Constraining a Possible Time Variation of the Gravitational Constant through “Gravitochemical Heating” of Neutron Stars

A hypothetical time variation of the gravitational constant G would cause neutron star matter to depart from beta equilibrium, due to the changing hydrostatic equilibrium. This induces nonequilibrium beta processes, which release energy that is invested partly in neutrino emission and partly in internal heating. Eventually, the star arrives at a stationary state in which the temperature remains nearly constant, as the forcing through the change of G is balanced by the ongoing reactions. Using the surface temperature of the nearest millisecond pulsar, PSR J0437-4715, inferred from ultraviolet observations, we estimate two upper limits for this variation: (1) |G˙/G|<2×10^-10  yr^-1, if direct Urca reactions are allowed, and (2) |G˙/G|<4×10^-12  yr^-1, considering only modified Urca reactions. The latter is among the most restrictive obtained by other methods.