Mapping the universe in three dimensions

Abstract

The determination of the three-dimensional layout of galaxies is critical to our understanding of the evolution of galaxies and the structures in which they lie, to our determination of the fundamental parameters of cosmology, and to our understanding of both the past and future histories of the universe at large. The mapping of the large scale structure in the universe via the determination of galaxy red shifts (Doppler shifts) is a rapidly growing industry thanks to technological developments in detectors and spectrometers at radio and optical wavelengths. First-order application of the red shift-distance relation (Hubble’s law) allows the analysis of the large-scale distribution of galaxies on scales of hundreds of megaparsecs. Locally, the large-scale structure is very complex but the overall topology is not yet clear. Comparison of the observed red shifts with ones expected on the basis of other distance estimates allows mapping of the gravitational field and the underlying total density distribution. The next decade holds great promise for our understanding of the character of large-scale structure and its origin.

One of the most elusive tasks of astronomy is the development of a clear picture of how galaxies are distributed into clusters and superclusters and at the same time avoid the large empty void regions. The difficulty in constructing such a picture rests on our ability to interpret the observed projected distribution of galaxies on the sky and ultimately to measure the true location in space of large numbers of galaxies. In this paper, I will adopt the standard view that the dominant motion in the universe is the smooth expansion described by Hubble’s law, relating a galaxy’s distance d to its observed recessional velocity cz by a simple constant of proportionality, the Hubble constant (H_o). In fairness, it should be recognized that the adoption of a simple red shift-distance relation is not universally accepted (e.g., ref. 1). However, Hubble’s law arises as a natural consequence of the expansion of a homogenous and isotropic universe, as predicted by the assumption that the cosmological principle holds. Adopting the law, the distance to a galaxy can be estimated to first order (see the discussion of peculiar velocities below) simply by measuring its doppler shift z = δλ/λ. For discussions of structural characteristics, the Hubble constant is only a scale factor, and is not critical to the present discussion. Note that we astronomers use the terms “recessional velocity” and “red shift” interchangeably, and have the bad habit of talking about distances in velocity units.

The fundamental objective of surveys of galaxy red shifts is to provide a first-order measurement of galaxy distance: d = cz/H_o. Beyond the Local Supercluster at least, recessional velocities dominate peculiar ones, and thus observed red shifts can be used to trace large-scale structure. Recent advances in spectrometers at both optical and radio wavelengths have made the redshift industry is a fast-paced one, showing a greater than exponential growth. A recent more detailed review of red shift surveys was presented by Giovanelli and Haynes (2). In this discussion, I hope to convey some sense of the complexity of large-scale structure as well as the promise of the next decade to advance our understanding of it.

Large-Scale Structure from Red Shift Surveys

That galaxies tend to cluster has been recognized for more than a century, even before their extragalactic nature was understood. The cosmological principle states that, on some large scale, the universe is homogenous and isotropic. The delineation of the topological description of the distribution of galaxies in the local universe is an attempt to test whether, and on what scale, the cosmological principle holds.

The Milky Way is one of two spiral galaxies (the other is the Andromeda galaxy, M31) that dominate the Local Group, a loose aggregate of about 20 galaxies within a volume of radius about 1 Mpc (1 Mpc = 3.1 × 10²² m or 3.26 × 10⁶ light years). The Local Group itself lies on the outskirts of a flattened structure of a radius about 15 Mpc known as the Local Supercluster, centered on a rich cluster of galaxies, the Virgo cluster. A number of other superclusters are recognized within a few 100 Mpc, but the overall characteristic scale and topological description are still issues for debate. Here, we will simply examine the qualitative appearance of structures seen in the local universe.

Figs. 1, 2, 3 attempt to illustrate the kind of structure seen in the red shift distribution of nearby galaxies. In each case, galaxies are projected onto an Aitoff equal area projection in celestial coordinates, right ascension (R.A.) and declination (Decl.), and centered on R.A. = 6^h, Decl. = 0°. Fig. 1 shows the distribution of some 14000 galaxies with known recessional velocities cz < 12,000 km s⁻¹. If the Hubble constant has a value of H_o = 65 km s⁻¹·Mpc⁻¹, then to first order, the volume contained extends to 184 Mpc. Dotted lines denote the locus of points at galactic latitudes b = −20°, 0, and +20°, delineating the Zone of Avoidance, within which distant galaxies are obscured at optical wavelengths by the dust and gas within the Milky Way. The distribution of galaxies within this volume is not random; galaxies tend to cluster. Two major structures are easily seen. To the left of the map, the strong concentration of galaxies in the central region of the Local Supercluster in the Virgo region is clearly noticeable. On the upper right side, the linear string of galaxies running diagonally (and almost perpendicular to the b = −20° line) is the Pisces–Perseus supercluster (PPS).

