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tokens: ACKNOWLEDGEMENTS The authors thank Frank van den Bosch for insightful discussions and Shun Saito for helping us estimate the fraction of satellite galaxies in our sample. We also thank Felipe Ardilla and Christopher Bradshaw for useful comments. SH thanks Feng-Shan Liu for sharing the μ ⋆ profile of the z ∼ 1 BCG from his work. This material is based upon work supported by the National Science Foundation under grant no. 1714610. The HSC collaboration includes the astronomical communities of Japan and Taiwan, and Princeton University. The HSC instrumentation and software were developed by National Astronomical Observatory of Japan (NAOJ), Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), University of Tokyo, High Energy Accelerator Research Organization (KEK), Academia Sinica Institute for Astronomy and Astrophysics in Taiwan (ASIAA), and Princeton University. Funding was contributed by the FIRST program from Japanese Cabinet Office, Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan Society for the Promotion of Science (JSPS), Japan Science and Technology Agency (JST), Toray Science Foundation, NAOJ, Kavli IPMU, KEK, ASIAA, and Princeton University. Funding for SDSS-III has been provided by Alfred P. Sloan Foundation, the Participating Institutions, National Science Foundation, and U.S. Department of Energy. The SDSS-III website is http://www.sdss3.org . SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration, including University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, University of Cambridge, University of Florida, the French Participation Group, the German Participation Group, Instituto de Astrofisica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, New Mexico State University, New York University, Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington, and Yale University. The Pan-STARRS1 surveys (PS1) have been made possible through contributions of Institute for Astronomy; University of Hawaii; the Pan-STARRS Project Office; the Max-Planck Society and its participating institutes: the Max Planck Institute for Astronomy, Heidelberg, and the Max Planck Institute for Extraterrestrial Physics, Garching; Johns Hopkins University; Durham University; University of Edinburgh; Queen’s University Belfast; Harvard-Smithsonian Center for Astrophysics; Las Cumbres Observatory Global Telescope Network Incorporated; National Central University of Taiwan; Space Telescope Science Institute; National Aeronautics and Space Administration under grant no. NNX08AR22G issued through the Planetary Science Division of the NASA Science Mission Directorate; National Science Foundation under grant no. AST-1238877; University of Maryland, and Eotvos Lorand University. This paper makes use of software developed for the LSST. We thank the LSST project for making their code available as free software at http://dm.lsstcorp.org . This research was supported in part by National Science Foundation under grant no. NSF PHY11-25915 and grant no. NSF PHY17-48958 This research made use of STSCI_PYTHON , a general astronomical data analysis infrastructure in Python. STSCI_PYTHON is a product of the Space Telescope Science Institute, which is operated by Association of Universities for Research in Astronomy (AURA) for NASA; SciPy , an open source scientific tool for Python (Jones et al. 2001 ); NumPy , a fundamental package for scientific computing with Python (Walt, Colbert Varoquaux 2011 ); Matplotlib , a 2D plotting library for Python (Hunter 2007 ); Astropy , a community-developed core Python package for astronomy (Astropy Collaboration 2013 ); scikit-learn , a machine-learning library in Python (Pedregosa et al. 2011 ); astroML , a machine-learning library for astrophysics (Vanderplas et al. 2012 ); IPython , an interactive computing system for Python (Pérez Granger 2007 ); sep Source Extraction and Photometry in Python (Barbary 2016 ); palettable , colour palettes for Python; emcee , Seriously Kick-Ass MCMC in Python; Colossus , COsmology, haLO and large-Scale StrUcture toolS (Diemer 2015 ).