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Numerous models of neutron star (NS) equation of state (EoS) exist based on different superdense-matter physics approaches. Nevertheless, some NS properties show universal (EoS-independent) relations. Here, we propose a novel class of such universalities. Despite different physics inputs, a wide class of realistic nucleonic, hyperonic, and hybrid EoS models can be accurately described using only three parameters. For a given EoS, these are the mass and radius of the maximum-mass NS (or pressure and density in its center) and the radius of a half-maximum-mass star. With such a parametrization, we build universal analytic expressions for mass-radius and pressure-density relations. They form a semi-analytic mapping from the mass-radius relation to the EoS in NS cores (the so-called inverse Oppenheimer-Volkoff mapping). This mapping simplifies the process of inferring the EoS from observations of NS masses and radii. Applying it to current NS observations we set new limits on the high-density end of the EoS., Comment: Main text: 11 pages, 8 figures, 2 tables + Appendix: 8 pages, 1 figures, 2 tables

Analysis of Chandra observations of the neutron star (NS) in the centre of the Cassiopeia A supernova remnant taken in the subarray (FAINT) mode of the ACIS detector performed by Posselt and collaborators revealed, after inclusion of the most recent (May 2020) observations, a significant decrease of the source surface temperature from 2006 to 2020. The obtained cooling rate is consistent with those obtained from analysis of the 2000$-$2019 data taken in the GRADED mode of the ACIS detector, which is potentially more strongly affected by instrumental effects. We performed a joint spectral analysis using all ACIS data to constrain the NS parameters and cooling rate. We constrain the mass of the Cassiopeia A NS at $M=1.55\pm0.25~M_\odot$, and its radius at $R=13.5\pm 1.5$ km. The surface temperature cooling rate is found to be $2.2\pm 0.3$ per cent in 10 years if the absorbing hydrogen column density is allowed to vary and $1.6\pm 0.2$ per cent in 10 years if it is fixed. The observed cooling can be explained by enhanced neutrino emission from the superfluid NS interior due to Cooper Pair Formation (CPF) process. Based on analysis of all ACIS data, we constrain the maximal critical temperature of triplet neutron pairing within the NS core at $(4-9.5)\times 10^{8}$ K. In accordance with previous studies, the required effective strength of the CPF neutrino emission is at least a factor of 2 higher than existing microscopic calculations suggest., Comment: 20 pages, 17 figures. Accepted for publication in MNRAS

We review the calculations of the kinetic coefficients (thermal conductivity, shear viscosity, momentum transfer rates) of the neutron star core matter within the framework of the Landau Fermi-liquid theory. We restrict ourselves to the case of normal (i.e. non-superfluid) matter. As an example we consider simplest $npe\mu$ composition of neutron star core matter. Utilizing the CompOSE database of dense matter equations of state and several microscopic interactions we analyze the uncertainties in calculations of the kinetic coefficients that result from the insufficient knowledge of the properties of the dense nuclear matter and suggest possible approximate treatment. In our study we also take into account non-quantizing magnetic field. The presence of magnetic field makes transport anisotropic leading to the tensor structure of kinetic coefficients. We find that the moderate ($B\lesssim 10^{12}$ G) magnetic field do not affect considerably thermal conductivity of neutron star core matter, since the latter is mainly governed by the electrically neutral neutrons. In contrast, shear viscosity is affected even by the moderate $B\sim 10^8 - 10^{10}$ G. Based on the in-vacuum nucleon interactions we provide practical expressions for calculation of transport coefficients for any equation of state of dense matter., Comment: 53 pages, 12 figures; accepted for publication in European Physical Journal A

