Non-Equilibrium Beta Processes in Neutron Stars: A Relationship between the Net Reaction Rate and the Total Emissivity of Neutrinos

Abstract

Several different processes could be changing the density in the core of a neutron star, leading to a departure from $\beta$ equilibrium, quantified by the chemical potential difference $\delta \mu \equiv {\mu }_n-{\mu }_p-{\mu }_e$. 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 $\beta$ decay and capture rates), ${\Gamma }_{\mathrm{net}}(T,\delta \mu )$, and the total emissivity (total energy emission rate in the form of neutrinos and antineutrinos), ${\epsilon }_{\mathrm{tot}}(T,\delta \mu )$. Here, we present a simple and general relationship between these variables, $\partial {\epsilon }_{\mathrm{tot}}/\partial \delta \mu =3{\Gamma }_{\mathrm{net}}$, 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.

Accepted for publication in MNRAS. 8 pages, non tables nor figures, uses aastex.cls

References in corpus (1)

• Non-equilibrium beta processes in superfluid neutron star cores

Cited by in corpus (1)

• Internal heating and thermal emission from old neutron stars: Constraints on dense-matter and gravitational physics