CONSTRAINING DENSE MATTER SUPERFLUIDITY THROUGH THERMAL EMISSION FROMMILLISECOND PULSARS

As a neutron star spins down, the diminishing centrifugal force gradua lly increases the density of any given fluid element in the star's int erior. Since the ''chemical'' (or ''beta'') equilibrium state is deter mined 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 elect rons. 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 mechanis m 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 del ta 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) o ver dot(rot). The threshold imbalance, and therefore the luminous stag e, 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., milliseco nd pulsars. A preliminary study of 11 millisecond pulsars with reporte d ROSAT observations shows that the latter can already be used to star t constraining superfluid energy gaps in the theoretically interesting range, approximately 0.1-1 MeV.