The rate of $\mathbb{F}$-convergence for Ricci flows with closed and smooth tangent flows

This article is a continuation of [CMZ21b], where we proved that a Ricci flow with a closed and smooth tangent flow has unique tangent flow, and its corresponding forward or backward modified Ricci flow converges in the rate of $t^{-\beta}$ for some $\beta>0$. In this article, we calculate the corresponding $\mathbb{F}$-convergence rate: after being scaled by a factor $\lambda>0$, a Ricci flow with closed and smooth tangent flow is $|\log \lambda|^{-\theta}$ close to its tangent flow in the $\mathbb{F}$-sense, where $\theta$ is a positive number, $\lambda\gg 1$ in the blow-up case, and $\lambda\ll 1$ in the blow-down case.