Luminosity functions give the space densities of source populations as functions of spectral luminosity. They constrain source physics, clustering, cosmological evolution, and contributions to the radiation background. Extragalactic radio sources span eight decades of luminosity, so dividing them into luminosity ranges effectively separates them by energy generation mechanism and other fundamental properties. Multivariate luminosity functions divide the source population in additional ways (e.g., by optical morphology, optical absolute magnitude, or radio spectral index) selected to emphasize particular source characteristics.

Relations between various classes of AGN should show up when examining their LFs. For Seyfert galaxies, such studies have been affected by the prevalence of (essentially) integrated magnitudes. Proper nuclear magnitudes have been determined in an effort of CCD imaging, which enable an appropriate comparison with QSOs.

We report the result of the VLA observations of all the 80 AGN in the Cambridge-Cambridge ROSAT Serendipity Survey (CRSS, Boyle et al. 1995), a new well defined sample of 80 X-ray selected AGN with fx (0.5-2.0keV)≥ 2 × 10–14 erg s–1 cm–2. Our aim was to obtain a complete classification of the sample members as Radio-loud (RL) or Radio-quiet (RQ) in order to determine well-constrained X-ray luminosity function (XLF) for X-ray selected RQ and RL AGN separately.

This contribution gives further insight into the problem of an ‘evolution’ of the function G(> R) [R is the ratio between radio and optical luminosity of a QSO] suggested by Visnovsky et al.(1992,ApJ,391,560), and recently by Schmidt et al.(1995,AJ,109,473). Using the Optical Luminosity Function for optically selected quasars derived by Boyle et al.(1988,MNRAS, 235,935), and evolving (cf. Schmidt et al. 1995) or non-evolving (cf. Marshall 1987,ApJ,316,84) G(> R) function, an evolutionary function E(z) for the population of both radio quiet and radio loud quasars is determined by modelling the distributions of redshift n(z), as well as counts of apparent optical blue magnitude n(B) and radio 5 GHz flux density n(S) in samples with different radio and optical limits, respectively, and fitting them to the available observational data.

This paper sets out the status of data determining the space distribution of extragalactic radio-source populations, describes some recent results from analyses of the data, and indicates why and how the analyses need revision in the light of unified models. It concludes by emphasizing the severity of the effects of large-scale structure on modern survey data.

As radio survey frequency is raised the proportion of flat-spectrum sources increases in bright flux-limited samples (eg Wall 1994, Aust J Phys47, 625). Differential source counts show a corresponding broadening of the central maximum due to the increasing proportion of flat-spectrum sources. Orr & Browne (1982, MNRAS200, 1067) modelled this change in shape of the source count by proposing a unifying scheme which states that the core-dominated, flat-spectrum radio sources are the steep-spectrum sources with their cores Doppler-boosted due to the alignment of the jets with the line of sight.

The properties of the μJy radio sources are described in this paper. The results were obtained from deep VLA observations of four fields, shown in Table 1. Deep optical images have been obtained for the Bootes and Lilly 1 fields.

During the preliminary deep imaging phase of our large spectroscopic survey of faint field galaxies (CFRS), one of our fields (10 arcmin × 10 arcmin) was chosen to coincide with the Fomalont et al (1991, A.J. 102,1258, hereafter FWKK) radio source field, including 36 S≃ 16μJy radio sources of their complete sample. All sources but two have been identified to V < 25 and/or IAB ≤ 24, and/or KAB ≤ 21.

The microJy population is mainly constituted of three distinct populations of galaxies with different redshift regimes: early-type galaxies at z > 0.75 with a low powered AGN in their cores, post-starburst galaxies at intermediate redshifts (z = 0.375 to z = 0.8 or slightly > 1), and emission-line galaxies at z < 0.45 containing AGNs. The fraction of μJy sources with z > 1 could be as high as 30%. Most of the μJy radio sources (> 50%) are likely associated to AGNs, conversely to what is found at mJy levels (mostly starburst galaxies, Benn et al, 1993, MNRAS, 263, 98). Only one galaxy in our sample has a classical starburst spectrum.

