VOIDS, EXTRAGALACTIC VALERIE DE LAPPARENT-GURRIET Part of the progress in our understanding of the distribution of galaxies outside the Milky Way was achieved by examining galaxy catalogs that map the angular position on the sky of galaxies brighter than a chosen magnitude limit (see Fig. 1). These "projected" onto the celestial sphere-or "two-dimensional" catalogs showed the inhomogeneity of the light-emitting component of the universe and led to the discovery of concentrations of galaxies on scales from approximately 1-100 Mpc (1 Mpc *3x10* ly), corresponding to clusters and superclusters. Parallel to the acquisition of larger galaxy catalogs, the application of the Hubble law allowed recovery of the third coordinate, the distance of the galaxies from the Milky Way. By measuring the recessional velocities of the galaxies from their redshifts over selected regions of projected catalogs, it was then possible to obtain "three-dimensional" maps of the galaxy distribution, also called redshift surveys. These new maps confirmed that most superclusters in projected catalogs were real superclusters in three-dimensional space and also indicated that the superclusters are associated with large voids. These "extragalactic" voids are defined by regions of supercluster size that are underdense compared to the surroundings and are frequently devoid of any galaxies brighter than the catalog limit. OBSERVATIONS Most of the early redshift surveys contained empty regions of about 10-20 Mpc. Considering the low signal-to-noise ratio in the delineation of the structures, some of these voids could be statistical accidents. However, the discovery of a strikingly large void in a redshift survey toward the Bootes constellation suggested that voids might be real structures. The Bootes void is enclosed in a sphere with a diameter of 60 Mpc (for a Hubble constant of 100 km s** Mpc**; we use this value hereafter) and centered at 150 Mpc from the Milky Way. Given the clustering properties of galaxies and the characteristics of the sample in which the Bootes void was discovered, the probability that such a large void could be a chance fluctuation is very small (about one chance in a million). Results from a recent redshift survey suggest a new picture of the galaxy distribution in which structures like the Bootes void are common features. This new survey has the configuration of a "slice": the galaxy catalog is a thin strip of the sky of 6ø in declination by 117* in right ascension, which lies in Fig. 1 between the heavy tick marks and contains 1059 galaxies. The "pie diagram" of Fig. 2 plots the recessional velocity in kilometers per second of all the galaxies in the strip (marked as dots) as a function of right ascension (a galaxy with a velocity of 10,000 kms** is at a distance of 100 Mpc from the Milky Way, located at the apex of the cone). The declination coordinate is suppressed because of the narrow angle covered. Because the catalog is limited by a threshold in apparent magnitude (blue magnitude brighter than 15.5), the density of galaxies decreases at large velocity where only the intrinsically brightest galaxies are detected. This decrease in density defines a characteristic depth for the catalog of approximately 100 Mpc. The concentration of points in the center of the map in Fig. 2 corresponds to the Coma cluster of galaxies (see Fig. 1). The peculiar velocities of the galaxies in the gravitational potential of the cluster cause the elongation along the line of sight, the "finger-of-god" effect. Outside clusters, the distortions due to the peculiar velocities are small (a few 100 km s**), and the map in velocity approximates the map in real space. Figure 2 suggests that the galaxy distribution is dominated by large voids with diameters ranging from 20-50 Mpc and delineated by sharp linear structures. The picture in which galaxies are distributed in thin sheet-like or shell-like structures surrounding vast voids provides a simple interpretation for this cellular network. The comparatively smooth distribution of galaxies in projection onto the sky (see Fig. 1) supports this interpretation. Moreover, additional data for adjacent slices to the one in Fig. 2 do show that the voids and sheets extend in declination across more than 30 Mpc. The alternation of superclusters with voids in most previous catalogs had already suggested a cellular pattern for the galaxy distribution, but the distribution was not sampled densely enough for clear delineation of the sheets. For example, in pie diagrams of the Bootes void, the edges of the void are poorly defined because redshifts were measured for only 2% of the galaxies in the region and the separation between the galaxies in the sheets is of the order of the size of the void. In the map of Fig. 2, the separation between the galaxies is much smaller than the size of the voids. If these sheet-like structures are frequent, the filament-like superclusters observed in other surveys might be portions of shells intersected by the survey. In addition, all superclusters are connected, and they are geometrical arrangements rather than dynamical systems. The real physical units could be the voids: A smaller amount of energy would be required to move matter across the radii of the voids than across the longer span of the connected shells. IMPLICATIONS OF VOIDS AND SHEETS The size and the geometry of the voids and sheets challenge the measurement of the average properties of the galaxy distribution. Because the size of the largest voids in Fig. 2 is comparable with the depth of the map, this survey is not a fair representation of the general galaxy distribution, and the mean density of galaxies is poorly determined. Under reasonable assumptions on the spectrum of void diameters, the fluctuations in the mean number of galaxies are determined by the number of the largest voids in the sample. Therefore, a better determination of the mean matter density associated with galaxies requires the completion of redshift surveys extending to larger velocities and thus containing more of the largest voids. Because the largest void that can be detected in a survey is limited by the depth of the survey, voids with diameters larger than the present upper limit of 50 Mpc could also be discovered in deeper redshift surveys. Such surveys, requiring use of the largest existing ground-based telescopes, would provide better observational limits on the scale above which the visible universe might become homogeneous. In addition, deeper surveys might reveal a yet undetected population of very faint objects inside the observed voids. So far, other types of galaxies that might not have been included in the Catalogue of Galaxies and of Clusters of Galaxies by Fritz Zwicky and his collaborators (i.e., low-surface-brightness, emission-line, or IRAS galaxies) trace the same large-scale structures as in Fig. 2. The strong asymmetry and contrast of the sheets delineating the voids require using statistical measures of the galaxy distribution that make no assumptions of local spherical symmetry and are poorly sensitive on the mean density. Simple statistics satisfying these requirements were applied to the map of Fig. 2 and put tight constraints on the theoretical models for the formation of large-scale structure: The fraction of the total volume occupied by galaxies (20%); the thickness of the sheets (5 Mpc); and the shape and the radius of the voids. More sophisticated statistics like the probability of finding a void of a given volume or the radius of curvature of the sheets constrain the general topology of the distribution. Some of these statistics are useful for discriminating between a bubble-like topology, where all the voids are isolated from each other by shells, and a sponge-like topology, where the high-and low-density regions are equivalent and form two interwoven networks, and further constrain the theoretical models. Additional Reading Burns, J.O.(1986). Very large structures in the universe. Scientific American 255 (No. 1) 38. Geller, M.J. and Huchra, J.P.(1989). Mapping the universe. Science 246 897. Hubble, E.(1936). The Realm of the Nebulae. University Press, New Haven. Oort, J.H.(1983). Superclusters. Ann. Rev. Astron. Ap. 21 373. Peebles, P.J.E.(1980). The large-Scale Structure of the Universe. Princeton University Press, Princeton. Zeldovich, Ya.B., Einasto, J., and Shandarin, S.F.(1982). Giant voids in the universe. Nature 300 407. Zwicky, F., Herzog, E., Wild, P., Karpowics, M., and Kowal, C.T. (1961-1968). Catalogue of Galaxies and of Clusters of Galaxies. Vols. 1-6. California Institute of Technology, Pasadena.