We thank K. Dalmasse, S. Guidoni, A. Higginson, S. Masson, and K. Muglach for illuminating discussions and helpful suggestions, and we greatly appreciate J. Karpen's contribution of the artwork shown in Figure 1 . K.J.K. acknowledges support for this work by a cooperative agreement between the Catholic University of America and the NASA Goddard Space Flight Center, as well as additional funding received through the NASA Earth and Space Science Fellowship program. The participation of S.KA. and C.R.D. was sponsored by NASA's Heliophysics Theory and Supporting Research programs. The numerical simulations were supported by a grant of NASA High End Computing resources to C.R.D.

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The authors are grateful to the anonymous referee who provided a variety of insightful comments that helped to strengthen and clarify the results presented here.

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Acknowledgments We thank Georges Meynet for improving the paper as a referee. We also thank Zoltn Haiman, Takashi Hosokawa, Sylvia Ekstrm and Tilman Hartwig for useful discussions. This work is partially supported by the Simons Foundation through the Simons Society of Fellows (KI), Flatiron Fellowship (KH), by the Japan Society for the Promotion of Science (JSPS) research fellowship for young scientists (RH, No. 16J07613) and by JSPS KAKENHI Grant (TK, No. JP16818962).

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We thank Adam Ingram and Guglielmo Mastroserio for kindly providing the most recent reltrans model and for discussions on implementing it. B.M.C. and E.M.C. gratefully acknowledge support through NSF CAREER award No. AST-1351222. Software: XSPEC (v12.9.1; Arnaud 1996 ), reltrans (Mastroserio et al. 2018 , 2019 ; Ingram et al. 2019 ).

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We thank the anonymous referee for the careful reading of the manuscript and for the helpful comments. Based on data products from observations made with ESO Telescopes at the La Silla Paranal Observatory under programme ID 188.B-3002. 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 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. M.M. acknowledges financial support from the Italian Ministry of Education, University and Research (MIUR) through grant FIRB 2012 RBFR12PM1F, from INAF through grant PRIN-2011-1 and from CONACyT through grant 169554. The authors acknowledge the CINECA Award N. HP10B3BJEW, HP10CLI3BX, HP10CXB7O8, HP10C894X7, HP10CGUBV0, HP10CP6XSO and HP10C3ANJY for the availability of high performance computing resources and support.

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We thank David Marsh for stimulating discussions. This work is supported in part by the National Science Council of Taiwan under the grant MOST 103-2112-M-002-020-MY3.

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We warmly thank an anonymous referee for comments that helped improve the presentation of our results and Vincent Bouillot, Ravi Sheth, Andrea Lapi, Luigi Danese and Ignacio Trujillo for useful discussions.

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The authors thank J. Mauerhan for sharing his late-time spectra of SN 2013ej and S. Valenti for sharing his photometry of SN 2013by. CSB's research is supported in part by a Fellowship from Dartmouth’s School of Graduate and Advanced Studies. This paper includes data gathered with the 6.5 meter Magellan Telescopes located at Las Campanas Observatory, Chile. Archival observations of SNe were downloaded from the Open Supernova Catalog ( https://sne.space/ ).

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ACKNOWLEDGEMENTS The authors are grateful to an anonymous referee for valuable comments that helped to improve the manuscript. They also thank V. Afanasiev and R. Uklein for a collaboration. The observations at the 6-meter BTA telescope were carried out with the financial support of the Ministry of Education and Science of the Russian Federation (agreement No. 14.619.21.0004, project ID RFMEFI61914X0004). The reduction of the spectral data were supported by The Russian Science Foundation (RSCF) grant No. 17-72-20119. The estimate of the metallicity and its interpretaion were supported by Russian Foundation for Basic Research grant No. 18-32-20120. The authors acknowledge the usage of the HyperLeda database ( http://leda.univ-lyon1.fr ). Authors acknowledge the support from the Leading Scientific School in astrophysics (direction: extragalactic astronomy) at Moscow State University. Funding for the Sloan Digital Sky Survey IV has been provided by the Alfred P. Sloan Foundation, the U.S. Department of Energy Office of Science, and the Participating Institutions. SDSS-IV acknowledges support and resources from the Center for High-Performance Computing at the University of Utah. The SDSS web site is www.sdss.org . SDSS-IV is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS Collaboration including the Brazilian Participation Group, the Carnegie Institution for Science, Carnegie Mellon University, the Chilean Participation Group, the French Participation Group, Harvard-Smithsonian Center for Astrophysics, Instituto de Astrofísica de Canarias, The Johns Hopkins University, Kavli Institute for the Physics and Mathematics of the Universe (IPMU) / University of Tokyo, Lawrence Berkeley National Laboratory, Leibniz Institut für Astrophysik Potsdam (AIP), Max-Planck-Institut für Astronomie (MPIA Heidelberg), Max-Planck-Institut für Astrophysik (MPA Garching), Max-Planck-Institut für Extraterrestrische Physik (MPE), National Astronomical Observatories of China, New Mexico State University, New York University, University of Notre Dame, Observatário Nacional/MCTI, The Ohio State University, Pennsylvania State University, Shanghai Astronomical Observatory, United Kingdom Participation Group, Universidad Nacional Autónoma de México, University of Arizona, University of Colorado Boulder, University of Oxford, University of Portsmouth, University of Utah, University of Virginia, University of Washington, University of Wisconsin, Vanderbilt University, and Yale University.

