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As the reconstruction of the star-formation histories (SFH) of galaxies fromspectroscopic data becomes increasingly popular, we explore the best ageresolution achievable with stellar population synthesis (SPS) models, relyingon different constraints: broad-band colours, absorption indices, a combinationof the two, and the full spectrum. We perform idealized experiments on SPSmodels and show that the minimum resolvable relative duration of astar-formation episode (time difference between 10% and 90% of the stellar massformed divided by the median age) is never better than 0.4, even when usingspectra with signal-to-noise ratio (SNR) larger than 100 per AA. Typically, thebest relative age resolution ranges between 0.4 and 0.7 over most of theage-metallicity plane, corresponding to minimum bin sizes for SFH samplingbetween 0.15 and 0.25 dex. This resolution makes the spectroscopic explorationof distant galaxies mandatory in order to reconstruct the early phases ofgalaxies' SFHs. We show that spectroscopy with SNR $\gtrsim$ 2/AA is essentialfor good age resolution. Remarkably, using the full spectrum does not provesignificantly more effective than relying on absorption indices, especially atSNR $\lesssim$ 20/AA. We discuss the physical origins of the age resolutiontrends as a function of age and metallicity, and identify the presence ofmaxima in age resolution (i.e. minima in measurable relative time duration) atthe characteristic ages that correspond to quick time variations in spectralabsorption features. We connect these maxima to bumps commonly observed inreconstructed SFHs.

On the maximum age resolution achievable through stellar population synthesis models