On the Limitations of Neutrino Emissivity Formula of Iwamoto

The neutrino emissivity from two and three flavour quark matter is numerically calculated and compared with Iwamoto's formula. We find that the calculated emissivity is smaller than Iwamoto's result by orders of magnitude when $p_{f}(u)+p_{f}(e)-p_{f}(d(s))$ is comparable with the temperature. We attribute it to the severe restriction imposed by momentum conservation on the phase space integral. We obtain an alternate formula for the neutrino emissivity which is valid when the quarks and electrons are degenerate and $p_{f}(u)~+~p_{f}(e)~-~p_{f}(d(s))$ is large compared to the temperature.