So far, we have assumed structural homology. Sersic’s (1968) law allows to characterize structural differences between galaxies using the the shape parameter n : I(r) ∝ exp[−(r / r0)1/n], where I(r) is the surface brightness profile and r0 some characteristic radius. For n = 4 and n = 1, we retrieve the usual R1/4 and exponential profiles. Imposing the R1/4 law leads to biased measurements of Re and Ie (and σ) and affects the tilt of the FP; the departure from virial expectation is reduced when using Sersic profiles and deprojected quantities.
Galaxies and bulges are better fitted by Sersic law and show a great variety of shapes: n extends from over 10 to 0.5 as one goes from brightest cluster galaxies to normal ellipticals and S0s, bulges, and dwarfs (Graham et al. 1996). For bulges alone, n varies systematically from 6 to 1 from early to late-type systems (high to low bulge-to-disk ratio), with weaker trends as a function of luminosity and size (see Fig. 3; Andredakis, Peletier, & Balcells 1995). This again suggests a similar formation mechanism for all spheroids, as different mechanisms for early and late-type systems (or normal and pseudo bulges, see below) would likely lead to a bimodal distribution of n.
Figure 3. Shape of bulges. Sersic's (1968) shape parameter n plotted as a function of the host galaxy morphological type. Circles: Andredakis et al. (1995) sample. Crosses: Kent (1986) sample. Open symbols represent barred galaxies. No error bars are plotted for clarity. Reproduced with permission from Andredakis et al. (1995).
In violent relaxation, galaxies with deep central potentials lead to high n (Hjorth & Madsen 1995); conversely, the central potential increases with n (Ciotti 1991; both for spherical isotropic models). For bulges, the formation or interaction with the disk may affect the density distribution. The continua of properties mentioned above thus somewhat support the suggestion that all spheroids harbor a disk (e.g. Burstein et al. 2001), although their influence is probably small in large ellipticals and there are few indications of disks in dwarfs.
Kormendy (1993) also argues that a number of bulges, referred to as pseudo-bulges, show structural and kinematic evidence for disk-like dynamics. These include: i) σ smaller than expected from the FJ relation; ii) fast rotation, with V / σ above the isotropic oblate rotator line in the V / σ − є diagram; iii) bulges as flat as the disk; iv) spiral structure within R1/4 profiles; and v) substantial population I material in later types. This suggests that pseudo-bulges may really be high surface brightness central disks, and that disks may have a steeper inner light profile than the inward extrapolation of an exponential. A transition from bulge to disk-dominated properties is suggested at types Sb–Sbc.
This picture is consistent with simulations of gas flow in barred galaxies, which lead to high (and flat) central gas concentrations, possibly feeding a central BH and forming stars (e.g. Friedli & Benz 1993, Heller & Shlosman 1994). The bulge and disk scalelengths also correlate, independently of type, further suggesting that at least some bulges grow secularly out of disk material (de Jong 1996). Evolution is then more than the simple aging of the stellar populations.