Abstract

Several different processes could be changing the density in the core of a neutron star, leading to a departure from β equilibrium, quantified by the chemical potential difference δμ ≡ μn -μ p - μe. The evolution of this quantity is coupled to that of the star's interior temperature T by two functions that quantify the rate at which neutrino-emitting reactions proceed: the net reaction rate (difference between β decay and capture rates), ΓnetT, δμ). and the total emissivity (total energy-emission rate in the form of neutrinos and antineutrinos), ∈tot(T, δμ). Here, we present a simple and general relationship between these variables, ∂∈tot/∂δμ = 3Γnet, and show that it holds even in the case of superfluid nucleons. This relation may simplify the numerical calculation of these quantities, including superfluid reduction factors. © 2006 RAS.