= Roche-lobe radius response exponent
{c}
{title2=$\zeta_L=d\log R_L/d\log M_d$}
For <conservative binary mass transfer> and $R_L\propto a(M_d/M)^{1/3}$,
$$
\zeta_L=2q-\frac53,\qquad q=\frac{M_d}{M_a}.
$$
The <conservation of angular momentum> gives $d\log a/d\log M_d=-2(1-q)$. Since a mass loss has $d\log M_d<0$, the donor moves inside its lobe when $\zeta_{\rm ad}>\zeta_L$. An ideal fully convective donor with $\zeta_{\rm ad}=-1/3$ is therefore stable for $q<2/3$ and unstable for $q>2/3$ under these assumptions.
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