According to recent results of Ho & Heinke, the Cassiopeia A supernova remnant contains a young (≈330-yr-old) neutron star (NS) which has carbon atmosphere and shows notable decline of the effective surface temperature. We report a new (2010 November) 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 cn (ρ) for the onset of neutron superfluidity [T cn (ρ) should have a wide peak with maximum ≈ (7-9) × 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.

We calculate the shear viscosity η ≈ ηeµ +ηn in a neutron star core composed of nucleons, electrons and muons (ηeµ being the electron-muon viscosity, mediated by collisions of electrons and muons with charged particles, and ηn the neutron viscosity, mediated by neutron-neutron and neutronproton collisions). Deriving ηeµ, we take into account the Landau damping in collisions of electrons and muons with charged particles via the exchange of transverse plasmons. It lowers ηeµ and leads to the non-standard temperature behavior ηeµ ∝ T −5/3 . The viscosity ηn is calculated taking into account that in-medium effects modify nucleon effective masses in dense matter. Both viscosities, ηeµ and ηn, can be important, and both are calculated including the effects of proton superfluidity. They are presented in the form valid for any equation of state of nucleon dense matter. We analyze the density and temperature dependence of η for different equations of state in neutron star cores, and compare η with the bulk viscosity in the core and with the shear viscosity in the crust.

We simulate the cooling of the neutron star in the X‐ray transient KS 1731−260 after the source returned to quiescence in 2001 from a long (≳12.5 yr) outburst state. We show that the cooling can be explained assuming that the crust underwent deep heating during the outburst stage. In our best theoretical scenario the neutron star has no enhanced neutrino emission in the core, and its crust is thin, superfluid, and has the normal thermal conductivity. The thermal afterburst crust–core relaxation in the star may not be over.

We explore the thermal state of the neutron star in the Cassiopeia A supernova remnant using the recent result of Ho & Heinke 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 candlesstars 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 , 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 ( 10 −13 M ) carbon envelope, we find the efficiency f ∼ 1 (standard cooling) for x 0.5 and f ∼ 0.02 (slower cooling) for a maximum compactness x ≈ 0.7. A heat blanket containing the maximum mass (∼10 −8 M ) of light elements increases f by a factor of 50. We also examine the (unlikely) possibility that the star is still thermally non-relaxed.

X-ray observations of transiently accreting neutron stars during quiescence provide information about the structure of neutron star crusts and the properties of dense matter. Interpretation of the observational data requires an understanding of the nuclear reactions that heat and cool the crust during accretion, and define its nonequilibrium composition. We identify here in detail the typical nuclear reaction sequences down to a depth in the inner crust where the mass density is ρ = 2 × 10 12 g cm −3 using a full nuclear reaction network for a range of initial compositions. The reaction sequences differ substantially from previous work. We find a robust reduction of crust impurity at the transition to the inner crust regardless of initial composition, though shell effects can delay the formation of a pure crust somewhat to densities beyond ρ = 2 × 10 12 g cm −3 . This naturally explains the small inner crust impurity inferred from observations of a broad range of systems. The exception are initial compositions with A ≥ 102 nuclei, where the inner crust remains impure with an impurity parameter of Q imp ≈ 20 due to the N = 82 shell closure. In agreement with previous work we find that nuclear heating is relatively robust and independent of initial composition, while cooling via nuclear Urca cycles in the outer crust depends strongly on initial composition. This work forms a basis for future studies of the sensitivity of crust models to nuclear physics and provides profiles of composition for realistic crust models.

We calculate the thermal conductivity of electrons and muons κeµ produced owing to electromagnetic interactions of charged particles in neutron star cores and show that these interactions are dominated by the exchange of transverse plasmons (via the Landau damping of these plasmons in nonsuperconducting matter and via a specific plasma screening in the presence of proton superconductivity). For normal protons, the Landau damping strongly reduces κeµ and makes it temperature independent. Proton superconductivity suppresses the reduction and restores the Fermi-liquid behavior κeµ ∝ T −1 . Comparing with the thermal conductivity of neutrons κn, we obtain κeµ κn for T 2 × 10 9 K in normal matter and for any T in superconducting matter with proton critical temperatures Tcp 3 × 10 9 K. The results are described by simple analytic formulae. PACS numbers: 52.25.Fi, 95.30.Tg, 97.20.Rp, 97.60.Jd II. ELECTRON-MUON THERMAL CONDUCTIVITY IN NORMAL MATTERThe electrons and muons in a neutron star core constitute strongly degenerate almost ideal Fermi gases [1]. The electrons are ultrarelativistic. The muons can be

