 Type I migration timescale from disk torque

For a circular fixed-mass planet, $L=M_p{a}^2\Omega$ and $\dot{a}=2\Gamma /(M_{p}a\Omega )$. With $\Gamma =C(q/h{)}^2\Sigma a^4{\Omega }^2$, the radial migration timescale is $a/|\dot{a}|=(M_{\star }/M_p)[M_{\star }/(\Sigma a^2)]h^2/(2|C|\Omega )$. The factor of two distinguishes radial evolution from $L/|\Gamma |$. The dimensionless coefficient and its sign depend on the disk model.