The stellar populations in the outer regions of M33. III. Star formation history

We present a detailed analysis of the star formation history (SFH) of three fields in M33 located approximately four to six visual scale lengths from its nucleus. These fields were imaged with the Advanced Camera for Surveys on the Hubble Space Telescope and reach similar to 2.5 mag below the red clump of core helium-burning stars. The observed color-magnitude diagrams are modeled as linear combinations of individual synthetic populations with different ages and metallicities. To gain a better understanding of the systematic errors, we have conducted the analysis with two different sets of stellar evolutionary tracks, which we designate as Padova and Teramo. The precise details of the results depend on which tracks are used, but we can make several conclusions that are fairly robust despite the differences. Both sets of tracks predict the mean age to increase and the mean metallicity to decrease with radius. Allowing age and metallicity to be free parameters and assuming that star formation began similar to 14 Gyr ago, we find that the mean age of all stars and stellar remnants increases from similar to 6 to similar to 8 Gyr, and the mean global metallicity decreases from approximately similar to 0.7 to approximately similar to 0.9. The fraction of stars formed by 4.5 Gyr ago increases from similar to 65% to similar to 80%. The mean star formation rate 80-800 Myr ago decreases from similar to 30% of the lifetime average to just similar to 5%. The random errors on these estimates are similar to 10%, 1.0 Gyr, and 0.1 dex. By comparing the results of the two sets of stellar tracks for the real data and for test populations with known SFHs, we have estimated the systematic errors to be 15%, 1.0 Gyr, and 0.2 dex. These do not include uncertainties in the bolometric corrections or variations in alpha-element abundance, which deserve future study.