Formation Timescales for High-Mass X-ray Binaries in M33

We have identified 55 candidate high-mass X-ray binaries (HMXBs) in M33 using available archival {it HST} and {it Chandra} imaging to find blue stars associated with X-ray positions. We use the {it HST} photometric data to model the color-magnitude diagrams in the vicinity of each candidate HMXB to measure a resolved recent star formation history (SFH), and thus a formation timescale, or age for the source. Taken together, the SFHs for all candidate HMXBs in M33 yield an age distribution that suggests preferred formation timescales for HMXBs in M33 of $<$ 5 Myr and $sim$ 40 Myr after the initial star formation episode. The population at 40 Myr is seen in other Local Group galaxies, and can be attributed to a peak in formation efficiency of HMXBs with neutron stars as compact objects and B star secondary companions. This timescale is preferred as neutron stars should form in abundance from $sim$ 8 M$_{odot}$ core-collapse progenitors on these timescales, and B stars are shown observationally to be most actively losing mass around this time. The young population at $<$ 5 Myr has not be observed in other Local Group HMXB population studies, but may be attributed to a population of very massive progenitors forming black holes very early on. We discuss these results in the context of massive binary evolution, and the implications for compact object binaries and gravitational wave sources.