by Jaan Einasto
7.2 Redshift surveys and catalogues
7.2.1 Redshift surveys
Our first 3-dimensional pictures of the distribution of galaxies were based on the Second Reference Catalogue of Galaxies by de Vaucouleurs et al. (1976), as well as on the published redshifts of nearby clusters and Markarian and other active (radio) galaxies. As new redshifts became available (Sandage & Tammann (1981), the first Harvard Center forAstrophysics redshift survey, and ZCAT by John Huchra 1981), we made more detailed analyses of the Local, Coma, Perseus and Hercules superclusters, and the huge void between these superclusters.
In 1979 at Princeton a conference was held to discuss observing programs for the Hubble Space Telescope. I had the luck to be one of the participants. After the conference our small delegation from the Soviet Union made a trip to Center for Astrophysics of Harvard University. We had a chance to meet Riccardo Giacconi, who was just discussing first results of the Einstein X-ray orbiting observatory. Also I had long discussions with John Huchra, one of the initiators of the First Harvard Redshift Survey. He showed me a model of the distribution of nearby galaxies, made of small plastic balls, similar to our model made a few years earlier. Huchra’s model was better made—the balls were smaller and better fixed, so it was possible to put the model in the lobby of the Center. The filamentary distribution of galaxies in the nearby Universe was very well seen.
In autumn 1982 I got an invitation to attend the Texas Symposium which was held in Texas. The organisers were ready to cover all my travel expenses to the Symposium and to other places in USA of interest. Just in summer 1982 I had a chance to discuss during the IAU Symposium in Crete the large scale distribution of clusters with George Abell, who was preparing the Southern extension of his cluster catalogue. I phoned George and asked, would it be possible to have a visit to the University of California in Los Angeles, where he worked? His reply was very positive. Thereafter I phoned Harvard and asked whether a visit to Center for Astrophysics would be possible to discuss the distribution of galaxies. Here I got also a positive response. In short, I had the chance to visit several major astronomical centres in the USA in a three month visit.
In Austin I had long discussions with Gerard de Vaucouleurs. Thereafter, in the trip to Los Angeles I had a stop at Tucson, Arizona, where the headquarters of the Kitt Peak Observatory is located. Here I visited Kitt Peak Observatory headquarters.I met Bart Bok, and discussed with him the nature of dark matter. He agreed with my arguments that dark matter is a new population, different from the conventional halo consisting of old metal-poor stars, thus it is better to use the term “corona” instead of “halo” to avoid confusion.
Also I had an agreement with John Huchra to visit the Mount Hopkins Observatory, where the 60 inch telescope used by John and his team to collect redshifts of galaxies for the Harvard Redshift Survey is located. John arrived, rented a huge SUV, and we drove up to the mountain. Margaret Geller was already there. Here I was witness how well survey observations were prepared and made. Finding charts of galaxies were made from Palomar Sky Survey prints with exact coordinates. So when the recording of the spectrum of a galaxy was finished, it was possible to turn the telescope very fast to the next object and to continue the observation.
It was autumn and galaxies in the Perseus region were in the program. I saw in their list a small group of galaxies close to the Milky Way zone of avoidance. In our study of the Perseus–Pisces supercluster we noticed that a filament of poor nearby clusters extends in the Northern direction away from the Perseus main cluster. This group was just one of these groups we noticed in our study (Zwicky cluster 22 in Fig. 5.7). So I said that the expected redshift of these galaxies is about 5,000 km/s. John was surprised and asked how I know this. Then I told him the results of our study of the Perseus–Pisces supercluster, and the presence of several filaments, in addition to the main cluster chain seen in Figs. 5.5 and 5.4. Observations confirmed that this chain of groups, seen in Fig. 5.7, is really part of the Perseus-Pisces supercluster.
