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tokens: We thank the members of the ENIGMA group at the MPIA, as well as the members of office 217, for the fruitful discussions and helpful comments. We thank the anonymous referee for carefully reading our manuscript and for insightful comments and suggestions that significantly improved the quality of this work. Special thanks to Martin White for providing us with collisionless simulations. Some data presented in this work were obtained from the Keck Observatory Database of Ionized Absorbers toward QSOs (KODIAQ), which was funded through NASA ADAP grants NNX10AE84G and NNX16AF52G, along with NSF award number 1516777. This research used resources of the National Energy Research Scientific Computing Center (NERSC), which is supported by the Office of Science of the U.S. Department of Energy under contract No. DE-AC02-05CH11231. Calculations presented in this paper used the hydra and draco clusters of the Max Planck Computing and Data Facility (MPCDF, formerly known as RZG). MPCDF is a competence center of the Max Planck Society located in Garching (Germany).