Proc. Natl. Acad. Sci. USA Vol. 90, pp. 4848-4852, June 1993 Colloquium Paper
This paper was presented at a colloquium entitled "Physical Cosmology, " organized by a committee chaired by David N. Schramm, held March 27 and 28, 1992, at the National Academy of Sciences, Irvine, CA.
Clusters, superclusters, and large-scale structure: A consistent picture NETA A. BAHCALL Astrophysical Sciences, Princeton University, Princeton, NJ 08544-1001
ABSTRACT Observations of the large-scale structure in tary in shape. Gregory and Thompson (5) obtained a redshift the universe using different tracers and techniques, including survey of galaxies in the direction ofthe Coma cluster. They the spatial distribution of galaxies, clusters of galaxies, narrow found the large, flattened Coma supercluster, which is part of pencil-beam surveys, and quasars, appear to be yielding a the recently named "Great Wall," extending to at least %40 consistent picture of the universal structure. A network of Mpc. The supercluster surrounds a large underdense region large-scale superclusters with scales up to -l50h-1 Mpc is of comparable size. Additional surveys (6, 7) yielded similar suggested (where h - 0.5-1 is the Hubble constant in units of results in the Hercules and Perseus superclusters. More 100 km-s"Mpc'1; 1 pc = 3.09 x 1016 m; h = 1 is used recent galaxy redshift surveys (8-10) revealed similar large- throughout this paper). The supercluster network surrounds scale low-density regions, suggesting a "cellular" structure of the superclusters surrounding low-density regions. universe. The universal dimensionless cluster correlation func- Large-scale superclusters have been traced very success- tion, supported by new data from automated cluster surveys, fully by rich clusters of galaxies (4, 11, 12). A complete is consistent with this picture. The "standard" Qi = 1 cold dark catalog of superclusters-defined as clusters of clusters of matter (CDM) model for the universe appears to be inconsistent galaxies-was constructed by Bahcall and Soneira (11) from with the details of the observed large-scale structure distribu- a complete redshift sample of rich Abell (4) clusters to z < tion; a low-density, Q1 0.2-0.3, CDM model provides a 0.08. The catalog identifies all superclusters that have a considerably better fit to the observations. spatial density enhancementf2 20 times larger than the mean cluster density. The mean density of the Bahcall-Soneira Statistical analysis of the spatial distribution of galaxies (1) (BS) superclusters is ::=10-6 Mpc-3, with an average mean suggests that, on average, the galaxy distribution is uniform supercluster separation of %100 Mpc. The superclusters on scales larger than -20h-1 Mpc. At the same time the contain a large fraction of all clusters: -54% atf - 20. The existence of some specific large-scale structure in the uni- linear size of the largest superclusters is =150 Mpc (e.g., verse has been known for over half a century. Shapley (2) Corona Borealis) and they are elongated in shape. The noticed a large remote "cloud of galaxies" in Centaurus, fractional volume of space occupied by the superclusters is known today as the Shapley Supercluster: an %50-Mpc very small: -3% at f - 20. Similar results were recently structure that is rich and dense in clusters of galaxies (3). obtained by Postman et al. (12). Zwicky (49) noticed the very large galaxy concentration in A redshift-cone diagram of the superclusters in the decli- Pisces that also encompasses several clusters. Abell (4) nation slice 8 = 0o-40° has been presented by Bahcall (13). recognized that rich clusters of galaxies were themselves The mean separation of the superclusters, =100 Mpc, is clustered into second-order clustering-i.e., superclusters. apparent. We shall also see below that the superclusters The scales of the above superclusters reached tens of mega- surround large, low-density regions such as the Bootes void parsecs. (between the Hercules and Corona Borealis superclusters) as Over the last decade, a great deal has been learned about well as underdense regions seen in pencil-beam surveys. the large-scale structure in our nearby universe. While the How do these superclusters compare with the structures specific nature of the structure, its topology, and its extent found by galaxy redshift surveys? Superimposing the super- are not fully understood, a consistent picture is emerging cluster contours on the cumulative galaxy redshift map from from different types of observations: the spatial distribution the Center for Astrophysics (CfA) survey (14) shows that the ofgalaxies, clusters ofgalaxies, narrow pencil-beam surveys, superclusters identified by the clustering ofclusters highlight as well as the distribution ofquasars and active galactic nuclei well the main large-scale systems seen in the galaxy survey. (AGNs). The consistent picture suggests a network of large- In particular, the union ofthe Coma and Hercules superclus- scale superclusters, up