The Classification of Galaxies

A useful first step towards an understanding of galaxies is a classification based on their various forms. Although such a morphological classification must always be to some extent subjective, it provides a framework within which the quantitative properties of galaxies can be discussed in a systematic fashion. However, it should always be remembered that the picture thus obtained will be limited to those galaxies that are large and bright enough to be easily visible in the sky. An idea of the consequent limitations can be obtained from Fig. 18.1, showing the radii and magnitudes of normal galaxies. One sees that only within a narrow region of this diagram can galaxies be easily found. If a galaxy has too large a radius for its magnitude (small surface brightness), it will disappear in the background light from the

Fig. 18.1. Magnitudes and diameters of observable extragalac-tic objects. Objects to the upper left look like stars. The quasars in this region have been discovered on the basis of their spectra. Objects to the lower right have a surface brightness much smaller than that of the night sky. In recent years large numbers of low surface brightness galaxies have been discovered in this region. (Arp, H. (1965): Astrophys. J. 142, 402)

Hannu Karttunen et al. (Eds.), Galaxies.

In: Hannu Karttunen et al. (Eds.), Fundamental Astronomy, 5th Edition. pp. 367-391 (2007) DOI: 11685739_18 © Springer-Verlag Berlin Heidelberg 2007

night sky. On the other hand, if its radius is too small, it looks like a star and is not noticed on a photographic plate. In the following, we shall mainly be concerned with bright galaxies that fit within these limits.

If a classification is to be useful, it should at least roughly correspond to important physical properties of the galaxies. Most classifications accord in their main features with the one put forward by Edwin Hubble in 1926. Hubble's own version of the Hubble sequence is shown in Fig. 18.2. The various types of galaxies are ordered in a sequence from early to late types. There are three main types: elliptical, lenticular, and spiral galaxies. The spirals are divided into two sequences, normal and barred spirals. In addition, Hubble included a class of irregular galaxies.

The elliptical galaxies appear in the sky as elliptical concentrations of stars, in which the density falls off in a regular fashion as one goes outwards. Usually there are no signs of interstellar matter (dark bands of dust, bright young stars). The ellipticals differ from each other only in shape and on this basis they are classified as E0, E1,..., E7. If the major and minor axes of an elliptical galaxy are a and b, its type is defined to be En, where n = 10[ 1 - -

An E0 galaxy thus looks circular in the sky. The apparent shape of an E galaxy depends on the direction from which it is seen. In reality an E0 galaxy may therefore be truly spherical or it may be a circular disc viewed directly from above.

A later addition to the Hubble sequence is a class of giant elliptical galaxies denoted cD. These are gener ally found in the middle of clusters of galaxies. They consist of a central part looking like a normal elliptical surrounded by an extended fainter halo of stars.

In the Hubble sequence the lenticulars or S0 galaxies are placed between the elliptical and the spiral types. Like the ellipticals they contain only little interstellar matter and show no signs of spiral structure. However, in addition to the usual elliptical stellar component, they also contain a flat disc made up of stars. In this respect they are like spiral galaxies (Figs. 18.3, 18.4).

The characteristic feature of spiral galaxies is a more or less well-defined spiral pattern in the disc. Spiral galaxies consist of a central bulge, which is structurally similar to an E galaxy, and of a stellar disc, like in an S0 galaxy. In addition to these, there is a thin disc of gas and other interstellar matter, where young stars are being born, forming the spiral pattern. There are two sequences of spirals, normal Sa-Sb-Sc, and barred SBa-SBb-SBc spirals. In the barred spirals the spiral pattern ends at a central bar, whereas in the normal spirals the spiral pattern may end at an inner ring or continue all the way to the centre. The position of a galaxy within the spiral sequence is determined on the basis of three criteria (which are not always in agreement): later types have a smaller central bulge, more narrow spiral arms and a more open spiral pattern. The Milky Way Galaxy is thought to be of type SABbc (intermediate between Sb and Sc, and between normal and barred spirals).

