  High resolution sub-mm observations of protoplanetary disks with ALMA have
revealed that dust rings are common in large, bright disks. The leading
explanation for these structures is dust-trapping in a local gas pressure
maximum, caused by an embedded planet or other dynamical process. Independent
of origin, such dust traps should be stable for many orbits to collect
significant dust. However, ring-like perturbations in gas disks are also known
to trigger the Rossby Wave Instability (RWI). We investigate whether
axisymmetric pressure bumps can simultaneously trap dust and remain stable to
the RWI. The answer depends on the thermodynamic properties of pressure bumps.
For isothermal bumps, dust traps are RWI-stable for widths from ${\sim}1$ to
several gas scale-heights. Adiabatic dust traps are stable over a smaller range
of widths. For temperature bumps with no surface density component, however,
all dust traps tend to be unstable. Smaller values of disk aspect ratio allow
stable dust trapping at lower bump amplitudes and over a larger range of
widths. We also report a new approximate criterion for RWI. Instability occurs
when the radial oscillation frequency is $\lesssim75$\% of the Keplerian
frequency, which differs from the well-known Lovelace necessary (but not
sufficient) criterion for instability. Our results can guide ALMA observations
of molecular gas by constraining the resolution and sensitivity needed to
identify the pressure bumps thought to be responsible for dust rings.

Earth and Planetary Astrophysics