to 100-150 Mpc in scale, that sur- ters constitutes the Great Wall seen in the CfA survey; the rounds lower-density regions. A "cellular" structure of the Great Wall is thus a merging of two BS superclusters, with a universe, similar to the "pancake" model discussed by total extent of =150 Mpc and thickness of 510 Mpc. This Zeldovich and collaborators (50), is suggested by the data. extent and flattened shape are comparable to those of the These data provide critical constraints to possible cosmolog- other large superclusters in the BS catalog; for example, the ical models of the universe. Corona Borealis supercluster is another such Great Wall, considerably greater and richer than Coma-Hercules. It is Superclusters located behind the large void in Bootes. This comparison of the galaxy and cluster distribution indicates that the large- Early redshift surveys of galaxies have already revealed that scale structures traced by both galaxies and rich clusters are superclusters are large systems that are flattened or filamen- Abbreviations: AGN, active galactic nuclei; APM, automated plate The publication costs of this article were defrayed in part by page charge measuring machine; BS, Bahcall-Soneira; BEKS, Broadhurst et al.; payment. This article must therefore be hereby marked "advertisement" CDM, cold dark matter; CfA, Center for Astrophysics; EDCC, in accordance with 18 U.S.C. §1734 solely to indicate this fact. Edinburgh-Durham Cluster Catalog. 4848 Downloaded by guest on September 29, 2021 Colloquium Paper: Bahcall Proc. Natl. Acad. Sci. USA 90 (1993) 4849 consistent with each other; both find the same superclusters. ond northern clump is mostly due to the large Corona While the rich clusters are most efficient in finding the Borealis supercluster (BS 12) (13). largest-scale structures, the galaxies trace the small-scale The narrow-beam survey of BEKS is directed toward the connectedness to the larger scales. north and south galactic poles. Some of the BS superclusters A different method of finding superclusters is that used by coincident with the BEKS peaks are located at projected Lynden-Bell et al. (15), who utilized peculiar velocities to distances of up to 50-100 Mpc from the poles. This suggests, infer the existence of massive superclusters such as the Great similar to the Bootes void analysis, that the high-density Attractor. The estimated mass of the Great Attractor, -5 x supercluster regions are embedded in larger halo surfaces, 1016 times the mass of the sun (Mo) (15), is comparable to that =100 Mpc in size, and that these large structures surround of the large BS superclusters. The Great Attractor does not large underdense regions. The observed number of clumps appear, however, to contain rich clusters. and their mean separation are consistent with the number We thus see that clusters, galaxies, and velocity fields, as density of superclusters and their average extent. well as pencil-beam surveys (see below), appear to trace The narrow widths of the BEKS peaks are consistent with, similar superclusters. These superclusters are the largest and imply, flat superclusters. Simulations of superclusters systems yet observed. Their sizes extend to -1502 x 20 and pencil beams (21) showed that the observed peak-widths Mpc3, and their mass is estimated to be 2-10 x 1016M® (16). distribution is consistent with that expected of randomly This mass is comparable to the mass of 20-50 rich clusters. placed superclusters with s20-Mpc width (and =150-Mpc There are some indications that the supercluster distribution extent). The apparent periodicity in the galaxy distribution is is not random (17), suggesting positive correlations among expected to be greatly reduced when pencil beams in various superclusters on the 100- to 150-Mpc scale. directions are combined. Superclusters Around Voids Cellular Model of Large-Scale Structure The observational data described above suggest a "cellular" The area around the large, -60-Mpc-diameter void of galax- structure in the universe (e.g., a Zeldovich "pancake" mod- ies in Bootes (18) was studied (19) using the BS supercluster el), in which large-scale flattened superclusters surround catalog. The largest, densest superclusters are located near low-density regions. Such a model was simulated (22) with and around the area devoid ofgalaxies (-'14.5h + 500). In the galaxies placed on surfaces of randomly placed shells, and redshift-cone diagram (13), the void is located between clusters placed at shell intersections. This model produced Hercules (part of the Great Wall) and Corona Borealis (the cluster correlations that are consistent with observations, next Great Wall). The overdensity of galaxies observed on showing the large increase in correlation strength (see below) both redshift sides of the void (18), at z = 0.03 and z = 0.08, from galaxies to clusters. The model galaxy correlations are coincide in redshift space with these two surrounding super- also consistent with observations, even