Origin of reduced dynamical friction by dark matter haloes with net prograde rotation

We provide an explanation for the reduced dynamical friction on galactic bars in spinning dark matter haloes. Earlier work based on linear theory predicted an increase in dynamical friction when dark haloes have a net forward rotation because prograde orbits couple to bars with greater strength than retrograde orbits. Subsequent numerical studies, however, found the opposite trend: dynamical friction weakens with increasing spin of the halo. We revisit this problem and demonstrate that linear theory in fact correctly predicts a reduced torque in forward-rotating haloes. We show that shifting the halo mass from retrograde to prograde phase space generates a positive gradient in the distribution function near the origin of the z-angular momentum (L-z = 0), which results in a resonant transfer of L-z to the bar, making the net dynamical friction weaker. While this effect is subdominant for the major resonances, including the corotation resonance, it leads to a significant positive torque on the bar for the series of direct radial resonances as these resonances are strongest at L-z = 0. The overall dynamical friction from spinning haloes is shown to decrease with the halo's spin in agreement with the secular behaviour of N-body simulations. We validate our linear calculation by computing the non-linear torque from individual resonances using the angle-averaged Hamiltonian.