ACKNOWLEDGEMENTS MV is supported by INFN/PD51 Indark, PRIN-INAF, PRIN-MIUR, and ERC-StG (European Research Council-Starting Grant) ‘cosmoIGM’ grants under ERC Grant agreement 257670-cosmoIGM. TSK is supported by ERC-StG ‘cosmoIGM’. TSK also acknowledges the support from ‘NSF-AST118913’. CM wishes to thank D. Goz, E. Munari, and A. Zoldan for useful discussion. We are grateful to an anonymous referee who provided very useful comments that allowed us to clarify several points in the paper.

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ACKNOWLEDGEMENTS The Atmospheric Chemistry Experiment (ACE), also known as SCISAT, is a Canadian-led mission mainly supported by the Canadian Space Agency. EJRM is funded by a McGill Science Undergraduate Research Award. The authors thank Yi Huang for his insight on the ACE-FTS data and on stratospheric clouds, Mark Swain for the idea of investigating Earth’s sodium layer, and Emily Pass for her helpful comments on this work. We also thank Yan Bétrémieux, Tyler Robinson, and an anonymous referee for their comments, which significantly improved this work. NBC acknowledges funding from NSERC and FRQNT.

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We would like to thank the anonymous referee for very helpful comments, which help to improve the paper significantly. This work is partially supported by the National Key RD Program of China 2018YFA0404203 and 2018YFA0404204, NSFC grants U1738122, U1931204 and 11761131007, the Natural Science Foundation for Young Scholars of Jiangsu Province, China (No. BK20191109), and by the International Partnership Program of Chinese Academy of Sciences, grant No.114332KYSB20170008.

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ACKNOWLEDGEMENTS I thank P. Behroozi and C. Pacifici for the inspiring discussions to work on this, to B. Diemer, G. Lemson, Y. Feng for help in various steps of obtaining and analysing the data, and many others for conversations, comments, and questions, including S. Alam, M. van Daalen, N. Dalal, R. Dave, and A. Kravtsov. I also thank other participants at the Santa Barbara Galaxy-Halo connection workshop in June 2017, members of the Royal Observatory of Edinburgh, and participants at the Berkeley Center for Cosmological physics workshop and Nordita workshop in July 2017 for the opportunity to talk on this work and for their feedback and suggestions, and the Royal Observatory and Nordita for their kind hospitality. B. Diemer and C. Pacifici generously provided many helpful suggestions and criticisms of an earlier draft. I am especially grateful to M. White for innumerable discussions and suggestions, as well as encouragement. I also thank the referee for many helpful suggestions and questions. The Millennium simulation data bases used in this paper and the web application providing online access to them were constructed as part of the activities of the German Astrophysical Virtual Observatory (GAVO).

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ACKNOWLEDGEMENTS FUZ, MF, AGAJ, DRMC and CAA acknowledge funding through Fondecyt Regular No. 1180291 and BASAL Centro de Astrofisica y Tecnologias Afines (CATA) AFB-170002. MF acknowledges funding through the Concurso Proyectos Internacionales de Investigacion No. PII20150171 and Conicyt Quimal 170001. AGAJ acknowledges financial support from Carnegie Observatories through the Carnegie-Chile fellowship.

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This material is based upon work supported by the National Science Foundation under Grant No. AST 0507473.

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ACKNOWLEDGEMENTS We thank the anonymous referee for useful comments. We also thank A. Ballone, S. Gillessen and G. Hajdu for very helpful discussions. This work was partially developed while JC was on sabbatical leave at MPE. DC and JC acknowledge the kind hospitality of MPE, and funding from the Max Planck Society through a ‘Partner Group’ grant. We acknowledge support from CONICYT-Chile through FONDECYT (1141175) and Basal (PFB0609) grants. DC is supported by CONICYT-PCHA/Doctorado Nacional (2015-21151574).

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This research was supported by the Ministerio de Economía y Competitividad under project FIS2012-31079. We would like to thank the technical staff of the Calar Alto Observatory in Spain for all its help with the observations.

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This paper makes use of the following ALMA data: ADS/JAO.ALMA#2011.0.000010.SV. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), NSC and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ. We are grateful to Antonio Garufi for many discussions and for sharing his infrared polarization images. We thank Sebastian Stammler for insightful discussions on the effect of the CO snowline on dust and for showing us the results of his simulations in advance of publication. We thank the anonymous referee for the helpful comments. Part of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. The fits have been carried out on the computing facilities of the Computational Center for Particle and Astrophysics (C2PAP) as part of the approved project “Dust evolution in protoplanetary disks”. M.T. and L.T. are grateful for the experienced support by F. Beaujean (C2PAP). This work was partly supported by the Italian Ministero dell’Istruzione, Università e Ricerca through the grant Progetti Premiali 2012 – iALMA (CUP C52I13000140001).

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This work is supported by the Japan Society for the Promotion of Science KAKENHI grant numbers 16K17673 (S.K.), 26800100 (K.M.), 16K17667 (Y.S.). The work by K.M. is supported by the World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan.

