We investigate whether the satellite luminosity function (LF) of primary galaxies identified in the Sloan Digital Sky Survey (SDSS) depends on whether the host galaxy is in a filament or not. Isolated primary galaxies are identified in the SDSS spectroscopic sample while potential satellites (that are up to 4 magnitudes fainter than their hosts) are searched for in the much deeper photometric sample. Filaments are constructed from the galaxy distribution by the Bisous process. Isolated primary galaxies are divided into two subsamples: those in filaments and those not in filaments. We examine the stacked mean satellite LF of both the filament and non-filament sample and find that, on average, the satellite LFs of galaxies in filaments is significantly higher than those of galaxies not in filaments. The filamentary environment can increases the abundance of the brightest satellites ($M_mathrm{sat.} < M_mathrm{prim.} + 2.0$), by a factor of $sim 2$ compared with non-filament isolated galaxies. This result is independent of primary galaxy magnitude although the satellite LF of galaxies in the faintest magnitude bin, is too noisy to determine if such a dependence exists. Since our filaments are extracted from a spectroscopic flux-limited sample, we consider the possibility that the difference in satellite LF is due to a redshift, colour or environmental bias, finding these to be insufficient to explain our result. The dependence of the satellite LF on the cosmic web suggests that the filamentary environment may have a strong effect on the efficiency of galaxy formation.
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