ACKNOWLEDGEMENTS This paper was based on the observation data collected at OHP Observatory, France. TM, TG, MP, and FKT are grateful for the support from the Swiss National Science Foundation, project SCOPES No. IZ73Z0152485. MP acknowledges significant support to NuGrid from NSF grant PHY-1430152 (JINA Center for the Evolution of the Elements) and STFC (through the University of Hull’s Consolidated Grant ST/R000840/1), and access to viper , the University of Hull High Performance Computing Facility. MP acknowledges the support from the ‘Lendlet-2014’ Programme of the Hungarian Academy of Sciences(Hungary), and from the BRIDGCE UK network. FKT acknowledges support from the European Research Council (FP7) under ERC Advanced Grant Agreement 321263 FISH. BC and MP acknowledges support from the ERC Consolidator Grant(Hungary) funding scheme (project RADIOSTAR, G.A. n. 724560) and from the National Science Foundation (USA) under grant No. PHY-1430152 (JINA Center for the Evolution of the Elements). This article is based upon work from the ChETEC COST Action (CA16117), supported by COST (European Cooperation in Science and Technology). TM thanks to S. Korotin for discussions. The authors appreciate very useful comments provided by the anonymous referee.

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We thank M. Auger for useful discussions. SS, GC, SHS, and AY thank the Max Planck Society for support through the Max Planck Research Group for SHS. This research was supported in part by Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through the Department of Innovation, Science and Economic Development and by the Province of Ontario through the Ministry of Research, Innovation and Science. The analysis is based on the following: (1) observations made with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. These observations were done in May 2010 with Proposal ID 11602 and in November 2011 with Proposal ID 12266; (2) observations obtained at the Gemini Observatory, 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).

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We are indebted to Brian Marsden, who performed the orbit calculations that made these observations possible. S.G. and J.C.R. thank the International Space Science Institute (Bern, Switzerland) for the opportunity to discuss this work within the International Study Team program. SOHO is a project of international cooperation between ESA and NASA. UVCS is a joint project of NASA, Italian Space Agency (ASI), and the Swiss Funding Agencies. LASCO was built by a consortium of the Naval Research Laboratory, USA; the Laboratoire d'Astrophysique de Marseille (formerly Laboratoire d'Astronomie Spatiale), France; the Max-Planck-Institut für Sonnensystemforschung (formerly Max Planck Institute für Aeronomie), Germany; and the School of Physics and Astronomy, University of Birmingham, UK. This work was supported by NASA grant NAG5-12814. Facility: SOHO (UVCS, LASCO)

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T.W. thanks Durham University Department of Mathematical Sciences for funding his Ph.D. studentship. A.R.Y. thanks STFC for financial support. A.R.Y. and G.J.D.P. thank ISSI, Bern for supporting their collaboration as part of an International Team on global magnetic modelling. A.M.J. is very grateful to George Fisher and Stuart Bale for their support at the University of California, Berkeley, and Phil Scherrer for his support at Stanford University. This research is partly funded by the NASA Grand Challenge grant NNH13ZDA001N and NASA LWS grant NNX16AB77G. Data were acquired by SOLIS instruments operated by NISP/NSO/AURA/NSF. We are grateful to David Hathaway for also supplying data for this study and to Ian Vernon for his invaluable statistical advice as well as to the anonymous referee for useful suggestions.

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We acknowledge useful conversations with Dan Coe on this topic, who has been attempting similar measurements on his triply imaged z ∼ 11 candidate. SMW acknowledges support from the Science and Technology Facilities Council. IL acknowledges support from the European Research Council grant HIGHZ no. 227749 and the Netherlands Organization for Scientific Research Spinoza grant. The Dark Cosmology Centre is funded by the Danish National Research Foundation.

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We would like to thank J.C. Augereau for providing the GraTeR code used to create our disk models. R. Asensio-Torres and M. Janson gratefully acknowledge funding from the Knut and Alice Wallenberg foundation. J. Carson acknowledges support via the US National Science Foundation under Award No. 1009203.

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S.B. thanks the Wihuri Foundation for continued funding throughout the project, the Finnish Cultural Foundation for funding the last part of the research, and the University of Turku Foundation and the StarryStory Foundation for funding travel related to the project. We are grateful for the help provided by Marina Rejkuba during the telescope application period and analysis of the 40 kpc NGC 5128 halo field, to Glen Mackie for very useful discussions, and for the care and interest taken by the referee during the reviewal process. This work has made use of BaSTI web tools.

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Acknowledgements Most of this work was made possible by support from the US National Science Foundation grant 09-68296 as well as National Aeronautics and Space Administration (NASA) Space Grants. One of us (JR) also thanks the Anton Pannekoek Astronomical Institute of the University of Amsterdam for their support. The Arecibo Observatory is operated by SRI International under a cooperative agreement with the US National Science Foundation, and in alliance with SRI, the Ana G. Méndez-Universidad Metropolitana and the Universities Space Research Association. This work made use of the NASA ADS astronomical data system. One of us (KS) thanks the US National Science Foundation for their support under the Physics Frontiers Center award number 1430284.