The classical Hubble sequence is essentially based on bright galaxies; faint galaxies have been less easy to fit into it (Fig. 18.5). For example, the irregular galaxies of the original Hubble sequence can be divided into the classes Irr I and Irr II. The Irr I galaxies form a continua-

Fig. 18.2. The Hubble sequence in Hubble's 1936 version. At this stage the existence of type S0 was still doubtful. Photographs of the Hubble types are shown in Figs. 18.6 and 18.15 (E); 18.3 and 18.4 (S0 and S); 18.12 (S and Irr II); 18.5 (Irr I and dE). (Hubble, E.P. (1936): The Realm of the Nebulae (Yale University Press, New Haven))

Fig. 18.2. The Hubble sequence in Hubble's 1936 version. At this stage the existence of type S0 was still doubtful. Photographs of the Hubble types are shown in Figs. 18.6 and 18.15 (E); 18.3 and 18.4 (S0 and S); 18.12 (S and Irr II); 18.5 (Irr I and dE). (Hubble, E.P. (1936): The Realm of the Nebulae (Yale University Press, New Haven))

NGC488 Type Sab NGC628 M74 TypeSc

Fig. 18.3. The classification of normal spiral and S0 galaxies. (Mt. Wilson Observatory)

NGC488 Type Sab NGC628 M74 TypeSc

Fig. 18.3. The classification of normal spiral and S0 galaxies. (Mt. Wilson Observatory)

Type SBb(s)

Type SBb(r)

Type SBb(r)

Type SBc(sr)

Type SBb(s)

Type SBc(s)

Fig. 18.4. Different types of SB0 and SB galaxies. The type (r) or (s) depends on whether the galaxy has a central ring or not. (Mt. Wilson Observatory)

Fig. 18.5. Above: The Small Magellanic Cloud (Hubble type Irr I), a dwarf companion of the Milky Way. (Royal Observatory, Edinburgh). Below: The Sculptor Galaxy, a dE dwarf spheroidal. (ESO)

Fig. 18.6. M32 (type E2), a small elliptical companion of the Andromeda Galaxy. (NOAO/Kitt Peak National Observatory)

Fig. 18.6. M32 (type E2), a small elliptical companion of the Andromeda Galaxy. (NOAO/Kitt Peak National Observatory)

tion of the Hubble sequence towards later types beyond the Sc galaxies. They are rich in gas and contain many young stars. Type Irr II are dusty, somewhat irregular small ellipticals. Other types of dwarf galaxies are often introduced. One example is the dwarf spheroidal type dE, similar to the ellipticals, but with a much less centrally concentrated star distribution. Another is the blue compact galaxies (also called extragalactic HII regions), in which essentially all the light comes from a small region of bright, newly formed stars.

18.2 Luminosities and Masses

Distances. In order to determine the absolute luminosities and linear dimensions of galaxies one needs to know their distances. Distances are also needed in order to estimate the masses of galaxies, because these estimates depend on the absolute linear size. Distances within the Local Group can be measured by the same methods as inside the Milky Way, most importantly by means of variable stars. On the very large scale (beyond 50 Mpc), the distances can be deduced on the basis of the expansion of the Universe (see Sect. 19.1). In order to connect these two regions one needs methods of distance determination based on the properties of individual galaxies.

To some extent local distances can be determined using structural components of galaxies, such as the sizes of H II regions or the magnitudes of globular clusters. However, to measure distances of tens of megaparsecs, one needs a distance-independent method to determine the absolute luminosities of entire galaxies. Several such methods have been proposed. For example, a luminosity classification has been introduced for late spiral types by Sidney van den Bergh. This is based on a correlation between the luminosity of a galaxy and the prominence of its spiral pattern.

Other distance indicators are obtained if there is some intrinsic property of the galaxy, which is correlated with its total luminosity, and which can be measured independently of the distance. Such properties are the colour, the surface brightness and the internal velocities in galaxies. All of these have been used to measure distances to both spiral and elliptical galaxies. For example, the absolute luminosity of a galaxy should depend on its

Fig. 18.7. Compound luminosity function of thirteen clusters of galaxies. The open symbols have been obtained by omitting the cD galaxies. The distribution is then well described by (18.2). The cD galaxies (filled symbols) cause a deviation at the bright end. (Schechter, P. (1976): Astrophys. J. 203, 297)

measure the luminosity of a galaxy out to a given value of the surface brightness, e.g. to 26.5mag/sq.arcsec. For a given Hubble type, the total luminosity L may vary widely.

As in the case of stars, the distribution of galaxy luminosities is described by the luminosity function 0( L). This is defined so that the space density of galaxies with luminosities between L and L + d L is 0( L) d L .It can be determined from the observed magnitudes of galaxies, once their distances have been estimated in some way. In practice, one assumes some suitable functional form for 0(L), which is then fitted to the observations. One common form is Schechter's luminosity function,

Fig. 18.7. Compound luminosity function of thirteen clusters of galaxies. The open symbols have been obtained by omitting the cD galaxies. The distribution is then well described by (18.2). The cD galaxies (filled symbols) cause a deviation at the bright end. (Schechter, P. (1976): Astrophys. J. 203, 297)

mass. The mass, in turn, will be reflected in the velocities of stars and gas in the galaxy. Accordingly there is a relationship between the absolute luminosity and the velocity dispersion (in ellipticals) and the rotational velocity (in spirals). Since rotational velocities can be measured very accurately from the width of the hydrogen 21-cm line, the latter relationship (known as the Tully-Fisher relation) is perhaps the best distance indicator currently available.