In Los Angeles I had long discussions with George Abell about the Southern Survey of rich clusters of galaxies. Our experience has shown that all clusters are markers of the cosmic web, thus it makes sense to include into the catalogue also clusters they notice during the search, but which have less galaxies than their criterion for inclusion. Of course, these clusters do not form a statistically homogeneous sample; their role is to be the markers of the web.
A month later I was in Harvard and discussed our quantitative analysis of the cosmic web. The Harvard team was preparing for the Second Redshift Survey. We discovered that our approaches to the study of the large scale distribution of galaxies were very similar. So far most observers studying the distribution of galaxies in the mid 1970’s concentrated their efforts on studying the environment of rich clusters. These studies confirmed the existence of superclusters — i.e. systems of galaxies around rich clusters. These studies found also the existence of voids in the distribution of galaxies. One of the first studies to apply this approach was made by Gregory & Thompson (1978). But these studies did not yield information on the presence of the cosmic web.
In contrast, both the Tartu and the Harvard teams understood the need for wide field surveys, covering a contiguous and substantial area on the sky, and the full range of galaxy densities from the richest clusters to the emptiest voids. These observations could provide the key to a better theoretical understanding of the history of the formation of the large-scale structure of the Universe. Our Tartu team started the study in the mid 1970’s by collecting data from all possible sources in the whole Northern hemisphere. Almost at the same time the Harvard team started the First Redshift Survey, covering the whole Northern hemisphere, up to apparent magnitude 14.5. In the Second Survey the Harvard team planned to observe the same area again but with the magnitude limit 15.5.
These two approaches, the detailed study of smaller deeper areas and the study of less deep but larger contiguous areas, complement each other. The second approach allowed us to see the global features of the cosmic web earlier. The price was that wide surveys did not initially give an answer to the question, how empty voids actually are, because in wide field surveys it was not possible to have as faint a magnitude limit as in small-area studies for a given amount of observing time.
One item we discussed in Harvard was: how to plan observations in such a way that already the first slice observed can give significant results to understand major properties of the cosmic web. One favorable region is a slice which crosses the Coma, Hercules, Perseus–Pisces and Ursa-Major superclusters, and galaxy filaments joining these superclusters. This slice also crosses several voids: voids between the Local supercluster and the Coma and the Perseus–Pisces superclusters, as well voids behind the Perseus–Pisces and Hercules superclusters. The last one is called the Bootes Void.
Results of the first slice of the Second Harvard Redshift Survey were very interesting (de Lapparent et al., 1986). The slice covered a strip of the Northern galactic hemisphere between declinations 26°.5 and 32°.5 of length 117°. Basic structural elements of the cosmic web were clearly visible. I was happy to read that authors thanked me for discussion. What surprised me a bit was the absence of references to our early papers (Jõeveer & Einasto, 1978; Jõeveer et al., 1978; Einasto et al., 1980a), only our main review paper (Zeldovich et al., 1982) to describe the cellular character of the structure was discussed.
de Lapparent et al. (1986) emphasised the sharpness of structures, and suggested that this hints to the presence of hydrodynamical processes during the galaxy formation. The authors argued that the sharpness can be explained in the framework of the Ostriker & Cowie (1981) explosive model of structure formation.
At the same time our team compared the observed structure with the ΛCDM model by Gramann (1987). Our quantitative comparison suggests that the ΛCDM model explains the observed structure very well (Einasto et al., 1986a), confirming our earlier comparison of the CDM model with observations (M
elott et al., 1983). The sharpness of structures was not addressed in our model. Modern high- resolution ΛCDM simulations explain this feature very well.
At the IAU symposium on large-scale structure in Hungary in 1987 I met Margaret Geller and congratulated her for the very important results of the CfA 2nd Redshift Survey. A popular discussion of these results by Geller & Huchra (1989) received great attention. The astronomical community as well as the general public recognised the presence of voids, superclusters and walls in the galaxy distribution after these publications, about ten years later than the actual discovery of the comic web, discussed in the Tallinn IAU Symposium.