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A.I. and N.J.T. thank Mario Flock, Cornelis Dullemond, Thomas Henning, Wilhelm Kley, Wladimir Lyra, and Roy van Boekel for helpful discussions, and Ruobing Dong, Nienke Van der Marel, and Myriam Benisty for sharing images of SAO206463 and J1604. A.I. and N.J.T. acknowledge support from the NASA Origins of Solar Systems program through award NNX15AB06G and from the JPL Research Technology Development Program through award R.16.183.037. A.I. acknowledges support from the NSF Grants Nos. AST-1535809 and AST-1715718. This work was carried out in part at the Jet Propulsion Laboratory, California Institute of Technology, under contract with NASA.

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Acknowledgments We thank the anonymous referee for their constructive comments. AC (ORCID 0000-0003-4578-514X) acknowledges support from the UK Science and Technology Facilities Council (STFC) consolidated grant ST/L000652/1. MTS acknowledges support from a Royal Society Leverhulme Trust Senior Research Fellowship (LT150041). We acknowledge financial support from the Swiss National Science Foundation (AC, project PBEZP2_137312), from the Agence Nationale de la Recherche (AC and ElF, contract no. ANR- 12-JS05-0008-01) and from the E. C. through an ERC grant (AC and FB, StG-257720). GEM acknowledges support from the ERC Consolidator Grant funding scheme (project ConTExt, grant no. 648179) and a research grant (13160) from Villum Fonden. WR is supported by a CUniverse Grant (CUAASC) from Chulalongkorn University and JSPS KAKENHI grant no. JP15K17604. This paper makes use of the following ALMA data: ADS/JAO.ALMA#2013.1.01271.S. ALMA is a partnership of European Southern Obseratory (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. The research leading to these results has received funding from the European Commission Seventh Framework Programme (FP/2007-2013) under grant agreement no. 283393 (RadioNet3).

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We thank the anonymous referee for the very useful comments that improved the content and clarity of the manuscript. This work was partially supported by the Consejo Nacional de Investigaciones Cientficas y Tcnicas (CONICET, Argentina) and the Secretara de Ciencia y Tecnologa de la Universidad Nacional de Crdoba (SeCyT-UNC, Argentina). 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 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 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. This research has made use of NASAs Astrophysics Data System and Cornell University arXiv repository. We made an extensive use of the following python libraries: http://www.numpy.org/ , http://www.scipy.org/ , http://roban.github.com/CosmoloPy/ and http://www.matplotlib.org/ .

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Acknowledgements JLS and EJL acknowledge the support of the STFC. We thank members of the Institute of Astronomy Streams group for discussions and comments as this work was in progress. The anonymous referee is thanked for a number of helpful suggestions.

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ACKNOWLEDGEMENTS AO acknowledges support from the Deutsche Forschungsgemeinschaft (DFG) through the excellence cluster ‘The Hamburg Center for Ultrafast Imaging - Structure, Dynamics and Control of Matter at the Atomic Scale’ (CUI, EXC1074). SY acknowledges support from the COST action MOLIM No. CM1405. VS acknowledges the research project RVO:61388963 (IOCB) and support from the Czech Science Foundation (grant P209/15-10267S).

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We thank the enitre T’DA team for useful comments and discussions, in particular Andrew Tkachenko. We also acknowledge Marc Hon, Keaton Bell, and James Kuszlewicz for useful comments on the manuscript. L.B. and R.A.G. acknowledge the support from PLATO and GOLF CNES grants. S.M. acknowledges support by the Ramon y Cajal fellowship number RYC-2015-17697. O.J.H. and B.M.R. acknowledge the support of the UK Science and Technology Facilities Council (STFC). M.N.L. acknowledges the support of the ESA PRODEX programme (PEA 4000119301). Funding for the Stellar Astrophysics Centre is provided by the Danish National Research Foundation (Grant DNRF106).

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ACKNOWLEDGEMENTS This work is a part of the Project 176002 ‘Influence of collisional processes on astrophysical plasma line shapes’ supported by the Ministry of Education, Science and Technological Development of Serbia.

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Acknowledgements The authors thank the ESO staff for conducting the observations. We are grateful to D. Lachapelle for providing the spectra of HIP 78530 B and USco 1610-1913 B. We also thank J. Bouvier for advising us on accretion process and chromospheric activity effects. We acknowledge financial support from the Programme National de Planétologie (PNP), the Programme National de Physique Stellaire (PNPS) of CNRS-INSU in France, and the Agence Nationale de la Recherche (GIPSE project; grant ANR-14-CE33-0018). This research has made use of the SIMBAD database and VizieR catalogue access tool (operated at CDS, Strasbourg, France). This research has made use of NASA’s Astrophysics Data System and of the Extrasolar Planet Encyclopedia ( http:// exoplanet.eu/ ). This publication makes use of VOSA, developed under the Spanish Virtual Observatory project supported from the Spanish MINECO through grant AyA2017-84089. G-DM acknowledges the support of the DFG priority program SPP 1992 “Exploring the Diversity of Extrasolar Planets” (KU 2849/7-1).

