Evolution Of Neutron Stars Research Articles

Effect of magnetized phonons on electrical and thermal conductivity of neutron star crust

We study electrical and thermal conductivities of degenerate electrons emitting and absorbing phonons in a strongly magnetized crystalline neutron star crust. We take into account modification of the phonon spectrum of a Coulomb solid of ions caused by a strong magnetic field. Boltzmann transport equation is solved using a generalized variational method. The ensuing three-dimensional integrals over the transferred momenta are evaluated by two different numerical techniques, the Monte-Carlo method and a regular integration over the first Brillouin zone. The results of the two numerical approaches are shown to be in a good agreement. An appreciable growth of electrical and thermal resistivities is reported at quantum and intermediate temperatures $T \lesssim 0.1 T_{\rm p}$ ($T_{\rm p}$ is the ion plasma temperature) in a wide range of chemical compositions and mass densities of matter even for moderately magnetized crystals $\omega_{\rm B} \sim \omega_{\rm p}$ ($\omega_{\rm B}$ and $\omega_{\rm p}$ are the ion cyclotron and plasma frequencies). This effect is due to an appearance of a soft ($\omega \propto k^2$) phonon mode in the magnetized ion Coulomb crystal, which turns out to be easier to excite than acoustic phonons characteristic of the field-free case. These results are important for modelling magneto-thermal evolution of neutron stars.

General relativity and neutron stars

General Relativity affects all major aspects of neutron star structure and evolution including radiation from the surface, neutron star models, evolution in compact binaries. It is widely used for neutron star mass measurements and for studying properties of superdense matter in neutron stars. Observations of neutron stars help testing General Relativity and planning gravitational wave experiments. No deviations from Einstein Theory of Gravity have been detected so far from observations of neutron stars.

Simulated magnetic field expulsion in neutron star cores

The study of long-term evolution of neutron star (NS) magnetic fields is key to understanding the rich diversity of NS observations, and to unifying their nature despite the different emission mechanisms and observed properties. Such studies in principle permit a deeper understanding of the most important parameters driving their apparent variety, e.g. radio pulsars, magnetars, x-ray dim isolated neutron stars, gamma-ray pulsars. We describe, for the first time, the results from self-consistent magneto-thermal simulations considering not only the effects of the Hall-driven field dissipation in the crust, but adding a complete set of proposed driving forces in a superconducting core. We emphasize how each of these core-field processes drive magnetic evolution and affect observables, and show that when all forces are considered together in vectorial form, the net expulsion of core magnetic flux is negligible, and will have no observable effect in the crust (consequently in the observed surface emission) on megayear time-scales. Our new simulations suggest that strong magnetic fields in NS cores (and the signatures on the NS surface) will persist long after the crustal magnetic field has evolved and decayed, due to the weak combined effects of dissipation and expulsion in the stellar core.

Physical Environment of Accreting Neutron Stars

Neutron stars (NSs) powered by accretion, which are known as accretion-powered NSs, always are located in binary systems and manifest themselves as X-ray sources. Physical processes taking place during the accretion of material from their companions form a challenging and appealing topic, because of the strong magnetic field of NSs. In this paper, we review the physical process of accretion onto magnetized NS in X-ray binary systems. We, firstly, give an introduction to accretion-powered NSs and review the accretion mechanism in X-ray binaries. This review is mostly focused on accretion-induced evolution of NSs, which includes scenario of NSs both in high-mass binaries and in low-mass systems.

Statistical approach to thermal evolution of neutron stars

Studying thermal evolution of neutron stars (NSs) is one of a few ways to investigate the properties of superdense matter in their cores. We study the cooling of isolated NSs (INSs) and deep crustal heating of transiently accreting NSs in X-ray transients (XRTs, binary systems with low-mass companions). Currently, nearly 50 of such NSs are observed, and one can apply statistical methods to analyze the whole dataset. We propose a method for such analysis based on thermal evolution theory for individual stars and on averaging the results over NS mass distributions. We calculate the distributions of INSs and accreting NSs (ANSs) in XRTs over cooling and heating diagrams respectively. Comparing theoretical and observational distributions one can infer information on physical properties of superdense matter and on mass distributions of INSs and ANSs.

Thermal evolution of hybrid stars within the framework of a nonlocal Nambu–Jona-Lasinio model

We study the thermal evolution of neutron stars containing deconfined quark matter in their core. Such objects are generally referred to as quark-hybrid stars. The confined hadronic matter in their core is described in the framework of non-linear relativistic nuclear field theory. For the quark phase we use a non-local extension of the SU(3) Nambu Jona-Lasinio model with vector interactions. The Gibbs condition is used to model phase equilibrium between confined hadronic matter and deconfined quark matter. Our study indicates that high-mass neutron stars may contain between 35 and 40 % deconfined quark-hybrid matter in their cores. Neutron stars with canonical masses of around $1.4\, M_\odot$ would not contain deconfined quark matter. The central proton fractions of the stars are found to be high, enabling them to cool rapidly. Very good agreement with the temperature evolution established for the neutron star in Cassiopeia A (Cas A) is obtained for one of our models (based on the popular NL3 nuclear parametrization), if the protons in the core of our stellar models are strongly paired, the repulsion among the quarks is mildly repulsive, and the mass of Cas A has a canonical value of $1.4\, M_\odot$.

