Vol 44, No 1 (2018)

We study relation between stellar mass and halo mass for high-mass halos using a sample of galaxy clusters with accurate measurements of stellar masses from optical and ifrared data and total masses from X-ray observations. We find that stellar mass of the brightest cluster galaxies (BCGs) scales as M_*,BCG ∝ M₅₀₀^αBCG with the best fit slope of α_BCG ≈ 0.4 ± 0.1. We measure scatter of M_*,BCG at a fixed M₅₀₀ of ≈0.2 dex. We show that stellar mass-halo mass relations from abundance matching or halo modelling reported in recent studies underestimate masses of BCGs by a factor of ∼2−4. We argue that this is because these studies used stellar mass functions (SMF) based on photometry that severely underestimates the outer surface brightness profiles of massive galaxies. We show that M_*−M relation derived using abundance matching with the recent SMF calibration by Bernardi et al. (2013) based on improved photometry is in a much better agreement with the relation we derive via direct calibration for observed clusters. The total stellar mass of galaxies correlates with total mass M₅₀₀ with the slope of ≈0.6 ± 0.1 and scatter of 0.1 dex. This indicates that efficiency with which baryons are converted into stars decreases with increasing cluster mass. The low scatter is due to large contribution of satellite galaxies: the stellar mass in satellite galaxies correlates with M₅₀₀ with scatter of ≈0.1 dex and best fit slope of α_sat ≈ 0.8 ± 0.1. We show that for a fixed choice of the initial mass function (IMF) total stellar fraction in clusters is only a factor of 3−5 lower than the peak stellar fraction reached in M ≈ 10¹²M_⊙ halos. The difference is only a factor of ∼1.5−3 if the IMF becomes progressively more bottom heavy with increasing mass in early type galaxies, as indicated by recent observational analyses. This means that the overall efficiency of star formation in massive halos is only moderately suppressed compared to L_* galaxies and is considerably less suppressed than previously thought. The larger normalization and slope of the M_*−M relation derived in this study shows that feedback and associated suppression of star formation in massive halos should be weaker than assumed in most of the current semi-analytic models and simulations.

The Lidov–Kozai theory developed by each of the authors independently in 1961–1962 is based on qualitative methods of studying the evolution of orbits for the satellite version of the restricted three-body problem (Hill’s problem). At present, this theory is in demand in various fields of science: in the field of planetary research within the Solar system, the field of exoplanetary systems, and the field of high-energy physics in interstellar and intergalactic space. This has prompted me to popularize the ideas that underlie the Lidov–Kozai theory based on the experience of using this theory as an efficient tool for solving various problems related to the study of the secular evolution of the orbits of artificial planetary satellites under the influence of external gravitational perturbations with allowance made for the perturbations due to the polar planetary oblateness.