4.4. Fueling nuclear activity
The main problem to fuel the nucleus is to solve the transfer of angular momentum problem. Torques due to the bar are very efficient, but gas can be stalled in a nuclear ring at ILR. Other mechanisms can then be invoked: viscous torques, or dynamical friction of giant clouds (GMC) against stars. The viscosity is in general completely unefficient over the galactic disk, but the corresponding time-scale is decreasing with decreasing radius. Unfortunately, in the center of galaxies, the rotation is almost rigid, the shear is considerably reduced, and so are the viscous torques. The time-scale for dynamical friction becomes competitive below r = 100pc from the center (about 107 (r / 100pc)2 yr for a GMC of 107 M). For the intermediate scales, a new mechanism is required.
Note that if there is a supermassive black hole in the nucleus, it is easier to bring the gas to the center. Indeed, the presence of a large mass can change the behaviour of the precessing rate of orbits - / 2: instead of increasing with radius inside ILR (as in fig 4), it will decrease.
Due to cloud collisions, the gas clouds lose energy, and their galactocentric distance shrinks. Since it tends to follow the periodic orbits, the gas streams in elliptical trajectories at lower and lower radii, with their major axes leading more and more the periodic orbit, since the precession rate (estimated by - / 2 in the axisymmetric limit, for orbits near ILR, and by + / 2 near OLR) increases with decreasing radii in most of the disk (fig 8). This regular shift forces the gas into a trailing spiral structure, from which the sense of the gravity torques can be easily derived. Inside corotation, the torques are negative, and the gas is driven inwards towards the inner Lindblad resonance (ILR). Inside ILR, and from the center, the precessing rate is increasing with radius, so that the gas pattern due to collisions will be a leading spiral, instead of a trailing one (see Figure 9). The gravity torques are positive, which also contributes to the accumulation of gas at the ILR ring. This situation is only inverted in the case of a central mass concentration (for instance a black hole), for which the precession rate - / 2 is monotonically increasing towards infinity with decreasing radii. Only then, the gravity torques will pull the gas towards the very center, and ``fuel'' the nucleus.
Figure 8. a) Periodic orbits in a barred galaxy (cos 2 potential, oriented horizontally). Their orientation rotates by / 2 at each resonance. b) The gas tends to follow these orbits, but is forced to precess more rapidly while losing energy and angular momentum, since - / 2 is a decreasing function of radius.
The problem reduces to forming the black hole in the first place. We show next that the accumulation of matter towards the center can produce a decoupling of a second bar inside the primary bar. This nuclear bar, and possibly other ones nested inside like russian dolls, can take over the action of gravity torques to drive the gas to the nucleus, as first proposed by Shlosman et al. (1989).
Figure 9. a) Without a central mass concentration, - / 2 is increasing with radius in the center: the gas winds up in a leading spiral inside the ILR ring; b) with a central mass concentration, it is the reverse and the gas follows a trailing spiral structure, inside ILR.