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fragments. Our analysis finds that of the Ca-rich systems outlined by Hollands et al. ( 2018 ), only one can be attributed to being crust-rich (SDSSJ0744+4649 to 5σ significance), whilst for two other systems (SDSSJ1033+1809 and SDSSJ1351+2645) there is insufficient information available for a crustal model to be the best fit. SDSSJ1055+3725 was no longer included in the sample (see § 2.1 ). The three Fe-rich systems (SDSS1043+3516 (5.2σ), SDSSJ0741+3146 (2.8σ) and SDSSJ0823+0546 (10σ) are indeed found to be core-rich. Both the two two Mg-rich systems, SDSSJ0956+5912 and SDSSJ1158+1845 actually have fairly typical Mg/Fe ratios and due to the combination of sinking time-scales, the best-fitting models suggest that both systems are core-rich to 2σ. 4.3.3 The mass of white dwarf pollutants For those systems in the declining phase, accretion has finished and the mass in the atmosphere, combined with the sinking time-scales can be converted into the total mass of the polluting body. This calculation no longer yields a lower limit as there cannot be any material left in a circumstellar orbit which is yet to accrete. Such systems uniquely probe the mass of the polluting bodies. As shown in Fig. 11 , the bodies polluting the white dwarfs considered here are found to have masses between just half that of Vesta and the mass of the Moon. The bodies polluting white dwarfs are likely to be similar to large Solar System asteroids, as previously concluded in the literature (Farihi et al. 2010a ; Girven et al. 2012 ), although at least two systems have accreted planetary bodies approaching the mass of the Moon. Figure 11. The posterior distributions for the total mass accreted on to the thirteen polluted white dwarfs whose abundances suggest that they are in the declining phase. During the declining phase, accretion has ceased and therefore, the mass currently in the atmosphere, alongside the sinking time-scales, can be used to calculate the total mass accreted. The masses range from Vesta to the Moon. 4.3.4 Constraints on the accretion event lifetimes The accretion event lifetime for a system can be constrained from the abundances because the duration of accretion affects the probability that the system will be observed in build-up, steady state, or declining phase. The accretion event lifetimes from the 202 systems analysed here suggests that the average accretion events last yr. This result is consistent with the result derived in Girven et al. ( 2012 ) and is consistent with the theoretical predictions of Rafikov ( 2011a ) and Rafikov ( 2011b ), but is in stark contrast to the short accretion event (or disc) lifetimes predicted by Wyatt et al. ( 2014 ) to explain the difference between observed accretion rates of DA and DB white dwarfs. 5 CONCLUSIONS In this work, we present a Bayesian model to explain the abundances of planetary material observed in the atmospheres of some white dwarfs. Our method reproduces the abundance patterns observed in polluted


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ACKNOWLEDGEMENTS We thank the referee, Georges Meynet, for his very detailed and valuable comments. This research was supported by the Israel Science Foundation and by the Pazy Research Foundation. NZ thanks the support of the PEF's Alfred and Anna Grey Excellence Scholarship.


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I thank the referee, Richard Durisen, for a number of perceptive and constructive comments on the manuscript and Sandy Keiser for computer systems support. The calculations were performed primarily on the flash cluster at DTM and also on the Carnegie memex cluster at Stanford University.


