ARlogo Annu. Rev. Astron. Astrophys. 2004. 42: 603-683
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4.2. Exponential Bulges

The pseudobulge galaxies NGC 1553 and NGC 6384 (Figures 10, 12) have nearly exponential bulge profiles. Andredakis & Sanders (1994) discovered that this is a general phenomenon: The bulges of late-type galaxies are better described by exponentials than by r1/4-law surface brightness profiles. Andredakis, Peletier, & Balcells (1995) generalized this result and showed that the index n of a Sérsic (1968) function fitted to the central profile varies from n appeq 3.7 (standard deviation = 1.3) in S0 and S0/a bulges to n appeq 2.4 (standard deviation = 0.66) in Sa - Sb galaxies to n appeq 1.6 (standard deviation = 0.52) in Sbc - Sd galaxies. "For Sc and later, the profiles are very close to pure exponentials." An example of an Sbc with an exponential bulge is our Galaxy (Kent, Dame, & Fazio 1991). The above trend parallels the trend that pseudobulges get more common in later-type galaxies. Evidently small n values are pseudobulge signatures.

The time was right for Sérsic functions to become the canonical fitting function for bulges and ellipticals. Caon, Capaccioli, & D'Onofrio (1993) had recently demonstrated that they fit ellipticals and bulges better than do r1/4 laws. They note that this is not a surprise, because r1/n profiles have three parameters, while r1/4 laws have only two. The argument that n has physical meaning is the observation that it correlates with the effective radius re and total absolute magnitude MB, bulge of the elliptical or bulge. This was confirmed by D'Onofrio, Capaccioli, & Caon (1994); Graham et al. (1996); Binggeli & Jerjen (1998); Graham (2001); Trujillo et al. (2002), and numerous subsequent papers.

The idea that late-type "bulges" have n appeq 1 to 2 immediately gained acceptance and got simplified in many people's minds (and in our title) to the notion that they are exponential. One reason was that confirmation followed quickly. Courteau, de Jong, & Broeils (1996) carried out bulge-disk decompositions for 243 galaxies from Courteau (1996a) and 86 galaxies from de Jong & van der Kruit (1994) and from de Jong (1996a, b). For the Courteau sample, they conclude that "about 85 % of [the] Sb's and Sc's are best fitted by the double exponential, while the remainder [are] better fitted with an r1/4 bulge profile." For the de Jong sample, they conclude that 60 % of the galaxies are best modeled by a double exponential, ~ 25 % (mostly Sa's and Sb's) are best modeled with n = 2 and only ~ 15 % are best fitted by an r1/4 law. These results are broadly consistent with the statistics in Section 4.1, which refer to a different galaxy sample and which are partly based on morphology and partly on Sérsic function indices.

As a diagnostic of formation processes, Courteau et al. (1996) go on to examine the ratio hb / hd of the scale lengths of the inner and outer exponentials. For the combined sample, they find that hb / hd = 0.08 ± 0.05, and for the de Jong sample, they find that hb / hd = 0.09 ± 0.04. From this, they conclude that: "Our measurements of exponential stellar density profiles [in bulges] as well as a restricted range of [bulge-to-disk] scale lengths provide strong observational support for secular evolution models. Self-consistent numerical simulations of disk galaxies evolve toward a double exponential profile with a typical ratio between bulge and disk scale lengths near 0.1 (D. Friedli 1995, private communication) in excellent agreement with our measured values" (see Courteau et al. 1996 for details). MacArthur, Courteau, & Holtzman (2003) find that hb / hd = 0.13 ± 0.06 for late-type spirals and again note the connection with secular evolution. We can add one more connection. The above ratios of hb / hd, together with the observation that bars are typically about 1 scale length hd long (e.g., Kormendy 1979b), imply that the scale length of the inner exponential is similar to the radius of star-forming rings (Figure 8) discussed in Section 2.3. We suggested there that these rings are building pseudobulges.

There is a caveat: An examination of the above papers shows that many bulges in late-type galaxies rise above the disk profile by only small amounts. Leverage is limited. Even the conclusion that some bulges are exponential can be uncertain.

HST confirmation of the above results has therefore been welcome (e.g., Phillips et al. 1996, Balcells et al. 2003, Fathi & Peletier 2003). Carollo et al. (2002) provide the best statistics. Their Table 1 classifies central components as "r1/4-law", "exponential," or "not fitted" based on the V-band images. Galaxies were "not fitted" when the brightness distribution was badly affected by dust, young stars, or patchiness. After correcting the Hubble type of NGC 2344 from Sc (RC3) to Sb (UGC), the V-band statistics are as follows: r1/4-law bulges, exponential pseudobulges, and galaxies not fitted account for the following percentages of the Hubble types indicated. S0 + Sa: 50%, 10%, 40%; Sab: 60%, 0%, 40%; Sb: 17%, 11%, 72%; Sbc: 0%, 28%, 72%; Sc: 0%, 60%, 40%; and Scd to Sm: 0%, 50%, 50% of the galaxies. When we classify the 45 galaxies that were not fitted in V-band using the H-band images and V - H images, we get 11 classical bulges and 34 pseudobulges. The statistics on classical and pseudobulges then become as follows: S0 + Sa: 50%, 50%; Sab: 60%, 40%; Sb: 44%, 56%; Sbc: 6%; 94%; and Sc to Sm: 0%, 100%. The V+ H-band results are in satisfactory agreement with the optical results. The majority of early-type galaxies have classical bulges; there is a sharp transition at Hubble type Sb, and later-type galaxies mostly contain pseudobulges.

Balcells (2001) reviews implications. Andredakis (1988) comments that "The exponential bulges ... remain essentially unexplained; [his results] suggest that they ... were probably formed, at least in part, by different processes from those of early-type spirals." Even though we do not understand quantitatively how inner exponentials are built, their close association with other disky bulge phenomena supports our tentative conclusion and that of many other authors that Sérsic indices n ~ 1 are a signature of secular formation.

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