O B-Person O O O O B-Organization I-Organization I-Organization O O B-Grant O O B-Survey O O O O O B-Organization I-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Survey O O O B-URL O B-Survey O O O O B-Collaboration I-Collaboration I-Collaboration O O O O O O B-Collaboration I-Collaboration O O B-Organization I-Organization I-Organization O B-Collaboration I-Collaboration I-Collaboration B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O B-Collaboration I-Collaboration I-Collaboration O B-Collaboration I-Collaboration I-Collaboration B-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Collaboration I-Collaboration I-Collaboration I-Collaboration I-Collaboration B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization O B-Collaboration I-Collaboration I-Collaboration B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O B-Organization I-Organization O O O O O O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O B-Grant O O O O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant B-Grant I-Grant B-Organization B-Location O O O O O O O B-ComputingFacility I-ComputingFacility O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility B-Observatory I-Observatory I-Observatory O B-Location B-Person O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O B-Grant B-Person O O O O B-Fellowship I-Fellowship B-Person O O O O B-Organization I-Organization B-Grant I-Grant I-Grant O O B-Grant I-Grant B-Organization B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O O B-Grant O O B-Grant B-Person O O O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant B-Grant B-Grant I-Grant O B-Grant I-Grant I-Grant I-Grant I-Grant

Acknowledgments FB acknowledges support from the UK Space Agency through grant ST/N00180X/1. 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. This research used resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the US Department of Energy under Contract no. DE-AC02-05CH11231. This work was supported by World Premier International Research Center Initiative (WPI Initiative), MEXT, Japan. Numerical computations were partly carried out on Cray XC30 at Center for Computational Astrophysics, National Astronomical Observatory of Japan. H-JS is supported by the US Department of Energy, Office of Science, Office of High Energy Physics under Award number DE-SC0014329. C-HC acknowledges support as a MultiDark Fellow. C-HC acknowledges support from the Spanish MICINNs Consolider-Ingenio 2010 Programme under grant MultiDark CSD2009-00064, MINECO Centro de Excelencia Severo Ochoa Programme under grant SEV-2012-0249, and grant AYA2014-60641-C2-1-P. MV is partially supported by Programa de Apoyo a Proyectos de Investigacin e Innovacin Tecnolgica (PAPITT) No IA102516 and Proyecto Conacyt Fronteras No 281.


O O O B-Person I-Person B-Person I-Person B-Person I-Person O B-Person I-Person O O O O O O O O O O O O O O O B-Organization I-Organization I-Organization O O B-Grant O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Grant

ACKNOWLEDGEMENTS We thank Kat Volk, Rachel Smullen, Renu Malhotra, and Andrew Youdin for helpful discussions. We thank the reviewer for helpful comments. We gratefully acknowledge support from National Science Foundation Grant no. AAG-1410174 and National Aeronautics and Space Administration Grant no. 17-ATP17-0070.


O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula 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 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 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 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 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 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-Citation I-Citation I-Citation O B-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation 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 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 O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O B-Wavelength 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 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

to T bb > 10 5 K, n H 10 12 cm −3 or ξ 0 10 4 . In this region of the parameter space, the properties of the warm corona are mainly driven by χ . However, for smaller T bb or larger density, n H , or ionization parameter, ξ 0 , the radiative and spectral properties of the corona depend significantly on these parameter values. The background colors in Fig. 5 correspond to the Compton-cooling-to-corona-heating ratio p compt / q h , whose color scale is reported on the right of the figure. The dependencies of the corona emission spectral shape on T bb and n H can be explained by the properties of the Comptonization process in an environment in radiative equilibrium. At low density or high disk temperature, our simulations show that the corona emission is dominated by Comptonization. In this case, as long as the heating over cooling of the warm corona remains constant, no significant spectral variability is expected. The corona heating is directly related to the sum of the internal heating Q and the illumination ξ 0 while the cooling is related to . They are all related to one another through the net flux crossing the base of the corona (see Eq. ( 10 )). As long as the illumination is negligible with respect to warm corona internal heating power, a constant χ implies a constant heating-to-cooling ratio and the warm corona temperature is not expected to change. The warm corona optical depth being fixed, the spectral shape of the warm corona emission remains roughly constant. This is very similar to the constancy of the spectral shape of the emission from a hot optically thin corona in radiative equilibrium with the surrounding soft photon field (e.g., Haardt Maraschi 1991 ; Haardt 1993 ; Petrucci et al. 2000 ; Tortosa et al. 2018 ). However, for densities larger than ∼10 12 cm −3 and disk temperatures lower than ∼10 5 K, the dependence on these parameters becomes important. This is due to the fact that in this part of the parameter space, the corona radiative processes are less dominated by Comptonization, either because the soft seed photon flux decreases (at low T bb ) or the free-free and bound-free processes increase (at high density) through their dependence on the density squared. The previous discussion in terms of radiative equilibrium no longer holds. At constant χ , decreasing T bb or increasing n H results in a decrease of the temperature and a steepening of the warm corona spectrum. These conditions are thus less favorable to producing spectra that could reach the soft X-ray band and produce a significant soft X-ray excess. The dependence of the spectral shape and temperature of the warm corona on the ionization parameter ξ 0 is quite different. The spectral shape and temperature are almost independent of ξ 0 unless this latter becomes larger than a few 10 4 erg s −1 cm. While for such values of ξ 0 , the warm corona is dominated by Compton cooling, the spectral shape (photon index and temperature) varies with ξ 0 and the lower the χ


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 O O O O O O O B-Telescope O O O B-CelestialObject I-CelestialObject O O B-Telescope O O O O O O O B-Wavelength B-Wavelength B-Wavelength B-Wavelength B-Wavelength B-Wavelength O B-Wavelength I-Wavelength O O B-Telescope 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 O O O O O O O O O O O O O O O O O O B-Wavelength B-Wavelength O O O O O O O B-Wavelength B-Wavelength O B-Wavelength I-Wavelength 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-CelestialObject I-CelestialObject 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 B-Wavelength I-Wavelength 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-Model I-Model I-Model I-Model O O O O O O O O O O O O O B-Model I-Model I-Model I-Model 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-Telescope O B-Telescope O O B-Telescope I-Telescope I-Telescope O O B-Telescope I-Telescope I-Telescope O O O B-Telescope O O O O O O O O B-Organization B-Software I-Software I-Software I-Software B-Software B-Citation I-Citation O O O O O O O O O B-TextGarbage I-TextGarbage B-URL O O O O B-Model I-Model I-Model O O O O O O O O O O O O O B-Database I-Database 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-Software O B-Software 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-CelestialObject B-CelestialObject I-CelestialObject O B-CelestialObject I-CelestialObject O O O O O


O O O O B-Person I-Person O O O B-Person I-Person O O O O B-Instrument O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O B-ComputingFacility I-ComputingFacility O O O B-ComputingFacility I-ComputingFacility I-ComputingFacility 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 B-Person O O O B-Organization I-Organization I-Organization O B-Grant O O O O O O O B-Observatory O B-Identifier B-Observatory O O O O O B-Observatory O O O O B-Organization B-Location O B-Organization B-Location O O O B-Organization B-Location B-Organization O B-Organization B-Location O B-Organization B-Location I-Location I-Location O O O O B-Location I-Location I-Location O B-Observatory I-Observatory I-Observatory O O O O B-Observatory B-Organization O B-Observatory O B-Observatory I-Observatory I-Observatory I-Observatory O O O O O B-Organization I-Organization I-Organization O O O O O B-Organization I-Organization I-Organization B-Person O O O O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O O O O B-Observatory B-Observatory B-Grant I-Grant I-Grant I-Grant I-Grant