The luminosity of the brightest galaxies in clusters has been found to be reasonably constant. This fact can be used to measure even larger distances, providing a method which is important in cosmology.

Luminosities. The definition of the total luminosity of a galaxy is to some extent arbitrary, since galaxies do not have a sharp outer edge. The usual convention is to

The values of the parameters 0*, L*, a are observation-ally determined for different types of objects; in general, they will be functions of position.

The shape of the luminosity function is described by the parameters a and L *. The relative number of faint galaxies is described by a. Since its observed value is about —1.1, the density of galaxies grows monotonically as one goes towards fainter luminosities. The luminosity function falls off steeply above the luminosity L *, which therefore represents a characteristic luminosity of bright galaxies. The observed L* corresponds to an absolute magnitude M* = — 21.0 mag. The corresponding magnitude for the Milky Way Galaxy is probably — 20.2 mag. The cD giant galaxies do not obey this brightness distribution; their magnitudes may be —24 mag and even brighter.

The parameter 0* is proportional to the space density of galaxies and is therefore a strong function of position. Since the total number density of galaxies predicted by relation (18.2) is infinite, we define n* = density of galaxies with luminosity > L *. The observed average value of n* over a large volume of space is n* = 3.5 x 10—3 Mpc—3. The mean separation between galaxies corresponding to this density is 4 Mpc. Since most galaxies are fainter than L *, and since, in addition, they often belong to groups, we see that the distances between normal galaxies are generally not much larger than their diameters.

Masses. The distribution of mass in galaxies is a crucial quantity, both for cosmology and for theories of the origin and evolution of galaxies. Observationally it is determined from the velocities of the stars and interstellar gas. Total masses of galaxies can also be derived from their motions in clusters of galaxies. The results are usually given in terms of the corresponding mass-luminosity ratio M/L, using the solar mass and luminosity as units. The value measured in the solar neighbourhood of the Milky Way is M/L = 3. If M/ L were constant, the mass distribution could be determined from the observed luminosity distribution by multiplying with M/L.

The masses of eliptical galaxies may be obtained from the stellar velocity dispersion given by the broadening of spectral lines. The method is based on the virial theorem (see Sect. 6.10), which says that in a system in equilibrium, the kinetic energy T and the potential energy U are related according to the equation

Since ellipticals rotate slowly, the kinetic energy of the stars may be written

where M is the total mass of the galaxy and v the velocity width of the spectral lines. The potential energy is

where R is a suitable average radius of the galaxy that can be estimated or calculated from the light distribution. Introducing (18.4) and (18.5) into (18.3) we obtain:

From this formula the mass of an elliptical galaxy can be calculated when v2 and R are known. Some observations of velocities in elliptical galaxies are given in Fig. 18.8. These will be further discussed in Sect. 18.4. The value of M/L derived from such observations is about 10 within a radius of 10 kpc. The mass of a bright elliptical might thus be up to 1013 M0.

The masses of spiral galaxies are obtained from their rotation curve v(R), which gives the variation of their rotational velocity with radius. Assuming that most of the mass is in the almost spherical bulge, the mass within radius R, M(R), can be estimated from Kepler's third law:

Some typical rotation curves are shown in Fig. 18.9. In the outer parts of many spirals, v(R) does not depend on R. This means that M(R) is directly proportional to the radius - the further out one goes, the larger the interior mass is. Since the outer parts of spirals are very faint, at large radii the value of M/L is directly proportional to the radius. For the disc, one finds that M/L = 8 for early and M/L = 4 for late spiral types. The largest measured total mass is 2 x 1012 M0.

