= Dynamical stability of binary mass transfer
<Dynamical stability of binary mass transfer> asks whether an infinitesimal mass loss reduces or increases a donor's overfill of its <Roche lobe>. Define $\zeta_{\rm ad}=d\ln R_\star/d\ln M_d$ for the donor's rapid, approximately adiabatic response and $\zeta_L=d\ln R_L/d\ln M_d$ for the <Roche lobe>. Then
$$
d\ln(R_\star/R_L)=(\zeta_{\rm ad}-\zeta_L)d\ln M_d.
$$
Because mass loss has $d\ln M_d<0$, the overfill decreases when $\zeta_{\rm ad}>\zeta_L$ and grows in the opposite case.
The <stellar radius response exponent> depends on the donor's structure, while the <Roche-lobe radius response exponent> depends on orbital and mass-loss assumptions. There is consequently no universal critical <binary mass ratio>. Transfer that is dynamically stable can still evolve on a thermal or nuclear timescale.
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