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A superconductor of paired protons is thought to form in the core of neutron stars soon after their birth. Minimum energy conditions suggest magnetic flux is expelled from the superconducting region due to the Meissner effect, such that the neutron star core is largely devoid of magnetic fields for some nuclear equation of state and proton pairing models. We show via neutron star cooling simulations that the superconducting region expands faster than flux is expected to be expelled because cooling timescales are much shorter than timescales of magnetic field diffusion. Thus magnetic fields remain in the bulk of the neutron star core for at least 10^6-10^7 yr. We estimate the size of flux free regions at 10^7 yr to be <~ 100 m for a magnetic field of 10^11 G and possibly smaller for stronger field strengths. For proton pairing models that are narrow, magnetic flux may be completely expelled from a thin shell of approximately the above size after 10^5 yr. This shell may insulate lower conductivity outer layers, where magnetic fields can diffuse and decay faster, from fields maintained in the highly conducting deep core.
The thermal evolution of isothermal neutron stars is studied with matter both in the hadronic phase as well as in the mixed phase of hadronic matter and strange quark matter. In our models, the dominant early-stage cooling process is neutrino emissio
Isolated neutron stars show a diversity in timing and spectral properties, which has historically led to a classification in different sub-classes. The magnetic field plays a key role in many aspects of the neutron star phenomenology: it regulates th
We present models of temperature distribution in the crust of a neutron star in the presence of a strong toroidal component superposed to the poloidal component of the magnetic field. The presence of such a toroidal field hinders heat flow toward the
In this review, I present a brief summary of the impact of nucleon pairing at supra-nuclear densities on the cooling of neutron stars. I also describe how the recent observation of the cooling of the neutron star in the supernova remnant Cassiopeia A
Observations of thermal radiation from neutron stars can potentially provide information about the states of supranuclear matter in the interiors of these stars with the aid of the theory of neutron-star thermal evolution. We review the basics of thi