Evolution of non-spherical pulsars with plasma-filled magnetospheres

Pulsars are famous for their rotational stability. Most of them steadily spin down and display a highly repetitive pulse shape. But some pulsars experience timing irregularities such as nulling, intermittency, mode changing and timing noise. As changes in the pulse shape are often correlated with timing irregularities, precession is a possible cause of these phenomena. Whereas pulsar magnetospheres are filled with plasma, most pulsar precession studies were carried out within the vacuum approximation and neglected the effects of magnetospheric currents and charges. Recent numerical simulations of plasma-filled pulsar magnetospheres provide us with a detailed quantitative description of magnetospheric torques exerted on the pulsar surface. In this paper, we present the study of neutron star evolution using these new torque expressions. We show that they lead to (1) much slower long-term evolution of pulsar parameters and (2) much less extreme solutions for these parameters than the vacuum magnetosphere models. To facilitate the interpretation of observed pulsar timing residuals, we derive an analytic model that (1) describes the time evolution of non-spherical pulsars and (2) translates the observed pulsar timing residuals into the geometrical parameters of the pulsar. We apply this model to two pulsars with very different temporal behaviours. For the pulsar B1828-11, we demonstrate that the timing residual curves allow two pulsar geometries: one with stellar deformation pointing along the magnetic axis and one along the rotational axis. For the Crab pulsar, we use the model show that the recent observation of its magnetic and rotational axes moving away from each other can be explained by precession.

Thermal evolution of neutron stars with decaying magnetic fields

Rotochemical heating originates in the deviation from beta equilibrium due to spin-down compression, which is closely related to the dipole magnetic field. We numerically calculate the deviation from chemical equilibrium and thermal evolution of neutron stars with decaying magnetic fields. We find that the power-law long term decay of the magnetic field slightly affects the deviation from chemical equilibrium and surface temperature. However, the magnetic decay leads to older neutron stars that could have a different surface temperature with the same magnetic field strength. That is, older neutron stars with a low magnetic field (108 G) could have a lower temperature even with rotochemical heating in operation, which probably explains the lack of other observations on older millisecond pulsars with higher surface temperature, except millisecond pulsar J0437–4715.

Thermal properties of hot and dense matter with finite range interactions

We explore the thermal properties of hot and dense matter using a model that reproduces the empirical properties of isospin symmetric and asymmetric bulk nuclear matter, optical model fits to nucleon-nucleus scattering data, heavy-ion flow data in the energy range 0.5-2 GeV/A, and the largest well-measured neutron star mass of 2 $\rm{M}_\odot$. Results of this model which incorporates finite range interactions through Yukawa type forces are contrasted with those of a zero-range Skyrme model that yields nearly identical zero-temperature properties at all densities for symmetric and asymmetric nucleonic matter and the maximum neutron star mass, but fails to account for heavy-ion flow data due to the lack of an appropriate momentum dependence in its mean field. Similarities and differences in the thermal state variables and the specific heats between the two models are highlighted. Checks of our exact numerical calculations are performed from formulas derived in the strongly degenerate and non-degenerate limits. Our studies of the thermal and adiabatic indices, and the speed of sound in hot and dense matter for conditions of relevance to core-collapse supernovae, the thermal evolution of neutron stars from their birth and mergers of compact binary stars reveal that substantial variations begin to occur at sub-saturation densities before asymptotic values are reached at supra-nuclear densities.

