Balough et al., astro-ph/0801.0990, Figure 2

caption: The stellar mass fraction f∗= M∗,500/M500, including intracluster light, is shown as a function of total mass M500. The LM data (red squares) include a correction for ICL estimated from the GZZ data (circles). The two open circles represent clusters A2405 and APMC020, which are systems strongly affected by line-of-sight structure. The 1 error bars are

derived from the published uncertainties on M500, and the tilt reflects the correlated uncertainty in M500 and M∗,500/M500 as described in § 2.2. The horizontal, dotted line shows the global baryon fraction measured by WMAP3 (Spergel et al. 2007). The two solid lines show constant slopes of −0.35 and −0.05, for comparison with our most conservative theoretical lower limit, and the Bower et al. (2006) model prediction, respectively.

Based on LCDM simulations, the authors argue that the steepest slope you can get for the plotted relation is about -0.35; the observations suggest something more like -0.65.

The basic method is to assume a relation for M*/M500 as a function of M500, feed it into a collection of LCDM merger trees, and then look at the z~0 M*/M500--M500 relation that comes out : if you get too many groups/clusters with values of M*/M500 which are too high, then this model is inconsistent and can be ruled out; groups/clusters with values of M*/M500 which are too low need some in situ star formation to preserve the relation. Essentially, the 'mixing' that comes with merging halos of different masses leads to M*/M500 being more or less independent of M500 -- lots of merging leads to a flat slope. The steepest slope for which the authors find consistency is around -0.35, even allowing the relation to evolve. This appears to be consistent with one shallower data set, but not a deeper one.

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