  The transition between receiving a PhD and securing a tenure track faculty
position is challenging for nearly every astronomer interested in working in
academia. Here we use a publicly available database of recently hired faculty
(the Astrophysics Job Rumor Mill) to examine the amount of time astronomers
typically spend in this transitory state. Using these data as a starting point
to examine the experiences of astronomy postdocs, we find that the average time
spent between receiving a PhD and being hired into a faculty position is
4.9$\pm$0.3 years, with female astronomers hired on average 4.2$\pm$0.4 years
after receiving a PhD while male astronomers are typically hired after
5.3$\pm$0.4 years. Using a simple model of the labor market, we attempt to
recreate this gendered difference in time spent as a postdoc. We can rule out
the role of the increasing representation of women among astronomy PhDs, as
well as any bias in favor of hiring female astronomers in response to efforts
to diversify the faculty ranks. Instead the most likely explanation is that
female astronomers are leaving the academic labor market, at a rate that is 3-4
times higher than male astronomers. This scenario explains the distinct hiring
time distributions between male and female astronomers, as well as the measured
percentage of female assistant professors, and the fraction of female
applicants within a typical faculty search. These results provide evidence that
more work needs to be done to support and retain female astronomers during the
postdoctoral phase of their careers.
