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

Be X-ray binaries (Be-XRBs) are one of the largest subclasses of high-mass X-ray binaries, comprised of a rapidly rotating Be star and neutron star companion in an eccentric orbit, intermittently accreting material from a decretion disk around the donor. 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 state-of-the-art BPS code, POSYDON, which relies on 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 detailed examination of the rotational distribution of Be stars in multiple phases of evolution. 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 rapidly rotating population ($\omega/\omega_\mathrm{crit} \gtrsim 0.3$) of Be-XRB-like systems with a strong peak at intermediate rotation rates ($\omega/\omega_\mathrm{crit} \simeq 0.6$) in close alignment with observations. All Be-XRBs undergo a 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 derive a physically motivated MT efficiency distribution, finding that most Be-XRBs have undergone highly non-conservative MT ($\bar{\beta}_\mathrm{rot} \simeq 0.05$). 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.