A Census of Blue Stragglers in Gaia DR2 Open Clusters as a Test of Population Synthesis and Mass Transfer Physics

We use photometry and proper motions from Gaia DR2 to determine the blue straggler star (BSS) populations of 16 old (1-10 Gyr), nearby ($d< 3500$ pc) open clusters. We find that the fractional number of BSS compared to RGB stars increases with age, starting near zero at 1 Gyr and flattening to $\sim 0.35$ by 4 Gyr. Fitting stellar evolutionary tracks to these BSS, we find that their mass distribution peaks at a few tenths of a solar mass above the main-sequence turnoff. BSS more than 0.5 $M_\odot$ above the turnoff make up only $\sim25$\% of the sample, and BSS more than 1.0 $M_\odot$ above the turnoff are rare. We compare this to population synthesis models of BSS formed via mass transfer using the Compact Object Synthesis and Monte Carlo Investigation Code (COSMIC). We find that standard population synthesis assumptions dramatically under-produce the number of BSS in old open clusters. We also find that these models overproduce high mass BSS relative to lower mass BSS. Expected numbers of BSS formed through dynamics do not fully account for this discrepancy. We conclude that in order to explain the observed BSS populations from Roche lobe overflow, mass-transfer from giant donors must be more stable than assumed in canonical mass-transfer prescriptions, and including non-conservative mass transfer is important in producing realistic BSS masses. Even with these modifications, it is difficult to achieve the large number of BSS observed in the oldest open clusters. We discuss some additional physics that may explain the large number of observed blue stragglers among old stellar populations.