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ABSTRACT DARK MATTER George Lake Institute Of 331 DARK MATTER George Lake Institute of Astronomy Cambridge University ABSTRACT I review what is known about the form and distribution of dark matter as deduced from the internal dynamics and clustering of galaxies . From their internal dynamics, there are indications that later type galaxies have relative!) more dark mass . It is shown that all available evidence argues for the continuity of the galaxian two-point covariance function over a factor of roughly 103 - lkpc to 5h- 1Mpc) and a factor of in luminosity. in radius (Sh JOO Using velocity data on scales from 50h-lkpc to 10 Mpc and the Cosmic Virial Equation, the deduced value of is found to consistently lie in the range of Q 0.08 - 0.12. It is further argued that massive neutrinos are not consistent with this result as their maximum Jeans mass (the scale below which perturbations are erased by Landau damp ing) is 1000 galaxy masses even for a neutrino mass as large as 75eV. Instead of explaining� observed features of galaxies, they prevent their formation by any known process. 332 I. Introduction A theory of galaxy formation from first principles is greatly hampered by the elusiveness of the dark ma tter which pervades galactic haloes and clusters of galaxies. As if this isn' t bad enough , there is remarkab ly little infor­ mation about conditions in the universe at even a moderate redshift of one or two . This makes it exceedingly simp le to abandon the standard model and obtain all the observational consequences of the hot Universe theory from cold initial conditions (for examp le Zel'dovich and Starobinsky 1976, Carr 1977) . The standard model has unmi stakably aesthetic appeal and concrete successes - predictions of the microwave background , the helium abundance and perhaps now the entropy per baryon . Even more recently, the possibility that the neutrino -B has a finite mass of order 10 � has led to numerous discussions of its viability as the dark matter . I will review what is known about the form and the distribution of the dark matter from studies of the internal dynamics of galaxies and the clustering of galaxies . I think these features make it exceedingly imp lausible that the dark mass is neutrinos , though they do indicate that the dark mass is universal and perhaps linked to a very early cosmological epoch . II. Dark Matter in Galaxies a) Evidence for larger mass-to-light ratios The luminosity profiles of spiral galaxies betray two basic components ; a central bulge with a profile much like that of an elliptical galaxy surrounded by a disk with an exponential surface density (see Kormendy 1980 for a thorough review) . An examination of rotation curves prior to 1973 shows the peak expected from the central bulge and the broad maximum characteristic of the disk surface density. They were extrapolated (with dashed lines) as Kep lerian rotation profiles . Ostriker and Peebles (1973) found that rotationally-supported self­ gravitating systems are subject to large-scale bar instabilities , When app lied to Sc galaxies with large disk/bulge ratios , this indicated that a large fraction of the mass inside the observed axisynune tric disk must be in a pressure­ supported stab ilizing 11halo". Ro tation curves out to 5 disk scale lengths now exist for a large number of galaxies , and show constant or weakly rising ve locity with radius (see Faber and Gallagher 1979; hereafter F6) . In Sc galaxies, this yields a mass-to-light ratio (M/L ) of � 5, whereas B stellar population models (Larson and Tinsley 1978; hereafter LT) suggest a value of 2. 333 b) Where is the Mass ? One alternative for the observed increase in mass with radius has been a changing mass-to-light radius in the disk. The absence of strong color gradients have long suggested that the mass-to-light ratio should be constant with radius (see for example, Freeman 1970) , but there are even better dynamical arguments. The outer regions of galactic disks are often observed to be warped, appearing as hat brims when viewed edge-on. To prevent the precession time from being too short requires a potential which must be more spherical than that resulting from a disk (Saar 1978, Tubbs and Sanders 1979) . A more detailed analysis of bending waves (Bertin and Mark 1980, Lake and Mark 1980) indicates that the mass-to-light ratio is a constant . This is derived from a relationship between the height of bending and the surface density applied to our galaxy , NGC 2841 and M33; the three galaxies with adequate data for a comparison. Van der Kruit (1980) has examined the scale height of the neutral hydrogen in the edge-on galaxy NGC 891. The observed constancy of velocity dispersion with radius in face-on galaxies enables a calculation of the local surface density