Urca Cooling in Neutron Star Crusts and Oceans: Effects of Nuclear Excitations

The excited-state structure of atomic nuclei can modify nuclear processes in stellar environments. In this Letter, we study the influence of nuclear excitations on Urca cooling (repeated back-and-forth $\beta$ decay and electron capture in a pair of nuclear isotopes) in the crust and ocean of neutron stars. We provide for the first time an expression for Urca process neutrino luminosity which accounts for a thermal Boltzmann distribution of excited states in both members of an Urca pair. We use our new formula with state-of-the-art nuclear structure inputs to compute neutrino luminosities of candidate Urca cooling pairs. Our nuclear inputs consist of the latest experimental data supplemented with calculations using the projected shell model. We show that, in contrast to previous results that only consider the ground states of both nuclei in the pair, our calculated neutrino luminosities for different Urca pairs vary sensitively with the environment temperature and can be radically different from those obtained in the one-transition approximation. We find that nuclear excitations can lead to an enhancement in total Urca neutrino luminosities in the accreted neutron star crust by about 5 times as compared with the previous Urca results, which is expected to cause significant observational effects.

Figure 1

Schematic energy diagram for the Urca process. EC and ${\beta }^{-}$ decay cycle rapidly between nuclear states with energies $E\lesssim kT$ when the electron chemical potential ${\mu }_e$ is sufficient to overcome the $Q$ value (${\mu }_e\approx |Q_{ϵ\beta }|$).

Figure 2

(a) Schematic nuclear energy-level diagrams for the ${}^{31}\mathrm{Al}\text{−}{}^{31}\mathrm{Mg}$ $\mathrm{EC}/{\beta }^{-}$-decay Urca pair for neutron star crust. The energies (in keV) and $J^{\pi }$ for the ground states and lowest-lying states, as well as the available data and calculated results (in parentheses) for $\log ft$ of transitions in ${\beta }^{-}$-decays between different states are shown. (b). The corresponding $L_{34}$ calculated by Eqs. (3) and (6) as functions of temperature $T_9$. Calculations with all transitions considered are compared with those with one transition as well as the previous result. See text for details.

Figure 3

The same as Fig. 2 but for the ${}^{25}\mathrm{Mg}\text{−}{}^{25}\mathrm{Na}$ $\mathrm{EC}/{\beta }^{-}$-decay Urca pair for neutron star ocean.

Figure 4

Updated total neutrino luminosities for the NS crust compared with the previous results, as well as those from electron-nucleus bremsstrahlung and plasmon decay. The crust heating band indicates a representative range of accretion-driven heating rates for observed neutron stars [13].