ARlogo Annu. Rev. Astron. Astrophys. 2004. 42: 603-683
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How general are the results of the previous section? We reviewed the effects of bars on disks as the most clear-cut example of internal secular evolution. However, we do not mean to create the impression that such evolution is important only in the approximately one third of all disk galaxies that look barred at optical wavelengths. In this section we first review evidence that many apparently unbarred galaxies clearly show bars in the infrared. With the previous section as a guide, we then argue that similar evolution happens in unbarred but oval galaxies and at slower rates in global-pattern spirals. In fact, any nonaxisymmetry in the gravitational potential can rearrange disk gas.

3.1. Many Apparently Unbarred Galaxies Show Bars in the Infrared

Near-infrared images penetrate dust absorption and are insensitive to the low-M / L frosting of young stars in Sb-Sm disks. We then see the underlying old stars that trace the mass distribution. The most important revelation is that bars are hidden in many galaxies that appear unbarred at optical wavelengths (Block & Wainscoat 1991; Mulchaey & Regan 1997; Mulchaey et al. 1997; Seigar & James 1998; Knapen et al. 2000; Eskridge et al. 2000, 2002; Block et al. 2001; Laurikainen & Salo 2002). Approximately two thirds of all spiral galaxies look barred in the infrared. Quantitative measures of bar strengths based on infrared images (Buta & Block 2001; Block et al. 2001; Laurikainen & Salo 2002) will prove useful in gauging the consequences for secular evolution.

Some bars are weak in amplitude. But secular evolution can be more important than this suggests, because many bars are embedded in oval disks (Section 3.2) that contribute at least as much to the nonaxisymmetric potential as do the bars. NGC 1068 is one example (Scoville et al. 1988; Thronson et al. 1989; Pompea & Rieke 1990); for others, see Hackwell & Schweizer (1983); Block et al. (2002); Jarrett et al. (2003). Hidden bars are the first reason why the results of Section 2 are relevant to more than just the galaxies that look barred at optical wavelengths.

3.2. Oval Galaxies

A strong bar has an axial ratio of ~ 0.2 and a mass of approximately one third of the disk mass. In this section we discuss unbarred but globally oval galaxies in which the whole inner disk has an axial ratio of ~ 0.85. Ovals are less elongated than bars, but more of the disk mass participates in the nonaxisymmetry. As a result, barred and oval galaxies evolve similarly.

Strongly oval galaxies can be recognized independently by photometric criteria (Kormendy & Norman 1979; Kormendy 1982a) and by kinematic criteria (Bosma 1981a, b). The diagnostics are illustrated in Figure 9.

Figure 9

Figure 9. Criteria for recognizing strongly oval but unbarred galaxies shown schematically at left and with observations of NGC 4151 at right. This figure is adapted from Kormendy (1982a). The NGC 4151 HI velocity field is from Bosma, Ekers, & Lequeux (1977a).

3.2.1. BRIGHTNESS DISTRIBUTIONS   In prototypical ovals, the disk consists of two nested ovals, each with a shallow surface brightness gradient interior to a sharp outer edge. The inner oval is much brighter than the outer one. The two shelves in the brightness distribution have different axial ratios and position angles, so they must be oval if they are coplanar. But the flatness of edge-on galaxies shows that such disks really are oval. Warped disks are common, but they occur at lower surface brightnesses.

Nested ovals in unbarred galaxies are analogous, in barred galaxies, to lenses with embedded bars interior to outer rings. For the purposes of this paper, lenses in early-type galaxies and oval disks in late-type galaxies are functionally equivalent. Both are elliptical shelves in the disk density, and both are nonaxisymmetric enough to drive secular evolution.