We present analysis of multiple Chandra and XMM-Newton spectra, separated by 9-19 years, of four of the youngest central compact objects (CCOs) with ages < 2500 yr: CXOU J232327.9+584842 (Cassiopeia A), CXOU J160103.1-513353 (G330.2+1.0), 1WGA J1713.4-3949 (G347.3-0.5), and XMMU J172054.5-372652 (G350.1-0.3). By fitting these spectra with thermal models, we attempt to constrain each CCO's long-term cooling rate, composition, and magnetic field. For the CCO in Cassiopeia A, 14 measurements over 19 years indicate a decreasing temperature at a ten-year rate of 2.2+/-0.2 or 2.8+/-0.3 percent (1sigma error) for a constant or changing X-ray absorption, respectively. We obtain cooling rate upper limits of 17 percent for CXOU J160103.1-513353 and 6 percent for XMMU J172054.5-372652. For the oldest CCO, 1WGA J1713.4-3949, its temperature seems to have increased by 4+/-2 percent over a ten year period. Assuming each CCO's preferred distance and an emission area that is a large fraction of the total stellar surface, a non-magnetic carbon atmosphere spectrum is a good fit to spectra of all four CCOs. If distances are larger and emission areas are somewhat smaller, then equally good spectral fits are obtained using a hydrogen atmosphere with B <= 7x10^10 G or B >= 10^12 G for CXOU J160103.1-513353, B <= 10^10 G or B >= 10^12 G for XMMU J172054.5-372652, and non-magnetic hydrogen atmosphere for 1WGA J1713.4-3949. In a unified picture of CCO evolution, our results suggest most CCOs, and hence a sizable fraction of young neutron stars, have a surface magnetic field that is low early in their life but builds up over several thousand years., Comment: 15 pages, 9 figures; accepted for publication in MNRAS

We consider transport properties of the hypernuclear matter in neutron star cores. In particular, we calculate the thermal conductivity, the shear viscosity, and the momentum transfer rates for np$\Sigma^{-}\Lambda e\mu$ composition of dense matter in $\beta$--equilibrium for baryon number densities in the range $0.1-1$~fm$^{-3}$. The calculations are based on baryon interactions treated within the framework of the non-relativistic Brueckner-Hartree-Fock theory. Bare nucleon-nucleon (NN) interactions are described by the Argonne v18 phenomenological potential supplemented with the Urbana IX three-nucleon force. Nucleon-hyperon (NY) and hyperon-hyperon (YY) interactions are based on the \new{NSC97e and NSC97a models} of the Nijmegen group. We find that the baryon contribution to transport coefficients is dominated by the neutron one as in the case of neutron star cores containing only nucleons. In particular, we find that neutrons dominate the total thermal conductivity over the whole range of densities explored and that, due to the onset of $\Sigma^-$ which leads to the deleptonization of the neutron star core, they dominate also the shear viscosity in the high density region, in contrast with the pure nucleonic case where the lepton contribution is always the dominant one., Comment: 22 pages, 10 figures, accepted in the Universe, the special issue "Fundamental Processes in Neutron Stars and Supernovae"

We present a new model-independent (applicable for a broad range of equations of state) analysis of the neutrino emissivity due to triplet neutron pairing in neutron star cores. We find that the integrated neutrino luminosity of the Cooper Pair Formation (CPF) process can be written as a product of two factors. The first factor depends on the neutron star mass, radius and maximal critical temperature of neutron pairing in the core, $T_{Cn \mathrm{max}}$, but not on the particular superfluidity model; it can be expressed by an analytical formula valid for many nucleon equations of state. The second factor depends on the shape of the critical temperature profile within the star, the ratio of the temperature $T$ to $T_{Cn \mathrm{max}}$, but not on the maximal critical temperature itself. While this second factor depends on the superfluidity model, it obeys several model-independent constraints. This property allows one to analyse the thermal evolution of neutron stars with superfluid cores without relying on a specific model of their interiors. The constructed expressions allow us to perform a self-consistent analysis of spectral data and neutron star cooling theory. We apply these findings to the cooling neutron star in the Cassiopeia A supernova remnant using 14 sets of observations taken over 19 years. We constrain $T_{Cn\mathrm{max}}$ to the range of $ (5-10)\times 10^8$ K. This value depends weakly on the equation of state and superfluidity model, and will not change much if cooling is slower than the current data suggest. We also constrain the overall efficiency of the CPF neutrino luminosity., Comment: 18 pages, 14 figures, 6 tables; accepted for publication in MNRAS

We formulate hydrodynamic equations for nonsuperfluid multicomponent magnetized charged relativistic mixtures, taking into account chemical reactions as well as viscosity, diffusion, thermodiffusion, and thermal conductivity effects. The resulting equations have a rather simple form and can be readily applied, e.g., for studying magnetothermal evolution of neutron stars. We also establish a link between our formalism and the results known in the literature, and express the phenomenological diffusion coefficients through momentum transfer rates which are calculated from microscopic theory., Comment: 25 pages, 2 figures, published in PRD

