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Progress on bulge formation is dominated by two conceptual advances. This section revisits secular evolution in disk galaxies. This is a major addition that complements our picture of galaxy evolution by hierarchical clustering. I begin here because all further discussion depends on the resulting realization that the dense central components in galaxies come in two varieties with different formation processes, classical and pseudo bulges. Section 3 discusses the second conceptual advance, the discovery of a new channel for the formation of classical bulges. This is the formation at high z of unstable clumps in gas-rich disks; they sink to the center along with lots of disk gas and starburst and relax violently. In this way, bulge formation proceeds largely as it does during major mergers. This leads to a discussion of the merger formation of both bulges and ellipticals in Section 4.

Our pictures of the merger formation of classical bulges and ellipticals and the secular growth of pseudobulges out of disks both got their start in the late 1970s. The importance of major mergers (Toomre & Toomre 1972; Toomre 1977) in a hierarchically clustering universe (White & Rees 1978) got a major boost from the realization that CDM halos make galaxy collision cross sections much bigger than they look. This subject “took off” and rapidly came to control our formation paradigm. Secular evolution is a more difficult subject – slow processes are hard to study – and it did not get a similar boost from the CDM revolution. However, the earliest papers on the subject come from the same time period: e.g., Kormendy (1979a) emphasized the importance of slow interactions between nonaxisymmetric galaxy components; Kormendy (1979b) first pointed out the existence of surprisingly disky bulges; Combes & Sanders (1981) showed that boxy pseudobulges are edge-on bars. Kormendy (1981, 1982) reviewed and extended the results on disky bulges. This subject did not penetrate the galaxy formation folklore; rather, it remained a series of active but unconnected “cottage industries” for the next two decades. Nevertheless, by the 1990s, the concept–if not yet the name– of disky pseudobulges was well established (see Kormendy 1993 for a review), and the idea that boxy bulges are edge-on bars was well accepted (see Athanassoula 2005 for a more recent and thorough discussion). I hope it is fair to say that the comprehensive review by Kormendy & Kennicutt (2004) has helped to convert this subject into a recognized paradigm – it certainly is so in this book – although it is still not as widely understood or taken into account as is hierarchical clustering.

Kormendy & Kennicutt (2004) remains up-to-date and comprehensive on the basic results and on observations of prototypical pseudobulges. However, new reviews extend and complement it. Kormendy & Fisher (2005, 2008) and Kormendy (2008, 2012) provide the most important physical argument that was missing in Kormendy & Kennicutt (2004): Essentially all self-gravitating systems evolve toward more negative total energies (more strongly bound configurations) by processes that transport kinetic energy or angular momentum outward. In this sense, the secular growth of pseudobulges in galaxy disks is analogous to the growth of stars in protostellar disks, the growth of black holes in black hole accretion disks, the sinking of Jupiters via the production of colder Neptunes in protoplanetary disks, core collapse in globular clusters, and the evolution of stars into red (super)giants with central proto white dwarfs, neutron stars, or stellar-mass black holes. All of these evolution processes are related. So secular disk evolution and the growth of pseudobulges is very fundamental, provided that some process redistributes angular momentum in the disk. My Canary Islands Winter School lectures (Kormendy 2012) are an up-to-date observational review that includes environmental secular evolution. Sellwood (2014) provides an excellent theoretical review.

Boxy pseudobulges are discussed in four chapters of this book; I concentrate on disky pseudobulges. Fisher & Drory (2015) review the distinction between classical and pseudo bulges from a purely phenomenological point of view. That is, they intercompare observational diagnostics to distinguish between the two bulge types with no reference to physical interpretation. This is useful, because it gives relatively unbiased failure probabilities for each diagnostic. They are not wholly independent, of course, because they are intercompared. But they are independent enough in execution so that we get a sufficient estimate of the failure probability when they are combined by multiplying the individual failure probabilities.

