Modelling the Milky Way galaxy: global mode analysis [GA]

A stellar dynamical model of the Milky Way Galaxy composed of an exponential disc, a cuspy bulge, and a NFW halo is studied. The model is subject to instability that form a bar with a pattern speed of 56 km/s/kpc and an exponential growth timescale of 250 Myr. The bar slows down after formation with a variable rate, which is largest just after formation, then decrease to 7 km/s/kpc per Gyr.
If the live halo of particles is substituted by a fixed external potential (rigid halo), the exponential growth timescale increases to 500 Myr, which would increase bar formation time from 3 to 6 Gyr in a disc represented by $10^{11}$ stars. Spectral analysis combined with time Fourier transformation shows the presence of bisymmetric `quasi-modes’ with pattern speeds smaller than that of the bar. These modes disappear when the bar is strong enough, meanwhile a new nonlinear mode coupled to the bar appears with a pattern speed about 70 … 75 % of the bar. This mode has a form of a trailing spiral extending to its corotation radius. Unlike the instability growth times, values of pattern speeds of bar- and quasi-modes in live and rigid halo models are similar.
A possibile reason for bar formation in a galaxy with cuspy bulge is due to the initial disc thickness, to which the pattern speed and orbit resonances are very sensitive. When a disc particle orbit reaches a height above the galactic plane comparable to radial distance, the motion is no longer periodic in radial direction. As a consequence, for radii of the order of the characteristic disc height, the radial frequency is ill defined and the inner Lindblad resonance (ILR) is smeared out. Accounting for the disc thickness in a toy model allows us to reproduce the bar mode in the rigid halo by a global mode analysis in the framework of linear perturbation theory. The dissipating role of the ILR is discussed.

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E. Polyachenko, P. Berczik and A. Just
Mon, 25 Jan 16

Comments: 13 pages, 13 figures, submitted to MNRAS Dec 2015