  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 $\epsilon\sim T^7$. 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 $m$ is the electric screening scale and $m\gg T$ 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.