We consider the thermal conductivity, shear viscosity, and momentum relaxation rates in the nucleon cores of the neutron stars. We study how the choice of the nuclear interaction and the model for three-body forces may affect these transport coefficients calculated within the Brueckner-Hartree-Fock many-body nuclear theory. We find that at relatively large densities the model dependence of the results is substantial. In addition we provide the analytical approximations which allow to incorporate our results in practical simulations., Comment: 18 pages; 17 figures; minor edits to match the accepted version

The bright radio pulsar B1727$-$47 with a characteristic age of 80 kyr is among the first pulsars discovered 50 yr ago. Using its regular timing observations and interferometric positions at three epochs, we measured, for the first time, the pulsar proper motion of $151 \pm 19$ mas yr$^{-1}$. At the dispersion measure distance of $\gtrsim 2.7$ kpc, this would suggest a record transverse velocity of the pulsar $\gtrsim 1900$ km s$^{-1}$. However, a backward extrapolation of the pulsar track to its birth epoch points remarkably close to the center of the evolved nearby supernova remnant RCW 114, which suggests genuine association of the two objects. In this case, the pulsar is substantially closer ($\sim 0.6$ kpc) and younger ($\sim 50$ kyr), and its velocity ($\sim400$ km s$^{-1}$) is compatible with the observed pulsar velocity distribution. We also identified two new glitches of the pulsar. We discuss implications of our results on the pulsar and remnant properties., Comment: 21 pages, 13 figures; accepted to ApJ

Now 50 years since the existence of the neutron star crust was proposed, we review the current understanding of the nuclear physics of the outer layers of accreting neutron stars. Nuclei produced during nuclear burning replace the nascent composition of the neutron star ocean and crust. Non-equilibrium nuclear reactions driven by compression alter the outer thermal structure and chemical composition, leaving observable imprints on astronomical phenomena. As observations of bursting neutron stars and cooling neutron stars have increased, the recent volume of astronomical data allows new insights into the microphysics of the neutron star interior and the possibility to test nuclear physics input in model calculations. Despite numerous advances in our understanding of neutron star interiors and observed neutron star phenomena, many challenges remain in the astrophysics theory of accreting neutron stars, the nuclear theory of neutron-rich nuclei, and the reach and precision of terrestrial nuclear physics experiments., Comment: Invited review to appear in Journal of Physics G (70 pages)

I consider the thermal conductivity and shear viscosity of leptons (electrons and muons) in the nucleon NS cores where protons are in the superconducting state. I restrict the consideration to the case of not too high temperatures $T\lesssim 0.35T_{\mathrm{c}p}$, where $T_{\mathrm{c}p}$ is the critical temperature of the proton pairing. In this case, lepton collisions with protons can be neglected. Charged lepton collision frequencies are mainly determined by the transverse plasmon exchange and are mediated by the character of the transverse plasma screening. In our previous works [Shternin \& Yakovlev, Phys. Rev. D {\bf 75} 103004 (2007); {\bf 78} 063006 (2008)] the superconducting proton contribution to the transverse screening was considered in the Pippard limit $\Delta \ll \hbar q v_{\mathrm{F}p}$, where $\Delta$ is the proton pairing gap, $v_{\mathrm{F}p}$ is the proton Fermi velocity, and $\hbar q$ is the typical transferred momentum in collisions. However, for large critical temperatures (large $\Delta$) and relatively small densities (small $q$) the Pippard limit may become invalid. In the present study I show that this is indeed the case and that the older calculations severely underestimated the screening in a certain range of the parameters appropriate to the neutron star cores. As a consequence, the kinetic coefficients at $T\ll T_{\mathrm{c}p}$ are found to be smaller than in previous calculations., Comment: 18 pages, 11 figures, accepted for publication in PRD. In v.2 new figure 9 is added and BSK21 results are corrected

Understanding signals from neutron stars requires knowledge about the transport inside the star. We review the transport properties and the underlying reaction rates of dense hadronic and quark matter in the crust and the core of neutron stars and point out open problems and future directions., Comment: 74 pages; commissioned for the book "Physics and Astrophysics of Neutron Stars", NewCompStar COST Action MP1304; version 3: minor changes, references updated, overview graphic added in the introduction, improvements in Sec IV.A.4

