Proc. Natl. Acad. Sci. USA Vol. 93, pp. 14216–14220, December 1996 Colloquium Paper

This paper was presented at a colloquium entitled ‘‘Symmetries Throughout the Sciences,’’ organized by Ernest M. Henley, held May 11–12, 1996, at the National Academy of Sciences in Irvine, CA.

Mapping the universe in three dimensions (red shift͞galaxy͞cluster of galaxies͞supercluster͞peculiar velocity)

MARTHA P. HAYNES

Center for Radiophysics and Space Research and National Astronomy and Ionosphere Center, Cornell University, Ithaca, NY 14853

ABSTRACT The determination of the three-dimensional spectrometers at both optical and radio wavelengths have layout of galaxies is critical to our understanding of the made the redshift industry is a fast-paced one, showing a evolution of galaxies and the structures in which they lie, to greater than exponential growth. A recent more detailed our determination of the fundamental parameters of cosmol- review of red shift surveys was presented by Giovanelli and ogy, and to our understanding of both the past and future Haynes (2). In this discussion, I hope to convey some sense of histories of the universe at large. The mapping of the large the complexity of large-scale structure as well as the promise scale structure in the universe via the determination of galaxy of the next decade to advance our understanding of it. red shifts (Doppler shifts) is a rapidly growing industry thanks to technological developments in detectors and spec- Large-Scale Structure from Red Shift Surveys trometers at radio and optical wavelengths. First-order application of the red shift-distance relation (Hubble’s law) That galaxies tend to cluster has been recognized for more allows the analysis of the large-scale distribution of galaxies than a century, even before their extragalactic nature was on scales of hundreds of megaparsecs. Locally, the large- understood. The cosmological principle states that, on some scale structure is very complex but the overall topology is large scale, the universe is homogenous and isotropic. The not yet clear. Comparison of the observed red shifts with delineation of the topological description of the distribution of ones expected on the basis of other distance estimates allows galaxies in the local universe is an attempt to test whether, and mapping of the gravitational field and the underlying total on what scale, the cosmological principle holds. density distribution. The next decade holds great promise The Milky Way is one of two spiral galaxies (the other is the for our understanding of the character of large-scale struc- Andromeda galaxy, M31) that dominate the Local Group, a ture and its origin. loose aggregate of about 20 galaxies within a volume of radius about 1 Mpc (1 Mpc ϭ 3.1 ϫ 1022 m or 3.26 ϫ 106 light years). One of the most elusive tasks of astronomy is the development The Local Group itself lies on the outskirts of a flattened of a clear picture of how galaxies are distributed into clusters structure of a radius about 15 Mpc known as the Local and superclusters and at the same time avoid the large empty Supercluster, centered on a rich cluster of galaxies, the Virgo void regions. The difficulty in constructing such a picture rests cluster. A number of other superclusters are recognized within on our ability to interpret the observed projected distribution a few 100 Mpc, but the overall characteristic scale and topo- of galaxies on the sky and ultimately to measure the true logical description are still issues for debate. Here, we will location in space of large numbers of galaxies. In this paper, I simply examine the qualitative appearance of structures seen will adopt the standard view that the dominant motion in the in the local universe. universe is the smooth expansion described by Hubble’s law, Figs. 1–3 attempt to illustrate the kind of structure seen in relating a galaxy’s distance d to its observed recessional the red shift distribution of nearby galaxies. In each case, velocity cz by a simple constant of proportionality, the Hubble galaxies are projected onto an Aitoff equal area projection in constant (Ho). In fairness, it should be recognized that the celestial coordinates, right ascension (R.A.) and declination adoption of a simple red shift-distance relation is not univer- (Decl.), and centered on R.A. ϭ 6h, Decl. ϭ 0Њ. Fig. 1 shows sally accepted (e.g., ref. 1). However, Hubble’s law arises as a the distribution of some 14000 galaxies with known recessional natural consequence of the expansion of a homogenous and velocities cz Ͻ 12,000 km sϪ1. If the Hubble constant has a Ϫ1 Ϫ1 isotropic universe, as predicted by the assumption that the value of Ho ϭ 65 km s ⅐Mpc , then to first order, the volume cosmological principle holds. Adopting the law, the distance to contained extends to 184 Mpc. Dotted lines denote the locus a galaxy can be estimated to first order (see the discussion of of points at galactic latitudes b ϭϪ20Њ, 0, and ϩ20Њ, delin- peculiar velocities below) simply by measuring its doppler shift eating the Zone of Avoidance, within which distant galaxies z ϭ ␦␭͞␭. For discussions of structural characteristics, the are obscured at optical wavelengths by the dust and gas within Hubble constant is only a scale factor, and is not critical to the the Milky Way. The distribution of galaxies within this volume present discussion. Note that we astronomers use the terms is not random; galaxies tend to cluster. Two major structures ‘‘recessional velocity’’ and ‘‘red shift’’ interchangeably, and are easily seen. To the left of the map, the strong concentration have the bad habit of talking about distances in velocity units. of galaxies in the central region of the Local Supercluster in the The fundamental objective of surveys of galaxy red shifts is Virgo region is clearly noticeable. On the upper right side, the to provide a first-order measurement of galaxy distance: d ϭ linear string of galaxies running diagonally (and almost per- cz͞Ho. Beyond the Local Supercluster at least, recessional pendicular to the b ϭϪ20Њ line) is the Pisces–Perseus velocities dominate peculiar ones, and thus observed red shifts supercluster (PPS). can be used to trace large-scale structure. Recent advances in Fig. 2 shows galaxies with velocities lower than 3000 km sϪ1: the Local Supercluster. It is clear in this representation that there are more galaxies on the left side of the map than on the The publication costs of this article were defrayed in part by page charge payment. This article must therefore be hereby marked ‘‘advertisement’’ in accordance with 18 U.S.C. §1734 solely to indicate this fact. Abbreviation: PPS, Pisces–Perseus supercluster.

