We report extensive radial-velocity measurements of the two giant components of the detached , 104-day period binary system of Capella .
Our highly accurate three-dimensional orbital solution based on all existing spectroscopic and astrometric observations including our own yields much improved masses for the primary and secondary of 2.466 \pm 0.018 ~ { } M _ { \sun } and 2.443 \pm 0.013 ~ { } M _ { \sun } , with relative errors of only 0.7 % and 0.5 % , respectively .
The mass ratio is considerably closer to unity than previously believed , which has an impact on assessing the evolutionary state of the system .
Improved values are presented also for the radii ( 11.87 \pm 0.56 ~ { } R _ { \sun } and 8.75 \pm 0.32 ~ { } R _ { \sun } ) , effective temperatures ( 4920 \pm 70 K and 5680 \pm 70 K ) , and luminosities ( 79.5 \pm 4.8 ~ { } L _ { \sun } and 72.1 \pm 3.6 ~ { } L _ { \sun } ) .
The distance is determined to be 13.042 \pm 0.028 pc , based on the accurate orbital parallax .
The projected rotational velocities and individual rotation periods are also known .
Capella is unique among evolved stars in that , in addition to all of the above , the chemical composition is known as well .
This includes the overall metallicity [ m/H ] , the carbon isotope ratio ^ { 12 } C/ ^ { 13 } C for the primary , and the lithium abundance and C/N ratios for both components .
We present new or revised values for some of these .
The latter three quantities are sensitive diagnostics of evolution , and change drastically for giants as a result of the deepening of the convective envelope during the first dredge-up .
The secondary is crossing the Hertzprung gap , while the primary is believed to be in the longer-lived core-helium burning phase .
Previous studies using only the masses , temperatures , and luminosities have found good agreement with stellar evolution models placing the primary in the clump .
Here we compare all of the constraints simultaneously against three sets of current models .
We find that they are unable to match all of the observations for both components at the same time , and at a single age , for any evolutionary state of the primary .
This shows the great importance of chemical information for assessing the evolutionary state of giant stars .
A comparison with models of tidal evolution yields similarly disappointing results , when tested against the fact that the orbit is circular , the primary is rotating synchronously , the secondary \sim 12 times faster than synchronous , and the spin axes are apparently aligned with the axis of the orbit .
When confronted in detail , our understanding of the advanced stages of stellar evolution is thus still very incomplete .