On the Timescale for Star Formation in Galaxies
  The timescale for star formation, a measure of how quickly neutral gas is
being converted to stars, is considerably longer than typical dynamical
timescales associated with a galactic disk. For purposes of modeling galaxy
evolution, however, it would be extremely attractive if the star formation
timescale were proportional to an easily derived dynamical timescale. We
compare estimates of the star formation timescale within nearby galaxies, based
on the work of Leroy et al. (2008) and existing BIMA SONG CO data, with three
simple forms of the dynamical time: the orbital time, the free-fall time at the
midplane density, and the disk Jeans time (the growth time for gravitational
instabilities in a disk). When taking into account the gravity of the stellar
disk in an approximate way, all three timescales show correlations with the
star formation timescale, though none of the correlations can be accurately
described as linear. Systematic errors in estimating appropriate gas masses and
the stellar velocity dispersion may obscure an underlying correlation, but we
focus instead on a model where the timescale for H_2 formation from HI is
decoupled from the timescale for star formation from H_2. The Jeans time
correlates well with the first of these timescales, but the relationship is
still non-linear, and requires a characteristic GMC lifetime that increases
toward galaxy centers.
