Testing the inward migration by dynamical friction in a disk. The solid curves refer to N-body simulations of a BH of mass m starting in a circular orbit at r_i within a thin live Mestel disk with an isothermal halo as an external potential. The left and right panels refer to r_i​ = ​0.07R₀ and 0.1R₀. Shown for comparison are analytic estimates based on Eq. (21) (dotted) and Eq. (22) (dashed), crudely normalized for best overall fit in the four cases. We learn from this comparison that the analytic approximations are realistic conservative estimates.