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Acknowledgements We thank the anonymous referee for a number of good suggestions helping to improve the presentation of this work. This paper makes use of the following ALMA data: ADS/JAO.ALMA#2013.1.00955.S. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), NSC and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAOand NAOJ. The group of JKJ acknowledges support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No 646908) through ERC Consolidator Grant “S4F”. Research at the Centre for Star and Planet Formation is funded by the Danish National Research Foundation.

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Based on data products from observations made with ESO Telescopes at the La Silla Paranal Observatory under program ID 188.B-3002 and 193.B-0936. These data products have been processed by the Cambridge Astronomy Survey Unit (CASU) at the Institute of Astronomy, University of Cambridge, and by the FLAMES/UVES reduction team at INAF–Osservatorio Astrofisico di Arcetri. These data have been obtained from the Gaia -ESO Survey Data Archive, prepared and hosted by the Wide Field Astronomy Unit, Institute for Astronomy, University of Edinburgh, which is funded by the UK Science and Technology Facilities Council. This work was partly supported by the European Union FP7 program through ERC grant number 320360 and by the Leverhulme Trust through grant RPG-2012-541. We acknowledge the support from INAF and Ministero dell’Istruzione, dell’Università e della Ricerca (MIUR) in the form of the grant “Premiale VLT 2012”. The results presented here benefit from discussions held during the Gaia -ESO workshops and conferences supported by the ESF (European Science Foundation) through the GREAT Research Network Programme. S.F. and T.B. acknowledge the support from the New Milky Way project funded by a grant from the Knut and Alice Wallenberg foundation. C.L. gratefully acknowledges financial support from the European Research Council (ERC-CoG-646928, Multi-Pop, PI: N. Bastian). U.H. and A.J.K acknowledge support from the Swedish National Space Board (Rymdstyrelsen). The research of A.L. has been subsidized by the Belgian Federal Science Policy Office under contract No. BR/143/A2/BRASS. R.S. acknowledges support by the National Science Center of Poland through grant 2014/15/B/ST9/03981. C.A.P. is thankful for support from the Spanish Ministry of Economy and Competitiveness (MINECO) through grant AYA2014-56359-P. J.M. acknowledges support from the ERC Consolidator Grant funding scheme (project STARKEY, G.A. No. 615604). T.M. acknowledges financial support from Belspo for contract PRODEX Gaia -DPAC. S.G.S acknowledges the support by Fundação para a Ciência e Tecnologia (FCT) through national funds and a research grant (project ref. UID/FIS/04434/2013, and PTDC/FIS-AST/7073/2014). S.G.S. also acknowledge the support from FCT through Investigador FCT contract of reference IF/00028/2014 and POPH/FSE (EC) by FEDER funding through the program “Programa Operacional de Factores de Competitividade – COMPETE”. L.S. acknowledges support by the Ministry of Economy, Development, and Tourism’s Millennium Science Initiative through grant IC120009, awarded to The Millennium Institute of Astrophysics (MAS). M.Z. acknowledges support by the Ministry of Economy, Development, and Tourism’s Millennium Science Initiative through grant IC120009, awarded to The Millennium Institute of Astrophysics (MAS), by Fondecyt Regular 1150345 and by the BASAL CATA PFB-06. E.J.A. and M.T.C acknowledge the financial support from the Spanish Ministerio de Economía y Competitividad, through grant AYA2013-40611-P. S.Z. acknowledge the support from the INAF grant “PRIN INAF 2014”, “Star won’t tell their ages to Gaia , Galactic Archaelogy with wide-area asterosismic”. This research has made use of the WEBDA database, operated at the Department of Theoretical Physics and Astrophysics of the Masaryk University; of the TOPCAT catalogue handling and plotting tool ( Taylor 2005 ); of the Simbad database and the VizieR catalog access tool, CDS, Strasbourg, France ( Ochsenbein et al. 2000 ); and of NASA’s Astrophysics Data System.

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We wish to thank Roelof de Jong and Ned Taylor for valuable discussions, and Dustin Lang for making the WISE magnitudes of Lang et al. ( 2014 ) available for testing before their publication. We also wish to thank the anonymous referee for their helpful suggestions on presenting some aspects of our results. This work was partially supported by NSF-AST 1514835. This research has made use of NASA's Astrophysics Data System Bibliographic Services. This publication makes use of data products from the Wide-field Infrared Survey Explorer , which is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory/California Institute of Technology, funded by the National Aeronautics and Space Administration. This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation. Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and the US Department of Energy Office of Science. The SDSS-III web site is http://www.sdss3.org/ . SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, Carnegie Mellon University, University of Florida, the French Participation Group, the German Participation Group, Harvard University, the 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, Max Planck Institute for Extraterrestrial Physics, 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.

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V.A. acknowledges financial support from NASA/ Chandra grants GO3-14051X, AR4-15003X, NNX15AR30G, and NASA/ADAP grant NNX10AH47G. A.Z. acknowledges financial support from NASA/ADAP grant NNX12AN05G, and funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007–2013)/ERC Grant Agreement no. 617001. J.D., P.P., and T.G. acknowledge financial support from NASA contract NAS8-03060. M.S. acknowledges support by the the Deutsche Forschungsgemeinschaft through the Heisenberg Programme (SA 2131/3-1). S.L. acknowledges financial support from NASA/ADAP grant NNX14-AF77G. The OGLE project has received funding from the National Science Centre, Poland, Grant MAESTRO 2014/14/A/ST9/00121 to AU. We thank the anonymous referee for helpful comments and suggestions.