The strong decrease of the radio spectral index from sub-mJy to μJy counts appears to be due to a combination of three factors: (1) the emergence of an elliptical population at high redshifts with moderate radio emission (2) an increasing fraction of narrow emission-line AGNs (Seyfert 2 and LINER); (3) a higher contribution of the thermal radiation to the radio emission from spirals, and the almost complete disappearance of starburst galaxies. Details of the results summarized here can be found in Hammer et al (1995, MNRAS, 276, 1085).

An upper limit on the space density of quasars at z > 5 is obtained independent of any optical magnitude limit, from the complete identification of a large sample of flat-spectrum radio sources. This upper limit is below the observed space density at z ≃ 2 − 3, showing that the turnover in space density is real and not merely due to obscuration.

The study of cosmological evolution of the sizes of extragalactic radio sources started about a quarter century back. From the very first angular size-redshift (θ-z) plots (Miley 1968, 1971; Legg 1970) and angular size-flux density (θ-S) plots (Swarup 1975; Kapahi 1975) it became evident that some sort of cosmic epoch-dependent evolution in the size distribution for the population of extragalactic radio source needs to be proposed; the sources at earlier epochs appeared on the average to have smaller physical sizes. However, a suitable luminosity-linear size (P-l) correlation among the radio source population could also explain the observations, without invoking a size evolution with redshift. The only reliable way to disentangle these two separate effects is to investigate the size distribution in the luminosity-redshift plane, where one could examine not only the l-z relation for a given luminosity class, but could also check for a P-l correlation in a given redshift bin.

In any flux-limited sample a tight correlation of luminosity (P) and redshift (z) is inevitable. It is therefore necessary to obtain complete samples at lower and lower flux-limits in order to have adequate coverage of the P–z plane, essential if we are to decouple the trends in epoch from trends in luminosity. This we have done for a number of flux-limits — giving coverage of the P–z plane seen in Fig. 1. Our redshift information is spectroscopic; the results of Eales et al (in prep.), namely the increased scatter in the

K-z plot for samples lower in luminosity than 3C, strongly warn us against using redshifts estimated from K-magnitudes.

Cosmological evolution of synchrotron spectra of the powerful extragalactic radio sources was studied by many authors. Some indications of such an evolution had been found firstly by analysis of ‘spectral index - flux density’ (α – S) relation for the sample of relatively strong radio sources. Later Gopal-Krishna and Steppe extended the analysis to weaker sources and found that the slope of αmed (S) curve changes dramatically at intermediate flux densities. Gopal-Krishna and Steppe pointed out that the maxima of the αmed (S) curve and of differential source counts are at almost the same flux density ranges (see, Fig. 2). It has to be noticed that the all mentioned results were obtained using the low-frequency spectral indices and on the basis of low frequency samples.

One hundred years after G. Marconi recorded radio waves over a distance of more than 1000 m, the most sensitive radio telescopes are able to detect the radio emission from light travel distances at least 1.4 × 1023 times greater. The electromagnetic waves from these distant objects are red shifted by Δλ/λ = z > 4. It is not the mere distance of high redshift objects which is fascinating, but rather the fact that one looks back into the early history of the universe by observing them: Objects at a redshift of 4 shined at a time when the universe had reached only about 1/5 of its present age.

Together with several of my colleagues I have embarked on a comprehensive program to study the radio–aligned restframe UV structures in high redshift radio galaxies (HzRGs) using some of the world's premier optical telescopes: the Hubble Space Telescope for high spatial resolution imaging, and the Keck 10m telescope for high S/N spectropolarimetry. I will discuss some of our latest results from these observations which elucidate, and at the same time obscure, our evolving understanding of HzRGs.

The study of radio galaxies selected at mJy flux levels has the potential to resolve two important issues in observational cosmology provided redshifts can be determined or reliably estimated for complete samples of such sources. First, the deep flux limit, combined with the shape of the radio luminosity function means that the redshift distribution of such samples provides a much more powerful test of the existence of a high-redshift cutoff for radio sources (Dunlop & Peacock 1990) than can be provided by further studies of brighter radio samples. Second, as a consequence of selection from bright radio surveys, the detailed study of galaxies at z > 2 has to date been confined to objects of extreme radio power (e.g. 4C41.17, Chambers et al. 1990; B2 0902+34, Eales et al. 1993), and it has now become clear that the ultraviolet-infrared properties of such sources are strongly contaminated by processes connected to the AGN (Eales & Rawlings 1993; Dunlop & Peacock 1993). Being 100-1000 times less radio luminous than these extreme sources, mJy radio galaxies at comparable redshifts should provide much more representative probes of the formation and evolution of elliptical galaxies in general.

