Rodrigo Negreiros, Stefan Schramm, Fridolin Weber
The unexpected temperature evolution of the compact object in the Cassiopeia A supernova remnant (Cas A for short) has renewed tremendous interest in the cooling mechanisms of neutron stars. In particular, the formations of superconducting protons and superfluid neutrons in the cores of neutron stars became focal points in the discussions of the observed temperature data of this object. In this paper, we present a systematic study of the effects of proton superconductivity on the cooling of neutron stars. Using the Cas A data as guidance, we study a series of (phenomenological) proton-pairing models to determine the maximum density (henceforth referred to as "depth" of the proton superconducitivity phase) at which one ought to find superconducting protons and establish a (heretofore unkown) relationship between the mass of a neutron star and the depth of the proton superconduciting phase. For example, if the mass of Cas A should be $1.4 \msun$ the depth of the proton superconducting phase will be $3.5 n_0$ (with $n_0$ being the nuclear matter saturation density). If Cas A should be a massive neutron star of $1.8 \msun$, the depth will increase to $5.5 n_0$. Conversely if a reliable microscopic model of proton superconducitivity in neutron star matter will become available in the future, our study will be helpful to reveal the mass of the neutron star in Cas A (or any other neutron star whose temperature has been accurately monitored).
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http://arxiv.org/abs/1305.0845
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