Constraining dense matter superfluidity through thermal emission from millisecond pulsars

As a neutron star spins down, the diminishing centrifugal force gradually increases the density of any given fluid element in the star's interior. Since the ''chemical'' (or ''beta'') equilibrium state is determined by the local density, this process leads to a chemical imbalance quantified by a chemical potential difference, e.g., delta mu = mu(n) - mu(p) - mu e, where n, p, and e denote neutrons, protons, and electrons. In the presence of superfluid energy gaps, in this case Delta(n) and Delta(p), reactions are strongly inhibited as long as both Delta(m)u and kT are much smaller than the gaps. Thus, no restoring mechanism is available, and the imbalance will grow unimpeded until delta mu = delta mu(thr) similar to Delta(n) + Delta(p). At this threshold, the reaction rate increases dramatically, preventing further growth of delta mu and converting the excess chemical energy into heat. The thermal luminosity resulting from this ''rotochemical heating'' process is L similar to 2 x 10(-4)(Delta mu(thr)/0.1 MeV)(E) over dot(rot), similar to the typical X-ray luminosity of pulsars with spin-down power (E) over dot(rot). The threshold imbalance, and therefore the luminous stage, are only reached by stars whose initial rotation period is P-i less than or similar to 13(delta mu(thr)/0.1 MeV)(-1/2)ms, i.e., millisecond pulsars. A preliminary study of 11 millisecond pulsars with reported ROSAT observations shows that the latter can already be used to start constraining superfluid energy gaps in the theoretically interesting range, approximately 0.1-1 MeV.