Analytic tracks (dashed lines) in Z–﹩{\tau }_{s}﹩ space for a disk with ﹩\alpha ={10}^{-2}﹩, ﹩\beta =1/2﹩, and various ratios of the particle-to-gas accretion rate. Particles evolve from the lower right to the upper left under radial drift. The red curve defines the approximate region within which prompt planetesimal formation is possible. The green (for millimeter-sized particles) and blue (centimeter-sized) curves show tracks that include a sink term for planetesimal formation, for ﹩K={10}^{2}﹩ (solid curves), ﹩K={10}^{3}﹩ and ﹩K={10}^{4}﹩ (dashed curves). The disk model has ﹩\dot{M}={10}^{-8}\ {M}_{\odot }\ {\mathrm{yr}}^{-1}﹩ and ﹩T=150{(r/3\mathrm{au})}^{-0.5}\ {\rm{K}}﹩.