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The dynamic evolution of galactic bars in standard $\Lambda$CDM models isdominated by angular momentum loss to the dark matter haloes via dynamicalfriction. Traditional approximations to dynamical friction are formulated usingthe linearized collisionless Boltzmann equation and have been shown to be validin the fast limit, i.e. for rapidly slowing bars. However, the linearassumption breaks down within a few dynamical periods for typical slowlyevolving bars, which trap a significant amount of disc stars and dark matter inresonances. Recent observations of the Galactic bar imply this slow regime atthe main bar resonances. We formulate the time-dependent dynamical friction inthe slow limit and explore its mechanism in the general slow regime withtest-particle simulations. Here, angular momentum exchange is dominated byresonantly trapped orbits which slowly librate around the resonances. Intypical equilibrium haloes, the initial phase-space density within the trappedzone is higher at lower angular momentum. Since the libration frequency fallstowards the separatrix, this density contrast winds up into a phase-spacespiral, resulting in a dynamical friction that oscillates with $\sim$Gyrperiods and damps over secular timescales. We quantify the long-term behaviourof this torque with secular perturbation theory, and predict two observableconsequences: i) The phase-space spirals may be detectable in the stellar discwhere the number of windings encodes the age of the bar. ii) The torque causesweak oscillations in the bar's pattern speed, overlaying the overall slowdown-- while not discussed, this feature is visible in previous simulations.

Oscillating dynamical friction on galactic bars by trapped dark matter