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Long-orbital-period subdwarf B (sdB) stars with main-sequence companions arebelieved to be the product of stable Roche Lobe overflow (RLOF), a scenariochallenged by recent observations. Here we represent the results of asystematic study of the orbital-period distribution of sdB binaries in thischannel using detailed binary evolution calculations. We show that the observedorbital-period distribution of long-period sdB binaries can be well explainedby this scenario. Furthermore, we find that, if the progenitors of the sdBstars have initial masses below the helium flash mass, the sdB binariesproduced from stable RLOF follow a unique mass -- orbital period relation for agiven metallicity $Z$; increasing the orbital period from $\sim 400$ to $\sim1100$\,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. Themass -- orbital period relation can be tested observationally if the mass ofthe sdB star can be determined precisely, e.g.\ from asteroseismology. Usingthis relation, we revise the orbital period distribution of sdB binariesproduced by the first stable RLOF channel for the best fitting model of Han etal (2003), and show that the orbital period has a peak around 830\,d.

The orbital periods of subdwarf B binaries produced by the first stable Roche overflow channel