Wind-driven Roche-lobe overflow ($q<\frac{1+3n}{3(1-n)}$)

A fast escaping Jeans-mode mass loss wind can drive a giant into Roche-lobe overflow because its radius changes as it loses mass, even though the wind itself is not substantially captured. This differs from slow Wind Roche-lobe overflow. For $R_d\propto M_d^{-n}$ and $R_L\propto a(M_d/M{)}^{1/3}$, wind alone gives $d\log (R_d/R_L)/dt=\dot{M}[3(1-n)q-(1+3n)]/[3M_d(1+q)]$, where $q=M_d/M_a$ and $\dot{M}<0$ is the escaping wind rate. The displayed inequality is exactly the condition that overfill increases.

Let Roche-lobe overflow transfer mass conservatively within a circular binary while a separate fast wind escapes with the donor's specific orbital angular momentum. Then ${\dot{M}}_d=\dot{M}-{\dot{M}}_a$ and $\dot{a}/a=-\dot{M}/M+2{\dot{M}}_a(1/M_d-1/M_a)$. Differentiating the donor and Roche lobe radii and enforcing contact gives the displayed rate. It is positive and stabilizing when the wind drives overfill and $6q<5-3n$. When the latter inequality is reversed, transfer increases the overfill, producing runaway rather than a steady negative-transfer solution.