THE MEGASECONDCHANDRAX-RAY VISIONARY PROJECT OBSERVATION OF NGC 3115. II. PROPERTIES OF POINT SOURCES

We have carried out an in-depth study of low-mass X-ray binaries (LMXBs) detected in the nearby lenticular galaxy NGC 3115, using the Megasecond Chandra X-Ray Visionary Project observation (total exposure time 1.1 Ms). In total we found 136 candidate LMXBs in the field and 49 in globular clusters (GCs) above 2\sigma\ detection, with 0.3--8 keV luminosity L_X ~10^36-10^39 erg/s. Other than 13 transient candidates, the sources overall have less long-term variability at higher luminosity, at least at L_X > 2x10^37 erg/s. In order to identify the nature and spectral state of our sources, we compared their collective spectral properties based on single-component models (a simple power law or a multicolor disk) with the spectral evolution seen in representative Galactic LMXBs. We found that in the L_X versus photon index \Gamma_PL and L_X versus disk temperature kT_MCD plots, most of our sources fall on a narrow track in which the spectral shape hardens with increasing luminosity below L_X~7x10^37 erg/s but is relatively constant (\Gamma_PL~1.5 or kT_MCD~1.5 keV) above this luminosity, similar to the spectral evolution of Galactic neutron star (NS) LMXBs in the soft state in the Chandra bandpass. Therefore we identified the track as the NS LMXB soft-state track and suggested sources with L_X<7x10^37 erg/s as atolls in the soft state and those with L_X>7x10^37 erg/s as Z sources. Ten other sources (five are transients) displayed significantly softer spectra and are probably black hole X-ray binaries in the thermal state. One of them (persistent) is in a metal-poor GC.

Constraints on millicharged particles by neutron stars

We have constrained the charge-mass ($\varepsilon-m$) phase space of millicharged particles through the simulation of the rotational evolution of neutron stars, where an extra slow-down effect due to the accretions of millicharged dark matter particles is considered. For a canonical neutron star of $M=1.4~M_{\odot}$ and $R=10~{\rm km}$ with typical magnetic field strength $B_{0}=10^{12}$ G, we have shown an upper limit of millicharged particles, which is compatible with recently experimental and observational bounds. Meanwhile, we have also explored the influences on the $\varepsilon-m$ phase space of millicharged particles for different magnetic fields $B_{0}$ and dark matter density $\rho_{\rm{DM}}$ in the vicinity of the neutron star.

Effects of the nuclear equation of state on ther-mode instability and evolution of neutron stars

I study the effect of nuclear equation of state on the r-mode instability of a rotating neutron star. I consider the case where the crust of the neutron star is perfectly rigid and I employ the related theory introduced by Lindblom {\it et al.} \cite{Lidblom-2000}. The gravitational and the viscous time scales, the critical angular velocity and the critical temperature are evaluated by employing a phenomenological nuclear model for the neutron star matter. The predicted equations of state for the $\beta$-stable nuclear matter are parameterized by varying the slope $L$ of the symmetry energy at saturation density on the interval $72.5 {\rm MeV} \leq L \leq 110 {\rm MeV}$. The effects of the density dependence of the nuclear symmetry energy on r-mode instability properties and the time evolution of the angular velocity are presented and analyzed. A comparison of theoretical predictions with observed neutron stars in low-mass x-ray binaries (LMXBs) and millisecond radio pulsars (MSRPs) is also performed and analyzed. I estimate that it may be possible to impose constraints on the nuclear equation of state, by a suitable treatment of observations and theoretical predictions of the rotational frequency and spindown rate evolution of known neutron stars.

Statistical theory of thermal evolution of neutron stars

Thermal evolution of neutron stars is known to depend on the properties of superdense matter in neutron star cores. We suggest a statistical analysis of isolated cooling middle-aged neutron stars and old transiently accreting quasi-stationary neutron stars warmed up by deep crustal heating in low-mass X-ray binaries. The method is based on simulations of the evolution of stars of different masses and on averaging the results over respective mass distributions. This gives theoretical distributions of isolated neutron stars in the surface temperature--age plane and of accreting stars in the photon thermal luminosity--mean mass accretion rate plane to be compared with observations. This approach permits to explore not only superdense matter but also the mass distributions of isolated and accreting neutron stars. We show that the observations of these stars can be reasonably well explained by assuming the presence of the powerful direct Urca process of neutrino emission in the inner cores of massive stars, introducing a slight broadening of the direct Urca threshold (for instance, by proton superfluidity), and by tuning mass distributions of isolated and accreted neutron stars.

Thermal evolution of neutron stars with global and local neutrality

Globally neutral neutron stars, obtained from the solution of the called Einstein-Maxwell-Thomas-Fermi equations that account for all the fundamental interactions, have been recently introduced. These configurations have a more general character than the ones obtained with the traditional Tolman-Oppenheimer-Volkoff, which impose the condition of local charge neutrality. The resulting configurations have a less massive and thinner crust, leading to a new mass-radius relation. Signatures of this new structure of the neutron star on the thermal evolution might be a potential test for this theory. We compute the cooling curves by integrating numerically the energy balance and transport equations in general relativity, for globally neutral neutron stars with crusts of different masses and sizes, according to this theory for different core-crust transition interfaces. We compare and contrast our study with known results for local charge neutrality. We found a new behavior for the relaxation time, depending upon the density at the base of the crust, $\rho_{\rm crust}$. In particular, we find that the traditional increase of the relaxation time with the crust thickness holds only for configurations whose density of the base of the crust is greater than $\approx 5\times 10^{13}$ g cm$^{-3}$. The reason for this is that neutron star crusts with very thin or absent inner crust have some neutrino emission process blocked which keep the crust hotter for longer times. Therefore, accurate observations of the thermal relaxation phase of neutron stars might give crucial information on the core-crust transition which may aid us in probing the inner composition/structure of these objects.