once the scale height is known . Van der Kruit finds a constant mass­ to-light ratio (M/L ) for the disk population of 3, about the same as the stellar B population of LT but considerably different from the total M/L of 8.2 (FG) . B A final method of constraining mass-to-light ratios in the disk population is to study the bar instability, The work of Ostriker and Peebles (1973) has been challenged on the grounds that it neglects the effects of resonances, anisotropic dispersion velocities and strongly varying velocity dispersions with radius (for recent discus sions see Toomre 1977 and Lake and Ostriker 1980) . Efstathiou, Negroponte and I (1981) have avoided most of these complications by simulating disks with exponential profiles in halos which reproduce the observed rotation curves . Our results yield a limit to the mass fraction which is in the disk (this is an upper limit for galaxies without bars, a lower limit for barred galaxies) , which with adequate photometry yields a limit to the mass-to­ light ratio for the disk. We find M/L � 1 for the disks of Sd galaxies , in B agreement with LT . c) Universality of Dark Matter Are all galaxies comprised of similar admixtures of luminous and dark material? Galaxies with rotation velocities between roughly 80 km/sec and 275 km/sec come in both barred and unbarred flavors . This indicates that, in the mean , they are only marginally stable which would imp ly that M(bulge halo) / & M(disk) is constant inside a few disk scale lengths . Since the later type 334 galaxies of this group (Sbc, Sc, Scd) have larger disk/bulge ratios , this may be an indicator that they have relatively more dark mass . Galaxies of still later Hubble type (Sd, Sdm, Sm) with rotation ve locities 75-80 km/sec are nearly all barred . This may be due to a lesser halo mass, � or due to a larger gas fraction; the criterion for gas stability being slightly different than for stars . A further ambiguity arises in that these smaller galaxies are nearly all satellites of larger galaxies. Flat rotation curves have also been observed in SO galaxies (cf. Illingworth 1981 and references therein) . The use of absorption lines for stellar rotation velocities greatly limits the radial extent of the measurements; but is indic­ ative of a changing mass-to-light ratio with distance . In elliptical galaxies , there is still greater ambiguity. Davies (1981) finds velocity dispersions decreasing with radius , indicating a constant mass­ to-ratio . Strangely, it seems that the most flattened ellipticals observed (e .g. NGC 4473 and NGC 4697) have flat velocity dispersion profiles . Perhaps anisotropies are accentuated in a collapse through a halo in the same manner as rotation (Fall and Efstathiou 1980) . In the large dominant galaxies in clusters of galaxies (designated cD galaxies), enormous changes in the mass-to-light ratios are seen, (see Matthews (1978) and Dressler (1980) for discussions on M87 and the cD in Abell 2029, respectively) . The results on these objects are more indicative of cluster dynami cs (stripping, cannibalism) than of any intrinsic trend of M/L with luminosity. Tinsley (1980) has also concluded that the relative amount of dark mass must be greater in late-type (bluer) galaxies . Her results depend on stellar population models and rather uncertain corrections for the mass in gas . She corrects for gas mass by examining the quantity M /(M 2 ) where luminous tot - �I ' is the mass of netural hydrogen , the 2 is a rough correction factor for �I mo lecular gas and M is calculated from stellar population models and luminous total luminosity. If one examines instead (Mluminous + 2MHI)/Mtot' the trend seen by Tinsley nearly vanishes . This seems like a more reasonable quantity, since the gas mass is distributed through the disk rather than like the dark matter. The above discussion makes it likely that the general trend is there , only difficult to discern through the uncertainty of population synthesis . (For a discussion of the cause of the observed correlation of MHI with type , see Efstathiou and Lake (1981).) III Clustering a) Continuity of the two-point correlation function The use of the galaxy covariance function c(r) (Totsuji and Kihara 1969; Peebles 1974) has provided a simple and powerful discription of the large-scale 335 distribution of matter (cf. Fall 1979; Peebles 1980) . Peebles and Hauser (1974) found that s (r) (defined as the fractional increase in the density of galaxies caused by the presence of a galaxy a distance r away ) is well-represented by a power law, (I) -I - I Over distances of 50h kpc < r <Sh Mpc (h is the Hubble constant in units of 100 km/s/Mp c ), 1.8 (Peebles and Hauser 1974) and r = (4 .2 ± 0.3)h-1Mpc y = e (Kirschner, Oemler and Schecter 1979; Peebles 1979) .
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