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The authors wish to thank Ettore Perozzi, Michael Freyberg, Frank Haberl, Matteo Guainazzi and the XMM–Newton calibration team for checking that the observed jitter has no instrumental origin. We thank Jan-Uwe Ness, Ignacio de la Calle and the rest of the XMM–Newton scheduling team for the enormous support that made the new XMM–Newton observations possible. We also thank Barbara De Marco, Thomas Tauris, Jonathan Ferreira, Pierre-Olivier Petrucci, Henri Gilles and Rosario Iaria for very useful discussion as well as the referee for the very useful comments that significantly improved the paper. This research has made use primarily of data obtained with XMM–Newton , an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA , and on data obtained from the Chandra and ASCA Data Archives. The GC XMM–Newton monitoring project is supported by the Bundesministerium für Wirtschaft und Technologie/Deutsches Zentrum für Luft- und Raumfahrt (BMWI/DLR, FKZ 50 OR 1408 and FKZ 50 OR 1604) and the Max Planck Society . KD would like to thank MPE for the hospitality during his stay, and the German Academic Exchange Service (DAAD) for the fellowship which supported his participation in the project. TMD acknowledges support by the Spanish Ministry of Economy and Competitiveness (MINECO) under the grant AYA2013-42627 . LS acknowledges partial support from ASI INAF I/004/11/1 .


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L.M. and M.J. contributed equally to this manuscript. Fruitful discussions with Maria Lugaro, Carolyn Doherty, and Emese Plachy are gratefully acknowledged. L.M. was supported by the Premium Postdoctoral Research Program of the Hungarian Academy of Sciences. The research leading to these results has received funding from the LP2014-17 and LP2018-7 Lendület grants of the Hungarian Academy of Sciences and from the NKFIH K-115709 grant of the National Research, Development and Innovation Office of Hungary. We acknowledge with thanks the variable star observations from the AAVSO International Database contributed by observers worldwide and used in this research. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France, and NASA’s Astrophysics Data System Bibliographic Services. M.J. was supported by Martin Asplund, the Research School of Astronomy and Astrophysics at Australian National University, and funding from Australian Research Council grant No. DP150100250. M.J. wishes to acknowledge John Bourke for his assistance in revising this manuscript and Maria Lugaro for financial support of her scientific residences at Konkoly Observatory. Facility: AAVSO. Software: MESA (Paxton et al. 2018 ), GYRE (Townsend Teitler 2013 ), astropy (Astropy Collaboration et al. 2013 ; Price-Whelan et al. 2018 ), matplotlib (Hunter 2007 ), numpy (van der Walt et al. 2011 ), scipy (Jones et al. 2001 ), Period04 (Lenz Breger 2005 ), gnuplot.


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ACKNOWLEDGEMENTS Software for this project was developed under NASA’s Applied Information Systems and Astrophysics Data Programs. This work is based in part on observations made with the Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA. Support for this work was provided by NASA through an award issued by JPL/Caltech. Other aspects of this work were supported in part by NASA Astrophysics Data Analysis Program grant NNX11AF89G and NSF grant AST 0908370. As usual, 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.


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Much of this work was in progress at the time of Steve Murray’s untimely death in 2015. This work would not have been possible without his generous GTO contribution to the XBoötes data set and his strong support of Boötes multiwavelength surveys. He will be greatly missed by all of us. We thank the referee for a careful reading and constructive suggestions that have improved the manuscript. C.-T.J.C. was supported by the William H. Neukom 1964 Institute for Computational Science. R.C.H. acknowledges support from the National Science Foundation through AST award no. 1515364 and from an Alfred P. Sloan Research Fellowship. R.J.A. was supported by FONDECYT grant no. 1151408. This publication makes use of data products from the Wide-field Infrared Survey Explorer , which is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory/California Institute of Technology, funded by the National Aeronautics and Space Administration. This publication also makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation. Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and the U.S. Department of Energy Office of Science. The SDSS-III Web site is http://www.sdss3.org/ .


