Effect of irradiation on the spin of millisecond pulsars

A millisecond pulsar (MSP) is an old neutron star (NS) that has accreted material from its companion star, causing it to spin up, which is known as the recycling scenario. During the mass transfer phase, the system manifests itself as an X-ray binary. PSR J1402+13 is an MSP with a spin period of $5.89~{\rm ms}$ and a spin period derivative of $\log\dot{P}_{\rm spin}=-16.32$. These properties make it a notable object within the pulsar population, as MSPs typically exhibit low spin period derivatives. In this paper, we aim to explain how an MSP can posses high spin period derivative by binary evolution. By utilizing the stellar evolution code \textsc{MESA}, we examine the effects of irradiation on the companion star and the propeller effect on the NS during binary evolution. We demonstrate that irradiation can modify the spin period and mass of an MSP, resulting in a higher spin period derivative. These results suggest that the irradiation effect may serve as a key factor in explaining MSPs with high spin period derivatives.