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Radio Observations of High Redshift Radio Galaxies

We review some aspects of radio continuum polarimetric imaging of high redshift radio galaxies. The correlation between extreme values of Faraday rotation observed toward radio emitting structures in nearby radio galaxies, and X-ray emitting cluster atmospheres, is presented as a method for targeting objects at high redshift for deep X-ray searches. We present an X-ray detection of the extreme rotation measure radio galaxy PKS 1138-262 at z = 2.156, and we argue that the X-ray emission is from a cluster atmosphere with a luminosity of 1.7x10^{44} h^{-2} ergs sec^{-1}. We also present results on the correlation between size and redshift for a sample of ultra-luminous radio galaxies between 0<z<4.3. Source sizes decrease systematically with redshift, suggesting either denser environments, or younger sources, at high redshift. An alternative explanation is significant inverse Compton losses off the microwave background at high redshift.


Introduction
Searches for high redshift radio galaxies begin with surveys of the sky at radio frequencies typically below 1.4 GHz. Although these sources are targeted for study due to their radio properties, subsequent work has focused primarily on the optical and near IR properties of these systems. Sensitive, high resolution, multifrequency radio continuum polarimetric imaging provides unique information about the physics of these sources, and their environments, in a number of ways, including: (i) identification of the location of the active nucleus, (ii) study of alignments between radio and optical structures on sub-kpc scales (Best et al. this volume, van Breugel et al. this volume), (iii) determination of the pressure in the ambient medium, (iv) determination of the strength and morphology of source magnetic fields, (v) searching for small scale gravitational lensing events towards the extended radio structures (Carilli, Owen, and Harris 1994, Carilli 1995, Kochanek and Lawrence 1990, (vi) searching for extreme rotation measures and ultra-steep spectrum regions (Carilli et al. 1997b), (vii) study of the cosmological evolution of radio source structure Miley 1989, Singal 1993), (viii) tests of quasar-radio galaxy unification schemes as a function of redshift (Antonucci 1993), and (ix) constraining basic cosmological parameters (Guerra and Daly 1998).
An extensive review of jet theory for powering the double radio lobes in powerful extragalactic radio sources can be found in Carilli and Barthel (1996). In this paper we consider a few topics of particular interest for understanding the environment and evolution of powerful radio galaxies at high redshift.

Extreme Rotation Measures: Cluster Atmospheres at High Redshift
Rich clusters of galaxies constitute the extreme high mass end of the cosmic mass distribution function, and study of such rare objects provides unique leverage into theories of structure formation in the universe (Peebles 1993). Unfortunately, optical studies of distant clusters can be corrupted by field galaxy contamination (Frenk et al. 1990), while searching for X-ray emission from cluster atmospheres at z > 1 requires very long integration times for marginal detections. Thus far the three most distant X-ray cluster candidates currently known are all associated with powerful radio sources at z ≈ 1 , Crawford and Fabian 1995, Dickinson 1997, Worrall et al. 1994. One of the more important results in the study of extragalactic radio sources in the past 10 years has been the discovery of extreme values of Faraday rotation toward extended radio emitting structures (Dreher, Carilli, and Perley 1987, Taylor, Barton, and Ge 1994, Carilli et al. 1997a. Rotation measure (RM) values up to 20000 rad m −2 have been detected, as well as gradients in RM ≥ 1000 rad m −2 arcsec −1 . Observations of lower redshift radio galaxies have shown a clear correlation between extreme rotation measures and cluster environment: all sources located at the centers of dense, X-ray emitting cluster atmospheres show large amounts of Faraday rotation (Taylor et al. 1994). An important point is that this correlation is independent of radio source luminosity and morphological class, and hence is most likely a probe of cluster properties, and not radio source properties. The implication is that the hot cluster gas must be substantially magnetized, with field strengths of order a few µG (Carilli et al. 1997a).
The correlation between cluster X-ray properties and extreme rotation measures provides a potentially powerful criterion for selecting high z sources for deep X-ray observations. We have been conducting a systematic search for extreme RM sources at high redshift in order to exploit this correlation, and thereby potentially discover X-ray emitting clusters at high redshift (Carilli et al. 1997b).