Calvera is an unusual isolated neutron star with pure thermal X-ray spectrum typical for central compact objects in supernova remnants. On the other hand, its rotation period and spin-down rate are typical for ordinary rotation-powered pulsars. It was discovered and studied in X-rays and not yet detected in other spectral domains. We present deep optical imaging of the Calvera field obtained with the Gran Telescopio Canarias in $g'$ and $i'$ bands. Within $\approx 1^{\prime\prime}$ vicinity of Calvera, we detected two point-like objects invisible at previous shallow observations. However, accurate astrometry showed that none of them can be identified with the pulsar. We put new upper limits on its optical brightness of $g' > 27.87$ and $i' > 26.84$. We also reanalyzed all available archival X-ray data on Calvera. Comparison of the Calvera thermal emission parameters and upper limits on optical and non-thermal X-ray emission with respective data on rotation-powered pulsars shows that Calvera might belong to the class of ordinary middle-aged pulsars, if we assume that its distance is in the range of $1.5-5$ kpc., Comment: 20 pages, 5 figures, 4 tables

We analysed Chandra observations of the bright Fermi pulsar J0633+0632 and found evidence of an absorption feature in its spectrum at $804^{+42}_{-26}$ eV (the errors here and below are at 90% confidence) with equivalent width of $63^{+47}_{-36}$ eV. In addition, we analysed in detail the X-ray spectral continuum taking into account correlations between the interstellar absorption and the distance to the source. We confirm early findings by Ray et al. (2011) that the spectrum contains non-thermal and thermal components. The latter is equally well described by the blackbody and magnetised atmosphere models and can be attributed to the emission from the bulk of the stellar surface in both cases. The distance to the pulsar is constrained in a range of 1--4 kpc from the spectral fits. We infer the blackbody surface temperature of $108^{+22}_{-14}$ eV, while for the atmosphere model, the temperature, as seen by a distant observer, is $53^{+12}_{-7}$ eV. In the latter case J0633+0632 is one of the coldest middle-aged isolated neutron stars with measured temperatures. Finally, it powers an extended pulsar wind nebula whose shape suggests a high pulsar proper motion. Looking backwards the direction of the presumed proper motion we found a likely birthplace of the pulsar -- the Rosette nebula, a 50-Myr-old active star-forming region located at about 1$.\!\!^\circ$5 from the pulsar. If true, this constrains the distance to the pulsar in the range of 1.2--1.8 kpc., Comment: 15 pages, 9 figures, 3 tables

PSR J2021+3651 is a 17 kyr old rotation powered pulsar detected in the radio, X-rays, and $\gamma$-rays. It powers a torus-like pulsar wind nebula with jets, dubbed the Dragonfly, which is very similar to that of the Vela pulsar. The Dragonfly is likely associated with the extended TeV source VER J2019+368 and extended radio emission. We conducted first deep optical observations with the GTC in the Sloan $r'$ band to search for optical counterparts of the pulsar and its nebula. No counterparts were detected down to $r'\gtrsim27.2$ and $\gtrsim24.8$ for the point-like pulsar and the compact X-ray nebula, respectively. We also reanalyzed Chandra archival X-ray data taking into account an interstellar extinction--distance relation, constructed by us for the Dragonfly line of sight using the red-clump stars as standard candles. This allowed us to constrain the distance to the pulsar, $D=1.8^{+1.7}_{-1.4}$ kpc at 90% confidence. It is much smaller than the dispersion measure distance of $\sim$12 kpc but compatible with a $\gamma$-ray "pseudo-distance" of 1 kpc. Based on that and the optical upper limits, we conclude that PSR J2021+3651, similar to the Vela pulsar, is a very inefficient nonthermal emitter in the optical and X-rays, while its $\gamma$-ray efficiency is consistent with an average efficiency for $\gamma$-pulsars of similar age. Our optical flux upper limit for the pulsar is consistent with the long-wavelength extrapolation of its X-ray spectrum while the nebula flux upper limit does not constrain the respective extrapolation., Comment: 17 pages, 4 figures, 1 table, accepted for publication in ApJ

