Stellar Orbital Studies in Normal Spiral Galaxies II: Restrictions to Structural and Dynamical parameters on Spiral Arms

Abstract

Making use of a set of detailed potential models for normal spiral galaxies, we analyze the disk stellar orbital dynamics as the structural and dynamical parameters of the spiral arms (mass, pattern speed and pitch angle) are gradually modified. With this comprehensive study of ordered and chaotic behavior, we constructed an assemblage of orbitally supported galactic models and plausible parameters for orbitally self-consistent spiral arms models. We find that, to maintain orbital support for the spiral arms, the spiral arm mass, M$_{sp}$, must decrease with the increase of the pitch angle, $i$; if $i$ is smaller than $\sim10°$, M$_{sp}$ can be as large as $\sim7\%$, $\sim6\%$, $\sim5\%$ of the disk mass, for Sa, Sb, and Sc galaxies, respectively. If $i$ increases up to $\sim25°$, the maximum M$_{sp}$ is $\sim1\%$ of the disk mass independently in this case of morphological type. For values larger than these limits, spiral arms would likely act as transient features. Regarding the limits posed by extreme chaotic behavior, we find a strong restriction on the maximum plausible values of spiral arms parameters on disk galaxies beyond which, chaotic behavior becomes pervasive. We find that for $i$ smaller than $\sim20°$, $\sim25°$, $\sim30°$, for Sa, Sb, and Sc galaxies, respectively, M$_{sp}$ can go up to $\sim10\%$, of the mass of the disk. If the corresponding $i$ is around $\sim40°$, $\sim45°$, $\sim50°$, M$_{sp}$ is $\sim1\%$, $\sim2\%$, $\sim3\%$ of the mass of the disk. Beyond these values, chaos dominates phase space, destroying the main periodic and the neighboring quasi-periodic orbits.