The previous section suggests that bars increase the central mass concentration of disks, but it does not explain how to make bulges that are thick in the axial direction. This section reviews a heating process that may allow bars to manufacture box-shaped bulges out of disks. This has clearly captured the interest of the n-body modeling community; it has been discussed repeatedly at this meeting.
The idea is this: at radii where the vertical oscillation frequency z of disk stars is in resonance with the pattern speed B of the bar, the vertical motions are amplified by the bar. The most important such resonance is vertical inner Lindblad resonance (ILR), B = - z / 2 ( is the angular velocity of rotation about the center). At vertical ILR, the z oscillations look periodic to the bar, so perturbations accumulate quickly. The effect is analogous to azimuthal disk heating at planar ILR by bars and spiral arms. The result is that the disk thickens. Many authors have developed this picture; they show that the result is a rapidly rotating box-shaped "bulge" (Combes and Sanders 1981; Pfenniger 1984, 1985; Combes et al. 1990; Pfenniger and Norman 1990; Friedli and Pfenniger 1990; Pfenniger and Friedli 1991; Raha et al. 1991). A number of papers at this meeting further develop the theme (Friedli and Udry 1993; Hasan and Norman 1993; Pfenniger 1993; Sellwood 1993).
The process is attractive because it is specific (we can simulate it rigorously) and because it seems to work. The heating must happen. It also agrees in important ways with the observations: the resulting box-shaped bulges rotate cylindrically. But we do not yet know whether this process is sufficient in practice or whether it is the main process making boxy bulges. I am especially concerned about the extreme view that boxy bulges are bars seen side-on:
(i) Edge-on bars are very flat, and in some cases they coexist with a boxy bulge. One example is NGC 4762 (Hubble Atlas; Wakamatsu and Hamabe 1984).
(ii) If boxy bulges are side-on bars, then the longest major axes of boxy bulges should equal the lengths of bars in face-on galaxies.
(iii) The distributions of luminosity and B/T ratio for boxy bulges should equal the analogous distributions for bars in face-on galaxies.
Predictions (ii) and (iii) can be checked observationally. I suspect that all three points will be problems for the idea that boxy bulges are side-on bars. But I know of no observation that conflicts with the idea that boxy bulges are manufactured by vertical heating of the centrally concentrated disks discussed in sections 4 and 5.