  Young planets embedded in protoplanetary discs (PPDs) excite spiral density
waves, which propagate, shock and deposit angular momentum in the disc. This
results in gap opening around the planetary orbit, even for low (sub-thermal)
mass planets, provided that the effective viscosity in the disc is low. The
edges of these planet-induced gaps are known to be prone to emergence of
observable vortices via the Rossby Wave Instability (RWI). We study timescales
for the development of vortices driven by low mass planets in inviscid discs.
We employ a recently developed semi-analytical theory of vortensity production
by the planet-driven shock to predict vortensity evolution near the planet,
from which we derive the radial profile of the planet-induced gap as a function
of time (this procedure can have multiple other uses, e.g. to study dust
trapping, suppression of pebble accretion, etc.). We then analyze the linear
stability of the gap edges against the RWI, obtaining the timescales for the
first appearance of unstable modes and (later) fully developed vortices at gap
edges. We present useful formulae for these timescales as functions of
planetary and disc parameters and provide their physical justification. We also
thoroughly test our semi-analytical framework against high resolution 2D
hydrodynamic simulations, confirming the accuracy of our theoretical
predictions. We discuss ways in which our semi-analytical framework can be
extended to incorporate additional physics, e.g. planetary accretion,
migration, and non-zero disc viscosity. Our results can be used to interpret
observations of PPDs and to predict emergence of vortices in simulations.
