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We employ a large sample of 20171 optically-selected groups and clusters at0.15 < z < 0.4 in the SDSS to investigate how the stacked stellar mass fractionvaries across a wide range of total mass, $M_{500}$. Our study improves uponprevious observational studies in a number of important ways, including havinga much larger sample size, an explicit inclusion of the intracluster light(ICL) component, and a thorough examination of the accuracy of our total massestimates via comparisons to simulations and weak lensing observations. We findthat the stellar mass fraction depends only weakly on total mass and that thecontribution of ICL to the total stellar mass fraction is significant(typically 20-40 per cent). Both of these findings are in excellent accordancewith the predictions of cosmological simulations. Under the assumption of aChabrier (Salpeter) IMF, the derived star formation efficiency($f_{star}$/$f_{b}$, where $f_b=\Omega_b/\Omega_m$) is relatively low at 8 percent (14 per cent) and is consistent with the global star formation efficiencyof semi-analytic models that reproduce the galaxy stellar mass function. Whenour measured stellar mass fractions are combined with the observed relationbetween hot gas mass fraction and total mass from X-ray observations, ourresults imply that galaxy groups have significantly lower baryon fractions thanmassive clusters. Ejection of gas due to energetic AGN feedback (most likely athigh redshift) provides a plausible mechanism for explaining the trends weobserve.

The similarity of the stellar mass fractions of galaxy groups and clusters