On the maximum age resolution achievable through stellar population synthesis models

As the reconstruction of the star formation histories (SFHs) of galaxies from spectroscopic data becomes increasingly popular, we explore the best age resolution achievable with stellar population synthesis (SPS) models, relying on different constraints: broad-band colours, absorption indices, a combination of the two, and the full spectrum. We perform idealized experiments on SPS models and show that the minimum resolvable relative duration of a star formation episode (time difference between 10 percent and 90 percent of the stellar mass formed divided by the median age) is never better than 0.4, even when using spectra with signal-to-noise ratio (SNR) larger than 100 per angstrom. Typically, the best relative age resolution ranges between 0.4 and 0.7 over most of the age-metallicity plane, corresponding to minimum bin sizes for SFH sampling between 0.15 and 0.25 dex. This resolution makes the spectroscopic exploration of distant galaxies mandatory in order to reconstruct the early phases of galaxies' SFHs. We show that spectroscopy with SNR greater than or similar to 20 angstrom(-1) is essential for good age resolution. Remarkably, using the full spectrum does not prove significantly more effective than relying on absorption indices, especially at SNR less than or similar to 20 angstrom(-1). We discuss the physical origins of the age resolution trends as a function of age and metallicity, and identify the presence of maxima in age resolution (i.e. minima in measurable relative time duration) at the characteristic ages that correspond to quick time variations in spectral absorption features. We connect these maxima to bumps commonly observed in reconstructed SFHs.