2.3. Redshift Surveys
In the past years redshift surveys have played a very important role in mapping out the structure of the universe. Today, the number of available galaxy redshifts numbers in the tens of thousands, though these are divided among different galaxy catalogues often having rather different selection criteria. Some of these catalogues are based on optically selected galaxies, and then sometimes by limiting magnitude and at other times by limiting angular diameter. Some catalogues select disk galaxies, some select dwarfs and others select ellipticals. There is an important database based on the IRAS satellite data where candidate galaxies are selected according to diverse spectral classification criteria.
There is then the type of survey to consider: is it an all-sky survey, or is it a sector of sky or a small but deep pencil beam? Pencil beams go to great depths, but lack any transverse spatial resolution. The whole sky surveys have good three dimensional discrimination, but cannot go very deep.
2.3.1. Optical Galaxy Samples
Redshift surveys of galaxies involving thousands of galaxies do not suffer from projection effects and so reveal more clearly the true large scale structure of the universe. However, because the map is in redshift space, it suffers from artifacts such as the "finger of God" effect in which clusters of galaxies appear as long fingers pointing radially towards the observer. It is difficult to correct for these effects, so one must be rather careful when interpreting the apparent structures.
The CfA redshift survey (de Lapparent, Geller and Huchra, 1986, 1988) was the first survey to reveal the structures that nowadays dominate much of our thinking about the large scale structure. That survey, and the corresponding Southern Sky Redshift Survey (da Costa et al., 1988), show the familiar filaments surrounding voids: the "bubble-like" texture of the galaxy distribution. These structures in the galaxy distribution appear on scales where the galaxy-galaxy correlation function is negligible. (This is however not surprising. See the comment on this in section 3.1).
The original surveys have now been extended to other slices and they conclude that the structures are essentially sheet-like, and that the scale of the sheets is limited only by the scale of the survey. The most remarkable feature is the so-called "great wall" (Geller and Huchra, 1989) which appears to be a coherent sheet of galaxies extending over an area of at least 60h-1 × 170h-1 Mpc. Although the appearance of the Geller-Huchra wall is enhanced by the selection function for the sample, it is clear that such features appear in other deep wide angle surveys such as the extension of the SSRS reported by da Costa (1991). It is also apparent that the regular features being detected in the deep pencil beam surveys (Broadhurst et al., 1990; discussed below) are related to these walls. For a discussion of this see Fong, Hale-Sutton and Shanks (1991).
Great Walls do not bound great voids, but seem to surround collections of smaller voids that are themselves bounded by not-so-great walls. It could be that the great walls are simply lesser features (not-so-great walls) picked out and correlated by eye to build a larger structures. In this case the enhancement by the observational selection function would be important in causing us to recognize the local (Geller-Huchra) Great Wall. Looking at N-body models suggests this kind of effect because it is easy for the brain to identify coherent structures on scales where there is no physical mechanism for generating structure.
The Durham deep redshift sample (Metcalfe et al., 1989; Hale-Sutton et al., 1989) is confined to a set of narrow solid angles in the sky. The survey samples one galaxy in three down to magnitude J = 16.8 and contains 264 redshifts. Analysis of the data reveals a redshift space correlation function having a scale length of 7h-1 Mpc., beyond which there is a steep break in the slope. There is persistent evidence that the correlation function is not a power law, but has a feature ("shoulder") on scales 2 - 5h-1 Mpc., though this could be an effect due to the fact that the data is seen in redshift space (Shanks et al., 1989). There is also evidence that the correlation function goes negative around 20h-1 Mpc., never becoming positive again. However, this may simply be due to the fact that the survey areas appear not to contain any notable galaxy clusters. Confirmation of such results is only possible with very large redshift surveys, covering a substantial solid angle of sky.
Klypin, Karachentsev and Lebedev (1990) have made a small survey in a strip of sky 10' × 63° that overlaps with the de Lapparent slice, but goes twice as deep (mB < 17.6). The sample is small, 283 galaxies, but large enough to be able to display the homogeneity of the universe on the largest scales (an issue that had been raised on a number of occasions (for example by Coleman, Pietronero and Sanders, 1988). Again, as in the Durham survey, there is some evidence that the correlation function goes negative on the largest scales.
2.3.2. Surveys based on the IRAS catalogue
Two important redshift surveys have been based on the IRAS catalogue: one is a complete redshift sample of all sources brighter than a given flux (I shall refer to that simply as the "IRAS survey") and the other (called the "QDOT" survey) is a sparse sample of redshifts in which only 1 galaxy in 6 has its redshift taken. (QDOT is an acronym for the participating institutions: Queen Mary and Westfield College, Durham, Oxford and Toronto). The advantage of QDOT is that it goes deeper than the IRAS survey, but because of the sparse sampling it is shot-noise dominated at larger distances.
The IRAS galaxy catalogue does not include early type galaxies, these do not have strong infrared fluxes, and the intrinsically brighter IRAS galaxies tend to be starburst galaxies. This means that despite the fact that the IRAS galaxies trace all known structures, the observed populations do depend on the local density. It also means that the more distant galaxies in the survey tend to be starburst galaxies and so there may be a systematic and environment dependent bias as a function of depth. Having said that, the sky coverage of the IRAS galaxies is only obscured slightly by the galactic plane and this is a considerable advantage, particularly in view of the fact that some of the key structures in which we are interested seem to lie close to the plane. Taking redshifts of objects in the galactic plane is, however, more difficult, so redshift surveys still have to contend with galactic absorption.