14216 Downloaded by guest on September 26, 2021 Colloquium Paper: Haynes Proc. Natl. Acad. Sci. USA 93 (1996) 14217

FIG. 1. The sky distribution of 14,000 galaxies with known recessional velocities cz Ͻ 12,000 km sϪ1. The projection is an Aitoff equal area one in celestial coordinates. The continuous lines that rise diagonally through the center of the map show the locus in celestial coordinates of the lines of constant galactic latitude at Ϫ20Њ,0Њ, and ϩ20Њ.

right side. This asymmetry occurs because the Local Group is Large-scale clustering is quite easily visible also in Fig. 3, located on the edge of the Local Supercluster. When we look which displays objects in the red shift range 3000 Ͻ cz Ͻ 6000 towards the center, we see lots of galaxies; when we look away km sϪ1. The PPS is visible in the northwest quadrant. The from the center, we see many fewer. Using more imagination, adopted centering tends to deemphasize the overdensity in the one can trace a continuous line through the concentration in Cen-Hyd-Pavo-Ind region in the southern hemisphere, al- Virgo, across the zone of avoidance, through the right side and though it is still visible. Numerous other structures are also back again through the north pole. This continuous distribu- seen. Published datasets currently sample both hemispheres tion is the Supergalactic plane. Although less well-defined than quite well to this depth; at larger red shifts, however, the the galactic plane, its presence indicates that the Local Super- asymmetry in the distribution of telescope sites favoring the cluster, like the Milky Way, is a flattened structure. Within the northern hemisphere becomes critical. Local Supercluster, galaxies tend to be found in groups and Noticeable in Fig. 1 despite its distance, the PPS is one of the clouds, with other regions being relatively empty. most prominent structures in the local extragalactic sky. It must

FIG. 2. Similar to Fig. 1, but showing only the sky distribution of galaxies with known recessional velocities cz Ͻ 3000 km sϪ1. Downloaded by guest on September 26, 2021 14218 Colloquium Paper: Haynes Proc. Natl. Acad. Sci. USA 93 (1996)

