Evolutionary trajectories of ultra-compact "black widow" pulsars with very low mass companions

The existence of millisecond pulsars with planet-mass companions (Bailes et al., 2011) in close orbits is challenging from the stellar evolution point of view. We calculate in detail the evolution of binary systems self-consistently, including mass transfer, evaporation and irradiation of the donor by X-rays feedback, demonstrating the existence of a new evolutionary path leading to short periods and compact donors as required by the observations of PSR J1719-1438. We also point out the alternative of an exotic nature of the companion planet-mass star.