There is a correlation between the bulge mass of the three main galaxies of the Local Group (LG), i.e., M31, Milky Way (MW), and M33, and the number of their dwarf spheroidal galaxies. A similar correlation has also been reported for spiral galaxies with comparable luminosities outside the LG. These correlations do not appear to be expected in standard hierarchical galaxy formation. In this paper, and for the first time, we present a quantitative investigation of the expectations of the standard model of cosmology for this possible relation using a galaxy catalog based on the Millennium-II simulation. Our main sample consists of disk galaxies at the centers of halos with a range of virial masses similar to M33, MW, and M31. For this sample, we find an average trend (though with very large scatter) similar to that observed in the LG; disk galaxies in heavier halos on average host heavier bulges and a larger number of satellites. In addition, we study sub-samples of disk galaxies with very similar stellar or halo masses (but spanning a range of 2–3 orders of magnitude in bulge mass) and find no obvious trend in the number of satellites versus bulge mass. We conclude that, while for a wide galaxy mass range a relation arises (which seems to be a manifestation of the satellite number–halo mass correlation), for a narrow range there is no relation between number of satellites and bulge mass in the standard model. Further studies are needed to better understand the expectations of the standard model for this possible relation.
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