Kormendy & Kennicutt (2004), Kormendy (2012), and KH13 strongly advocate the use of as many bulge classification criteria as possible. The reason is that any one criterion has a non-zero probability of failure. Confusion in the literature (e.g., Graham 2011) results from the fact that some authors use a single classification criterion (e.g., Sérsic index) and so get results that conflict with those derived using multiple criteria. But we have long known that most classical bulges have n ≥ 2, that most pseudobulges have n < 2, and that there are exceptions to both criteria. No-one should be surprised that Sérsic index sometimes fails to correctly classify a bulge. This is the point that Fisher & Drory (2015) make quantitative.

Fisher & Drory (2015) show that the failure probability of each classification criterion that they test is typically 10–20%. A few criteria are completely robust (if B / T ≳ 0.5, then the bulge is classical) and a few are less reliable (star formation rate cannot be used for S0s). But, by and large, it is reasonable to conclude that the use of M criteria, each with failure probability єm, results in a classification with a failure probability of order the product of the individual failure probabilities, Π1m єm. This becomes very small very quickly as M grows even to 2 and especially to M > 2. For example, essentially all bulge-pseudobulge classifications in KH13 were made using at least two and sometimes as many as five criteria.

Fisher & Drory (2015) also contribute new criteria that become practical as new technology such as intergral-field spectroscopy gets applied to large samples of galaxies. These are incorporated into an enlarged list of classification criteria below.

A shortcoming of Fisher & Drory's approach is that it is applied without regard to galaxy Hubble types. But we know that both many S0s and many Sbcs contain pseudobulges, but the latter all tend to be star-forming whereas the former generally are not. This is one reason for their conclusion (e.g.) that high star formation rate near the galaxy center robustly implies a pseudobulge, but no star formation near the center fails to prove that the bulge is classical. Classification criteria that involve gas content and star formation rate cannot be applied to S0 galaxies. Application to Sas is also fragile. Fortunately, most criteria do work for early-type galaxies.

2.1. Enlarged List of Bulge-Pseudobulge Classification Criteria

Kormendy & Kennicutt (2004), Kormendy (2012), and Fisher & Drory (2015) together provide the following improved list of (pseudo)bulge classification criteria. I note again: The failure rate for individual criteria ranges from 0% to roughly 25%. Therefore the use of more criteria quickly gives much more reliable results.

  1. If the galaxy center is dominated by young stars and gas but there is no sign of a merger in progress, then the bulge is mostly pseudo. Ubiquitous star formation must be secular. Fisher & Drory (2015) make this quantitative: if the specific star formation rate sSFR ≥ 10−11 yr−1, then the bulge is likely to be pseudo; whereas if sSFR < 10−11 yr−1, then the bulge is likely to be classical. Also, if the bulge is very blue, BV < 0.5, then it is pseudo. Criteria (1) cannot be used for S0s.
  2. Disky pseudobulges (a) generally have apparent flattening similar to that of the outer disk or (b) contain spiral structure all the way to the galaxy center. Classical bulges are much rounder than their disks unless they are seen almost face-on, and they cannot have spiral structure. Criterion 2(a) can be used for S0s; 2(b) can not.
  3. Pseudobulges are more rotation-dominated than are classical bulges in the Vmax / σ–є diagram; Vmax is maximum rotation velocity, σ is near-central velocity dispersion, and є is ellipticity. Integral-field spectroscopy often shows that the central surface brightness excess over the inward extrapolation of the disk profile is a flat central component that rotates rapidly and has small σ.
  4. Many pseudobulges are low-σ outliers in the Faber-Jackson (1976) correlation between (pseudo)bulge luminosity and velocity dispersion. Integral-field spectra often show that σ decreases from the disk into a pseudobulge. Fisher and Drory make this quantitative: Pseudobulges have rather flat logarithmic derivatives of the dispersion profile dlogσ / dlogr ≥ −0.1 and V2 / σ2 ≥ 0.35. In contrast, if dlogσ / dlogr < −0.1 or if central σ0 > 130 km s−1, then the bulge is classical.
  5. Small bulge-to-total luminosity ratios do not guarantee that a bulge is pseudo, but almost all pseudobulges have PB / T ≲ 0.35. If B / T ≳0.5, the bulge is classical.
  6. Most pseudobulges have Sérsic index n < 2; most classical bulges have n ≥ 2.
  7. Classical bulges fit the fundamental plane correlations for elliptical galaxies. Some pseudobulges do, too, and then the correlations are not useful for classification. More extreme pseudobulges are fluffier than classical bulges; they have larger effective radii re and fainter effective surface brightnesses µe. These pseudobulges can be identified using fundamental plane correlations.
  8. In face-on galaxies, the presence of a nuclear bar shows that a pseudobulge dominates the central light. Bars are disk phenomena. Triaxiality in giant Es involves different physics – slow (not rapid) rotation and box (not x1 tube) orbits.
  9. In edge-on galaxies, boxy bulges are edge-on bars; seeing one identifies a pseudobulge. The boxy-core-nonrotating side of the “E – E dichotomy” between two kinds of elliptical galaxies (see Section 4.1.1) cannot be confused with boxy, edge-on bars because boxy ellipticals – even if they occur in disk galaxies (we do not know of an example) – are so luminous that we would measure B / T > 0.5. Then point (5) would tell us that this bulge is classical.
  10. Fisher & Drory (2015) conclude that pseudobulges have weak Fe and Mg b lines: equivalent width of [Fe λ5150Å] < 3.95 Å; equivalent width of [Mgb] < 2.35 Å. In their sample, no classical bulge has such weak lines. Some pseudobulges have stronger lines, so this criterion, like most others, is not 100% reliable.
  11. If a bulge deviates from the [Mg b] – σ or [Mg b] – [Fe] correlations for elliptical galaxies by Δ[Mg b] < 0.7 – that is, if the [Mg] line strength is lower than the scatter for Es – then the bulge is likely to be pseudo (Fisher & Drory 2015).