FIG. 3. Similar to Fig. 1, but showing only the sky distribution of galaxies with known recessional velocities 3000 Ͻ cz Ͻ 6000 km sϪ1.

be emphasized that the PPS is not a random volume of the We can examine this structure by looking at the two- universe. As discussed by Giovanelli et al. (3), the optical dimensional distributions of galaxies in the region of the catalog used to select targets for the red shift surveys of this supercluster. Fig. 4 shows the distribution on the plane of the region is particularly suited to tracing volume density enhance- sky of galaxies in a 90Њ by 30Њ slice across the supercluster. The ments with characteristic sizes of 5 to 20 Mpc if they are main ridge is roughly outlined by straight lines. This is the same situated at a distance of about 5000 km sϪ1. In other words, if feature seen on the right side of Fig. 1. Note the clumpiness of the galaxy luminosity function does not vary, such structures the galaxies, particularly the continuous structure within the will be emphasized in a catalog of such depth in apparent outlined region. Notice also the absence of galaxies in other magnitude and yet will not be confused by background objects. portions of the map. Some of the empty regions to the extreme

FIG. 4. The distribution of galaxies in the region of the PPS. (Upper) The galaxy distribution on the sky. (Lower) The red shift distribution of the same galaxies as a function of right ascension. Downloaded by guest on September 26, 2021 Colloquium Paper: Haynes Proc. Natl. Acad. Sci. USA 93 (1996) 14219

