The Missing Satellites Problem Is Real

If LambdaCDM (sometimes known as the Standard Model of Cosmology which stands for the cosmological constant of General Relativity plus cold dark matter) is correct and we have a simple, effectively collisionless single type of dark matter particle with effectively no non-gravitational interactions, then dark matter halo masses should obey a simple power law relationship between size and number per volume of space. 

In that paradigm, dark matter halos of any given size should have roughly proportionally sized galaxies in them. 

The image on the left is a rough sketch of what we would expect from LambdaCDM theory and the image on the right is a rough sketch of what we actually see (from the blog post linked below). The gap between the number of galaxies predicted and the number seen a lower masses is big and non-linear. 

Alternatively, is the expected dark matter halo frequency is matched to frequency with which we see observable matter in a galaxy, smaller galaxies have proportionately much more dark matter. 

 

They don't. The number of small galaxies observed is much smaller than the number of small dark matter halos expected. This is called the "missing satellites problem" because satellite galaxies in the vicinity of larger galaxies that are predicted to exist aren't seen by astronomers. 

Also, reversing the relationship, galaxies in which dark matter halos are particularly large don't have dark matter halos that are as large as expected.

The amount of dark matter inferred from dynamics is expected to occur naturally in MOND-like modified gravity theory (as predicted in the early 1980s), but one really has to grasp at straws to get Cold Dark Matter to behave the same way on a consistent basis. Mostly CDM astronomers are fighting hard to find ways that the data doesn't accurately portray reality, and not finding enough to bridge the gap.

It isn't an easy point to establish. 

There is a lot of uncertainty in the data.

The discrepancy for the Milky Way galaxy isn't as glaring as for the data set as a whole. 

Statistical assumptions that could support this possibility with the available data (like a high degree of scatter in the dark matter halo size-luminous matter amount relationship) have to be ruled out primarily because other empirical relationships, like the Tully-Fischer relation, that would also be affected by the same high scatter assumption, don't show the same amount of scatter. 

Small galaxies are going to be missed in astronomy observations more often than big ones, but the amount of bias that this could produce isn't strong enough to produce the observed disparity.

Stacey McGaugh explains all of this in his latest blog post. He closes with this analysis:

Having the satellite galaxies that inhabit subhalos be low in surface brightness is a necessary but not sufficient criterion. It is also necessary to have a highly non-linear stellar mass-halo mass relation at low mass. In effect, luminosity and halo mass become decoupled: satellite galaxies spanning a vast range in luminosity must live in dark matter halos that cover only a tiny range. This means that it should not be possible to predict stellar motions in these galaxies from their luminosity. The relation between mass and light has just become too weak and messy.

And yet, we can do exactly that. Over and over again. This simply should not be possible in LCDM.