Dependence of ϵ_cM_★, rem/(Δm₁ − Δm₂) on β in our simulations, where ϵ_c is normalized to GM_★/R_★. The solid blue line and shaded region represent the best-fit linear relationship between ϵ_cM_★/(Δm₁ − Δm₂) and β in logarithmic coordinates and the corresponding 95% confidence interval, respectively. The solid red line and shaded region show the equivalent relationship for ϵ_cM_rem/(Δm₁ − Δm₂).