91

DARK MATTER FROM SURVEYS

SOPHIE MAUROGORDATO Centre National de la Recherche Scientifique U A 173 Departement d 'Astrophysique Extragalactique et de Cosmologie Observatoire de Paris - Meudon, 92195 Meudon, France

Abstract

We briefly review the implications on dark matter from galaxy surveys. The amount and nature of dark matter play a fundamental role in the formation of large-scale struc­ tures. Once the primordial density fluctuations and the cosmological model are specified, the distribution of mass can be predicted. can then be confronted to the galaxy distri­ bution from 2D and 3D galaxy surveys, assumingIt a simple relation between the mass and the galaxy distribution. We will present a general view of the 'archetypes' of recent galaxy surveys and of the statistical formalism developed to quantify the analysis of the galaxy distribution and to compare to theoretical predictions at the light of COBE results. A second very promising approach will be adressed which allowsto recover the mass density field from the measurement of peculiar velocities without any hypothesis on the relation between mass and galaxy distribution. We will show that presently available results are not still conclusive about the (baryonic or non-baryonic) dark matter components of mod­ els and about the value of However the size and depth of surveys is evolving so rapidly that one should hope to obtain11. an answer in the next future. 92

1 Introduction

The history of large-scale clustering in the Universe has undergone a rapid evolution in the last decades. Several groups have focused on the more salient high density structures evidenced from the angular distribution on the sky introducing the concept of supercluster as for instance the Coma supercluster (Gregory and Thomson 1978), Hydra-Centaurus (Chincarini and Rood 1979), Hercules (Tarenghi et al. 1979), Pisces-Perseus (Gregory et al. 1981), or the Local supercluster (Yahil et al.1980), and verifying their reality by intensive measurements. Underdense regions have been discovered too, the most spectacular one being the 'Bootes Void' (Kirschner et al. 1981, Kirschner et al. 1987) which spreads over a diameter of 6000kms-1• On the other side, the statistical analysis of the projected galaxy distribution under the care of Peebles began to give substantial results (Hauser and Peebles 1973, Davis and Peebles 1977, Fry and Peebles 1978). The need of representative tridimensional samples became urgent and led to the completion of flux-limited redshift catalogs which should allow a real quantitative analysis of the frequence and size of structures in the Universe. This was realized thanks to the Center for Astrophysics . While the wide-angle surveys give a detailed vision of the structure of the nearby Universe, the 'pencil-beam' surveys, complete to much fainter magnitudes on a very small region on the sky, allow to probe very deep regions of the Universe. The recent development of distance indicators independent of redshift gives access to the velocity and to the dynamical density field. The statistical indicators computed from the different surveys are then confronted to models of galaxy formation, allowing to set constraints on the nature of dark matter ingredients, on the value of !1 and on the 'biasing' mechanism.

2 Wide-angle 3D catalogs

The wide-angle, flux-limited redshift surveys have been determinant to analyse the statistical properties of the galaxy distribution. The CfA redshift survey (Huchra et al. 1983) allowed to make the firstjump forward in the measurement of spatial statistical indicators. The of magnitude mpg ::; 14.5 have been selected from a tnixing of the Nilson and of the Zwicky catalogs . The sample, mostly in the Northern Hemisphere, is divided in two parts of 1845 and 556 galaxies centered respectively on the Northen (1.83 sr) and Southern galactic caps (0.83 sr), and satisfying the following criteria: 40° and 0°, -30° and -2.5°. bu 2': /j 2': bu ::; /j 2': 93

The Southern Sky Redshift Survey (da Costa et al. 1989) has been completed in the Southern Hemisphere, providing 2028 galaxies centered on the Southern galactic cap: -30° , bn :::; 5 -17.5° . The galaxies have been selected from the ESQ catalog with a limit on the face-on :::; diameter 1'. From CfA and later from SSRS, the first real statistical analysis of the

a'

5'

