ARlogo Annu. Rev. Astron. Astrophys. 2004. 42: 603-683
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3.3. The Demise of Bars

Bars commit suicide if they drive gas inward and build up too large a central mass concentration (Hasan & Norman 1990; Freidli & Pfenniger 1991; Friedli & Benz 1993; Hasan, Pfenniger, & Norman 1993; Norman, Sellwood, & Hasan 1996; Heller & Shlosman 1996; Berentzen et al. 1998; Sellwood & Moore 1999; Shen & Sellwood 2004). This is another example of an internal secular evolution process. For example, Norman et al. (1996) grew a point mass at the center of an n-body disk that previously had formed a bar. Before they switched on the point mass, they checked that the bar was stable and long-lasting. As they gradually turned on the point mass, the bar amplitude weakened. It weakened more for larger point masses; central masses of 5 - 7 % of the disk mass were enough to dissolve the bar completely. The result was a nearly axisymmetric galaxy.

Why? A heuristic understanding is provided by Section 2.2. Inward gas transport increases the circular-orbit rotation curve and the associated epicyclic frequency kappa(r) of radial oscillations near the center. As a result, Omega - kappa / 2 increases more rapidly toward small radii. That is, it is less nearly constant. So it is more difficult for self-gravity to persuade x1 orbits with different radii to precess together at Omegap and not almost together at Omega(r) - kappa(r) / 2. Furthermore, while Omega - kappa / 2 increases because the central mass concentration increases, the bar slows down because it transfers angular momentum to the outer disk. That is, Omegap and Omega - kappa / 2 evolve in opposite directions. This makes it still harder for Omegap to be approximately equal to Omega - kappa / 2. And as the radius of ILR grows, the radius range of the x2 orbits that are perpendicular to the bar and that cannot support it also grows. Real bars get nonlinear as their amplitude grows, so the epicyclic approximation on which this discussion is based eventually breaks down 3 For example, in Norman et al. (1996), Omegap increases slightly late in the simulation as the internal structure of the dissolving bar changes (Sellwood & Debattista 1993a). Nevertheless, it provides a plausibility argument for the result found in the simulations, which is that more and more orbits become chaotic and cease to support the bar.

How much central mass is required to destroy the bar differs in different papers. In some simulations, a central mass of 2 % of the disk already weakens the bar (Berentzen et al. 1998). Shen & Sellwood (2004) investigate this problem and find that great care is needed to make the time step short enough near the central mass; otherwise, the bar erodes erroneously quickly. They also find that "hard" central masses - ones with small radii, like supermassive black holes - destroy bars more easily than "soft" masses - ones with radii of several hundred parsec, like molecular clouds and pseudobulges. A bar can tolerate a soft central mass of 10 % of the disk mass, although its amplitude is reduced by a factor of ~ 2.

What does a defunct bar look like? Kormendy (1979b, 1981, 1982a) suggested that some bars evolve into lens components. The suggestion was based partly on the observation (point 7 in Section 2.1) that, when they occur together, the bar almost always fills the lens in its longest dimension. At the time, no reason for such evolution was known. However, the large velocity dispersion observed in the lens of NGC 1553 (Kormendy 1984) is consistent with the above idea, as follows. Elmegreen & Elmegreen (1985) find that early-type galaxies tend to have bars with flat brightness profiles, while late-type galaxies tend to have bars with exponential profiles. Therefore, azimuthal phase-mixing of an early-type bar would produce a hot disk with a brightness distribution like that of a lens, while azimuthal phase-mixing of a late-type bar would produce a brightness distribution that is indistinguishable from that of a late-type unbarred galaxy. Lenses do occur preferentially in early-type galaxies (Kormendy 1979b). To test whether bars evolve into lenses, we need an n-body simulation in which a bar with a flat profile and a sharp outer edge is destroyed by growing a central mass. The bars in published simulations have steep density profiles.

Therefore, secular evolution tends to kill the bar that drives it. The important implication is this: Even if a disk galaxy does not currently have a bar, bar-driven secular evolution may have happened in the past.

3 For example, in Norman et al. (1996), Omegap increases slightly late in the simulation as the internal structure of the dissolving bar changes (Sellwood & Debattista 1993a). Back.

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