It is important to emphasize that classical and pseudo bulges can occur together. Fisher & Drory (2015) review examples of dominant pseudobulges that have small central classical bulges. And some giant classical bulges contain nuclear disks (e.g., NGC 3115: Kormendy et al. 1996b; NGC 4594: Kormendy et al. 1996a).

Criterion (9) for boxy pseudobulges works only for edge-on and near-edge-on galaxies. In face-on galaxies, it is easy to identify the elongated parts of bars, but they also have rounder, denser central parts, and these are not easily distinguished from classical bulges (Athanassoula 2015; Laurikainen & Salo 2015). So the above criteria almost certainly fail to find some pseudobulges in face-on barred galaxies.

2.2. Secular Evolution in Disk Galaxies: Applications

Progress in many subjects depends on a full integration of the picture of disk secular evolution into our paradigm of galaxy evolution. Examples include the following:

  1. If the smallest bulges are pseudo and not classical, then the luminosity and mass functions of classical bulges and ellipticals are very bounded: MK ≲ −19; MV ≲ −16; LV ≳108.5 L; stellar mass Mbulge ≳109 M. In simulations (Brooks & Christensen 2015; Section 4 here), the physics that makes classical bulges and ellipticals does not need to explain objects that are smaller than the above. More accurately: If the same generic physics (e.g., major mergers) is relevant for smaller objects, it does not have to produce remnants that are consistent with low-mass extrapolations of parameter correlations for classical bulges and ellipticals. One possible reason may be that the progenitors of that physics are very gas-rich.
  2. Our understanding that, below the above limits, lower-mass bulges are essentially all pseudo makes it harder to understand how galaxy formation by hierarchical clustering of CDM makes so many giant, classical-bulge-less (i.e., pure-disk) galaxies. This was the theme of the observational papers Kormendy et al. (2010) and Fisher & Drory (2011). It is addressed in Brooks & Christensen (2015). We return to this issue in Section 4.
  3. Understanding how supermassive black holes (BHs) affect galaxy evolution requires an understanding that classical and pseudo bulges are different. Classical bulges participate in the correlations between BH mass and bulge luminosity, stellar mass, and velocity dispersion. Pseudobulges essentially do not. This is some of the evidence that BHs coevolve with classical bulges and ellipticals in ways to be determined, whereas BHs exist in but do not influence the evolution of disks or of disk-grown pseudobulges. We return to this subject in Section 6.

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