Figure 1: By courtesy of L.da Costa, M.J. Geller, J.P. Huchra, 1994. This cone diagram shows galaxies of CfA2 and SSRS2 with 22° 151 40° and cz :<::; 15000km/ Note the Northern 8. Great Wall, the Southern Wall and the:<::; presence :<::; of large voids.

and magnitudes of about 2 millions of galaxies with a limiting magnitude bj 20.5 in the area = delimitated by 5 -20° and bn -40°. The Stromlo-APM redshift survey (Loveday et al. :<::; :<::; 1992) consists in the spectroscopic follow-up of a bright sub-sample of galaxies of magnitudes bj :<::; 17.5 selected randomly at a rate of 1 in 20. The EDSGC provides about 106 galaxies up to a limiting magnitude of bj 20. = Several redshift surveys have been completed as the Durham/ AAT and the Durham/SAAO (Metcalfe et al. 1988). The ESO Slice Project, an ESO Key program (Vettolani et al. 1992), is based too on the EDSGC. It aims to measure the redshifts of about 3000 galaxies in a slice of 1 22° up to magnitude bj 19.4 in the South Galactic Pole region. The first slice is x = now complete, and shows a very dense structure at 300h-1 Mpc spreading over nearly all the � range in right ascension surrounded by large voids. The second strategy to get a 2D catalog is to map the survey area with CCD frames,leading to very high astrometric and photometric precision, but it requires a considerable effort in view of the amount of data and the complexity of data reduction. This method has been chosen for the Las Campanas Deep Redshift Survey (Oemler et al.1992), a digital and spectroscopic 95 survey of 20000 galaxies up to R magnitude 18 ( B 20) undertaken on 600 squares � � = degrees on the sky split in "bricks"of 1.5x3° which once allcompleted should formcontiguous strips of 1.5° wide in declination. The visual impression resulting from the cone diagrams with 12000 galaxies is the recurrence of CfA-like structures, with maximum void sizes of the order of 5oh-1 Mpc.

3 Infrared and radio surveys

3.1 The IRAS catalog

Complementary to the optical approach, surveys at the other wavelengths have undergone a rapid rise. In particular, the catalog of galaxies detected by the lnfraRedAstronomical Satellite has been used to complete flux-limited redshift surveys which have the advantages of a nearly all-sky coverage with an uniform calibration, avoiding (mostly) the problems of the galactic plane extinction. Below 30°, optical surveys are affected by confusion and obscuration [bu[ = due to the galacticpla ne, and statistical analysis becomes difficult. However, surveys of galaxies focused on the galactic plane (Dressler et al. 1991, Kraan-Korteweg et al. 1992) show the importance of clustering through the 'zone of avoidance'. From IRAS was then completed the '2 Jy' redshift survey (Strauss et al. 1990), which consists of 2600 galaxies with a flux limit at wavelength 60µm, 2Jy. Going fainter in flux S6 0 � led to the '1.2 Jy' survey (Fisher et al. 1992) of 5313 galaxies and to the QDOT sparse sample (rate 1 in 6) of 2163 galaxies up to 0.6 Jy, which is currently being fully completed (Saunders et al. 1994) These surveys, which provides an unique combination of sky coverage and depth (74% of the sky, down to galactic latitude 10°) are particularly adapted to derive the density [bu[ = field of the IRAS galaxy distribution. This allows to derive the galaxy motions. Moreover, the confrontation of the properties of the optical/IRAS distribution is particularly fruitful for determining if and how galaxies trace the mass and the values of the combination bn-0·6•

3.2 The Pisces Perseus Supercluster Survey This redshift sample has been assembled by Giovanelli and Haynes during the last decade, using the neutral hydrogen 2lcm line to measure the redshifts of galaxies (PPSS, Giovanelli and Haynes 1993). The boundaries of the sample are: -10° and 0° leading to b S 8 � 6000 galaxies with mpg 15.7. The most salient feature is the main ridge of the Perseus- � S 96

Pisces Supercluster, spreading across the sample along more than 80h-1 Mpc, which is a severe challenge for models in terms of formation times.