The thermal evolution of young neutron stars (NSs) reflects the neutrino emission properties of their cores. Heinke & Ho (2010) measured a 3.6 ± 0.6% decay in the surface temperature of the Cassiopeia A (Cas A) NS between 2000 and 2009, using archival data from the Chandra X-ray Observatory ACIS-S detector in Graded mode. Page et al. (2011) andShternin et al. (2011) attributed this decay to enhanced neutrino emission from a superfluid neutron transition in the core. Here we test this decline, combining analysis of the Cas A NS using all Chandra X-ray detectors and modes (HRC-S, HRC-I, ACIS-I, ACIS-S in Faint mode, and ACIS-S in Graded mode) and adding a 2012 May ACIS-S Graded mode observation, using the most current calibrations (CALDB 4.5.5.1). We measure the temperature changes from each detector separately and test for systematic effects due to the nearby filaments of the supernova remnant. We find a 0.92%-2.0% decay over 10 years in the effective temperature, inferred from HRC-S data, depending on the choice of source and background extraction regions, with a best-fit decay of 1.0 ± 0.7%. In comparison, the ACIS-S Graded data indicate a temperature decay of 3.1%-5.0% over 10 years, with a best-fit decay of 3.5 ± 0.4%. Shallower observations using the other detectors yield temperature decays of 2.6 ± 1.9% (ACIS-I), 2.1 ± 1.0% (HRC-I), and 2.1 ± 1.9% (ACIS-S Faint mode) over 10 years. Our best estimate indicates a decline of 2.9 ± 0.5 stat ± 1.0 sys % over 10 years. The complexity of the bright and varying supernova remnant background makes a definitive interpretation of archival Cas A Chandra observations difficult. A temperature decline of 1-3.5% over 10 years would indicate extraordinarily fast cooling of the NS that can be regulated by superfluidity of nucleons in the stellar core.

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. arXiv:1711.06520v3 [astro-ph.HE] 29 Oct 2018 65 References 66 I. INTRODUCTION A. ContextTransport describes how conserved quantities such as energy, momentum, particle number, or electric charge are transferred from one region to another. Such a transfer occurs if the system is out of equilibrium, for instance through a temperature gradient or a non-uniform chemical composition. Different theoretical methods are used to understand transport, depending on how far the system is away from its equilibrium state. If the system is close to equilibrium locally and perturbations are on large scales in space and time, hydrodynamics is a powerful technique. Further away from equilibrium other techniques are required, for example kinetic theory, which can also be used to provide the transport coefficients needed in the hydrodynamic equations. In any case, transport is determined by interactions on a microscopic level, and it is the resulting transport properties that we are concerned with in this review.Signals from neutron stars are sensitive to equilibrium properties such as the equation of state but also, to a large extent, to transport properties -here, by neutron stars we mean all objects with a radius of about 10 km and a mass of about 1-2 solar masses, including the possibilities of hybrid stars, which have a quark matter core, and pure quark stars. Therefore, understanding transport is crucial to interpret astrophysical observations, and, turning the argument around, we can use astrophysical observations to improve our understanding of transport in dense matter and thus ultimately our understanding of the microscopic interactions.Transport properties are most commonly computed from particle collisions. (Although, in strongly coupled systems, the picture of well-defined particles scattering off each other has to be taken with care.) These can be scattering processes in which energy and momentum is exchanged without changing the chemical composition of the system, or these can be flavor-changing processes from the electroweak interaction. Understanding transport thus amounts to understanding the rates of these processes, as a function of temperature and density. Electroweak processes are well understood, but large uncertainties arise if the strong interaction is involved in a reaction that contributes to transport. Therefore, approximations such as weak-coupling techniques or one-pion exchange for nucleon-nucleon collisions are being used, and efforts in current research aim at improving these approximations.In a neutron star, most of the particles involved in these processes are fermions: electrons, muons, neutrinos, neutrons, protons, hyperons, and quarks. Since the Fermi momenta of these fermions are typically much larger tha...