Exponential galactic disk

A thin exponential galactic disk has surface density $\Sigma (R)={\Sigma }_0{e}^{-R/R_d}$ and total mass $2\pi {\Sigma }_0{R}_d^2$.

For an exponential galactic disk, the first nonspherical term in the Legendre expansion of thin-disk gravity is positive and proportional to $R^{-3}$ in $v_c^2$. The missing enclosed mass and exterior-ring terms are exponentially small at large radius. Hence the galaxy rotation curve approaches the point-mass Keplerian curve from above.

The maximum disk hypothesis assigns the largest stellar mass-to-light ratio compatible with a measured rotation curve, conventionally making the disk supply about $85\%$ of the circular speed near $2.2R_d$.