A middle-aged radio-quiet pulsar J0357+3205 was discovered in gamma-rays with $Fermi$ and later in X-rays with $Chandra$ and $XMM$-$Newton$ observatories. It produces an unusual thermally-emitting pulsar wind nebula observed in X-rays. Deep optical observations were obtained to search for the pulsar optical counterpart and its nebula using the Gran Telescopio Canarias (GTC). The direct imaging mode in the Sloan $g'$ band was used. Archival X-ray data were reanalysed and compared with the optical data. No pulsar optical counterpart was detected down to $g'\geq~28_{\cdotp}^{\text{m}}1$. No pulsar nebula was either identified in the optical. We confirm early results that the X-ray spectrum of the pulsar consists of a nonthermal power-law component of the pulsar magnetospheric origin dominating at high energies and a soft thermal component from the neutron star surface. Using magnetised partially ionised hydrogen atmosphere models in X-ray spectral fits we found that the thermal component can come from entire surface of the cooling neutron star with a temperature of 36$^{+9}_{-6}$ eV, making it one of the coldest among cooling neutron stars known. The surface temperature agrees with the standard neutron star cooling scenario. The optical upper limit does not put any additional constraints on the thermal component, however it implies a strong spectral break for the nonthermal component between the optical and X-rays as is observed in other middle-aged pulsars. The thermal emission from the entire surface of the neutron star likely dominates over the nonthermal emission in the UV range. Observations of the PSR J0357+3205 in this range are promising to put more stringent constraints on its thermal properties., Comment: 7 pages, 6 figures, 2 tables, accepted for publication in Astronomy and Astrophysics

According to recent results of Ho & Heinke (2009) and Heinke & Ho (2010), the Cassiopeia A supernova remnant contains a young neutron star which has carbon atmosphere and shows noticeable decline of the effective surface temperature. We report a new (November 2010) Chandra observation which confirms the previously reported decline rate. The decline is naturally explained if neutrons have recently become superfluid (in triplet-state) in the NS core, producing a splash of neutrino emission due to Cooper pair formation (CPF) process that currently accelerates the cooling. This scenario puts stringent constraints on poorly known properties of NS cores: on density dependence of the temperature $T_\mathrm{cn}(\rho)$ for the onset of neutron superfluidity [$T_\mathrm{cn}(\rho)$ should have a wide peak with maximum $\approx (7-9)\times 10^8$ K], on the reduction factor $q$ of CPF process by collective effects in superfluid matter ($q > 0.4$), and on the intensity of neutrino emission before the onset of neutron superfluidity (30--100 times weaker than the standard modified Urca process). This is serious evidence for nucleon superfluidity in NS cores that comes from observations of cooling NSs., Comment: 6 pages, 3 figures, accepted for publication in MNRAS Letters

We explore the thermal state of the neutron star in the Cassiopeia A supernova remnant using the recent result of Ho & Heinke (Nature, 462, 71 (2009)) that the thermal radiation of this star is well-described by a carbon atmosphere model and the emission comes from the entire stellar surface. Starting from neutron star cooling theory, we formulate a robust method to extract neutrino cooling rates of thermally relaxed stars at the neutrino cooling stage from observations of thermal surface radiation. We show how to compare these rates with the rates of standard candles -- stars with non-superfluid nucleon cores cooling slowly via the modified Urca process. We find that the internal temperature of standard candles is a well-defined function of the stellar compactness parameter $x=r_g/R$, irrespective of the equation of state of neutron star matter ($R$ and $r_g$ are circumferential and gravitational radii, respectively). We demonstrate that the data on the Cassiopeia A neutron star can be explained in terms of three parameters: $f_\ell$, the neutrino cooling efficiency with respect to the standard candle; the compactness $x$; and the amount of light elements in the heat blanketing envelope. For an ordinary (iron) heat blanketing envelope or a low-mass ($\lesssim 10^{-13}\,M_\odot$) carbon envelope, we find the efficiency $f_\ell \sim 1$ (standard cooling) for $x \lesssim 0.5$ and $f_\ell \sim 0.02$ (slower cooling) for a maximum compactness $x\approx 0.7$. A heat blanket containing the maximum mass ($\sim 10^{-8}\,M_\odot$) of light elements increases $f_\ell$ by a factor of 50. We also examine the (unlikely) possibility that the star is still thermally non-relaxed., Comment: accepted for publication in MNRAS; 12 pages, 6 figures