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The work of JHM and CK is supported by the Science and Technology Facilities Council (STFC), via studentships and a consolidated grant, respectively. The work of NSH is supported by NASA under Astrophysics Theory Program grants NNX11AI96G and NNX14AK44G. We would like to thank the anonymous referee for a helpful and constructive report, and we are grateful to A. F. Palah and B. T. Gaensicke for the IX Vel XSHOOTER data set. We would also like to thank J. V. Hernandez Santisteban, S. W. Mangham and I. Hubeny for useful discussions. We acknowledge the use of the IRIDIS High Performance Computing Facility, and associated support services at the University of Southampton, in the completion of this work.

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Acknowledgements The anonymous referee of our paper offered many helpful suggestions for improvement, and we thank him/her for performing such a careful review. We also thank Paolo Ventura and Sergio Cristallo for providing answers to our enquiries regarding the details of the ATON (Ventura) and FRUITY (Cristallo) model predictions and in some cases sending us additional output. We also appreciate the help provided by Gloria Delgado-Inglada concerning her group's recently updated ICFs. Portions of the UV data employed in our project came from HST programme number GO12600. BGS is grateful for summer support by the US National Science Foundation (NSF) through the Research Experience for Undergraduates programme. MMBB was supported by ANPCyT through grant PICT-2014-2708 and by a Return Fellowship from the Alexander von Humboldt Foundation. Finally, RBCH, BGS, KBK, and BB are grateful to their home institutions for travel support.

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ACKNOWLEDGEMENTS The authors thank the anonymous referee, Iain A. Steele, Phil James, Dan Hoak, David Bersier, and Hendrik van Eerten for useful comments. This research was supported by Science Technology and Facilities Council grants. GPL was partially supported by International Astronomical Union and Royal Astronomical Society grants.

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Acknowledgments We dedicate this paper to our colleague Y.Y. Zhang: we are indebted to her work (Zhang etal. 2011 ) for the analysis discussed in Paper I , on which this paper is based. We thank H. Ebeling for useful information about the ME-MACS sample and T. Reiprich for providing the concentration parameters of HIFLUGCS clusters.

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The current work benefited from discussions with visiting researchers at the institute for Solar Physics in Stockholm. The authors specially wish to thank Carlos Díaz Baso, Andrés Asensio Ramos, Marian Martínez Gonzalez, Lindsey Fletcher and Paulo Simões for useful advice on the presented work. We also wish to thank the anonymous referee for valuable comments which improved the content of the paper. We made use of routines by Rob Rutten to align SDO data with SST data. The observers thank Pit Sutterlin for support during the observing campaign at the SST. TL acknowledges financial support from the C HROMOBS project funded by the Knut and Alice Wallenberg Foundation. JdlCR is supported by grants from the Swedish Research Council (2015-03994) and the Swedish National Space Board (128/15) and has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (SUNMAG, grant agreement 759548). JdlCR and SD are also supported by the Swedish Civil Contingencies Agency (MSB). The inversions were performed on resources provided by the Swedish National Infrastructure for Computing (SNIC) at the High Performance Computing Center North at Umeå University. The Swedish 1 m Solar Telescope is operated on the island of La Palma by the Institute for Solar Physics of Stockholm University in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias. This research has made use of NASA’s Astrophysics Data System Bibliographic Services.

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Based on observations obtained at the Gemini Observatory (processed using the Gemini iraf package), which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the National Research Council (Canada), CONICYT (Chile), Ministerio de Ciencia, Tecnologa e Innovacin Productiva (Argentina), and Ministrio da Cincia, Tecnologia e Inovao (Brazil), and observations collected at the Centro Astronmico Hispano Alemn (CAHA), operated jointly by the Max-Planck Institut fr Astronomie and the Instituto de Astrofisica de Andalucia (CSIC). VVG acknowledges the Russian Science Foundation grant 14-12-01096. JM acknowledges funding from a Royal Society Science Foundation Ireland University Research Fellowship (No. 14/RS-URF/3219). AYK acknowledges support from the National Research Foundation (NRF) of South Africa and the Russian Foundation for Basic Research grant 16-02-00148. TJH is funded by an Imperial College Junior Research Fellowship. This research was supported by the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., on behalf of the international Gemini partnership of Argentina, Brazil, Canada, Chile, and the United States of America, and has made use of the NASA/IPAC Infrared Science Archive, which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration, the SIMBAD data base and the VizieR catalogue access tool, both operated at CDS, Strasbourg, France.

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We thank Willy Benz for insightful discussions. This work was supported in part by the European Research Council under grant 239605. This work has been carried out within the framework of the NCCR PlanetS supported by the Swiss National Science Foundation. The author acknowledges the financial support of the SNSF.

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We are grateful to Dr J. S. Jenkins for discussions that led to important improvements of this Letter. C.L. acknowledges the financial support of the Swiss National Science Foundation (SNSF). This research made use of Astropy 2 (Astropy Collaboration 2013) , and of the SIMBAD (Wenger et al. 2000) , VIZIER (CDS, Strasbourg, France) and NASA’s Astrophysics Data System databases.

