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Fast Modes and Dusty Horseshoes in Transitional Disks

The brightest transitional protoplanetary disks are often azimuthally asymmetric: their mm-wave thermal emission peaks strongly on one side. Dust overdensities can exceed $\sim$100:1, while gas densities vary by factors less than a few. We propose that these remarkable ALMA observations---which may bear on how planetesimals form---reflect a gravitational global mode in the gas disk. The mode is (1) fast---its pattern speed equals the disk's mean Keplerian frequency; (2) of azimuthal wavenumber $m=1$, displacing the host star from the barycenter; and (3) Toomre-stable. We solve for gas streamlines including the indirect stellar potential in the frame rotating with the pattern speed, under the drastic simplification that gas does not feel its own gravity. Near co-rotation, the gas disk takes the form of a horseshoe-shaped annulus. Dust particles with aerodynamic stopping times much shorter or much longer than the orbital period are dragged by gas toward the horseshoe center. For intermediate stopping times, dust converges toward a $\sim$45$^\circ$-wide arc on the co-rotation circle. Particles that do not reach their final accumulation points within disk lifetimes, either because of gas turbulence or long particle drift times, conform to horseshoe-shaped gas streamlines. Our mode is not self-consistent because we neglect gas self-gravity; still, we expect that trends between accumulation location and particle size, similar to those we have found, are generically predicted by fast modes and are potentially observable. Unlike vortices, global modes are not restricted in radial width to the pressure scale height; their large radial and azimuthal extents may better match observations.