Annu. Rev. Astron. Astrophys. 2004. 42: 603-683 Copyright © 2004 by Annual Reviews. All rights reserved

5.3. Constraining Evolution Timescales and Pseudobulge Growth

We can combine the data on SFRs and gas contents of the central regions of galaxies to constrain the evolutionary timescales and formation rates of pseudobulges. We first consider the prominent circumnuclear star-forming rings, which represent only the high-luminosity exttreme of this activity, but for which we can derive relatively hard constraints. A search of the literature reveals 20 galaxies with circumnuclear star formation and reliable data on the SFRs, central gas masses, and sizes of the star-forming regions. For each galaxy, we derived the mean molecular gas surface density (using standard CO - H₂ conversion factors) and the mean SFR surface density within the circumnuclear regions. These are plotted as filled squares with error bars in Figure 21. The SFRs were derived using a combination of methods, extinction-corrected H and Pa fluxes or far-infrared fluxes. The large error bars reflect considerable uncertainties in the SFRs due to dust extinction and possible AGN contamination and uncertainties in the CO - H₂ conversions that provide the gas masses. Ignoring atomic gas introduces another uncertainty, but this is expected to be of order 10 % or less (e.g., Young & Scoville 1991, Sanders & Mirabel 1996). For comparison, Figure 21 also shows the disk-averaged SFR and total gas densities for 61 spiral galaxies (solid circles), and the same data for the centers of these galaxies when spatially resolved data are available (open circles).

Figure 21. Correlation between SFR surface density and total gas surface density for 20 circumnuclear star-forming rings (filled squares with error bars) compared to disk-averaged values for 61 spiral galaxies (filled circles) and the centers of these galaxies (open circles). The circumnuclear data are compiled in this paper, and the comparison data are from Kennicutt (1998b). The solid diagonal lines show constant gas consumption time scales (increasing downward) of 0.1, 1, and 10 Gyr.

Figure 21 clearly shows that the circumnuclear rings populate a unique regime of molecular gas density and SFR. They extend the Schmidt SFR power law that is seen in the other galaxies (Kennicutt 1998b). For the sake of consistency, we adopted the same standard CO-H₂ conversion factor for all of the points; adopting a lower conversion factor for the centers would move the filled squares and open circles to the left by up to 0.3 - 0.5 dex. This would increase the best-fitting Schmidt-law slope from N ~ 1.4 to N ~ 1.5.

The same diagram can be used to constrain the timescale on which the circumnuclear gas disks turn into stellar disks. Figure 21 shows lines of constant gas consumption times of 0.1, 1, and 10 Gyr. The outer star-forming disks of these galaxies are characterized by mean star formation efficiencies of approximately 5 % per 10⁸ yr and gas depletion times of ~ 2 Gyr on average. However the star formation efficiencies in most the circumnuclear disks are much higher, of order 10 - 50 % per 10⁸ yr. Gas consumption timescales are 0.2 - 1 Gyr. If we assume that we observe the average disk at the midpoint of a gas accretion and starburst episode, this means that the typical formation timescales for these pseudobulges is approximately 0.4 - 2 Gyr. This is reasonably consistent with the (luminosity-averaged!) star cluster ages of 0.0 - 0.3 Gyr inferred in the HST studies cited earlier. Note, however, that if the standard CO-H₂ conversion factor overestimates the molecular masses of the disks, this would lower the inferred timescales, probably by a comparable amount.

We can now put together a rough picture of the growth rates of pseudobulges in present-day spirals. We infer a typical formation timescale of ~ 1 Gyr for the central disks from the arguments given above. When we combine this with a typical SFR range of 0.01 - 10 M yr^-1, we expect these gas accretion episodes to form pseudobulges with masses of order 10⁷ -10¹⁰ M. Typical systems like the examples in Figure 8 fall in the 10⁸ to (2 - 3) × 10⁹ M range. Furthermore, circumnuclear star-forming rings of this type are seen in ~ 10 % of intermediate-type spiral galaxies (Sérsic 1973, Maoz et al. 1996). As discussed earlier, lookback studies suggest that strong bars first formed at least 5 Gyr ago. Combining these numbers suggests that approximately half of unbarred spirals and nearly all barred spirals may have formed a pseudobulge in this mass range. Of course this rough calculation is subject to a chain of possible systematic errors. However, it demonstrates that a scenario in which pseudobulges are a common or even ubiquitous constituent of intermediate-Hubble-type, massive spiral galaxies is plausible.

So far, our results are based solely on the occurrence of the most prominent circumnuclear star-forming rings in barred galaxies. Is there independent evidence based on the statistics of central molecular gas disks for lower levels of star formation in central pseudobulge disks? To make such an estimate, we used the BIMA SONG survey (Helfer et al. 2003) to derive the median central molecular gas surface density in their objectively selected sample of 44 nearby spiral galaxies. This is ~ 200 M pc^-2, for a standard CO-H₂ conversion factor. Interestingly. this gas density already exceeds the typical stellar surface density in local spiral disks. A typical, late-type disk has a mass-to-light ratio M / L_B 1 and a central surface brightness µ_B = 21.7 mag arcsec^-2 (Freeman 1970). The corresponding stellar density is ~ 130 M pc^-2. Consequently, if the current gas disks are converted into stars, the central surface brightness of the disk will more than double. If the gas infall continues for a few Gyr, a proportionally brighter stellar component will be formed.

We can repeat this calculation by using Figure 21 to estimate the typical SFR densities in the centers of these barred galaxies, and combine this with the typical star formation timescales derived earlier to estimate the total surface density of stars formed. This calculation is not entirely independent, because the star formation timescales are partly derived from the measured molecular gas densities. However, there are independent constraints on the star formation timescales from HST studies of the star clusters in circumnuclear starbursts and from photometric constraints from integrated light. For a typical SFR density of 0.1-1 M yr^-1 kpc^-2 (Figure 21), we expect to build up central stellar densities of 50 - 500 M pc^-2 for star formation lifetimes of 0.5 Gyr, and 500 - 5000 M pc^-2 if the feeding of gas from the bar persists for 5 Gyr. This compares to "Freeman disk" central densities of ~ 100 - 250 M pc^-2 for M / L_B = 1 - 2. The total masses in these components are of the same order as the observed molecular gas disks in the centers of these galaxies, 10⁷ -10⁹ M, if there is no continued feeding of the nuclear disks, and up to 5 times larger if the gas feeding persists for 5 Gyr at a rate that is sufficient to replace the mass lost from star formation.

We reiterate that there are large uncertainties in these numbers. The most important uncertainties are the total duration of the inward gas transport in the bars, the CO-H₂ conversion factors used to estimate the molecular gas masses, and uncertainty in separating "pseudobulge" star formation from steady-state disk and/or nuclear star formation. However, our estimates demonstrate that in a typical barred spiral, the total central star formation that results from secular gas inflow can easily exceed that in the underlying disk. By the same token, even the high end of the mass ranges described here falls 1 - 2 orders of magnitude short of the massive bulges that are typical of giant S0 - Sab and elliptical galaxies.