M_max>2 M_sol for stable 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, it is likely that the high density instability of quark matter (reconfinement) indicates actually the inadequacy of the point-particle model of baryons in dense matter at very high densities.

astro-ph.SR↗