Characteristic timescale as function of radial distance for sublimation (Eq. (15)), P–R drag (Eq. (2)), and mutual collisions (minimum timescale, Eq. (23)), for β = 0.5 particles in a debris disk around a solar-mass star with a very dense (η₀ ≫ 1) parent belt located at 30 AU. The gray vertical lines indicate the radial distances used by the analytical model: r_pile is the radius for which the sublimation timescale equals the P–R drag timescale, r_crit is the radius for which the P–R drag timescale equals the collisional timescale, and r₀ is the location of the parent belt. For the sublimation timescale, we assume that the dust grains are solid spheres of graphite (see Sect. 2.2.1 for the values of the sublimation parameters) with a radius of s = 0.64 μm (the size corresponding to β = 0.5).