Figure 1.

The sky distribution of 14,000 galaxies with known recessional velocities cz < 12,000 km s⁻¹. 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 −20°, 0°, and +20°.

Figure 2.

Similar to Fig. 1, but showing only the sky distribution of galaxies with known recessional velocities cz < 3000 km s⁻¹.

Figure 3.

Similar to Fig. 1, but showing only the sky distribution of galaxies with known recessional velocities 3000 < cz < 6000 km s⁻¹.

Fig. 2 shows galaxies with velocities lower than 3000 km s⁻¹: the Local Supercluster. It is clear in this representation that there are more galaxies on the left side of the map than on the right side. This asymmetry occurs because the Local Group is located on the edge of the Local Supercluster. When we look towards the center, we see lots of galaxies; when we look away from the center, we see many fewer. Using more imagination, one can trace a continuous line through the concentration in Virgo, across the zone of avoidance, through the right side and back again through the north pole. This continuous distribution is the Supergalactic plane. Although less well-defined than the galactic plane, its presence indicates that the Local Supercluster, like the Milky Way, is a flattened structure. Within the Local Supercluster, galaxies tend to be found in groups and clouds, with other regions being relatively empty.

Large-scale clustering is quite easily visible also in Fig. 3, which displays objects in the red shift range 3000 < cz < 6000 km s⁻¹. The PPS is visible in the northwest quadrant. The adopted centering tends to deemphasize the overdensity in the Cen-Hyd-Pavo-Ind region in the southern hemisphere, although it is still visible. Numerous other structures are also seen. Published datasets currently sample both hemispheres quite well to this depth; at larger red shifts, however, the asymmetry in the distribution of telescope sites favoring the northern hemisphere becomes critical.

Noticeable in Fig. 1 despite its distance, the PPS is one of the most prominent structures in the local extragalactic sky. It must be emphasized that the PPS is not a random volume of the universe. As discussed by Giovanelli et al. (3), the optical catalog used to select targets for the red shift surveys of this region is particularly suited to tracing volume density enhancements with characteristic sizes of 5 to 20 Mpc if they are situated at a distance of about 5000 km s⁻¹. In other words, if the galaxy luminosity function does not vary, such structures will be emphasized in a catalog of such depth in apparent magnitude and yet will not be confused by background objects.

We can examine this structure by looking at the two-dimensional distributions of galaxies in the region of the supercluster. Fig. 4 shows the distribution on the plane of the sky of galaxies in a 90° by 30° slice across the supercluster. The main ridge is roughly outlined by straight lines. This is the same feature seen on the right side of Fig. 1. Note the clumpiness of the galaxies, particularly the continuous structure within the outlined region. Notice also the absence of galaxies in other portions of the map. Some of the empty regions to the extreme left (east) and at the top (north) are partly caused by obscuration within the Milky Way. However, most of the structure 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 outlined in the top one. This representation does not give adequate comparison of nearby and distant structures (see below), but it is clear that the majority of galaxies seen in the enhanced region in the upper plot all lie at approximately the same red shift. Fig. 5 shows the red shift distribution of the same galaxies shown in Fig. 4, but in this case, the spatial coordinate is shown as a true angle. This representation is called a cone diagram and gives a more accurate comparison between nearby and distant structures.

Figure 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.

Figure 5.

Cone diagram of the galaxies contained within the outlined region in Fig. 4, identified with the main ridge of the PPS.

Velocity crowding into narrow lanes of width about 250 to 500 km s⁻¹ shows that most of the structures seen confined on the plane of the sky are also confined in the red shift dimension. They are therefore two-dimensional linear structures. Occasional larger spreads in velocity are seen in the regions of rich clusters, where orbital velocities within the cluster potential are added to the Hubble expansion velocity. The relative isolation of the supercluster from the Local Supercluster in the foreground and from other structures at larger distances is emphasized in the cone diagram.

The main ridge of the PPS shows a volume density enhancement of more than a factor of 10 and can be traced over 90° across the sky. It lies at a mean red shift of about 5500 km s⁻¹ and is best described as a linear “filament” with an axial ratio of at least 8:1, inclined by less than 12° to the plane of the sky. The supercluster extends over 45 Mpc in length before it disappears into the Zone of Avoidance on the east. The empty “voids” are nonspherical regions of true galaxy underdensity.

