Resonance sweeping by a decelerating bar
We provide the first quantitative evidence for the deceleration/growth of the Galactic bar from local stellar kinematics thus confirming dynamical friction within expectations for a typical dark matter halo. The kinematic response of the stellar disk to a decelerating bar is studied using secular perturbation theory and test particle simulations. We show that the velocity distribution at any point in the disk affected by a naturally slowing bar is qualitatively different from that perturbed by a steadily rotating bar with the same current pattern speed $\Omega_p$ and amplitude. When the bar slows with rate $d\Omega_p/dt$, its resonances sweep through phase space. Depending on $d{\Omega}_p/dt$, they trap and drag along a portion of previously free orbits. This enhances occupation on resonances, but also changes the distribution of stars within the resonant region. Helped by this accumulation of orbits near the boundary of the resonant region, the decelerating bar model reproduces with its corotation resonance the offset and strength of the Hercules stream in the local $v_R-v_\varphi$ plane and the double-peaked structure of $ $ in the $L_z-\varphi$ plane. On the outer/inner Lindblad resonances and other higher order resonances, resonant dragging by a slowing bar is associated with a continuing increase in radial action. We compare the model to data in the action plane, identifying multiple resonance ridges. This work shows models using a constant bar pattern speed ($d\Omega_p/dt=0$) likely lead to qualitatively wrong conclusions. Most importantly we provide the first quantitative estimate of the slowing rate of the bar: $d\Omega_p/dt = (-5.0 \pm 2.5)$ km/s/kpc/Gyr.