Galactic classification is harder than stellar classification because galaxies come in an enormous range of forms. Classification schemes based on local examples, including the standard Hubble system, may have to give way to quantitative measures of morphology as investigations probe the universe at redshifts of z = 0.5 and beyond.
Here I summarize four general and widely-used schemes of galaxy classification. These systems are more completely described by Sandage (1975); also see Chapter 5.1 of Mihalas & Binney (1981; hereafter MB81).
Hubble's classification system is most completely described in the Hubble Atlas of Galaxies (Sandage 1961). The wonderful large-scale galaxy photos in this atlas serve as examples of each type; galaxies of unknown type are classified by comparison with these examples.
S0 --- Sa --- Sb --- Sc / . E0 --- E7 Irr \ . SB0 -- SBa -- SBb -- SBc
The classic `tuning-fork' diagram illustrates the main types within Hubble's scheme. E galaxies are featureless ovals, graded by flattening. S0 & SB0 galaxies are essentially disk galaxies without spiral structure. S & SB are spiral galaxies, graded by (i) bulge/disk ratio, (ii) pitch angle of spiral arms, and (iii) `resolution' of arms. SB0 & SB galaxies have strong central bars. Finally, Irr galaxies have irregular forms; these objects may be connected to late-type spirals through the provisional Sd type. See Chapter 1.1 of Binney & Tremaine (1987; hereafter BT87) for a recent discussion of these types.
The grading E galaxies by apparent axial ratio is objective and unambiguous; it is also rather superficial. On the other hand, the grading S and SB galaxies, while somewhat subjective and uncertain, reflects real physical distinctions.
The Reference Catalogue of Bright Galaxies by G. & A. de Vaucouleurs (1964) employs a galactic classification scheme offering a finer level of discrimination than Hubble's system. This expanded system locates each galaxy within a lemon-shaped 3-D classification volume; the major axis of the lemon defines a progression from ellipticals to lenticulars to spirals to irregulars roughly analogous to Hubble's E - S0 - S - Irr sequence. Each slice perpendicular to the major axis defines a 2-D space of possible forms including various combinations of spirals, bars, and rings. The de Vaucouleurs system also interpolates Sd and Sm types between spirals and irregulars.
Developed at Yerkes observatory (Morgan 1958), this scheme is motivated by a correlation between the central concentration of a galaxy's light and the dominant spectral class of its stellar population (Morgan \& Mayall 1957). Galaxies with spread-out luminosity profiles exhibit spectral absorption features typical of A stars, while those with highly-concentrated profiles generally have spectral features of K stars. While this classification scheme is based on the appearance of galaxies, it labels them according to anticipated spectral type. The complete scheme employs three classification dimensions:
The DDO system, developed by van den Bergh (1960a,b), combines elements of the Hubble and Yerkes systems, and introduces `quality and length of spiral arms' as a proxy for luminosity.
S0a -- S0b -- S0c / / E - Aa --- Ab --- Ac \ \ Sa --- Sb --- Sc --- Irr
In this `trident' diagram the horizontal axis indicates degree of central concentration or bulge/disk ratio; E galaxies are the most concentrated, while Irr galaxies are the most spread-out. The vertical axis indicates strength of spiral structure; S0 galaxies show no spiral patterns, A galaxies have low-contrast spirals, and S galaxies have strong, well-defined spirals. Barred disk galaxies are indicated by a B after the S0, A, or S. Finally, late-type galaxies are graded by the appearance of their spiral arms into luminosity classes I to III (for Sb galaxies) or I to V (for Sc galaxies).
The primary dimensions of this system all correlate with physical characteristics of galaxies. As in Yerkes system, central concentration correlates with stellar population. The sequence from S0 to A to S is a progression in neutral hydrogen gas content. And the luminosity classes roughly correspond to 1 mag steps in absolute magnitude.
Many nearby galaxies can be characterized photometrically as superpositions of spheroid and disk components with standardized luminosity profiles (eg. Gilmore, King, \& amp van der Kruit 1989, Chapter 5-2,3). At moderate and high redshifts, however, a galaxy's image may cover only about 10^2 independent pixels, precluding detailed photometric decomposition; such images can be roughly classified by image-processing procedures.