Our best example to date is the narrow emission line radio galaxy PKS 1138−262 at z = 2.156. This source has the largest known RM at z > 2, with (rest frame) RM values up to 6250 rad m −2 (Carilli et al. 1997b). The optical continuum morphology of 1138−262 is comprised of many blue 'knots' of emission, distributed over an area of about 100 kpc ( Figure 1). The Lyα emission shows similar clumpy structure on a similar scale. Pentericci et al. (1997) interpret this distribution as a group of star forming galaxies in the act of merging into a giant elliptical galaxy. The radio source has the most disturbed morphology of any z > 2 radio galaxy yet identified, indicating strong interaction between the radio jet and the ambient medium. Such interaction is supported by optical spectroscopy, showing large velocities, and velocity dispersions, for the line emitting gas in regions associated with the brightest radio knots. All these data provide strong, although circumstantial, evidence that the 1138−262 radio source is in a dense environment, perhaps a hot, cluster-type atmosphere. To test this hypothesis we observed 1138−262 with the High Resolution Imager on the ROSAT X-ray satellite (Carilli et al. 1998).
The ROSAT observation shows a clear detection of an X-ray source close to the position of the radio and optical nucleus of 1138−262 ( Figure 2). The X-ray luminosity for 1138−262 is 1.7±0.3×10 44 h −2 ergs sec −1 for emitted energies between 2 keV and 10 keV. The optical, radio, and X-ray data all favor a hot cluster gas origin for the X-rays from 1138−262, however we cannot preclude an AGN contribution (see Carilli et al. 1998 for a detailed discussion). If the X-ray emission is from a hot cluster atmosphere, then the total gravitational mass is a few×10 14 M ⊙ , and the total gas mass is a few×10 13 M ⊙ .
We proceed under the assumption that the X-ray emission from 1138−262 is from a typical massive cluster atmosphere at z = 2.156, and we speculate on possible physical implications. First, models for structure formation such as CDM using standard cosmologies predict that any large scale structure observed at z ≈ 2 must be dynamically young, having just separated from the general expansion of the universe (Peebles 1993). Alternatively, massive structures at large redshift might indicate an open universe (Ω << 1). Second, the existence of a hot cluster-type atmosphere at high redshift would argue for shock heated, primordial in-fall as the origin of the cluster gas, rather than ejecta from cluster galaxies (Sarazin 1986). Such a model would require an early epoch of star formation in order to supply the metals observed in the associated optical nebulosity (Ostriker and Gnedin 1996). Third, the large rotation measures observed raise the question of the origin of cluster magnetic fields at early epochs. One possible mechanism is amplification of seed fields by a turbulent dynamo operating during the formation process of the cluster as driven by successive accretion events (Loeb and Mao 1994). And forth, the observation of X-ray emission from 1138−262 would then verify the technique of using extreme rotation measure sources as targets for searches for cluster X-ray emission at high redshift. Thus far there have been a total of 11 radio galaxies at z > 2 with source frame rotation measures greater than 1000 rad m −2 , the most distant being at z = 3.8 (Carilli et al. 1997b, Ramana et al. 1998, Carilli, Owen, and Harris 1994. An interesting alternative to a massive cluster atmosphere giving rise to the X-ray emission from 1138−262 is thermal emission from a very dense, subcluster 'halo', perhaps associated with the (forming) cD galaxy on a scale ≤ 100 kpc. For instance, increasing the gas density from 0.01 cm −3 to 0.1 cm −3 would decrease the required hot gas mass by the same factor (at fixed X-ray luminosity), and could possibly alleviate constraints on cosmological structure formation models. The pressure in this gas would be very high (10 −9 dynes cm −2 ), comparable to the pressure in the optical line emitting nebulosity and to the minimum pressure in the radio source, and the cooling time would be short (≤ few×10 8 years). Circumstantial evidence for such very dense, hot gas enveloping some high z radio sources has been reviewed by Fabian et al. (1986). Fabian (1991) suggests that in some cases the 'inferred pressures are close to the maximum that can be obtained by gas cooling in a potential well of a galaxy' (ie. the cooling time ≈ gravitational free-fall time), and he designates such systems as 'maximal cooling flows', with implied cooling flow rates up to 2000 M ⊙ year −1 . High resolution X-ray imaging with AXAF should be able to test whether 1138−262 has a normal cluster atmosphere, a 'maximal cooling flow', or an unusually X-ray loud AGN.