On the cooling of globally-neutral neutron stars

We compute the thermal evolution of neutron stars by taking into account the strong, weak, electromagnetic and gravitational interactions within the framework of general relativity and by satisfying the condition of global, but not local, charge neutrality. We focus on the isothermal phase following the thermal relaxation of the star and compare the result with observational data from isolated neutron stars.

Rotation and cooling of neutron stars

AbstractDriven by the loss of energy, isolated rotating neutron stars (pulsars) are gradually slowing down to lower frequencies, which increases the tremendous compression of the matter inside of them. This increase in compression changes both the global properties of rotating neutron stars as well as their hadronic core compositions. Both effects may register themselves observationally in the thermal evolution of such stars, as demonstrated in this work. The rotation‐driven particle process which we consider here is the direct Urca (DU) process, which is known to become operative in neutron stars if the number of protons in the stellar core exceeds a critical limit of around 11 % to 15 %. We find that neutron stars spinning down from moderately high rotation rates of a few hundred Hertz may be creating just the right conditions where the DU process becomes operative, leading to an observable effect (enhanced cooling) in the temperature evolution of such neutron stars. We will also study the thermal evolution of neutron stars whose spherical symmetry has been broken due to non‐zero rotation. For this we will derive the energy balance and transport equations, taking into account the metric of a rotating fluid distribution and solve these equations numerically. (© 2014 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Evolutions of eccentric binary neutron stars with improved initial data

Evolutions of eccentric binary neutron stars with improved initial data

An investigation into surface temperature distributions of high-magnetic-field pulsars

Abstract Bearing in mind the application to high-magnetic-field (high-B) radio pulsars, we investigate two-dimensional (2D) thermal evolutions of neutron stars (NSs). We pay particular attention to the influence of different equilibrium configurations on the surface temperature distributions. The equilibrium configurations are constructed in a systematic manner, in which both toroidal and poloidal magnetic fields are determined self-consistently with the inclusion of general relativistic effects. To solve the 2D heat transfer inside the NS interior out to the crust, we have developed an implicit code based on a finite-difference scheme that deals with anisotropic thermal conductivity and relevant cooling processes in the context of a standard cooling scenario. In agreement with previous studies, the surface temperatures near the pole become higher than those in the vicinity of the equator as a result of anisotropic heat transfer. Our results show that the ratio of the highest to the lowest surface temperatures changes maximally by one order of magnitude, depending on the equilibrium configurations. Despite such difference, we find that the area of such hot and cold spots is so small that the simulated X-ray spectrum could be well reproduced by a single temperature blackbody fitting.

Unifying neutron stars getting to GUNS

AbstractThe variety of the observational appearance of young isolated neutron stars must find an explanation in the framework of some unifying approach. Nowadays it is believed that such scenario must include magnetic field decay, the possibility of magnetic field emergence on a time scale of ≲104–105 yr, significant contribution of non‐dipolar fields, and appropriate initial parameter distributions. We present our results on the initial spin period distribution, and suggest that inconsistencies between distributions derived by different methods for samples with different average ages can uncover field decay or/and emerging field. We describe a new method to probe the magnetic field decay in normal pulsars. The method is a modified pulsar current approach, where we study pulsar flow along the line of increasing characteristic age for constant field. Our calculations, performed with this method, can be fitted with an exponential decay for ages in the range of 8×104– 3.5×105 yr with a time scale of ∼5×105 yr. We discuss several issues related to the unifying scenario. At first, we note that the dichotomy, among local thermally emitting neutron stars, between normal pulsars and the Magnificent Seven remains unexplained. Then we discuss the role of high‐mass X‐ray binaries in the unification of neutron star evolution. We note, that such systems allow to check evolutionary effects on a time scale longer than what can be probed with normal pulsars alone. We conclude with a brief discussion of the importance of discovering old neutron stars accreting from the interstellar medium. (© 2014 WILEY‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

GENERAL RELATIVISTIC EQUILIBRIUM MODELS OF MAGNETIZED NEUTRON STARS

Magnetic fields play a crucial role in many astrophysical scenarios and, in particular, are of paramount importance in the emission mechanism and evolution of Neutron Stars (NSs). To understand the role of the magnetic field in compact objects it is important to obtain, as a first step, accurate equilibrium models for magnetized NSs. Using the conformally flat approximation we solve the Einstein's equations together with the GRMHD equations in the case of a static axisymmetric NS taking into account different types of magnetic configuration. This allows us to investigate the effect of the magnetic field on global properties of NSs such as their deformation.