Besides NGC 4736 (Figure 2) and NGC 4151 (Figure 9), oval disks illustrated in the Hubble Atlas (Sandage 1961) include NGC 4457 (Sa), NGC 3368 (Sa), NGC 4941 (Sa/Sb), NGC 1068 (Sb), NGC 210 (Sb), NGC 4258 (Sb), NGC 5248 (Sc), and NGC 2903 (Sc). Their similarity to barred galaxies can be seen by comparing the two shelves in their brightness distributions with similar ones in NGC 1291 (Figure 2), NGC 3945 and NGC 3081 (Figure 5), and, in the Hubble Atlas, NGC 2859 (SB0), NGC 5101 (SB0), NGC 5566 (SBa), NGC 3504 (SBb), and NGC 1097 (SBb).

3.2.2. KINEMATICS   Velocity fields in oval disks are symmetric and regular, but (a) the kinematic major axis twists with radius, (b) the optical and kinematic major axes are different, and (c) the kinematic major and minor axes are not perpendicular. Twists in the kinematic principal axes are also seen when disks warp. Warps in HI disks are common, but Bosma (1981a, b) points out that they happen at larger radii and lower surface brightnesses than oval structures, which are obvious in Figures 2 and 9 even at small radii. Also, observations (b) and (c) imply ovals, not warps.

As pointed out in Kormendy (1982a), the photometric and kinematic criteria for recognizing ovals are in excellent agreement. These strong ovals are expected to evolve similarly to barred galaxies, because the nonaxisymmetry in the potential is similar to that in barred galaxies. In fact, many simulations of the response of gas to bars actually assumed (presumably for computational convenience) that all of the potential is somewhat oval rather than that part of the potential is strongly barred and the rest is not. NGC 4736 is representative of the many unbarred but oval galaxies with strong evidence for secular evolution (see Figure 8 for star formation and Figure 17 for dynamical evidence).

So strongly oval galaxies are readily recognizable. Many are classified SAB; some are SA. However, statistical analyses of large samples of galaxies show that even unbarred disks are slightly oval. The scatter in the Tully-Fisher relation implies that the ellipticity in the potential that controls the disk lies in the range 0-0.06. (Franx & de Zeeuw 1992). The corresponding axial ratio of the density distribution is 0.84-1.0. Analyses of the velocity fields of individual galaxies give similar results (e.g., Andersen et al. 2001). And, in a study of 18 face-on spiral galaxies using K'-band photometry, Rix & Zaritsky (1995) showed that the typical disk has axial ratio 0.91. Not surprisingly, typical disks are more circular than easily recognized ovals. But they are not round. This is plausible, because disks live inside cold dark matter halos that are predicted to be very triaxial (Frenk et al. 1988, Warren et al. 1992, Cole & Lacey 1996). We now need an investigation of how much secular evolution is driven by the above, small nonaxisymmetries.

3.3. The Demise of Bars

Bars destroy themselves 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 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) investigated this problem and found that great care is needed to make the time step short enough near the central mass; otherwise, the bar erodes erroneously quickly. They also found 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) has 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 this idea, as follows. Elmegreen & Elmegreen (1985) found 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.

3.4. Global Pattern Spirals

Our picture of global spiral structure in galaxies is by now well developed (Toomre 1977b). Global spirals are density waves that propagate through the disk. Like water waves in an ocean but unlike bars, they are not always made of the same material. In general, stars and gas revolve around the center faster than the spiral arms, so they catch up to the arms from behind and pass through them. Central to our understanding of why young and bright but short-lived stars are concentrated in the arms is the concept that star formation is triggered when gas passes through the arms. As in the bar case, the gas accelerates as it approaches the arms and decelerates as it leaves them. Again, shocks form where the gas piles up. This time the shocks have a spiral shape. Their observational manifestations are dust lanes located on the concave side of the spiral arms (e.g., NGC 5236 in Figure 7). The strength of the shocks can be predicted from the rotation curve: The mass determines the rotation velocity, and the central concentration determines the arm pitch angle and hence the angle at which the gas enters the arms. The results (Roberts, Roberts & Shu 1975) provide the basis of our understanding of van den Bergh (1960a, b) luminosity classes of galaxies. More massive galaxies tend to have more differential rotation and stronger shocks, so star formation is enhanced and the arms seen in young stars are thinner and more regular.