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We would like to thank Thorsten Lisker for the valuable help and discussions during the whole FDS project. A.V. would like to thank the Vilho, Yrjö, and Kalle Väisälä Foundation of the Finnish Academy of Science and Letters for the financial support during the writing of this paper. GvdV acknowledges funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program under grant agreement No 724857 (Consolidator Grant ArcheoDyn). R.F.P., T.L., E.L., H.S., E.I., and J.J. acknowledge financial support from the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement No. 721463 to the SUNDIAL ITN network. H.S., E.L., and A.V. are also supported by the Academy of Finland grant n:o 297738. C.W. is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) through project 394551440. J.F-B acknowledges support from grant AYA2016-77237-C3-1-P from the Spanish Ministry of Economy and Competitiveness (MINECO).

O O O O O B-Person I-Person O O O O O O O O O B-Survey I-Survey B-Person O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O O O O O O O O B-Person O O O O B-Organization I-Organization I-Organization B-Organization O O B-Location I-Location B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O B-Grant I-Grant I-Grant I-Grant B-Grant I-Grant I-Grant B-Person B-Person B-Person B-Person B-Person O B-Person O O O O O B-Location I-Location B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O O B-Collaboration I-Collaboration I-Collaboration B-Person B-Person O B-Person O O O O O B-Organization I-Organization I-Organization B-Grant I-Grant I-Grant B-Person O O O O B-Organization I-Organization B-Organization B-Organization I-Organization I-Organization O B-Grant I-Grant B-Person O O O B-Grant I-Grant O O B-Location B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization


Studies of the evolution of hot gas in elliptical galaxies at UC Santa Cruz were supported during the earlier phases of this work by the NSF and are currently supported by a NASA-funded Chandra Theory Grant for which we are very grateful. F.B. is supported in part by the Prin MIUR grant 2010LY5N2T “The Chemical and Dynamical Evolution of the Milky Way and Local Group Galaxies.”

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The Arecibo Observatory is operated by SRI International under a cooperative agreement with the National Science Foundation (AST-1100968) and in alliance with Ana G. Méndez-Universidad Metropolitana and the Universities Space Research Association. Facilities : Planck , Arecibo, IRAS.

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We thank Hanno Rein, Daniel Tamayo, and Edmund Bertschinger for helpful discussions. DMH acknowledges support by an NSF Graduate Research Fellowship under grant no. 1122374.

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O O O O O O O B-Person I-Person O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O B-Location O B-Grant I-Grant O B-Grant O O O O O O O O O O O B-ComputingFacility I-ComputingFacility I-ComputingFacility O O B-Location B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O O O O O B-Collaboration B-Collaboration I-Collaboration I-Collaboration I-Collaboration I-Collaboration I-Collaboration I-Collaboration I-Collaboration I-Collaboration I-Collaboration O O O O O O O O O O O O O O O O O O O O O O B-URL O O O O O O O O O O O O O O O O O O O O O O O B-Collaboration O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


ACKNOWLEDGEMENTS We thank the referee Duncan Lorimer for constructive suggestions that improved this Letter and Prof. D. Li for helpful conversation. This work was supported by the Natural Science Foundation of China (Nos. 11603010, 11133001, 11333004, 11773015, and 11563003), the National Program on Key Research and Development Project (Grant No. 2016YFA0400803), and the Natural Science Foundation for the Youth of Jiangsu Province (No. BK20160611).

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ACKNOWLEDGEMENTS The authors would like to thank the anonymous referee for his/her detailed reading of our work and the many suggestions which improved this manuscript considerably. The authors gratefully acknowledge the Gauss Centre for Supercomputing e.V. ( www.gauss-centre.eu ) for funding this project by providing computing time on the GCS Supercomputer SuperMUC at Leibniz Supercomputing Centre ( http://www.lrz.de ) through project pr49zo, and the Leibniz Gemeinschaft for funding this project through grant SAW-2012-AIP-5 129.

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The authors thank Russell Keeney for his tireless efforts in maintaining and operating the OVRO 40 m Telescope. We thank Sterl Phinney and Shrinivas Kulkarni for useful discussions. The OVRO 40 m program has been supported by NASA grants NNG06GG1G, NNX08AW31G, NNX11A043G, and NNX13AQ89G and NSF grants AST-0808050, and AST-1109911. The Submillimeter Array is a joint project between the Smithsonian Astrophysical Observatory and the Academia Sinica Institute of Astronomy and Astrophysics and is funded by the Smithsonian Institution and the Academia Sinica. H. Vedantham is an RA and GB Millikan fellow of experimental physics. T. Hovatta was supported in part by the Academy of Finland project number 267324. R. Reeves gratefully acknowledges support from the Chilean Basal Centro de Excelencia en Astrofisica y Tecnologias Afines (CATA) grant PFB-06/2007. Facilities: OVRO:40 m, Keck:I (LRIS), Metsähovi Radio Observatory, SMA.

