Calibrating convective properties of solar-like stars in the Kepler field of view

Stellar models generally use simple parameterizations to treat convection. The most widely used parameterization is the so-called mixing-length theory where the convective eddy sizes are described using a single number, α, the mixing-length parameter. This is a free parameter, and the general practice is to calibrate α using the known properties of the Sun and apply that to all stars. Using data from NASA's Kepler mission we show that using the solar-calibrated α is not always appropriate, and that in many cases it would lead to estimates of initial helium abundances that are lower than the primordial helium abundance. Kepler data allow us to calibrate α for many other stars and we show that for the sample of stars we have studied, the mixing-length parameter is generally lower than the solar value. We studied the correlation between α and stellar properties, and we find that α increases with metallicity. We therefore conclude that results obtained by fitting stellar models or by using population-synthesis models constructed with solar values of α are likely to have large systematic errors. Our results also confirm theoretical expectations that the mixing-length parameter should vary with stellar properties.