Transient LMXBs that host neutron stars (NSs) provide excellent laboratories for probing the dense matter physics present in NS crusts. During accretion outbursts in LMXBs, exothermic reactions may heat the NS crust, disrupting the crust-core equilibrium. When the outburst ceases, the crust cools to restore thermal equilibrium with the core. Monitoring this evolution allows us to probe the dense matter physics in the crust. Properties of the deeper crustal layers can be probed at later times after the end of the outburst. We report on the unexpected late-time temperature evolution (>2000 days after the end of their outbursts) of two NSs in LMXBs, XTE J1701-462 and EXO 0748-676. Although both these sources exhibited very different outbursts (in terms of duration and the average accretion rate), they exhibit an unusually steep decay of ~7 eV in the observed effective temperature (occurring in a time span of ~700 days) around ~2000 days after the end of their outbursts. Furthermore, they both showed an even more unexpected rise of ~3 eV in temperature (over a time period of ~500-2000 days) after this steep decay. This rise was significant at the 2.4σ and 8.5σ level for XTE J1701-462 and EXO 0748-676, respectively. The physical explanation for such behaviour is unknown and cannot be straightforwardly be explained within the cooling hypothesis. In addition, this observed evolution cannot be well explained by low-level accretion either without invoking many assumptions. We investigate the potential pathways in the theoretical heating and cooling models that could reproduce this unusual behaviour, which so far has been observed in two crust-cooling sources. Such a temperature increase has not been observed in the other NS crust-cooling sources at similarly late times, although it cannot be excluded that this might be a result of the inadequate sampling obtained at such late times.
The heating and cooling of transiently accreting neutron stars provides a powerful probe of the structure and composition of their crust. Observations of superbursts and crust cooling of accretion-heated neutron stars require more heat release than is accounted for in current models. Obtaining firm constraints on the depth and magnitude of this extra heat is challenging and therefore its origin remains uncertain. We report on Swift and XMM-Newton observations of the transient neutron star low-mass X-ray binary XTE J1709-267, which were made in 2012 September-October when it transitioned to qui…
We present Rossi X-Ray Timing Explorer and Swift observations made during the final three weeks of the 2006-2007 outburst of the super-Eddington neutron star (NS) transient XTE J1701-462, as well as Chandra and XMM-Newton observations covering the first ~800 days of the subsequent quiescent phase. The source transitioned quickly from active accretion to quiescence, with the luminosity dropping by over 3 orders of magnitude in ~13 days. The spectra obtained during quiescence exhibit both a thermal component, presumed to originate in emission from the NS surface, and a non-thermal component of u…
We monitored the quiescent thermal emission from neutron stars in low-mass X-ray binaries after active periods of intense activity in x-rays (outbursts). The theoretical modeling of the thermal relaxation of the neutron star crust may be used to establish constraints on the crust composition and transport properties, depending on the astrophysical scenarios assumed. We numerically simulated the thermal evolution of the neutron star crust and compared them with inferred surface temperatures for five sources: MXB 1659-29, KS 1731-260, EXO 0748-676, XTE J1701-462 and IGR J17480-2446. We find that…
We discuss candidates for non-radial modes excited in a mass accreting and rapidly rotating neutron star to explain the coherent frequency identified in the light curves of a millisecond X-ray pulsar XTE J1751-305. The spin frequency of the pulsar is $ν_{\rm spin}\cong435$Hz and the identified coherent frequency is $ν_{\rm osc}=0.5727595\timesν_{\rm spin}$. Assuming the frequency identified is that observed in the corotating frame of the neutron star, we find that the surface $r$-modes of $l^\prime=m=1$ and 2 excited by $ε$-mechanism due to helium burning in the thin shell can give the frequen…
X-ray observations of quiescent X-ray binaries have the potential to provide insight into the structure and the composition of neutron stars. EXO 0748-676 had been actively accreting for over 24 yr before its outburst ceased in late 2008. Subsequent X-ray monitoring revealed a gradual decay of the quiescent thermal emission that can be attributed to cooling of the accretion-heated neutron star crust. In this work, we report on new Chandra and Swift observations that extend the quiescent monitoring to ~5 yr post-outburst. We find that the neutron star temperature remained at ~117 eV between 200…
