Neutrino Emission from Ungapped Quark Matter

We study neutrino emission from a normal, ungapped, quark phase in the core of a compact star. Neutrino emission from non-interacting quark matter leads to an emissivity that scales as $ϵ\sim T^7$. We show that the emissivity is enhanced by a combination of Fermi liquid and non-Fermi liquid effects. Fermi liquid effects lead to an emissivity that scales as $\epsilon\sim \alpha_s T^6$, as originally shown by Iwamoto. We demonstrate that non-Fermi liquid effects further enhance the rate, leading to $\epsilon\sim \alpha_s^3 T^6\log(m/T)^2$,where$m$istheelectricscreeningscaleand$m\gg T$ under the conditions found in compact stars. We show, however, that combined with non-Fermi liquid effects in the specific heat the enhancement in the emissivity only leads to a modest reduction in the temperature of the star at late times. Our results confirm existing bounds on the presence of ungapped quark matter in compact stars. We also discuss neutrino emission from superconducting phases with ungapped fermionic excitations.