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We conduct a comprehensive and statistical study of the luminosity functions(LFs) for satellite galaxies, by counting photometric galaxies from HSC, DECaLSand SDSS around isolated central galaxies (ICGs) and paired galaxies from theSDSS/DR7 spectroscopic sample. Results of different surveys show very goodagreement. The satellite LFs can be measured down to $M_V\sim-10$, and forcentral 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--8satellites with $M_V<-10$ around LMC-mass ICGs. The bright end cutoff ofsatellite LFs and the satellite abundance are both sensitive to the magnitudegap between the primary and its companions, indicating galaxy systems withlarger magnitude gaps are on average hosted by less massive dark matter haloes.By selecting primaries with stellar mass similar to our MW, we discovered thati) the averaged satellite LFs of ICGs with different magnitude gaps to theircompanions and of galaxy pairs with different colour or colour combinations allshow steeper slopes than the MW satellite LF; ii) there are on average moresatellites with $-15<M_V<-10$ than those in our MW; iii) there are on average1.5 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 satellitesystem are statistically atypical of our sample of MW-mass systems. Inconsequence, our MW is not a good representative of other MW-mass galaxies.Strong cosmological implications based on only MW satellites await additionaldiscoveries of fainter satellites in extra-galactic systems. Interestingly, theMW satellite LF is typical among other MW-mass systems within 40~Mpc in thelocal Universe, perhaps implying the Local Volume is an under-dense region.

A comparative study of satellite galaxies in Milky Way-like galaxies from HSC, DECaLS and SDSS