3 Properties of Sources at High Redshift

The Ultra-luminous Sample
An extensively investigated property of extragalactic radio sources has been the relationships between radio power (P), source size (D), and redshift (z), i.e. the P-D-z relationships (Singal 1993, Blundell et al. 1996. Such studies address the possibility of using radio sources as standard-rulers for cosmological models (cf. Daly 1994), or perhaps more reasonably as probes of the evolution of the local gaseous environments of the sources (cf. Neeser et al. 1995, Eilek and Shore 1989, Subrahmanian and Swarup 1990, Gopal-Krishna and Wiita 1991, Wellman and Daly 1995. Although much work has been done on this topic, there remains fundamental disagreements between various studies. Some studies favor a steep evolution for source size with redshift: D ∝ (1 + z) −n , with n ≥ 3, and favor a finite correlation between source size and radio power: D ∝ P m , with m ≈ 0.3±0.1 (Singal 1993, McCarthy this volume). Other studies find a more gradual size evolution with redshift, with n ≈ 1.5, and find essentially no correlation between power and size, m ≈ 0 (Neeser et al. 1995, Eales this volume). Neeser et al. (1995) show that some of these differences could arise due to limitations in the data, including: (i) the strong Malmquist bias inherent in flux limited samples, (ii) the incompleteness of samples, in particular due to surface brightness selection effects and/or the lack of redshifts for sources in a given sample, (iii) mixing sources of different morphological class, and including or excluding compact steep spectrum objects from a sample, and (iv) limited redshift ranges covered for most samples.
The Leiden observatory has, for some years, been performing a systematic search for radio galaxies at high redshift under the direction of G. Miley. We have assembled a data set of physical parameters for a sample of ultra-luminous ('UL') radio galaxies spanning the redshift range 0 to 4.3. The data for the high redshift sources come mostly from the Leiden program, including data from a follow-up high resolution, multifrequency radio continuum imaging survey of high redshift radio galaxies (Carilli et al. 1997b). These data have been supplemented with data on lower redshift sources from the 3CR sample as defined and compiled for FRII radio galaxies by McCarthy, van Breugel, and Kapahi (1991b), and data from other published samples of radio galaxies, including the Molongolo sample (McCarthy et al. 1990(McCarthy et al. , 1991a, the B2 sample Keel 1995, Lilly 1988), and the 8C sample (Lacy et al. 1994). Figure 3 shows the distribution of rest frame spectral luminosity at 178MHz, P 178 , versus redshift, for all 3CR Fanaroff-Riley class II radio galaxies, supplemented with sources from studies as listed above. Note the strong correlation between P 178 and redshift in the 3C sample, and how adding lower flux density sources beyond z = 1 to the 3C sample 'fills-in' the distribution. The 'Ultra-Luminous (UL) sample' is defined as FRII radio galaxies with: 34.7 ≤ log(P 178 ) ≤ 36.3, i.e. sources with luminosities roughly within a factor of ± five of Cygnus A (about 100 sources total). It is clear from Figure 3 that by adding the lower flux density sources at high redshift to the higher luminosity sources in the 3C sample, this UL sample reduces the effect of the Malmquist bias inherent in the 3C sample alone, although becoming necessarily sparse at z ≤ 0.4. The UL sample has good statistics to high redshift, is fully identified, including spectroscopic redshifts, and contains only FRII class radio galaxies. Perhaps most importantly, the UL sample is relatively restricted in radio luminosity, thereby mitigating problems with residual correlations in P-D, although information on the correlation of source properties with power is lost. Readhead et al. (1996) have proposed a classification scheme for extragalactic radio sources based on source sizes. In the context of their scheme, the UL sample contains no Compact Symmetric Objects, 12% Medium Symmetric Objects, and 88% Large Symmetric Objects.
