We explore the thermal state of the neutron star in the Cassiopeia A supernova remnant using the recent result of Ho & Heinke ( 24 ) 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 .