= Density-slope satellite torque
{title2=$\Gamma=(4\chi/9)\beta q^2\Sigma_0r_0^4\Omega^2(H/r_0)^{-2}$}
A local odd <mass density> slope $\Sigma(x)-\Sigma(-x)=2\Sigma_0\beta x/r_0$ changes the cancelling one-sided <torques> into this net <torque>. A local outer cutoff $L$ adds the factor $1-(H/L)^2$. Positive slope transfers net <angular momentum> from satellite to disk. An infinite linear <mass density> law is only a formal local extension, since it cannot remain nonnegative on both sides.
Back to article page
