Evolution of neutron star + He star binaries: an alternative evolutionary channel to intermediate-mass binary pulsars

It is difficult for intermediate-mass X-ray binaries to form compact intermediate-mass binary pulsars (IMBPs) with a short orbital-period ($\la 3 \rm d$), which have a heavy ($\ga 0.4 M_{\odot}$) CO or ONeMg white dwarf companions. Since neutron star + He star binaries may experience common-envelope evolution, they have some advantage to account for the formation of short orbital-period IMBPs. In this work, we explore the probability of IMBPs formed by this evolutionary channel. Using Eggleton's stellar evolution code, considering that the dead pulsars were spun up by the accreting material and angular momentum from the He star companions, we have calculated the evolution of a large number of neutron star + He star binaries. Our simulated results indicate that, the NS + He star evolutionary channel can produce IMBPs with a WD of $\sim0.5 - 1.1 M_{\odot}$ and an orbital period of $0.03 - 20$ d, in which pulsars have a spin-period of $1.4 - 200$ ms. Comparing the calculated results with the observational parameters (spin period and orbital period) of 9 compact IMBPs, the NS + He star evolutionary channel can account for the formation of 4 sources. Therefore, NS + He star binaries offer an alternative evolutionary channel to compact IMBPs.