转移质量的有效速度：动量规定如何决定双星轨道演化
The Effective Velocity of Transferred Mass: How Momentum Prescriptions Determine Binary Orbital Evolution
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中文总结 AI 辅助
该研究针对双星质量转移的角动量重新分配问题，引入以η为参数的动量规定族，推导角动量变化与轨道半长轴演化的闭式解，明确保守质量转移对应的η取值，揭示不同η值导致的轨道演化差异。
中文摘要 AI 辅助
在双星恒星演化中，轨道对质量转移的响应取决于角动量的重新分配方式。我们引入了一个以η为特征的单参数规定族，η是转移质量有效速度中供体速度的分数权重：v_trans = η v₁ + (1−η) v₂。我们推导了每次转移事件的角动量变化的闭式表达式：ΔL/L = δm [(1−η)/M₂ − η/M₁]。两个端点规定（η=1和η=0）产生符号相反的角动量变化，在所有质量比下产生性质不同的轨道演化。保守质量转移（ΔL=0）唯一对应η=M₁/M_tot，即v_trans = v_COM。对于恒定η，我们推导了通用闭式解：a_f/a₀ = [(1−f)^(2(1−η)) (1+f q₀)^(2η)]⁻¹。
英文摘要
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 $η$, the fractional weight of the donor velocity in the effective velocity of the transferred mass: $v_{\rm trans} = η\, v_1 + (1-η) \, v_2$. We derive a closed-form expression for the angular momentum change per transfer event, $ΔL/L = δm \, [(1-η)/M_2 - η/M_1]$. The two endpoint prescriptions ($η= 1$ and $η= 0$) produce angular momentum changes of opposite sign, yielding qualitatively different orbital evolution at every mass ratio. Conservative mass transfer ($ΔL = 0$) corresponds uniquely to $η= M_1/M_{\rm tot}$, i.e. $v_{\rm trans} = v_{\rm COM}$. For constant $η$, we derive the general closed-form solution $a_f/a_0 = [(1-f)^{2(1-η)}(1+f q_0)^{2η}]^{-1}$.