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ACKNOWLEDGEMENTS The authors acknowledge financial support from the following funding agencies: Centre National de la Recherche Scientifique (CNRS), Commissariat à l’énergie atomique et aux énergies alternatives (CEA), Commission Européenne (FEDER fund and Marie Curie Program), Institut Universitaire de France (IUF), IdEx program and UnivEarthS Labex program at Sorbonne Paris Cité (ANR-10-LABX-0023 and ANR-11-IDEX-0005-02), Labex OCEVU (ANR-11-LABX-0060) and the A*MIDEX project (ANR-11-IDEX-0001-02), Région Île-de-France (DIM-ACAV), Région Alsace (contrat CPER), Région Provence-Alpes-Côte d’Azur, Département du Var and Ville de La Seyne-sur-Mer, France; Bundesministerium für Bildung und Forschung (BMBF), Germany; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Stichting voor Fundamenteel Onderzoek der Materie (FOM), Nederlandse organisatie voor Wetenschappelijk Onderzoek (NWO), the Netherlands; Council of the President of the Russian Federation for young scientists and leading scientific schools supporting grants, Russia; National Authority for Scientific Research (ANCS), Romania; Ministerio de Economía y Competitividad (MINECO): Plan Estatal de Investigación (refs. FPA2015-65150-C3-1-P, -2-P and -3-P, (MINECO/FEDER)), Severo Ochoa Centre of Excellence and MultiDark Consolider (MINECO), and Prometeo and Grisolía programs (Generalitat Valenciana), Spain; Ministry of Higher Education, Scientific Research and Professional Training, Morocco. We also acknowledge technical support from Ifremer, AIM and Foselev Marine for the sea operation and CC-IN2P3 for the computing facilities.


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Resources supporting this work were provided by the NASA High-End Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center. We thank Tom Quinn and James Wadsley for use of the proprietary code Gasoline , and Charlotte Christensen for help in creating the simulations. The pynbody package (Pontzen et al. 2013 ) was used in portions of this analysis.


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Support for this work was provided by the National Aeronautics and Space Administration through Chandra grant number GO-213103A, issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of NASA under contract NAS8-03060. This work was also supported by the National Aeronautics and Space Administration through HST grant number GO-12762.007 issued by the Space Telescope Science Institute. We thank Derek Hammer for producing the HST images used here. Finally, we must thank the referee for pointing out a number of places where we needed to make the commentary more pointed. Facilities: Chandra (ACIS) , HST (ACS).


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Acknowledgments This work was funded with grants from Consejo Nacional de Investigaciones Cientificas y Tecnicas de la Republica Argentina ( CONICET ). Thanks are also due to Dr E. Irene Vega for her continuous support during the redaction of this work.


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probably also affects the density distribution along the loop and is the reason that we scaled our model emission nonlinearly with a power of 0.4 in Fig. 2 (while the observations are scaled closer to linear with a power of 0.7). The loops in our model corona look more like those in a potential field than like the loops in the observations. In our model we only prescribed the vertical component of the magnetic field, but not the horizontal component (which is not available at 45 s cadence and for this large field of view with HMI). We would therefore miss any helical component of the magnetic field, which would lead to a more twisted appearance of the magnetic field. Moreover, this would increase the energy input into the system and thus help alleviate the problem described above, at least to some extent. Finally, we assume periodic boundary conditions in our model (as do most other 3D MHD models of the solar atmosphere). This implies that the field lines of the fan loops on the western (right) side of the active region leave the box on that side and enter the box again on the other side. In the model, the fan loops therefore connect to an active region (different from the first). On the real Sun, such a connected active region would be far away, at a distance that is far larger than the size of an active region. We tried to account for this in the model by surrounding the active region by enough quiet Sun, so that the appearance of the fan loops is hopefully realistic. None of the above limitations are expected to alter the main conclusion of our study: our data-driven model can account for the structures seen on the real Sun. Future models will have to address these remaining problems step by step, however. 6. Conclusions We showed that we can reproduce many aspects of the corona above an active region using a data-driven 3D MHD model. The emission that we synthesized from the model qualitatively reproduces the observed coronal features of this active region: long loops, fan-like loops, and small transient loops in the active region core. We also showed that these model features are embedded in a diffuse background of coronal emission, as is the case on the real Sun, where a typical loop has a low contrast of only 10% to 30% to the background. Our data-driven model shows that the structure of the observed photospheric magnetic field and its temporal evolution fully govern the appearance of the corona in an active region. Driving the magnetic field at the surface induces currents in the corona at just the correct places: here the plasma is heated and forms EUV loops in the model at exactly the same place where they also appear in the real observations. The energy input in our model is solely based on the driving of the magnetic field and is thus very similar to the scenarios of field-line braiding ( Parker 1988 ) and flux-tube tectonics scenarios ( Priest et al. 2002 ). The success of our model therefore supports these heating scenarios. The


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universes can measure very different power spectra of events, just because of cosmic variance. This effect dominates any dependence of predicted anisotropies on the class of EGMF models studied here, limiting the possibility of inferring the origin of EGMF based on the observed properties of UHECRs. It also stresses the importance of a realistic characterization of the local environment of the observer to interpret observations on Earth. This can be studied further making use of ‘Constrained Simulations’ of the local Universe (e.g. Jasche Wandelt 2013 ; Sorce et al. 2016 ). 3.3 Separation angle Abreu et al. ( 2010 ) investigated the anisotropy of the UHECR arrival signal by considering the angular distance of events from Cen A. Due to its similarity, all the graphics presented in this section, if not stated otherwise, are shown for observer ID61 whose closest source is at ∼4Mpc distance. The separation angle of pairs of events in Fig. 13 was computed via the scalar product of their arrival direction, i.e. the normalized negative momentum vector of the UHECRs at time of observation. The theoretical prediction for isotropy for the distribution of events over a sphere is given by the cumulative sine function and is in good agreement with the simulated isotropic cases. We can also predict the influence of the observer effect (cf. Section 2.3 ) for the signal of the closest source. To do so, we produced a test simulation without magnetic fields with a single source of UHECRs at a distance comparable to that of the closest source for observer ID61. The separation angle function of this test gives our prediction for the finite observer effect for pairs of events that both originated from the closest source. Figure 13. The fraction of pairs of observed events, E > 58, 100 EeV (left, right), separated by less than the given angle. The coloured lines indicate the magnetic field model, the error bars show the Poissonian noise. The thick black line shows the isotropic plus the geometric prediction. The left-hand panel of Fig. 13 can be compared with fig. 8 in Abreu et al. ( 2010 ). For events above E > 58 EeV there is no significant deviation from isotropy, but for E > 100 EeV there is a clear excess. This is expected because, due to lower average travel distances at higher energies, there is a higher number of events that originated from the closest source. The influence of the geometric effect changes the form of this plot by flattening the slope in the low separation part. We emphasize that this actually affects all events from close-by sources, while our geometric prediction only considers those from the closest source. None the less, there is a significant difference between the magnetic field models: the magnetic field free case ( b0 , black) and the simulation with the lowest magnetization ( agnl , purple, cf. Fig. 1 ) show the strongest deviation from isotropy. However, for other observers the case is different and the presence of nearby sources