We are grateful to Hui Li for useful discussions, Myriam Benisty for making available the SPHERE image of MWC 758, and an anonymous referee for constructive suggestions that largely improved the quality of the paper. Numerical calculations were performed on the SAVIO cluster provided by the Berkeley Research Computing program, supported by the UC Berkeley Vice Chancellor for Research and the Berkeley Center for Integrative Planetary Science. Y.P. was supported by Russian Science Foundation grant 17-12-01168. This paper makes use of the following ALMA data: 2017.1.00492.S. ALMA is a partnership of the ESO (representing its member states), NSF (USA), and NINS (Japan), together with the NRC (Canada), MOST and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by the ESO, AUI/NRAO, and NAOJ. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. Y.H. is currently supported by the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. This work was supported by NAOJ ALMA Scientific Research Grant Number 2016-02A.


B-Person O B-Person O O O O B-Telescope I-Telescope O O O O O O O O O B-Telescope I-Telescope O B-Person O O O B-Person I-Person O O O O O B-Telescope O O O B-Person I-Person O O O O O O O B-Telescope O O B-Model O B-Model O B-Person O O O O O B-Organization O B-Organization B-Location B-Person O O O O B-Organization I-Organization O B-Grant O O B-Organization O O O O B-Organization I-Organization I-Organization B-Organization O O O O B-Grant B-Person O O O O O O B-Organization I-Organization I-Organization B-Organization O B-Grant I-Grant B-Person O O O O B-Organization I-Organization B-Organization O O O O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O O O O O O O O O O O B-Organization I-Organization B-Grant I-Grant I-Grant B-Grant O O O B-Grant I-Grant B-Grant

F.F. and A.P. are grateful to the IRAM-30 m staff for their help with the observations at the IRAM-30 m telescope. G.B. is grateful to Amanda Kepley for her help during the GBT observations and to Jeff Magnum for providing the procedures for converting the GBT spectra from GBTIDL to CLASS format. A.P. acknowledges the financial support from UNAM, and CONACyT, México. G.B. is supported by the Spanish MICINN grant AYA2008–06189–C03–01 (co-funded with FEDER funds) and by the Italian Space Agency (ASI) fellowship under contract number I/005/07/01. P.C. acknowledges the financial support of the European Research Council (ERC; project PALs 320620). A.S.-M. is supported by the Deutsche Forschungsgemeinschaft (DFG) through the collaborative research grant SFB 956 “Conditions and Impact of Star Formation”, project area A6. The research leading to these results has received funding from the European Commission Seventh Framework Programme (FP/2007-2013) under grant agreement Na 283393 (RadioNet3).


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-Citation I-Citation I-Citation I-Citation I-Citation I-Citation 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-CelestialObject 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 O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation 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 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 B-Citation I-Citation I-Citation O O O O O O O O O O O O B-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion 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-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation 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-Model I-Model I-Model O B-CelestialObject O B-CelestialObject 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-CelestialObject B-Citation I-Citation I-Citation I-Citation 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-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation 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-CelestialObject O O B-Model I-Model O O O O O O O O O O O O O O O O O

the protosolar disk. In addition, D/H ratios can readily be modified by non-nebular processes. For example, the D/H ratio of Rumuruti type and ordinary chondrites is higher than that in comets, which Alexander et al. ( 2012 ) attribute to iron oxidation in their parent bodies. 4.5. Water in Chondrites If carbonaceous and non-carbonaceous chondrites formed on opposite sides of the snowline, where Jupiter formed, why do some carbonaceous chondrites have relatively low water and carbon contents like those in some non-carbonaceous chondrites? CM, CI, and CR chondrites have the highest contents of water and carbon among chondrites, but CO and CV have lower amounts that are comparable to those in some of the least metamorphosed ordinary chondrites (Krot et al. 2014 ). Krot et al. ( 2015 ) infer that CI, CM, and CR chondrites were altered under water/rock mass ratios of up to 0.6, whereas CV and CO chondrites were altered at lower water/rock ratios of 0.1–0.2. We do not know the answer to this issue but note that water contents of carbonaceous chondrites are related to matrix contents and that the coarse-grained matrix material likely contained more water than the fine-grained matrix rims. Thus, the low water content of CO and CV chondrites may reflect their low content of coarse-grained matrix material relative to CI, CM, and CR chondrites (Scott Krot 2014 ). We also note that comets can contain more rock than ice (Brownlee 2014 ; Davidsson et al. 2016 ), much less ice than the predicted theoretical water-rock ratio beyond the snowline of 1.2 (Krot et al. 2014 ; Palme et al. 2014 ). 5. How and When Were the Two Isotopic Populations Mixed Together in the Asteroid Belt? The isotopic dichotomy in the solar system lasted until at least 3–4 Myr after CAI formation, the likely accretion time of CR chondrites, which are the least metamorphosed and altered chondrites and have the highest concentration of presolar grains (Zhao et al. 2013 ; Budde et al. 2017 ; Krot Nagashima 2017 ). The two isotopic populations were then intermixed, most likely by the migration of the giant planets before the gas had dissipated in the disk. In the Grand Tack model, once Jupiter and Saturn reached masses of ∼50 M ⊕ , they migrated inward across the asteroid belt so that it was first emptied and then repopulated with S-type asteroids, which formed in the belt, and C-types, which formed outside Jupiter (Walsh et al. 2011 ). Alternatively, planetesimals from the giant planet region may have been scattered into the asteroid belt as a natural side-effect of the growth of giant planets (Kretke et al. 2017 ; Raymond Izidoro 2017 ). Raymond Izidoro ( 2017 ) show that scattering during the rapid growth of the gaseous envelopes of giant planets would have scattered nearby planetesimals in all directions and may have delivered water to the growing Earth. However, the Grand-Tack model has the advantage that it creates a strongly mass-depleted belt with roughly equal masses of S- and


O O O O O O O B-Organization I-Organization I-Organization O O B-Grant I-Grant O O O B-Organization I-Organization O B-Grant B-Grant O B-Grant B-Person O O B-Organization I-Organization I-Organization O O B-Grant O O O O O O O O B-Observatory I-Observatory O O O O O O B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person O B-Person I-Person O O O O O O O O B-Collaboration I-Collaboration I-Collaboration O B-Organization I-Organization O O O O O O O O B-Organization I-Organization I-Organization

This research was partially supported by the National Science Foundation under grant NSF PHY-1125915 and by the Polish NCN grants 2014/14/M/ST9/00707, 2015/19/B/ST9/01099, and 2016/22/E/ST9/00037. M.A.A. acknowledges the Czech Science Foundation grant No. 17-16287S, which supported one of his visits to the Paris Observatory. The authors benefited from discussions with Ramesh Narayan, Paweł Haensel, Avi Loeb, Axel Brandenburg, and Krzysztof Belczyński. Some of this work was conducted at the Black Hole Initiative at Harvard University, which is funded through a grant from the John Templeton Foundation.