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It is a pleasure to thank Jerry Sellwood, Barbara Pichardo and Jonathan Bird for helpful discussions during the course of this work. We thank the anonymous referee for comments which strengthened the discussion in this paper. This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under grant no. DGE-1232825 and National Science Foundation Grants AST-0908326 and OIA-1124403.

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H.D. acknowledges financial support from the Spanish Ministry of Economy and Competitiveness (MINECO) under the 2014 Ramón y Cajal program MINECO RYC-2014-15686. J.L.W. acknowledges support from an STFC Ernest Rutherford Fellowship. D.R. acknowledges support from the National Science Foundation under grant number AST-1614213. G.D.Z. acknowledges support from ASI/INAF agreement n. 2014-024-R.1. We pay special thanks to the useful feedback provided on the draft version of this work to D. Farrah, J. Greenslade, M. J. Michalowski, and I. Valtchanov. This research has made use of data from Her MES project ( http://hermes.sussex.ac.uk/ ). Her MES is a Herschel Key Programme utilizing Guaranteed Time from the SPIRE instrument team, ESAC scientists and a mission scientist. The H -ATLAS is a project with Herschel , which is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA. The H -ATLAS website is http://www.h-atlas.org . US participants in H -ATLAS acknowledge support from NASA through a contract from JPL. This publication is based on data acquired with the Atacama Pathfinder Experiment (APEX). APEX is a collaboration between the Max-Planck-Institut für Radioastronomie, the European Southern Observatory, and the Onsala Space Observatory. Based on observations made with APEX under European Southern Observatory program E-191.A-0748 and Max Planck Institute (MPI) programs M-090.F-0025-2012, M-091.F-0021-2013 and M-092.F-0015-2013. Facilities: APEX , Herschel .

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Acknowledgements The authors would like to thank the referee and the editor for careful reading and comments, which significantly improved this paper.

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R.L. thanks Andrew Wetzler, Wen-fai Fong, Mark Sullivan, Dan Milisavljevic, Giorgos Leloudas, Jesper Sollerman, and Ryan Chornock for useful discussions and acknowledges helpful interactions with Lars Bildsten, Eliot Quataert, and Dan Kasen at a PTF Theory Network retreat funded by the Gordon and Betty Moore Foundation through Grant GBMF5076. We thank J. Silverman, B. Dilday, J. Bloom, B. Sesar, D. Levitan, P. Groot, D. Perley, A. Horesh, K. Mooley, and D. Xu for assisting with the observations presented in this paper. The Intermediate Palomar Transient Factory project is a scientific collaboration among the California Institute of Technology, Los Alamos National Laboratory, the University of Wisconsin–Milwaukee, the Oskar Klein Center, the Weizmann Institute of Science, the TANGO Program of the University System of Taiwan, and the Kavli Institute for the Physics and Mathematics of the Universe. Support for HST Program GO-13864 was provided by NASA through a grant from the Space Telescope Science Institute, which is operated by the AURA, Inc., under NASA contract NAS 5-26555. We thank F. Yuan, M. Sullivan, D. Perley, R. M. Quimby, and S. B. Cenko for their contributions to the HST proposal. This work was supported by the GROWTH project funded by the National Science Foundation under Grant 1545949. The National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231, provided staff, computational resources, and data storage for this project. A.G.-Y. is supported by the EU/FP7 via ERC grant No. 307260, the Quantum Universe I-Core program by the Israeli Committee for planning and funding, and the ISF, Minerva and ISF grants, WIS-UK “making connections,” and Kimmel and YeS awards. A.V.F. is grateful for financial support from the Christopher R. Redlich Fund, the TABASGO Foundation, and NSF grant AST-1211916. D.A.H. and C.M. are supported by NSF grant AST-313484. 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. Some of the data presented herein were obtained at the W.M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W.M. Keck Foundation. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain. Facilities: PO:1.2m, PO:1.5m, PO:Hale, Keck:I, Keck:II, Subaru, HST .

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We thank the GMRT staff who have made these observations possible. The GMRT is run by the National Centre for Radio Astrophysics of the Tata Institute of Fundamental Research. N.K. acknowledges support from the Department of Science and Technology via a Swarnajayanti Fellowship (DST/SJF/PSA-01/2012-13). A.B. thanks Jayaram Chengalur and Prasun Dutta for useful discussions. We thank Mark Krumholz for discussions and much advice about the application of his model to our results, and an anonymous referee for detailed comments and suggestions on an earlier version of the manuscript.

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This project is financed by the SoMoPro II programme (3SGA5916). The research leading to these results received a financial grant from the People Programme (Marie Curie action) of the Seventh Framework Programme of the EU according to REA Grant Agreement No. 291782. The research is further co-financed by the South-Moravian Region. It was also supported by grant 7AMB14AT015 and the financial contributions of the Austrian Agency for International Cooperation in Education and Research (BG-03/2013 and CZ-09/2014). We thank the referee, Luca Fossati, for helpful comments and suggestions that helped to improve the paper. This work reflects only the author’s views so the European Union is not liable for any use that may be made of the information contained therein.

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Acknowledgments TS acknowledges financial support from the Japan Society for the Promotion of Science (JSPS) under grant numbers JSPS23103002, JSPS24253004 and JSPS26247023. NK is supported by Grant-in-Aid for JSPS Fellows. The MOA project is supported by JSPS grants JSPS25103508 and JSPS23340064 and by the Royal Society of New Zealand Marsden Grant MAU1104. NJR acknowledges the contribution of NeSI high-performance computing facilities to the results of this research. New Zealands national facilities are provided by the NZ eScience Infrastructure and funded jointly by NeSIs collaborator institutions and through the Ministry of Business, Innovation Employments Research Infrastructure programme ( https://www.nesi.org.nz ). The OGLE team thanks Prof. M. Kubiak and G. Pietrzyski, former members of the OGLE team, for their contribution to the collection of the OGLE photometric data over the past years. The OGLE project has received funding from the National Science Centre, Poland, grant MAESTRO 2014/14/A/ST9/00121 to AU. The Danish 1.54m telescope is operated based on a grant from the Danish Natural Science Foundation (FNU). The MiNDSTEp monitoring campaign is powered by ARTEMiS (Automated Terrestrial Exoplanet Microlensing Search; Dominik etal. 2008 ). This publication was made possible by NPRP grant nos. X-019-1-006 and 09-467-1-078 from the Qatar National Research Fund (a member of Qatar Foundation). KH acknowledges support from STFC grant ST/M001296/1. GD acknowledges Regione Campania for support from POR-FSE Campania 2014-2020. TCH acknowledges support from the Korea Research Council of Fundamental Science Technology (KRCF) via the KRCF Young Scientist Research Fellowship Programme and for financial support from KASI travel grant number 2014-1-400-06. JS acknowledges support from the Communaut franaise de Belgique - Actions de recherche concertes - Acadmie Wallonie-Europe. This work has made extensive use of the ADS service, for which we are thankful. This work makes use of observations from the LCOGT network, which includes three SUPAscopes owned by the University of St Andrews. The RoboNET programme is an LCOGT Key Project using time allocations from the University of St Andrews, LCOGT and the University of Heidelberg together with time on the Liverpool Telescope through the Science and Technology Facilities Council (STFC), UK. This research has made use of the LCOGT Archive, which is operated by the California Institute of Technology, under contract with the Las Cumbres Observatory. The authors thank Matthew Penny for his comments on this manuscript.

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This work made use of data from the NuSTAR mission, a project led by the California Institute of Technology, managed by the Jet Propulsion Laboratory, and funded by the National Aeronautics and Space Administration. 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). Data from Chandra were also used, and the work on serendipitous NuSTAR sources is partially funded by Chandra grants GO5-16154X and GO6-17135X. This work has made use of data from the European Space Agency (ESA) mission Gaia , processed by the Gaia Data Processing and Analysis Consortium (DPAC). Funding for the DPAC has been provided by national institutions, in particular the institutions participating in the Gaia Multilateral Agreement. This research had made use of the SIMBAD database and the VizieR catalog access tool, CDS, Strasbourg, France as well as the VISTA and WISE databases and publicly available images from PanSTARRS, SDSS, and IPHAS.

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Acknowledgments The author gratefully acknowledges support from the ECOGAL project, grant agreement 291227, funded by the European Research Council under ERC-2011-ADG, and warmly thanks David Armstrong, Andrew Collier-Cameron, Ian Dobbs-Dixon, David Kipping, Joe Llama, Annelies Mortier and Hugh Osborn for stimulating discussions, and Tyler Robinson for an insightful review of this manuscript. This research has made use of NASA's Astrophysics Data System bibliographic services.

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This work made use of pyke (Still Barclay 2012 ), a software package for the reduction and analysis of Kepler data. This open source software project is developed and distributed by the NASA Kepler Guest Observer Office. Part of this work is based on observations obtained with the HERMES spectrograph, which is supported by the Fund for Scientific Research of Flanders (FWO), Belgium, the Research Council of K.U. Leuven, Belgium, the Fonds National de la Recherche Scientifique (F.R.S.-FNRS), Belgium, the Royal Observatory of Belgium, the Observatoire de Genée, Switzerland, and the TLS, Germany. Calculations have been carried out in Wrocław Centre for Networking and Supercomputing ( http://www.wcss.pl ), grant no. 214. EN acknowledges support from the NCN grant no. 2014/13/B/ST9/00902. SJM acknowledges research support by the Australian Research Council. Funding for the Stellar Astrophysics Centre is provided by the Danish National Research Foundation (grant agreement no.: DNRF106). The research is supported by the ASTERISK project (ASTERoseismic Investigations with SONG and Kepler) funded by the European Research Council (grant agreement no.: 267864). MSC is supported by FCT through research grant UID/FIS/04434/2013 and through the Investigador FCT contract of reference IF/00894/2012 and POPH/FSE (EC) by FEDER funding through the programme COMPETE. Funds for this work were provided also by the EC, under FP7, through the project FP7-SPACE-2012-31284. LAB wishes to thank the National Research Foundation of South Africa for financial support. MB is F.R.S.-FNRS Postdoctoral Researcher, Belgium. AOT acknowledges support from Sonderforschungsbereich SFB 881 ‘The Milky Way System’ (subprojects A4 and A5) of the German Research Foundation (DFG).

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We thank the referee for his/her very helpful comments/suggestions on the manuscript. This work is supported by the NSFC (grants 11233006 and 11220101002), the Strategic Priority Research Program “The Emergence of Cosmological Structures” of CAS (grant No. XDB09000000), and Shanghai Municipality.

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X.L. and J.Z. appreciate useful input from Maxim Lyutikov, in particular the suggestion to simplify the description of FFE eigenmodes by using the temporal gauge. A.M.B. is supported by NASA grant NNX17AK37G and a grant from the Simons Foundation No. 446228.

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The authors thank the anonymous referee for helpful comments on the paper. MIS wants to thank Frank Verbunt, Chris Tout, Elliot Lynch, Avishai Gilkis, and Glenn-Michael Oomen for the science discussions during the development of this project.

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We are grateful to the anonymous referee for useful suggestions. This work was supported by the Russian Science Foundation (project no. 14-50-00034). The theoretical investigation was carried out in the Ussuriisk Astrophysical Observatory and the numerical calculations in the Far Eastern Federal University.

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Acknowledgements This paper makes use of the following ALMA data: ADS/JAO.ALMA#2015.1.00296.S. ALMA is a partnership of ESO (representing its member states), NSF (USA), and NINS (Japan), together with NRC (Canada) and 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. This work was supported by the National Programs PCMI and PNPS from INSU-CNRS. DS acknowledges support from the Heidelberg Institute of Theoretical Studies for the project “Chemical kinetics models and visualization tools: Bridging biology and astronomy”. DF and CF acknowledge support from the Italian Ministry of Education, Universities and Research, project SIR (RBSI14ZRHR). This research made use of NASA’s Astrophysics Data System. The figures in this paper were constructed with the MATPLOTLIB package ( Hunter 2007 ) and APLPY package hosted at http://aplpy.github.io .

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ACKNOWLEDGEMENTS This research is supported by a Marsden Grant from the Royal Society of New Zealand (AFM). JMDK gratefully acknowledges funding from the German Research Foundation (DFG) in the form of an Emmy Noether Research Group (grant number KR4801/1-1) and from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme via the ERC Starting Grant MUSTANG (grant agreement number 714907). We thank M. Krumholz, P. Crowther, and S. Glover for the useful discussions. This research made use of astropy , a community-developed core python package for Astronomy (Astropy Collaboration 2018), as well as Astrodendro, a python package to compute dendrograms of Astronomical data ( http://www.dendrograms.org/ ), pyspeckit (Ginsburg Mirocha 2011 ), and Spectral Cube ( https://spectral-cube.readthedocs.io/ ).