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This work was supported by Australian Research Council grants ( DP0662810, DP1096533 ). The Mopra Telescope is part of the Australia Telescope and is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO. The University of New South Wales Mopra Spectrometer Digital Filter Bank used for these Mopra observations was provided with support from the Australian Research Council, together with the University of New South Wales, University of Sydney, Monash University and the CSIRO. We would like to thank the anonymous referee whose comments served to increase the quality of our manuscript and maximize the exploitation of our data.

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We would like to thank the anonymous referee for their detailed and helpful comments which improved the quality of this work.

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This work was supported by the National Research Foundation of Korea (NRF-2012 R1A2A1A 03670387). Facilities: Big Bear Solar Observatory

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Acknowledgements This work is supported by the European Community through the grant LENA (ERC StG no. 678282) within the H2020 Framework Program.

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ACKNOWLEDGEMENTS I thank R. Srianand and Neeraj Gupta for their invaluable comments and inputs, that helped in improving the paper significantly. I also thank the staff of the GMRT who have made these observations possible. The GMRT is run by the National Centre for Radio Astrophysics of the Tata Institute of Fundamental Research. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. Further, I acknowledge support from the Indo-French Centre for the Promotion of Advanced Research under Project 5504-B (PIs: N. Gupta, P. Noterdaeme). I thank the anonymous referee for a very helpful report that significantly improved the quality of the paper.

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Acknowledgements This article is dedicated to the memory of H.-J. Bode, J. G. Greenhill and O. Faragó for their long-standing support and participation to occultation campaigns. The work leading to these results has received funding from the European Research Council under the European Community’s H2020 2014-2020 ERC Grant Agreement n° 669416 “Lucky Star”. E.M. thanks support from Concytec-Fondecyt-PE and GA, FC-UNI for providing support during the 2012 July 18 occultation. B.S. thanks S. Para for partly supporting this research though a donation, J. P. Beaulieu for helping us accessing to the Hobart Observatory facilities and B. Warner, B. L. Gary, C. Erickson, H. Reitsema, L. Albert, P. J. Merritt, T. Hall, W. J. Romanishin, Y. J. Choi for providing data during the 2007 March 18 occultation. M.A. thanks CNPq (Grants 427700/2018-3, 310683/2017-3 and 473002/2013-2) and FAPERJ (Grant E-26/111.488/2013). J.L.O. thanks support from grant AYA2017-89637-R. P.S.S. acknowledges financial support from the European Union’s Horizon 2020 Research and Innovation Programme, under Grant Agreement no 687378, as part of the project “Small Bodies Near and Far” (SBNAF). J.L.O., R.D., P.S.S. and N.M. acknowledge financial support from the State Agency for Research of the Spanish MCIU through the “Center of Excellence Severo Ochoa” award for the Instituto de Astrofísica de Andalucía (SEV-2017-0709). F.B.R. acknowledges CNPq support process 309578/2017-5. G.B.R. thanks support from the grant CAPES-FAPERJ/PAPDRJ (E26/203.173/2016). J.I.B.C. acknowledges CNPq grant 308150/2016-3. R.V.M. thanks the grants: CNPq-304544/2017-5, 401903/2016-8, and Faperj: PAPDRJ-45/2013 and E-26/203.026/2015. B.M. thanks the CAPES/Cofecub-394/2016-05 grant and CAPES/Brazil – Finance Code 001. B.M. and A.R.G.J. were financed in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) – Finance Code 001. TRAPPIST-North is a project funded by the University of Liège, in collaboration with Cadi Ayyad University of Marrakech (Morocco). TRAPPIST-South is a project funded by the Belgian Fonds (National) de la Recherche Scientifique (F.R.S.-FNRS) under grant FRFC 2.5.594.09.F, with the participation of the Swiss National Science Foundation (FNS/SNSF). VSD, SPL, TRM and ULTRACAM are all supported by the STFC. K.G. acknowledges help from the team of Archenhold-Observatory, Berlin, and A.R. thanks G. Román (Granada) for help during the observation of the 2016 July 19 occultation. A.J.C.T. acknowledges support from the Spanish Ministry Project AYA2015-71718-R (including EU funds). We thank Caisey Harlingten for the repeated use of his 50 cm telescopes in San Pedro de Atacama, Chile. We thank the Italian Telescopio Nazionale Galileo (TNG), operated on the island of La Palma by the Fundación Galileo Galilei of the INAF (Istituto Nazionale di Astrofisica) at the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias. L.M. acknowledges support from the Italian Minister of Instruction, University and Research (MIUR) through FFABR 2017 fund and support from the University of Rome Tor Vergata through “Mission: Sustainability 2016” fund. The Astronomical Observatory of the Autonomous Region of the Aosta Valley (OAVdA) is managed by the Fondazione Clément Fillietroz-ONLUS, which is supported by the Regional Governmentof the Aosta Valley, the Town Municipality of Nus and the “Unité des Communes valdôtaines Mont-Émilius”. The research was partially funded by a 2016 “Research and Education”s grant from Fondazione CRT. We thank D.P. Hinson for his constructive and detailed comments that helped to improve this article.

