Constraining Dense Matter Superfluidity through Thermal Emission from Millisecond Pulsars

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Abstract
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., δμ ≡ μn - μp - μe, where n, p, and e denote neutrons, protons, and electrons. In the presence of superfluid energy gaps, in this case Δn and Δp, reactions are strongly inhibited as long as both δμ and kT are much smaller than the gaps. Thus, no restoring mechanism is available, and the imbalance will grow unimpeded until δμ = δμthr ~ Δn + Δp. At this threshold, the reaction rate increases dramatically, preventing further growth of δμ and converting the excess chemical energy into heat. The thermal luminosity resulting from this "rotochemical heating" process is L ~ 2 × 10-4(δμthr/0.1 MeV)Ėrot, similar to the typical X-ray luminosity of pulsars with spin-down power Ėrot. The threshold imbalance, and therefore the luminous stage, are only reached by stars whose initial rotation period is Pi 13(δμthr/0.1 MeV)-1/2ms, 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.
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