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O.M. acknowledges support from CNES. This work has been partly carried out thanks to the support of the A*MIDEX project (n° ANR-11-IDEX-0001-02) funded by the “Investissements d’Avenir” French Government program, managed by the French National Research Agency (A.N.R.). This work also benefited from the support of CNRS-INSU national program for planetology (P.N.P.). J.I.L. appreciates support from NASA through the JWST project. A.L.-K. acknowledges support from NASA JPL (subcontract no. 1496541).

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Acknowledgments This work has been supported by Narodowe Centrum Nauki through research projects DEC-2011/01/B/ST9/03183 (JN) and DEC-2013/10/E/ST9/00662 (OK, JN and AB). MP acknowledges support through grant PO 1508/1-2 of the Deutsche Forschungsgemeinschaft. The numerical experiment was possible through a 7 Mcore-hour allocation on the 2.399 PFlop Prometheus system at ACC Cyfronet AGH. Part of the numerical work was conducted on resources provided by the North-German Supercomputing Alliance (HLRN) under project bbp00003 and also at the Pleiades facility at the NASA Advanced Supercomputing (NAS).

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We thank the anonymous referee for the constructive comments that helped us to improve the manuscript and the vertical reconstruction procedure. This work was supported by RFBR grant 17-02-00644. The simulations were performed on the Vienna Scientific Cluster (VSC-2), on the Shared Hierarchical Academic Research Computing Network (SHARCNET), on the Atlantic Computational Excellence Network (ACEnet). This publication is supported by the Austrian Science Fund (FWF).

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ACKNOWLEDGEMENTS I acknowledge computing time awarded at CDAC National Param supercomputing facility, India, under the grant ‘Hydromagnetic-Turbulence-PR’ and the use of ‘Nova’ cluster at IIA. I also thank the Science and Engineering Research Board (SERB) of the Department of Science Technology (DST), Government of India, for support through research grant ECR/2017/001535. It is a pleasure to thank Kandaswamy Subramanian for insightful discussions on decaying (M)HD turbulence and for his comments on the manuscript. I also thank the anonymous referee for a timely and and constructive report that helped to improve the quality of the paper. The software used in this work was in part developed by the DOE NNSA-ASC OASCR Flash Center at the University of Chicago.

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Acknowledgements We thank the anonymous referee for the helpful and constructive comments. The results presented in this paper expand one chapter of PC's PhD thesis. We thank Michael Brown, Casey Papovich, and Ray Sharples for their constructive feedback and suggestions. This work was performed on the gSTAR national facility at Swinburne University of Technology. gSTAR is funded by Swinburne and the Australian Governments Education Investment Fund. We thank the Swinburne supercomputing and Information Technology teams for their support. We would like to thank Bianca Maria Poggianti and Alessia Moretti for providing us with the latest versions of the WINGS catalogues. We also thank Boris Häußler for providing the latest up to date scripts for galaxy image simulations. We thank Julie B. Nantais for providing updated redshift catalogues for the cluster RDCS J1252.9−2927. We thank Yara Jaffé for providing suggestions and stimulating discussions on the use of the EDisCS and WINGS data. PC acknowledges the support provided by FONDECYT postdoctoral research grant no. 3160375, by a Swinburne Chancellor Research Scholarship and an AAO PhD Scholarship. WJC gratefully acknowledges the financial support of an Australian Research Council Discovery Project grant throughout the course of this work. RD gratefully acknowledges the support provided by the BASAL Center for Astrophysics and Associated Technologies (CATA), and by FONDECYT grant no. 1130528. The data in this paper were based in part on observations obtained at the ESO Paranal Observatory (ESO programme 084.A-0214). Based on 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). Based on observations made with the NASA/ESA Hubble Space Telescope , obtained from the data archive at the Space Telescope Science Institute. STScI is operated by the Association of Universities for Research in Astronomy, Inc. under NASA contract NAS 5-26555. These observations are associated with Program ID 12051. Based on data obtained from the ESO Science Archive Facility (Program ID 073.A-0737(A)). Part of the data presented herein were obtained at the W.M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W.M. Keck Foundation. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain.

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We thank SeyedAbdolreza Sadjadi and Renaud Papoular for helpful discussions. The fitting models were done using the NASA Ames Research Center PAH IR Spectroscopic Database and software, and we thank Christiaan Boersma for making these resources publicly available. This work was partially supported by the Research Grants Council of the Hong Kong Special Administrative Region, China (project No. HKU 7031/10P).

