Roche lobe overflow (stage Principal Evolutionary States of Main-sequence stars (stage I)

Post main sequence stars (stage II)

The star leaves the main sequence and goes toward the red (super)giant region in the Hertzsprung-Russell diagram (as before, the star still does not fill its RL). The duration of this stage for a binary component is no longer a function of the stellar mass alone (as in the case of single stars), but also depends on the initial binary type (A, B or C) (Iben and Tutukov, 1985, 1987[74, 75]):

The radius of the post-MS star rapidly increases (on a thermal time-scale)   and reaches characteristic giant values. For most of the period it is burning helium the star has such a large radius. In the framework of our approximate description, we take the radius of the giant star to be equal to the maximum value, which depends strongly on the mass of its core ( ) and is calculated according to Webbink's mass transfer modes as follows:

This maximum radius can formally exceed the RL size; in such cases, we put it equal to during our stage II. Binaries with compact companions are the most sensitive to this crude approximation, so we overestimate, for example, the number of X-ray pulsars.  However, these stage are less important for our analysis than the stages with RL-filling companions. Of course, a more detailed treatment of normal star evolution (given, for example, by Pols and Marinus, 1994[163]) can reduce such uncertainties.

Luminosities of giants are taken from De Jager (1980)[41]:

Radii of (super)giants are determined by using the effective temperature and luminosities. Typical effective temperatures are taken from Allen (1973)[4]: