Pitch angle restrictions in late-type spiral galaxies based on chaotic and ordered orbital behavior

Abstract

We built models for low bulge mass spiral galaxies (late type as defined by the Hubble classification) using a three-dimensional self-gravitating model for spiral arms, and analyzed the orbital dynamics as a function of pitch angle, ranging from 10°to 60°. Indirectly testing orbital self-consistency, we search for the main periodic orbits and studied the density response. For pitch angles up to approximately 20°, the response closely supports the potential readily permitting the presence of long-lasting spiral structures. The density response tends to "avoid" larger pitch angles in the potential by keeping smaller pitch angles in the corresponding response. Spiral arms with pitch angles larger than 20°would not be long-lasting structures but would rather be transient. On the other hand, from an extensive orbital study in phase space, we also find that for late-type galaxies with pitch angles larger than 50°, chaos becomes pervasive, destroying the ordered phase space surrounding the main stable periodic orbits and even destroying them. This result is in good agreement with observations of late-type galaxies, where the maximum observed pitch angle is 50°. © 2012. The American Astronomical Society. All rights reserved..