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Part of this work was supported by the Agencia Nacional de Promoción Científica y Tecnológica (ANPCyT) through the Programa de Modernización Tecnolǵica BID 1728/OC-AR, by the PIP 112-200801-00940 grant from CONICET (Argentina). Some simulations were run on IFLySiB’s Cluster, which is part of SNCAD-MinCyT, Argentina.

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ACKNOWLEDGEMENTS The authors would like to thank the anonymous referee for their very helpful comments in assisting with the discussions in this paper. In addition, would like to thank Russet McMillan for her help taking images to create a master I -band fringe pattern for the ARCTIC imager. We would also like to thank Dr. Stacy McGaugh for discussions on LSB photometry, especially morphological classifications. This research 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. This research made use of astropy , a community-developed core python package for Astronomy (Astropy Collaboration 2013 , 2018 ). We acknowledge the usage of the HyperLeda data base ( http://leda.univ-lyon1.fr ).

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DK thanks Norbert Werner for a useful discussion about the links between the observed emission-line gas and the large-scale X-ray properties of NGC 5813. DK also thanks Michele Cappellari and Richard McDermid for comments on an early version of the paper. Based on observations made with ESO telescopes at the La Silla Paranal Observatory under programme ID 60.A-9100(A). RB acknowledges support from the ERC advanced grant 339659-MUSICOS.

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We gratefully acknowledge support from NSF grants AST-0709356 (L.Y.H. and L.L.C.) and AST-1313150 (A.J.B.), as well as the John Simon Guggenheim Memorial Foundation and Trustees of the William F. Vilas Estate (A.J.B.). I.R.S. acknowledges support from STFC (ST/L00075X/1), the ERC Advanced Investigator programme DUSTYGAL (321334), and a Royal Society/Wolfson Merit Award. The James Clerk Maxwell Telescope is operated by the East Asian Observatory on behalf of The National Astronomical Observatory of Japan, Academia Sinica Institute of Astronomy and Astrophysics, the Korea Astronomy and Space Science Institute, the National Astronomical Observatories of China and the Chinese Academy of Sciences (Grant No. XDB09000000), with additional funding support from the Science and Technology Facilities Council of the United Kingdom and participating universities in the United Kingdom and Canada. The James Clerk Maxwell Telescope has historically been operated by the Joint Astronomy Centre on behalf of the Science and Technology Facilities Council of the United Kingdom, the National Research Council of Canada and the Netherlands Organisation for Scientific Research. Additional funds for the construction of SCUBA-2 were provided by the Canada Foundation for Innovation. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. We acknowledge the cultural significance that the summit of Maunakea has to the indigenous Hawaiian community.

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ACKNOWLEDGEMENTS DSE acknowledges the financial support of the Science and Technology Facilities Council through a studentship award. We would like to thank the anonymous referee for constructive comments that helped to improve this paper as well as Jose Oñorbe, Tilman Hartwig, Bhaskar Agarwal, and Marta Volonteri for their useful discussions and comments. This research made use of astropy , a community-developed core python package for Astronomy (Astropy Collaboration 2013 ).

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The authors wish to thank the CoRoT and Kepler Teams whose efforts made these results possible. The CoRoT space mission has been developed and was operated by CNES, with contributions from Austria, Belgium, Brazil, ESA (RSSD and Science Program), Germany, and Spain. Funding for Kepler ’s Discovery mission is provided by NASA’s Science Mission Directorate. S.B.F. wishes to thank E. Michel for encouraging him to study Scuti stars, and the Solar Physics Team of the Universitat de les Illes Balears (UIB) for hosting his stay in Majorca. He has received financial support from the Spanish Ministry of Science and Innovation (MICINN) under the grant AYA2010-20982-C02-02. A.G.H. acknowledges support from Fundação para a Ciência e a Tecnologia (FCT, Portugal) through the fellowship SFRH/BPD/80619/2011. R.A.G. acknowledges the financial support from the ANR (Agence Nationale de la Recherche, France) program IDEE (n ANR-12-BS05-0008) “Interaction Des Étoiles et des Exoplanètes” and from the CNES GOLF and PLATO grants at CEA.

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We would like to thank our referee, Ralph Schönrich, whose detailed and accurate comments much improved the presentation of our paper. T.T. also thanks Takuma Suda for his advice on practical use of the SAGA database. This work was supported by JSPS KAKENHI grant Nos. 18H01258, 18H04593, 16H04081, 18H01248, 17H02870, and 18K03711.