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ACKNOWLEDGEMENTS Based on observations obtained with SITELLE, a joint project of Université Laval, ABB, Université de Montréal, and the Canada–France–Hawaii Telescope (CFHT), which is operated by the National Research Council of Canada, the Institut National des Sciences de l’Univers of the Centre National de la Recherche Scientifique of France, and the University of Hawaii. The authors wish to recognize and acknowledge the very significant cultural role that the summit of Mauna Kea has always had within the indigenous Hawaiian community. We are most grateful to have the opportunity to conduct observations from this mountain. We thank the referee for a very thorough and constructive report, leading to significant improvements on this paper. LD, CR, GJ, and ST are grateful to the Natural Sciences and Engineering Research Council of Canada, the Fonds de Recherche du Québec, and the Canada Foundation for Innovation for funding. LD and CR are very grateful to the Department of Physics and Astronomy, University of Hawaii Hilo, as well as the CFHT, for having provided them with an ideal and very enjoyable working environment during their sabbatical stay on the Big Island.

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T.L. thanks Cole Miller for helpful discussions and the referee(s) for their comments. S.G. is supported in part by NSF AAG grant 1616566. Partial support for T.L. was provided by NANOGrav NSF Physics Frontiers Center award No. 1430284. This research has made use of the VizieR catalog access tool, CDS, Strasbourg, France. This work makes use of observations from the LCO network. These results made use of the Discovery Channel Telescope at Lowell Observatory. Lowell is a private, nonprofit institution dedicated to astrophysical research and public appreciation of astronomy and operates the DCT in partnership with Boston University, the University of Maryland, the University of Toledo, Northern Arizona University, and Yale University. The LMI construction was supported by grant AST-1005313 from the National Science Foundation. The upgrade of the DeVeny optical spectrograph has been funded by a generous grant from John and Ginger Giovale. Based on observations obtained at the Gemini Observatory (acquired through the Gemini Science Archive and processed using the Gemini IRAF package), which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the National Research Council (Canada), CONICYT (Chile), Ministerio de Ciencia, Tecnología e Innovación Productiva (Argentina), and Ministério da Ciência, Tecnologia e Inovação (Brazil). The Pan-STARRS1 surveys (PS1) have been made possible through contributions of the IfA, the University of Hawaii, the Pan-STARRS Project Office, the Max Planck Society and its participating institutes, MPIA, Heidelberg and MPE, Garching, JHU, Durham University, the University of Edinburgh, QUB, the Harvard-Smithsonian CfA, LCOGT Inc., the National Central University of Taiwan, STScI, NASA under grant No. NNX08AR22G issued through the Planetary Science Division of the NASA Science Mission Directorate, the NSF under grant No. AST-1238877, the University of Maryland, and Eotvos Lorand University. Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and the U.S. Department of Energy Office of Science. The SDSS-III website is http://www.sdss3.org/ . The SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration, including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, Carnegie Mellon University, the University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofisica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, the Max Planck Institute for Astrophysics, the Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, Ohio State University, Pennsylvania State University, the University of Portsmouth, Princeton University, the Spanish Participation Group, the University of Tokyo, the University of Utah, Vanderbilt University, the University of Virginia, the University of Washington, and Yale University. Software: Astropy (Astropy Collaboration et al. 2013 ), create_fringes (Snodgrass Carry 2013 ), IRAF (Tody 1986 , 1993 ), remove_fringes (Snodgrass Carry 2013 ), SCAMP (Bertin 2006 ), SExtractor (Bertin Arnouts 1996 ), SWARP (Bertin et al. 2002 ).

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ACKNOWLEDGEMENTS We thank the referee for a constructive report which improved the manuscript. We are grateful to Richard Booth, Cathie Clarke, Ruth Murray-Clay, and Giovanni Rosotti for interesting discussions. JEO is supported by a Royal Society University Research Fellowship.

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ACKNOWLEDGEMENTS We thank Daniele Viganò for useful comments. This work is supported in part by the Spanish MINECO/FEDER grants AYA2015-66899-C2-1-P, AYA2015-66899-C2-2-P, the grant of Generalitat Valenciana PROMETEOII-2014-069, and by the PHAROS COST action CA16214. PC acknowledges the support from the Ramón y Cajal program of the Spanish MINECO (RYC-2015-19074).

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This material is based upon work supported by the National Science Foundation under grant AST-1614018 to C.W.M. and grants AST-1515876 and AST-1814440 to C.S.K. COSMOGRAIL is made possible thanks to the continuous work of all observers and technical staff obtaining the monitoring observations, in particular, at the Swiss Leonhard Euler telescope at La Silla Observatory, which is supported by the Swiss National Science Foundation. V.B. and F.C. are also supported by the Swiss National Science Foundation (SNSF). This work is partly based on observations obtained with the Small and Moderate Aperture Research Telescope System (SMARTS) 1.3 m, which is operated by the SMARTS Consortium. Thanks are due to V. Motta for helpful discussions about black hole masses and to R. Witt for many hours of help with the USNA High Performance Computing Cluster.