left (east) and at the top (north) are partly caused by obscu- arise from ongoing interactions with neighboring galaxies ration within the Milky Way. However, most of the structure and͞or the intergalactic environment. seen in this map is real. Fig. 4 Lower shows the distribution in red shift space of all of the galaxies contained within the area Peculiar Velocities outlined in the top one. This representation does not give adequate comparison of nearby and distant structures (see Because on the scales of superclusters, the cosmological below), but it is clear that the majority of galaxies seen in the principle does not hold, deviations from pure Hubble expan- enhanced region in the upper plot all lie at approximately the sion are expected. The measurement of such ‘‘peculiar veloc- same red shift. Fig. 5 shows the red shift distribution of the ities’’ offers the possibility of uncovering the true distribution same galaxies shown in Fig. 4, but in this case, the spatial of mass, not just of the visible galaxies. If we describe the coordinate is shown as a true angle. This representation is perturbed density field in terms of the density contrast ␦ ϭ called a cone diagram and gives a more accurate comparison ␦␳͗͞␳͘, and assume that linear perturbation theory holds (true between nearby and distant structures. except in the vicinity of clusters), then the equation governing Velocity crowding into narrow lanes of width about 250 to the growth of the density fluctuations, as a function of 500 km sϪ1 shows that most of the structures seen confined on comoving xជ and t, is written: Ѩ2␦͞Ѩt2 ϩ 2H(t)Ѩ␦͞Ѩt ϭ the plane of the sky are also confined in the red shift 4␲G͗␳͘␦. This can be treated as an ordinary differential dimension. They are therefore two-dimensional linear struc- equation; we need consider only the growing solution. The tures. Occasional larger spreads in velocity are seen in the importance of this description is that the density, the pertur- regions of rich clusters, where orbital velocities within the bation potential ⌽(xជ), and the peculiar gravity gជ are all cluster potential are added to the Hubble expansion velocity. self-similar. Furthermore, the peculiar velocity has the same The relative isolation of the supercluster from the Local direction and is proportional to the present gravitational Supercluster in the foreground and from other structures at acceleration. Thus, derivation of the peculiar velocity field larger distances is emphasized in the cone diagram. allows the reconstruction of the underlying density field, which The main ridge of the PPS shows a volume density enhance- in turn can be compared with that derived from the distribu- ment of more than a factor of 10 and can be traced over 90Њ tion of light (i.e., the visible galaxies). across the sky. It lies at a mean red shift of about 5500 km sϪ1 The recent Cosmic Background Explorer measurement (5) and is best described as a linear ‘‘filament’’ with an axial ratio of the microwave background radiation confirms the dipole of at least 8:1, inclined by less than 12Њ to the plane of the sky. anisotropy of amplitude 3.365 Ϯ 0.027 mK in the direction (l, The supercluster extends over 45 Mpc in length before it b) ϭ (264.4ЊϮ0.3Њ, ϩ48.4ЊϮ0.5Њ). This inhomogeneity is disappears into the Zone of Avoidance on the east. The empty usually interpreted as a motion of the Local Group of ampli- Ϫ1 ‘‘voids’’ are nonspherical regions of true galaxy underdensity. tude VCMB ϭ 627 Ϯ 22 km s toward (lCMB, bCMB) ϭ (276ЊϮ To add a significant complication, the study of three- 3Њ,ϩ30ЊϮ3Њ). The critical point is that a simple Virgo infall dimensional structure requires an understanding of the well- model does not agree with the magnitude or direction of the known morphology density relation, such as quantified by motion implied by the cosmic microwave background dipole Dressler (4). Elliptical and lenticular galaxies show a much anisotropy. The discrepancy cannot be explained by the rota- greater tendency to cluster than their spiral counterparts. tion of the Local Supercluster either. Segregation is also seen among galaxies of different surface Controversy is currently focussed on whether the sources of brightness and luminosity; high-luminosity galaxies are pref- this motion are local (distributed within 5000 Ho Mpc) or erentially found in high-density regions. While both high- and distant (spread out to distances in excess of 10,000 Ho Mpc), low-luminosity (or E͞S0 and spiral) galaxies trace the same i.e., on the size of the so-called ‘‘convergence depth.’’ Recent large-scale structures, the density contrasts derived from sep- results on the scale of the convergence depth have often arate samples vary significantly. Numerous observational and conflicted. The Seven Samurai results (e.g., ref. 6) placed the theoretical studies have addressed the issue as to whether the ‘‘Great Attractor’’ more distant than Hydra–Centaurus, processes responsible for such segregation act as a continuous whereas the major perturber as inferred from infrared flux function of galaxy density and reflect the local environmental limited, red shift samples of galaxies is more in line with a conditions at the time of galaxy formation or whether they picture where light traces mass. The concept of ‘‘bulk motion’’ extending over scale several times larger than the Great Attractor model has been suggested by several authors, ex- tending even to scales of cz Ϸ 13,000 km sϪ1. See Dekel (7) and Strauss and Willick (8) for recent reviews. At this time, the true situation is far from clear, though the methodology and peculiar motion data sets are beginning to achieve a level of refinement that imply maturity. Work with which I have been associated, in disagreement with some others, finds a close linkage between the distribution of the luminous matter and the total mass distribution as inferred from the velocity field. da Costa et al. (9) find that the velocity field derived from the velocity-linewidth relation for Sc gal- axies resembles closely the velocity field predicted from self- consistent reconstructions based on all-sky red shift surveys. While we detect a bulk motion of Ϸ300 km sϪ1 within a top-hat window 6000 km sϪ1 in radius, the flow within the surveyed volume is not coherent. It results from the known asymmetry of the mass distribution within that volume and the location of the Local Group in a region characterized by a large gradient in the mass density. Giovanelli et al. (10) show that, while nearby clusters are seen to move with us, the average of distant clusters is at rest, implying that the convergence depth is on the Ϫ1 FIG. 5. Cone diagram of the galaxies contained within the outlined order of 6000 km s . We conclude that locally at least, light region in Fig. 4, identified with the main ridge of the PPS. traces mass. Downloaded by guest on September 26, 2021 14220 Colloquium Paper: Haynes Proc. Natl. Acad. Sci. USA 93 (1996)

