Neutrino Pair Emission from Cooper Pair Breaking and Recombination in Superfluid Quark Matter

For the low energy Standard Model neutrino-matter interactions, we calculate neutrino pair (νν̄) emissivites in superfluid quark matter. Just below the critical temperature, Cooper pairs continuously break and recombine, resulting in the emission of νν̄ pairs with a rate that greatly exceeds the standard quark modified Urca and bremsstrahlung rates. At the same baryon density in baryonic and quark matter, the ratio of baryon to quark νν̄ emissivites lies in the range 2−5 for the densities of interest in the long-term cooling of solar mass compact stars. We also find that in matter containing hyperons, νν̄ emission can occur with hyperons of all species. PACS: 97.60.Jd, 24.85.+p, 26.60.+c, 95.30.Cq In a prescient paper, Flowers, Ruderman, and Sutherland [1] showed that just below the critical temperature Tc, the neutrino pair (νν̄) emissivity from the breaking and recombination of superfluid neutron pairs (n+n → n+ n+ ν + ν̄) greatly exceeds that from the so-called modified Urca processes (n+ n → n+ p+ e + ν̄ and n+ p → n+ n+ e + ν) in neutron star interiors. It is only recently that the pair breaking and formation (PBF) processes have been included in calculations of the long term cooling of neutron stars [2]. The principal effect of the PBF process is to rapidly cool the star during its early hundreds of years of thermal evolution, until competing ν-emitting processes (for recent reviews see Ref. [3]) begin to dominate the further cooling of the star for several thousands or million years that they might remain observable with such instruments as HST, Chandra, and XMM. The precise extent to which the core temperature falls depends on the smallest of the pairing gaps among the superfluid species present in the star (cf. [4] and references therein). To date, the role of PBF processes has been explored only for baryon superfluidity [2]. In this work, we calculate the νν̄ emissivity in superfluid quark matter likely to be encountered in neutron star interiors [5]. For the low energy Standard Model neutrino-matter interactions, we show that the predominant contribution to the total νν̄ emissivity comes from the vector channel, while the axial channel provides a small correction. This heirarchy is similar to that found in baryonic matter [1]. We also consider the effect of quark masses on the emissivities in limiting cases. We compare our results for νν̄ emissivities with those of the modified Urca and bremsstrahlung processes in both quark and nucleonic matter [6–8]. Expected νν̄ emissivities from hyperons in baryonic matter and from p-wave pairing in quark matter are also addressed.