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 $J\sim M(GM_\star R)^{1/2}$. Thus
$$
\boxed{R\propto t^{1/(2-m+2n)}},
\qquad
\boxed{J\propto t^{1/[2(2-m+2n)]}}.
$$
The central torque supplies the <angular momentum> that allows the fixed disk mass to spread.

Solution

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

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/iii/paper-321/2/b/solution