Multiple pattern speeds and the manifold spirals in a simulation of a barred spiral galaxy

Observations of real galaxies as well as N-body simulations often indicate the presence of multiple pattern speeds in the disc of a barred spiral galaxy. In this paper we use an accurate frequency extraction algorithm (NAFF) to determine the pattern speeds in an N-body model simulation of a secularly evolving barred spiral galaxy. Then, we compute the manifold spirals under multiple pattern speeds using the algorithm proposed in a previous paper by Efthymiopoulos et al. Our main new results are: (i) We demonstrate that precise frequency extraction algorithms as NAFF allow for a determination of pattern speeds in time windows of length much shorter than the one required by the traditional time-Fourier spectrum of the m = 2 mode. This is particularly convenient in cases where the pattern speeds slowly change in time due to secular evolution in the disc, and/or, the different modes spatially overlap in the disc. (ii) Once we get the frequencies, we compute the approximate gravitational potential, and the manifolds (iii) We show that the observed structures formed by the spiral arms in the simulation (change of form, formation of 'bridges', etc.) can be modelled by manifolds, and that this is consistent with the fact that the bar and spirals have different pattern speeds.