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Acknowledgements The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. Y.W., H.B., S.B., and J.D.S. acknowledge support from the European Research Council under the Horizon 2020 Framework Program via the ERC Consolidator Grant CSF-648505, and R.S.K. via the ERC AdvancedGrant 339177 (STARLIGHT). H.B., S.C.O.G., and M.R. acknowledge support from the Deutsche Forschungsgemeinschaft in the Collaborative Research Center (SFB 881) “The Milky Way System” (subproject B1, B2, B8). R.S.K. and S.C.O.G. also acknowledge support from the DFG via Germany’s Excellence Strategy EXC-2181/1 - 390900948 (the Heidelberg STRUCTURES Cluster of Excellence). This work was carried out in part at the Jet Propulsion Laboratory which is operated for NASA by the California Institute of Technology. N.S. acknowledges support by the french ANR and the german DFG through the project “GENESIS” (ANR-16-CE92-0035-01/DFG1591/2-1). F.B. acknowledges funding from the European Union’s Horizon 2020 research and innovation program (grant agreement No 726384). This research made use of Astropy and affiliated packages, a community-developed core Python package for Astronomy ( Astropy Collaboration 2018 ), Python package SciPy 3 , APLpy, an open-source plotting package for Python ( Robitaille Bressert 2012 ), and software TOPCAT ( Taylor 2005 ). The authors thank the anonymous referee for the constructive comments that improve the paper.

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We thank Sera Markoff, Heino Falcke, and Geoffrey Bower for constructive discussions and the anonymous referee for useful comments. This work was supported in part by the Natural Science Foundation of China (grants 11103061, 11133005, 11121062, and 11103059), the National Basic Research Program of China (973 Program, grant 2014CB845800), and the Strategic Priority Research Program “The Emergence of Cosmological Structures” of the Chinese Academy of Sciences (grant XDB09000000).

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We thank Marta Volonteri and Stefano Bovino for interesting discussions and helpful suggestions. The research leading to these results has received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/20072013 Grant Agreement no. 614199, project “BLACK”). DRGS is indebted to the Scuola Normale Superiore (SNS) in Pisa for an invitation as a “Distinguished Scientist”, which has stimulated the research described in this manuscript.

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We thank our collaborators as well as the anonymous referee for constructive comments that improved the paper. This work was supported in part by the National Aeronautics and Space Administration under grant number NNX15AU32H issued through the NASA Education Minority University Research Education Project (MUREP) through the NASA Harriett G. Jenkins Graduate Fellowship activity. R.C.H. acknowledges support from the National Science Foundation through CAREER grant number 1554584. This research has made use of NASA’s Astrophysics Data System.

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We wish to thank the anonymous referee for the extremely useful comments. Based on data products from observations made with ESO Telescopes at the La Silla Paranal Observatory under programme ID 188.B-3002. This work was partly supported by the European Union FP7 programme through ERC grant number 320360 and by the Leverhulme Trust through grant RPG-2012-541. We acknowledge the support from INAF and Ministero dell’Istruzione, dell’Università e della Ricerca (MIUR) in the form of the grant “Premiale VLT 2012”. The results presented here benefit from discussions held during the Gaia -ESO workshops and conferences supported by the ESF (European Science Foundation) through the GREAT Research Network Programme. We wish to thank C. Bailer-Jones and C. Babusiaux for extremely useful comments. M. Schultheis, A. Recio-Blanco, P. de Laverny, and V. Hill acknowledge the support of the “Programme National de Cosmologie et Galaxies” (PNCG) of CNRS/INSU, France. T.B. is funded by grant No. 621-2009- 3911 from the Swedish Research Council.

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We thank Karl Gebhardt, Georges Meylan, Ben MacLean and Sandro Villanova for sharing unpublished radial velocity data with us. We are also grateful to Long Wang for sending us data from his simulations. We finally thank Pouria Khalaj and two anonymous referees for comments that helped improve the presentation of the paper. This work has made use of BaSTI web tools.

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We thank Dmitrii Barsukov, Serge Balashev and Aida Kirichenko for discussions. The work was supported by the Russian Science Foundation, grant 14-12-00316. For Fig. 6 we used the data from the VGPS survey conducted by the National Radio Astronomy Observatory (NRAO) instruments. NRAO is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.

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This research was funded by the European Union’s Seventh Framework programme under grant agreement 337595 (ERC Starting Grant, “CoSMass”). A.F. wishes to acknowledge Finnish Academy award, decision 266918. This work was supported in part by the National Science Foundation under Grant No. PHYS-1066293 and the hospitality of the Aspen Center for Physics. This work is partly based on data products from observations made with ESO Telescopes at the La Silla Paranal Observatory under ESO programme ID 179.A-2005 and and 185.A-0791 and on data products produced by TERAPIX and the Cambridge Astronomy Survey Unit on behalf of the UltraVISTA consortium. This research has made use of NASA’s Astrophysics Data System, and the NASA/IPAC Infrared Science Archive, which is operated by the JPL, California Institute of Technology, under contract with the NASA. We greatfully acknowledge the contributions of the entire COSMOS collaboration consisting of more than 100 scientists. More information on the COSMOS survey is available at http://www.astro.caltech.edu/~cosmos . We thank the VUDS team for making the data in the COSMOS field available prior to public release.

