Observations of Elliptical Galaxies. II

Astronomy 626: Spring 1995

Correlations between the global parameters of elliptical galaxies lead to a variety of useful relationships, the most important being the fundamental plane. Correlations between core parameters imply that ellipticals are similar to the bulges of disk galaxies, but that both are different from dwarf spheroidal galaxies.

Color & Line-Strength Gradients

As a rule, E galaxies become redder toward their centers; a factor of 10 decrease in radius typically produces an ~0.03 change in b-V and a ~0.10 change in u-V (KD89). The bulges of disk galaxies show even stronger gradients (Wirth & Shaw 1983).
Absorption features in the integrated spectra of E galaxies also show significant gradients with radius: Metal lines become stronger with decreasing radius, while H-beta lines may get stronger or weaker. Line-strength gradients in bright galaxies are smaller than those in faint galaxies but there are large variations from galaxy to galaxy (Gorgas & Efstathiou 1987, Franx et al. 1989).
Color and line-strength gradients are both consistent with the interpretation that metalicity is the primary factor varying with radius (Faber 1977). The logarithmic slope of the metal abundance is estimated to be about -0.2 for a typical elliptical (KD89).
Spectral synthesis models indicate that the stars at any given radius span a range in metal abundance (e.g. Pickles 1987). This is consistent with the ~2 dex spread in metalicity seen in the bulge of the Milky Way (Whitford & Rich 1983).
Evidence for a spread in ages may be present in the deep Balmer lines seen some systems and in indications of blue light above & beyond what one expects for a purely old population (Pickles 1987).

Global Parameter Correlations

Integrated colors of E galaxies show systematic trends with luminosity: Brighter galaxies are redder by ~0.10 in u-V per magnitude (Mihalas & Binney 1981, Chap. 5-4). As within individual galaxies, it appears that here too the changes in color may be largely explained by changes in metalicity (KD89).
The luminosities of E galaxies are highly correlated with their velocity dispersions; this is the Faber-Jackson relation, generally expressed as a power law,
```
                     n
(1)         L ~ sigma ,
        
```
where L is the galaxy luminosity, sigma is the central line-of-sight velocity dispersion, and the index n is about 4, but shows significant variations from sample to sample (KD89).
A significant correlation is also seen between the effective (or half-light) radius, R_e, and the surface brightness at that radius, I_e, of the form (KD89)
```
                     -0.83
(2)         R_e ~ I_e     .
        
```

The Fundamental Plane of Elliptical Galaxies

Most of the scatter in the Faber-Jackson relationship is intrinsic; it reflects real galaxian properties, not measurement errors. A number of authors attempted to identify the `second parameter' which would account for this scatter.
Modern data show that elliptical galaxies obey a relationship of the form
```
                       1.4    -0.9
(3)         R_e ~ sigma    I_e    
        
```
(KD89). This is called the fundamental plane because in a space whose axies are log R_r, log sigma, and log I_e, elliptical galaxies lie on a rather thin, nearly planar surface.
On dimensional grounds, a self-gravitating system should obey a relationship of the form
```
                 2     M
(4)         sigma  ~ G - ,
                       R
        
```
where G is the gravitational constant, M is a characteristic mass, and R is e.g. the half-mass radius. In terms of the system's mass-to-light ratio (M/L), this implies
```
                     2    -1      -1
(5)         R ~ sigma  I_e   (M/L)   ,
        
```
a relationship very similar to Eq. 3 (KD89).
The fact that the exponents appearing in Eq. 5 are not quite the same as those in Eq. 3 can be explained if (M/L) is a slowly-varying function of galaxy mass; the observed exponents are obtained from Eq. 5 if (KD89).
```
                     0.2
(6)         (M/L) ~ M    .
        
```
The fundamental plane is a valuable tool for estimating distances to galaxies; sigma and I_e are measured from spectroscopy and photometry and used in Eq. 3 to obtain the physical radius R_e in kpc; comparison with the apparent R_e then yields the distance.
But if, for example, (M/L) is a function of galaxy environment, then this procedure will yield biased estimates of the distance. Some researchers have found evidence that the fundamental plane does depend on cluster richness (KD89).

Core Parameters & Galaxy Families

From high-resolution surface photometry, the cores of elliptical galaxies and bulges may be characterized by two numbers: the central surface brightness I_0 and the core radius r_c, defined by convention as the radius where the surface brightness is 0.5 I_0.
Surface brightnesses and core radii are highly correlated with each other, following a relationship of the form (K87)
```
                     -0.82
(7)         I_0 ~ r_c     .
        
```
Both surface brightness and core radius are correlated with overall galaxy luminosity, following relations of the form
```
                   -0.86            1.09
(8)         I_0 ~ L     ,    r_c ~ L    .
        
```
Through the Faber-Jackson relationship, I_0 and r_c are also correlated with velocity dispersion (K87).
The bulges of disk galaxies follow essentially the same core-parameter correlations as elliptical galaxies do. This implies that bulges and ellipticals (or at least their cores) are similar systems (K87).
The core parameters of the dwarf spheroidal galaxies do not obey the same relations obeyed by the core parameters of ellipticals and bulges (Kormendy 1985). These objects represent a distinct family of stellar systems.

Homework

Due date: 2/2/95

6. Suppose that all galaxies are actually extremely thin disks, aligned randomly to our line of sight. What distribution of axial ratios would we expect to see in this case?

7. Using Eq. 4, the definition of the mass-to-light ratio (M/L), and the assumption that all elliptical galaxies have similar forms, derive Eq. 5.

8. How could you use the correlation between central surface brightness I_0 and core radius r_c (see Eq. 7) as a tool for measuring distances? What kind of accuracy could you achieve, assuming all the scatter shown in Fig. 6 of K87 is intrinsic?

References

de Zeeuw, T. (ed) 1987. Structure and Dynamics of Elliptical Galaxies.
Faber, S.M. 1977. in The Evolution of Galaxies and Stellar Populations, ed. B.M. Tinsley & R.B. Larson, p. 157.
Franx, M. et al. 1989. A. J. 98, 538.
Gorgas, J. & Efstathiou, G. 1987. in de Zeeuw 1987, p. 189.
Kormendy, J. 1985. Ap. J. 295, 73.
Kormendy, J. 1987. in de Zeeuw 1987, p. 17 (K87).
Kormendy, J. & Djorgovski, S. 1989. Ann. Rev. Astr. Ap. 27, 235 (KD89).
Mihalas, D. & Binney, J.J. 1981, Galactic Astronomy.
Pickles, A. 1987. in de Zeeuw 1987, p. 203.
Whitford, A.E. & Rich, R.M. 1983. Ap. J. 274, 723.
Wirth, A. & Shaw, R. 1983. A. J. 88, 171.

Joshua E. Barnes (barnes@zeno.ifa.hawaii.edu)

Last modified: January 24, 1995