Observational evidence on the angular diameter-redshift relation using radio sources has, until recently, been confined to studies of the overall angular size. In this paper a different approach is described in which the very compact hot spots in radio sources are used as standard measuring rods. Such hot spots appear to be especially suitable for cosmological studies for the following reasons.

1. (a) Hot spots which contain one half or more of the total flux density are generally found only in the most powerful sources (P178 ≳ 1027 W Hz−1 sr−1).

2. (b) Hot spots appear to show a smaller dispersion in physical size than the overall source dimensions.

This paper is a partial and preliminary report on a review of the optical and radio properties of 3CR sources (Kristian, 1977). It will treat the overall status of the identifications and a few of the optical properties of the identified sources, including evidence for a faint magnitude cutoff in the apparent brightness of 3CR quasars. A summary of the status of 3 CR identifications as of early 1976 has been prepared by Smith, Spinrad, and Smith (1976). The present work includes new data on several dozen sources, as well as a systematic reevaluation of previous identifications.

For the past few years a co–operative programme involving astronomers at the Universities of Cambridge, Sydney and Groningen and Lick and Steward observatories has been in progress aimed in part at obtaining a complete sample of QSO's in a selected region down to given limits of optical and radio flux. The radio sample from the 408 MHz Mills Cross at Molonglo covers two declination strips each 2° wide and centred at declinations ∼11°N and ∼17°N respectively. Part of the survey has been published as the MC2 and MC3 catalogues (Sutton et al. 1974) covering the 11° strips in the R.A. interval 11h28m–01h23m and the 17° strip in the interval 13h30m–04h13m and this section is complete to a flux limit (S) of 0.45 Jy. The rest of the survey consists of an extension of the 11° strip around the rest of the sky and to a lower flux limit of about 0.15 Jy.

The WSRT yields samples of radio sources which are well suited for systematic identification work for the following reasons:

1. a) The surface density is high: at 1415 MHz an average of 10 to 30 sources can be detected within 0°.55 from the field centre; at 610 MHz the numbers are 40 to 100 within 1°.0. In any given field, most sources will fall within the boundaries of plates for the present generation of optical telescopes.

2. b) The positional accuracy is, on the whole, rather high. One can thus propose identifications based on positional agreement only, avoiding selection effects present when selecting “on type”.

The monochromatic luminosity function of radio sources (RLF) is the number of sources per unit volume as a function of the luminosity P at a frequency v and of the cosmic epoch (z). Symbol : n(P(v),z). It is often given per interval of log P, or Mr, the absolute radio magnitude. This function is determined only for sources associated with optical objects (galaxies and QSO's). It can be given for all kinds of associations, or for sources associated with a specific type of object. In this case the normalized, or fractional, RLF is sometimes used, Fi (P,z) = ni (P,z)/ρi (z), where ρi is the space density of type i objects. The word “bivariate” is used for the RLF defined per interval of the optical luminosity (or magnitude M). A RLF can be determined using either a radio–optically complete sample of identified sources, or the radio observation of an optically selected sample. The merits of methods used to estimate a RLF from a complete sample are discussed by Felten (1976). Translation of a RLF from one frequency to another must be done with care if, at the two frequencies, different radio components (like the extended and the compact) would be preferentially sampled. We shall review the estimates of local (z = 0) RLF's using Ho = 100 Kms−1 Mpc−1 and the unit WHz−1 for P.

It is well known from the pioneering work of Baade and Minkowski that radio galaxies very often have strong emission lines in the spectra of their nuclei, indicating the presence of relatively large amounts of ionized gas. For instance, in the early survey of radio galaxies by Schmidt (1965), of the 35 galaxies observed, 32 had at least [0 II] λ3727 in their spectra and well over half had relatively strong [0 II] and other observable emission lines as well. In the recent review of optical identifications and spectroscopy of the revised 3C catalogue of radio sources by Smith et al. (1976), 137 radio galaxies are listed. Of these descriptive spectral information is given for 98, of which 49 show strong–emission line spectra, 19 intermediate–strength emission, 12 weak emission, and 18 a pure absorption–line spectrum without detectable emission lines. The fraction of objects with emission line–spectra is much higher than for normal galaxies. It is thus apparent that though the presence of emission lines is neither a necessary nor a sufficient condition that a galaxy be an observable radio source, nevertheless a large fraction of radio galaxies do contain ionized gas in their nuclei.

