The mass at which a transition is made between stars that have radiative or convective cores throughout the core H-burning phase is a fairly sensitive function of Z ( particularly , the CNO abundances ) .
As a consequence , the \sim 4 Gyr , open cluster M 67 provides a constraint on Z _ { \odot } ( and the solar heavy-element mixture ) because ( i ) high-resolution spectroscopy indicates that this system has virtually the same metal abundances as the Sun , and ( ii ) its turnoff stars have masses just above the lower limit for sustained core convection on the main sequence .
In this study , evolutionary tracks and isochrones using the latest MARCS model atmospheres as boundary conditions have been computed for 0.6– 1.4 { \cal M _ { \odot } } on the assumption of a metals mix ( implying Z _ { \odot } \approx 0.0125 ) based on the solar abundances derived by M. Asplund and collaborators using 3-D model atmospheres .
These calculations do not predict a turnoff gap where one is observed in M 67 .
No such difficulty is found if the analysis uses isochrones for Z _ { \odot } = 0.0165 , assuming the Grevesse & Sauval ( 1998 ) mix of heavy elements .
Our findings , like the inferences from helioseismology , indicate a problem with the Asplund et al .
abundances .
However , it is possible that low- Z models with diffusive processes taken into account will be less problematic .