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Acknowledgments We would like to thank Aseem Paranjape, Sowgat Muzahid and Charles Danforth for useful discussion on statistics and observations. All the computations were performed using the PERSEUS cluster at IUCAA and the HPC cluster at NCRA.

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We wish to thank the anonymous referee for a careful reading and useful comments on our manuscript. The Kagoshima University 1 m telescope is a member of the Optical and Near-infrared Astronomy Inter-University Cooperation Program and supported by it. 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. 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. R.B. acknowledges support through the EACOA Fellowship from the East Asian Core Observatories Association.

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We would like to thank M. Serylak and the anonymous referee for useful comments which have improved this manuscript. NJY also acknowledges financial support from the South African SKA (SKA SA) project.

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This work is supported by NASA Origins of the Solar System grant No. NNX13AH79G. The authors thank A.A. Vidotto (Geneva) L. Fletcher (Glasgow) for providing helpful comments and suggestions. We would also like to thank the anonymous referee for feedback and thought-provoking questions on the manuscript.

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This project has received funding from the European Union’s Seventh Framework Programme for research, technological development, and demonstration under grant agreement no. 284515 (SHOCK). Website: project-shock.eu/home/. A.V. acknowledges the Interuniversity Attraction Poles Programme initiated by the Belgian Science Policy Office (IAP P7/08 CHARM). P.H. acknowledges grant P209/12/2023 of the Grant Agency of the Czech Republic. Computational resources were provided by CINECA (grant 2014 HP10CLF0ZB and HP10CNMQX2M).

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Acknowledgements The authors warmly thank Julien Milli, Grant Kennedy, and Jean-Charles Augereau for enlightening discussions.

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We thank the ISCRA staff for allowing us to perform our simulations on the Cineca Supercomputing Cluster GALILEO. We acknowledge P. F. Hopkins and G. Lodato for very useful discussion and comments on this work. E.R.C. acknowledges support by NASA through the Einstein Fellowship Program, grant PF6-170150. This work was also supported by the Packard grant and NASA ATP grant NNX14AH37G (ER). We also thank the referee, H. B. Perets, for valuable comments on the manuscript and very constructive suggestions.

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We acknowledge the CLUSTER FGM and EFW P.Is. and teams and the ESA Cluster Science Archive team for making the data used in this work available. The research leading to these results has received funding from the European Community’s Seventh Framework Programme ([FP7/2007–2013]) under grant agreement No. 313038/STORM. S.G. acknowledges support from the Agenzia Spaziale Italiana (ASI) under contract ASI-INAF n. I/022/10/2.

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This paper is based on observations made at the Laboratório Nacional de Astrofísica (LNA), Itajubá-MG, Brazil. The authors thank the referee Dr D. Pascu for his constructive comments. BM thanks the financial support by the CAPES/Brazil. MA thanks the CNPq (Grants 473002/2013-2 and 308721/2011-0) and FAPERJ (Grant E-26/111.488/2013). RVM acknowledges the following grants: CNPq-306885/2013, CAPES/Cofecub-2506/2015, FAPERJ/PAPDRJ-45/2013 and FAPERJ/CNE/05-2015. JIBC acknowledges CNPq for a PQ2 fellowship (process number 308489/2013-6). ADO is thankful for the support of the CAPES (BEX 9110/12-7) FAPERJ/PAPDRJ (E-26/200.464/2015) grants. ARGJ thanks CAPES/Brazil.

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We thank the anonymous referee for the useful comments and suggestions that improved the manuscript. G.B.C, G.R. and K.I.C. acknowledge funding from the European Research Council through the award of the Consolidator Grant ID 681627-BUILDUP. C.G. acknowledges support by VILLUM FONDEN Young Investigator programme grant 10123. A.M. acknowledges funding from the INAF PRIN-SKA 2017 programme 1.05.01.88.04. K.U. acknowledges support from the Ministry of Science and Technology of Taiwan (grant MOST 106-2628-M-001-003-MY3) and from Academia Sinica (grant AS-IA-107-M01). R.D. gratefully acknowledges support from the Chilean Centro de Excelencia en Astrofísica y Tecnologías Afines (CATA) BASAL grant AFB-170002 This research made use of Astropy, ( http://www.astropy.org ) a community-developed core Python package for Astronomy ( Astropy Collaboration 2013 , 2018 ). This work made use of the CHE cluster, managed and funded by ICRA/CBPF/MCTI, with financial support from FINEP (grant 01.07.0515.00 from CT-INFRA – 01/2006) and FAPERJ (grants E-26/171.206/2006 and E-26/110.516/2012). This work made use of data taken under the ESO programme IDs 186.A-0798, 095.A-0525, 096.A-0105, 096.A-0650, 097.A-0909 and 098.A-0590.

