 Roche-lobe-filling period-density relation

ID: roche-lobe-filling-period-density-relation

R_{2} = R_{L} ≃ C a (M_{2} / M)^{1/3}

P = \frac{2 π}{G C ^{3}} (\frac{R _{2}^{3}}{M _{2}})^{1/2} .

Thus a Roche lobe-filling star's period measures its inverse square-root mean mass density, largely independently of the companion mass in this approximation. A local mass-radius relation

R_{2} \propto M_{2}^{ζ}

gives

P \propto M_{2}^{(3 ζ - 1) /2}

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