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We would like to acknowledge the continual assistance with the Hyperion code from Dr. Thomas Robitaille and the useful discussions with Brian Kloppenborg and Kathy Geise. We thank the referee for useful comments and suggestions. This work was supported in part by the bequest of William Herschel Womble in support of astronomy at the University of Denver, as well as a Grant-In-Aid of Research from the National Academy of Sciences, administered by Sigma Xi, The Scientific Research Society, for which we are grateful.

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We thank the referee for comments that pushed us to improve the analysis of Sect. 3.3. S.C. warmly thanks the financial support by PRIN-INAF2014 (PI: S. Cassisi) and the Economy and Competitiveness Ministry of the Kingdom of Spain (grant AYA2013-42781-P). A.P. acknowledges financial support by PRIN-INAF 2012 The M4 Core Project with Hubble Space Telescope (P.I.: L. Bedin).

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ACKNOWLEDGEMENTS We are grateful to Ling Sun, Joe Romano, David Keitel, and Paul Schale for useful discussion and comments. We also thank Tyson Littenberg for insightful comments and suggestions that improved the paper. SB acknowledges support by the Hoff Lu Fellowship at the University of Minnesota, and by NSF grant PHY-1806630. MWC is supported by the David and Ellen Lee Postdoctoral Fellowship at the California Institute of Technology. PDL is supported by ARC Future Fellowship FT160100112 and ARC Discovery Project DP180103155. ET and CT are supported by CE170100004. ET is supported by FT150100281. The authors are thankful for the computing resources provided by LIGO Laboratory. LIGO was constructed by the California Institute of Technology and Massachusetts Institute of Technology with funding from the National Science Foundation and operates under cooperative agreement PHY-0757058. All posterior corner plots were made with ChainConsumer (Hinton 2016 ). The code for the analysis in this paper is available upon request. A public release is being planned for the near future. This paper has been assigned document number LIGO-P1900107.

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We greatly appreciate the lengthy conversations with Cole Miller regarding the development of the MCMC code. We thank the referee for carefully reading the manuscript and providing many helpful comments that led to its improvement. This research was supported in part by the Howard Hughes Medical Institute through the Undergraduate Science Education Program. We also are grateful for the generous support of the Michigan Space Grant Consortium, the National Science Foundation under Grant Nos. REU: PHY/DMR-1004811 and RUI: AST-1009731, the Fermi Guest Investigator Program Cycle 3 under Grant No. NNH09ZDA001N-FERMI3, and the NASA Astrophysics Theory and Fundamental Physics Program under Grant No. NNX13AO12G.

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S.K. and P.M.W. received funding through BMBF Verbundforschung (project MUSE-AO, grant 05A14BAC and 05A14MGA). S.K. further acknowledges support from DFG via SFB 963/1 “Astrophysical flow instabilities and turbulence” (project A12).

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ACKNOWLEDGEMENTS We would like to thank the referee for providing a clear, constructive, and concise report that greatly improved the interpretations presented here. We would also like to thank Karl Gordon for an enlightening discussion in the early stages of this work. KEH and PJ acknowledge support by a Project Grant (162948-051) from The Icelandic Research Fund. The Cosmic Dawn Center is funded by the Danish National Research Foundation (DNRF).

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It is a pleasure to thank the anonymous referee for their positive and helpful suggestions. NI thanks NSERC Discovery and Canada Research Chairs Program. SJ thanks the Chinese Academy of Sciences and National Science Foundation of China, project numbers 11250110055 and 11350110324. PhP thanks the Umezawa Fund for hospitality. This work was supported in part by the National Science Foundation under Grant no. NSF PHY11-25915, Grant no. PHYS-1066293 and the hospitality of the Aspen Center for Physics.

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The authors wish to thank Dr. Kevin Walsh and Dr. Dan Durda at SwRI Boulder, Dr. Dave Jewitt at UCLA, and Dr. Tony Dobrovolskis at SETI Institute for useful comments on the present work.

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This research is part of the project GLENCO, funded under the European Seventh Framework Programme, Ideas, Grant Agreement no. 259349. The analysis presented in this paper is based on observations made with the NASA/ESA Hubble Space Telescope , and obtained from the Hubble Legacy Archive, which is a collaboration between the Space Telescope Science Institute (STScI/NASA), the Space Telescope European Coordinating Facility (ST-ECF/ESA) and the Canadian Astronomy Data Centre (CADC/NRC/CSA).

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We thank Rodolfo Barniol Duran, Ehud Nakar, Re’em Sari, Elad Steinberg, and Almog Yalinewich for helpful discussions. J.K. and R.C. would like to thank the Hebrew University and its Institute for Advanced Studies for hospitality while the key ideas of this paper were developed. We are also grateful to Ehud Nakar for a loan of office space. This work was supported by the following grants: I-CORE 1829/12, ISA 3-10417 (T.P.); NSF AST-1028111 and AST-1516299, and NASA/ATP NNX14AB43G (J.K.).

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This research has been supported by the National Science Foundation under grants PHY 11-25915 and AST 11-09174. This project was also supported by JINA (NSF grant PHY 08-22648). FH and DV acknowledge funding from Natural Sciences and Engineering Research Council of Canada. PD is grateful to the staff of the Max-Planck-Institut für Astrophysik, where this project was completed, for their warm hospitality. We thank M. Salaris who has generously provided us with the Sbordone et al. bolometric corrections.