O O O O O O O O O O O O O O O B-Person B-Person O B-Person O O O O B-Organization I-Organization I-Organization O O O O O B-Grant I-Grant I-Grant I-Grant B-Person O O O B-Organization I-Organization B-Grant I-Grant I-Grant I-Grant I-Grant B-Person O O O O B-Organization B-Grant I-Grant I-Grant I-Grant B-Person O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Location B-Grant I-Grant I-Grant O O B-Organization I-Organization B-Grant I-Grant B-Person O O O O O B-Location B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization B-Grant I-Grant I-Grant O O O O O B-Software O B-URL O O O O B-Software O O O O B-Citation I-Citation I-Citation O B-Citation O O O O O O O B-ComputingFacility I-ComputingFacility O O O O B-Organization O O O O B-Organization B-Grant I-Grant O B-Organization O B-Grant O B-Organization B-Grant I-Grant O B-Grant O O O O O O O O O B-Observatory B-Proposal I-Proposal I-Proposal B-Proposal B-Proposal B-Proposal B-Proposal O B-Proposal


Acknowledgments We thank the anonymous referee for a helpful report that allowed us to improve the manuscript. We thank Arwa Dabbech, Chiara Ferrari, Ivan Marti-Vidal, Stephen Wilkins and Ilana Feain for useful discussions. DM acknowledges support from the Science and Technology Facilities Council (grant number ST/M503836/1). MTS acknowledges support from a Royal Society Leverhulme Trust Senior Research Fellowship. PPP is supported by an Ernest Rutherford Fellowship. JS was supported in part by ERC Project No. 267117 (DARK) hosted by Universit Pierre et Marie Curie (UPMC) Paris 6. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. This research made use of aplpy , an open-source plotting package for python hosted at http://aplpy.github.com . This research made use of astropy , a community-developed core python package for Astronomy (Astropy Collaboration 2013 ).

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We thank the anonymous referee for their careful reading and constructive comments that improved the presentation of our work. 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 and the VizieR catalog access tool, CDS, Strasbourg, France. D.C.L. acknowledges support from NSF grants AST-1009571 and AST-1210311, under which part of this research was carried out. This research was also supported by NSF grants AST-1210599 (UA) and AST-1210372 (U. Denver). Some observations reported here were obtained at the MMT Observatory, a joint facility of the University of Arizona and the Smithsonian Institution.

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C. A. M. is supported by an Irish Research Council Government of Ireland Postgraduate Scholarship. E. P. C. is supported by the European Commission Horizon 2020 INFRADEV-1-2017 LOFAR4SW project, no. 777442. We would like to acknowledge NOAA’s National Centers for Environmental Information SUVI team for providing data on the 2017 September 2 event, particular thanks to Dan Seaton for preparing the data. We are grateful to the GOES, Wind and LASCO teams for open access to their data. I-LOFAR received funding from Science Foundation Ireland (SFI) grant no. 15/RI/3204. ORFÉES is part of the FEDOME project, partly funded by the French Ministry of Defense. We would like to thank Pietro Zucca for his assistance with the Zucca et al. (2014a) model.

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We wish to thank our colleagues in the CANDELS, 3D-HST, and CLEAR collaborations for their intense work to make these data sets usable. The authors thank the anonymous referee for their constructive report, which improved the quality and clarity of this paper. We also thank them (and others) for productive conversations, comments, suggestions, and information, including Charlie Conroy, Romeel Davé, Sandy Faber, Kristian Finlator, Rob Kennicutt, Marcin Sawicki, Corentin Schreiber, and Sarah Wellons. V.E.C. acknowledges generous support from the Hagler Institute for Advanced Study at Texas AM University. This work benefited from generous support from George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy at Texas AM University. This work is based on data obtained from the Hubble Space Telescope through program number GO 14227. Support for program number GO 14227 was provided by NASA through a grant from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Incorporated, under NASA contract NAS5-26555.

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Data from observations are courtesy of NASA SDO /AIA and the HMI science teams. The computational work was carried out on TianHe-1 (A) at the National Supercomputer Center in Tianjin, China. This work is supported by the National Natural Science Foundation of China (NSFC 41822404, 41731067, 41574170, 41531073), the Fundamental Research Funds for the Central Universities (grant No. HIT.BRETIV.201901), and Shenzhen Technology Project JCYJ20170307150645407. C.J. and Q.H. also acknowledge NSF grant AGS-1650854 and NASA grant 80NSSC17K0016 for partial support. R.L. acknowledges support by NSFC 41474151, 41774150, and 41761134088. P.V. acknowledges support by an INSPIRE grant of the AORC scheme under the Department of Science and Technology of India. We are very grateful to the anonymous referee for his meaningful comments and suggestions.

