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Only in gaseous disks, where the pressure forces dominate, acoustic waves can propagate outside this range. Considering the m = 1 waves, for a pure keplerian potential (neglecting the self-gravity of the disk), Ω = κ, and the perturbations are neutral. If there is some self-gravity in the disk, then (Ω − κ) < 0, there is only an outer Lindblad resonance and a corotation, but no inner resonance (for prograde modes with Ωp > 0), and therefore the radial range for the development of m = 1 perturbations is quite large.

However the relative velocity between galaxies is higher in clusters and hence the encounters are weaker in strength. The accumulation of a large number of weak interactions has been called the galaxy harassment (Lake, Kat z, & Moore 1998). The asymmetry in NGC 4252 including the smoothly varying HI velocity field along the tidal tail, has been attributed to this effect (Haynes, Giovanelli & Kent 2007). The amplitude of lopsidedness generated due to tidal encounters is expected to be weaker in this case because of the quick encounters.

22. Evolution with time of the three coordinates of the “nucleus” consisting in the central 1024 particles, selected from an N-body simulation of 100 352 particles. The saturation of the amplitude of oscillations is visible. From Miller & Smith (1992). Taga & Iye (1998a) studied the oscillations of a central massive black hole in a rotating galaxy, and also confirmed that the phenomenon is not an N −1/2 random noise effect, but a true physical phenomenon. They found by N-body simulations that a massive central body can undertake long-lasting oscillations, but only when its mass is lower than 10% of the disk mass.

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Accretion Discs, Jets and High Energy Phenom. in Astrophysics by Beskin et al.,

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