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Vortex Dynamics in Color-Superconducting Quark stars: The Re-heating of Magnetars

Compact stars made of quark matter rather than confined hadronic matter, are expected to form a color superconductor. This superconductor ought to be threaded with rotational vortex lines within which the star's interior magnetic field is confined. The vortices (and thus magnetic flux) would be expelled from the star during stellar spin-down, leading to magnetic reconnection at the surface of the star and the prolific production of thermal energy. In this Letter, we show that this energy release can re-heat quark stars to exceptionally high temperatures, such as observed for Soft Gamma Repeaters (SGRs), Anomalous X-Ray pulsars (AXPs), and X-ray dim isolated neutron stars (XDINs). Moreover, our numerical investigations of the temperature evolution, spin-down rate, and magnetic field behavior of such superconducting quark stars suggest that SGRs, AXPs, and XDINs may be linked ancestrally. Finally, we discuss the possibility of a time delay before the star enters the color superconducting phase, which can be used to estimate the density at which quarks deconfine. We find this density to be five times that of nuclear saturation.