paper

Constraining dense-matter superfluidity through thermal emission from millisecond pulsars

arXiv:astro-ph/9612179 · doi:10.1086/304417

Abstract

As a neutron star spins down, the gradual decrease of the centrifugal force produces a progressive increase of the density of any given fluid element in its 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=μ_n-μ_p-μ_e, where n, p, and e denote neutrons, protons, and electrons. In the presence of superfluid energy gaps, in this case Δ_n and Δ_p, reactions are strongly inhibited as long as both δμand kT are much smaller than the gaps. Thus, no restoring mechanism is available, and the imbalance will grow unimpeded until δμ=δμ_{thr}=Δ_n+Δ_p. 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 $L\sim 2\times 10^{-4}(δμ_{thr}/0.1\MeV)\dot E_{rot}$, similar to the typical x-ray luminosity of pulsars with spin-down power \dot E_{rot}. The threshold imbalance, and therefore the luminous stage, are only reached by millisecond pulsars. A preliminary study of eleven 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, ~ 0.1 - 1 MeV.

10 pages, including 2 figures, LaTeX, submitted to ApJ

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