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Acknowledgments We thank Igor Soszynski for providing calibrated OGLE light curves of stars in our field. This work made use of python routines based on gatspy and astroML methods. This project was supported by DGAPA-UNAM grant through project IN106615. DMB acknowledges NPRP grant X-019-1-006 from the Qatar National Research Fund (a member of Qatar Foundation). This work makes use of observations from the LCOGT network. This work has made a large use of the SIMBAD and ADS services.

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This paper arose, in part, out of discussions early on with Don VandenBerg, to whom the authors are grateful. SJ is a fellow of the Alexander von Humboldt Foundation. FH acknowledges funding through a Discovery Grant from NSERC. MP acknowledges support from the ‘Lendület-2014’ Programme of the Hungarian Academy of Sciences (Hungary) and from SNF (Switzerland). MP is also thankful for support from EuroGENESIS. MGB's research is supported by the US Department of Energy, Office of Nuclear Physics. BP is supported by the NSF under grants PHY 11- 25915, AST 11-09174, and ACI 13-39581.

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The authors are grateful to Makoto Sakuda and Tomonori Totani for valuable comments. We would also like to thank Yusuke Koshio for providing us the data of upper limits from Super-Kamiokande. In this work, numerical computations were partially performed on the supercomputers at Research Center for Nuclear Physics (RCNP) in Osaka University. This work was partially supported by Grants-in-Aids for the Scientific Research (No. 24105008, No. 26104006, No. 26105515, and No. 26870615) from MEXT in Japan.

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Acknowledgements The author is grateful to the referee, Lothar Frommhold, for his valuable remarks which contributed to improving the quality of this work, and to Burkhard Militzer for useful comments and to share numerical data used in Fig. 9 . Valuable comments from A. Dewaele and C. Iglesias are also acknowledged. This research was supported by the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET, Argentina) through grant no. PIP 114-201101-00208 and the Ministerio de Ciencia, Tecnología e Innovación Productiva (Argentina) through Grant No. PICT 2016-1128.

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We would like to thank Jonathan Gair, James Guillochon, and Alberto Sesana for useful discussions and suggestions. C.J.H. acknowledges support from CIERA though a visiting pre-doctoral fellowship and a travel grant from the RAS. F.A. was supported by a CIERA postdoctoral fellowship and from a NASA Fermi Grant NNX15AU69G. We acknowledge the use of computing resources at CIERA funded by NSF PHY-1126812.

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ACKNOWLEDGEMENTS JC thanks the Science and Technology Facilities Council and the Royal Astronomical Society for their financial support. DA thanks the Royal Society, and the International Space Science Institute ( ISSI ) for its support. ND is supported by a Vidi grant from the Dutch Organisation for Scientific Research (NWO). TB acknowledges financial contribution from the agreement ASI-INAF n.2017-14-H.0 between Istituto Nazionale di Astrofisica (INAF) and the Agenzia Spaziale Italiana (ASI). The authors acknowledge the use of astropy (Astropy Collaboration et al. 2013 ), numpy (Jones et al. 2001 ), and matplotlib (Hunter 2007 ) libraries for python . We also acknowledge the use of public data from the RXTE (Bradt et al. 1993 ) archive, as well as FTOOLS (Blackburn 1995 ) for data manipulation. Results provided by the ASM/ RXTE teams at MIT and at the RXTE Science Operations Facility and Guest Observer Facility at NASA’s Goddard Space Flight Centre.

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This research has made use of data obtained with NuSTAR , a project led by the California Institute of Technology, managed by the Jet Propulsion Laboratory, and funded by NASA. We thank the NuSTAR Operations, Software and Calibration teams for support with the execution and analysis of these observations. This research has made use of the NuSTAR Data Analysis Software (NuSTARDAS) jointly developed by the ASI Science Data Center (ASDC, Italy) and the California Institute of Technology (USA). Support for this work was provided by the National Aeronautics and Space Administration through Chandra Award Number GO6-17080X issued by the Chandra X-ray Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of the National Aeronautics Space Administration under contract NAS8-03060. This research has made use of software provided by the Chandra X-ray Center (CXC) in the application package ciao . We also acknowledge the use of public data from the Swift data archive. D.J.W. acknowledges support from an STFC Ernest Rutherford Fellowship. Facilities: Chandra (ACIS) , NuSTAR , Swift (XRT).

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The authors would like to thank the anonymous referee for their very constructive comments. LG thanks R. Valiante for the invaluable support during the gamete refactoring and re-engineering. SS acknowledges support from the Netherlands Organization for Scientific Research (NWO), VENI grant 639.041.233. RS, AM and SS wish to thank the Osservatorio Astrofisico di Arcetri where the project was originally conceived and developed in successive meetings. The authors acknowledge Andrea Ferrara and Benedetta Ciardi for their very constructive comments. We also thank the 4C Institute at the Scuola Normale Superiore of Pisa for the computational resources necessary to develop and test gamesh . We also acknowledge PRACE 9 for awarding us access to the CEA HPC facility CURIE@GENCI 10 under the Type B project: High Performance Release of the gamesh Pipeline. The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP/2007-2013)/ERC Grant Agreement no. 306476.

