## Modeling nearby FGK Population I stars: A new form of estimating stellar parameters using an optimization approach

^{1} CFC, Department of Mathematics and Astronomical Observatory, University of Coimbra, Portugal

e-mail: jmfernan@mat.uc.pt
^{2} Department of Production and Systems, University of Minho, Portugal

e-mail: aivaz@dps.uminho.pt
^{3} CMUC, Department of Mathematics, University of Coimbra, Portugal

e-mail: lnv@mat.uc.pt

Received: 17 October 2008

Accepted: 27 May 2011

*Context.* Modeling a single star with theoretical stellar evolutionary tracks is a nontrivial problem because of a large number of unknowns compared to the number of observations. A current way of estimating stellar age and mass consists of using interpolations in grids of stellar models and/or isochrones, assuming ad hoc values for the mixing length parameter and the metal-to-helium enrichment, which is normally scaled to the solar values.

*Aims.* We present a new method to model the FGK main-sequence of Population I stars. This method is capable of simultaneously estimating a set of stellar parameters, namely the mass, the age, the helium and metal abundances, the mixing length parameter, and the overshooting.

*Methods.* The proposed method is based on the application of a global optimization algorithm (PSwarm) to solve an optimization problem that in turn consists of finding the values of the stellar parameters that lead to the best possible fit of the given observations. The evaluation of the fitting objective function requires the use of a stellar evolution simulation code, however.

*Results.* The methodology is tested using the Sun and five FGK fictitious stars, and is then adapted to 115 stars with a detailed spectroscopic analysis; half of these are planet-hosting stars.

*Conclusions.* We present and discuss the stellar parameters estimated for each star in the context of previous works.

Key words: methods: numerical / stars: fundamental parameters / Hertzsprung-Russell (HR) and C-M diagrams / planetary systems

*© ESO, 2011*