Chaos caused by resonance overlap in the solar neighborhood -- Spiral structure at the Bar's 2:1 outer Lindblad resonance

We consider the nature of orbits near the solar neighborhood which are perturbed by local spiral arms and the Milky Way bar. We present a simplified Hamiltonian model which 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 2-armed pattern, or near the 4:1 ILR in the case of a 4-armed pattern. When this happens both the quasiperiodic orbits which 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 which passes through the OLR must be faster than 0.45 times the solar neighborhood angular rotation rate if it is 2-armed or faster than 0.75 times this value if it is 4-armed. Alternatively the OLR may form a boundary between spiral modes at different pattern speeds. In all cases we find that spiral structure is disrupted by the OLR over a narrow range of radius and the extent of the orbits aligned perpendicular to the bar at the OLR is limited by the spiral perturbations.