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When a subhalo interacts with a cold stellar stream it perturbs its otherwisenearly smooth distribution of stars, and this leads to the creation of a gap.The properties of such gaps depend on the parameters of the interaction. Theircharacterisation could thus lead to the determination of the mass spectrum ofthe perturbers and possibly reveal the existence of dark subhalos orbiting theMilky Way. Our goal is to construct a fully analytical model of the formationand evolution of gaps embedded in streams orbiting in a realistic Milky Waypotential. To this end, we extend the model of Helmi & Koppelman (2016) forspherical potentials, and predict the properties of gaps in streams evolving inaxisymmetric St\"ackel potentials. We make use of action-angles and theirsimple behaviour to calculate the divergence of initially nearby orbitsslightly perturbed by the interaction with a subhalo. Our model, corroboratedby N-body experiments, predicts that the size of a gap grows linearly withtime. We obtain analytical expressions for the dependencies of the growth rateon the orbit of the stream, the properties of the subhalo (mass, scale-radius),and the geometry of the encounter (relative velocity, impact parameter). Wefind that the density at the centre of the gap decreases with time as apower-law in the same way as the density of a stream. This results in thedensity-contrast between a pristine and a perturbed stream on the same orbitasymptotically reaching a constant value dependent only on the encounterparameters. We find that at a fixed age, smallish gaps are sensitive mostly tothe mass of the subhalo, while gaps formed by subhalo flybys with a lowrelative velocity, or when the stream and subhalo move parallel, are degenerateto the encounter parameters.

Time evolution of gaps in stellar streams in axisymmetric St\"ackel potentials