= One-sided impulse torque on a disk
{title2=$\Gamma_+=\chi r_0(GM_s)^2S^{-2}\int_H^\infty\Sigma(x)x^{-4}dx$}
Multiply encounter mass flux $\Sigma(x)Sx\,dx$ by specific angular-momentum gain $r_0\Delta v_y$. The net disk <torque> replaces $\Sigma(x)$ by $\Sigma(x)-\Sigma(-x)$, so a symmetric <mass density> gives zero net <torque>. For constant <surface density>, <Keplerian shear> and the full-flyby value $\chi=2$, the one-sided coefficient is $8/27$ in $q^2\Sigma r_0^4\Omega^2(r_0/H)^3$, matching https://academic.oup.com/mnras/article/468/4/4610/3098191[the primary coplanar impulse normalization].
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