The QDOT data is described by Saunders et al. (1990) (though much of analysis of the sample is presented in Rowan-Robinson et al., 1990) and consists of some 2163 galaxies with 60µm flux brighter than 0.6Jy. It samples the universe to a redshift of 0.1 and provides useful data out to a distance of some 200h-1 Mpc. A number of papers have appeared analyzing that data in various ways.
The luminosity function of the QDOT sample is given by Saunders et al. (1990) and this determines the selection function S(r) for the sample. S(r) is the expected number of galaxies in the survey out to a distance r on the assumption that the distribution was Poisson. The pictures of Saunders et al. (1991) and the subsequent analysis of Moore (1991) show that the survey contains all known structures. Thus the QDOT survey does indeed map out the universe, despite the fact that it is a sparse sample of a sparse sample. It should be noted, however, that according to Saunders et al. (1990) the luminosity function of the QDOT galaxies evolves with redshift as
Their analysis argues that this is consistent with a luminosity evolution for the galaxies:
but that there is no evidence for any change in the shape of the luminosity function. The intrinsically brighter galaxies in the catalogue are starburst galaxies and these are the ones seen at the greatest distances.
Efstathiou et al. (1990) and Saunders et al. (1991) look at the counts in cells distribution and compare that with the predictions of the CDM models.
Not surprisingly, they find that the variance of the counts cannot be accommodated by standard CDM, but it should be remarked that on those problems arising out of the sparse sampling procedure (shot noise). Rare but rich areas like the Hercules supercluster complex could also bias the cell counts. Rowan-Robinson et al. (1990) have used the convergence of the microwave background dipole to constrain the value of 0 and find
(see also Kaiser et al., 1991). If we believe 0 = 1 this can be read as saying that the bias parameter is b = 1.23 ± 0.23 for this sample of galaxies. Interestingly, Rowan-Robinson et al. are able to account for the peculiar motion of the local group, in both magnitude and direction, entirely in terms of clusters that can be recognised in the QDOT survey. They do not need to postulate any further unseen masses lying behind the galactic plane. The situation is not unlike that found by Plionis and Valdarmini (1991) who account for the dipole in terms of clusters of galaxies drawn from already existing catalogues. I shall comment further on this in section 2.6.2.
The IRAS survey data is reported by Strauss, Davis, Yahil and Huchra (1990) and consists of redshifts of 2649 IRAS galaxies brighter than 1.9Jy. First results from this survey were discussed by Strauss and Davis (1988) and by Yahil (1988) at the Vatican Study Week (Rubin and Coyne, 1988). Work is in progress on a deeper survey ("IRAS2" for want of a better name) going to 1.2Jy (Fisher et al, 1991), the survey contains some 5300 galaxies having redshifts.
Babul and Postman (1990) compare the distribution of an incomplete redshift survey of IRAS galaxies with the CfA slice (de Lapparent, Geller and Huchra, 1986, 1988). Correlation analysis suggests that the bias parameter for the IRAS sample is a factor 1.6 down on that for the CfA sample: bCfA / bIRAS 1.6. Nevertheless the IRAS galaxies do not appear to favour the voids any more than the CfA survey galaxies. This would be easily explained if the IRAS galaxies were merely a subset of the CfA galaxies.
Lahav, Nemiroff and Piran (1990) estimated the ratios of the bias parameters for the IRAS catalog of galaxies and an optical catalog. The two catalogs show different correlation lengths, which reflects the lack of ellipticals in the IRAS catalog and is presumably due to a different level of bias in the catalogs. The two catalogs also provide different estimates for the density parameter 0.
2.3.3. Pencil Beam Surveys
Broadhurst et al. (1990) have combined four deep narrow-angle surveys of galaxy redshifts that give a picture of the distribution to 2000h-1 Mpc. The interesting outcome of this is an apparent regularity in the distribution of radial velocities on a scale ~ 120h-1 Mpc. The authors conclude that `it is difficult to understand how so many features could maintain organized regularity over such a long baseline'.
The result, if confirmed, is indeed surprising and points to a hitherto unsuspected order in the universe. It is not clear to what extent various numerical models of the formation of large scale structure could explain this. It has been claimed that cold dark matter models do indeed show the effect (White et al., 1987; Park and Gott, 1991), but that is difficult to understand since we now know that the cold dark matter model is in fact deficient in large scale power.
It is significant that the one model which does seem to explain this observation is the Voronoi Clustering model (van de Weygaert, 1991). In that model the galaxy clusters are taken as being located at the vertices of a three-dimensional Voronoi tessellation, this provides the normalization for the model and so the model has no free parameters to juggle. The galaxies are then distributed on the faces of the Voronoi polyhedra and "observed" by drilling pencil-beams through the resultant distribution. The pair separation histograms show as much clustering as the Broadhurst et al. survey about one time in six.
It appears that pencil beams which start by going through the center of a void and almost perpendicular to the next wall have a good chance of going almost perpendicularly through the following wall. The cells of the Voronoi tessellation are highly correlated. However, many beams will intersect a wall at an angle such that the wall runs along the line of sight for a large distance, in which case there will be no periodicity observed.
What is lacking at the present moment is an objective series of statistical tests that will quantify the statistical significance of the pencil-beam data and objectively compare with model predictions. The situation is so serious that Kaiser and Peacock (1991) have argued that the apparent periodicity is not statistically significant and can be reproduced by a model in which galaxies are placed in randomly distributed clusters. Their argument is strong, but does not deny the possibility that the regularity is nevertheless real.