In late 2008, the quasi-persistent neutron star X-ray transient and eclipsing binary EXO 0748-676 started a transition from outburst to quiescence, after it had been actively accreting for more than 24 years. In a previous work, we discussed Chandra and Swift observations obtained during the first five months after this transition. Here, we report on further X-ray observations of EXO 0748-676, extending the quiescent monitoring to 1.6 years. Chandra and XMM-Newton data reveal quiescent X-ray spectra composed of a soft, thermal component that is well-fitted by a neutron star atmosphere model. A…
We present the results of continued monitoring of the quiescent neutron star low-mass X-ray binary XTE J1701-462 with Chandra and Swift. A new Chandra observation from 2010 October extends our tracking of the neutron star surface temperature from ~800 days to ~1160 days since the end of an exceptionally luminous 19 month outburst. This observation indicates that the neutron star crust may still be slowly cooling toward thermal equilibrium with the core; another observation further into quiescence is needed to verify this. The shape of the overall cooling curve is consistent with that of a brok…
It is now possible to model thermal relaxation of neutron stars after bouts of accretion during which the star is heated out of equilibrium by nuclear reactions in its crust. Major uncertainties in these models can be encapsulated in modest variations of a handful of fudge parameters that change the crustal thermal conductivity, specific heat, and heating rates. Observations of thermal relaxation constrain these fudge parameters and allow us to predict longer term variability in terms of the neutron star core temperature. We demonstrate this explicitly by modeling ongoing thermal relaxation in…
A quasi-statistical equilibrium model is constructed to simulate the multicomponent composition of the crust of an accreting neutron star. The ashes of rp-process nucleosynthesis are driven by accretion through a series of electron captures, neutron emissions, and pycnonuclear fusions up to densities near the transition between the neutron star crust and core. A liquid droplet model which includes nuclear shell effects is used to provide nuclear masses far from stability. Reaction pathways are determined consistently with the nuclear mass model. The nuclear symmetry energy is an important unce…
The accretion behaviour in low-mass X-ray binaries (LMXBs) at low luminosities, especially at <E34 erg/s, is not well known. This is an important regime to study to obtain a complete understanding of the accretion process in LMXBs, and to determine if systems that host neutron stars with accretion-heated crusts can be used probe the physics of dense matter (which requires their quiescent thermal emission to be uncontaminated by residual accretion). Here we examine ultraviolet (UV) and X-ray data obtained when EXO 0748-676, a crust-cooling source, was in quiescence. Our Hubble Space Telescope s…
On a re-examination of neutron star cooling in transient sources -- No shallow heating required?
Institut d’Astronomie et d’Astrophysique, Université Libre de Bruxelles（布鲁塞尔自由大学天体物理研究所）；Departamento de Astrofísica, Universidad de La Laguna（拉古纳大学天体物理学系）；Instituto de Astrofísica de Canarias（加那利天体物理研究所）；Center for Nuclear Astrophysics across Messengers (CeNAM)（跨信使核天体物理学中心）；Instituto de Astronomía, Universidad Nacional Autónoma de México（墨西哥国立自治大学天文学研究所）
The deep crustal heating, associated with exothermal nuclear reactions, is believed to be a key parameter for describing the thermal evolution of accreting neutron stars. In this paper, we present the first thermodynamically consistent calculations of the crustal heating for realistic compositions of thermonuclear ashes. In contrast to previous studies based on the traditional approach, we account for neutron hydrostatic/diffusion (nHD) equilibrium condition imposed by superfluidity of neutrons in a major part of the inner crust and rapid diffusion in the remaining part of the inner crust. We …
We propose a new heating mechanism in magnetar crusts. Magnetars' crustal magnetic fields are much stronger than their surface fields; therefore, magnetic pressure partially supports the crust against gravity. The crust loses magnetic pressure support as the field decays and must compensate by increasing the electron degeneracy pressure; the accompanying increase in the electron Fermi energy induces nonequilibrium, exothermic electron captures. The total heat released via field-decay electron captures is comparable to the total magnetic energy in the crust. Thus, field-decay electron captures …
Observed temperatures of transiently accreting neutron stars in the quiescent state are generally believed to be supported by deep crustal heating, associated with non-equilibrium exothermic reactions in the crust. Traditionally, these reactions are studied by considering nuclear evolution governed by compression of the accreted matter. Here we show that this approach has a basic weakness, that is that in some regions of the inner crust the conservative forces, applied for matter components (nuclei and neutrons), are not in mechanical equilibrium. In principle the force balance can be restored…
Neutron stars in low-mass binary systems are subject to accretion. The common assumption in studying the properties of the neutron star crust is the fully accreted crust approximation. However, observations of some X-ray transient sources indicate that the original crust has not been completely replaced by accreted material, but is partly composed of the compressed original crust. A two-part (or hybrid) crust made of the original crust that is compressed and of the accreted material crashing onto it was reconstructed as a function of the accretion stage. The differences in the composition and …
The neutron star low-mass X-ray binary EXO 0748-676 started a transition from outburst to quiescence in August 2008, after more than 24 years of continuous accretion. The return of the source to quiescence has been monitored extensively by several X-ray observatories. Here, we report on four XMM-Newton observations elapsing a period of more than 19 months and starting in November 2008. The X-ray spectra show a soft thermal component which we fit with a neutron star atmosphere model. Only in the first observation do we find a significant second component above ~ 3 keV accounting for ~ 7 % of th…
Thermal evolution of neo-neutron stars. II. Temperature-dependent crusts
National Institute for Physics and Nuclear Engineering (IFIN-HH)（罗马尼亚国家物理与核工程研究所）；Instituto de Astronomía, Universidad Nacional Autónoma de México（墨西哥国立自治大学天文学研究所）
The neutron star ocean is a plasma of ions and electrons that extends from the base of the neutron star's envelope to a depth where the plasma crystallizes into a solid crust. During an accretion outburst in an X-ray transient, material accumulates in the envelope of the neutron star primary. This accumulation compresses the neutron star's outer layers and induces nuclear reactions in the ocean and crust. Accretion-driven heating raises the ocean's temperature and increases the frequencies of g-modes in the ocean; when accretion halts, the ocean cools and ocean g-mode frequencies decrease. If …
The authors try to probe the inner components of rapidly rotating compact stars such as the millisecond pulsar SAX J1808.4-3658 and the possible sub-millisecond pulsar XTE J1739-285 in their own way by comparing the genuine rotation frequencies under different theoretical models with the observational data, which may exert more stringent constraint on matter composition of compact stars. According to their treatment, the SAX J1808.4-3658 is a star with exotic matter and XTE J1739-285 a hybrid star.
Transient neutron star (NS) LMXBs undergo episodes of accretion, alternated with quiescent periods. During an accretion outburst, the NS heats up due to exothermic accretion-induced processes taking place in the crust. Besides the long-known deep crustal heating of nuclear origin, a likely non-nuclear source of heat, dubbed 'shallow heating', is present at lower densities. Most of the accretion-induced heat slowly diffuses into the core on a timescale of years. Over many outburst cycles, a state of equilibrium is reached when the core temperature is high enough that the heating and cooling (ph…
We investigate outer crust compositions for a wide range of magnetic field strengths, up to $B\simeq 4\times10^{18}$ G, employing the latest experimental nuclear masses supplemented with various mass models. The essential effects of the magnetic field are twoholds: 1) Enhancement of electron fraction, which is connected to that of protons via the charge neutrality condition, due to the Landau-Rabi quantization of electron motion perpendicular to the field, namely, neutron-richness is suppressed for a given pressure. As a result, 2) nuclei can exist at higher pressures without dripping out neut…
The persistent thermal luminosity of magnetars and their outbursts suggest the existence of some internal heat sources located in their outer crust. The compression of matter accompanying the decay of the magnetic field may trigger exothermic electron captures and, possibly, pycnonuclear fusions of light elements that may have been accreted onto the surface from the fallback of supernova debris, from a disk or from the interstellar medium. This scenario bears some resemblance to deep crustal heating in accreting neutron stars, although the matter composition and the thermodynamic conditions ar…
We present a simple model for electron transport in a possible layer of exotic nuclear clusters (in the so called nuclear pasta layer) between the crust and liquid core of a strongly magnetized neutron star. The electron transport there can be strongly anisotropic and gyrotropic. The anisotropy is produced by different electron effective collision frequencies along and across local symmetry axis in domains of exotic ordered nuclear clusters and by complicated effects of the magnetic field. We also calculate averaged kinetic coefficients in case local domains are freely oriented. Possible appli…
We examine to what extent the inferred surface temperature of magnetars in quiescence can constrain the presence of a superfluid in the neutron star core and the role of magnetic field decay in the core. By performing detailed simulations of neutron star cooling, we show that extremely strong heating from field decay in the core cannot produce the high observed surface temperatures nor delay the onset of neutron superfluidity in the core. We verify the results of Kaminker et al., namely that the high magnetar surface temperatures require heating in the neutron star crust, and crust heating is …