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ACKNOWLEDGEMENTS We thank the referee for the useful comments that improved the quality of the work. This project has received funding from the European Unions Horizon 2020 research and innovation programme under grant agreement No.607254; this publication reflects only the authors view, and the European Union is not responsible for any use that may be made of the information contained therein. SD acknowledges support from the Science and Technology Facilities Council (grant number ST/M503836/1). SO acknowledges support from the Science and Technology Facilities Council (grant number ST/L000652/1). We would like to thank M. P. Viero for his very useful help with the simstack code. The Herschel spacecraft was designed, built, tested, and launched under a contract to ESA managed by the Herschel or Planck Project team by an industrial consortium under the overall responsibility of the prime contractor Thales Alenia Space (Cannes), and including Astrium (Friedrichshafen) responsible for the payload module and for system testing at spacecraft level, Thales Alenia Space (Turin) responsible for the service module, and Astrium (Toulouse) responsible for the telescope, with in excess of a hundred subcontractors SPIRE has been developed by a consortium of institutes led by Cardiff University (UK) and including University of Lethbridge (Canada); NAOC (China); CEA, LAM (France); IFSI, University of Padua (Italy); IAC (Spain); Stockholm Observatory (Sweden); Imperial College London, RAL, UCL-MSSL, UKATC, University of Sussex (UK); and Caltech, JPL, NHSC, University of Colorado (USA). This development has been supported by national funding agencies CSA (Canada); NAOC (China); CEA, CNES, CNRS (France); ASI (Italy); MCINN (Spain); SNSB (Sweden); STFC, UKSA (UK); and NASA (USA).

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We thank the referee for comments that help us to improve the manuscript. We acknowledge the 2011 PRIN-INAF grant for financial support. We acknowledge the financial support of the UnivEarthS Labex program at Sorbonne Paris Cité (ANR-10-LABX-0023 and ANR-11-IDEX-0005-02). G.G. thanks the Observatoire de Paris (Meudon) for support and hospitality during the completion of this work. We thank S. Campana and G. Tagliaferri for contributing to useful discussions.

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Acknowledgments This research was supported by projects GOA/2015-014 (2014-2018 KU Leuven) and the Interuniversity Attraction Poles Programme by the Belgian Science Policy Office (IAP P7/08 CHARM) The computational resources and services used in this work were provided by the VSC (Flemish Supercomputer Center), funded by the Research Foundation Flanders (FWO) and the Flemish Government department EWI. BR likes to thank Lorenzo Sironi, Fabio Bacchini, Norbert Magyar, Jannis Teunissen, Kirit Makwana, Matthieu Leroy and Dimitris Millas for fruitful discussions and comments.

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DM would like to thank Philip Massey, Scott Adams, Michael Fausnaugh, Rubab Khan, Ben Shappee and Obright Lorain for helpful discussions that contributed greatly to this paper. We also wish to thank the anonymous referee, who provided numerous useful comments and aided the betterment of this manuscript. Based on observations made with the NASA GALEX . Some of the data presented in this paper were obtained from the Mikulski Archive for Space Telescopes (MAST). STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. Support for MAST for non-HST data is provided by the NASA Office of Space Science via grant NNX13AC07G and by other grants and contracts. Some/all of the data presented in this paper were obtained from the Mikulski Archive for Space Telescopes (MAST). STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. Support for MAST for non-HST data is provided by the NASA Office of Space Science via grant NNX09AF08G and by other grants and contracts.

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Acknowledgements The authors thank the referee for their very useful comments. This work has been financially supported by the Programme National Hautes Energies (PNHE), project 994584. LO and AN thank Integrated Activities in the High Energy Astrophysics Domain project for support that enabled this work. L.O. acknowledges support from the DLR grant 50 OR 1612. TB was supported by the FNP grant TEAM/2016-3/19. LO and TB thank Kavli Institute for Theoretical Physics, University of California, where this project have been initiated, for their support. This research has made use of the SIMBAD database, the VizieR catalogue access tool, operated at CDS, Strasbourg, France, and 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. The scientific results reported in this article are based to a significant degree on the data obtained from the Chandra and XMM-Newton Data Archives.

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EC acknowledges the support of the Royal Astronomical Society via a RAS Research Fellowship. EC would like to thank Ajinkya Patil, Cathryn Trott, Jonathan Pritchard, Geraint Harker and Harish Vedantham for useful discussions. FBA acknowledges the support of the Royal Society via a University Research Fellowship. VJ would like to thank the Netherlands Foundation for Scientific Research (NWO) for financial support through VENI grant 639.041.336. The work involving oskar was performed using the Darwin Supercomputer of the University of Cambridge High Performance Computing Service ( http://www.hpc.cam.ac.uk/ ), provided by Dell Inc. using Strategic Research Infrastructure Funding from the Higher Education Funding Council for England and funding from the Science and Technology Facilities Council.