showing the tail of clusters. This suggests that the large superclusters surround weak positive correlations at large separations recently re- the galaxy void (at z = 0.05), and that the halos oftheir galaxy ported by the automated plate measuring machine (APM) distribution account for the overdensities observed ;100 survey (23). These results suggest that the observed strong Mpc away. This connection provides a strong indication of cluster correlation function may be due to the global geom- large halos (-150 Mpc) to rich superclusters. etry in which clusters are positioned on randomly placed Previous observational evidence (5-7), together with these shells or similar structures; the typical structure radius is =20 results, as well as similar conclusions regarding pencil-beam Mpc. Similar simulations based on the explosion model for surveys (below) and galaxy redshift surveys, suggests that shell formation were also carried out (24) with similar results. galaxy voids are associated with surrounding galaxy ex- cesses; the bigger the void, the stronger may be the related The Cluster Correlation Function excess. The concentration of a large fraction of clusters (Z50%) in Pencil-Beam Surveys superclusters is the cause of the strong correlation function observed among clusters. The cluster correlation function is Recent observations of the redshift distribution of galaxies in stronger than the galaxy correlation function by an order of narrow (=40 arcmin) pencil-beam surveys to z S 0.3 (ref. 20; magnitude (16, 25-32); the correlations yield &c = 260 r-1.8 hereafter BEKS) reveal a highly clumped and apparently for clusters of richness R 2 1 versus 4=fg 20 r-1.8 for periodic distribution of galaxies. The distribution features galaxies. Many different samples and catalogs of clusters peaks of galaxy counts with an apparently regular separation have now been analyzed, all yielding results consistent with of 128 Mpc, with few galaxies between the peaks. What is the the correlations above (25-32). / origin of this clumpy, periodic distribution ofgalaxies? What All observational determinations ofthe correlations ofrich does it imply for the nature ofthe large-scale structure and the clusters, for richness class R 2 1, yield correlation scales that properties discussed above? Bahcall (13) investigated these are in the range r.0 22 + 2 Mpc for R 2 1 clusters [where questions observationally, by comparing the specific galaxy 4(r) = Ar-1.8 = (r/r.)-1'8]. This includes different catalogs, as distribution with the distribution ofknown superclusters. The well as x-ray-selected clusters and cD-selected clusters. The results show that the observed galaxy clumps originate from correlation results do not appear to be significantly influ- the tails of the large BS superclusters. When the narrow enced by systematics or projection effects. beams intersect these superclusters, which have a mean It has also been shown (16, 25, 33) that the cluster corre- separation of -100 Mpc, the BEKS galaxy distribution is lation function is richness-dependent: the correlation ampli- reproduced. tude increases with the richness of the galaxy clusters. This The redshift distribution of the superclusters in the 8 = richness dependence is presented in Fig. 1. 0°-40° slice matches exactly the BEKS galaxy distribution for An approximate relation describing this dependence is z S 0.1, showing identical peaks (13). It indicates that the 6{Ni) = (4N1)r-18, (33), where Ni is the median Abell galaxy clumps observed in the pencil-beam survey originate richness of cluster sample i and 6{MN,) is the correlation from these superclusters as the beam crosses the superclus- function of clusters of richness Ni. The recently determined ters' surface. The first northern clump originates from the cluster correlation function of the APM cluster survey (34) is Coma-Hercules supercluster (i.e., the Great Wall); the sec- consistent with the prediction of the richness-dependent Downloaded by guest on September 29, 2021 4850 Colloquium Paper: Bahcall Proc. Natl. Acad. Sci. USA 90 (1993) - I gI'"W'I w|x|Xs'"|I ||sTI Table 1. Cluster correlations O - Abell cl 1000 * - ACO cl nc, h3 d, h-1 * - Zwicky cl Catalog Mpc-3 Mpc ro(obs) r. = 0.4d * - Shectman cl 500 - X-ray cl A, = 4N, Abell, R 22 1.2 x 10-6 94 42 ± 10 37.6 A - cD cl * - Groups Abell, R . 1 6 x lo-6 55 22 ± 3 22.0 V - Galaxies 0 EDCC 15 x 10-6 40.5 16 ± 4 16.2 11 B - QSOs * - Radio QSOs APM 24 x 10-6 34.7 13 ± 2 13.9
0.001 10 APM, d=34.7h-'Mpc
0.000 1
10-5
10-6 A *APM, d=34.7 - 0.1 CD| 0=1, h=0.5, b=2.0 10- 0=1, h=0.5, b= 1.0 1 " 0=1, h=0.5, b=2.0 0=0.25, h=0.5, b=1.0 0=0.2, h=0.5, b= 1.0 .0=0.35, h=0.75, b=1.3 .4 --- 0=0.25, h=0.75, b=1.3
1-8 0.01 1013 1014 100 l1016 10 100 M (:! 1 .5h-'Mpc) (h-IM.D) R (h-1Mpc) FIG. 3. Cluster mass function from observations and from dif- FIG. 5. Two-point correlation function ofthe APM clusters, with ferent CDM simulations (48). mean separation 34.7h-1 Mpc, from observations and simulations.
