Annu. Rev. Astron. Astrophys. 1997. 35: 637-675
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5.3. Disk-Bars-Bulges, Etc

Recall that the broadband color distributions of disk galaxies show smooth continuity across the transition between disk and bulge. In the mean, there is approximate equality between the colors of the inner disk and the bulge in any one galaxy (de Jong 1996, Peletier & Balcells 1996). These data may be interpreted as showing similar mean age and metallicity for inner disk and bulge (de Jong 1996, Peletier & Balcells 1996), but the degeneracy of age and of metallicity on the colors of stellar populations cause uncertainties (see, for example, Peletier & Balcells 1996). Courteau et al (1996) find further that the scale lengths of disk and bulge are correlated. They argue that this relationship implies that the bulge formed via secular evolution of the disk. In principle this is possible if disks are bar-unstable and bars are themselves unstable, and if significant angular-momentum transport is feasible.

The secular evolution of collisionless stellar disks has been studied in some detail recently, in particular through three-dimensional N-body simulations (Combes et al 1990, Raha et al 1991; see Combes 1994, Pfenniger 1993 for interesting reviews). These simulations demonstrated that not only are thin disks often unstable to bar formation, but bars themselves can be unstable, in particular to deformations out of the plane of the disk, perhaps leading to peanut-shaped bulges. The kinematics of stars in "peanut bulges" lend some observational support for the association of peanut bulges with bars (Kuijken & Merrifield 1995). Thus stars initially in the inner disk end up in the bulge, which provides a natural explanation for the continuity observed in the properties of the stellar populations in disks and in bulges.

Merritt & Sellwood (1994; see also Merrifield 1996) provided a detailed description of the physics of instabilities of stellar disks. They demonstrated that the buckling instability of the stellar bar that produces a peanut bulge (Combes et al 1990, Raha et al 1991) is a collective phenomenon, similar to a forced harmonic oscillator. Thus the instability involves the bar in general, not only stars on special resonant orbits, as had been earlier proposed (e.g. Combes et al 1990). Not all instabilities form peanuts, which is just as well for this class of model for bulge formation, because, although box/peanut bulges are perhaps fairly common, comprising 20% of galaxies (Shaw 1987), the subset of these that rotate on cylinders is small (e.g. Shaw 1993 and references therein). Relevant photometric studies show that the light in a peanut bulge is additional to that in a smooth underlying disk, not subtracted from it (e.g. Shaw et al 1990, Shaw 1993), which rather weakens the case for these models.

The extant simulations of bar instabilities also find that a very small mass concentration at the center of the galaxy can destroy a bar. Such a mass concentration is very likely, since inflow, driven by gravitational torques, is probable after a bar is formed. Hasan & Norman (1990) suggested that a sufficiently large central mass concentration could eventually destroy the bar. Norman et al (1996) used three-dimensional N-body simulations to follow the evolution of a bar-unstable disk galaxy and attempted to incorporate the effects of gas inflow by allowing the growth of a very centrally concentrated component. Indeed, in time the fraction of material in this central component is sufficient to destroy the bar, fattening it into a "bulge-like" component. Bulges may be built up by successive cycles of disk instability-bar formation-bar dissolution (Hasan et al 1993). The time scales and duty cycles are not clear. Some simulations (e.g. Friedli 1994) find that as little as 1% of the mass in a central component is sufficient to dissolve a bar. This is a potential problem, as Miller (1996) points out, since the fact that one observes bars in around 50% of disk galaxies means that bars cannot be too fragile. A numerical example supporting Miller's important point is provided by Dehnen (1996), who finds that his bar is stable even with a cuspy density profile in the underlying disk. The simulations are clearly not yet mature.

A further potential problem with the general applicability of this scenario of bulge formation is the different light profiles of bars in galaxies of different bulge-to-disk ratio - early-type disk galaxies have bars with flat surface density profiles (e.g. Noguchi 1996, Elmegreen et al 1996), whereas late-type galaxies have bars with steeper surface brightness profiles than their disks. The Courteau et al correlation, that bulge scale lengths are around one-eighth that of disks, was found for a sample of late-type galaxies. In this scenario, the color of a bar should also be the same color as its surrounding disk, so that the subsequent bulge is the same color as the disk. While colors of bars are complicated by dust lanes and associated star formation, barred structures are often identified by means of color maps (e.g. Quillen et al 1996), suggesting problems for this class of model.

Specific counter-examples to models where the bulge forms through secular evolution of the inner disk are the high-luminosity but low surface brightness disk galaxies, such as Malin 1 (McGaugh et al 1995), which have apparently "normal" bulges (e.g. surface brightnesses and scale lengths typical of galaxies with high surface brightness disks) that clearly could not have formed by a disk instability.

Dissipationless formation of bulges from disks suffers yet a further problem, in that the phase space density of bulges is too high (Ostriker 1990, Wyse 1997). This also manifests itself in the fact that the spatial densities of bulges are higher than those of inner disks. Thus one must appeal to dissipational processes to form bulges, such as gas flows. The presence of color gradients in some external bulges would support a dissipative collapse with accompanying star formation (e.g. Balcells & Peletier 1994). Indeed, Kormendy (1993) has argued that many bulges are actually inner extensions of disks, formed through gas inflow from the disk, with later in situ star formation. This complicates the interpretation of the similarity between the colors of bulges and inner disks, which was a natural product of a stellar instability to form bulges from disk stars. One should note also that should bulges indeed not be formed at high redshift, then dissipation is also implicated in the production of the high spatial densities of their central regions.

It is also important to note that the term bar is used no less generically than is the term bulge. There is a fundamental, and rarely clarified, difference between a detectable perturbation to the luminosity distribution and a substantial m = 2 perturbation to the galactic gravitational potential. Inspection of the delightful pictures in the Carnegie Atlas of Galaxies (Sandage & Bedke 1994) suggests a continuum of structures, with all degrees of symmetry and asymmetry (i.e. m = 1, 2, ...) and relative amplitudes. When is a bar fundamentally more than the region where spiral arms meet the center? More important for the continuing debate about the center of the Milky Way, is it true that all these structures are seen in the cold disks only? Is there such a thing as a bar-bulge?

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