The UK Infrared Telescope M33 monitoring project. V. The star formation
  history across the galactic disc
  We have conducted a near-infrared monitoring campaign at the UK InfraRed
Telescope (UKIRT), of the Local Group spiral galaxy M33 (Triangulum). On the
basis of their variability, we have identified stars in the very final stage of
their evolution, and for which the luminosity is more directly related to the
birth mass than the more numerous less-evolved giant stars that continue to
increase in luminosity. In this fifth paper of the series, we construct the
birth mass function and hence derive the star formation history across the
galactic disc of M33. The star formation rate has varied between
$\sim0.010\pm0.001$ ($\sim0.012\pm0.007$) and 0.060$\pm0.005$
(0.052$\pm0.009$)M$_\odot$ yr$^{-1}$ kpc$^{-2}$ statistically (systematically)
in the central square kiloparsec of M33, comparable with the values derived
previously with another camera. The total star formation rate in M33 within a
galactocentric radius of 14 kpc has varied between $\sim0.110\pm0.005$
($\sim0.174\pm0.060$) and $\sim0.560\pm0.028$ ($\sim0.503\pm0.100$) M$_\odot$
yr$^{-1}$ statistically (systematically). We find evidence of two epochs during
which the star formation rate was enhanced by a factor of a few -- one that
started $\sim6$ Gyr ago and lasted $\sim3$ Gyr and produced $\geq71$% of the
total mass in stars, and one $\sim250$ Myr ago that lasted $\sim200$ Myr and
formed $\leq13$% of the mass in stars. Radial star formation history profiles
suggest that the inner disc of M33 was formed in an inside-out formation
scenario. The outskirts of the disc are dominated by the old population, which
may be the result of dynamical effects over many Gyr. We find correspondence to
spiral structure for all stars, but enhanced only for stars younger than
$\sim100$ Myr; this suggests that the spiral arms are transient features and
not part of a global density wave potential.
