To a first approximation, a disk galaxy may be viewed as a combination of
At large radii, face-on disk galaxies typically have exponential luminosity profiles; the log of the surface brightness falls as a linear function of radius, or
r (1) I(r) = I_0 exp(- ---) r_0where I_0 is the (extrapolated) surface brightness at the center of the disk, and r_0 is the disk's exponential scale length. At smaller radii, the luminosity profile may deviate either above or below the exponential line; the former are known as `Type I' profiles, the latter as `Type II' (Freeman 1970).
The range of I_0 values obtained for bright disk galaxies is remarkably small; the `magic' number is 21.65 +/- 0.3 mag/arcsec^2 in the B band (Freeman 1970). There are, however, indications that this result is partly a selection effect: disk galaxies with lower surface brightnesses are not easily detected (Disney 1976, MB81). Moreover, some of the light attributed to disks may in fact come from spheroidal components (Kormendy 1977, K82).
Observations of edge-on disks show that most of the luminosity comes from a rather thin component which is reasonably well-fit by
2 z (2) I(z) = I(z=0) sech (---) , z_0where z_0 is the vertical scale height. This functional form is characteristic of a self-gravitating sheet with velocity dispersion independent of z. Moreover, z_0 does not appear to depend on radius; the scale height of a given disk galaxy is constant (van der Kruit & Searle 1981a,b).
Combining the above results leads to a widely-used fitting function for the 3-D luminosity distribution of galactic disks:
r 2 z (3) L(r,z) = L_0 exp(- ---) sech (---) , r_0 z_0where L_0 is the in-plane luminosity density at the center of the disk. While the vertical fitting function has some theoretical basis, the radial function is strictly empirical, and only tested over a rather small range of surface brightness.
Galactic disks are often truncated in radius; the luminosity density falls rapidly toward zero beyond about (4.2 +/- 0.6) r_0 (van der Kruit & Searle 1982).
Some edge-on disk galaxies appear to have `thick disks' (Burstein 1979); these are components with flattenings intermediate between the disk and bulge which remain when a luminosity model following Eq. 3 is subtracted from the photometry (van der Kruit & Searle 1981a,b, 1982).
In galaxies whose bulges dominate the total light distribution, the morphological resemblance between bulges and elliptical galaxies is quite close; thus such bulges have luminosity profiles reasonably well-approximated by de Vaucouleurs' law:
1/4 (4) I(r) = I_e exp(-7.67 ((r/R_e) - 1)) ,where R_e is the projected half-light radius and I_e is the surface brightness at R_e.
In galaxies with more substantial disks the bulge component is often identified with whatever is left when the disk is subtracted from the surface photometry (by this definition, the thick disk is part of the bulge, a point of view endorsed by K82). This residual component may or may not follow de Vaucouleurs' law.
The isophote shapes of bulges provide evidence that at least some of these objects are not simply ellipticals which have acquired disks. Bulges of edge-on galaxies are often quite `boxy', and in some cases these isophotal distortions are so extreme that the bulge appears `peanut-shaped' (e.g. NGC 128).
Interstellar gas and dust are conspicuous in disk galaxies of type Sa and later. Most of this interstellar material is found in a disk with a scale height significantly smaller than that of the stellar disk.
The radial distribution of gas in disk galaxies does not always follow the exponential distribution seen in the starlight. Neutral hydrogen profiles for disk galaxies show a wide range of forms; some galaxies have central holes, while in others the gas extends far beyond the stellar disk. Molecular clouds tend to be more concentrated towards the centers of galaxies, often in the form of rings of dense gas.
Bulge colors are generally similar to those of elliptical galaxies of the same luminosity, and to the extent that color gradients can be measured in the presence of a disk, bulges show radial color gradients similar to those of ellipticals (GKvdK89, Chapter 5.3).
The colors of galactic disks do not reveal the systematic trends with radius and total luminosity seen in elliptical galaxies (Wevers et al. 1986). The integrated colors of disk galaxies reflect ongoing star formation; broadband color indexes are largely a function of the average star formation rate over the last 10^8 years (Tinsley 1980).
Disk galaxies exhibit a wide variety of spiral structure, a point explicitly recognized in the de Vaucouleurs' classification system. `Grand design' spirals have rather regular patterns dominated by a pair of symmetrically-placed spiral arms. Such spirals are often found in galaxies with close companions (e.g. M51); they may be the result of tidal interactions. `Flocculent' spirals have many short spiral arms, with no overall pattern (e.g. NGC 2841).