Recent observations of distant radio galaxies show that there is a strong link between the radio source and the optical continuum and Lyα line emission from the galaxy. This link is discussed in terms of differences in age, orientation and environment between the radio sources.

The Hubble diagram of GPS galaxies has a low dispersion and a steep slope compared with that for 3C galaxies. The relative faintness of GPS galaxies at high redshift may be due to the absence of the aligned optical/uv component seen in high redshift 3C galaxies. The GPS Hubble relation is too steep to fit with evolution models for passively evolving ellipticals. This could be caused by the dynamical evolution of the GPS galaxies.

Stellar populations of high redshift radio galaxies (HzRG) (z up to 4.2) are the oldest stellar systems known, that is the ones formed at the earliest cosmological epochs. Therefore they are the best objects for providing us with information about the epoch of galaxy formation. The information on the stellar populations in HzRG are obtained from the study of their Integrated Spectral Energy Distribution (ISED) which are gathered both from spectra and integrated magnitudes. The most common approach for the interpretation of colors and spectral features of the energy distribution of galaxies is the Evolutionary Population Synthesis (EPS), which has been introduced for the first time by Tinsley in 1972. EPS models have often been used in the past to interpret the ISED of HzRG (Chambers & Charlot 1990; Lilly & Longair 1984; di Serego Alighieri et al. 1994) in order to draw conclusions on the age of the stellar populations and therefore on the epoch of galaxy formation. The results are sometimes conflicting and a number of very recent EPS models have become available (Bressan et al. 1995; Bruzual & Charlot 1993; Buzzoni 1989; Guiderdoni & Rocca-Volmerange 1987): we are therefore analysing the differences between the various EPS models with the aim of assessing their suitability to study the stellar population at early epochs. The EPS models assume for stars a given Initial Mass Function(IMF) as well as a Star Formation Rate (SFR). Then one can compute the number of stars with given mass present in the galaxy as a function of time. The position of each star in the HR diagram is determined by means of the isochrones, which are calculated from stellar evolutionary models. The ISED of a galaxy is obtained from the superposition of the spectra of single stars obtained from a stellar spectral library. Thus these models describe the galaxy ISED as a function of the time, giving a complete evolutionary picture.

We present the preliminary results of the “BIG TRIO” project of penetration into the “Dark Age” of the Universe, between the recombination epoch and the epoch of the first QSO using RATAN-600 “Cold Experiment” deep (few mJy) multi-frequency strip survey (Parijskij, Korolkov, 1986; Parijskij et.al,1991,1992). Our general approach is close to the classical SS FRII RG selection rules of very distant galaxies with old stellar population (McCarthy, 1993) with small improvements. Details may be found in (Kopylov et al, 1995). Mean estimated z of our SS FRII RG's is about 1.5, 20% of all objects have z larger than 3. Before the direct spectroscopy of all SS FRII objects we have estimated their redshifts by different methods: using the updated Hubble diagram, θ-z and flux density-z relations and now begun to use multi-color measuring all our objects to estimate “color z” and a stellar age of the parent galaxies using available models of stellar population evolution in such objects (gE class). The first subgroup of 16 objects (not the weakest ones) measured in BVRI gave us the following preliminary results using Bruzual-Charlot model (Bruzual et al., 1993). Looking at this Table, we can make the following statements: mean color z occurred to be very close (within 15%) to the photometric z, but individual redshifts may differ. A mean age of the stellar population is about 1 Gyr, and, at least in some objects, star formation began when the Universe was only 1 Gyr old (Ω0 = 1, H 0 = 50), that is older than the most distant QSOs. One object, RC0934+0505, happened to be the oldest object found up to now. We estimate, that there are about 10000 objects with such an age on the sky which can be easily selected (especially with new generation of radio and optical catalogs now in preparation) and fully studied spectroscopically even by present day facilities. The only evolution effect we have noticed is that more distant objects have smaller ages of stellar populations. There is weak z-dependence of the ratio of radio to optical luminosities in the objects of our list, which disappears when we take into account the K- correction to the SED in gE.