Using MESA code ( Modules for Experiments in Stellar Astrophysics , version 9575 ) , an evaluation was made of the evolutionary state of the epsilon Aurigae binary system ( HD 31964 , F0Iap + disk ) .
We sought to satisfy several observational constraints : 1 ) requiring evolutionary tracks to pass close to the current temperature and luminosity of the primary star ; 2 ) obtaining a period near the observed value of 27.1 years ; 3 ) matching a mass function of 3.0 ; 4 ) concurrent Roche lobe overflow and mass transfer ; 5 ) an isotopic ratio ^ { 12 } C / ^ { 13 } C = 5 and , ( 6 ) matching the interferometrically determined angular diameter .
A MESA model starting with binary masses of 9.85 + 4.5 M _ { \odot } , with a 100 day initial period , produces a 1.2 + 10.6 M _ { \odot } result having a 547 day period , and a single digit ^ { 12 } C / ^ { 13 } C ratio .
These values were reached near an age of 20 Myr , when the donor star comes close to the observed luminosity and temperature for epsilon Aurigae A , as a post-RGB/pre-AGB star .
Contemporaneously , the accretor then appears as an upper main sequence , early B-type star .
This benchmark model can provide a basis for further exploration of this interacting binary , and other long period binary stars .