O O O O B-Person I-Person I-Person O O O O O B-Telescope O B-Telescope O O O B-Survey O B-Person O O O O O B-Organization B-Grant I-Grant O O O B-Survey O B-Survey O O O O O B-Organization I-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization O B-Location B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Location B-Organization O B-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization O B-Location O B-Survey O O O B-URL O O B-Survey O O O O B-Collaboration I-Collaboration I-Collaboration O O O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization B-Organization O B-Organization I-Organization I-Organization I-Organization O B-Collaboration I-Collaboration I-Collaboration B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Collaboration I-Collaboration I-Collaboration O B-Organization I-Organization I-Organization I-Organization B-Telescope B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization B-Organization O B-Organization I-Organization I-Organization B-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization O B-Observatory I-Observatory I-Observatory I-Observatory O O B-Organization I-Organization I-Organization

We are grateful to Ho Seong Hwang for providing his catalogues of AKARI and IRAS fluxes for matched SDSS galaxies. SLE acknowledges the receipt of an NSERC Discovery Grant. Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the US Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society and the Higher Education Funding Council for England. The SDSS Web Site is http://www.sdss.org/ . The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions. The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory and the University of Washington.


O O O B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person O B-Person I-Person O O O B-Person B-Person O B-Person O O O O B-Location B-Organization I-Organization I-Organization B-Organization O O B-Grant I-Grant O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization B-Person O O O O O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility O O O B-Organization I-Organization I-Organization B-Organization B-Organization I-Organization I-Organization I-Organization I-Organization O O O B-Grant B-Person O O O B-Organization I-Organization O O B-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship B-Person O B-Person O O O O B-Location B-Organization I-Organization I-Organization B-Organization O O B-Grant I-Grant B-Person O O O O O B-Organization I-Organization I-Organization O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O O B-Grant O O O O O B-Grant I-Grant I-Grant B-Person O O O B-Organization O O B-Grant I-Grant B-Person O O O O B-Organization O B-Grant B-Person O O O O B-Fellowship I-Fellowship I-Fellowship O O O O O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility O B-URL O O O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility B-ComputingFacility B-URL O O O O B-Software I-Software O O O O O O O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility B-URL O O B-Software I-Software O O O O O B-Grant I-Grant O O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility B-ComputingFacility O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization B-Organization I-Organization I-Organization O O O O O B-Software O O O O O O O O O O B-Software B-Citation I-Citation I-Citation O B-Software O B-URL O B-Software B-Citation I-Citation O B-Software B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O B-Software B-Citation I-Citation I-Citation I-Citation O O O O O O B-Archive I-Archive I-Archive I-Archive O O O

ACKNOWLEDGEMENTS We thank Brian Batell, Arthur Kosowsky, Rachel Mandelbaum, Dazhuang Mao, Jeffrey Newman, Troy Raen, Li-Cheng Tsai, and Rongpu Zhou for useful discussions. KW, ARZ, and ASV are supported by the US National Science Foundation (NSF) through grant AST 1517563 and by the Pittsburgh Particle Physics Astrophysics and Cosmology Center (PITT PACC). ASV is additionally supported by the Argonne Leadership Computing Facility, which is a Department of Energy (DOE) Office of Science User Facility supported under Contract DE-AC02-06CH11357. YYM is supported by PITT PACC through the Samuel P. Langley Postdoctoral Fellowship. FvdB and JUL are supported by the US National Science Foundation (NSF) through grant AST 1516962. FvdB received additional support from the Klaus Tschira foundation, and from the National Aeronautics and Space Administration through Grant No. 17-ATP17-0028 issued as part of the Astrophysics Theory Program. CMS is supported by NSF through grant DMS 1521786. APH is supported under the DOE contract DE-AC02-06CH11357. DC is supported by a McWilliams Postdoctoral Fellowship. The authors gratefully acknowledge the Gauss Centre for Supercomputing e.V. ( www.gauss-centre.eu ) and the Partnership for Advanced Supercomputing in Europe (PRACE, http://www.prace-ri.eu ) for funding the MultiDark simulation project by providing computing time on the GCS Supercomputer SuperMUC at Leibniz Supercomputing Centre (LRZ, http://www.lrz.de ). The Bolshoi simulations have been performed within the Bolshoi project of the University of California High-Performance AstroComputing Center (UC-HiPACC) and were run at the National Aeronautics and Space Administration (NASA) Ames Research Center. This research made use of python , along with many community-developed or maintained software packages, including ipython (Pérez Granger 2007 ), jupyter ( jupyter.org ), matplotlib (Hunter 2007 ), numpy (van der Walt, Colbert Varoquaux 2011 ), and scipy (Jones et al. 2001 ). This research made use of NASA’s Astrophysics Data System for bibliographic information.


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We would like to thank the referee for constructive comments that helped improved the presentation of this work. We would like to thank A. Casey for discussions that improved this work. K.H. is funded by the British Marshall Scholarship program and the King’s College, Cambridge Studentship. This work was partly supported by the European Union FP7 programme through ERC grant number 320360. U.H. acknowledges support from the Swedish National Space Board (Rymdstyrelsen).


O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O B-Formula I-Formula I-Formula I-Formula 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-Model O B-Model O O B-Model 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 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-Model B-Model O B-Model O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O B-Model I-Model 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 B-Model I-Model O O O O O O O O B-Model O B-Model O O B-Model 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 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-Formula I-Formula I-Formula O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O B-Model I-Model 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 O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O

1, 2), etc., while the (1, 1, 0) mode is not important. We should therefore conclude that magnetic relaxation towards the k = 1 ABC state is more advanced in our k ini = 4 simulation. Figure 5. Energy contribution of the dominant Fourier modes of the B x magnetic field component as function of simulation time ct / L for simulations k2_T5_1024M (left), k2_T6ic_1152P (middle), and k4_T5_1152P (right). The black lines show the total energy of the B x component, represented as . The red lines show the contribution of the initial ‘ABC’ modes: (0, k ini , 0) and (0, 0, k ini ); the green lines show the contribution of the (1, 1, 0) modes; the blue lines show the contribution of the ‘Taylor’ modes (0, 1, 0) and (0, 0, 1); and the grey lines show the residual energy contained in all other modes. Fig. 6 shows the magnetic energy spectra for simulations k2_T5_1024M, k2_T6ic_1152P, and k4_T5_1152P for a range of simulation times. The magnetic energy spectra are dominated by the white noise for for the T5 simulations and for for the k2_T6ic_1152P simulation. The inertial subrange extends over at least one order of magnitude in wavenumber . In all cases, we observe a freely decaying turbulent cascade that can be described roughly as a power law , with significant deviations in either direction. The cascade appears to be most regular for simulation k4_T5_1152P. Figure 6. Magnetic energy spectra calculated for simulations k2_T5_1024M (left), k2_T6ic_1152P (middle), and k4_T5_1152P (right). Line colours indicate the progression of simulation time from deep blue to brown within the time ranges indicated in the bottom-left corner of each panel. The thick dashed lines indicate the power-law slopes of −5/3, −2, −2.5, −3. Fourier decomposition was also attempted for electric field , and for velocity field , however, the corresponding spectra of electric and kinetic energies are dominated by the white noise. 3.4 Particle momentum distribution Fig. 7 presents the time evolution of the particle momentum distributions for all five simulations. For ultra-relativistic electrons with Θ ≫ 1, the dimensionless particle momentum is basically equivalent to the dimensionless particle energy u = γβ = p /( m e c ) ≃ γ. For all simulations, the initial momentum distribution is adopted to be the Maxwell–Jüttner distribution (Section 2). Figure 7. Particle momentum distributions u 2 N ( u ) compared for all simulations. The distributions are normalized to the peak of the initial distribution for each simulation. Line colours indicate the progression of simulation time from deep blue to brown over the range indicated in the top-left corner of each panel. We find evidence for non-thermal particle acceleration for all simulations with k ini = 2. The effective power-law indices p (such that N ( u )∝ u − p ) are estimated roughly by finding a power-law slope that makes a line parallel to the data (see Werner et al. 2016 for more elaborate fitting methods), with a different approach used


