Rotochemical heating in millisecond pulsars: modified Urca reactions with uniform Cooper pairing gaps

Understand

Context: When a rotating neutron star loses angular momentum, the reduction in the centrifugal force makes it contract.

• This perturbs each fluid element, raising the local pressure and originating deviations from beta equilibrium that enhance the neutrino emissivity and produce thermal energy.
• This mechanism is named rotochemical heating and has previously been studied for neutron stars of nonsuperfluid matter, finding that they reach a quasi-steady configuration in which the rate at which the spin-down modifies the equilibrium concentrations is the same at which neutrino reactions restore the equilibrium.
• Aims: We describe the thermal effects of Cooper pairing with spatially uniform energy gaps of neutrons \Delta_n and protons \Delta_p on the rotochemical heating in millisecond pulsars (MSPs) when only modified Urca reactions are allowed.