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The problems we list here mostly relate to properties of galaxies. The first ten are well established and are ordered such that those which are generic to any form of DM come before those specific to particular DM models. The last two are less well established observationally but are potentially just as thorny. The physics of galaxy formation is undeniably messy, creating scope for counter-arguments that may avert individual difficulties. We do not have space here to evaluate the many such arguments that have been advanced, but no combination of such ideas comes anywhere near to resolving all these problems.

  1. The ``disk-halo conspiracy'' (Bahcall & Casertano 1986) describes the absence of a feature in galaxy rotation curves at which the dominant source of central attraction changes from luminous matter to dark. Many galaxies are now known in which the rotation curve does drop somewhat at the edge of the visible disk (e.g. Casertano & van Gorkom 1991; Verheijen 1997; Bosma 1999), but it is extremely rare for the drop to exceed about 10%. Blumenthal et al. (1986) showed that a featureless rotation curve is expected if DM dominates galaxies right to their centers, but it is much harder to understand why the circular orbital speed from the luminous matter, which dominates the inner region (see Section 2), should be so similar to that from the DM at larger radii. For any galaxy dominated by stars in its center, initial conditions for the dark and luminous matter must be finely tuned to produce a flat rotation curve.

  2. Extreme low-SB galaxies lie on the same Tully-Fisher relation (TFR) derived from high-SB galaxies, with somewhat greater scatter (Zwaan et al. 1995; Sprayberry et al. 1995; McGaugh et al. 2000). Thus we observe similar circular speeds in all galaxies of a given luminosity, no matter how widely the luminous material is spread. This amazing result requires that the overall M/L of the galaxy rises with decreasing SB in just the right way so as to preserve a tight relation between total luminosity and circular speed. Either the true M/L of the stellar population changes with surface brightness, which seems unlikely (de Blok & McGaugh 1997), or the DM fraction rises as the luminous surface density declines. The needed variations would be minor if DM dominated in all galaxies, but since stars dominate the mass in the inner parts of high-SB galaxies (Section 2), eliminating the SB dependence again requires careful tuning.

  3. Sanders (1990), Milgrom (1998) and McGaugh (1999a) show that mass discrepancies begin to be detectable only when the acceleration drops below ~ 10-8 cm s-2. Any DM model must reproduce this characteristic acceleration scale over a wide range of galaxy sizes, but none has yet done so convincingly.

  4. Aside from the disk M/L, DM halo fits to rotation curves generally employ two extra parameters: e.g. the core radius and asymptotic velocity, or the scale radius and concentration index. Actual galaxy rotation curves do not require all this freedom, however, since they can be fitted with only the disk M/L as a parameter (e.g. Sanders & Verheijen 1998) when a modified gravitational force law of the MOND form (Milgrom 1983) is employed. Any DM model must therefore contain a physical mechanism that relates the halo parameters to the luminous mass distribution.

  5. A merging hierarchy causes the cooled baryonic fraction to lose angular momentum to the halo, making disks that are too small (Navarro & White 1994; Navarro & Steinmetz 1997). The predicted angular momentum of the disk is at least an order of magnitude less than that observed. The problem is only partially ameliorated (MacLow & Ferrara 1999; Navarro & Steinmetz 2000b) if some process (usually described as ``feedback from star formation'') prevents most of the gas from cooling until after the galaxy is assembled. While this difficulty is best known within the CDM context, merging protogalaxies in any hierarchical structure formation model with DM will involve chronic angular momentum loss to the halos (e.g. Barnes 1992).

  6. Every collapsed halo should manifest the same peak phase space density, fmax, if DM is collisionless, was initially homogeneously distributed, and had an initially finite fmax (Liouville's theorem). Further, the finite central density of galaxy halos (Section 2) both suggests that halos collapsed from material having in initially finite fmax (infinite initial phase space density forms cusped halos) and also allows fmax to be estimated easily. The spectacular variation of fmax between galaxies found by Sellwood (2000) and Dalcanton & Hogan (2000) indicates that DM cannot be a simple collisionless particle.

  7. High-resolution simulations that follow the formation and evolution of individual galaxy halos in CDM find strongly cusped density profiles (Moore et al. 1998; Klypin et al. 2000) even before the baryonic component cools and settles to the center. No observational evidence requires halos to have the predicted cusps. Further, the ``concentration index'' has a wide range (Bullock et al. 1999), but most fits to rotation curves yield values well below the predicted range in all types of galaxy (Section 2) - even the Milky Way (Navarro & Steinmetz 2000a).

  8. Navarro & Steinmetz (2000a) describe their failure to predict the zero-point of the TFR as a ``fatal problem for the LambdaCDM paradigm.'' They show that no matter what M/L is assumed for the disk, the predicted circular speed at a given luminosity is too high because the halo density is too high.

  9. Simulations produce numerous sub-clumps within large DM halos (Klypin et al. 1999; Moore et al. 1999). The clumps are more numerous than the numbers of observed satellite galaxies, and may threaten the survival of a thin disk in the host galaxy.

  10. The TFR discrepancy is even worse, since CDM predicts L propto V3 (Dalcanton, Spergel & Summers 1997; Mo, Mao & White 1998), whereas Verheijen (1997) stresses that when V is interpreted as the circular velocity of the flat part of the rotation curve, the true relation is very nearly L propto V4. Any mechanism which systematically boosts luminosity as a function of mass must also reproduce the very small scatter in the TFR.

  11. The DM halos that form in simulations are generally tri-axial (Dubinski & Carlberg 1991; Warren et al. 1992), but become nearly oblate in their inner parts when a disk is added (Dubinski 1994). Current constraints on halo shapes (Sackett 1999) are generally thought to be consistent with these predictions. However, the halo of NGC 2403 seems to become more nearly axisymmetrat larger radii (Schoenmakers 1998), opposite to the CDM expectation, and Franx et al. (1994) find IC 2006 to be impressively round at 6 Re. Much more data are needed to determine whether this behavior is typical or anomalous.

  12. The first precision measurements of the microwave background power spectrum at sub-degree scales show a second acoustic peak greatly suppressed compared to the first (de Bernardis et al. 2000; Hanany et al. 2000), producing an uncomfortable fit to standard cosmological models (e.g. Lange et al. 2000; Tegmark et al. 2000). McGaugh (1999b) has pointed out that unforced acoustic oscillations, as might be expected in the absence of dark matter potential wells, give such a peak height ratio.

Only three of these problems hinge on the properties mentioned in Section 2: If disks in bright galaxies are significantly sub-maximal, problem 1 would largely go away and 7 would be weakened (while 2 would be altered, not solved). If halos have mild density cusps, problem 6 would go away and 7 would again be weakened.

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