Proc. Natl. Acad. Sci. USA Vol. 95, pp. 78–81, January 1998 Colloquium Paper This paper was presented at a colloquium entitled ‘‘The Age of the Universe, Dark Matter, and Structure Formation,’’ organized by David N. Schramm, held March 21–23, 1997, sponsored by the National Academy of Sciences at the Beckman Center in Irvine, CA. Cosmic velocity fields and their interpretation MARC DAVIS Departments of Astronomy and Physics, University of California, Berkeley, CA 94720 ABSTRACT We review the current status of our knowl- survey (1), has been the standard method of estimating the edge of cosmic velocity fields, on both small and large scales. thermal state of the distribution of galaxies. It is well known A new statistic is described that characterizes the incoherent, that this statistic is dominated by the pairs contributed by rare, thermal component of the velocity field on scales less than rich clusters of galaxies and is thus an unstable measure. Its 21 21 21 2h Mpc (h is H0y100 kmzs zMpc , where H0 is the Hubble interpretation in terms of the cosmic virial theorem is com- constant and 1 Mpc 5 3.09 3 1022 m) and smaller. The derived plicated by the difficulties of evaluating the necessary integral velocity is found to be quite stable across different catalogs over the three-point correlation function of the mass distri- and is of remarkably low amplitude, consistent with an bution (2, 3). effective V ; 0.15 on this scale. We advocate the use of this Recently Davis, Miller, and White (4) have suggested an statistic as a standard diagnostic of the small-scale kinetic alternative measure of the thermal state of the galaxy distri- s energy of the galaxy distribution. The analysis of large-scale bution, which they label 1. This statistic is the rms motion of flows probes the velocity field on scales of 10–60 h21 Mpc and galaxies relative to their neighbors within projected cylinders 21 s should be adequately described by linear perturbation theory. of radius 2h Mpc; it is similar to the traditional [12], with the Recent work has focused on the comparison of gravity or major difference being that each galaxy is given equal weight density fields derived from whole-sky redshift surveys of in the computed distribution function of the redshift separa- galaxies [e.g., the Infrared Astronomical Satellite (IRAS)] tion of neighbors, rather than each pair of galaxies. Either of with velocity fields derived from a variety of sources. All the these statistics is evaluated using only redshift space informa- algorithms that directly compare the gravity and velocity tion, and thus they can be applied to large distant redshift s fields suggest low values of the density parameter, while the surveys of galaxies. The 1 measure can be interpreted in terms POTENT analysis, using the same data but comparing the of a filtered version of the cosmic-energy equation, which is derived IRAS galaxy density field with the Mark-III derived lower order than the cosmic virial theorem, because it depends j matter density field, leads to much higher estimates of the on an integral of the two-point correlation function , rather z inferred density. Since the IRAS and Mark-III fields are not than the three-point function . This is much easier to evaluate fully consistent with each other, the present discrepancies and is expected to be much more stable in different samples. might result from the very different weighting applied to the Indeed, tests of this statistic within mock catalogs and with data in the competing methods. different samples of real galaxies confirm remarkable stability. s 5 6 y Davis et al. (4) report 1 96 16 km s for the Infrared Astronomical Satellite (IRAS) 1.2-Jansky (Jy; 1 Jy 5 10226 The deviations of the local galaxy distribution from smooth 2 2 Wzm 2zHz 1) sample of galaxies, and s 5 130 6 15 kmys for Hubble flow, known as peculiar velocities, can be character- 1 2 a redshift sample drawn from the Uppsala General Catalog ized in a number of ways. On scales of order 1h 1 megaparsec 2 2 (UGC) sample of galaxies. Analysis of the Las Campanas (Mpc; 1 Mpc 5 3.09 3 1022 m; h is H y100 kmzs 1zMpc 1, 0 Redshift Survey (M.D., H. Lin, and R. Kirshner, unpublished H where 0 is the Hubble constant), the galaxy clustering is work) leads to similar conclusions as for the UGC, with known to be highly nonlinear and the peculiar velocities near consistency observed for the six individual slices of the Las most galaxies can be expected to be incoherent and random. Campanas Redshift Survey. This must be compared with Details will of course depend on the local environment, but it results derived from mock catalogs extracted from N-body is of interest to estimate the rms amplitude of the peculiar simulations with nearly