Cosmology. The Origin and Evolution of Cosmic Structure - Coles P., Lucchin F

68 Observational Properties of the Universe

where a light year is the distance travelled by light in a time of one year. A thousand parsecs is called a kiloparsec (kpc) and a million parsecs a megaparsec (Mpc). The typical separation of stars in a galaxy like the Milky Way is of the order of a parsec, while the typical separation of bright galaxies is of the order of an Mpc. The most useful unit for cosmology is therefore the megaparsec. One typically has to use the Hubble law (1.4.6) to estimate extragalactic distances from velocities, since distances are hard to measure directly. There has always been some uncertainty in the value of the Hubble constant H0, with the result that cosmologists usually still parametrise it in terms of a dimensionless number h, where

Using this notation, distances inferred from velocities have units h−1 Mpc. We discuss the distance scale further in Section 4.2.

The usual unit of mass is the solar mass

and for luminosity L we adopt the solar luminosity

The absolute luminosity L of a source is simply the total energy emitted by the source per unit time, while the apparent luminosity l is the energy received by an observer per unit time per unit area from the source. The latter obviously depends on the distance from the source to the observer. In place of L and l, astronomers frequently use absolute magnitude M and apparent magnitude m. These quantities were defined in Section 1.8, based on a logarithmic scale in which five magnitudes correspond to a factor 100 in luminosity. In fact there are several definitions of apparent magnitude (mU, mB, mV, mIR, etc.) because one often cannot measure the total flux from a source, but only that part which lies within some finite band of wavelengths to which a particular instrument is sensitive. The above examples stand for ultraviolet, blue, visible and infrared, respectively, and are all based on standard filters. The total apparent luminosity of a source, integrated over all wavelengths, is called the bolometric luminosity. In all cases the relationship between apparent magnitude and apparent luminosity is defined in such a way that the apparent magnitudes are the same for stars of spectral type A0V.

We shall also, from time to time, have need to use astronomical coordinate systems to describe the location of various objects on the sky. Because we are dealing exclusively with extragalactic objects, we prefer to use galactic coordinates whenever possible. The galactic latitude b is the angle made by a source and the galactic plane; an object in the galactic plane has b = 0 and an object vertically above or below the plane has b = ±90◦; the northern galactic pole is defined to be at b = +90◦ and this pole lies in the northern part of the sky as visible from Earth. Galactic longitude is measured anticlockwise with respect to the

Introduction 69

Figure 4.1 The Hubble ‘tuning fork’ classification of galaxies. The sequence from left to right runs through various types of elliptical galaxies (E), then divides into two branches, corresponding to ‘normal’ spirals (S0, Sa, Sb, Sc) and barred spirals (SB0, SBa, SBb, SBc). Irregular galaxies are not shown.

galactic meridian, the plane passing through the centre of the galaxy, the Earth and the north and south galactic poles. Standard books on spherical trigonometry explain how to convert l and b coordinates into the usual right ascension α and declination δ.

4.1.2Galaxies

Observational cosmology is concerned with the distribution of matter on scales much larger than that of individual stars, or even individual galaxies. For many purposes, therefore, we can regard the basic building block of cosmology to be the galaxy. Much of this book is concerned with the problem of understanding galaxy formation and we shall defer a detailed study of galaxies and the way they are distributed until Part 4, where we confront the theories we have described with the observed facts. It is worth, however, describing some of the basic properties of galaxies to give an idea of the richness of structure one can observe.

Galaxies come in three basic types: spirals, ellipticals and irregular. Hubble proposed a morphological classification, or taxonomy, for galaxies in which he envisaged these three types as forming a kind of evolutionary sequence. Although it is now not thought that this evolutionary sequence is correct, Hubble’s nomenclature, in which ellipticals are ‘early’ type and spirals and irregulars ‘late’, is still commonly used. Figure 4.1 shows Hubble’s classification scheme. The elliptical galaxies (E), which account for only around 10% of observed bright galaxies, are elliptical in shape and have no discernible spiral structure. They are usually red in colour, have very little dust and show no sign of active star formation. The

70 Observational Properties of the Universe

luminosity profile of an elliptical galaxy is of the form

where I0 and R are constants and r is the distance from the centre. The scale length R is typically around 1 kpc. The classification of elliptical galaxies into En depends on the ratio of major to minor axes of the ellipse: the integer n is defined by n 10(1 − b/a), where a and b are the major and minor axes, respectively. Ellipticals show no significant rotational motions and their shape is thought to be sustained by the anisotropic ‘thermal’ motions of the stars within them. Ellipticals occur preferentially in dense regions, i.e. inside clusters of galaxies.