Fig. 18.8. Velocity of rotation V(R) [km s 1 ] and velocity dispersion a( R) [kms-1] as functions of radius [kpc] for types E2

Fig. 18.8. Velocity of rotation V(R) [km s 1 ] and velocity dispersion a( R) [kms-1] as functions of radius [kpc] for types E2

1100 1000

1100 1000

y

iii

ï

S f

'h

-

Si

1

f f

} ï

i

r 1 .

and E5. The latter galaxy is rotating, the former is not. (Davies, R. L. (1981): Mon. Not. R. Astron. Soc. 194, 879)

and E5. The latter galaxy is rotating, the former is not. (Davies, R. L. (1981): Mon. Not. R. Astron. Soc. 194, 879)

Fig. 18.9. Rotation curves for seven spiral galaxies. (Rubin, V.C., Ford, W.K., Thonnard, N. (1978): As-trophys. J. (Lett.) 225, L107)

In order to measure the mass at even larger radii where no emission can be detected, motions in systems of galaxies have to be used. One possibility is to use pairs of galaxies. In principle, the method is the same as for binary stars. However, because the orbital period of a binary galaxy is about 109 years, only statistical information can be obtained in this way. The results are still uncertain, but seem to indicate values of M/L = 20-30 at pair separations of about 50 kpc.

A fourth method to determine galaxy masses is to apply the virial theorem to clusters of galaxies, assuming that these are in equilibrium. The kinetic energy T in (18.4) can then be calculated from the observed red-shifts and the potential energy U , from the separations between cluster galaxies. If it is assumed that the masses of galaxies are proportional to their luminosities, it is found that M/L is about 200 within 1 Mpc of the cluster centre. However, there is a large variation from cluster to cluster.

Present results suggest that as one samples larger volumes of space, one obtains larger values for the mass-luminosity ratio. Thus a large fraction of the total mass of galaxies must be in an invisible and unknown form, mostly found in the outer parts. This is known as the missing mass problem, and is one of the central unsolved questions of extragalactic astronomy.

18.3 Galactic Structures

Ellipticals and Bulges. In all galaxies the oldest stars have a more or less round distribution. In the Milky Way this component is represented by the population II stars. Its inner parts are called the bulge, and its outer parts are often referred to as the halo. There does not appear to be any physically significant difference between the bulge and the halo. The population of old stars can be best studied in ellipticals, which only contain this component. The bulges of spiral and S0 galaxies are very similar to ellipticals of the same size.

The surface brightness distribution in elliptical galaxies essentially depends only on the distance from the centre and the orientation of the major and minor axis. If r is the radius along the major axis, the surface brightness I(r) is well described by de Vaucouleurs' law:

The constants in (18.8) have been chosen so that half of the total light of the galaxy is radiated from within the radius re and the surface brightness at that radius is Ie. The parameters re and Ie are determined by fitting (18.8) to observed brightness profiles. Typical values for r e

elliptical, normal spiral and SO galaxies are in the ranges re = 1-10 kpc and Ie corresponds to 20-23 magnitudes per square arc second.

Although de Vaucouleurs' law is a purely empirical relation, it still gives a remarkably good representation of the observed light distribution. However, in the outer regions of elliptical galaxies, departures may often occur: the surface brightness of dwarf spheroidals often falls off more rapidly than (18.8), perhaps because the outer parts of these galaxies have been torn off in tidal encounters with other galaxies. In the giant galaxies of type cD, the surface brightness falls off more slowly (see Fig. 18.10). It is thought that this is connected with their central position in clusters of galaxies.

Although the isophotes in elliptical galaxies are ellipses to a good approximation, their ellipticities and the orientation of their major axes may vary as a function of radius. Different galaxies differ widely in this respect, indicating that the structure of ellipticals is not as simple as it might appear. In particular, the fact that the direction of the major axis sometimes changes within a galaxy suggests that some ellipticals may not be axially symmetric in shape.

From the distribution of surface brightness, the three-dimensional structure of a galaxy may be inferred as explained in *Three-Dimensional Shape of Galaxies.

The relation (18.8) gives a brightness profile which is very strongly peaked towards the centre. The real distribution of axial ratios for ellipticals can be statistically inferred from the observed one. On the (questionable) assumption that they are rotationally symmetric, one obtains a broad distribution with a maximum corresponding to types E3-E4. If the true shape is not axisymmetric, it cannot even statistically be uniquely determined from the observations.

Discs. A bright, massive stellar disc is characteristic for S0 and spiral galaxies, which are therefore called disc galaxies. There are indications that in some ellipticals there is also a faint disc hidden behind the bright bulge. In the Milky Way the disc is formed by population I stars.

