Shrinking Discs: How Fast Radial Drift Erodes the Dust Disc's Outer Edge, and What the Observed Sizes Require

A dust disc should eat itself from the outside in: the grains at its outer edge drift inward at a speed that, on a standard profile, does not depend on radius, so the edge marches inward at a constant rate and the disc's dust radius is a clock. This paper winds the clock. The drift speed is 11 m per second at Stokes 0.1, 1.1 at Stokes 0.01 and 0.32 at Stokes 0.003 (radius-independent to within a factor of 1.00 on this profile). A disc born with its dust edge at 100 AU shrinks to 30 AU in 0.10 Myr at Stokes 0.03 and 0.31 Myr at Stokes 0.01; after 1 Myr the edge of a Stokes-0.003 population still sits at 32 AU, while a Stokes-0.01 population has drained to the inner disc entirely. Observed dust discs in 1 to 3 Myr-old regions have radii of tens of AU — consistent with the clock only if the emitting grains sit at Stokes numbers of a few thousandths, well below the fragmentation ceilings, or if pressure traps hold the edge. Gas discs, measured in CO, are systematically larger than dust discs by factors of two to three, the expected fingerprint of an inward-marching dust edge. Computed from stated assumptions, not measured.