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ACKNOWLEDGEMENTS IB is supported by an Alexander von Humboldt postdoctoral fellowship. The authors are grateful for comments by the referee which greatly improved this manuscript. The algorithms were set up using matlab ® .

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F.D. and V.K. acknowledge support from grant NSF AST-1517753 and Northwestern University through the “Reach for the Stars” program. The authors also thank our colleagues Dimitri Veras, Jeremy Sepinsky, Michael Efroimsky, and Lorenzo Iorio who provided insight and expertise that greatly assisted the research. We are thankful for their comments that greatly improved the manuscript during its composition and revising stages.

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We thank Phil Armitage, Ilse Cleeves, Ilaria Pascucci, Richard Teague, and Upasana Das for useful discussions related to this work. We also thank the anonymous referee whose comments improved the quality of this paper. J.B.S. acknowledges support from NASA grants NNX13AI58G and NNX16AB42G, and from NSF grant AST 1313021. The computations were performed on Stampede , Stampede 2 , and Maverick through XSEDE grants TG-AST120062 and TG-AST140001. We thank the Kavli Institute for Theoretical Physics, supported in part by the National Science Foundation under Grant No. NSF PHY-1125915, for hospitality during the completion of the paper. Software: Athena (Stone et al. 2008 ).

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We would like to thank the late Prof. Janusz Gil for his leadership and inspiration, which have motivated us to start the MSPES project. We thank the referee for his comments, which helped to improve the paper. We thank Prof. Joanna Rankin and Dr. W. Lewandowski for critical comments on the manuscript. We would like to thank the staff of GMRT and NCRA for providing valuable support in carrying out this project. This work was supported by grants DEC-2012/05/B/ST9/03924 and DEC-2013/09/B/ST9/02177 of the Polish National Science Centre. This work has been supported by Polish National Science Centre grant DEC-2011/03/D/ST9/00656 (K.K.). This work was financed by the Netherlands Organisation for Scientific Research (NWO) under project ”CleanMachine” (614.001.301).

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ACKNOWLEDGEMENTS We thank Guillermo Barro for sharing Σ 1 values and Dale Kocevski for helpful advice. QN, GY, and WNB acknowledge support from Chandra X-ray Center grant GO8-19076X, NASA ADP grant 80NSSC18K0878, the V.M. Willaman Endowment, and Penn State ACIS Instrument Team Contract SV4-74018 (issued by the Chandra X-ray Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of NASA under contract NAS8-03060). DMA thanks the Science and Technology Facilities Council (STFC) for support from grant ST/L00075X/1. BL acknowledges financial support from the National Key RD Program of China grant 2016YFA0400702 and National Natural Science Foundation of China grant 11673010. FV acknowledges financial support from CONICYT and CASSACA through the Fourth call for tenders of the CAS-CONICYT Fund. YQX acknowledges support from the 973 Program (2015CB857004), NSFC-11890693,NSFC-11421303, the CAS Frontier Science Key Research Program (QYZDJ-SSW-SLH006), andK.C. Wong Education Foundation. The Chandra Guaranteed Time Observations (GTO) for the GOODS-N were selected by the ACIS Instrument Principal Investigator, Gordon P. Garmire, currently of the Huntingdon Institute for X-ray Astronomy, LLC, which is under contract to the Smithsonian Astrophysical Observatory via Contract SV2-82024.

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Acknowledgements We thank Zoltán Haiman and Kazuyuki Sugimura for useful discussions. This work is partially supported by the Simons Foundation through the Simons Society of Fellows (KI) and by Japan Society for the Promotion of Science Grant-in-Aid for Scientific Research (A) (17H01102 KO), for Scientific Research (C) (15K05036 KO; 16K05309 KO and 17K05383 SM)) and for Young Scientists (17K14260 HRT). This research was also supported by the Ministry of Education, Culture, Sports, Science and Technology as ‘Priority Issue on Post-K computer’ (Elucidation of the Fundamental Laws and Evolution of the Universe) and the Joint Institute for Computational Fundamental Science. Numerical computations were carried out on Cray XC30 at Center for Computational Astrophysics, National Astronomical Observatory of Japan.

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Acknowledgements This research has made use of data and software provided by the High Energy Astrophysics Science Archive Research Center (HEASARC), which is a service of the Astrophysics Science Division at NASA/GSFC and the High Energy Astrophysics Division of the Smithsonian Astrophysical Observatory. It is additionally based on observations obtained with XMMNewton , an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA. The research also made use of the Swift /BAT transient monitor results provided by the Swift /BAT team. We would like to thank all the proposers of the archival observations used in this work. We would also like to thank the anonymous referee for his/her suggestions, which helped improve the manuscript.

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We wish to thank Dick Manchester and George Hobbs for helpful discussion and suggestions. Furthermore, we thank Hao Tong and Mingyu Ge for communication on the latest progress on the time delay measurements of the Crab Pulsar. This research is supported by the National Natural Science Foundation of China, under the grant NSFC11373018 and NSFC11503006. We are also thankful for the support of the grant Beyond the Horizons 2012, and the support of the Strategic Priority Research Program of the Chinese Academy of Sciences Grant No. XDB23010200.

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