Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 321 / 2 / b / Solution

If no mass is accreted, $M$ is constant and $\Sigma \sim M/R^2$. The viscous-time estimate becomes $t\propto R^{2-m+2n}$, while $J\sim M(G{M}_{\star }R{)}^{1/2}$. ThusThe central torque supplies the angular momentum that allows the fixed disk mass to spread.