Oscillating dynamical friction on galactic bars by trapped dark matter
  The dynamic evolution of galactic bars in standard $\Lambda$CDM models is
dominated by angular momentum loss to the dark matter haloes via dynamical
friction. Traditional approximations to dynamical friction are formulated using
the linearized collisionless Boltzmann equation and have been shown to be valid
in the fast limit, i.e. for rapidly slowing bars. However, the linear
assumption breaks down within a few dynamical periods for typical slowly
evolving bars, which trap a significant amount of disc stars and dark matter in
resonances. Recent observations of the Galactic bar imply this slow regime at
the main bar resonances. We formulate the time-dependent dynamical friction in
the slow limit and explore its mechanism in the general slow regime with
test-particle simulations. Here, angular momentum exchange is dominated by
resonantly trapped orbits which slowly librate around the resonances. In
typical equilibrium haloes, the initial phase-space density within the trapped
zone is higher at lower angular momentum. Since the libration frequency falls
towards the separatrix, this density contrast winds up into a phase-space
spiral, resulting in a dynamical friction that oscillates with $\sim$Gyr
periods and damps over secular timescales. We quantify the long-term behaviour
of this torque with secular perturbation theory, and predict two observable
consequences: i) The phase-space spirals may be detectable in the stellar disc
where the number of windings encodes the age of the bar. ii) The torque causes
weak oscillations in the bar's pattern speed, overlaying the overall slowdown
-- while not discussed, this feature is visible in previous simulations.