In the following years a number of other surveys covering large areas of the sky were made. John Huchra initiated a near-infrared survey of nearby galaxies, the Two MicronAll-Sky Survey (2MASS). The advantage of this survey is the coverage of low galactic latitudes up to 5 degrees from the Galactic equator. The filamentary character of the distribution of galaxies is very well seen. During the Aspen workshop on voids in summer 2006 John told the story of this Survey. His initial suggestion was to make the Survey from space. But one referee, who gave a very positive opinion to the project, suggested that the Survey can be done using ground based observations. Thus the space project was rejected. The same referee later participated very actively in the Survey. However, from ground the Survey took much more time, and the total costs were approximately the same as the expected costs from the space version.
The largest so far wide area surveys are the Two-degree Field Galaxy Redshift Survey made with the Anglo–Australian 4-m telescope, and the Sloan Digital Sky Survey. When visiting Australian observatories in 1989 I had a chance to see the giant fiber robot later used for the 2dF Survey. Our Tartu team has made extensive use of both these surveys, which allowed us to investigate the structure of the cosmic web in great detail.
In recent years a number of new deep wide-field redshift surveys have been initiated. One survey is directed to the study of baryonic acoustic oscillations (BOSS), first results of this survey were discussed by White et al. (2011). BOSS is part of the SDSS-III survey; it makes use of luminous galaxies selected from the SDSS images to probe large-scale structure at intermediate redshift, z < 0.7. It uses the same telescope as SDSS-I and II, but a better spectrograph with 1000 fibers instead of 640 in previous surveys. Another new surveys is directed to find very large structures of the Sloan Great Wall type. This HectoMAP project was discussed by Geller et al. (2011), it has the goal to measure redshifts of red galaxies up to magnitude r = 21 in an area covering 50 square degrees in a 1.5 degree wide strip. Observations are made with the 6.5-m Multi Mirror Telescope on Mount Hopkins, Arizona, using a 300 fiber robotic spectrograph.
7.2.2 Catalogues of groups and clusters of galaxies
Most galaxies are located in systems of various richness — groups, clusters and superclusters. In our early studies we noticed that giant galaxies are surrounded by dwarf galaxies, and that companion galaxies are segregated by morphology: elliptical companions lie closer to the main galaxy than spiral and dwarf irregular galaxies (Einasto et al., 1974c, 1975b). Thus groups of galaxies have a certain structure; additionally they contain dark matter which can be considered as the extended corona of the main galaxy. The dark corona is so large that practically all dwarf companion galaxies are located inside the corona. If we consider the corona as a population of the main galaxy, then this means that dwarf companions lie inside of the main galaxy. To avoid confusion, we called such systems “hypergalaxies” (Einasto et al., 1974a), and prepared lists of hypergalaxies (Einasto et al., 1977; Vennik, 1984). This term has not been accepted by the astronomical community, probably because hypergalaxies are actually small groups of galaxies with one concentration center. The difference between groups in general lies in the fact that in hypergalaxies there is only one centrally located bright galaxy, and that companion galaxies are clearly morphologically segregated. Large groups contain several subgroups, and the segregation of satellite galaxies by morphology is not so clear.
Our main goal in the late 1990’s and early 2000’s was to investigate the general properties of the cosmic web. At this time fairly deep wide-field galaxy redshift surveys were already available, which allowed us to use galaxies as indicators of the web. The first such survey was the Two-degree Field (2dF) Galaxy Redshift Survey. This Survey allowed us to prepare group and supercluster catalogues, and to study properties of superclusters and the web in general. The first step in such studies is the preparation of a group catalogue to suppress the Finger of God effect (random motions of galaxies in groups) which distorts the estimation of distances using redshifts as distance indicators.
