Direct Measurement of the H i-halo Mass Relation through Stacking

We thank the anonymous reviewer for the helpful comments that improve the presentation of this paper. We acknowledge the work of the entire ALFALFA team for observing, flagging, and performing signal extraction. We thank Benedikt Diemer for providing the gas properties from the Illustris and IllustrisTNG simulations. We also thank Carlton Baugh, Cheng Li, Zheng Zheng, Claudia Lagos, Garima Chauhan, and Adam Stevens for helpful discussions. This work is supported by the National Key R&D Program of China (grant No. 2018YFA0404503), National Science Foundation of China (Nos. 11773049, 11833005, 11828302, 11922305), and Spanish Science Ministry “Centro de Excelencia Severo Ochoa” program under grant SEV-2017-0709. M.G.J. is supported by a Juan de la Cierva formacion fellowship (FJCI-2016-29685). M.G.J. also acknowledges support from the grants AYA2015-65973-C3-1-R and RTI2018-096228-B-C31 (MINECO/FEDER, UE). M.P.H. acknowledges support from NSF/AST-1714828 and the Brinson Foundation. J.F. acknowledges the support by the Youth innovation Promotion Association CAS and Shanghai Committee of Science and Technology grant (No.19ZR1466700). This research was supported by the Munich Institute for Astro- and Particle Physics (MIAPP), which is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy C EXC-2094 C 390783311. Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England. The SDSS website is http://www.sdss.org/.