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instrument (Pfeiffer, Frank Baumuller 1992 ). The experiment had two goals. The first one was to understand whether the precision of a single astrocomb is confirmed by an independent system, and the second one was to assess zero-point offsets in the wavelength calibration introduced by switching between the two astrocombs. Probst et al. ( 2020 ) analyses the same data set, but with a focus on describing the experimental set-up, astrocomb hardware and its optimization during the campaign before the astrocomb’s deployment in 2015 May. This paper, on the other hand, focuses on data analysis techniques and advanced algorithms that will provide wavelength calibration precision required by the ELT projects discussed above. The paper is divided as follows. In Section 2 , we briefly describe the experimental set-up – the spectrograph and the two astrocombs. Section 3 describes the data set and general properties of the spectra. Section 4 gives details on our automatic algorithm to detect astrocomb lines and obtaining their centres and wavelengths. Wavelength calibration is discussed in Section 5 , where we describe how we deal with instrumental effects that impact significantly on wavelength calibration precision and accuracy, e.g. defects associated with the CCD manufacturing process. In the same section, we describe our findings on the optimal wavelength calibration model for HARPS spectra. We present our findings on precision and consistency in Section 6 , where we also consider and model the contribution of flux dependent velocity shifts. Finally, our results are presented in Section 7 and discussed in Section 8 . 2 EXPERIMENTAL SET-UP 2.1 The HARPS instrument The High Accuracy Radial velocity Planet Searcher (HARPS; Mayor et al. 2003 ) was built for extreme stability and precision and is one of the most stable astronomical spectrographs in existence. HARPS is a fibre fed, high-resolution ( R = λ/Δλ = 115 000), R4 grism cross-dispersed echelle spectrograph installed on the 3.6m telescope at ESO’s La Silla Observatory and the first instrument to be equipped with an astrocomb for regular operations (Probst et al. 2016 ). The light of the two input fibres is dispersed into 72 echelle orders on the detector, simultaneously covering the wavelength range between 378 and 691 nm. The spectrograph is enclosed in a thermal and pressure controlled vacuum vessel, with long-term temperature variations at the 0.01 K level and operating pressure below . Several thermal and mechanical effects can slightly shift the positions of the spectrum on the detector with time, an unavoidable effect that is eliminated through simultaneous referencing: drifts in the science fibre are tracked by simultaneously observing a spectrum rich in velocity information content (e.g. ThAr, an astrocomb, or a Fabry–Pérot etalon) in the secondary fibre (Baranne et al. 1996 ). Each fibre has a static double scrambler. A servo controller (‘secondary guiding’) ensures that the object image is


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ACKNOWLEDGEMENTS We thank N. Kylafis for useful comments and discussions. We also thank the anonymous referee for useful comments that helped improved this paper. The software used in this work was in part developed by the DOE NNSA-ASC OASCR Flash Center at the University of Chicago. For post-processing our results we partly used yt analysis toolkit (Turk et al. 2011 ). KT and AT acknowledge support by FP7 through Marie Curie Career Integration Grant PCIG-GA-2011-293531 ‘SFOnset’. AT and KT would like to acknowledge partial support from the EU FP7 Grant a39353*PIRSES-GA-2012-31578 ‘EuroCal’. Usage of the Metropolis HPC Facility at the Crete Center for Quantum Complexity and Nanotechnology of the University of Crete, supported by the European Union Seventh Framework Programme (FP7-REGPOT-2012-2013-1) under grant agreement no. 316165, is alsoacknowledged.


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We thank Gabriel Brammer for insightful discussions related to this work. This paper is based on observations made with the NASA/ESA Hubble Space Telescope . The Space Telescope Science Institute (STScI) is operated by the Association of Universities for Research in Astronomy, Inc. (AURA) under NASA contract NAS 5-26555. ACS was developed under NASA contract NAS 5-32864. The Spitzer Space Telescope is operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA. These observations are associated with program GO-14096. Archival data are associated with programs GO-9270, GO-12166, GO-12477, and GO-12253. Some of the data presented in this paper were obtained from the Mikulski Archive for Space Telescopes (MAST). This research made use of Photutils, an Astropy package for detection and photometry of astronomical sources (Bradley et al. 2019 ). This research made use of Astropy, a community-developed core Python package for Astronomy (The Astropy Collaboration et al. 2018 ). This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. F.A.-S. acknowledges support from Chandra grant G03-14131X. M.B. and V.S. acknowledge support by NASA through ADAP grant 80NSSC18K0945, NASA/ HST through HST -GO-14096, HST -GO-13666 and two awards issued by Spitzer/JPL/Caltech associated with SRELICS_DEEP and SRELICS programs.


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ACKNOWLEDGEMENTS MWF and PAW gratefully acknowledge the receipt of research grants from the National Research Foundation (NRF) of South Africa. MWF thanks Dr. L. Balona for some help with the data for the early years.


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Acknowledgments This research was funded through a VICI grant of NWO (the Netherlands Organization for Scientific Research) and an A-ERC grant 291141 CHEMPLAN. Financial support by NOVA (the Netherlands Research School for Astronomy) and the Royal Netherlands Academy of Arts and Sciences (KNAW) through a professor prize are acknowledged. The described work has had much advantage from collaborations within the framework of the FP7 ITN LASSIE consortium (GA238258). SI acknowledges the Royal Society for financial support. We thank D. M. Paardekooper and V. Taquet for discussions on the laser interference measurements and gas-phase formation of COMs, respectively. We also acknowledge Rachel James for careful proof reading.


