**AAS 196th Meeting, June 2000**

*Session 51. Galaxy Evolution and Populations/Clusters*

Display, Thursday, June 8, 2000, 9:20am-4:00pm, Empire Hall South
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## [51.03] A Metropolis sampler applied to Stellar Population Synthesis

*J.R. Leao (UFSC-Brazil), R. Cid Fernandes (JHU & UFSC-Brazil), H.R. Schmitt (STScI), L. Sodre (IAG-USP-Brazil)*

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 A_{V}, 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**,A_{V}) space, whereas we implement
a more efficient Markov chain Monte Carlo sampling scheme.
The probability P(**x**,A_{V}) 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 \times\ 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 A_{V} 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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