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J-M M acknowledges financial support from the Spanish Ministerio de Economía y Competitividad (grants AYA2013-40979-P, and AYA2013-48226-C3-2-P) and from the local Autonomous Government (Generalitat Valenciana, grant Prometeo-II/2014/069). The author also acknowledges fruitful discussions with Professors J. A. Miralles and M. Perucho, and the anonymous referee for comments and criticism that helped to improve this manuscript.

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ACKNOWLEDGEMENTS We are grateful to the anonymous referee for his/her thoughtful and constructive comments which enabled us to improve the first edition of this paper. This work has been supported financially by Research Institute for Astronomy and Astrophysics of Maragha (RIAAM) under research project No. 1/6275-1.

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C. S. Peri and P.B. are supported by the ANPCyT PICT-2012/00878. P.B. also acknowledges support from CONICET PIP 0078 and UNLP G11/115 projects. This publication makes uses 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. We thank the SIMBAD database, operated at CDS, Strasbourg, France, and 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. We also thank the HubbleSite, which is produced by the Space Telescope Science Institute (STScI). STScI is operated by the Association of Universities for Research in Astronomy, Inc. (AURA) for NASA, under contract with the Goddard Space Flight Center, Greenbelt, MD. The Hubble Space Telescope is a project of international cooperation between NASA and the European Space Agency (ESA). We thank 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). Finally, we appreciate the suggestions of A. Noriega-Crespo, and insightful discussions with M. V. del Valle and L. J. Pellizza. We thank the anonymous AA referee for comments and suggestions that improved the article.

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OSIRIS was built by a consortium of the Max-Planck-Institut für Sonnensystemforschung, Göttingen, Germany, CISAS-University of Padova, Italy, the Laboratoire d’Astrophysique de Marseille, France, the Instituto de Astrofísica de Andalucia, CSIC, Granada, Spain, the Research and Scientific Support Department of the European Space Agency, Noordwijk, The Netherlands, the Instituto Nacional de Técnica Aeroespacial, Madrid, Spain, the Universidad Politéchnica de Madrid, Spain, the Department of Physics and Astronomy of Uppsala University, Sweden, and the Institut für Datentechnik und Kommunikationsnetze der Technischen Universität Braunschweig, Germany. VIRTIS was built by a consortium from Italy, France, and Germany, under the scientific responsibility of IAPS, Istituto di Astrofisica e Planetologia Spaziali of INAF, Rome, which lead also the scientific operations. The VIRTIS instrument development for ESA has been funded and managed by ASI (Italy), with contributions from Observatoire de Meudon (France) financed by CNES and from DLR (Germany). The VIRTIS instrument industrial prime contractor was former Officine Galileo, now Finmeccanica in Campi Bisenzio, Florence, Italy. The support of the national funding agencies of Germany (DLR), France (CNES), Italy (ASI), Spain (MEC), Sweden (SNSB), and the ESA Technical Directorate is gratefully acknowledged.

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ACKNOWLEDGEMENTS We thank the referee for helpful comments and suggestions that have improved this manuscript. We thank Kathryn Disher for her helpful discussion. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE1255832. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation. This research has made use of the National Aeronautics and Space Administration Exoplanet Archive, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program.

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The authors acknowledge the anonymous referees for their valuable suggestions that have helped to improve this paper. The authors are also grateful to Takahiro Sumi for providing the MOA-II survey data. SA gratefully acknowledges the support from the Thai Government Scholarship and the University of Manchester President's Doctoral Scholar Award.

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Acknowledgments We thank an anonymous referee for comments that improved this paper. The Australia Telescope Compact Array (ATCA) is part of the Australia Telescope National Facility that is funded by the Australian Government for operation as a National Facility managed by CSIRO. This paper includes archived data obtained through the Australia Telescope Online Archive ( http://atoa.atnf.csiro.au ). This research has made use of the SIMBAD data base (Wenger et al. 2000 ), operated at CDS, Strasbourg, France. This research has made use of the VizieR catalogue (Ochsenbein, Bauer Marcout 2000 ) access tool, CDS, Strasbourg, France.

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Acknowledgements All calculations are run on MPCDF clusters Draco and Cobra. We thank Anish Amarsi for kindly providing us with the H collision rates computed using the Kaulakys recipe. This study is supported by SFB 881 of the DFG (subprojects A05, A10) and by the Research Council of Norway through its Centres of Excellence scheme, project number 262622. S.A.Y. and A.K.B. gratefully acknowledge support from the Ministry for Education and Science (Russian Federation), projects No. 3.5042.2017/6.7, 3.1738.2017/4.6. J.L. has received support through a grant from the Knut och och Alice Wallenberg foundation (2016.0019). Funding for the Stellar Astrophysics Centre is provided by The Danish National Research Foundation (Grant agreement no.: DNRF106). B.P. is partially supported by the CNES, Centre National d’Etudes Spatiales.

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