Disentangling discrepancies between stellar evolution theory and sub-solar mass stars - The influence of the mixing length parameter for the UV Psc binary

Serious discrepancies have recently been observed between predictions of stellar evolution models in the 0.7-1.1  M(circled dot operator) mass range and accurately measured properties of binary stars with components in this mass range. We study one of these objects, the eclipsing binary UV Piscium, which is particularly interesting because Popper (1997) derived age estimates for each component that differed by more than a factor of two. In an attempt to solve this significant discrepancy (a difference in age of 11 Gyr), we compute a large grid of stellar evolution models with the CESAM code for each component. By fixing the masses to their accurately determined values (relative error smaller than 1% for both stars), we consider a wide range of possible metallicities Z (0.01 to 0.05), and helium content Y (0.25 to 0.34) uncorrelated to Z. In addition, the mixing length parameter (alpha)MLT is left as another free parameter. We obtain a best fit in the T(eff)-radius diagram for a common chemical composition ( Z, Y)  = (0.012, 0.31), but a different MLT parameter (alpha)MLT, A  = 0.95  +-0.12(statistical)+0.30(systematic) and (alpha)MLT, B  = 0.65  +0.07(stat)+0.10(syst). The apparent age discrepancy found by Popper (1997) disappears with this solution, the components being coeval to within 1%. This suggests that fixing (alpha)MLT to its solar value (~1.6), a common hypothesis assumed in most stellar evolutionary models, may not be correct. Secondly, since (alpha)MLT is smaller for the less massive component, this suggests that the (alpha)MLT parameter may decrease with stellar mass, showing yet another shortcoming of the mixing length theory to explain stellar convection. This trend needs further confirmation with other binary stars with accurate data.