richness-dependent cluster correlation function, as well as yield correlations that are too weak, and not enough power with the universal dimensionless correlations, when the mean on large scales, when compared with the observations. The separation of the parent groups is used. low-density CDM models (Ql 0.25) that are consistent with The above suggests that, like the quasars, the radio-galaxy the cluster mass function (Fig. 3) are also consistent with the clustering arises from their preferential location in galaxy cluster correlations. groups. Radio galaxies, and quasars, may thus be a good A comparison of the universal cluster correlation function tracer of superclusters in the universe, especially at inter- with the model expectation (Fig. 6) also indicates that the mediate to high redshifts. low-density CDM model agrees well with the observed dependence of the cluster correlation length on cluster mean Cosmological Models separation. Similar results for a low-density CDM model are also Large-scale (L = 400h-1 Mpc box) simulations of a universe suggested from the observed tail of the angular galaxy dominated by cold dark matter (CDM) were recently tested correlation function (23). by Bahcall and Cen (48) against two fundamental properties of clusters of galaxies: the cluster mass function and the Conclusions cluster correlation function. The observed mass function of clusters (48) is shown in A consistent picture regarding the phenomenology of large- Fig. 3, together with the results of five CDM model simula- scale structure in the universe is emerging from observations tions: standard = 1 CDM with a bias of b = and fQ 1, 1.3, 2, using different tracers: galaxies, clusters, pencil-beam sur- and low-density models with Qi = 0.25 and 0.35 (b = 1 and 1.3, veys, quasars, and radio galaxies. respectively). It is clear that standard fl = 1 CDM models, Large-scale superclusters are observed to scales of 150 with any bias parameter, are inconsistent with the observed Mpc in the distribution of galaxies, clusters of galaxies, and cluster mass function; low-bias models yield too many rich probably quasars and AGNs. The same superclusters are clusters, while high-bias models have too steep a mass function. traced well by galaxies and by rich clusters. The superclus- The cluster correlation functions for R 2 1 Abell clusters ters appear to be flattened systems, with dimensions of up to x mean %._10-6 and for the APM clusters are shown in Figs. 4 and 5, together =1502 20 Mpc3; their space density is low, with the simulation results for clusters of the same mean Mpc-3; and their mean separation is =100 Mpc. Great generic separation. The l = 1 biased CDM models are inconsistent Walls, Great Attractors, and the superclus- with either the R 2 1 or the APM correlations; the models ters are all similar structures with different names. They appear to surround large underdense regions. These super-
10 AAe ellRI1 clusters, d=55h-1Mpc 50 * Abell R !2 0 Abell R 21 a EDCC 40 - 0 APM L galaxies --- CDM (0=0.2, h=0.5, b=1) 0 - - -CDM (0=1.0, h=0.5, b=1.3) 30 0,
0.1 10 1, h=0.5, b= 1.3 0= h=0.5, --- 0=0.2,0=1, h=0.5,b=2.0b=1.0 10 0=0.25, h=0.75, b= 1.3 0.01l,,, I, 10 100 ...... ,, ...... I,,,,I,.,1,,,,,,1,,,,1.I...1.I...... I...... I...... I OL R (h-1Mpc) 0 10 20 30 40 50 60 70 80 90 100 d (h-1Mpc) FIG. 4. Two-point correlation functions of Abell R - 1 rich clusters, with mean separation 55h-1 Mpc, from observations and FIG. 6. Correlation length as a function of cluster separation, CDM simulations. from observations and simulations (48). Downloaded by guest on September 29, 2021 4852 Colloquium Paper: Bahcall Proc. NatL Acad. Sci. USA 90 (1993) clusters are the main origin of the galaxy peaks observed at 18. Kirshner, R. P., Oemler, A., Jr., Schechter, P. L. & Shectman, 100- to 150-Mpc intervals in narrow pencil-beam surveys. S. A. (1981) Astrophys. J. Lett. 248, L57-L60. The peaks originate when the narrow beam crosses the 19. Bahcall, N. A. & Soneira, R. M. (1982) Astrophys. J. Lett. 258, L17-L21. large-scale superclusters. 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