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The equilibrium composition of neutron star matter is achieved through weakinteractions (direct and inverse beta decays), which proceed on relatively longtime scales. If the density of a matter element is perturbed, it will relax tothe new chemical equilibrium through non-equilibrium reactions, which produceentropy that is partly released through neutrino emission, while a similarfraction heats the matter and is eventually radiated as thermal photons. Weexamined two possible mechanisms causing such density perturbations: 1) thereduction in centrifugal force caused by spin-down (particularly in millisecondpulsars), leading to "rotochemical heating", and 2) a hypotheticaltime-variation of the gravitational constant, as predicted by some theories ofgravity and current cosmological models, leading to "gravitochemical heating".If only slow weak interactions are allowed in the neutron star (modified Urcareactions, with or without Cooper pairing), rotochemical heating can accountfor the observed ultraviolet emission from the closest millisecond pulsar, PSRJ0437-4715, which also provides a constraint on |dG/dt| of the same order asthe best available in the literature.Comment: 6 pages, 7 figures. To appear in the proceedings of "Isolated Neutron  Stars: from the Interior to the Surface", a conference held in London in  April 2006 (special issue of Astrophysics and Space Science, edited by Dany  Page, Roberto Turolla, & Silvia Zane

Internal heating and thermal emission from old neutron stars