Thermal evolution of neutron stars with decaying magnetic fields

Rotochemical heating originates in the deviation from beta equilibrium due to spin-down compression, which is closely related to the dipole magnetic field. We numerically calculate the deviation from chemical equilibrium and thermal evolution of neutron stars with decaying magnetic fields. We find that the power-law long term decay of the magnetic field slightly affects the deviation from chemical equilibrium and surface temperature. However, the magnetic decay leads to older neutron stars that could have a different surface temperature with the same magnetic field strength. That is, older neutron stars with a low magnetic field(108G) could have a lower temperature even with rotochemical heating in operation, which probably explains the lack of other observations on older millisecond pulsars with higher surface temperature,except millisecond pulsar J0437–4715.