Magnetothermal Evolution of Neutron Stars with Emphasis to Radio Pulsars

The magnetic and thermal evolution of neutron stars is a very complex process with many nonlinear interactions. For a decent understanding of neutron star physics, these evolutions cannot be considered isolated. A brief overview is presented, which describes the main magnetothermal interactions that determine the fate of both isolated neutron stars and accreting ones. Special attention is devoted to the interplay of thermal and magnetic evolution at the polar cap of radio pulsars. There, a strong meridional temperature gradient is maintained over the lifetime of radio pulsars. It may be strong enough to drive thermoelectric magnetic field creation which perpetuate a toroidal magnetic field around the polar cap rim. Such a local field component may amplify and curve the poloidal surface field at the cap, forming a strong and small scale magnetic field as required for the radio emission of pulsars