4 Deep surveys

A complementary strategy to wide-angle 3D surveys which map the 'nearby' Universe is the 'pencil beam' survey approach. Broadhurst et al. (1990) combined two fields with 20' of diam­ eter centered on the Northern and Southern galactic poles, complete to a limiting magnitude bJ = 21.5, in order to test the distribution on scales of � 2000h-1 Mpc. From their analysis, clustering is still present at separations larger than lOOh-1 Mpc. They detected regular peaks in the redshift distribution with an unexpected periodicity of 128h-1 Mpc. The two nearby peaks have recently be shown to coincide respectively with the Northern Great Wall and with the Southern Wall ( da Costa et al. 1994). Several deep surveys are on-going (Koo et al. in progress and test the reproducibility of this periodicity on other areas of the sky. ) will The ESQ Key Programme: 'A Redshift Survey of galaxies with z :::; 0.6' (de Lapparent et al. 1989) aims to cover 0.4deg2 up to magnitude R :::; 20.5 at high southern galactic latitude, reaching an effective depth of about 1400h-1 Mpc. This survey should go about 15 times deeper than CfA and should provide the diameter and frequencyof distribution of the 'shells' evidenced in wide-angle nearby surveys.

The Canada-France Deep Redshift Survey (Crampton, Hammer, Le Fevre, Lilly 1994, Tresse et al. 1993) covers several 10' by 10' fields up to magnitude I :::; 22.1 ( � B :::; 23.5) providing a sample complete up to z � 1. Another important implication of the deep 'pencil beam' surveys is the spectrophotometric evolution of field galaxies (Coless et al. 1990, LDSS).

5 Statistical indicators

On flux-limited 2D and 3D catalogs, various statistical tools are used to characterize the density distribution. As a first approximation, the mass and galaxy fluctuations are often assumed to be related by a linear relation: linear biasing . The amplitude of large­ lip9/p9 = b/ipM/pM, ( ) scale fluctuations is now fixed by COBE, as well as a range for the index n of the spectrum of initial fluctuations (Smoot et al. 1992). Confrontation of the statistics from the data to the predictions of the models can be done at the light of COBE's results, setting severe limits on

the value of b and of n. 97

5.1 The two-point correlation fu nction The two-point correlation function has been the most popular statistical indicator since it was introduced by Peebles in the 70's to analyze the galaxy distribution. The spatial two-point cor­ relation function e(r) is directly connected to the power-spectrum by a Fourier transform, and so is very useful to confront the theoretical predictions from models of galaxy formation to data. From the 2D catalogs, the projected angular two-point correlation function w(li)is measured, which scales with the depth of the survey as w(li) = n-1w(liD) where Wis a function only of the shape of the catalog, so a comparison of w( li)for 2D catalogs with different flux limit is possible. The avaibility of flux-limited redshift catalogs has allowed to estimate the spatial cor- relation function. When the scales involved are sufficient to ignore the effect of random peculiar

velocities (above � 2h-1Mpc), the real space correlation function e(r) is approximated by the direction-averaged redshift correlation function with: , '12 which can e(s) 8 = (V,2+Vi-2��2cosB, ) be directly derived from the 3D redshift catalogs. The two-point correlation function is commonly estimated by weighted counts of the galaxy­ galaxy pairs DD(s) and of the galaxy-random pairs DR(s) in a random catalog with the same geometry as the galaxy one . DD(s) =I;; L:; w;w;Nvv and DR(s) =I;; L:; w;w;NvR· Then, 1 + This method has the great advantage of accounting directly e(s) = ��I:);;:. for edge effects. Several weighting schemes have been advocated : the uniform weighting , the selection function weighting, and the minimum variance weighting. The uniform weighting is generally used when working on complete sub-samples limited both in distance and in absolute magnitude, so of roughly constant density. When analysing magnitude-limited samples, one has to take into account the fall-offof the density with radial distance. In this case, the uniform weighting gives too much weight to foreground galaxies. A classical weighting is to multiply the contribution of each galaxy by the inverse of the selection function (Davis and Peebles,

1980) w; = 1/

w; = 1/47rp

0.1 10

Figure 2: From Maddox et al. 1990. The angular correlation function w(li)for magnitude limited sub-samples of APM scaled to Lick (filled symbols) compared to Groth and Peebles (1977) estimates on the Lick catalogue (open symbols), and to CDM models with h=0.5 (dotted line) and h=0.4 (solid line).

