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In this third paper of a series on the precision of obtaining ages of stellarpopulations using the full spectrum fitting technique, we examine the precisionof this technique in deriving possible age spreads within a star cluster. Wetest how well an internal age spread can be resolved as a function of clusterage, population mass fraction, and signal-to-noise (S/N) ratio. For this test,the two ages (Age (SSP1) and Age (SSP2)) are free parameters along with themass fraction of SSP1. We perform the analysis on 118,800 mock star clusterscovering all ages in the range 6.8 < log (age/yr) < 10.2, with mass fractionsfrom 10% to 90% for two age gaps (0.2 dex and 0.5 dex). Random noise is addedto the model spectra to achieve S/N ratios between 50 to 100 per wavelengthpixel. We find that the mean of the derived Age (SSP1) generally matches thereal Age (SSP1) to within 0.1 dex up to ages around log (age/yr) = 9.5. Theprecision decreases for log (age/yr) > 9.6 for any mass fraction or S/N, due tothe similarity of SED shapes for those ages. In terms of the recovery of agespreads, we find that the derived age spreads are often larger than the realones, especially for log(age/yr) < 8.0 and high mass fractions of SSP1.Increasing the age gap in the mock clusters improves the derived parameters,but Age (SSP2) is still overestimated for the younger ages.

On the Precision of Full-spectrum Fitting of Stellar Populations. III. Identifying Age Spreads