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additionally with 10 6 , 10 6.5 , 10 7.5 , and 10 8 particles for convergence tests, plus 12 miscellaneous tests with 10 7 particles detailed in Section 3.3 . To be precise, these stated particle numbers refer to the number of particles per Earth mass (the bare target plus impactor mass is 1.02 M ⊕ ). Thus, the numerical resolution stays the same for simulations with different-mass planets. For example, a “10 7 ” simulation that includes a 0.1 M ⊕ atmosphere actually contains a total of ∼1.12 × 10 7 particles. For most of the suite we focus on the 10 −2 M ⊕ atmosphere. Figure 2 summarizes the parameters for each simulation. Note that the v c = 0.75 v esc scenarios would require some third body to have slowed down the impactor during its approach to below the mutual escape speed. This is unlikely in the case of primary impactors falling in to Earth in our solar system but is a useful test for the consequences of a highly grazing impact resulting in a large bound fragment that will re-impact at a later time. It also lets us compare with other models, which predict little erosion in this regime. Figure 2. Suite of simulation scenarios, arranged by their speed and impact parameter at contact (see Figure 1 and Appendix A ). As shown in the legend, the nested marker colors indicate the mass of the atmosphere (in Earth masses) for each simulation, while the line angles indicate the number of particles per Earth mass. At the high-speed end, given Earth’s position in the solar system, 5 v esc is around the highest typical velocity that might be expected for an impact (Raymond et al. 2009 ). For context, Earth’s orbital speed around the Sun is about 3 v esc . The suite’s extension to 8 v esc both allows us to test the extreme end of the parameter space and is a regime that could be more common in other planetary systems, for example, with a more massive star or a target planet deeper in the star’s potential well. Furthermore, in studies like that by Inamdar Schlichting ( 2015 ) where erosion is estimated as a function of the impactor’s momentum, using very high velocities will allow us to test the degeneracy between impactor mass and speed across a wide range of momenta in future suites with different impactor masses. For the relatively small impactor mass used here, even 8 v esc is not predicted by Inamdar Schlichting ( 2015 ) to remove more than 3/4 of the atmosphere. The simulations are run using SWIFT with a simple “vanilla” form of SPH plus the Balsara ( 1995 ) switch for the artificial viscosity as described in Kegerreis et al. ( 2019 ) to a simulation time of 100,000 s (roughly 28 hr) in a cubic box of side 80 R ⊕ to allow the tracking of ejecta. Any particles that leave the box are removed from the simulation. Throughout the first 10 hr we record snapshots every 100 s, for high time resolution during the impact and its immediate aftermath. To reduce data storage requirements, we then output snapshots every 1000 s for the remainder. 2.3.


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beam = 058 × 050, PA = 81°; shown in the lower left corner). Contour levels are −3, 3, 5, 7, 9, 11, 13, 15, 17, 19, and 21 times the rms of the map, 19.3 μ Jy beam −1 . (b) Naturally weighted VLA image of the 3.0 cm emission obtained by combining data from A and B configurations (synthesized beam = 039 × 036, PA = 58°; shown in the lower left corner). Contour levels are −3, 3, 5, 7, 9, 11, 13 and 15 times the rms of the map, 2.1 μ Jy beam −1 . An image of the 3.0 cm emission is presented in Figure 2 (b). The emission shows a tripolar structure, suggesting a combination of dust emission from a disk and free–free emission from a monopolar (one-sided) radio jet perpendicular to it. This kind of morphology, with two perpendicular structures, has already been observed in other sources, such as HH 111 (Rodríguez et al. 2014 ) and HH 80–81 (Carrasco-González et al. 2012 ). In both cases, the emission was separated into two components by fitting two Gaussians to it. In the case of GM Aur, we estimate from the SED fit a dust contribution at 3.0 cm of ∼11 μ Jy, which represents only one-eighth of the detected emission at 3.0 cm. In order to check whether this flux density can account for the disk emission of GM Aur at 3.0 cm, we obtained an image of the estimated dust emission at 3.0 cm by scaling the 7 mm image with the dust spectral index obtained from the SED fit. We then subtracted this scaled image to the 3.0 cm image, which was previously convolved to have the same angular resolution as the 7 mm observations. The resulting image still showed significant emission from the disk. By fitting two Gaussians to the remaining 3.0 cm emission, we separated the source into a component with the same PA as the GM Aur disk ( S ν = 31 ± 3 μ Jy), and another one perpendicular to it ( S ν = 45 ± 3 μ Jy) 9 9 We note that none of the fit parameters were fixed and yet two perpendicular components were obtained. (Figure 3 ). We interpret these two components to be tracing the free–free emission from a photoevaporating disk and a radio jet, respectively (see Section 4 ). Figure 3. Superposition of the two components of the free–free emission at 3.0 cm obtained from our two-Gaussian fit (black and white contours) over the 7 mm emission of the transitional disk of GM Aur shown in Figure 2 (a) (color scale). We propose that the disk component (black contours) is produced by the photoevaporative winds arising from the disk, while the perpendicular component (white contours) is tracing the free–free emission from an accretion-driven radio jet. The 3.0 cm image was previously convolved to the same angular resolution (058 × 050, PA = 81°; shown in the lower left corner) as the 7 mm image. Contour levels are −3, 3, 4, 5, 6, 7, and 9 times the rms of the convolved 3.0 cm image, 2.8 μ Jy beam −1 . We also combined our new 5 cm observations with archival data (Table 1 ) to get a sensitive image (rms ≃ 2.5 μ Jy; beam = 053 × 036, PA = −74°). The image shows a compact


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Our images also show that the extended Ly emission is typically quite symmetric (albeit with interesting deviations in some objects) – information which is necessarily erased in any stacking process. It will be intriguing to compare the Ly halo maps obtained by MUSE with simulated views from (possibly competing) model predictions. In the context of our simple phenomenological model, two main parameters govern the overall appearance of a Ly halo at : the halo scale length, typically 10 times larger than the scale length of the central continuum source, and the fraction of the total Ly radiation emitted by the halo, typically between 40% and 90%. These two quantities are essentially uncorrelated in our sample, which may indicate that they are physically determined at different scales. The size of a halo would then mainly depend on the spatial distribution and kinematic structure of the circumgalactic gas, independently of how much Ly it emits. On the other hand, the halo luminosity fraction will depend on the origin of the Ly radiation, but also on the importance of resonant scattering of Ly photons from inside the galaxy into the halo. Energetically, our measurements are consistent with the idea that most of the observed Ly radiation is produced within the UV-bright star-forming regions of the galaxies and then scattered outwards. However, additional processes for powering the Ly emission in the extended haloes are not excluded, and more theoretical and modelling work will be required to explore the relative importance of different mechanisms. Additional clues will come from spatially resolved spectroscopy of Ly haloes, which MUSE will enable us to perform at least for the brighter sources (or in strongly lensed objects where the magnification helps to reach even higher spatial resolution; see Patrício et al. 2016 for a first case study using MUSE). By a remarkable coincidence, individual Ly haloes of nearby () galaxies have just now become a subject of detailed scrutiny through the LARS project ( Hayes et al. 2013 ; Östlin et al. 2014 ; Hayes et al. 2014 ; Guaita et al. 2015 ). While the LARS galaxies can be resolved in much greater detail than our faint HDFS sources, the overall comparison of high- and low-redshift Ly halo properties shows some similarities, but also intriguing differences. In particular, the huge discrepancy between the sizes of Ly-emitting regions around and galaxies (Fig. 12 ) suggests that the nature of the circumgalactic medium has changed drastically from the epoch of galaxy formation to the present-day Universe. For the first time, MUSE has allowed us to assess the level of diversity in the Ly halo properties of high-redshift galaxies. While admittedly our sample is too small to go very far in this direction, much more can be expected in the future, as MUSE has just commenced operation. Furthermore, the MUSE data need to be complemented by observations with other instruments and in other wavelengths. In this respect


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The presented research was made possible through funding from the Russian Scientific Foundation, project number 16-12-00071.


