The Effective Velocity of Transferred Mass: How Momentum Prescriptions Determine Binary Orbital Evolution

Abstract

In binary stellar evolution, the orbital response to mass transfer depends on how angular momentum is redistributed. We introduce a one-parameter family of prescriptions characterized by $\eta$, the fractional weight of the donor velocity in the effective velocity of the transferred mass: $v_{\mathrm{trans}}=\eta v_1+(1-\eta )v_2$. We derive a closed-form expression for the angular momentum change per transfer event, $\Delta L/L=\delta m[(1-\eta )/M_2-\eta /M_1]$. The two endpoint prescriptions ($\eta =1$ and $\eta =0$) produce angular momentum changes of opposite sign, yielding qualitatively different orbital evolution at every mass ratio. Conservative mass transfer ($\Delta L=0$) corresponds uniquely to $\eta =M_1/M_{\mathrm{tot}}$, i.e. $v_{\mathrm{trans}}=v_{\mathrm{COM}}$. For constant $\eta$, we derive the general closed-form solution $a_f/a_0=[(1-f{)}^{2(1-\eta )}(1+f{q}_0{)}^{2\eta }{]}^{-1}$.

11 pages, 6 figures. Submitted to Astronomische Nachrichten