Signatures of dark subhaloes in dwarf spheroidal galaxies: II. Transient and localised kinematic features
We use controlled N-body simulations to investigate whether dark matter subhaloes leave detectable signatures in the internal kinematics of dwarf spheroidal galaxies. At each snapshot, we fit a velocity distribution function to stellar line-of-sight velocities and proper motions, construct normalised residual fields for the projected velocity components, and analyse their power-spectra. We show that subhalo encounters generate a plethora of kinematic features. Amongst the most prominent are rotation-like signals, which arise in our models even though the stellar component is initialised without intrinsic rotation. In line-of-sight velocity alone, several snapshots resemble the classical blueshift--redshift pattern associated with stationary rotation. The plane-of-sky components, however, bring complexity, with alternating regions of expansion and contraction, as well as clockwise and anticlockwise streaming. Although we observe coherent streaming globally, these structures depart from typical equilibrium configurations, while their residual power-spectra quantify the characteristic spatial scales involved. This signal strengthens in models containing more massive subhaloes and becomes difficult to recover for small stellar samples: robust power-spectrum recovery of the full velocity-space signature usually requires O(10^{4}) tracers, although a rotation signal alone can be recovered with considerably smaller samples. These results suggest that dwarf spheroidal velocity fields can retain signatures of subhalo heating. Future spectroscopy, improved Gaia astrometry, and chemo-dynamical information should turn these diagnostics into population-level probes of dark matter substructure.