A comparative study of satellite galaxies in Milky Way-like galaxies
  from HSC, DECaLS and SDSS
  We conduct a comprehensive and statistical study of the luminosity functions
(LFs) for satellite galaxies, by counting photometric galaxies from HSC, DECaLS
and SDSS around isolated central galaxies (ICGs) and paired galaxies from the
SDSS/DR7 spectroscopic sample. Results of different surveys show very good
agreement. The satellite LFs can be measured down to $M_V\sim-10$, and for
central primary galaxies as small as $8.5<\log_{10}M_\ast/M_\odot<9.2$ and
$9.2<\log_{10}M_\ast/M_\odot<9.9$, implying there are on average 3--8
satellites with $M_V<-10$ around LMC-mass ICGs. The bright end cutoff of
satellite LFs and the satellite abundance are both sensitive to the magnitude
gap between the primary and its companions, indicating galaxy systems with
larger magnitude gaps are on average hosted by less massive dark matter haloes.
By selecting primaries with stellar mass similar to our MW, we discovered that
i) the averaged satellite LFs of ICGs with different magnitude gaps to their
companions and of galaxy pairs with different colour or colour combinations all
show steeper slopes than the MW satellite LF; ii) there are on average more
satellites with $-15<M_V<-10$ than those in our MW; iii) there are on average
1.5 to 2.5 satellites with $M_V<-16$ around ICGs, consistent with our MW; iv)
even after accounting for the large scatter predicted by numerical simulations,
the MW satellite LF is uncommon at $M_V>-12$. Hence the MW and its satellite
system are statistically atypical of our sample of MW-mass systems. In
consequence, our MW is not a good representative of other MW-mass galaxies.
Strong cosmological implications based on only MW satellites await additional
discoveries of fainter satellites in extra-galactic systems. Interestingly, the
MW satellite LF is typical among other MW-mass systems within 40~Mpc in the
local Universe, perhaps implying the Local Volume is an under-dense region.
