Neutrino Emission From Direct Urca Processes in Pion Condensed Quark Matter

We study neutrino emission from direct Urca processes in pion condensed quark matter. In compact stars with high baryon density, the emission is dominated by the gapless modes of the pion condensation which leads to an enhanced emissivity. While for massless quarks the enhancement is not remarkable, the emissivity is significantly larger and the cooling of the condensed matter is considerably faster than that in normal quark matter when the mass difference between $u$- and $d$-quarks is sizable.