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If galaxy formation is a local process, then on large scales galaxies must trace mass. This requires the study of how galaxies populate DM halos. In simulations one attempts to track galaxy and DM halo evolution across cosmic time in a physically consistent way, providing positions, velocities, star formation histories and other physical properties for the galaxy populations of interest.

Guo & al. [46] use abundance matching arguments to derive an accurate relation between galaxy stellar mass and DM halo mass. They combine a stellar mass function based on spectroscopic observations with a precise halo/subhalo mass function obtained from simulations. Assuming this stellar mass - halo mass relation to be unique and monotonic, they compare it with direct observational estimates of the mean mass of halos surrounding galaxies of given stellar mass inferred from gravitational lensing and satellite galaxy dynamics data, and use it to populate halos in simulations. The stellar mass - halo mass relation is shown in Fig. 10..

Figure 10

Figure 10. Dark matter halo mass Mhalo as a function of stellar mass M. The thick black curve is the prediction from abundance matching assuming no dispersion in the relation between the two masses. Red and green dashed curves assume some dispersion in logM. The dashed black curve is the satellite fraction as a function of stellar mass, as labeled on the axis at the right-hand side of the plot. From Qi Guo & al. [46].

The implied spatial clustering of stellar mass turns out to be in remarkably good agreement with a direct and precise measurement. By comparing the galaxy autocorrelation function with the total mass autocorrelation function, as averaged over the Local Supercluster (LSC) volume, one concludes that a large amount of matter in the LSC is dark.

A similar study is that of Boyarsky & al. [47] who find a universal relation between DM column density and DM halo mass, satisfied by matter distributions at all observable scales in halo sizes from 108 to 1016 Msun, as shown in Fig. 11. Such a universal property is difficult to explain without dark matter.

Figure 11

Figure 11. Dark matter column density vs. dark matter halo mass in solar units. From A. Boyarsky & al. [47]

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