1 Morphological Classification

The classification of galaxies according to their shape is a fundamental tool in extragalactic astronomy. It is through classification schemes that astronomers identify how different types of galaxies are interrelated and thus build a deeper understanding of how galaxies form and evolve ([van den Bergh(1998)]). The most widely used galaxy classification scheme was first proposed by [Hubble(1926)] and later variously refined by Hubble himself and others. In its definitive form, described by [Sandage(1961)] and visually illustrated by the famous ``tuning fork'' diagram shown in Figure 1, Hubble's scheme consists of four main morphological classes:

• Ellipticals (E) : elliptical galaxies are seen projected on the sky as more or less flattened ellipses, whose axis ratio roughly varies from 1 to 3. They have no particular substructure, and their surface brightness decreases very regularly from the center to the outer parts. They have no, or very little, interstellar matter, and a population of old stars. The effects of projection hinders us greatly in our attempts to determine the intrinsic shape of these galaxies, and the original long-standing hyphotesis of an axysimmetric ellipsoidal structure has recently been questioned.
• Lenticulars (S0) : lenticular galaxies consist of at least two components, namely a central stellar concentration, or bulge, structurally similar to an elliptical galaxy, and a rather flat stellar disk that shows no sign of spiral structures. In addition, they sometimes contain a bar-shaped stellar component crossing the galactic nucleus. Like E galaxies, they have little interstellar matter and a population of old stars.
• Spirals (S) : spiral galaxies consist of a stellar bulge, sharing the characteristics of an elliptical galaxy, and of a disk containing young stars, significant amounts of interstellar matter and a more or less well-defined spiral pattern. They can also contain a bar-like component as well as more unusual structures like rings and lenses, whose composition is similar, in general, to that of the disk component.
• Irregulars (Irr) : irregular galaxies are galaxies that cannot be classified in the three previous classes, usually owing to their lack of simmetry or of well-defined spiral arms. They frequently display structures like dust lanes or bright knots containing O and B stars.

These four basic classes can be divided into several further subclasses, but these finer distinctions will not be considered here.

Figure 1: An early version of Hubble's galaxy classification scheme of regular galaxies, also known as the ``tuning fork'' diagram. Reproduced from [Hubble(1936)].

As for the relative frequencies of the different morphological types, in recent years they have been extensively investigated via both visual and automated classification procedures. In particular, deep observation campaigns carried out with the HST, namely the Medium Deep Survey (MDS) and the Hubble Deep Field North (HDF-N), have proved that when such frequencies are calculated over magnitude-limited samples of different depths, then they strongly depend on the limiting magnitude, showing a sharp decrease in the number of spirals and an increase in the number of ellipticals and unclassifiable galaxies at faint magnitudes. Relative frequencies of morphological types in magnitude-limited samples of different limiting magnitudes are given in Table 1.

Table 1: Relative frequencies of DDO morphological types in magnitude-limited samples of different limiting magnitude. SAC stands for Shapley-Ames Catalog ([Shapley and Ames(1932)]), MDS for Medium Deep Survey ([Ratnatunga et al.(1999)]) and HDF-N for Hubble Deep Field North ([Williams et al.(1996)]), from Table 2 in [van den Bergh et al.(1996)]. Morphological classifications from [van den Bergh(1960)], [Abraham et al.(1996b)] and [Abraham et al.(1996a)], respectively. Wider DDO classification bins (E, S0, S, Ir and Unclassified) are indicated by horizontal lines. Note that the SAC makes no distinction between E, E/S0 ans S0, and that for the MDS and HDF data, only galaxies with $I$ less than $21$ and $24$, respectively, were considered, in order to obtain a truly magnitude-limited sample and thus more robust estimates.

Type	SAC	MDS	HDF-N
E		16.6	23.9
E/S0	22.2	3.3	0.7
S0		6.9	4.3
S0/Sa	0.0	0.0	0.7
E/Sa	1.3	0.0	1.4
Sa	6.9	7.5	14.6
Sab	0.2	3.1	1.4
Sb	26.9	7.1	4.3
Sbc	0.3	4.0	0.0
Sc	22.9	12.8	1.4
S	10.0	14.6	13.2
Sc/Ir	0.2	0.9	0.0
Ir	2.0	6.4	2.5
Unclassified	7.0	16.8	31.4

In Section 4 regular galaxies are divided into two classes, namely elliptical galaxies (E) and disk galaxies (D), on the basis of their surface brightness distribution. Taken the MDS frequencies from Table 1 as representative, it can be concluded that the relative frequencies of these two classes are of about 20% and 80% for E and D galaxies, respectively.