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Why do we think that secular evolution is happening? The observational evidence is discussed in Section 4, but the story begins with the forty-year history of simulations of the response of gas to bars. Figure 2 illustrates this response and how well it accounts for barred galaxy morphology. The angular momentum transfer from bar to disk that makes the bar grow also rearranges disk gas into outer rings near outer Lindblad resonance (O in the figure at upper-left), inner rings near bar corotation (C), and dense concentrations of gas near the center.

Figure 2

Figure 2. Evolution of gas in a rotating oval potential (Simkin, Su, & Schwarz 1980). The gas particles in this sticky-particle n-body model are shown after 2, 3, 5, and 7 bar rotations (top-left through center-left). Four SB0 or SB0/a galaxies are shown that have outer rings and a lens (NGC 3945) or an inner ring (most obvious in ESO 426-2 and in NGC 3081). Sources: NGC 3945 - Kormendy (1979); NGC 2217, NGC 3081 - Buta et al. (2004); ESO 426-2 - Buta & Crocker (1991). This figure is from Kormendy & Kennicutt (2004).

The essential features of Figure 2 are well confirmed by more recent, state-of-the-art simulations. In a particularly important paper, Athanassoula (1992) focuses on the gas shocks that are identified with dust lanes in bars. The shocks are a consequence of gravitational torques. Gas accelerates as it approaches and decelerates as it leaves the potential minimum of the bar. Therefore it piles up and shocks near the ridge line of the bar. Athanassoula finds that, if the mass distribution is centrally concentrated enough to result in an inner Lindblad resonance, then the shocks are offset in the forward (rotation) direction from the ridge line of the bar. That is, incoming gas overshoots the ridge line of the bar before it plows into the departing gas. The nearly radial dust lanes seen in bars are essentially always offset in the forward (rotation) direction. Compelling support for the identification of the shocks with these dust lanes is provided by the observation of large velocity jumps across the dust lanes (Pence & Blackman 1984; Lindblad, Lindblad, & Athanassoula 1996; Regan, Sheth, & Vogel 1999; Weiner et al. 2001; and especially Regan, Vogel, & Teuben 1997).

Shocks inevitably imply that gas flows toward the center. Because the shocks are nearly radial, the gas impacts them almost perpendicularly. Large amounts of dissipation make the gas sink rapidly. Athanassoula estimates that azimuthally averaged gas sinking rates are typically 1 km s-1 and in extreme cases up to ~ 6 km s-1. Because 1 km s-1 = 1 kpc (109 yr)-1, the implication is that most gas in the inner part of the disk finds its way to the vicinity of the center over the course of several billion years, if the bar lives that long.

Crunching gas likes to make stars. Expectations from the Schmidt (1959) law are consistent with observations of enhanced star formation, often in substantial starbursts near the center. Examples are shown in Figure 3. Most of these are barred galaxies illustrated in Sandage & Bedke (1994). NGC 4736 is a prototypical unbarred oval galaxy. It is included to illustrate the theme of the next section that barred and oval galaxies evolve similarly.

Figure 3

Figure 3. Nuclear star formation rings in barred and oval galaxies. Sources: NGC 4314 - Benedict et al. (2002); NGC 4736 - NOAO; NGC 1326 - Buta et al. (2000) and Zolt Levay (STScI); NGC 1512 - Maoz et al. (2001); NGC 6782 - Windhorst et al. (2002) and the Hubble Heritage Program. This figure is from Kormendy & Kennicutt (2004).

Kormendy & Kennicutt (2004) compile gas density and star formation rate (SFR) measurements for 20 nuclear star-forming rings. The SFR densities are 1 - 3 orders of magnitude higher than the SFR densities averaged over galactic disks. Gas densities are correspondingly high: nuclear star-forming rings lie on the extrapolation of the Schmidt law, SFR propto (gas density)1.4. The BIMA Survey of Nearby Galaxies (SONG) (Regan et al. 2001) shows that molecular gas densities follow stellar light densities, especially in barred and oval galaxies, even where the stellar densities rise toward the center above the inward extrapolation of an exponential fitted to the outer disk. Since star formation rates rise faster than linearly with gas density, this guarantees that the observed pseudobulges will grow in density faster than their associated disks. That is, pseudobulge-to-disk ratios increase with time. Growth rates to reach the observed stellar densities are a few billion years.

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