Spiral galaxies account for more than half the galaxies observed out to 100 Mpc and brighter than m = 14.5. Hubble’s division into normal (S) and barred (SB) spirals depends on whether the prominent spiral arms emerge directly from the nucleus, or originate at the ends of a luminous bar projecting symmetrically through the nucleus. Spirals often contain copious amounts of dust, and the spiral arms in particular show evidence of ongoing star formation (i.e. lots of young supergiant stars), giving the arms a blue colour. The nucleus of a spiral galaxy resembles an elliptical galaxy in morphology, luminosity profile and colour. Many spirals also demonstrate some kind of ‘activity’ (non-thermal emission processes). The intensity profile of spiral galaxies (outside the nucleus) does not follow Equation (4.1.4) but can instead be fitted by an exponential form:

The subdivision of S and SB into a, b or c depends on how tightly the spiral arms are wound up. Spirals show ordered rotational motion which can be used to estimate their masses (see Section 4.5).

Lenticular, or S0, galaxies were added later by Hubble to bridge the gap between normal spirals and ellipticals. Around 20% of galaxies we see have this morphology. They are more elongated than elliptical galaxies but have neither bars nor spiral structure. Irregular galaxies have no apparent structure and no rotational symmetry. They are relatively rare, are often faint and small and are consequently very hard to see. The distribution of masses of elliptical galaxies is very broad, extending from 105 to 1012M , which includes the mass scale of globular star clusters. Small elliptical galaxies appear to be very common: for example, 7 out of 17 galaxies in the Local Group are of this type. Spiral galaxies have a smaller spread in masses, with a typical mass of 1011M .

4.1.3 Active galaxies and quasars

Many galaxies, especially spirals, show various types of activity, characterised by non-thermal emission at a wide range of wavelengths from radio to X-ray. A full classification of all the di erent types of active galaxy is outside the scope of this book, let alone any attempt to explain the bewildering variety of properties they

Introduction 71

Figure 4.2 The ‘Whirlpool’ Galaxy M51, a fine example of a face-on spiral galaxy. Picture courtesy of the National Optical Astronomy Observatory/Association of Universities for Research in Astronomy/National Science Foundation.

possess. One possible explanation is that they are all basically the same kind of ‘animal’, but we happen to be observing them at di erent angles and therefore we see radiation from di erent regions within them. We shall not discuss this idea in detail, however, but merely restrict ourselves to listing the main types. The usual abbreviation for all these phenomena is AGN (active galactic nucleus).

Seyfert galaxies are usually spiral galaxies. They have very little radio emission and no sign of any jets. Seyferts display a strong continuum radiation all the way from the infrared to X-ray parts of the spectrum. They also have emission lines, which may be variable.

Radio galaxies are usually ellipticals. They typically possess two lobes of radio emission and sometimes have a compact core; often they show signs of some kind of ‘jet’. The nucleus of these sources tends to have spectral properties similar to Seyfert galaxies.

BL Lac objects have no emission lines, but a strong smooth continuum from radio to X-ray wavelengths. They show dramatic and extremely rapid variability. It is thought that these objects might be explained as the result of looking at a relativistic jet end-on. Relativistic e ects might shorten the apparent variability timescale, and the emission lines might be swamped by the jet.

72 Observational Properties of the Universe

Figure 4.3 The quasar 3C273, seen in optical light, showing a jet of radiating material. Photograph courtesy of the National Optical Astronomy Observatory/Association of Universities for Research in Astronomy/National Science Foundation.

Quasars are point-like objects and are typically at high redshifts. Indeed the current record holder has z 6! They are phenomenally luminous at all frequencies. Moreover, they are variable on a timescale of a few hours: this shows that much of their radiant energy must be emitted from within a region smaller than a few light hours across. Such is the energy they emit from a small region that it is thought they might be powered by accretion onto a central black hole. Most quasars are radio-quiet, but some are radio-loud. Long exposures sometimes reveal structure in the form of a jet.

A somewhat milder form of activity is displayed by the starburst galaxies, which, as their name suggests, are galaxies undergoing a strong burst of star formation which may be triggered by the interaction of the galaxy with a neighbour.

4.1.4 Galaxy clustering

All self-gravitating systems tend to form clumps, or density concentrations, so one should not be surprised to find that galaxies are not sprinkled randomly throughout space but are clustered. As we shall see in Chapter 16, the way galaxies cluster is approximately hierarchical: many galaxies occur in pairs or small groups which in turn are often clustered into larger associations. Just how large a scale this hierarchy reaches is an important test of theories of structure formation, as we shall see.

Introduction 73

Figure 4.4 The Coma cluster of galaxies observed in optical light. Only the central regions are shown; the cluster contains more than a thousand galaxies, most of which are elliptical. Picture courtesy of the National Optical Astronomy Observatory/Association of Universities for Research in Astronomy/National Science Foundation.