In addition to the characteristic emission lines, absorption lines frequently are seen in the spectra of QSOs, usually those with high redshift (zem ≳ 1.8). About 10 percent of all QSOs listed in the compilation of Burbidge et al. (1976a) are recorded as having at least one ‘identified’ absorption system, meaning that a pattern of several selected observed lines can be matched with the apparent wavelengths of transitions (generally from the ground level) in a physical plausible group of atoms or ions at the same, although arbitrary, redshift (Bahcall 1968, Aaronson et al. 1975). Identified absorption line redshifts range from being comparable with the associated emission line redshifts, to having very much smaller values with relative velocities exceeding 0.5c in the QSO frame. Added to this, there are many QSOs having absorption lines not yet recognised as belonging to identified systems, both those objects already having one or more identifications, and others with none.

Correlations between the radio and optical properties of radio sources have proved elusive and the main conclusion to be drawn from this is that there is a great variety of objects in the universe that emit nonthermal radiation, so that attempts to use these objects for cosmological purposes can be frustrated unless one can find some way of selecting objects that do have common intrinsic properties. Despite this, the search for relations and correlations is interesting quite apart from cosmology, because such correlations should provide a groundwork for a physical theory or theories of what is really happening in sources of nonthermal radiation.

One particular aspect of the relations between the radio and optical properties of radio sources has been examined for a complete sample of 3CR sources, namely the relation between the radio structure of a source and its optical identification. Possible differences between the radio structures of quasars and radio galaxies are investigated, and the data provide clues as to the optical nature of the unidentified sources.

The topic that I have to introduce today is concerned with the question as to whether or not we can obtain any cosmological information from radio astronomy. Alternatively, we may ask “Where does radio astronomy have an impact on cosmology?” There are several areas that must be discussed. They are:

1. 1) The discovery and interpretation of the microwave background radiation.

2. 2) The identification of powerful radio sources and the discovery that many of them have large redshifts. If we can prove that the large redshifts mean that the objects are at great distances, then we can use these radio sources as follows:

   1. (a) We can attempt to obtain a Hubble relation for the optical objects which are identified with radio galaxies;

   2. (b) We can look for a relation between the angular diameters of the radio sources and the redshifts of the optically identified objects and we can also look at relations between the angular diameter and the radio flux;

   3. (c) We can construct log N - log S curves and we can carry out luminosity volume tests.

The ultimate aim of statistical studies of redshift, magnitudes and flux densities of quasars is to derive the general luminosity function Φ(z, Fopt, Frad, α, …) which describes the space density as a function of redshift, intrinsic optical luminosity, intrinsic radio luminosity, spectral index, etc. We assume throughout that the emission-line redshifts z of quasars are cosmological. The function Φ contains information that will be pertinent for any theory of the formation and evolution of quasars.

Conventional interpretation of the N(S) relation requires cosmic evolution of the radio source population. Investigators agree on the general features of this evolution: it must be confined to the most luminous sources, and must be strong, the numbers of such sources at redshifts of 1 to 4 exceeding the present numbers by a factor ≳103. There is no consensus as to whether density or luminosity evolution prevails (or both), whether a cutoff in redshift is necessary, or whether the source populations found in high-frequency surveys follow even the general evolutionary picture deduced for the low-frequency survey population. It is therefore hardly surprising that the physical basis of the evolution, the ultimate goal of N(S) interpretation, remains largely “in the realm of imaginative speculation” (P. A. G. Scheuer).

We examine the Hubble diagram for radio galaxies and compare radio galaxies and first-ranked cluster galaxies as cosmological test objects. Radio source identification programs are now producing reliable identifications with galaxies as faint as V ≈ 23 and spectroscopy of these objects has already resulted in the discovery of galaxies with redshifts as high as 0.75, thus there are great expectations for progress in the near future. As in the past, indeterminate corrections, notably luminosity evolution and a possible correlation between radio power and optical luminosity, preclude the determination of qo.

We discuss in this talk the optical and radio Hubble-diagrams for the brightest quasars. We shall infer from our results: (1) a strong correlation between redshift and received flux that is consistent with the cosmological interpretation of the emission-line redshifts; and (2) a quantitative upper limit on the permissible amount of pure luminosity evolution. We establish these conclusions twice, by examining the Hubble diagrams both with and without corrections for the selection effects introduced by the flux limits of the quasar catalogs considered.

For some time there have been suggestions that there is a special association of radio galaxies with rich clusters of galaxies, and more recently that the radio galaxies in clusters may show different characteristics from those outside. I will discuss the evidence for three types of such differences, in luminosity function, morphology, and occurance of steep spectrum sources. In each case I will try to connect any difference I find to the cluster environment.

