  The discovery that axisymmetric dust rings are ubiquitous in protoplanetary
disks has provoked a flurry of research on the role of pressure bumps in planet
formation. High-resolution simulations by our group have shown that even a
modest bump can collect enough dust to trigger planetesimal formation by the
streaming instability. In this work, we probe the limits of planetesimal
formation when the external source of pressure bump reinforcement is extremely
weak. We conduct simulations of radially elongated shearing boxes to capture
the entire bump, which is generated and maintained over some timescale $t_{\rm
reinf}$ by a Newtonian relaxation scheme. We find that planetesimal formation
is extremely resilient for cm-sized grains. We reduced the strength of
reinforcement by up to a factor of 100 and the location and initial masses of
planetesimals were essentially unaffected. However, we do find that strong
reinforcement causes much faster pebble drift compared to the the standard
pebble drift rates. The resulting larger pebble flux enhances the planetesimal
growth rate by pebble accretion. We hypothesize that to sustain the bump, our
code has to extract angular momentum (the strength of this negative torque
depends on $t_{\rm reinf}$), and some of this torque is transferred to the
particles, causing them to drift faster for a stronger torque (i.e., smaller
$t_{\rm reinf}$). Since any physical process that sustains a pressure bump must
do so by torquing the gas, we conjecture that the effect on pebble drift is a
real phenomenon, motivating further work with physically realistic sources to
generate the bump.