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Acknowledgements We would like to thank Rob Rutten for the alignment of SST and AIA data for the June 19 dataset. This work was supported by the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013) / ERC Grant agreement No. 291058, and by the Research Council of Norway, project number 250810, and through its Centres of Excellence scheme, project number 262622. B.D.P. gratefully acknowledges support from NASA grants NNX16AG90G and NNG09FA40C (IRIS). IRIS is a NASA small explorer mission developed and operated by LMSAL with mission operations executed at NASA Ames Research Center and major contributions to downlink communications funded by ESA and the Norwegian Space Centre. The Swedish 1-m Solar Telescope is operated on the island of La Palma by the Institute for Solar Physics of Stockholm University in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias. To visualise, connect, and interpret the data we made extensive use of CRISPEX ( Vissers Rouppe van der Voort 2012 ).


O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O B-Citation I-Citation 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 O O O O O O O O O B-Wavelength O O O B-Wavelength O O O O O O O O O B-Citation I-Citation I-Citation I-Citation 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 O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation 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 B-Model O B-Model 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 B-Telescope 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 B-Telescope O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model I-Model B-Model O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O B-Model 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 O O O O O O O O O O O O O O

scales, might be interpreted in terms of a decrease of with increasing column density ( Matthews et al. 2001 ; Whittet et al. 2008 ). A leading theory for the process of dust grain alignment involves radiative torques by the incident radiation ( Lazarian Hoang 2007 ; Hoang Lazarian 2009 ; Andersson 2015 ). A critical parameter for this mechanism is the ratio between the dust grain size and the radiation wavelength. As the dust column density increases, only the longer wavelength radiation penetrates the cloud and the alignment decreases. Grains within a cloud (without embedded sources) should have lower than those at the periphery of the same cloud. There is evidence for this from near-infrared interstellar polarization and submillimetre polarization along lines of sight through starless cores ( Jones et al. 2015 ), albeit on smaller scales and higher column densities than considered here. If inside the cloud is very low, the observed polarized intensity would arise from the dust in the outer layers, tracing the magnetic field in the “skin” of the cloud. Then the observed orientation of is not necessarily correlated with the column density structure, which is seen in total intensity, or with the magnetic field deep in the cloud. Soler et al. (2013) presented the results of HRO analysis on a series of synthetic observations produced using models of how might decrease with increasing density. They showed that with a steep decrease there is no visible correlation between the inferred magnetic field orientation and the high- structure, corresponding to nearly flat HROs. The HRO analysis of MCs carried out here reveals a correlation between the polarization orientation and the column density structure. This suggests that the dust polarized emission samples the magnetic field structure homogeneously on the scales being probed at the resolution of the Planck observations or, alternatively, that the field deep within high- structures has the same orientation of the field in the skin. 6. Conclusions We have presented a study of the relative orientation of the magnetic field projected on the plane of the sky (), as inferred from the Planck dust polarized thermal emission, with respect to structures detected in gas column density (). The relative orientation study was performed by using the histogram of relative orientations (HRO), a novel statistical tool for characterizing extended polarization maps. With the unprecedented statistics of polarization observations in extended maps obtained by Planck , we analyze the HRO in regions with different column densities within ten nearby molecular clouds (MCs) and two test fields. In most of the regions analysed we find that the relative orientation between and structures changes systematically with from being parallel in the lowest column density areas to perpendicular in the highest column density areas. The switch occurs at . This change in relative orientation is particularly significant given that projection


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Acknowledgments This research is mainly supported by the University of Padova and by the ERC Consolidator Grant funding scheme (project STARKEY, G.A. n. 615604). The LUNA experiment was supported by INFN, DFG (BE 4100-2/1), NAVI (HGF VH-VI-417) and OTKA (K101328). We thank Maria Lugaro for helpful comments and discussion.


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 O O O O B-Wavelength I-Wavelength 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 B-CelestialObject O O O O O O B-Collaboration I-Collaboration O O O O O O O O O B-Dataset O B-Citation I-Citation I-Citation I-Citation O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O B-Dataset O O O O O O O B-Dataset 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-Wavelength 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-Wavelength B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O B-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion 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-Dataset I-Dataset I-Dataset I-Dataset B-Citation I-Citation I-Citation I-Citation O O O O B-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion 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 O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject 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-CelestialObject I-CelestialObject 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-Citation I-Citation I-Citation I-Citation I-Citation I-Citation 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 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

time interval, covering up to 15 ks after the beginning of the prompt emission, and adopt E min = 1 GeV to recover exposure. The condition in Equation ( 20 ) now returns 10,962 s of GTIs in the first 15 ks after t 0 . In this case, six events survive the cuts, among which a ∼10 GeV photon at t 0 + 2239 s. Note that there are still no photons during the prompt emission with this selection. We detect and localize the source producing a TS map for this time interval, with a likelihood model containing the appropriate Galactic and isotropic templates provided by the LAT collaboration as well as all the point sources from the 3FGL catalog (Acero et al. 2015 ). We model GRB 100724B as a point source with a power-law spectrum, and we keep the parameters for all 3FGL sources fixed to their catalog values. No 3FGL source is detected in the small time window of our analysis, thus this choice is irrelevant for our final results. This analysis results in a firm detection of the GRB with a significance of ∼7 σ . The best-fit power law has a photon index of α = −1.8 ± 0.4, a value typical for the high-energy emission of GRBs (Ackermann et al. 2013b ), with an average flux of erg cm −2 s −1 (1–100 GeV). Our localization is shown in Figure 15 . The cross marks the best-fit position, corresponding to R.A. = 12347 and decl. = 7588 (J2000), while the white lines correspond to the 68% and 90% c.l. containment regions. We used this position in the following analysis. The most accurate localization available in the literature before this work was reported in the Fermi /LAT GRB catalog (Ackermann et al. 2013b ), and corresponds to R.A. = 11959, decl. = 7586 (J2000) with a 68% containment radius of 088 (dashed line in Figure 15 ). This localization was based on the detection during the prompt phase, obtained by relaxing the zenith angle cut using a threshold of , and it is compatible with the one found in this work, but it features a much larger containment radius. The excess we find is not related to any known source and lies within the GBM localization region for GRB 100724B. The source is not detected in any other time interval. We therefore identify it as the high-energy counterpart of the burst. Figure 15. Localization of GRB 100724B: the white contours are, respectively, the 68% and 90% containment regions, while the dotted line is the margin of the much larger 68% containment region provided in Ackermann et al. ( 2013b ) based on the prompt interval. The black cross is the best-fit localization. Appendix B Likelihood Ratio Test The Likelihood Ratio Test (LRT) is a procedure for model selection. It is a statistical test that helps to select between two nested models, m 0 and m 1 , the one that best captures all significant features of the data. The model m 0 is the null hypothesis and represents the simpler model, while m 1 is the alternative hypothesis and is more complex than m 0 . The TS is twice the difference in the log-likelihood S between the two


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The authors would like to thank the referee for thoughtful comments which improved the manuscript. This paper is based on observations taken with the NASA/ESA Hubble Space Telescope obtained at the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS5-26555. These observations are associated with the program numbers 9490 and 11147.