The correlation functionis however very difficult to measure correctly at large scales where fluctuations are small compared to the mean, and where it is limited by the uncertainty on the mean density.

The first estimation of w( Ii) was performed on the Lick catalog of counts by Groth and Peebles in 1977, showing a clear power law behaviour w(li) 111--r with = 1.77. On the oc 'Y CfA data, Davis and Peebles (1983), fixing the slope to = 1.77 found e(r) = (r/r0)--r with 1 r0 = 5.4 ± 0.3h-1 Mpc. The values of the slope and of the correlation length have not changed dramatically during the last ten years: s0 = 7.5h-1 Mpc and = -1.6 (de Lapparent et al. 'Y 1988 on the first two slices of the CfA2), from volume-limited sub-samples of the CfAl and SSRSl to 40 and 80h-1 Mpc, for = -1.8, r0 is equal to 6.0 and 8.0 (CfAl) and 6.4 and 7.5 1 (SSRSl) h-1 Mpc. The APM catalog, providing the angular positions of about 2 million galaxies, has allowed to improve the precision on w( Ii) and thanks to its depth to measure it up to large angular

separations, up to = 20° (Fig. 2). The power law is confirmed up to 3° with a slope = 1.668. Ii 'Y Above 3°, a break is apparent in w(B). At large scales, the data show an excess of power which cannot be reconciled with the standard CDM model. A recent analysis of the 3D Stromlo-APM redshift survey gives a slightly shallower slope = 1.34 ± .08 and s0 = 5.7 ± 0.8h-1Mpc. 'Y A derived statistic is the variance, the r.m.s. fluctuation in cells. The variance of galaxy 99

counts reaches unity at Sh-1 Mpc (Loveday et al. 1992), so in the context of linear bias, the � variance of mass fluctuations in Sh-1 Mpc boxes is directly connected to the bias factor b8 by 1/ . us = bs

5.2 Clustering in redshift space and in real space

The existence of peculiar velocities induces some distortion between the redshift and the real space distribution. At small scales (s ::; lh-1 Mpc) e(s) and e(r) can be very different and one has to compute the components of the correlation function parallel and perpendicular to the line of sight. The distribution of peculiar velocities can be approximated successfully by an exponential model: J(V) e:llp(-2112)� (Davis and Peebles 1983). The value of pairwise r.m.s. relative peculiar oc velocity is particularly interesting as it can be related to 0 through the cosmic virial theorem (Peebles 1980). It was estimated to be 340 ± 40km/s at lh-1Mpc (Davis and Peebles 1983 u = on the CfA). The small value of at small scales is in contradiction with the predictions from u the COBE normalized CDM model ( 970 ± 160km/ s, Bertschinger et al. 1990, Ostriker u = 1993). At large scales, where the coherent velocity field may be important, the redshift direction averaged correlation function is enhanced towards the real space one. In the frame of the linear perturbation theory, the multiplicative factor is a constant which does only depend on 0 (Kaiser 1987): e.(s) (1 + in1.2)e.(s). The anisotropy of the clustering pattern at large scales = �0°·6 + should then yield an independent way of determining n.

