The stability of mass transfer is important in the formation of contact binaries from detached binaries when the primaries of the initially detached binaries fill their Roche lobes .
Using Eggleton ’ s stellar evolution code , we investigate the formation and the short-period limit of contact binaries by considering the effect of the instability of mass transfer .
It is found that with decreasing initial primary mass from 0.89M _ { \odot } to 0.63M _ { \odot } , the range of the initial mass ratio decreases for detached binaries that experience stable mass transfer and evolve into contact .
If the initial primary mass is less than 0.63M _ { \odot } , detached binaries would experience dynamically unstable mass transfer when the primaries of detached binaries fill their Roche lobes .
These systems would evolve into a common envelope situation and probably then to a complete merger of two components on a quite short timescale .
This results in a low mass limit at about 0.63M _ { \odot } for the primary mass of contact binaries , which might be a main reason why the period distribution of contact binaries has a short limit of about 0.22 days .
By comparing the theoretical period distribution of contact binaries with the observational data , it is found that the observed contact binaries are above the low mass limit for the primary mass of contact binaries and no observed contact binaries are below this limit .
This suggests that the short-period limit of contact binaries can be explained by the instability of the mass transfer that occurs when the primaries of the initially detached binaries fill their Roche lobes .