A critical challenge to the cold dark matter (CDM) paradigm is that there are fewer satellites observed around the Milky Way than found in simulations of dark matter substructure. We show that there is a match between the observed satellite counts corrected by the detection efficiency of the Sloan Digital Sky Survey (for luminosities L≳ 340 L⊙) and the number of luminous satellites predicted by CDM, assuming an empirical relation between stellar mass and halo mass. The "issing satellites problem", cast in terms of number counts, is thus solved, and imply that luminous satellites inhabit subhalos as small as 10^7−10^8 M⊙.

I do like the "issing satellites problem". But I'm very skeptical of this claim.

Although there are hints that the luminous satellite distribution is anisotropic [6, 13, 16–18], we assume it is sufficiently isotropic and spherical to be separable.

No, there's no "hint", it just is. Look, you can see it for yourself :
There it is, big as life. You can't just pretend it might not exist. And corrections for the incompleteness of surveys and the zone of avoidance (where the Milky Way blocks the view) have already been made and found to be minor. Also, while I think the work of Kroupa, Ibata, Pawlowski et al. is just wrong in many regards for the claims of other satellite planes around other galaxies, not citing them at all doesn't seem right.

Star formation in low-mass halos has been demonstrated to be suppressed by reionization and feedback. The discovery of many new dwarfs below the luminosity limit of the classical dwarfs have also closed the gap, as has the understanding that completeness corrections for the new dwarfs are large. In this Letter, we show that such corrections imply that the number of satellite galaxies that inhabit the Milky Way is consistent with the number of luminous satellites predicted by CDM.

Yes, but this has been known since Simon & Geha 2007. You can solve the problem, with enough complexity. The difficult part is not showing that any solution exists (which is what I think they've done here), but that any particular solution is the correct one. You need to show that the parameters required for the explanation are the ones which are actually true in reality.

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