Many high z radio galaxy searches involve a radio spectral index cut-off for source selection: α ≤ -1.0 or so. The question arises as to what biases such a selection introduces in the properties of sources in the resultant sample. We have used our database of integrated spectra of radio galaxies to determine the redshift evolution of radio spectral indices of the UL sample at both a fixed observed-frame frequency, and a fixed source rest-frame frequency. Figure 4a shows the spectral indices at an observed frequency of 2 GHz for the UL sample. Figure 4b shows the spectral indices for the UL sample at a rest frame frequency of 2 GHz, i.e. correcting for the redshift. Linear fits to the data yield a slope for spectral index versus redshift of -0.12±0.05 for the observed-frame data, and -0.08±0.05 for the K-corrected data, where the errors imply unit changes in reduced χ 2 assuming a reasonable error of ±0.1 for each spectral index measurement. For the non-K-corrected data the median spectral indices decrease from -0.94±0.08 for sources at z < 1, to -1.32±0.15 for sources at z > 2.9, while for the K-corrected sources the steepening with redshift is reduced, going from -0.91±0.08 at z < 1 to -1.08±0.15 at z > 2.9, where the errors indicate the inner quartile range of the distribution. Although the errors are significant, these data The open circles are the Fanaroff-Riley class II radio galaxies in the 3C sample. The filled circles are ultra-luminous sources from other surveys without explicit maximum angular size cut-offs. The stars are ultra-luminous sources from surveys with explicit maximum angular size cut-offs. The 'Ultra-Luminous (UL) sample' is defined as FRII radio galaxies with: 34.7 ≤ log(P 178 ) ≤ 36.3. suggest that the trend for spectral steepening with increasing redshift at a fixed observing frequency is principally due to the substantial K-correction involved. A similar conclusion was reached by van Breugel and McCarthy (1989). Some of the searches for high redshift radio galaxies include an explicit angular size upper limit, typically ≤ 20 ′′ . For redshifts beyond 0.4 or so, this implies a physical size limit of about 90 h −1 kpc. In our analysis we keep track of sources selected with and without explicit angular size cut-offs, and we find no significant differences between the results. We also find that the 3C source size distribution joins smoothly to that for the higher redshift sources.
A more insidious problem is the angular size cut-off implicit in identifying high redshift radio sources. An implicit cut-off might arise from missing sources in a radio survey due to the cosmological dimming in radio surface brightness. Again, selecting FRII radio sources, for which much of the emission comes from (typically) unresolved hot spots at the source extremities, mitigates this problem. A more difficult problem is that of identifying the observationally faint high redshift optical galaxies in large fields-of-view, as may occur in cases of wide-separation double radio sources. Again, the 3C sample is completely identified, as is the 6C sample of Neeser et al.. Hence, the 'dove-tailing' of results for the high redshift sources in the UL sample with those for the 3C sources, and the agreement between results from the UL sample with those from 6C (see below), gives us hope that this latter effect is not dominating the statistics.
3.2 4. The P-D-z-θ Relationships for the UL Sample Figure 5 shows physical size versus redshift for the UL sample. Physical sizes were derived from angular sizes assuming a standard cosmology with q o = 1/2, and h ≡ H o /100 km sec −1 Mpc −1 . The error bars show the range of median size as a function of redshift, for redshift bins chosen to have roughly equal numbers of sources in each bin (about 20 sources per bin, except for the highest redshift bin, which contains 12 sources). The error bars indicate the inner quartile range for the distribution within each bin. We have fit a power law in (1+z) to the median sizes using three different weighting schemes: weighted by the RMS for the distribution in each redshift bin, weighted by the inner quartile range error bars, and an unweighted fit. The results for the three different weighting methods are consistent, within the errors, with: D = 170±40h −1 (1+z) −n kpc, with n = 1.2 ± 0.3. The errors correspond to unit changes in reduced χ 2 for a least squares fit weighted by the RMS in each bin. We repeated the analysis using wider redshift bins, and using a narrower luminosity range, and obtained essentially the same results. We have also fit a power-law to all the data points (as opposed to the median values), which yields: D = 140 ± 20h −1 (1 + z) −n kpc, with n = 1.2 ± 0.1. Again, the errors correspond to unit changes in reduced χ 2 assuming a 10% error in each size measurement.
