DEVIATIONS FROM CHEMICAL-EQUILIBRIUM DUE TO SPIN-DOWN AS AN INTERNAL HEAT-SOURCE IN NEUTRON-STARS

The core of a neutron star contains several species of particles, whos e relative equilibrium concentrations are determined by the local dens ity. As the star spins down, its centrifugal force decreases continuou sly, and the star contracts. The density of any given fluid element in creases, changing its chemical equilibrium state. The relaxation towar d the new equilibrium takes a finite time, so the matter is not quite in chemical equilibrium, and energy is stored that can be released by reactions. For a neutron star core composed of neutrons (n), protons ( p), and electrons (e), the departure from chemical equilibrium is quan tified by the chemical potential difference delta mu = mu(p) + mu(e) - mu(n). A finite delta mu increases the reaction rates and the neutrin o emissivity. If large enough (\delta mu\ greater than or similar to 5 kT), it reduces the net cooling rate because some of the stored chemic al energy is converted into thermal energy, and can even lead to net h eating. A simple model (for nonsuperfluid matter) shows the effect of this heating mechanism on the thermal evolution of neutron stars. It i s particularly noticeable for old, rapidly spinning stars with weak ma gnetic fields. If the timescale for variations of the rotation rate is much longer than the cooling time, a quasi-equilibrium state is reach ed in which heating and cooling balance each other and the temperature is completely determined by the current value of P/P-3 (or the spin-d own power). If only modified Urea reactions are allowed, the predicted quasi-equilibrium X-ray luminosity of some millisecond pulsars approa ches the upper limits obtained by Danner, Kulkarni, & Thorsett (1994) from ROSAT data. The predicted X-ray luminosity is much lower if direc t Urea or other fast reactions are allowed. In both cases, the luminos ity is probably increased if the stellar interior is mostly superfluid .