Development of Bayesian methods for the characterization of galaxy star formation histories through stellar population synthesis models

Abstract: This project establishes parameters to characterize galaxy Star Formation History (SFH) beyond mean stellar age. We use ages at which fixed star fractions form to characterize SFH duration. We define Deltaage_n = (age_10 - age_90)/age_50 for SFH extension, where age_10, age_90, age_50 correspond to ages when 10%, 90%, and 50% of stars formed. Probability distributions for observed galaxies use robust Bayesian statistics comparing observed and model spectral features. We create composite stellar population (CSP) libraries using SEDlibrary software, implementing varied SFH, metallicity, and dust properties. We compare spectra using ten features: five spectral indices (D4000n, [Hdelta+Hgamma], Hbeta, [Mg_2Fe], [MgFe]') and five SDSS ugriz photometric fluxes. First, we focus on limiting Deltaage_n distinguishing extended from negligible SFH duration, Deltaage_n,min (time resolution). Using idealized CSP library of 5 million dust-free, burst-free models with fixed metallicities from subsolar to supersolar, Deltaage_n,min marks where spectral features depend on SFH duration. We find roughly flat log(Deltaage_n,min) around -0.3 dex over 4 magnitude orders in age. Deltaage_n,min decreases with higher SNR up to SNR=100, beyond which no improvement occurs. Second, we create mock datasets by perturbing 12,500 library models with realistic errors, testing retrieval capability for characteristic ages and SFH duration using realistic 500,000-model CSP library with up to 6 starbursts, dust, and variable metallicity. We constrain SFH duration log(Deltaage_n) within +-0.3 dex for most samples. For populations with strong Balmer absorption and mean age <10^9 yr, uncertainty exceeds 0.5 dex due to SFH degeneracies. These parameters will apply to current and upcoming deep spectroscopic galaxy surveys.