Investigating the stability of mass transfer in neutron star-helium white dwarf binaries

Abstract: Neutron star-helium white dwarf (NS+He WD) binaries are important evolutionary products of close-orbit binary star systems. They are often observed as millisecond pulsars and may continue evolving into ultra-compact X-ray binaries (UCXBs) and continuous gravitational wave (GW) sources that will be detected by space-borne GW observatories, such as LISA, TianQin and Taiji. Nevertheless, the stability of NS+He WD binaries undergoing mass transfer is not well studied and still under debate. In this paper, we model the evolution of NS+He WD binaries with WD masses ranging from 0.17-0.45 $M_{\odot}$, applying the detailed stellar evolution code mesa. Contrary to previous studies based on hydrodynamics, we find that apparently all NS+He WD binaries undergo stable mass transfer. We find for such UCXBs that the larger the WD mass, the larger the maximum mass-transfer rate and the smaller the minimum orbital period during their evolution. Finally, we demonstrate numerically and analytically that there is a tight correlation between WD mass and GW frequency for UCXBs, independent of NS mass.