The influence of the magnetic braking laws on the evolution of persistent and transient low-mass X-ray binaries

Swift J1858.6$-$0814 (hereafter J1858) is a transient neutron star low-mass X-ray binary (NS LMXB). There is controversy regarding its donor mass derived from observations and theoretical calculations. In this paper, we adopt seven magnetic braking (MB) prescriptions suggested in the literature and different metallicity $Z$ to simulate the evolution of the LMXB. Our results show that, employing the MB model proposed by \citet{2012ApJ...746...43R} ("rm12"), the Convection And Rotation Boosted ("carb") model \citep{2019ApJ...886L..31V}, as well as the Intermediate ("inter") and Convection-boosted ("cboost") models in \citet{2019MNRAS.483.5595V} can match (part of) the observational parameters of J1858 well. We then apply our method to other observed LMXBs and find that the "rm12" and "inter" MB laws are most promising in explaining transient LMXBs. In comparison, the simulations with the "cboost" and "carb" MB laws are more inclined to reproduce persistent LMXBs and ultra-compact X-ray binaries (UCXBs), respectively. Our results, though subject to computational and/or observational bias, show that it is challenging to find a unified MB law that applies to the NS LMXB sub-populations simultaneously, indicating our lack of understanding of the true MB law. In addition, we explore the influence of various MB laws on the magnitude of the bifurcation periods in LMXBs.