Spiral arms are often sites of star formation. In such disks azimuthal color variations are closely connected to the spiral pattern, with hot young stars and emission nebulae distributed along the ridge-lines of spiral arms (e.g. NGC 2997, shown on the cover of BT87). However, near-IR observations indicate that in many cases the older stars also follow a spiral pattern.
Whatever the type of spiral, the overall sense of structure is closely correlated with a galaxy's luminosity; bright disk galaxies tend to have rather neat and well-developed spiral patterns, while fainter galaxies look messier, and for low-luminosity systems the distinction between spiral and irregular galaxies becomes irrelevant.
A large fraction of disk galaxies have bars: narrow linear structures crossing the face of the galaxy. In barred S0 galaxies the bar is often the only structure visible in the disk. In types Sa and later the bar often connects to a spiral pattern extending to larger radii (e.g. 1300).
Viewed face-on, bars typically appear to have axial ratios a:b = 2:1 or greater. The surface brightness within the bar is often fairly constant. Some bars appear to be `squared off' at the ends. The true 3-D shapes of bars are difficult to determine, but many appear to be no thicker than the disks they occur in; if so then bars are the most flattened triaxial systems known (K82).
Many barred galaxies also contain luminous rings. Most striking are those in which the ring just encloses the bar (e.g. NGC 2523); these are known as inner rings and are designated by appending the symbol `(r)' to the morphological type. Less common are outer rings, which typically have diameters several times that of the bar (e.g. NGC 1291; see K82); these are designated with the symbol `(R)'. Inner rings often appear to be elongated in the direction of the bar, while outer rings seem to be more nearly circular.
In some cases the region inside the inner ring is more or less uniformly filled in with luminosity; these luminous oval structures are called lenses. Like bars, lenses have very shallow radial luminosity gradients. The close association between bars, inner rings, and lenses suggests an evolutionary connection (K82).
That disk galaxies rotate is obvious from their spiral patterns. Early observations could only reveal the rotation curves of the brightest inner regions; these typically show a fairly rapid increase with radius before leveling off. Assuming that rotation velocities dropped as v ~ r^-1/2 at larger radii, astronomers derived total masses for spiral galaxies comparable to the masses of the visible stars.
Improved observations, however, failed to show the expected Keplerian fall-off in rotation velocity. Optical studies showed rotation curves remaining nearly constant out to the last measurable point at a radius of 4 or 5 r_0 (Rubin 1983). Neutral hydrogen observations confirmed these results and in some cases extended them to radii several times greater still (e.g. van Albada et al. 1985). While some galaxies are now known to have gently declining rotation curves, a Keplerian rotation profile has not been observed in any galaxy. Consequently, we do not know the total mass of any disk galaxy.
The above results pertain mostly to the gas, because emission lines are relatively easy to observe. What about the disk stars? In practice, the stellar distribution rotates slightly slower than the gas (e.g. Gilmore et al. 1989, fig. 10.5). As will be shown, this difference is due to the velocity dispersion of the stellar component.
The kinematics of bulges are, to first order, similar to the kinematics of elliptical galaxies of the same luminosity; both bulges and low-luminosity ellipticals rotate fast enough to explain their observed flattenings. Unlike some elliptical galaxies, bulges generally have well-aligned rotation and minor axes. In normal bulges, rotation velocity decreases smoothly with increasing height above the disk. Boxy or peanut-shaped bulges, on the other hand, appear to rotate rapidly even well above the disk plane (e.g. K82).
While elliptical galaxies obey a number of different parameter correlations, rather few such relations are known for spiral galaxies. An important exception is the Tully-Fisher relation (Tully & Fisher 1977), a correlation between the rotation velocities and total luminosities of disk galaxies.
Because disk galaxies have essentially flat rotation curves, the integrated neutral hydrogen line profile of an inclined disk galaxy displays a characteristic `double horned' morphology. The width of such a line profile, corrected for galaxy inclination, provides a measure of the peak-to-peak amplitude of the rotation curve. In the published form of the TF relation (e.g. Pierce & Tully 1992), the inclination-corrected line width W is related to the total luminosity L by a power law,
n (5) L ~ W ,where the index n had a value close to 4. This is very similar to the Faber-Jackson relation for elliptical galaxies, which states that luminosity scales as the fourth power of the central velocity dispersion. No good theoretical explanation for these laws is yet available; the rotation curve amplitude of a disk galaxy is presumably set by its invisible halo, and it is not obvious why the halo parameters are so nicely correlated with the total luminosity. Nonetheless, the TF relation is very useful for measuring distances to disk galaxies.
Last modified: February 21, 1995