A Metropolis sampler applied to Stellar Population Synthesis

Details A Metropolis sampler applied to Stellar Population Synthesis A Metropolis sampler applied to Stellar Population Synthesis

May 2000

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000aas...196.5103l&link_type=abstract

American Astronomical Society, 196th AAS Meeting, #51.03; Bulletin of the American Astronomical Society, Vol. 32, p.755

Mathematics

Probability

Scientific paper

We use probability theory to elaborate a mathematical formulation of the problem of synthesizing spectral properties of a galaxy using a spectral base of simple stellar populations spanning a range of ages and metallicities. The method provides estimates for the population vector x, containing the contributions of different base elements to the integrated spectrum of a galaxy, and the extinction AV, as well as their full probability distributions, thus allowing a quantitative assessment of the uncertainties on these estimates. As an application, we developed a code which synthesizes equivalent widths of absorption lines and continuum colors with Bica's base of 12 elements built upon the observed properties of star-clusters. Previous studies with this base relied on mean ``solutions'' computed with a uniform sampling of the (x,AV) space, whereas we implement a more efficient Markov chain Monte Carlo sampling scheme. The probability P(x,AV) is sampled by a quasi-random walk through the parameter space, guided by the likelihood function. Extensive simulations were performed which confirmed the convergence of the method. We also investigate the ability to recover the detailed history of star formation and chemical evolution using this spectral base. This is studied as a function of (1) the magnitude of the measurement errors and (2) the set of observables used in the synthesis. It is found that only for extremely low errors (S/N > 100) all 12 base proportions can be recovered to better ~ 5%, though the observables are recovered very accurately even for S/N as low as 30 or less. For more realistic data only the age distribution can be retrieved reliably. This limitation is linked to internal correlations in the base which ultimately reflect the age x\ metallicity degeneracy. We also find that synthesizing equivalent widths and colors produces substantially better results that those obtained synthesizing only equivalent widths, despite the inclusion of AV as an extra parameter. This work was supported by the Brazilian agencies CNPq, CAPES, PRONEX and FAPESP, and by a NSF-Gemini fellowship.

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