Summary The National Astronomy and Ionosphere Center is operated by Cornell University under a cooperative agreement with the National The structure of the local universe as revealed from the Science Foundation. This work has been partially supported by the galaxy distribution is topologically complex. Numerous at- National Science Foundation Grants AST-9014850, AST-9218038, and tempts to characterize the structure have been made using, AST-9023450. for example, higher order correlation functions, the fractal 465, dimensionality, or a genus statistic, but are not discussed 1. Segal, I. E. & Nicoll, J. F. (1996) Astrophys. J. 578–594. 2. Giovanelli, R. & Haynes, M. P. (1991) Annu. Rev. Astron. Astro- here. No simple characterization describes the galaxy distri- phys. 29, 499–541. bution; little discussion relevant to the theme of symmetry of 3. Giovanelli, R., Haynes, M. P. & Chincarini, G. L. (1986) Astro- this symposium can be offered. The asymmetry seen in the phys. J. 300, 77–92. distribution of nearby galaxies (Fig. 2) arises from our 4. Dressler, A. (1980) Astrophys. J. 236, 351–365. particular location on the outskirts of the Local Supercluster. 5. Kogut, A., Lineweaver, C., Smooth, G. F., Bennett, C. L., Ban- And we might also remember the great geographical error day, A., Boggess, N. W., Cheng, E. S., de Amici, G., Fixsen, D. J., made by Giovanni da Verrazzano who, off the coast of the Hinshaw, G., Jackson, P. D., Janssen, M., Keegstra, P., Lowen- outer banks of North Carolina, mistakenly believed that he stein, K., Lubin, P., Mather, J. C., Tenorio, L., Weiss, R., had discovered the Pacific Ocean (11); sometimes the first Wilkinson, D. T. & Wright, E. L. (1993) Astrophys. J. 419, 1–6. impression, based on limited data, does not reveal the true 6. Lynden-Bell, D., Faber, S. M., Burstein, D., Davies, R. L., Astrophys. J. picture. At the same time, the apparent symmetry of the Dressler, A., Terlevich, R. J. & Wegner, G. (1988) 326, 19–49. underlying structures traced by the visible galaxies and by the 7. Dekel, A. (1994) Annu. Rev. Astron. Astrophys. 32, 371–418. gravitational potential offers a certain comfort. Mainly, it is 8. Strauss, M. A. & Willick, J. A. (1995) Phys. Rep. 261, 271–314. the richness of the local structure and the promise of the 9. da Costa, L. N., Freudling, W., Wegner, G., Giovanelli, R., future that should be most appreciated. Haynes, M. P. & Salzer, J. J. (1996) Astrophys. J. (Lett.) 469, The good news is that the next decade holds even greater L5–L8. prospects for growth of the red shift data base. The Las 10. Giovanelli, R., Haynes, M. P., Herter, T., Vogt, N., Chamaraux, Campanas Redshift Survey (12) has just contributed 26,000 P., da Costa, L. N., Freudling, W., Salzer, J. J. & Wegner, G. red shifts alone, and is not completed. The red shift component (1996) Astron. J., in press. of the Sloan Digital Sky Survey (13) will add dramatically. We 11. Morrison, S. E. (1971) The European Discovery of America: The can extrapolate that in less than a decade, red shifts will be Northern Voyages (Oxford Univ. Press, New York), p. 292. 12. Shectman, S. A., Landy, S. D., Oemler, A., Tucker, D. L., Kirsch- available for a million galaxies. Today, evidence for a charac- ner, R. P., Lin, S. & Schechter, P. L. (1996) Astrophys. J. 470, 172. teristic scale on the order of 100 Mpc is growing (e.g., ref. 14); 13. Gunn, J. E. & Knapp, G. R. (1993) in Sky Surveys: From Proto- where does this scale come from? And then follow the stars to Protogalaxies, ed. Soifer, B. T. (Astron. Soc. Pacific, San inevitable questions of how large-scale structure grows in the Francisco), Vol. 43, pp. 267–271. early universe and how it evolves with time. Soon, we should 14. Landy, S. D., Shectman, S. A., Lin, H. Kirschner, R. P., Oemler, actually have a chance to know the answers. A. & Tucker, D. L. (1996) Astrophys. J. (Lett.) 456, L1–L4. Downloaded by guest on September 26, 2021