O O O O O O B-Person I-Person I-Person B-Person I-Person B-Person I-Person I-Person B-Person I-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person I-Person B-Person I-Person I-Person B-Person I-Person I-Person B-Person I-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person I-Person B-Person I-Person I-Person B-Person I-Person B-Person I-Person I-Person B-Person I-Person I-Person B-Person I-Person I-Person B-Person I-Person B-Person I-Person I-Person B-Person I-Person B-Person I-Person B-Person I-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 O O O O O O O O O O O O B-Observatory O B-Observatory I-Observatory O O O O O O O O O O O O O O O O O O O B-Observatory I-Observatory I-Observatory I-Observatory O O O O O O O O O B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O O O O O O O O O O O B-Organization I-Organization I-Organization I-Organization O O O O O O O O O O O O O O O O O O B-Location O O O O O O B-Location O O O O O O O O O O O O O O O O O B-Observatory I-Observatory O O O O O O O O B-Organization O O O O O O O O O B-Person I-Person O B-Person I-Person B-Person I-Person B-Person O B-Person I-Person B-Person O B-Person I-Person B-Person I-Person O B-Person I-Person B-Person I-Person O B-Person I-Person I-Person B-Person O B-Person I-Person B-Person O B-Person I-Person B-Person I-Person B-Person O B-Person I-Person B-Person O B-Person I-Person B-Person I-Person O B-Person I-Person B-Person I-Person O B-Person I-Person B-Person I-Person O B-Person I-Person B-Person I-Person B-Person I-Person B-Person O B-Person I-Person B-Person I-Person O B-Person I-Person B-Person O B-Person I-Person B-Person O B-Person I-Person B-Person O B-Person I-Person B-Person O B-Person I-Person B-Person O B-Person I-Person B-Person O B-Person I-Person B-Person O B-Person I-Person B-Person I-Person B-Person O B-Person I-Person B-Person I-Person O B-Person I-Person B-Person I-Person O B-Person I-Person I-Person B-Person O B-Person I-Person B-Person O B-Person I-Person B-Person O B-Person I-Person B-Person O B-Person I-Person B-Person O B-Person I-Person B-Person O B-Person I-Person B-Person O B-Person I-Person B-Person I-Person O B-Person I-Person B-Person O B-Person I-Person O B-Organization I-Organization I-Organization I-Organization B-Person I-Person O B-Person I-Person B-Person I-Person B-Person O B-Person I-Person O B-Organization I-Organization I-Organization I-Organization I-Organization B-Person O B-Person I-Person B-Person O B-Person I-Person O O O B-Telescope O O O O O O O O O O B-Organization I-Organization I-Organization O B-Organization I-Organization B-Organization I-Organization B-Observatory I-Observatory O B-Organization O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization O O B-Person O O O O O O O O B-Organization I-Organization I-Organization B-Organization O B-Organization I-Organization B-Person O B-Person I-Person O B-Organization I-Organization I-Organization I-Organization 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 O O B-Organization I-Organization I-Organization I-Organization O O O O B-Organization O B-Grant O O O O O O O O O B-Event I-Event I-Event I-Event I-Event I-Event I-Event I-Event I-Event O B-Organization I-Organization O O O O O B-Organization O B-Grant O B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization O O O O O B-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Person O O O O O O O B-Database I-Database I-Database B-Database O O O O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization O O O B-Organization

