13.2. Self-gravitating Rings and Nuclear Spirals
When more self-gravity is introduced in the gas component, the nuclear rings formed at ILR are much more unstable, and short-lived. This has already been shown in simulations of gas flow in a bar potential, when self-gravity of the gas is taken into account (Fukunaga & Tosa 1991; Wada & Habe 1992; see also Elmegreen 1994a). In the presence of an ILR, the gas accumulates in a ring towards the center, but the local instabilities it undergoes there make the ring fragment into clumps; the ring is also more elongated, and more asymmetric. Two big clumps gather at the end of the elongated ring, and re-inforce the bar potential. This produces more gravity torques, and a rapid loss of angular momentum for the gas in the ring. The ring collapses towards the center in a few rotations.
However, the results of these simulations are highly dependent on the fact that the stellar potential remains fixed and barred, with an imposed pattern speed. In fact the gas infall, when sufficiently massive, will perturb significantly the potential in the center, the pattern speed of the bar, and even can destroy the bar (Friedli & Benz 1993). A more likely behavior is the formation of two ILR's, due to the high mass concentration, the formation of a phase-shifted bar, due to the existence of perpendicular x2 orbits (Shaw et al. 1993; Combes 1994), or the formation of a secondary bar inside the primary one (see section 16). Both behaviors represent mechanisms to fuel the gas towards the nucleus, and extend towards the center the effects of the gravity torques from the primary bar. The actual behavior depends however on the gas simulation code and on its assumed viscosity.
With the help of self-consistent simulations with stars and fluid-gas (through the beam-scheme hydrodynamical code, e.g., Sanders & Prendergast 1974), Junqueira & Combes (1996) have shown that a large mass concentration due to gas infall can both destroy the bar and help an m = 1 instability to grow. The latter phenomenon is quite stable, and prevents at the same time further gas infall.
Many galaxies are observed with their nuclei off-centered with respect to neighboring isophotes, and lopsided morphologies have been known for a long time (Baldwin et al. 1980). Asymmetric features are preferentially observed in the distribution of gas in late-type spiral galaxies. In a sample of 1700 galaxies, Richter & Sancisi (1994) have found that more then 50% of HI distributions are significantly asymmetrical. Stellar disks reveal also lopsidedness, in about 30% of cases, in the old population traced by the K-band (2.2µ, Rix & Zaritsky 1995). In several cases these features can be identified as one-armed spirals (m = 1 mode, e.g., Phookun et al. 1992, 1993). More frequently, nuclei of galaxies are observed displaced with respect to the gravity center, as in M33, M101 or M31 (Bacon et al. 1994). Our own galaxy appears to experience such an off-centering, at least as far as the gas disk is concerned: about three quarters of the molecular mass of the nuclear disk is at positive longitude, and one quarter at negative longitude (e.g., Bally et al. 1988). Asymmetries are also seen at larger scale in atomic gas, while much of the neutral gas between a few hundred parcsecs and 2 kiloparsecs from the nucleus lies in a tilted disk whose plane of symmetry is inclined by 20° with respect to the galactic plane (e.g., Burton 1992). Barred spiral galaxies can have their kinematical center displaced from the bar center (de Vaucouleurs & Freeman 1973; Marcelin & Athanassoula 1982; Phookun et al. 1992; Odewahn 1996). It has been suggested by Colin & Athanassoula (1989) that offset bars can generate a one-armed structure in the disk.
The frequency of asymmetries and lopsidedness in spiral galaxies requires some efficient dynamical mechanism to generate and maintain them. The swing amplifier can play a role, but the dominant amplified mode depends essentially on the degree of self-gravity of the disk (e.g., Jog 1992): high disk-to-halo mass ratio, low velocity dispersion, and high gas fraction are favorable. One can remark also that a direct m = 1 mode is favored by the absence of damping at resonances, since there is no ILR possible ( - < 0). Another mechanism can be the excitation of a leading m = 1 spiral by a retrograde companion (Thomasson et al. 1989). In that case, elongated orbits excited by the tide precess at a rapid and retrograde rate, and form a leading retrograde spiral. This occurs with a close interaction, when the disk of the target is embedded in a very massive halo. Since galaxies with leading arms are very rare, this might mean that the halo-to-disk mass within the visible disk is lower than unity for most spiral galaxies. It is a general observation that spiral galaxies with m = 1 structures display also higher order m = 2, 3, ... structures, and the sense of arms winding is usually the same for each set of structures. An interesting exception is NGC 4622, which we discuss specially in section 17.1. One of the results of the N-body simulations by Zang and Hohl (1978) is that the introduction of a significant fraction of counter-rotating stars can produce one-armed structures, in addition to the m = 2 instability. The m = 1 instability has been confirmed analytically by Palmer & Papaloizou (1990) in the case of equal numbers of direct and retrograde stars. However, one-armed spirals do not possess a larger fraction of stars in counterrotation than galaxies with two arms. Another possibility to trigger asymmetries and lopsidedness is infall of gas (Sancisi et al. 1990; Phookun et al. 1993).
