Cooling rates of neutron stars and the young neutron star in the Cassiopeia A supernova remnant

We explore the thermal state of the neutron star in the Cassiopeia A supernova remnant using the recent result of Ho & Heinke (Nature, 462, 71 (2009)) that the thermal radiation of this star is well-described by a carbon atmosphere model and the emission comes from the entire stellar surface. Starting from neutron star cooling theory, we formulate a robust method to extract neutrino cooling rates of thermally relaxed stars at the neutrino cooling stage from observations of thermal surface radiation. We show how to compare these rates with the rates of standard candles -- stars with non-superfluid nucleon cores cooling slowly via the modified Urca process. We find that the internal temperature of standard candles is a well-defined function of the stellar compactness parameter \(x=r_g/R\), irrespective of the equation of state of neutron star matter (\(R\) and \(r_g\) are circumferential and gravitational radii, respectively). We demonstrate that the data on the Cassiopeia A neutron star can be explained in terms of three parameters: \(f_\ell\), the neutrino cooling efficiency with respect to the standard candle; the compactness \(x\); and the amount of light elements in the heat blanketing envelope. For an ordinary (iron) heat blanketing envelope or a low-mass (\(\lesssim 10^{-13}\,M_\odot\)) carbon envelope, we find the efficiency \(f_\ell \sim 1\) (standard cooling) for \(x \lesssim 0.5\) and \(f_\ell \sim 0.02\) (slower cooling) for a maximum compactness \(x\approx 0.7\). A heat blanket containing the maximum mass (\(\sim 10^{-8}\,M_\odot\)) of light elements increases \(f_\ell\) by a factor of 50. We also examine the (unlikely) possibility that the star is still thermally non-relaxed.