E galaxies and the bulges of S galaxies are remarkably well-fit by de Vaucouleurs' (1948) law:
(1a) I(R) = I_0 exp(-k R^1/4) ,where I(R) is the radial intensity profile, I_0 is the central surface brightness, and k is a constant. Because the measured I_0 depends on seeing conditions, it's easier to use the alternate form
(1b) I(R) = I_e exp(-7.67 ((R/R_e)^1/4 - 1)) ,where I_e is the surface brightness of the isophote containing half the total light and R_e is the effective radius of that isophote; noncircular isophotes are handled using the ellipsoidal radius. This empirical rule has some theoretical justification; stellar systems subjected to rapidly changing gravitational fields often develop profiles which resemble (1).
The disks of S and S0 galaxies are often fit to an exponential law:
(2) I(R) = I_0 exp(-R/h) ,where I_0 is the (extrapolated) central surface brightness and h is the radial scale length of the disk. Such a law is a straight line on a plot of magnitude per square-arcsec versus radius. In practice the parameters I_0 and h are measured by fitting to the outer part of the luminosity profile where disk light dominates. This is an empirical rule with even less theoretical justification than (1); indeed many galactic disks are seen to deviate from (2) at smaller radii (MB81, Chapter 5-2).
The luminosity profiles of edge-on disk galaxies are often fit to the distribution predicted by the self-gravitating isothermal sheet model (van der Kruit & Searle 1981), which is
(3) I(z) = I_m sech^2(z/z_0) ,where I_m is the midplane surface brightness and z_0 is the vertical scale height.
It's not trivial to compare distant galaxies with nearby systems. Galaxies at redshift of about z = 0.5 produce images only a few tens of pixels across even with HST. Cosmological effects cause surface brightness to fall off as (1+z)^-4. Rest wavelengths covered by a fixed pass-band shift towards the blue with increasing z. All these effects can included when simulating the appearance of nearby objects at high z. Still, `attempts to classify galaxies at large redshifts represent a considerable extrapolation from, rather than an interpolation between, nearby morphological type and class standards' (Abraham et al. 1996).
Thus instead of forcing distant galaxies into classification schemes based on nearby samples, it makes more sense to define image parameters which may be used to classify galaxies. Abraham et al. (1996) use two parameters, one measuring the central concentration of the luminosity, the other the degree of asymmetry. The concentration parameter C is the fraction of light within an ellipsoidal radius of 0.3 times the outer isophotal radius, set at 1.5 sigma above sky level. The asymmetry parameter A is essentially the fraction of light in features which are not symmetric with respect to a rotation of pi radians.
Galaxies from the HST Medium Deep Survey have been classified by two independent observers and by measurement of the parameters C and A (Abraham et al. 1996). The two observers, `RSE' and `vdB', generally agree, except in their classifications of peculiar and merging systems. For galaxies fainter than about I = 21 mag the C parameter alone yields classifications as accurate as those provided by human observers. For brighter galaxies, C by itself fails to distinguish E from S0 galaxies, and Sb or Sc spirals from Sd and Irr galaxies. The latter degeneracy can be lifted by including the asymmetry parameter A. The analysis of the MDS galaxies suggests that while the populations of E and S galaxies have evolved relatively little between about z = 0.5 and the present, there has been a significant decrease in the number of highly asymmetric galaxies. Many of these asymmetric systems may actually have nearby analogs; they somewhat resemble the interacting, merging, and peculiar systems which are explicitly excluded from classification schemes for `nearly normal' galaxies.
Due date: 1/21/97
1. Open the Hubble Atlas to five different pages and classify one galaxy on each page according to the Morgan (1958) system; list each galaxy and your classification, and briefly note the features which led to your answer.
2. How does the apparent surface brightness (luminosity per unit solid angle) of a uniform, transparent, infinitely thin disk galaxy depend on the angle of inclination?
Last modified: January 15, 1997