Long-orbital-period subdwarf B ( sdB ) stars with main-sequence companions are believed to be the product of stable Roche Lobe overflow ( RLOF ) , a scenario challenged by recent observations .
Here we represent the results of a systematic study of the orbital-period distribution of sdB binaries in this channel using detailed binary evolution calculations .
We show that the observed orbital-period distribution of long-period sdB binaries can be well explained by this scenario .
Furthermore , we find that , if the progenitors of the sdB stars have initial masses below the helium flash mass , the sdB binaries produced from stable RLOF follow a unique mass – orbital period relation for a given metallicity Z ; increasing the orbital period from \sim 400 to \sim 1100 d corresponds to increasing the mass of the sdB star from \sim 0.40 to \sim 0.49 M _ { \odot } for Z = 0.02 .
We suggest that the longest sdB binaries ( with orbital period > 1100 d ) could be the result of atmospheric RLOF .
The mass – orbital period relation can be tested observationally if the mass of the sdB star can be determined precisely , e.g .
from asteroseismology .
Using this relation , we revise the orbital period distribution of sdB binaries produced by the first stable RLOF channel for the best fitting model of Han et al ( 2003 ) , and show that the orbital period has a peak around 830 d .