Miller & Smith (1992) have studied, through N-body simulations of disk galaxies, a peculiar oscillatory motion of the nucleus with respect to the rest of the axisymmetric galaxy. They interpret the phenomenon as a local instability, or overstability, of the center, but not in terms of a normal mode. Their models did not include any gas component. The presence of gas may change the picture considerably.
A qualitatively different mechanism has been studied in the context of massive gaseous disks around young stellar objects, i.e. nearly Keplerian disks, by Adams et al. (1989). They discovered numerically a family of unstable normal modes where the star did not lie at the center of mass of the system. The m = 1 instability arises essentially from the displacement of the central star from the center of mass of the system, which creates an effective forcing potential. Shu et al. (1990) presented an analytical description of a modal mechanism, the SLING amplification, or ``Stimulation by the Long-range Interaction of Newtonian Gravity''. This mechanism uses the corotation amplifier, where the birth of positive energy waves outside strengthens negative energy waves inside. In the SLING mechanism, a feedback cycle is provided by four waves outside corotation; long-trailing waves propagate from the OLR inward to the Q-barrier at CR where they refract in short trailing waves. These propagate outwards, cross the OLR, and reflect back to the outer edge of the disk. This is a critical point: the whole amplification mechanism depends on the reflecting character of this outer edge (cf. Noh et al. 1992). Then a short leading wave propagates inwards from the edge, through OLR, towards CR, where it refracts again into a long leading wave, which is then reflected at OLR. An essential point here is also the ability of waves not to be absorbed at OLR, which is why this mechanism applies to gaseous disks only. Using a WKBJ analysis, they derived from the dispersion relation, and the condition of a constructive reflection, the required pattern speed for these modes.
The same mechanism could be applied to massive gaseous disks in the central parts of galaxies possessing high central mass concentrations, as proposed by Junqueira & Combes (1996). At first, a bar instability accumulates gas towards the center, when it becomes unstable and forms an m = 1 spiral mode (Figure 80). The mode grows in a dynamical time, and remains quasi-steady until the end of simulations (during 2 x 109 yrs). The gaseous disk mass represents more than 25% of the central mass. In the density plots, the spiral is conspicuous until 3 kpc radius, and other more transient features, with much lower angular speeds, dominate at larger radii. The Fourier analysis of the total potential indicates a very high pattern speed of p = 400km s-1 kpc-1 for the central m = 1 spiral, which corresponds to the OLR at 3 kpc (Figure 81). This pattern speed is much higher than the speed at larger radii; there is no coupling between several modes, as was suggested for bars within bars. In the latter case, the corotation of the small bar is the inner resonance of the large one, and there exists a non-linear interaction between the two patterns (Tagger et al. 1987). A non-linear interaction between two modes with azimuthal mode numbers m = n and m = n + 1 was proposed by Laughlin & Korchagin (1996) to trigger m = 1 instabilities in low-mass disks, and was confirmed through self-consistent hydrodynamic simulations.
|m = 1 (potential)|
|m = 1 (gas)|
The power spectrum analysis for the gas density of Figure 80 and the corresponding total potential reveals that the influence of the fast-rotating m = 1 pattern extends towards the edge (Figure 81). This can be explained for the potential, since the m = 1 perturbation is a periodic move of the center of mass, and is instantaneously felt in the whole disk, but the signature in the gas density is more remarkable. The stellar component does not follow the m = 1 spiral with as much contrast, but the off-centering of its center of mass is also conspicuous. The two components oscillate in phase opposition, while the massive dark halo, represented by an analytical Plummer component, is nailed down to the center. The large gaseous condensations in the center of spiral galaxies can therefore give rise to new instabilities, and account for some of the observed off-centered nuclei or lopsided distributions.