identical clustering amplitude. In velocity field averaged over all galaxies. On much larger scales, V5 s s unbiased 1 simulations, the measured 1 dispersion is 1 linear theory should apply and there should exist a well defined 5 325 kmys, nearly three times higher than observed in velocity field. We discuss the present state of our knowledge of optically selected galaxy catalogs! If galaxies are unbiased mass both of these components of peculiar velocity and their tracers, the inferred density parameter from this test is V5 comparison to the field predicted on the basis of the observed 0.15 6 0.02. galaxy distribution. Because this comparison is the best V This test is important because it measures the thermal method of measuring the cosmological parameter ,itisof environment of a typical galaxy and is not biased by the rare considerable interest to fully understand the systematics of the rich clusters of galaxies. It confirms that the quiet thermal analysis. As we shall see below, the current status of the environment of a typical galaxy is well constrained and is very analysis is somewhat murky. different from the hot thermal environment characteristic on small scales in N-body simulations. Such a discrepancy is very Small-Scale Fields difficult to reconcile with high values of the density parameter, with or without bias in the galaxy distribution. For more than a decade, the pair weighted velocity dispersion s Peebles (5) has long argued that the ‘‘coldness’’ of the local [12](r), first employed by Davis and Peebles on the CfA1 flow of galaxies is a serious problem for high-density models © 1998 by The National Academy of Sciences 0027-8424y98y9578-4$2.00y0 Abbreviations: Mpc, megaparsec; IRAS, Infrared Astronomical Sat- PNAS is available online at http:yywww.pnas.org. ellite; Jy, Jansky; ITF, inverse Tully–Fisher. 78 Downloaded by guest on September 25, 2021 Colloquium Paper: Davis Proc. Natl. Acad. Sci. USA 95 (1998) 79 of structure formation. Schlegel et al. (6) measure deviations background radiation (CMBR) dipole is a difficult, dangerous from Hubble flow of only 60 kmys for galaxies within 5 Mpc game (22, 23). The amplitude and direction of the CMBR of the Local Group. Govertano et al. (7) show that candidate dipole are rather precisely known, but the coherence of the Local Groups within high-resolution N-body models never flow is completely uncertain. How large a region is flowing at exhibit such cold local flows, either in V51orV50.3 models. 620 kmys along with the Local Group of galaxies? Should a full Typical local group candidates in their simulations have much reflex of this dipole be detectable within 50, 100, or 3,000 Mpc? higher local velocity dispersions, including objects with blue- Without an answer to this question—i.e., an assumption of the shifts, which are not observed for the nearby galaxies outside nature of the large-scale power spectrum—it is not possible to our own Local Group. infer the cosmological density parameter by comparing the The small-scale ‘‘coldness’’ of the galaxy distribution is well CMBR dipole to the gravitational dipole inferred from galaxy known by alternative expressions: the high ‘‘mach number’’ of catalogs such as the 1.2-Jy IRAS survey. the cosmic velocity field (8) or the thinness of the observed However, the nonlocality does not apply to all aspects of the sheets of galaxies in redshift space (9). We want to emphasize velocity–gravity field comparison. Recall Einstein’s gedanken that the problems presented by such low amplitude peculiar experiment of an observer within an elevator. He cannot velocities are real and that they indicate a serious gap in our distinguish whether he is in an accelerating frame or is understanding of structure formation. stationary in an external gravitational field. If the elevator goes into freefall, he can detect the presence of an external gravi- Large-Scale Flows tational field only by its tidal influence on the matter within the elevator. Exactly the same considerations apply for the grav- 2 On scales greater than 5h 1 Mpc the deviations from Hubble itational field estimated from an imperfectly sampled galaxy flow are expected to be smaller than the Hubble flow itself, so distribution. A poorly sampled, distant cluster of galaxies will that in most regions galaxies are physically expanding from induce coherent errors in the nearby gravity field, but they will each other. In such a situation it is reasonable to expect the be tidal in nature. Working in the Local Group frame of velocity field to be largely irrotational. On slightly larger scales, reference rather than the cosmic microwave background frame one can expect linear perturbation theory to be a reasonably is conceptually cleaner for this analysis.