We have conducted a near-infrared monitoring campaign at the UK InfraRed Telescope ( UKIRT ) , of the Local Group spiral galaxy M 33 ( 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 M 33 .
The star formation rate has varied between \sim 0.010 \pm 0.001 ( \sim 0.012 \pm 0.007 ) and 0.060 \pm 0.005 ( 0.052 \pm 0.009 ) M _ { \odot } yr ^ { -1 } kpc ^ { -2 } statistically ( systematically ) in the central square kiloparsec of M 33 , comparable with the values derived previously with another camera .
The total star formation rate in M 33 within a galactocentric radius of 14 kpc has varied between \sim 0.110 \pm 0.005 ( \sim 0.174 \pm 0.060 ) and \sim 0.560 \pm 0.028 ( \sim 0.503 \pm 0.100 ) 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 \sim 6 Gyr ago and lasted \sim 3 Gyr and produced \geq 71 % of the total mass in stars , and one \sim 250 Myr ago that lasted \sim 200 Myr and formed \leq 13 % of the mass in stars .
Radial star formation history profiles suggest that the inner disc of M 33 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 \sim 100 Myr ; this suggests that the spiral arms are transient features and not part of a global density wave potential .