To Be or not to Be: the role of rotation in modeling Galactic Be X-ray Binaries

Be X-ray binaries (Be-XRBs) are crucial in understanding high-mass X-ray binaries, featuring a rapidly rotating Be star and a neutron star companion in an eccentric orbit, intermittently accreting material from the Be star's decretion disk. Originating from binary stellar evolution, Be-XRBs are of significant interest to binary population synthesis (BPS) studies, encapsulating the physics of supernovae, common envelope, and mass transfer (MT). Using the POSYDON BPS code, employing pre-computed grids of detailed binary stellar evolution models, we investigate the Galactic Be-XRB population. POSYDON incorporates stellar rotation self-consistently during MT phases, enabling a detailed examination of the rotational distribution of Be stars. Our fiducial BPS and Be-XRB model align well with the orbital properties of Galactic Be-XRBs, emphasizing the role of rotational constraints. Our modeling reveals a bimodal rotational distribution of Be-XRB-like systems, in excellent agreement with literature values. All Be-XRBs undergo an MT phase before the first compact object forms, with over half experiencing a second MT phase from a stripped helium companion (Case BB). Computing rotationally-limited MT efficiencies and applying them to our population, we find that the majority of Be-XRBs have undergone highly non-conservative MT (beta   0.15). Our study underscores the importance of detailed angular momentum modeling during MT in interpreting Be-XRB populations, emphasizing this population as a key probe for the stability and efficiency of MT in interacting binaries.