In the preparation of the group catalogue the method used to combine galaxies into groups plays a central role. Our earlier experience for nearby groups has shown that in rich groups bright galaxies are concentrated toward the group center, thus to find the group we can use the FoF method with constant neighbourhood linking length (radius). We applied the same scheme to the 2dF group catalogue and sent the paper to Monthly Notices. However we got a negative referee report. The referee was Vincent Eke, who has just compiled a group catalogue for the same 2dF Redshift Survey (Eke et al., 2004). His major criticism was the use of constant linking length in group finding. Thus we started to investigate the role of variable linking length in more detail.
Already in the early 1980’s several group catalogues had been constructed. One of the most widely known was the catalogue by Huchra & Geller (1982). Huchra & Geller applied a variable search radius depending on the mean volume density of galaxies at the distance of the group. The linking length was taken as l ~ f−1/3, where f is the selection function of galaxies at the particular distance from the observer. This scaling corresponds to the hypothesis that with increasing distance both the galaxy field in general, and that of the groups, are diluted in the same way by the absence of fainter galaxies at larger distance.
To see the difference between various group selection methods we compiled two versions of the group catalogue, one with a constant search radius, and the second one with a variable search radius, which increases with the distance according to the decrease of the mean number-density of galaxies, as done by the Eke team. Results of this test are shown in the Fig. 7.11 for the rich cluster Abell 933. We see that using a constant linking length the cluster A933 is divided into several concentrations. In contrast, if a variable linking length is used, depending on the number density of the whole sample, then a large filament around the cluster is also included into the system. The reason for this increase is the location of the cluster A933 in a rich supercluster.
In other words, the overall density of galaxies is not really relevant to determining the clustering parameters of groups; it is the galaxy number density within groups themselves that fixes the linking length. As a further check we calculated the mean sizes of Eke et al. groups. We found that the mean size of Eke groups increases considerably with the distance, i.e. the group catalogue is not homogeneous. To summarise, these tests indicated that both extreme linking methods have drawbacks, and a new linking method is needed.
In the search for a better method we decided to use real groups to study the scaling of group properties with distance. First we created a 2dF group catalogue with constant linking length, selected in the nearby volume (d < 100 h−1 Mpc), all rich groups, and determined for group galaxies their absolute magnitudes and radial velocities. Then we shifted the groups progressively to larger distances, and calculated new k-corrections and apparent magnitudes for the group members. As with increasing distance more and more fainter members of groups fall outside the observational window of apparent magnitudes, the group membership changes. We calculated the minimum FoF linking length necessary to keep the group together at this distance. To determine that, we built the minimal spanning tree for the group (Martínez & Saar, 2002), and found the maximum length of the MST links. The average linking length increases from redshift 0 to 0.2 by a fact
or of about 2. Using this scaling we found the 2dF group catalogue (Tago et al., 2006).
Fig. 7.11 The distribution of galaxies in and around the Abell cluster A933, located in the core of the supercluster SCL82 in the Sloan Great Wall. The circle shows the size of the Abell cluster. In the left panel galaxies that belong to different groups, found by using a constant linking length, are plotted with different symbols. Open circles show single galaxies or pairs of galaxies. All large symbols form a single group according to Eke et al. (2004). Small dots show field galaxies in the vicinity of the cluster. The right panel shows an extended region around the same cluster using FoF with a constant and a variable linking length, which increases with distance as the mean number-density of galaxies in the cluster decreases (Tago et al., 2006).
We regard every galaxy as a visible member of a group or cluster within the visible range of absolute magnitudes, corresponding to the observational window of apparent magnitudes at the distance of the galaxy. To calculate total luminosities of groups we have to find the estimated total luminosity per one visible galaxy, taking into account galaxies outside of the visibility window. For this purpose the observed luminosity of a galaxy is to be multiplied by the distance dependent weight:
the ratio of the expected total luminosity to the expected luminosity in the visibility window. Here F(L) is the luminosity function, and L1 and L2 are the lower and upper limit of the luminosity window, respectively. In our first group catalogues we used the Schechter luminosity function (Schechter, 1976); in our last catalogues we used the double power-law function with smooth transition:
