We study equation of state (EOS) of an accreting neutron star crust. Usually, such EOS is obtained assuming (implicitly) that the free (unbound) neutrons and nuclei in the inner crust move together. We argue, that this assumption violates the condition $μ_n^\infty={\rm const}$, required for hydrostatic (and diffusion) equilibrium of unbound neutrons ($μ^\infty_n$ is the redshifted neutron chemical potential). We construct a new EOS respecting this condition, working in the compressible liquid-drop approximation. We demonstrate that it is close to the catalyzed EOS in most part of the inner crust, being very different from EOSs of accreted crust discussed in the literature. In particular, the pressure at the outer-inner crust interface does not coincide with the neutron drip pressure, usually calculated in the literature, and is determined by hydrostatic (and diffusion) equilibrium conditions within the star. We also find an instability at the bottom of fully accreted crust that transforms nuclei into homogeneous nuclear matter. It guarantees that the structure of fully accreted crust remains self-similar during accretion.
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 …
Nuclear reactions heat and cool the crust of accreting neutron stars and need to be understood to interpret observations of X-ray bursts and of long-term cooling in transiently accreting systems. It was recently suggested that previously neglected neutron transfer reactions may play a significant role in the nuclear processes. We present results from full nuclear network calculations that now include these reactions and determine their impact on crust composition, crust impurity, heating, and cooling. We find that a large number of neutron transfer reactions indeed occur and impact crust model…
Accreting neutron stars host a number of astronomical observables which can be used to infer the properties of the underlying dense matter. These observables are sensitive to the heating and cooling processes taking place in the accreted neutron star (NS) crust. Within the past few years it has become apparent that electron-capture/beta-decay (urca) cycles can operate within the NS crust at high temperatures. Layers of nuclei undergoing urca cycling can create a thermal barrier, or Great Wall, between heating occurring deep in the crust and the regions above the urca layers. This paper briefly…
Testing the deep-crustal heating model using quiescent neutron-star very-faint X-ray transients and the possibility of partially accreted crusts in accreting neutron stars
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…
Observed thermal emission from accreting neutron stars (NSs) in a quiescent state is believed to be powered by nonequilibrium nuclear reactions that heat the stellar crust (deep crustal heating paradigm). We derive a simple universal formula for the heating efficiency, assuming that an NS has a fully accreted crust. We further show that, within the recently proposed thermodynamically consistent approach to the accreted crust, the heat release can be parametrized by the only one parameter -- the pressure $P_{\rm oi}$ at the outer-inner crust interface (as we argue, this pressure should not nece…
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 h…
$β$-decay Measurements Near the $N=40$ Island of Inversion to Quantify Cooling of Accreted Neutron Star Crusts
Michigan State University（密歇根州立大学）；Facility for Rare Isotope Beams, Michigan State University（稀有同位束设施，密歇根州立大学）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）
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 …
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 consist…
We analyze how the crust equation of state affects several neutron star properties and how it impacts on possible constraints inferred from astrophysical observations. Using three distinct crusts, we generate three sets of model-independent equations of state describing stellar matter from a Taylor expansion around saturation density. The equations of state are thermodynamically consistent, causal, and compatible with astrophysical observations. The relations between the tidal deformability $Λ$ and compactness $C$, Love number $k_2$ and radius of neutron star with mass $M$ are studied, and the…
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…
We study long-term thermal evolution of neutron stars in soft X-ray transients (SXTs), taking the deep crustal heating into account consistently with the changes of the composition of the crust. We collect observational estimates of average accretion rates and thermal luminosities of such neutron stars and compare the theory with observations. We perform simulations of thermal evolution of accreting neutron stars, considering the gradual replacement of the original nonaccreted crust by the reprocessed accreted matter, the neutrino and photon energy losses, and the deep crustal heating due to n…
We study thermal relaxation in a neutron star after internal heating events (outbursts) in the crust. We consider thin and thick spherically symmetric heaters, superfluid and non-superfluid crusts, stars with open and forbidden direct Urca processes in their cores. In particular, we analyze long-term thermal relaxation after deep crustal heating produced by nuclear transformations in fully or partly accreted crusts of transiently accreting neutron stars. This long-term relaxation has a typical relaxation time and an overall finite duration time for the crust to thermally equilibrate with the c…
We present a new mechanism for deep crustal heating in accreting neutron stars. Charged pions ($π^+$) are produced in nuclear collisions on the neutron star surface during active accretion and upon decay they provide a flux of neutrinos into the neutron star crust. For massive and/or compact neutron stars, neutrinos deposit $\approx 1\textrm{--} 2 \, \mathrm{MeV}$ of heat per accreted nucleon into the inner crust. The strength of neutrino heating is comparable to the previously known sources of deep crustal heating, such as from pycnonuclear fusion reactions, and is relevant for studies of coo…
We have monitored the transient neutron star low-mass X-ray binary 1RXS J180408.9-342058 in quiescence after its ~4.5 month outburst in 2015. The source has been observed using Swift and XMM-Newton. Its X-ray spectra were dominated by a thermal component. The thermal evolution showed a gradual X-ray luminosity decay from ~18 x 10^32 to ~4 x 10^32 (D/5.8 kpc)^2 erg s^{-1} between ~8 and ~379 d in quiescence, and the inferred neutron star surface temperature (for an observer at infinity; using a neutron star atmosphere model) decreased from ~100 to ~71 eV. This can be interpreted as cooling of a…
We study the effect of physics input on thermal evolution of neutron stars in soft X-ray transients (SXTs). In particular, we consider different modern models of the sources of deep crustal heating during accretion episodes and the effects brought about by impurities embedded in the crust during its formation. We simulate thermal structure and evolution of episodically accreting neutron stars under different assumptions on the crust composition and on the distribution of heat sources and impurities. For the nonaccreted crust, we consider the nuclear charge fluctuations that arise at crust form…
Role of the crust on the tidal deformability of a neutron star within a unified treatment of dense matter
Institute of Astronomy and Astrophysics, Université Libre de Bruxelles（布鲁塞尔自由大学天文学与天体物理研究所）；LUTH, Observatoire de Paris, PSL Research University, CNRS, Université Paris Diderot, Sorbonne Paris Cité（巴黎天文台宇宙论与天体物理学实验室，巴黎文理研究大学，法国国家科学研究中心，巴黎第七大学，索邦巴黎西岱大学）
We report on two new quiescent {\it XMM-Newton} observations (in addition to the earlier {\it Swift}/XRT and {\it XMM-Newton} coverage) of the cooling neutron star crust in the low-mass X-ray binary 1RXS J180408.9$-$342058. Its crust was heated during the $\sim$4.5 month accretion outburst of the source. From our quiescent observations, fitting the spectra with a neutron star atmosphere model, we found that the crust had cooled from $\sim$ 100 eV to $\sim$73 eV from $\sim$8 days to $\sim$479 days after the end of its outburst. However, during the most recent observation, taken $\sim$860 days a…
Dependable predictions of the X-ray burst ashes and light curves require a stringent constraint on the composition of the accreted material as an input parameter. Lower metallicity models are generally based on a metal deficient donor and all metals are summed up in CNO abundances or solar metal distribution is assumed. In this work, we study the alteration of accreted composition due to spallation in the atmosphere of accreting neutron stars considering a cascading destruction process. We find that the inclusion of the cascading process brings the replenishment of CNO elements and overall sur…
Transiently accreting neutron stars in low mass X-ray binaries are generally believed to be heated up by nuclear reactions in accreted matter during hydrostatic compression. Detailed modeling of these reactions is required for the correct interpretation of observations. In this paper, we construct a simplified reaction network, which can be easily implemented and depends mainly on atomic mass tables as nuclear physics input. We show that it reproduces results of the detailed network by Lau et al. (2018) very well, if one applies the same mass model. However, the composition and the heating pow…
MAXI J0556-332 is the hottest transient accreting neutron star at the beginning of its quiescence. A theoretical model with crustal heating indicates that an additional shallow heat source of Qshallow > 6 MeV per accreted nucleon is required in the shallow outer crust with respect to the deeper star crust by considering the observed decline in accretion rate at the end of outburst. However, the physical source of this shallow heating is still unclear. In the present investigation, we performed stellar evolutionary calculations, adopting the effects of outburst behavior of the accretion rate. A…
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 betwe…
We study the quiescent luminosities of accreting neutron stars by a new mechanism as neutrino heating for additional deep crustal heating, where the neutrino heating is produced by charged pions decay from the nuclear collisions on the surface of neutron star during its active accretion. For low mass neutron star($\lesssim1.4~M_{\odot}$), as the neutrino heating is little($\lesssim1$ MeV per accreted nucleon) or there would be no neutrino heating, the quiescent luminsoity will be not affected or slightly affected. While for massive neutron star ($\gtrsim2~M_{\odot}$), the quiescent luminosity …
We study the relative importance of several recent updates of microphysics input to the neutron star cooling theory and the effects brought about by superstrong magnetic fields of magnetars, including the effects of the Landau quantization in their crusts. We use a finite-difference code for simulation of neutron-star thermal evolution on timescales from hours to megayears with an updated microphysics input. The consideration of short timescales ($\lesssim1$ yr) is made possible by a treatment of the heat-blanketing envelope without the quasistationary approximation inherent to its treatment i…
An accretion outburst onto a neutron star deposits hydrogen-rich and/or helium-rich material into the neutron star's envelope. Thermonuclear burning of accreted material robustly produces Urca pairs\textrm{---}pairs of nuclei that undergo cycles of $e^-$-capture and $β^-$-decay. The strong $T^5$ dependence of the Urca cooling neutrino luminosity means that Urca pairs in the neutron star interior potentially remove heat from accretion-driven nuclear reactions. In this study, we identify Urca pairs in the neutron star's ocean \textrm{---} a plasma of ions and electrons overlaying the neutron sta…
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）
Type-I X-ray bursts are recurring thermonuclear explosions on the surface of accreting neutron stars. Matching observed bursts to computational models can help to constrain system properties, such as the neutron star mass and radius, crustal heating rates, and the accreted fuel composition, but systematic parameter studies to date have been limited. We apply Markov chain Monte Carlo methods to 1D burst models for the first time, and obtain system parameter estimations for the `Clocked Burster', GS 1826$-$238, by fitting multiple observed epochs simultaneously. We explore multiple parameters wh…
Many millisecond pulsars are thought to be old neutron stars spun up (`recycled') during an earlier accretion phase. They typically have relatively weak ($\lesssim 10^{9} \text{ G}$) dipole field strengths, consistent with accretion-induced magnetic burial. Recent data from the Neutron Star Interior Composition Explorer indicate that hot spots atop the recycled pulsar PSR J0030$+$0451 are not antipodal, so that the magnetic field cannot be that of a centered dipole. In this paper it is shown that multipolarity is naturally expected in the burial scenario because of equatorial field line compre…
