Observational Manifestation of Chaos in Grand Design Spiral Galaxies

Abstract

To study dynamic properties of the gaseous disk of the grand design spiral galaxy NGC 3631 we calculate the Lyapunov characteristic numbers (LCN) for different families of streamlines in the disk. For the trajectories near separatrices of the giant vortices and near saddle points presenting in the velocity field, the LCN turned out to be positive. The result is insensitive to the method of the calculation. Both methods — using two trajectories and based on linearized equations — give the identical results. The values of the LCN in the gaseous disk of NGC 3631 are independent on the Riemannian metric used for the calculations in agreement with the classical mathematical theorem. The spectra of the ‘short-time’ LCN (stretching numbers) evaluated for the same trajectories turned out to be non-invariant. We confirmed this result obtained for the real galactic disk on classical model examples.