Thermal relaxation in young neutron stars

Abstract

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.

Electron thermal conductivity owing to collisions between degenerate electrons

“…The conductivity κ ei is calculated using the formalism of Potekhin et al [12] and Gnedin et al [6].…”

“…[6]) for the same values of T , and the solid lines give the total conductivity κ e . For T = 10 8 and 10 9 , the effects of possible impurities in dense matter (atomic nuclei with charge numbers Z imp different from charge numbers Z i of ground-state nuclei) are expected to be small (e.g., Gnedin et al [6]). At T = 10 7 K, the effects of impurities can be substantial.…”

“…These fit expressions reproduce also all asymptotic limits mentioned above. The maximum fit errors of I l , I t , and I lt are, respectively, 0.2% (at u = 0.61 and θ = 3.8), 6.3% (at u = 0.878 and θ ∼ 0.175, where the electrons become nondegenerate) and 8.4% (at u = 0.19 and θ = 19). The maximum fit error of the total function I in Eq.…”

“…It is needed to study cooling of white dwarfs (e.g., Prada Moroni and Straniero [3]) and nuclear explosions of massive white dwarfs as type Ia supernovae (e.g., Baraffe, Heger and Woosley [4]). In neutron star envelopes it is required for many reasons -for simulating cooling of isolated neutron stars (see, e.g., Lattimer et al [5], Gnedin, Yakovlev and Potekhin [6], Page, Geppert and Weber [7]); for studying heat propagation and thermal relaxation in a neutron star envelope in response to the various processes of crustal energy release. In particular, these processes include pulsar glitches (e.g., Larson and Link [8], and references therein), deep crustal heating of accreting neutron stars in soft X-ray transients (e.g., Ushomirsky and Rutledge [9]), superbursts as powerful nuclear explosions at the base of the outer crust of an accreting neutron star (e.g., Strohmayer and Bildsten [10]; Page and Cumming [11]).…”

“…It is widely believed that the dominant contribution into κ e comes from the ei collisions. The associated partial conductivity κ ei has been studied in a number of papers (e.g., Potekhin et al [12], Gnedin et al [6] and references therein). The partial thermal conductivity κ ee owing to the ee collisions was calculated by Lampe [13], Flowers and Itoh [14], Urpin and Yakovlev [15], and Timmes [16].…”