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6.1. Evolution Along the Hubble Sequence

The qualitative arguments in Sections 2 - 4 and the star-formation measures in Section 5 imply that secular evolution increases bulge-to-total luminosity ratios B / T. How much evolution along the Hubble sequence is plausible?

This question is too important to be postponed, but we warn readers that the results of this section are very uncertain. To address the question, we compare predicted B / T ratios with the distribution of values observed by Simien & de Vaucouleurs (1986). They decomposed the B-band surface brightness profiles of 98 galaxies to measure B / T as a function of RC2 type. They added up all of the central light in excess of the inward extrapolation of exponentials fitted to the outer disks, so B / T measures the sum of bulge and pseudobulge light. They found that B / T is typically 2% in Sd galaxies, 9% in Sc galaxies, 16% in Sbc galaxies, 24% in Sb galaxies, and 41% in Sa galaxies. The scatter around these values is large. In Sections 5.1 and 5.2, we estimate that circumnuclear star-forming rings grow pseudobulges with masses of ~ 109 Modot. The plausible range of these masses is also large, from ~ 107 to 1010 Modot. The total stellar masses of these galaxies are of order (1 to 5) × 1010 Modot. Therefore secular evolution can reasonably have produced pseudobulges with masses ranging from 0% to >10% of the total stellar masses of the systems. This is comparable to the B / T value in Sc galaxies, consistent with our conclusion that Scs contain pseudobulges. Evolution of one Hubble stage - e.g., from Sd to Sc - is plausible at the late end of the Hubble sequence. Evolution from Sc to Sbc is also plausible.

However, it is less easy for secular processes to form the more massive bulges of S0-Sb galaxies. The B / T ratio in these galaxies is large, and the galaxies tend to be very massive. Total bulge masses are at least 1010 - 1011 Modot. The evidence from stellar populations (Section 8.1) is that the stars in these bulges formed quickly and long ago. We conclude that the stars in these bulges formed mostly during hierarchical clustering. That is, S0-Sb galaxies mainly contain classical bulges. Secular processes can contribute modestly to the growth of classical bulges, but evolution by half of a Hubble stage is expected to be unusual. Based on present star formation rates, Sab galaxies like NGC 4736 that have dominant pseudobulges should be rare.

In fact, they are not extremely rare, and even some S0s have pseudobulges. The above estimates are lower limits for at least two reasons. First, disk galaxies presumably contained more gas in the past. Second, some secular processes, such as buckling instabilities, do not depend on concurrent star formation. They elevate pre-existing disk stars into the pseudobulge.

6.2. Merger-Induced Versus Secular Star Formation in Bulges

Finally, we make a preliminary comparison of the relative importance of secular and merger-induced star formation in the present universe. As shown above, it is plausible that most of the stars in Sc-Sm (pseudo)bulges and a significant fraction of the stars in Sb-Sbc (pseudo)bulges formed as a result of secular evolution. Given the relative numbers of early- and late-type galaxies, classical bulges and pseudobulges are not very different in number. However, the masses of (mostly) classical bulges in early-type galaxies are at least one to two orders of magnitude larger than the masses of pseudobulges in late-type spirals. Integrated over the history of the universe, star formation caused by secular processes has contributed at most a few percent of bulge stars. The vast majority of bulge stars are believed to have formed in collapse and merger events.

However, most of these events occurred in the distant past. Observations show that merger rates increase dramatically with increasing cosmic lookback time (Patton et al. 2002, Conselice et al. 2003). The fractional contribution of galaxy interactions and mergers to the total present-day SFR in the universe has been estimated by many workers, starting with Larson & Tinsley (1978). Kennicutt et al. (1987) estimated that 6% ± 3% of current star formation is induced by galaxy-galaxy interactions. This contains two, partly compensating uncertainties. It underestimates dust-extincted star formation in bulges, but it overestimates bulge star formation because it includes a contribution from distant tidal interactions as well as mergers. How does this value compare to the contribution from secular evolution? In Section 5.3, we note that ~ 10% of intermediate-type spirals contain circumnuclear disks or rings and that their star formation accounts for 10-80% of the current SFR in those galaxies. These same intermediate-type spirals dominate the current total cosmic SFR (Brinchmann et al. 2003). Combining these numbers suggests that a few percent of present-day star formation is attributable to secular processes. Thus, galaxy mergers and secular evolution produce comparable star formation in the present universe. Both contributions are small compared with the dominant source of star formation at z = 0, namely the quiescent star formation in the disks of spiral and irregular galaxies. Nevertheless, as argued in the Introduction, we live approximately at the epoch of transition when secular processes are overtaking mergers as the primary mechanism that forms stars in the central parts of galaxies. We emphasize again that all the estimates in Sections 6.1 and 6.2 are very uncertain.

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