tokens: We would like to thank the anonymous referee for the many constructive remarks and suggestions that greatly helped us to improve the content and layout of the paper. MS thanks Giulia Despali, Chiara Mancini, and Alessia Moretti for helpful discussions and hints. CC would like to thank Rosaria Tantalo and Emanuela Chiosi for valuable collaboration and the Department of Physics and Astronomy of the Padua University for the friendly hospitality and computational support. The tool HMFcalc and the public data from the ILLUSTRIS project have been amply used in this study.
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