ACKNOWLEDGEMENTS We would like to thank Brian J. Barris, Peter Blanchard, Joshua S. Bloom, Bethany E. Cobb, Alison Coil, Louis-Benoit Desroches, Andrea Gilbert, Christopher V. Griffith, Luis C. Ho, Saurabh W. Jha, Michael T. Kandrashoff, Minkyu Kim, Nicholas Lee, Adam A. Miller, Matthew R. Moore, Aleksandir Morton, Robin E. Mostardi, Peter E. Nugent, Marina S. Papenkova, Sung Park, Daniel A. Perley, David Pooley, Dovi Poznanski, Adam G. Riess, Brad Tucker, Vivian U, XiangGao Wang, and Xiaofeng Wang for their assistance with some of the observations over the last three decades. We are grateful to the staff at Lick and Keck Observatories for their hard work in making the observations possible. 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 (NASA); 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 Maunakea has always had within the indigenous Hawaiian community; we are most fortunate to have the opportunity to conduct observations from this mountain. Research at Lick Observatory is partially supported by a generous gift from Google. We also greatly appreciate contributions from numerous individuals, including Charles Baxter and Jinee Tao, Firmin Berta, Marc and Cristina Bensadoun, Frank and Roberta Bliss, Eliza Brown and Hal Candee, Kathy Burck and Gilbert Mon toya, Alan and Jane Chew, David and Linda Cornfield, Michael Danylchuk, Jim and Hildy DeFrisco, William and Phyllis Draper, Luke Ellis and Laura Sawczuk, Jim Erbs and Shan Atkins, Alan Eustace and Kathy Kwan, David Friedberg, Harvey Glasser, Charles and Gretchen Gooding, Alan Gould and Diane Tokugawa, Thomas and Dana Grogan, Alan and Gladys Hoefer, Charles and Patricia Hunt, Stephen and Catherine Imbler, Adam and Rita Kablanian, Roger and Jody Lawler, Kenneth and Gloria Levy, Peter Maier, DuBose and Nancy Montgomery, Rand Morimoto and Ana Henderson, Sunil Nagaraj and Mary Katherine Stimmler, Peter and Kristan Norvig, James and Marie O’Brient, Emilie and Doug Ogden, Paul and Sandra Otellini, Jeanne and Sanford Robertson, Stanley and Miriam Schiffman, Thomas and Alison Schneider, Ajay Shah and Lata Krishnan, Alex and Irina Shubat, the Silicon Valley Community Foundation, Mary-Lou Smulders and Nicholas Hodson, Hans Spiller, Alan and Janet Stanford, the Hugh Stuart Center Charitable Trust, Clark and Sharon Winslow, Weldon and Ruth Wood, and many others. KAIT and its ongoing operation were made possible by donations from Sun Microsystems, Inc., the Hewlett-Packard Company, AutoScope Corporation, Lick Observatory, the NSF, the University of California, the Sylvia Jim Katzman Foundation, and the TABASGO Foundation. Support for A.V.F.’s SN research group has been provided by the National Science Foundation (NSF), the TABASGO Foundation, Gary and Cynthia Bengier, the Christopher R. Redlich Fund, and the Miller Institute for Basic Research in Science (U.C. Berkeley). A.V.F.’s work was conducted in part at the Aspen Center for Physics, which is supported by NSF grant PHY-1607611; he thanks the Center for its hospitality during the supermassive black holes workshop in June and July 2018. The U.C.S.C. group is supported in part by NSF grant AST-1518052, the Gordon Betty Moore Foundation, the Heising-Simons Foundation, and by fellowships from the Alfred P. Sloan Foundation and the David and Lucile Packard Foundation to R.J.F. 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.


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

H.R.W. acknowledges support from the UK Science Technology Facilities Council (STFC). The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement No. 336792. D.K.S. acknowledges support from STFC consolidated grant ST/J0016/1. The authors thank the anonymous referee for their useful feedback and comments. We would also like to thank D.S. Amundsen, B. Drummond, J. Barstow, and K. Heng for useful discussions.


O O O O O O O O O O O O O O O O O O O O O O O O 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 O O B-CelestialObject 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-Software I-Software I-Software I-Software O O B-Citation I-Citation I-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 O O O O 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 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 B-Citation I-Citation I-Citation I-Citation O B-Citation 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 B-Software O O O O O B-CelestialObject I-CelestialObject 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 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 B-Formula I-Formula I-Formula O O O O O O B-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O B-Instrument B-Wavelength O B-Wavelength 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 B-Model I-Model I-Model I-Model I-Model 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 B-Citation I-Citation I-Citation O 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 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

