arXiv subjects

P. Haensel

Publications and source records attributed to P. Haensel.

At least 19 recordsLinked to original sources

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

Model of heat diffusion in the outer crust of bursting neutron stars

We study heat diffusion after an energy release in a deep spherical layer of the outer neutron star crust (10^7 < ρ< 4 x 10^{11} g/cm^3). We demonstrate that this layer possesses specific heat-accumulating properties, absorbing heat and directing it mostly inside the star. It can absorb up to about 10^{43}-10^{44} erg due to its high heat capacity, until its temperature exceeds T ~ 3 x 10^9 K and triggers a rapid neutrino cooling. A warm layer with T ~ 10^8 - 3 x 10^9 K can serve as a good heat reservoir, which is thermally decoupled from the inner crust and the stellar core for a few months. We present a toy model to explore the heat diffusion within the heat-accumulating layer, and we test this model using numerical simulations. We formulate some generic features of the heat propagation which can be useful, for instance, for the interpretation of superbursts in accreting neutron stars. We present a self-similar analysis of late afterglow after such superbursts, which can be helpful to estimate properties of bursting stars.

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↗

arXiv2019

Bulk viscosity in neutron stars with hyperon cores

It is well-known that r-mode oscillations of rotating neutron stars may be unstable with respect to the gravitational wave emission. It is highly unlikely to observe a neutron star with the parameters within the instability window, a domain where this instability is not suppressed. But if one adopts the `minimal' (nucleonic) composition of the stellar interior, a lot of observed stars appear to be within the r-mode instability window. One of the possible solutions to this problem is to account for hyperons in the neutron star core. The presence of hyperons allows for a set of powerful (lepton-free) non-equilibrium weak processes, which increase the bulk viscosity, and thus suppress the r-mode instability. Existing calculations of the instability windows for hyperon NSs generally use reaction rates calculated for the $Σ^-Λ$ hyperonic composition via the contact $W$ boson exchange interaction. In contrast, here we employ hyperonic equations of state where the $Λ$ and $Ξ^-$ are the first hyperons to appear (the $Σ^-$'s, if they are present, appear at much larger densities), and consider the meson exchange channel, which is more effective for the lepton-free weak processes. We calculate the bulk viscosity for the non-paired $npeμΛΞ^-$ matter using the meson exchange weak interaction. A number of viscosity-generating non-equilibrium processes is considered (some of them for the first time in the neutron-star context). The calculated reaction rates and bulk viscosity are approximated by simple analytic formulas, easy-to-use in applications. Applying our results to calculation of the instability window, we argue that accounting for hyperons may be a viable solution to the r-mode problem.

astro-ph.HE↗

arXiv2018

Bulk viscosity in a neutron star mantle

We study the bulk viscosity in two (anti-spaghetti and Swiss cheese) phases of non- spherical nuclei in the mantle of an oscillating neutron star near the boundary with the stellar core. The bulk viscosity is produced by non-equilibrium Urca neutrino emis- sion processes. In the mantle, the direct Urca process may be open (Gusakov et al., 2004) if neutrons and protons move in a periodic potential created by a lattice of non- spherical nuclei (which allows the nucleons to have large quasi-momenta and satisfy direct Urca momentum-conservation). This bulk viscosity can dominate over that due to the modified Urca process in the outer stellar core and over the shear viscosity. The bulk viscosity depends strongly on temperature, oscillation frequency and nucleon superfluidity. The enhanced bulk viscosity in the mantle can control propagation and damping of neutron star oscillations.

astro-ph.HE↗

arXiv2018

In-medium enhancement of the modified Urca neutrino reaction rates

We calculate modified Urca neutrino emission rates in the dense nuclear matter in neutron star cores. We find that these rates are strongly enhanced in the beta-stable matter in regions of the core close to the direct Urca process threshold. This enhancement can be tracked to the use of the in-medium nucleon spectrum in the virtual nucleon propagator. We describe the in-medium nucleon scattering in the non-relativistic Bruckner-Hartree-Fock framework taking into account two-body as well as the effective three-body forces, although the proposed enhancement does not rely on a particular way of the nucleon interaction treatment. Finally we suggest a simple approximate expression for the emissivity of the n-branch of the modified Urca process that can be used in the neutron stars cooling simulations with any nucleon equation of state of dense matter.

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

Accurate ray tracing of realistic neutron star atmospheres for constraining their parameters

Thermal dominated X-ray spectra of neutron stars in quiescent transient X-ray binaries and neutron stars that undergo thermonuclear bursts are sensitive to mass and radius. The mass-radius relation of neutron stars depends on the equation of state that governs their interior. Constraining this relation accurately is thus of fundamental importance to understand the nature of dense matter. In this context we introduce a pipeline to calculate realistic model spectra of rotating neutron stars with hydrogen and helium atmospheres. An arbitrarily fast rotating neutron star with a given equation of state generates the spacetime in which the atmosphere emits radiation. We use the Lorene/nrotstar code to compute the spacetime numerically and the ATM24 code to solve the radiative transfer equations self-consistently. Emerging specific intensity spectra are then ray-traced through the neutron star's spacetime from the atmosphere to a distant observer with the Gyoto code. Here, we present and test our fully relativistic numerical pipeline. To discuss and illustrate the importance of realistic atmosphere models we compare our model spectra to simpler models like the commonly used isotropic color-corrected blackbody emission. We highlight the importance of considering realistic model-atmosphere spectra together with relativistic ray tracing to obtain accurate predictions. We also insist on the crucial impact of the star's rotation on the observables. Finally, we close a controversy that has been appearing in the literature in the recent years regarding the validity of the ATM24 code.

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

Nuclear symmetry energy and the role of three-body forces

Density dependence of nuclear symmetry energy as well as its partial wave decomposition is studied within the framework of lowest-order constrained variational (LOCV) method using AV18 two-body interaction supplemented by UIX three-body force. The main focus of the present work is to introduce a revised version of three-body force which is based on an isospin-dependent parametrization of coefficients in the UIX force, in order to overcome the inability to produce correct saturation-point parameters} in the framework of LOCV method. We find that employing the new model of {\ph three-body force} in the LOCV formalism leads to successfully reproducing the semi-empirical parameters of cold nuclear matter, including} $E_{sym}(\rho_0)$, $L$, and $K_{sym}$. All our models of three-body force combined with AV18 two-body force give maximum neutron star mass higher than $2\;M_\odot$. The fraction of protons in the nucleon cores of neutron stars strongly depends on the three-body force parametrization.

nucl-th↗

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

Theory of neutrino emission from nucleon-hyperon matter in neutron stars: Angular integrals

Investigations of thermal evolution of neutron stars with hyperon cores require neutrino emissivities for many neutrino reactions involving strongly degenerate particles (nucleons, hyperons, electrons, muons). We calculate the angular integrals $I_n$ (over orientations of momenta of $n$ degenerate particles) for major neutrino reactions with $n$ =3, 4, 5 at all possible combinations of particle Fermi momenta. The integrals $I_n$ are necessary ingredients for constructing a uniform database of neutrino emissivities in dense nucleon-hyperon matter. The results can also be used in many problems of physical kinetics of strongly degenerate systems.

astro-ph.HE↗

arXiv2016

Neutron star radii and crusts: uncertainties and unified equations of state

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]

astro-ph.SR↗

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↗