We have also considered the evolution of source bending angle, θ, as a function of redshift, where θ is defined as 180 o minus the angle between the two lines joining the core with the hot spot on either side of the source. Figure 6 shows the relationship between θ and redshift for the UL sample for sources with clearly defined hotspots and cores. The general trend is for increasing bending angle with redshift, at least out to z ≈ 3. The median value behaves as: θ = 6 o ± 3 o for z < 1, θ = 10 o ± 4 o for 1 < z < 2, θ = 14 o ± 3 o for 2 < z < 2.9, and θ = 10 o ± 5 o for 2.9 < z. A similar increase in bending angle with redshift has been seen by Barthel and Miley (1988) for radio quasars. The angles involved for the quasars are a factor two or so larger than those for radio galaxiesqualitatively consistent with unification schemes, i.e. larger projection angles for quasars relative to radio galaxies. One possible explanation for the decrease in source size with redshift at 'fixed' radio luminosity is an increase in the external density with redshift. Barthel and Miley (1988) show that the observed value of n ≈ 1.5 is consistent with a simple model in which the co-moving gas density evolves cosmologically: n x ∝ (1 + z) 3 . This leads to source size evolution according to: D ∝ (1 + z) −1.5 , assuming the ram pressure advance speed for a typical source behaves as n −0.5 x . Denser environments at high redshift could also explain the increase in bending angle with redshift, assuming that source bends are due to jet-cloud collisions (Icke 1991). A possible problem with the simple model of Barthel and Miley is that that the dynamical models of Begelman (1996) and Readhead et al. (1996) suggest that the source advance speed may have a weaker dependence on external density than n −0.5 x . Also, it is not clear that the local density of a structure that has separated from the general Hubble expansion will evolve as the cosmic background density.  has presented another model in which the decrease in source size with redshift is due to the sources being systematically younger at high redshift.
Overall, the data indicate that sizes of ultraluminous radio sources decrease with redshift. However, there remains a fundamental, unexplained, discrepancy between various studies of the D-z relationship, with some studies favoring a fairly shallow evolution, with an index of n ≈ −1.5 (the UL sample, and the study of Eales et al. this volume) , and others studies favoring a steep evolution, with an index of n ≈ −3.0 (McCarthy et al. this volume). The cosmic evolution of physical sizes of radio sources is a potentially powerful probe of the evolution of source physics, and/or source environments, and hence is an important issue to address with deeper, complete samples of radio sources now becoming available.

Inverse Compton Losses
An interesting alternative explanation of the D-z relationship for ultraluminous radio galaxies is that the larger sources may be 'snuffed-out' by inverse Compton losses at some nominal size which depends on redshift. The relative importance of inverse Compton losses versus synchrotron losses for the relativistic electrons in radio sources is hypothesized to be a strong function of redshift (Krolik andChen 1991, Daly 1992). The 'characteristic frequency', ν * , above which one should detect exponential spectral steepening due to inverse Compton losses behaves as: ν * ∝ (1 + z) −8 (measured in the source frame). This steep redshift dependence of ν * is due to the fact that the energy density in the microwave background, U γ , behaves as: U γ = 4.16x10 −13 (1 + z) 4 ergs cm −3 . At z = 3 this corresponds to a magnetic field of strength 50µG, comparable to the equipartition fields found for the lobes of ultraluminous radio galaxies. The majority of the sources in the UL sample were selected from flux limited samples at frequencies between 178 MHz and 408 MHz, implying rest frame frequencies of 800MHz to 1600 MHz at z = 3. The implied synchrotron/inverse Compton lifetimes for the radiating electrons are about 4 Myr. Adopting the nominal source advance speed of 0.02 times the speed of light proposed by Readhead et al. (1996) implies that the spectra of the high z sources in the sample might be exponentially cut-off when they reach radii of order 20 h −1 kpc, a value consistent with the lack of sources larger than about 40 h −1 kpc beyond z = 3 in the UL sample.
An argument against this idea is the lack of a strong residual redshift dependence in the K-corrected spectra shown in Figure 4b. The counter argument is that, if the cut-off is exponential, the affected sources may simply drop-out of the flux limited samples. These sources would appear as 'naked hot spots and cores', i.e. only sites of very active particle acceleration will be observed.