Annu. Rev. Astron. Astrophys. 1988. 26: 561-630
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8.3. High-Redshift Data

8.3.1. RADIO SOURCES   Hoyle's (1959) prediction of a minimum in Data redshift of z = 5/4 for q0 = 1/2 (and similar minima for other q0 > 0) has been searched for extensively. Miley (1968, 1971) was among the first to apply the test to double-lobe radio sources, showing that they obey a z-1 relation over the entire redshift range that reaches z = 2. Selection effects were invoked to explain the lack of turnup of theta(z). Because the radio sources are from a catalog that is limited to a given (bright) radio flux level, there is a strong variation of absolute radio power with redshift (Sandage 1972c, his Figure 7). Hence, if the linear separation of the radio lobes varies with power, the observed z might be explained. Note that because theta(z) is smaller than expected at large redshift, such an explanation requires that the more powerful radio emitters have the smaller linear dimensions. (Those at largest z have the highest power due to the flux limitation of the source catalog.)

Following Miley (1968, 1971), the data discussed by Legg (1970), Wardle & Miley (1974), Swarup (1975), and Kapahi (1975, 1985) continued to show the same problem. Kapahi's (1987, his Figure 7) comprehensive review of the most recent data again shows the need for size evolution of the sources, probably with look-back time rather than with radio power, to save the standard model.

8.3.2 CLUSTERS OF GALAXIES   The variation with redshift of a characteristic angular size of clusters of galaxies has been sought. Various definitions of "size" have been proposed. The most complete study is that by Hickson (1977a, b), who used the harmonic mean separation of the brightest 40 galaxies within a specified radius from the center. The problem with this definition is that the specified radius of 3 Mpc depends on q0 at large redshift. Bruzual & Spinrad (1978) show the partial degeneracy of this aperture-size problem to the galaxy selection with which to form the harmonic mean. Hickson (1977b; see also Hickson & Adams 1979) corrects for this effect by using the results of Monte Carlo simulations in the presence of field galaxies of given surface density, but the correction is model dependent. Bruzual & Spinrad choose to analyze their independent data by fitting a theoretical density profile to galaxy counts so as to determine a core radius for each cluster, a method similar to that used by Bahcall [see Bahcall (1977) for a review].

In an analysis of both sets of data, Hickson & Adams (1979) conclude that "evolution in the linear cluster sizes is required for agreement with [the] models. Unless q0 is considerably greater than 1, the mean cluster size is decreasing (i.e. evolving) at present with a time scale comparable to H0-1." The combined data from the two studies, uncorrected for evolution, are shown in Figure 13 as set out by Hickson & Adams (1979, their Table 1). The data of Bruzual & Spinrad are closer to the Friedmann lines of q0 = 0 and q0 = 1/2 than those of Hickson & Adams (note the systematic difference of the two data sets at large redshift).

Figure 13

Figure 13. The observed theta(z) relations for cluster size determined by a harmonic mean algorithm (left) and by fitting a standard profile to obtain a cluster core radius (right). The theoretical curves from Figure 11 are superposed. Observational data are from Hickson & Adams (1979) and Bruzual & Spinrad (1978).

To first order, the z-1 dependence at small redshifts is again clearly evident in the data. However, for the second-order effect (i.e. the q0 dependence) it is less certain that the data can even be meaningful because of the growing suspicion that clusters are not well-defined structures that have reached dynamic equilibrium. Most clusters appear to be young aggregates, still in the process of formation. The evidence comes from data on the Virgo cluster (Tully & Shaya 1984, Binggeli et al. 1987) and from the presence of substructure (multiple condensations) in most clusters studied in detail [Geller & Beers 1982, Baier 1983 (with many references to the earlier observational data), Beers & Tonry 1986]. Most important is the Dressler (1980) morphology-density effect within a given cluster, showing that virial mixing has not occurred.

With such pronounced subclustering, the meaning of the core radius or any other similar parameter becomes vague, depending on details of the forming cluster clumps. Measurement of the second-order curvature effect (i.e. q0) using such an evolving metric rod must be questioned, despite its power to determine the gross first-order term.

8.3.3. METRIC DIAMETERS OF FIRST-RANKED CLUSTER GALAXIES   It can be argued that the diameters of the brightest E galaxies in clusters are more stable than the sizes of the radio lobes of active galaxies or the sizes of clusters that are just forming. The evidence is the tightness of the m(z) Hubble diagram (Figure 5) despite the question of cannibalism (Section 6.2.1), unless the cannibals operate with an effect that has an almost dispersionless progression with redshift. (In principle, cannibalism can be studied by finding different cannibal rates in clusters of different density.)

Metric diameters must be used in a test of Equation 48. Petrosian's (1976) definition of a metric diameter (his eta index) has many advantages, such as its being nearly independent of luminosity evolution, of K correction, and of the wavelength of observation. It is defined as the radius in the image at which the ratio of surface brightness, averaged over the area interior to that radius, to the SB at that radius is an adopted fixed number. Because it is a ratio, many corrections cancel.

Other examples of metric measures of size are the radius that contains half the light (called the "effective radius" in the literature); the Hubble a radius, where the SB falls to one fourth its "central" value; and the King core radius, where the SB is one half the "central" value. Central SB is never measured because of finite seeing disks, but a fitting parameter (I0) can be inferred from global fits of the intermediate profile (i.e. for radii appropriately larger than the seeing disk).

A literature exists (cf. Oemler 1976, Kormendy 1977, Schombert 1986, Hoessel et al. 1987) on how some of these measures of radii vary with MB of the parent galaxy and of the dispersion about the mean correlation, but no large study yet exists of the stability of the Petrosian eta index for local galaxies. If it proves to be stable at some optimum SB ratio, the way would be open to test Equation 48 at large redshift. This is the only known test for the reality of the redshift, hence its extreme importance. The test has been tried by Geller & Peebles (1972), but it can be argued that they used isophotal rather than metric diameters, and further that they had only four data points.

Progress toward practical use of the Petrosian size has been reported by Djorgovski & Spinrad (1981). They measured the diameters of distant galaxies up to z = 1.17, but with only a few clusters to define the bright end. Their preliminary result is that the data, as measured, do not fit any part of the standard model parameter space (with Lambda = 0), and that to do so again requires application of an evolutionary correction to the first-ranked galaxy sizes as a function of redshift. If the evolution is due to cannibalism, it can in principle be corrected by making the measurements on lower-ranked (fainter) cluster members that have not partaken of the cannibal's feast.

The chief observational problem at the moment is that the angular diameter where eta = 2 mag is ~ 2 arcsec at z = 1; this is subject then to seeing corrections from the ground in order to obtain a proper eta value at this redshift.

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