Our galaxy, the Milky Way, is a member of a group of around 20 galaxies (most of them small) called the Local Group, which also includes the Andromeda spiral M31, and is altogether a few Mpc across. The nearest galaxies to us, the Large and Small Magellanic Clouds, are members of this group. Further away, at a distance of about 10h−1 Mpc, lies a prominent cluster of galaxies called the Virgo cluster which is pulling the Local Group towards itself. There are several prominent clusters within 100h−1 Mpc of the Local Group, the most impressive being the Coma cluster which lies about 60h−1 Mpc away and which contains literally thousands of galaxies. One should stress, however, that it is probably not helpful to think of clusters as discrete entities: all galaxies are clustered to some extent, but most of them reside in small groups with a low density contrast. When one looks at objects like Coma, one is seeing the upper extreme of the distribution of cluster sizes.

Nevertheless, an important part of the analysis of galaxy clustering is played by the study of the richest clusters. George Abell catalogued the most prominent clusters according to their apparent richness and estimated distance in the 1950s. The manner in which he did this was somewhat subjective and, as we shall discuss in Chapter 16, the methods he used to identify ‘Abell’ clusters may have introduced some systematic errors. Nevertheless, his catalogue is still used today for studies of large-scale structure. Rich clusters of galaxies also have other uses. These objects are so dense that they are probably gravitationally fully collapsed systems and one can therefore use statistical mechan-

74 Observational Properties of the Universe

Figure 4.5 The Lick map showing a region of the northern galactic sky. A strong visual impression of ‘bubbly’ and/or ‘filamentary’ pattern is revealed. Picture courtesy of Ed Groth.

ics to estimate their mass (see Section 4.5). Moreover, they are also very bright in the X-ray part of the spectrum because they contain large amounts of hot, ionised gas. X-ray observations can therefore be used to measure the relative contributions to the total cluster mass of individual galaxies and hot gas, as well as any unseen component of dark matter. Maps of the general pattern of clustering on the sky require systematic surveys of galaxies with some well-defined selection criterion (usually a strict apparent magnitude limit). Usually such surveys avoid regions of the sky close to the galactic plane, say with galactic latitude b < 20◦, because of the observational di culties posed by interstellar dust within our Galaxy. The first survey of galaxy positions was due to Shapley and Ames (1932) which catalogued 1250 galaxies with m < 13. This was the first strong indicator of galaxy clustering. Later, Zwicky accumulated a sample of 5000 galaxies with m < 15 using the Palomar Sky Survey. Enormous strides were then taken by Shane and Wirtanen (1967), who created the famous Lick map of galaxies. This shows around a million galaxies with m < 19 and covers most of the sky. Figure 4.5 shows clear evidence of clustering in the form of filamentary patterns, large clusters and regions of very low density. The Lick map was compiled using relatively primitive eyeball techniques. More recent surveys using automatic plate-measuring machines, such as the APM and COSMOS, have made the acquisition of large quantities of data rather less problematic. The APM catalogue, for example, contains about two million galaxies (Maddox et al. 1990). Important though these sky surveys are, because of the sheer num-

expansion was first discovered observationally by Slipher but he did not make the bold interpretation of his data that Hubble did. After many years of painstaking observations, Hubble (1929) formulated his law in the form that galaxies seem to be receding with a velocity v proportional to their distance d from the observer:

This relation is called the Hubble law and the constant of proportionality H0 is called the Hubble constant. The numerical value of H0 is most conveniently expressed in units of km s−1 for the velocity and Mpc for the distance, i.e. in km s−1 Mpc−1. As we have mentioned before, and shall discuss in much detail soon, H0 is very di cult to measure accurately. Until recently there was an uncertainty of about a factor of two in H0. Given the scale of the possible error, it is useful to introduce the dimensionless parameter h defined in (4.1.2).

We should now make some comments about the limits of the validity of Equation (4.2.1). For a start, the distance d must be su ciently large that the recession velocity deduced from (4.2.1) is much larger than the radial component of the peculiar velocities. This can be up to 1000 km s−1 for galaxies inside clusters; this places the requirement that d 10h−1 Mpc. In terms of redshift this means that z 10−2. On the other hand, the distance should not be so large that Equation (4.2.1) implies a recession velocity greater than the velocity of light. In fact Equation (4.2.1) is true if d is the proper distance of the galaxy, but we cannot measure this directly and one has to use measures such as the luminosity distance for which Equation (4.2.1) is no longer valid. Roughly speaking one should therefore only use this equation for d 300h−1 Mpc (or z 10−1). From Section 1.5 it can be shown that the distance d of a galaxy with redshift in the range 10−2 z 10−1 is given, to a good approximation, by

This equation should be thought of as the first approximation to the formula for the luminosity distance as a function of redshift for Friedmann models:

which one can prove quite easily starting from Equation (1.7.3) (see also Equation (2.4.15)).

As we have mentioned, Equation (4.2.1) can be derived from the assumption that the Universe is homogeneous and isotropic, i.e. that the Cosmological Principle applies. All the relations one can use to demonstrate this property from an observational point of view, such as the m–z (magnitude–redshift) and N–z relations, obviously contain the parameter H0 explicitly.