Synthesis of composite stellar populations models

Spectral synthesis is largely used in the literature to decompose stellar populations with integrated light of galaxies as if the star formation histories (SFH) could be approximated by single bursts. In the case of our method (see http://www.starlight.ufsc.br/ for the SEAGal - Semi Empirical Analysis of Galaxies - collaboration), the starlight code combines the spectra of simple stellar populations (SSP) of different ages and metallicities, computed with high spectral resolution evolutionary synthesis models of Bruzual & Charlot (2003), to reproduce the observed spectrum of a given galaxy from which we can derived a huge amount of galaxy properties such as: the population vector, stellar mass, extinction and others. We have done that for all galaxies of the SDSS database. Despite all the results of astrophysical interest, we have decided to use continuous composite stellar models (CSP) with a single metallicity and a star formation rate ∝ τ^-1e^-t/τ, where t stands for the time that the star formation started (1, 5 and 13 Gyr ago) and τ is the attenuation factor chosen to be 1, 5, 10 and 99 Gyr. When the attenuation with respect to the time t is very low, this mimics a single burst, and when we choose it to be very large (99 Gyr), this is almost a constant star formation rate. We have perturbed each composite model spectrum 10 times with three distinct signal/noise ratios equal to 10, 15 and 30 in λ₀ = 4020 Å. These models were inserted into our code to verify how a picture of single bursts deal with continuous composite models of galaxies. Our CSP models can be easily integrated in an analytical form. Therefore, we have derived theoretically the mean ages and metallicities and compared them to the output derived by the synthesis. We can see that the synthesized mean ages weighted by light tend to be lower than the models, due to the degeneracies involved in the problem. The same thing can be found for the mean metallicities weighted by light, which tend to be higher for the output values.