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 u…
We discuss different exotic phases and components of matter from the crust to the core of neutron stars based on theoretical models for equations of state relevant to core collapse supernova simulations and neutron star merger. Parameters of the models are constrained from laboratory experiments. It is observed that equations of state involving strangeness degrees of freedom such as hyperons and Bose-Einstein condensates are compatible with 2M$_{solar}$ neutron stars. The role of hyperons is explored on the evolution and stability of the protoneutron star (PNS) in the context of SN1987A. Momen…
We present results of targeted searches for signatures of non-radial oscillation modes (such as r- and g-modes) in neutron stars using {\it RXTE} data from several accreting millisecond X-ray pulsars (AMXPs). We search for potentially coherent signals in the neutron star rest frame by first removing the phase delays associated with the star's binary motion and computing FFT power spectra of continuous light curves with up to $2^{30}$ time bins. We search a range of frequencies in which both r- and g-modes are theoretically expected to reside. Using data from the discovery outburst of the 435 H…
Exotic non-spherical configurations of nuclei, known as ``pasta" phases, are expected to be present at the bottom of the inner crust of a neutron star. We study the properties of these configurations in catalyzed neutron stars within a compressible liquid-drop model approach, with surface parameters optimized to reproduce experimental nuclear masses. Our results show that the properties of the pasta phases exhibit strong model dependence. To estimate the model uncertainties, a Bayesian analysis is performed, combining information from nuclear physics experiments and chiral perturbation theoret…
Neutron Star Mass-Radius Constraints for EXO 0748$-$676 from 2008-2025 Quiescent X-ray Spectra
Xiamen University（厦门大学）；Yunnan Observatories, Chinese Academy of Sciences (CAS)（中国科学院云南天文台）；Key Laboratory for the Structure and Evolution of Celestial Objects, CAS（中国科学院天体结构与演化重点实验室）
Rapidly rotating neutron stars in Low Mass X-ray Binaries have been proposed as an interesting source of gravitational waves. In this chapter we present estimates of the gravitational wave emission for various scenarios, given the (electromagnetically) observed characteristics of these systems. First of all we focus on the r-mode instability and show that a 'minimal' neutron star model (which does not incorporate exotica in the core, dynamically important magnetic fields or superfluid degrees of freedom), is not consistent with observations. We then present estimates of both thermally induced …
We present upper limits on the amplitude of r-mode oscillations, and gravitational-radiation-induced spin-down rates, in low mass X-ray binary neutron stars, under the assumption that the quiescent neutron star luminosity is powered by dissipation from a steady-state r-mode. For masses $< 2 M_{\odot}$ we find dimensionless r-mode amplitudes in the range from about $1\times 10^{-8}$ to $1.5\times 10^{-6}$. For the accreting millisecond X-ray pulsar sources with known quiescent spin-down rates these limits suggest that $\lesssim 1%$ of the observed rate can be due to an unstable r-mode. Interest…
We perform a systematic analysis of neutron star radius constraints from five quiescent low-mass X-ray binaries and examine how they depend on measurements of their distances and amounts of intervening absorbing material, as well as their assumed atmospheric compositions. We construct and calibrate to published results a semi-analytic model of the neutron star atmosphere which approximates these effects for the predicted masses and radii. Starting from mass and radius probability distributions established from hydrogen-atmosphere spectral fits of quiescent sources, we apply this model to compu…
Modelling of crust heating and cooling across multiple accretion outbursts of the low mass X-ray binary MXB 1659-29 indicates that the neutrino luminosity of the neutron star core is consistent with direct Urca reactions occurring in $\sim 1\%$ of the core volume. We investigate this scenario with neutron star models that include a detailed equation of state parametrized by the slope of the nuclear symmetry energy $L$, and a range of neutron and proton superfluid gaps. We find that the predicted neutron star mass depends sensitively on $L$ and the assumed gaps. We discuss which combinations of…
Unified equations of state for cold nonaccreting neutron stars with Brussels-Montreal functionals. V. Improved parametrization of the nucleon density distributions
New {\em ab initio} constrained extended Skyrme equations of state for simulations of neutron stars, supernovae and binary mergers: I. Subsaturation density domain