is able to remove binary stars, and (b) that the removed fraction of stars in the range where we expect unresolved binary or triple stars is higher, in line with the previous point (a). We note that the filtering removes a substantial fraction of multiple systems. In particular, Gaia cannot find astrometric solutions typically for binaries. The exact fraction of binaries filtered out by which of the criteria is however a non-trivial problem and cannot be quantified here as this would depend on detailed modeling of the space craft and the stellar population at the distance of the ONC, see for example Michalik et al. (2014) . 4.2. PMS isochrones Stellar models have been computed using the most recent version of the Pisa stellar evolutionary code (see e.g., Tognelli et al. 2011 ) described in detail in previous papers (see Randich et al. 2018 ; Tognelli et al. 2018 , and references therein). We simply recall the main aspects relevant for the present analysis. The reference set of models adopts a solar calibrated 4 mixing length parameter, namely α ML = 2.0. However, for the comparison we also used a much lower value, namely α ML = 1.00 (low convection efficiency models) which produces cooler models with inflated radii (see e.g., Tognelli et al. 2012 , 2018 ). Evolutionary tracks of mass ≥1.20 M ⊙ have been computed adopting a core convective overshooting parameter β ov = 0.15, following the recent calibration of the Pisa models by means of the TZ Fornacis eclipsing binary ( Valle et al. 2017 ). From the models (in the mass range 0.1−20 M ⊙ ) we obtained isochrones in the age range [0.1, 100] Myr with a variable spacing in age (down to δ t = 0.1 Myr), allowing for a very good age resolution. For the reference set of models we used [Fe/H] = +0.0, corresponding to an initial helium abundance Y = 0.274 and metallicity Z = 0.013 given the Asplund et al. (2009) solar heavy-element mixture. We have converted the theoretical results into the OmegaCAM r and i absolute A B magnitudes using bolometric corrections we computed using a formalism similar to that described in Girardi et al. (2002) , employing the MARCS 2008 synthetic spectra library ( Gustafsson et al. 2008 ), which is available for T eff ∈ [2500, 8000] K, log g ∈ [ − 0.5, 5.5], and [Fe/H] ∈[−2.0, +0.5] completed with the Castelli Kurucz (2003) models for T eff > 8000 K. Next we compared the evolutionary models with the data in order to identify the best fitting isochrones for the observed PMS populations. This was performed by using the same Bayesian maximum likelihood technique described in Randich et al. (2018) . Briefly, the method computes the distance of each star in the observational plane from a given isochrone extracted from our database. The square of the distance is used to define the likelihood of a single star. Then, the total likelihood is defined as the product of all the single star likelihoods. The parameters to be recovered in this work are the age t and the reddening E (


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 O O O O O O O O O O O O O O O O O O O O O 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-Observatory O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O B-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 B-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

shifts of the energy-release region along the separator. Nevertheless, some hints concerning this issue can be drawn from the behavior of the emission spots as function of the radii of the energy-release spheres R , which are plotted by various colors in Figs. 3 and 5 . We also checked the patterns of emission obtained under the similar assumptions in a few other topological models of solar magnetic fields (i.e., involving the bifurcations of null points). In these models, however, we did not find the behavior of the ribbons as rich as in the GKSS model. This is most probably because only the latter model exhibits the genuine topological instability, i.e., when a small rearrangement of the magnetic sources results in the dramatic reconstruction of the magnetic field lines in the entire space. In summary, the four-ribbon configurations exist only in a quite small semilunar region of topological instability (where the bifurcation takes place); at all other locations of the fourth magnetic source, a three- (or even two-)ribbon emission appears. Hence, we should expect that fraction of the four-ribbon flares will be sufficiently small because of the relatively small area of the region of topological instability. This prediction agrees very well with the observations. Most of the anemone flares detected by Hinode satellite possess three ribbons; the four-ribbon flares also exist but they are formed seldomly. This is why we believe that our topological model, although not universal, provides a reasonable interpretation of the relevant phenomena by varying only a single parameter. Appendix A: Basic parameters of the separator in the two-dome structure In general, computing a spatial configuration of the separator is a non-trivial task: the separator is an inherently unstable structure, since any field line originating in its neighborhood quickly deviates outward. So, the straightforward numerical integration is meaningless, and a more elaborate type of algorithm should be applied. In the present work, we used the following procedure: Since footpoints of the separator, ( x f1 , y f1 ) and ( x f2 , y f2 ), are actually the null points of the magnetic field in z = 0 plane, we calculated the distribution of B 2 in this plane, sought for its minima, and finally checked that B 2 = 0 in these minima (and, therefore, B = 0). The analysis of the scalar function B 2 ( x , y ) was employed only because, from the computational point of view, it is much more simple and robust than the analysis of the vector field B ( x , y ). To find a position of the separator above the plane z = 0, we analyzed the following “global” behavior of the magnetic field lines: (a) First of all, we fixed a vertical plane intersecting the line connecting the opposite footpoints of the separator ( x f1 , y f1 , 0) and ( x f2 , y f2 , 0); to get a better accuracy, it is desirable that this plane be approximately perpendicular to the line. (b) Then, we generated a mesh of points