O O O O O O B-Grant I-Grant B-Grant O B-Organization O B-Grant B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant B-Grant I-Grant B-Grant B-Grant O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant B-Grant I-Grant B-Person O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Grant I-Grant O B-Grant O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O O B-Fellowship I-Fellowship I-Fellowship I-Fellowship O O B-Database B-Organization O B-Survey O O O O O O O O O B-Grant I-Grant I-Grant B-Grant 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 O B-Grant B-Observatory I-Observatory I-Observatory B-Organization I-Organization I-Organization I-Organization O O B-Grant I-Grant I-Grant I-Grant O O B-Organization I-Organization I-Organization O O O O B-Telescope I-Telescope O B-Observatory I-Observatory O O O O O O O O O B-Observatory I-Observatory I-Observatory B-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization

This work is supported by the SOC program (CHINARE2012-02-03), the NSFC grant (NSF11033007), National Basic Research Program of China (973 Program, 2013CB834905, 2015CB857005), and Fundamental Research Funds for the Central Universities (WK 2030220010). P.J. acknowledges support from the National Science Foundation of China with Grants NSFC 11233002 and NSFC11203022, the Fundamental Research Funds for the Central Universities, and the China Postdoctoral Science Foundation. Data from NED, NIST, and SDSS were used. This research uses data obtained through the Telescope Access Program (TAP), which has been funded by the Strategic Priority Research Program “The Emergence of Cosmological Structures” (grant No. XDB09000000). National Astronomical Observatories, Chinese Academy of Sciences, and the Special Fund for Astronomy from the Ministry of Finance. Observations obtained with the Hale Telescope at Palomar Observatory were obtained as part of an agreement between the National Astronomical Observatories, Chinese Academy of Sciences, and the California Institute of Technology.


O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject 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 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-CelestialObject I-CelestialObject 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-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O B-Citation I-Citation I-Citation I-Citation 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 B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O B-Wavelength I-Wavelength 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-Citation I-Citation O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O B-CelestialObject I-CelestialObject O O O O O O B-Citation 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-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject 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 B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject 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 B-CelestialObject I-CelestialObject O O O

of relatively pristine gas inflows in the local Universe, given the metallicity cut-off seen for LGRB progenitors. Our discovery of strong H ii region emission located at the explosion site of AT 2018cow appears a strong means to link the progenitor with ongoing star formation, and thus young (massive) stellar populations. This in contrast to inference from observing cold inflows of neutral gas, which provide an even more indirect indicator of current star formation. We note, however, that it is very difficult to make conclusive statements on a single object, given almost any location in a galaxy will have a significant line-of-sight population of old stars. 5.2 Tidal-disruption event Other explanations for AT 2018cow have been proposed that may not involve a massive star at all. One such scenario is the tidal disruption of a main-sequence star or white dwarf by an IMBH (Kuin et al. 2019 ; Perley et al. 2019 ). In the main-sequence TDE scenario (Perley et al. 2019 ), a BH mass of ∼10 4.3 M ⊙ is required. Such an IMBH would be expected to be located within a massive stellar cluster. For the case of a young parent cluster, we do indeed find a star-forming region underlying AT 2018cow, however, the explosion site is significantly offset from the peak of this source in both the white-light image of our MUSE cube and the centroid of the H α emission, where one would expect the massive IMBH to settle towards rapidly. For an older, globular cluster (GC) host, the hosting GC would lie at the upper end of the GC luminosity function (Harris 1996 ). A magnitude of the host of M V , ∼ − 9 to −11 mag follows from both extending the M–σ relation (e.g. Gültekin et al. 2009 ) to IMBH masses, and looking at the luminosities of GCs with signs of IMBHs (e.g. Noyola et al. 2010 ; Feldmeier et al. 2013 ; Lützgendorf et al. 2013 ). At the distance of CGCG 137-068 this would appear as a m V ∼ 23−25 mag source at the explosion site, and should be detectable in high-resolution imaging of the site. An alternate scenario, involving a more massive BH ∼10 5–6 M ⊙ and a low-mass white dwarf was presented by Kuin et al. ( 2019 ). Although white dwarfs may form at a few × 10 7 yr after star formation (Portegies Zwart, McMillan Makino 2007 ), i.e. comparable to the age we infer for the underlying H ii at the explosion site of AT 2018cow), these are the most massive white-dwarfs – low-mass white-dwarfs will form much later. In this case the co-location with star formation is a coincidence in this scenario. This BH required mass is comparable to that of a massive GC itself, and a dwarf satellite galaxy of CGCG 137-068 may be a more promising BH-host system. Notwithstanding the lack of spatial coincidence we find between AT 2018cow and the peak of any underlying source, we searched in our data for existence of a distinct system in the vicinity. In Fig. 6 , we show the results of fitting individual spaxels in a region surrounding the explosion site of AT 2018cow to look for


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A study (not shown here) of the possible effect of the geometry of the shock did not demonstrate a significant correlation between the observed spectra and the angle θ nB between the normal of the shock and the interplanetary magnetic field. The histogram shown in Figure 3 (d) indicates that the spectral slopes vary within the interval ∼[−2.2, −0.3] with a peak near −1.2. The bulk of the distribution is significantly shallower than the Kolmogorov scaling f −5/3 (red dashed line in Figure 3 (d)) and that reported in the solar wind (e.g., Smith et al. 2006 ). These observations question the ubiquity of the Kolmogorov scaling in the terrestrial magnetosheath, although a small fraction (17%) of the events showed a Kolmogorov spectrum (here defined as the spectral slope −1.5). Figure 3. 2D distribution of the slopes P α ( X GSE , Y GSE ) at MHD scales. The 2D distribution P α ( X GSE , Y GSE ) of the spectral slopes at MHD (a), and the integrated ones along the Y GSE direction (b) and X GSE direction (c). The blue curves represent the average magnetopause and bow shock positions computed using the paraboloidal bow shock model of Filbert Kellogg ( 1979 ) and the magnetopause model of Sibeck et al. ( 1991 ). The number in each bin represents the number of events. (d) The histogram of the measured spectral slopes where the red dashed line indicates the Kolmogorov slope −5/3. On the contrary, the slopes at the sub-ion scales were found not to depend on the location within the magnetosheath as can be seen in Figure 4 (a). This can be explained by the fact that the kinetic scales (≤100 km) are much smaller than the integral (size) scale of the magnetosheath (>10 4 km), meaning that the large-scale boundaries do not influence the small (kinetic) scale turbulence. Furthermore, the histogram of the slopes (Figure 4 (b)) is found to be similar to those reported in the solar wind (Alexandrova et al. 2012 ; Sahraoui et al. 2013 ) and in the magnetosheath (Huang et al. 2014 ; Hadid et al. 2015 ), with a peak near −2.8. This observation suggests that kinetic scale turbulence has a “universal-like” scaling distribution in the sense that it does not depend either on the explored region (magnetosheath or solar wind) or on the nature of the turbulence at MHD scale ( f −1 energy-containing range or f −5/3 inertial range), which is probably due to that kinetic scale turbulence is generated locally so its nature is not affected by large-scale inhomogeneities/fluctuations. Figure 4. 2D distribution of the slopes P α ( X GSE , Y GSE ) at sub-ion scales. The 2D distribution P α ( X GSE , Y GSE ) of the spectral slopes at sub-ion scales (a); the histogram of the spectral slopes (b). The number in each bin represents the number of events. Hadid et al. ( 2015 ) showed that the f −1 range in the magnetosheath of Saturn was populated by random-like fluctuations. It has been speculated that the interaction of the solar wind with the shock destroys the pre-existing correlations


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H.K. thanks Takeru Suzuki for inputs to develop the Heyney code and Takashi Noguchi for fruitful discussion about double-diffusive convection. This work was supported by Grants-in-Aid from the Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) (23244027 and 23103005). H.K. was supported by JSPS KAKENHI Grant Number 15J09448.


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-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O B-Model I-Model I-Model I-Model O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O B-Model I-Model O O O O O O O B-Model I-Model I-Model I-Model 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 B-Model I-Model O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O B-Model I-Model 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 O O O O O O O O O O O O O O O O O B-Model O B-Model I-Model I-Model 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 B-Model I-Model 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-Model I-Model O O O O O O O O O O O O O O O O O B-Model I-Model I-Model I-Model O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula 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 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

( 16 ), the BR emissivity in the classical limit then reads where p min is the minimal electron momentum that is required to produce a photon of energy ω = h ν/ m e c 2 . This is determined by ω = γ min − 1, which yields . In the last step of equation ( 17 ), we used a non-relativistic Maxwell–Boltzmann distribution function, with dimensionless electron temperature θ e = kT e / m e c 2 to carry out the integral. The above expressions explicitly assume p 1 , ω ≪ 1. Even without quantum corrections, to generalize the Kramers approximation to higher temperatures/energies, we shall use the relativistic Maxwell–Boltzmann distribution function where K 2 ( x ) is the modified Bessel function of second kind. 9 We also keep the full relativistic expression for and furthermore realize that at low frequencies the overall BR cross-section scales as towards higher electron energies (see the discussion about Bethe–Heitler limit). Thus, after multiplying the Kramers approximation, equation (2), by and carrying out the thermal average with the above modification, we have the relativistically improved Kramers approximation for the BR emissivity: This shows that in the classical treatment the improved asymptotic scales as for low temperatures. The origin of this correction is not quantum-mechanical but simply due to special relativistic effects. This modification absorbs the leading order corrections towards the BH limit, as we discuss next. We also mention that in equation (19) the temperature-dependent factor, is directly related to the differences in the normalization of the non-relativistic and relativistic Maxwell–Boltzmann distributions. At high temperatures, the corrections can become sizable, giving at and at , and thus should be taken into account for accurate calculations. 4.2 Definition of thermally averaged Gaunt factors The main quantity that enters the BR emission term in the photon Boltzmann equation, as well as the electron temperature evolution equation, is the thermally averaged Gaunt factor. It can be simply obtained by comparing the total plasma emissivity with the emissivity in the Kramers limit and is usually computed as In the last step, we explicitly assumed that the electrons follow a non-degenerate, relativistic Maxwell–Boltzmann distribution. 10 In the non-relativistic limit (γ 1 ≃ 1), equation ( 21 ) is a very good choice. However, for p 1 ≳ 1, the Gaunt factor scales at low frequencies (see Section 2.3 ). It is thus useful to multiply the Kramers cross-section by , which then yields a slightly modified definition for the BR Gaunt factor: This redefinition reduces the dynamic range of the Gaunt factor and is thus very useful for compressing the data in tabulations. The final BR emission term then takes the form where is given by equation ( 19b ) and by equation ( 20 ). Both definitions, of course, give exactly the same answer for the overall BR emission term. Nevertheless, in applications, is beneficial since it does not scale as


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 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 B-Citation I-Citation O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula 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 B-Citation I-Citation 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 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 B-Wavelength I-Wavelength 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-Citation I-Citation I-Citation I-Citation 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 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 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 B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O

TiO and FeH lines using the four free model parameters revealed for most stars T mag between 2000 and 2300 K with an average of 2100 K, which is approximately constant across the M1 to M7 spectral classes ( Fig. 4 b). These cool spots are also highly magnetic (see Sect. 5.3 ). Here, the difference between T phot and T mag reduces on average from 1700 K for an M1 dwarf to about 1000 K for an M7 dwarf. Interestingly, this range of spot temperature differences is typical for sunspots of various sizes (e.g., Berdyugina 2005 ). For a young, active M8.5 brown dwarf, Berdyugina et al. (2017) and Kuzmychov et al. (2017) determined T phot = 2800 K and T mag = 2200 K using also atomic and molecular lines. This result agrees with the found trend and extends our finding to ultra-cool dwarfs. The spot temperature difference with respect to the photosphere determined here for M dwarfs differs from that found from broad-band photometric measurements, as summarized by Berdyugina (2005) . This is probably due to a height-dependence of spot parameters as well as the higher sensitivity of molecular lines to the temperature than that of photometry (see Sect. 6 ). In summary, thanks to the variety of our spectral diagnostics, we found two kinds of magnetic regions with clearly different temperatures in M dwarf atmospheres as a function of the spectral class: one is cold (starspots), and the other is warm (network). Fig. 2 Illustration of the high temperature and magnetic sensitivity of FeH lines which is reproduced by our models. Observed (black) and synthetic (red) intensity and circular polarization profiles for FeH at 9897–9913 Å in the considered sample of M dwarfs. The synthetic profiles were calculated using two components: one non-magnetic (“photospheric”) and one magnetic (“spot”) atmosphere model ( Allard et al. 2001 ) with best-fit parameters obtained from fits of Stokes I and V spectra for FeH in the considered wavelength region only. All the following parameters were obtained simultaneously in one χ 2 minimization: the photosphere and spot temperatures, the magnetic field strength, the spot filling factor for the intensity f I , and the circular polarization f V . 5.3 The magnetic field strength The magnetic field strength B was determined during the same fitting procedure as described for T mag in Sect. 5.2 . It corresponds therefore to an average field strength of a given magnetic structure at a given layer of the atmosphere,as defined by the corresponding species. The B values found from atomic and molecular lines are confined to the range of 3–6 kG (there are only three outliers), with an average of about 5 kG ( Fig. 4 d). This average is practically constant throughout the considered spectral class range of M1–M7 dwarfs. Berdyugina et al. (2017) and Kuzmychov et al. (2017) similarly found B ~ 5 kG in their study of a young, active M8.5 brown dwarf. In summary, a cooler starspot atmosphere probed by the mol1 set and a hotter network atmosphere


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ACKNOWLEDGEMENTS We thank an anonymous referee for a careful reading of the manuscript and constructive comments. We acknowledge contributions of additional collaborators who helped with imaging observations to discover and monitor light echoes, as well as for discussions and contributions to proposals for telescope time for this and related projects: the Carnegie Supernova Project, Alejandro Clocchiatti, Steve Margheim, Doug Welch, and Nolan Walborn. In particular, Nolan Walborn provided helpful comments on the manuscript just weeks before he passed away, which occurred while this paper was under review. His contributions to massive star research have been tremendous, and his unique insight will be sorely missed. NS’s research on Eta Carinae’s light echoes and related LBV-like eruptions received support from NSF grants AST-1312221 and AST-1515559. Support for JLP is provided in part by FONDECYT through the grant 1151445 and by the Ministry of Economy, Development, and Tourism’s Millennium Science Initiative through grant IC120009, awarded to The Millennium Institute of Astrophysics, MAS. DJJ gratefully acknowledges support from the National Science Foundation, award AST-1440254. This paper includes data gathered with the 6.5m Magellan Telescopes located at Las Campanas Observatory, Chile. Based, in part, 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) (Program GS-2014B-Q-24).