DENSITY WAVE KINEMATICS AND GIANT MOLECULAR ASSOCIATION FORMATION IN M51

New spectroscopic observations of the ionized gas (Halpha and [N II] lines) in M51 are combined with existing CO, H I, and Halpha data to look for kinematic evidence that the gas is responding to a spiral density wave. Possible mechanisms for the formation of the approximately 3 x 10(7) M. giant molecular associations (GMAs) found in M51 are analyzed. Problems with the apparent boundedness of the GMAs are discussed, as is their eventual fate. We begin by presenting CO and H I rotation curves from the OVRO and VLA maps of M51 at 8'' resolution. The curves are strongly influenced by tangential streaming with a sense consistent with expectations of density wave theory. By comparing the CO rotation curve with an Ha rotation curve calculated from the 8'' resolution Fabry-Perot data of Tilanus and Allen, we find that the ionized gas appears to be rotating faster than the molecular gas. We show that this effect is due to a conspiracy between the tangential streaming motions and the known CO-Halpha spatial offset. The molecular, atomic, and ionized gas components all show the tangential and radial streaming motions along the major and minor axis at the arm crossings in the sense predicted by nonlinear density wave models, and we conclude that a strong density wave is present. The amplitude of the radial velocity shift for the western arm at 85'' from the nucleus is unusually large and may be due to nonlinearities associated with the 4:1 resonance. We address the issue of GMA formation and destruction. We first quantitatively assess the plausibility of GMA formation through gravitational instability by carrying out an analysis based on the Toomre criterion, and find it to be a viable mechanism. Given the many uncertainties in this calculation, it is concluded, but only marginally, that the arm gas is generally above the threshold for instabilities, while the interarm gas is close to the threshold. However, arm gas should always be more prone to instabilities than interarm ps. That the gas is everywhere not too far from the threshold may be a consequence of a self-regulating star formation process. The collapse time is sufficiently short so that bound GMAs can form in the arms. GMA formation by collisional agglomeration is also found to be plausible, but only if the collisions are not disruptive in general. It is likely, in fact, that these two processes work together to produce, in the end, a cloud with a characteristic mass roughly equal to that of a GMA. Between the arms, there is probably insufficient time to build a bound GMA through either process. A process of GMA formation by gravitational instability in a diffuse molecular medium followed by star formation would provide an explanation for the CO-Halpha offset. If they are bound, the arm GMAs must be rapidly destroyed as they move out of the arms. Star formation is the most likely agent to achieve this disruption, although direct evidence for such destructive power by star formation in M51 is still lacking. There are suggestions, however, that the calibration of molecular surface density from CO brightness may be somewhat lower in M51 than in our Galaxy. If so, then the arm GMAs may not be bound and could simply be disrupted by orbit divergence as they leave the arms. Regardless of the boundedness issue, the self-gravity of the gas must be important in determining its substructure along the arms.