A new method of determining galaxy star-formation histories (SFHs) is presented. Using the method, the feasibility of recovering SFHs with multi-band photometry is investigated. The method divides a galaxys history into discrete time intervals and reconstructs the average rate of star formation in each interval. This directly gives the total stellar mass. A simple linear inversion solves the problem of finding the most likely discretised SFH for a given set of galaxy parameters. It is shown how formulating the method within a Bayesian framework lets the data simultaneously select the optimal regularisation strength and the most appropriate number of discrete time intervals for the reconstructed SFH. The method is demonstrated by applying it to mono-metallic synthetic photometric catalogues created with different input SFHs, assessing how the accuracy of the recovered SFHs and stellar masses depend on the photometric passband set, signal-to-noise and redshift. The results show that reconstruction of SFHs using multi-band photometry is possible, being able to distinguish an early burst of star formation from a late one, provided an appropriate passband set is used. Although the resolution of the recovered SFHs is on average inferior compared to what can be achieved with spectroscopic data, the multi-band approach can process a significantly larger number of galaxies per unit exposure time.
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