Evolving neutron star+helium star systems to intermediate-mass binary pulsars

Intermediate-mass binary pulsars (IMBPs) are composed of neutron stars (NSs) and CO/ONe white dwarfs (WDs). It is generally suggested that IMBPs evolve from intermediate-mass X-ray binaries (IMXBs). However, this scenario is difficult to explain the formation of IMBPs with orbital periods ($P_{\rm orb}$) less than 3 d. It has recently been proposed that a system consisting of a neutron star (NS) and a helium (He) star can form IMBPs with $P_{\rm orb}$ less than 3 d (known as the NS+He star scenario), but previous works can only cover a few observed sources with short orbital periods. We aim to investigate the NS+He star scenario by adopting different descriptions of the Eddington accretion rate ($\dot M_{\rm Edd}$) for NSs and different NS masses ($M_{\rm NS}$) varying from $1.10\,\rm M_{\odot}$ to $1.80\,\rm M_{\odot}$. Our results can cover most of the observed IMBPs with short orbital periods and almost half of the observed IMBPs with long orbital periods. We found that $\dot{M}_{\rm Edd}$$\propto$$M_{\rm NS}$$^{\rm -1/3}$ could match the observations better than a specific value for all NSs. We also found that the final spin periods of NSs slightly decrease with the initial $M_{\rm NS}$. The observed parameters of PSR J0621+1002, which is one of the well-observed IMBPs whose pulsar mass has been precisely measured, can be reproduced by the present work.