Gas loses energy at the shocks and sinks toward the center. The effect is weaker than in barred galaxies, because the pitch angles of spiral arms are much less than 90°. The gas meets the shocks obliquely rather than head-on. Nevertheless, it must sink. Where it stalls depends on the mass distribution. In early-type spirals with big classical bulges, the spiral structure has an ILR at a large radius. The spiral arms become azimuthal at ILR and stop there. As the arm pitch angle approaches 0° and as the arm amplitude gets small, the energy loss drops to zero. The gas stalls near ILR. It may form some stars, but the bulge is already large, so the relative contribution of secular evolution is minor.

In contrast, late-type galaxies have no ILR, or the ILR radius is small. The gas reaches small radii and high densities; the result is expected to be star formation. If the process is fast enough, it can build a pseudobulge. Moreover, galaxies with no ILR are late in type. They have little or no classical bulge. Therefore, secular processes can contribute a central mass concentration that we would notice in just those galaxies in which the evolution is most important.

Is the evolution rapid enough to matter? Theoretical timescales are uncertain but look interestingly short. Gnedin, Goodman & Frei (1995) measure spiral arm torques from surface photometry of NGC 4321. They estimate that the timescale for the outward transport of angular momentum is 5-10 Gyr. Thus, even the stellar distribution should have evolved significantly if the spiral structure has consistently been as strong as it is now. NGC 4321 has unusually regular and high-amplitude spiral arms; weak spiral structure can easily imply angular momentum transport timescales that are an order of magnitude longer (Bertin 1983, Carlberg 1987). However, shocks speed up the sinking of gas; Carlberg (1987) estimates that it takes place on a Hubble timescale even for the weak spiral structure in his simulation. Zhang (1996, 1998, 1999, 2003) has derived even shorter timescales. Apart from such disagreements, we do not know how long the spiral structure has been as we observe it, a problem that Gnedin et al. (1995) understood.

Whatever the theoretical uncertainties, observations show that star formation takes place. Timescales are discussed in Section 5. Excellent examples of nuclear star formation in unbarred galaxies can be seen in M51 and NGC 4321 (Kormendy & Cornell 2004 show illustrations). Both galaxies have exceedingly regular global spiral structure. The spiral arms and their dust lanes wind down very close to the center, where both galaxies have bright regions of star formation. NGC 4321 is studied by Arsenault et al. (1988), Knapen et al. (1995a, b), Sakamoto et al. (1995), and García-Burillo et al. (1998). It is classified as Sc in Sandage (1961). In the RC3 (de Vaucouleurs et al. 1991), it is classified as SAB(s)bc; the spiral arms are distorted similar to pseudo-inner and -outer rings. There are signs of a weak bar in the infrared (see the above references and Jarrett et al. 2003). Nevertheless, NGC 4321 suggests that secular evolution can be important even in galaxies that do not show prominent bars at optical wavelengths.

Why doesn't every late-type galaxy have a pseudobulge? Calculations of spiral-arm shock strengths show that the shocks are weak if the rotation curve rises too linearly. The lowest-luminosity galaxies have little shear; it is not surprising that they do not make substantial pseudobulges.

In summary, late-type unbarred but global-pattern spirals are likely to evolve in substantially the same way as barred galaxies, only more slowly.

3.5. Conclusion

Barred galaxies give us a rich picture of secular evolution at work. One robust consequence is the buildup of the central mass concentration via the inward radial transport of gas. Infrared imaging shows that the majority of spiral galaxies have bars. Theoretical arguments and observational evidence suggest that similar processes are at work in many unbarred galaxies, especially in oval galaxies and in late-type, global-pattern spirals. In late-type galaxies, it is relatively easy for the central mass concentration that we see to be caused by secular processes, because the evolution happens most readily if a galaxy does not already have a classical bulge.

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

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