Goal The purpose of this webpage is to provide a tool for the estimation of stellar parameters by global derivativefree optimization. The parameters being estimated are the stellar mass, the abundance of hydrogen, the abundance of helium, the presence of other elements, the stellar age, the stellar surface convection, and the stellar nucleus overshooting. The procedure is based on applying PSwarm (a global derivativefree solver) to a leastsquares fitting function whose values are computed by the simulation code CESAM.
Astrophysical details The stellar mass M (related to the Sun mass M_{☺}), the abundance of hydrogen X (in percentage of the total stellar composition), the abundance of helium Y (also in percentage of the total stellar composition), the presence of other elements Z (Z=1XY), the stellar age t (related to the Sun age t_{☺}) in Gyr, the stellar surface convection α, and the stellar nucleus overshooting ov are the six stellar parameters to be determined by solving the following optimization problem:
Z can be then determined from the X and Y values. The observed data (subscript obs) is obtained with a absolute error value (prefix d). To evaluate the objective function above, on a given set of star parameters, a star evolution simulation is carried out using the CESAM code. The simulation provides, among other quantities, the effective surface temperature t_{eff}, the luminosity L, and the radius R (from which we can then compute the stellar gravity g=27397M/R^{2}). PSwarm is used to solve the above problem.
PSwarm PSwarm is a global optimization solver for bound and linear constrained problems (for which the derivatives of the objective function are unavailable, inaccurate or expensive). For details see its webpage.
Numerical results :: a sample of results with a set of 193 stars
Try it yourself :: Run PSwarm for a set of stellar parameters
Supporting material J.M. Fernandes, A.I.F. Vaz, and L.N. Vicente. Modelling nearby FGK Population I stars: A new form of estimating stellar parameters using an optimization approach. Astronomy & Astrophysics, 532:A20, 2011. (online version  report) A.I.F. Vaz and L.N. Vicente. A particle swarm pattern search method for bound constrained global optimization. Journal of Global Optimization, 38:197219, 2007. (online version  report) A.I.F. Vaz and L.N. Vicente. PSwarm: A hybrid solver for linearly constrained global derivativefree optimization. Optimization Methods and Software, 24: 669685, 2009. (online version  report)
Acknowledgements Support was provided by FCT under grants POCTISFA2675, POCI/MAT/58957/2004, POCI/MAT/59442/2004, PTDC/CTEAST /66181/2006, and PTDC/MAT/64838/2006, and by the CDSStrasbourg Database. JMF also acknowledges the support from Fundação Calouste Gulbenkian and the European Astronomical Society.