5.3 The Power Spectrum

The clustering at large scales is particularly interesting to quantify as this regime should be linked directly to initial conditions through the perturbation theory, without need to call for non-linear evolution. We noted previously that at these scales precisely where e(r) is small, its measurement is severely affected by local fluctuations of the mean density. In order to extract the statistical information on large scales, 3D statistics can be calculatedin the Fourier space as the Fourier components belonging to different wave vectors are statistically independent. The measurement of the power spectrum at one scale should then be independent of the measure­ ment at another scale, while the correlations on different scales are highly correlated. The power spectrum of the mass fluctuations today can be directly related to the angular power spectrum of the temperature fluctuations. Assuming the Harrison-Zeldovich formfor thepower spectrum 100

10'

'1 103 f

0.0 1 0.05 0.1 0.5

Figure 3: From Vogeley et al. 1992. The power spectrum for galaxy samples extracted from CfA2 (limited respectively to 100 and 145h-1 Mpc) compared to the predictions from models. From top to bottom: open Oh = 0.2 unbiased CDM (dashed line), standard Oh = 0.5 CDM with 1.4 and 1. cr8 = cr8 = of initial fluctuations k) Akn with n=l (in agreement with the first estimate from COBE P( = n = 1 ± 0.6, Smoot et al. 1992), the amplitude A is constrained by the RMS sky variation (Efstathiou et al. 1992): Qrms/To HJ OZ·77A112• So COBE fixes the amplitude of the power ex: spectrum at large scales (corresponding to wavenumbers k 0.0030g.oihMpc-1). From galaxy :S redshift surveys, the power spectrum is measured significantly for k 0.02hMpc -1 , so there is 2: nearly a factor 10 in scale between the higher scale tested and the scales involved by COBE. In order to link both measurements, one needs to extrapolate the power spectrum assuming a form dependent on the model. In the standard CDM frame, the normalization required to fit COBE data is = 1.1 ± 0.2 (Efstathiou et al. 1992), implying a low bias 0.9. cr8 b8 � The power spectrum has been widely measured on galaxy catalogs. Baumgart and Fry (1991) on the CfAl and on PPSS, Kaiser (1991) on the IRAS QDOT, Peacok and Nicholson (1991) on a sample of radio galaxies, Park et al. (1992) on the SSRS and CfAl. Vogeley et al. 1992 summarise the successive estimates and derives its value on the CfA2 (Fig. 3). This last analysis shows that the Oh 0.5 CDM model fails in reproducing the shape of = the power spectrum (Fig.3). This is independent of the normalization which can be set to fit or the small-scales, or the large-scales, but never both together, as the standard CDM power 101 spectrum shows too high a ratio of small scale over large scale power in confront to the data. Up to now, the open model with Oh = 0.2 and non-zero cosmological constant seems to fit the data, with all the critics that can be done to the 'fine-tuning' of A.

5.4 High order indicators

In order to describe the density distribution, the N-point correlation functions should be known up to high values of N. The first orders (up to N=4) can be calculated directly and show the existence of a 'hierarchical' relation, where the N-point correlation function is a sum of N 1 - products of 2-point correlation functions. Testing the existence of such a relation is very interesting as it reflects directly the type of initial fluctuations. For instance, in the case of non-Gaussian initial fluctuations, terms of higher order do appear. The information on high­ order correlation functions can be reached too calculating the moments (Bouchet et al. 1993 on IRAS), or through other indicators, like the Void Probability Function which involves indirectly correlations of all orders (Maurogordato and Lachieze-Rey 1987 on CfAl, Vogeley et al. 1991 on CfA2).

6 The velocity field

In parallel to the acquisition of redshift samples, the independent measurement of distances on still larger areas on the sky has strongly increased in the last five years. Empirical tight relations have been determined as the Tully-Fisher (for spiral galaxies) or the Dn for - u ellipticals and SO's (Dressler et al. 1988) and allowing to determine relative distance of the objects from the ratio between apparent and absolute luminosities . The main difficulty comes from the Malmquist bias which can affect seriously the extragalactic distance scale (Bottinelli et al. 1986). The radial peculiar velocities can then be deduced as = d. From the : v;;.c cz - pioneering samples of Burstein et al. (1987), a considerable effort has been endeavoured on the measurement of peculiar velocities, leading today to the compilation of more than 3000 galaxies (Faber et al. 1993). Large scale velocity gradients have been shown to exist, converging to very high density concentrations as the so-called 'Great Attractor' (Lyndell-Bell et al. 1988). From these data, through the POTENT method (Bertschinger and Dekel 1989), the dynamical field of velocity and mass-density fluctuations has been recovered (for a review see Dekel 1994). The main stages are to smooth the radial velocity field, to reconstruct the velocity field assuming a 102

