= Nuclear-driven Roche-overfill relaxation
{title2=$\dot x=t_{\rm nuc}^{-1}-A(q)x/(f t_{\rm dyn})$}
Let $x=\log(R/R_L)$, $q=M_1/M_2$, $\dot M_2=-f\dot M_1=M_1x/t_{\rm dyn}$, and $d\log R/dt=n\dot M_1/M_1+t_{\rm nuc}^{-1}$. Under the <binary period invariant for a constant wind angular-momentum factor> and $R_L=0.46a(M_1/M)^{1/3}$, the restoring coefficient is $A(q)=n+5/3-2fq-2(3\lambda+1)(1-f)q/[3(1+q)]$. Locally freezing the masses gives an attracting overfill $x_*=ft_{\rm dyn}/[A(q)t_{\rm nuc}]$ precisely when $A(q)>0$. If $A$ is of order one and $t_{\rm dyn}\ll t_{\rm nuc}$, transfer is driven slowly by nuclear expansion. A negative $A$ gives positive feedback on the short overfill timescale; detailed outcomes then exceed this linear contact model.
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