To add a significant complication, the study of three-dimensional structure requires an understanding of the well-known morphology density relation, such as quantified by Dressler (4). Elliptical and lenticular galaxies show a much greater tendency to cluster than their spiral counterparts. Segregation is also seen among galaxies of different surface brightness and luminosity; high-luminosity galaxies are preferentially found in high-density regions. While both high- and low-luminosity (or E/S0 and spiral) galaxies trace the same large-scale structures, the density contrasts derived from separate samples vary significantly. Numerous observational and theoretical studies have addressed the issue as to whether the processes responsible for such segregation act as a continuous function of galaxy density and reflect the local environmental conditions at the time of galaxy formation or whether they arise from ongoing interactions with neighboring galaxies and/or the intergalactic environment.

Peculiar Velocities

Because on the scales of superclusters, the cosmological principle does not hold, deviations from pure Hubble expansion are expected. The measurement of such “peculiar velocities” offers the possibility of uncovering the true distribution of mass, not just of the visible galaxies. If we describe the perturbed density field in terms of the density contrast δ = δρ/〈ρ〉, and assume that linear perturbation theory holds (true except in the vicinity of clusters), then the equation governing the growth of the density fluctuations, as a function of comoving x⃗ and t, is written: ∂²δ/∂t² + 2H(t)∂δ/∂t = 4πG〈ρ〉δ. This can be treated as an ordinary differential equation; we need consider only the growing solution. The importance of this description is that the density, the perturbation potential Φ(x⃗), and the peculiar gravity g⃗ are all self-similar. Furthermore, the peculiar velocity has the same direction and is proportional to the present gravitational acceleration. Thus, derivation of the peculiar velocity field allows the reconstruction of the underlying density field, which in turn can be compared with that derived from the distribution of light (i.e., the visible galaxies).

The recent Cosmic Background Explorer measurement (5) of the microwave background radiation confirms the dipole anisotropy of amplitude 3.365 ± 0.027 mK in the direction (l, b) = (264.4° ± 0.3°, +48.4° ± 0.5°). This inhomogeneity is usually interpreted as a motion of the Local Group of amplitude V_CMB = 627 ± 22 km s⁻¹ toward (l_CMB, b_CMB) = (276° ± 3°, +30° ± 3°). The critical point is that a simple Virgo infall model does not agree with the magnitude or direction of the motion implied by the cosmic microwave background dipole anisotropy. The discrepancy cannot be explained by the rotation of the Local Supercluster either.

Controversy is currently focussed on whether the sources of this motion are local (distributed within 5000 H_o Mpc) or distant (spread out to distances in excess of 10,000 H_o Mpc), i.e., on the size of the so-called “convergence depth.” Recent results on the scale of the convergence depth have often conflicted. The Seven Samurai results (e.g., ref. 6) placed the “Great Attractor” more distant than Hydra–Centaurus, whereas the major perturber as inferred from infrared flux limited, red shift samples of galaxies is more in line with a 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, extending even to scales of cz ≈ 13,000 km s⁻¹. 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 galaxies resembles closely the velocity field predicted from self-consistent reconstructions based on all-sky red shift surveys. While we detect a bulk motion of ≈300 km s⁻¹ within a top-hat window 6000 km s⁻¹ 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 order of 6000 km s⁻¹. We conclude that locally at least, light traces mass.

Summary

The structure of the local universe as revealed from the galaxy distribution is topologically complex. Numerous attempts to characterize the structure have been made using, for example, higher order correlation functions, the fractal dimensionality, or a genus statistic, but are not discussed here. No simple characterization describes the galaxy distribution; little discussion relevant to the theme of symmetry of this symposium can be offered. The asymmetry seen in the distribution of nearby galaxies (Fig. 2) arises from our particular location on the outskirts of the Local Supercluster. And we might also remember the great geographical error made by Giovanni da Verrazzano who, off the coast of the outer banks of North Carolina, mistakenly believed that he had discovered the Pacific Ocean (11); sometimes the first impression, based on limited data, does not reveal the true picture. At the same time, the apparent symmetry of the underlying structures traced by the visible galaxies and by the gravitational potential offers a certain comfort. Mainly, it is the richness of the local structure and the promise of the future that should be most appreciated.

The good news is that the next decade holds even greater prospects for growth of the red shift data base. The Las Campanas Redshift Survey (12) has just contributed 26,000 red shifts alone, and is not completed. The red shift component of the Sloan Digital Sky Survey (13) will add dramatically. We can extrapolate that in less than a decade, red shifts will be available for a million galaxies. Today, evidence for a characteristic scale on the order of 100 Mpc is growing (e.g., ref. 14); where does this scale come from? And then follow the inevitable questions of how large-scale structure grows in the early universe and how it evolves with time. Soon, we should actually have a chance to know the answers.