= Roche-lobe overflow feedback with a constant wind torque factor
{c}
{title2=$q>\frac{17-20f+10\beta}{23}$}
Let $q=M_1/M_2$, hold total binary mass fixed, use $R_L\propto a q^{3/10}$, and impose $d\log J=f\,d\log M_1$. The <circular-binary orbital angular momentum> then gives $d\log a/d\log M_1=2(q-1+f)$, whereas mass conservation gives $d\log q/d\log M_1=1+q$. Thus $\zeta_L=(23q-17+20f)/10$. If the donor obeys $R_1=KM_1^\beta$ with slowly varying $K$, loss of donor mass increases its overfill when $\zeta_L>\beta$, or $q>(17-20f+10\beta)/23$. This is a feedback criterion on the time scale of the assumed donor response, not automatically a dynamical instability for every choice of $\beta$. For $\beta=1/2$, the threshold is $(22-20f)/23$; if $f\geq11/10$, every positive mass ratio satisfies it.
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