We explore the thermal state of the neutron star in the Cassiopeia Asupernova remnant using the recent result of Ho & Heinke (Nature, 462, 71(2009)) that the thermal radiation of this star is well-described by a carbonatmosphere model and the emission comes from the entire stellar surface.Starting from neutron star cooling theory, we formulate a robust method toextract neutrino cooling rates of thermally relaxed stars at the neutrinocooling stage from observations of thermal surface radiation. We show how tocompare these rates with the rates of standard candles -- stars withnon-superfluid nucleon cores cooling slowly via the modified Urca process. Wefind that the internal temperature of standard candles is a well-definedfunction of the stellar compactness parameter $x=r_g/R$, irrespective of theequation of state of neutron star matter ($R$ and $r_g$ are circumferential andgravitational radii, respectively). We demonstrate that the data on theCassiopeia 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 blanketingenvelope. 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 $f_\ell \sim 0.02$ (slowercooling) for a maximum compactness $x\approx 0.7$. A heat blanket containingthe 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 isstill thermally non-relaxed.
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