The distribution of surface brightness in the disc is described by the expression

Figure 18.11 shows how the observed radial brightness distribution can be decomposed into a sum of two components: a centrally dominant bulge and a disc contributing significantly at larger radii. The central surface brightness I0 typically corresponds to 21-22 mag./sq.arcsec, and the radial scale

Fig. 18.10. The distribution of surface brightness in E and cD galaxies. Ordinate: surface magnitude, mag/sq.arcsec; abscissa: (radius [kpc])1/4. Equation (18.8) corresponds to a straight line in this representation. It fits well with an E galaxy, but for type cD the luminosity falls off more slowly in the outer regions. Comparison with Fig. 18.11 shows that the brightness distribution in S0 galaxies behaves in a similar fashion. cD galaxies have often been erroneously classified as S0. (Thuan, T.X., Romanishin, W. (1981): Astrophys. J. 248, 439)

Figure 18.11 shows how the observed radial brightness distribution can be decomposed into a sum of two components: a centrally dominant bulge and a disc contributing significantly at larger radii. The central surface brightness I0 typically corresponds to 21-22 mag./sq.arcsec, and the radial scale

Fig. 18.11. The distribution of surface brightness in types SO and Sb. Ordinate: mag/sq.arc sec; abscissa: radius [arc sec]. The observed surface brightness has been decomposed into a sum of bulge and disc contributions. Note the larger disc component in type Sb. (Boroson, T. (1981): As-trophys. J. Suppl. 46, 177)

Fig. 18.11. The distribution of surface brightness in types SO and Sb. Ordinate: mag/sq.arc sec; abscissa: radius [arc sec]. The observed surface brightness has been decomposed into a sum of bulge and disc contributions. Note the larger disc component in type Sb. (Boroson, T. (1981): As-trophys. J. Suppl. 46, 177)

length r0 = 1-5 kpc. In Sc galaxies the total brightness of the bulge is generally slightly smaller than that of the disc, whereas in earlier Hubble types the bulge has a larger total brightness. The thickness of the disc, measured in galaxies that are seen edge-on, may typically be about 1.2 kpc. Sometimes the disc has a sharp outer edge at about 4 r0.

The Interstellar Medium. Elliptical and SO galaxies contain very little interstellar gas. However, in some ellipticals neutral hydrogen amounting to about 0.1% of the total mass has been detected, and in the same galaxies there are also often signs of recent star formation. In some S0 galaxies much larger gas masses have been observed, but the relative amount of gas is very variable from one galaxy to another. The lack of gas in these galaxies is rather unexpected, since during their evolution the stars release much more gas than is observed.

The relative amount of neutral hydrogen in spiral galaxies is correlated with their Hubble type. Thus Sa spirals contain about 2%, Sc spirals 10%, and Irr I galaxies up to 30% or more.

The distribution of neutral atomic hydrogen has been mapped in detail in nearby galaxies by means of radio observations. In the inner parts of galaxies the gas forms a thin disc with a fairly constant thickness of about 200 pc, sometimes with a central hole of a few kpc diameter. The gas disc may continue far outside the optical disc, becoming thicker and often warped from the central disc plane.

Most of the interstellar gas in spiral galaxies is in the form of molecular hydrogen. The hydrogen molecule cannot be observed directly, but the distribution of carbon monoxide has been mapped by radio observations. The distribution of molecular hydrogen can then be derived by assuming that the ratio between the densities of CO and H2 is everywhere the same, although this may not always be true. It is found that the distribution obeys a similar exponential law as the young stars and HII regions, although in some galaxies (such as the Milky Way) there is a central density minimum. The surface density of molecular gas may be five times larger than that of H I, but because of its strong central concentration its total mass is only perhaps two times larger.

The distribution of cosmic rays and magnetic fields in galaxies can be mapped by means of radio observations of the synchrotron radiation from relativistic electrons. The strength of the magnetic field deduced in this way is typically 0.5-1 nT. The observed emission is polarized, showing that the magnetic field is fairly well-ordered on large scales. Since the plane of polarization is perpendicular to the magnetic field, the large-scale structure of the magnetic field can be mapped. However, the plane of polarization is changed by Faraday rotation, and for this reason observations at several wavelengths are needed in order to determine the direction of the field. The results show that the field is generally strongest in the plane of the disc, and is directed along the spiral arms in the plane. The field is thought to have been produced by the combined action of rising elements of gas, perhaps

produced by supernova explosions, and the differential rotation, in principle in the same way as the production of solar magnetic fields was explained in Chapter 12.

* Three-Dimensional Shape of Galaxies

Equations (18.8) and (18.9) describe the distribution of galactic light projected on the plane of the sky. The actual three-dimensional luminosity distribution in a galaxy is obtained by inverting the projection. This is easiest for spherical galaxies.

Let us suppose that a spherical galaxy has the projected luminosity distribution I(r) (e.g. as in (18.8)). With coordinates chosen according to the figure, I(r) is given in terms of the three-dimensional luminosity distribution p(R) by

This is known as an Abel integral equation for p(R), and has the solution p( R) = -

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