  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.