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ACKNOWLEDGEMENTS RG thanks Michael Fall for very useful discussions and comments on an earlier version of the manuscript, and the referee for providing a very constructive and useful report that led to the improvement of this paper. FvdV was supported by the Deutsche Forschungsgemeinschaft through project SP 709/5-1. JZ acknowledges funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 679145, project ‘COSMO-SIMS’). FAG acknowledges financial support from CONICYT through the project FONDECYT Regular Nr. 1181264, and funding from the Max Planck Society through a Partner Group grant. FM is supported through the Program ‘Rita Levi Montalcini’ of the Italian MIUR.

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We are grateful to John Peacock for his useful comments. Special thanks to Mark Taylor for the TOPCAT 8 ( Taylor 2005 ) and STILTS 9 ( Taylor 2006 ) software. Some of the results in this paper have been derived using the HEALPix package 10 ( Górski et al. 2005 ). 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, and NEOWISE, which is a project of the Jet Propulsion Laboratory/California Institute of Technology. WISE and NEOWISE are funded by the National Aeronautics and Space Administration. This research has made use of data obtained from the SuperCOSMOS Science 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. 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. M.B., K.M., A.P., A.K. and M.K. were supported by the Polish National Science Center under contract #UMO-2012/07/D/ST9/02785. T.K., K.M. and A.P. were supported by the National Science Centre (grants UMO-2012/07/B/ST9/04425 and UMO-2013/09/D/ST9/04030), the Polish-Swiss Astro Project (co-financed by a grant from Switzerland, through the Swiss Contribution to the enlarged European Union), and the European Associated Laboratory Astrophysics Poland-France HECOLS. M.B. was supported by the Netherlands Organization for Scientific Research, NWO, through grant No. 614.001.451, and through FP7 grant No. 279396 from the European Research Council.

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We thank M. A. T. Groenewengen for the helpful comments. We acknowledge the support from the ERC Consolidator Grant funding scheme ( project STARKEY , G.A. n. 615604). A. B. acknowledges support from PRIN-MIUR 2017. T. S. R. acknowledges financial support from Premiale 2015 MITiC (PI B. Garilli). For the plots we used matplotlib, a Python library for publication quality graphics ( Hunter 2007 ).

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Support for programme GO 11598 was provided by NASA through a grant from the Space Telescope Science Institute, operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. Much of the data presented herein were obtained at the W.M. Keck Observatory, which operates as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W.M. Keck Foundation. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain. Additionally, partial support for this work came from NASA ATP NNX12AH86G, HST grants HST-GO-11598 and HST-GO-12248, NASA ADP grant NNX08AJ44G, NSF grants AST-0847667 and AST-133514, and the South African National Research Foundation's Research Chairs programme. The simulations used here were run on computing facilities owned by the Carnegie Observatories. Computing resources used for this work were made possible by a grant from the Ahmanson foundation, and through grant DMS-0619881 from the National Science Foundation. Facilities : Keck: I (HIRES), Hubble (COS).

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Acknowledgements We would like to thank the anonymous referee for suggesting revisions that greatly improved the quality of the paper. We also thank Anatoly Klypin for insightful discussions, and Andrea Macciò and Aaron Dutton for generously providing their NIHAO data. AS acknowledges support from the Swiss National Science Foundation (PZ00P2_161363).

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We thank Xianyu Tan and Xi Zhang for helpful comments on an early draft of this manuscript and the anonymous referee for helpful comments that significantly improved the manuscript. T.D.K. and A.P.S. acknowledge support from the Technology and Research Initiative Fund (TRIF) at the University of Arizona. T.D.K. acknowledges funding from the 51 Pegasi b Fellowship in Planetary Astronomy sponsored by the Heising–Simons Foundation.

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We are grateful to N. Bucciantini, B. Metzger, T. Piran, and B. Zhang for useful discussions and comments. Support comes from the DFG Grant SFB/Transregio 7, from “NewCompStar,” COST Action MP1304, and from HIC for FAIR.

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ACKNOWLEDGEMENTS We appreciate the help of the anonymous referee that, during the revision process, provided us comments and suggestions that allowed improving the manuscript. CQN acknowledges the support of the ISAS/JAXA International Top Young Fellowship and the JSPS KAKENHI grant number 18K13596. The sunrise -3 project is supported in Japan by the funding from ISAS/JAXA for the small-scale program for novel solar observations and the JSPS KAKENHI grant numbers 18H03723 and 18H05234. This research was supported by the Research Council of Norway through its Centres of Excellence scheme, project number 262622. This work has also been supported by Spanish Ministry of Economy and Competitiveness through the project ESP-2016-77548-C5-1-R. DOS also acknowledges financial support through the Ramón y Cajal fellowships.

