On the cooling of neutron stars

Abstract

It has recently been pointed out that many models of dense nuclear matter allow the direct URCA process in highly dense systems like neutron stars. In view of this, we have calculated the energy loss in dense nuclear matter as a result of such processes at finite temperatures. For the description of nuclear matter we have used Walecka's mean-field theory. For the neutrino emissivity rates we have employed the Iwamoto model and evaluated the angular integrals involved exactly. We find that the emissivity rate is density dependent, being almost a constant at high densities, while at low densities it shows an exponential behaviour with temperature rather than the usual power law.

Bulk viscosity of strange quark matter in density dependent quark mass model

“…where  is given in [7]. For the sake of completeness, we reproduce the rather complicated expression for the angular integral  in the Appendix.…”

“…Neutrino cooling, once thought to be one of the best discriminating criterion, have lost much of its glamour since the revival of ordinary URCA processes in nuclear matter has narrowed down the difference in the expected neutrino cooling rates from two types of matter [6,7].…”

Neutrino opacity in magnetized hot and dense nuclear matter

“…The proton fraction calculation in nuclear matter is however very sensitive to the assumption that go into the microscopic theory of nuclear interactions which are not well known [15]. In the present work, this constraint is satisfied at moderately high densities namely n B > 1.5n 0 (see also [11,16]), whereas in some recent potential models with three-body interactions and boost corrections, this occurs at densities in excess of ∼ 4.5n 0 [17].Since the effect of magnetic field is to increase the proton fraction, at sufficiently high magnetic fields depending on the density, the constraint is satisfied and direct URCA process proceeds. In the case of extremely high magnetic fields capable of confining electrons and protons into the lowest Landau level, this constraint is not even required and the absorption process proceeds as can be seen from equation (42).…”

“…This effect on the dominant reaction ν e + n → p + e at densities near the electron-neutrino sphere was calculated by multyplying the phase space distribution of the final state electrons only and leaving the matrix elements unchanged [7]. However it was noted [8] that in the presence of large magnetic field ∼ 10 16 Gauss even the motion of degenerate electrons, at densities likely to be present near the neutrino sphere, is quantised and on account of charge neutrality viz. n e = n p , the protons too are forced to occupy the lowest Landau level.…”

Diffusion of neutrinos in proto-neutron star matter with quarks

“…We note that similar techniques were employed to calculate ν−emissivities in cold catalyzed neutron stars in Refs. [13,14]. (1) Scattering of degenerate neutrinos: The result is the same as for neutrino-electron scattering:…”