Figure 4: By courtesy of A.Dekel, 1994, AnnualReview of Astronomy and Astrophysics. The Potent reconstructed mass density and velocity fluctuation fields. The Local Group is at the center. Large-scale flows (and overdensities) are apparent as Great Attractor (left), Pisces­ Perseus (right), Cetus Southern Wall (bottom), and the Great Wall (top). potential flowso the velocity potential can be calculated by integrating the radial component of the velocity along the line of sight, and the two other components obtained by differentiation. One can then derive the density field under the Zeldovich approximation. The mass density field recovered through the peculiar velocities can then be compared to the galaxy density field. The optical density maps (Hudson and Dekel 1993) and the IRAS 1.2 Jy density ones (Strauss et al. 1993) are strikingly similar to the potent mass density (Dekel et al.1992), showing the main high-density features as Pisces-Perseus, the Great Attractor, Cetus Southern wall.... This similarity makes sense to assume a linear bias between optical galaxies, IRAS galaxies and mass, Oopt boptO and OJRAS brnAsO. In the linear approximation where OPotent the = = ex !1°·66, confrontation of these density fields sets constraints on both optical and IRAS bias and on !10• From Strauss et al. 1993, !1°·6/brnAS 1.28±8:r� and from Hudson and Dekel 1993, /bIRAS = n°·6 0.5-0. 7. These results are fully consistent with an 1, bopt 1.5, brnAs 1 cosmology. = !1 = = =

7 Discussion and conclusion

The statistical analysis of galaxy surveys has provided quantified information which combined to COBE results allows to test models of formation of structures, variating the dark matter 103 components (Cold Dark Matter, Hot Dark Matter, Mixed Dark Matter), the type of initial fluctuations (for instance through the index of the primordial spectrum), and the parameter 0. From wide-angle redshift surveys, the shape and amplitude of the correlation functions, the low value of pair-wise dispersions argues against an 1 CDM standard Universe and rather n = to an open 0.2, 0 Universe, while the large scale dynamics from peculiar velocities n � A =f strongly rules out n :5: 0.3 and strongly favours high values of n. So, a consensus is still not reached. On the other side, very strong constraints come from galaxy clusters: both from the abundance of rich clusters and from the cluster-cluster correlation function (Bahcall and Cen 1992). Some variations to the standard CDM are developed to match the whole set of constraints, as lowering the index 0.8 ('tilted' spectrum), or adding hot neutrinos keeping n � 1 (Mixed Dark Matter, Davis et al. 1992), or introducing non-gaussiannity in the initial n = fluctuations (as 'texture' models). In future, the measurement of the power-spectrum at very large scales, on samples big enough to minimize the density fluctuations (as the Century Survey, Geller et al. in progress, or the Digital Survey Gunn and Knapp in progress), will be determinant. The progress of full sky catalogs in other wavelengths, like 2-mass and Denis at 2µm, com­ bined to optical redshift surveys and to the measurement of peculiar velocities will have great insights on the determination of the density field. Recent results (Lauer and Postman 1994) from a full-sky velocity survey of Abell clusters of galaxies within 15000 km/s, show that the Abell cluster frame is moving at 689 ± l 78km/ in respect to the CMB dipole, implying the s existence of high-density mass concentrations beyond lOOh-1 Mpc. On the side of CMB mea­ surements, the ground-based experiments at smaller angular scales will, combined to COBE, constrain more the index of the primordial spectrum.

8 Acknowledgments

I would like to thank all the authors who helped me a lot for the graphic task of this review, providing me postscript files or allowing me to use their graphs: Luiz da Costa, Margaret Geller and John Huchra for providing me the cone diagram of CfA2 and SSRS2, Avishai Dekel for the updated figure of the density and velocity maps, Stefan Maddox and Michael Vogeley. am grateful to Chantal Balkowski and to Alberto Cappi for reading this manuscript. 104

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