For those enamoured of the primaeval fireball, the relict radiation has proved a tantalising mistress. Since the famous discovery in 1965, by Penzias and Wilson, of an excess antenna temperature consistent with cosmological expectations, many observers have succeeded in measuring a flux consistent with a thermodynamic temperature of ∼3K. Until recently, however, no direct spectral measurements had been made at wavelengths shorter than the Planckian peak corresponding to radiation at this temperature. At such wavelengths atmospheric emission and absorption are overwhelming from even the highest mountain site and observations must be made from at least balloon platforms. The pioneering broadband rocket and balloon measurements covering this wavelength region produced consternation when excessively high fluxes were reported; successive flights gradually eliminated the excess, emphasising the practical difficulties of such observations. A review of this phase of the pursuit is given by Blair1. Nevertheless, it is upon direct submillimetre measurement of the spectral density Iν that confidence in the interpretation of the longer wavelength results must reside. The outcome of the first such measurement, by Queen Mary College in 1974, seemed completely to justify such confidence. Unfortunately, the subsequent observations by Berkeley, although leading to the same conclusion about the value of the thermodynamic temperature, were so discrepant in detail from those of QMC as once again to raise doubts. We have since been eagerly awaiting the results of observations by independent groups but these have been frustrated by instrumental failures. We attempt here to assess the present situation. We conclude that although present measurements indicate a flux not inconsistent with a Planckian spectrum corresponding to a temperature of ∼3K, they do not demand such an interpretation. Moreover, because we may not actually expect a Planckian curve from a fireball, very much more detailed information is needed to obtain a view of the early thermal history of the universe.

According to current ideas, massive extragalactic systems such as galaxies and clusters of galaxies formed as a result of the growth of small fluctuations in density and velocity which were present in the early stages of expansion of the Universe under the influence of gravitational instability. According to the hot model of the Universe at the epoch corresponding to a redshift z ≈ 1500, recombination of primaeval hydrogen took place and as a result the optical depth of the Universe to Thomson scattering decreased abruptly from about 1000 to 1 - the Universe became transparent. Therefore the observed angular distribution of the microwave background radiation (MWBR) contains information about inhomogeneities in its spatial distribution at a redshift z ∼ 1000. Silk (1968) was the first to note that this “photograph” of the Universe at the epoch of recombination must be enscribed with fluctuations associated with perturbations in the space density and velocity of motion of matter which will later lead to the formation of galaxies and clusters of galaxies.

The problem described in the title has already been theoretically analysed several times (see for example Dautcourt, 1969 and Novikov, 1974). Recently, however some important new aspects of the problem have been discovered; they are discussed briefly in this report which is based upon the calculations of Doroshkevich, Lukash, Novikov and Polnarev. First consider the influence of primordial gravitational waves on the microwave background. It is natural to assume that in the Universe, in addition to acoustic (or adiabatic) density perturbations which result in galaxy formation and corresponding metric perturbations, there also exist metric perturbations in the form of gravitational waves with wavelengths of the same order of magnitude as the acoustic perturbations. The amplitude of such gravitational waves could in principle be quite arbitrary. Their amplitude can be estimated by comparing the theory of such waves in the expanding Universe with the observed fluctuations in the microwave background which are now available or will be in future.

There are two important questions in which the physics of radio sources impinges upon cosmology. The first is whether the large apparent expansion velocities of certain compact sources can be explained satisfactorily within the hypothesis that their red-shifts are due to the Hubble expansion. The second is the whole broad question of the evolution of the radio source population with epoch. I do not have a new and convincing answer to the first, and the second is pretty nebulous, since we do not even understand radio sources at the present epoch very well. So I shall not present a general survey: instead, I shall use my allotted time to discuss a smaller question to which one can now give a fairly definite answer.

The V/Vmax test for quasars and the counts of radio sources show that the most powerful extragalactic radio sources exhibit strong evolutionary changes with cosmological epoch (see M. Schmidt and J.V. Wall et al., this volume). It should be emphasised that these are very large changes indeed. Schmidt, for example, has shown that for the world model with Ω = 0, evolution functions of the form F(t)∝exp(-10t/to) can account for the observations, to being the present epoch and t cosmic time. Since the quasar population from which this law is derived extends at least to Z = 2.5, corresponding to t = to/3.5 if Ω = 0, the comoving space density of quasars at Z = 2.5 must have been about 1300 times greater than it is at the present epoch. It is not known whether or not this law continues to hold at larger redshifts but even if it does, the increase in comoving space density from Z = 2.5 to infinity is only a further factor of 17. Therefore the bulk of the evolution occurs within the range of observationally accessible redshifts. Notice that a characteristic time-scale for the decay of the quasar population of ≈ to/10 ≈ 109 years comes out of this analysis.