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S.V.E. is FRS-FNRS Research Associate. P.N. is Boursier F.R.I.A. (FNRS, Belgium). B.P.’s research is partially funded by the CNRS Programme National de Physique Stellaire. Support from the Fondation ULB is acknowledged. Based on observations made with the Mercator Telescope, operated on the island of La Palma by the Flemish Community, at the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias. Based on observations obtained with the HERMES spectrograph, which is supported by the Fund for Scientific Research of Flanders (FWO), Belgium, the Research Council of K.U. Leuven, Belgium, the Fonds de la Recherche Scientifique (F.R.S.-FNRS), Belgium, the Royal Observatory of Belgium, the Observatoire de Genève, Switzerland and the Thüringer Landessternwarte Tautenburg, Germany. This work was partly funded by an Action de recherche concertée (ARC) from the Direction générale de l’Enseignement non obligatoire et de la Recherche scientifique – Direction de la recherche scientifique – Communauté française de Belgique. We wish to thank the referee Ian Short for very helpful comments which improved this paper.

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This work was supported by NASA grant NNX13AI34G.

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We thank the referee for valuable suggestions that helped to improve the paper. The project was partially supported by National Science Centre, Poland, grant No. 2017/26/A/ST9/00756 (Maestro 9) and MNiSW grant DIR/WK/2018/12. V.K. acknowledges Czech Science Foundation No. 17-16287S. We acknowledges P. Du, Y.-R. Li, and J.-M. Wang for the provided data and comments that improved the paper. We acknowledge M. Bentz, C. J. Grier, J. Kuraszkiewicz, A. del Olmo, M. Fausnaugh, J. Mejía-Restrepo, and Y. Shen for the extra information required for the development of this work.

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This study uses data provided by the Calar Alto Legacy Integral Field Area (CALIFA) survey ( http://califa.caha.es/ ), which is based on observations collected at the Centro Astronómico Hispano Alemán (CAHA) at Calar Alto, operated jointly by the Max-Planck-Institut für Astronomie and the Instituto de Astrofísica de Andalucía (CSIC). This study also uses the 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.

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Acknowledgments The authors would like to thank the reviewer Professor M. Peimbert for comments and corrections and for pointing out the possible blend of the λ4089.29 line with an Si iv line. The work of PJS was supported in part by the STFC (grant ST/J000892/1). The complete data generated in this work can be obtained in electronic format with full precision from the Centre de Données astronomiques de Strasbourg (CDS) data base (catalog VI/150). The fortran 77 data server is compiled and tested thoroughly using gfortran, f77 and Intel fortran compilers on Ubuntu 12.04 and Scientific Linux platforms. Representative sample results from all these compilers and on all those platforms are compared and found to be identical within the stated numerical accuracy.

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Acknowledgments We thank Emily Levesque for helpful conversations and V. Ashely Villar for access to their SN 2010da spectra. We are grateful to our anonymous referee for a thoughtful and constructive review. The supernova research of AVF’s group at U.C. Berkeley is supported by Gary Cynthia Bengier, the Richard Rhoda Goldman Fund, the Christopher R. Redlich Fund, the TABASGO Foundation and NSF grant AST–1211916. Some of AVF’s work was completed at the Aspen Center for Physics, which is supported by NSF grant PHY-1066293; he thanks the Center for its hospitality during the black holes workshop in 2016 June and July. This research makes use of observations from the Las Cumbres Observatory (LCO) network and is supported by National Science Foundation (NSF) grant AST-1313484. This research is based in part on observations made at the W. M. Keck Observatory; we are grateful to the Keck staff for their assistance, and we extend special thanks to those of Hawaiian ancestry on whose sacred mountain we are privileged to be guests. The W. M. Keck Observatory is operated as a scientific partnership among the California Institute of Technology, the University of California and the National Aeronautics and Space Administration (NASA); it was made possible by the generous financial support of the W. M. Keck Foundation. We thank Daniel Perley and Brad Cenko for the use of, and assistance with, their Keck LRIS imaging and spectroscopy reduction pipeline. 5 We also thank WeiKang Zheng, Kelsey Clubb, Brad Tucker, Patrick Kelly and Isaac Shivvers for their assistance with the observations. 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 NASA. This work has made use of the Weizmann Interactive Supernova Data Repository (Yaron Gal-Yam 2012 ) at http://wiserep.weizmann.ac.il .

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