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We study satellite galaxy abundances by counting photometric galaxies from the Eighth Data Release of the Sloan Digital Sky Survey (SDSS/DR8) around isolated bright primary galaxies from SDSS/DR7. We present results as a function of the luminosity, stellar mass and colour of the satellites, and of the stellar mass and colour of the primaries. For massive primaries (log  M  ★ /M ⊙  &gt; 11.1) the luminosity and stellar mass functions of satellites with log  M  ★ /M ⊙  &gt; 8 are similar in shape to those of field galaxies, but for lower mass primaries they are significantly steeper, even accounting for exclusion effects due to the isolation criteria. The steepening is particularly marked for the stellar mass function. Satellite abundance increases strongly with primary stellar mass, approximately in proportion to expected dark halo mass. For log  M  ★ /M ⊙  &gt; 10.8, red primaries have more satellites than blue ones of the same stellar mass. The effect exceeds a factor of 2 at log  M  ★ /M ⊙  ∼ 11.2. Satellite galaxies are systematically redder than field galaxies of the same stellar mass, except around primaries with log  M  ★ /M ⊙  &lt; 10.8, where their colours are similar or even bluer. Satellites are also systematically redder around more massive primaries. At fixed primary mass, they are redder around red primaries. We select similarly isolated galaxies from mock catalogues based on the galaxy formation simulations of Guo et al. and analyse them in parallel with the SDSS data. The simulation reproduces all the above trends qualitatively, except for the steepening of the satellite luminosity and stellar mass functions with decreasing primary mass. Model satellites, however, are systematically redder than in the SDSS, particularly at low mass and around low‐mass primaries. Simulated haloes of a given mass have satellite abundances that are independent of central galaxy colour, but red centrals tend to have lower stellar masses, reflecting earlier quenching of star formation by feedback. This explains the correlation between satellite abundance and primary colour in the simulation. The correlation between satellite colour and primary colour arises because red centrals live in haloes which are more massive, older and more gas rich, so that satellite quenching is more efficient.

Satellite abundances around bright isolated galaxies