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.

The internal properties of the neutron star crust can be probed by observing the epoch of thermal relaxation. After the supernova explosion, powerful neutrino emission quickly cools the stellar core, while the crust stays hot. The cooling wave then propagates through the crust, as a result of its finite thermal conductivity. When the cooling wave reaches the surface (age 10–100 yr), the effective temperature drops sharply from 250 eV to 30 or 100 eV, depending on the cooling model. The crust relaxation time is sensitive to the (poorly known) microscopic properties of matter of subnuclear density, such as the heat capacity, thermal conductivity, and superfluidity of free neutrons. We calculate the cooling models with the new values of the electron thermal conductivity in the inner crust, based on a realistic treatment of the shapes of atomic nuclei. Superfluid effects may shorten the relaxation time by a factor of 4. The comparison of theoretical cooling curves with observations provides a potentially powerful method of studying the properties of the neutron superfluid and highly unusual atomic nuclei in the inner crust.

We study the thermal structure of neutron stars with magnetized envelopes composed of accreted material, using updated thermal conductivities of plasmas in quantizing magnetic fields, as well as the equation of state and radiative opacities for partially ionized hydrogen in strong magnetic fields. The relation between the internal and local surface temperatures is calculated and fitted by an analytic function of the internal temperature, magnetic field strength, angle between the field lines and the normal to the surface, surface gravity, and the mass of the accreted material. The luminosity of a neutron star with a dipole magnetic field is calculated for various values of the accreted mass, internal temperature, and magnetic field strength. Using these results, we simulate cooling of superfluid neutron stars with magnetized accreted envelopes. We consider slow and fast cooling regimes, paying special attention to very slow cooling of low-mass, superfluid neutron stars. In the latter case, the cooling is strongly affected by the combined effect of magnetized accreted envelopes and neutron superfluidity in the stellar crust. Our results are important for the interpretation of observations of the isolated neutron stars hottest for their age, such as RX J0822À43 and PSR B1055À52.

Abstract. The upper limit on the effective surface temperature of the neutron star (NS) PSR J0205+6449 in the supernova remnant 3C 58 obtained recently by Slane et al. (2002) is analyzed using a modern theory of NS cooling . The observations can be explained by cooling of a superfluid NS with the core composed of neutrons, protons, and electrons, where direct Urca process is forbidden. However, combined with the data on the surface temperatures of other isolated NSs, it gives evidence (emphasized by Slane et al.) that direct Urca process is open in the inner cores of massive NSs. This evidence turns out to be less stringent than that provided by the well known observations of Vela and Geminga.