Chaos caused by resonance overlap in the solar neighborhood: Spiral structure at the bar's outer Lindblad resonance

We consider the nature of orbits near the solar neighborhood that are perturbed by local spiral arms and the Milky Way bar. We present a simplified Hamiltonian model that includes resonant terms from both types of perturbations and is similar to the forced pendulum. Via numerical integration of this model, we construct Poincare maps to illustrate the nature and stability of the phase space. We find that resonance overlap is most likely to cause widespread chaos when the pattern of the spiral structure puts the solar neighborhood near the 2 : 1 inner Lindblad resonance (ILR) in the case of a two-armed pattern, or near the 4 : 1 ILR in the case of a four-armed pattern. When this happens, both the quasi-periodic orbits that support the spiral structure and those that oscillate with the bar are disrupted near the bar's 2 : 1 outer Lindblad resonance (OLR). Consequently, the pattern speed of spiral structure that passes through the bar's OLR must be faster than similar to0.45 times the solar neighborhood angular rotation rate if it is two-armed, or faster than 0.75 times this value if it is four-armed. Alternatively, the bar's OLR may form a boundary between spiral modes at different pattern speeds. In all cases, we find that spiral structure is disrupted by the bar's OLR over a narrow range of radius, and that the extent of the orbits aligned perpendicular to the bar at the bar's OLR is limited by the spiral perturbations. We find that the boundary, at an azimuthal velocity component of 30 km s(-1) below that of the Sun, of the u-anomaly in the velocity distribution in the solar neighborhood is due to the abrupt bifurcation of the orbit families associated with the OLR. The upper boundary at 60 km s(-1) is truncated by the spiral structure. The radial velocity width of the anomaly is probably bounded by chaotic regions that surround the family of quasi-periodic orbits oriented perpendicular to the bar.