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O B-Survey 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 B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation 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 B-Survey O O O O 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-Tag I-Tag I-Tag I-Tag I-Tag I-Tag I-Tag O O O O O O O O O O O B-Wavelength O O O O B-CelestialRegion I-CelestialRegion B-Citation I-Citation I-Citation I-Citation O B-Citation O O O O O O O O O O O O O O O O B-Survey O 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 B-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 B-Survey 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 B-Survey 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 B-Survey B-Citation I-Citation I-Citation I-Citation O O O O O O O B-Survey 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 B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-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 O O O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-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 O O O O O O O O O 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 O O O O O O O O O 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 I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-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 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 B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength O O O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength O O O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength O O O O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-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 O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength O O O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength O O O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength O O O O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

collisions with para -H 2 ( j 2 = 0). We also observe that the relative magnitudes of the rate coefficients for the transitions to the 1 01 level are different in Figs 2(a) and (b) . Figure 2. Rate coefficients as a function of temperature for de-excitation transitions to the final 1 01 level of ortho -H 2 S in collisions with (a) para -H 2 ( j 2 = 0) and (b) ortho -H 2 ( j 2 = 1). The initial levels are indicated on the plots. Comparing the plots in Figs 1(a) and 2(a) and the plots in Figs 1(b) and 2(b) , we see that for these lower rotational levels the rate coefficients for collision-induced transitions in ortho -H 2 S are somewhat larger than those in para -H 2 S. 4 DISCUSSION Since H 2 O–H 2 rate coefficients have been used as surrogates for H 2 S–H 2 rate coefficients (Crockett et al. 2014 ; Vastel et al. 2018 ), it is interesting to compare the overall magnitudes of these two sets of rate coefficients. Fig. 3 compares the rate coefficients for de-excitation transitions in ortho -H 2 O and ortho -H 2 S induced by collisions with para -H 2 ( j 2 = 0) and ortho -H 2 ( j 2 = 1) at temperatures of 5 and 100 K. Fig. 4 presents a similar comparison for para -H 2 O and para -H 2 S rate coefficients. The rate coefficients for H 2 S–H 2 collisions are taken from this work, while those for H 2 O–H 2 collisions were obtained from the work by Daniel et al. ( 2011 ). Figure 3. Comparison of de-excitation rate coefficients between the 12 lowest rotational levels of ortho -H 2 O and ortho -H 2 S in collisions with (a) para -H 2 ( j 2 = 0) at 5 K, (b) para -H 2 ( j 2 = 0) at 100 K, (c) ortho -H 2 ( j 2 = 1) at 5 K, and (d) ortho -H 2 ( j 2 = 1) at 100 K. The solid line denotes equal rate coefficients for ortho -H 2 O and ortho -H 2 S, while the dashed lines represent a factor of 2 difference in the rate coefficients. Figure 4. Comparison of de-excitation rate coefficients between the 12 lowest rotational levels of para -H 2 O and para -H 2 S in collisions with (a) para -H 2 ( j 2 = 0) at 5 K, (b) para -H 2 ( j 2 = 0) at 100 K, (c) ortho -H 2 ( j 2 = 1) at 5 K, and (d) ortho -H 2 ( j 2 = 1) at 100 K. The solid line denotes equal rate coefficients for para -H 2 O and para -H 2 S, while the dashed lines represent a factor of 2 difference in the rate coefficients. We see in both Figs 3 and 4 that the transitions in H 2 O with the largest rate coefficients are greater in magnitude than the corresponding transitions in H 2 S, that is to say, the points in upper right-hand corner of these figures are to the right of the solid diagonal line. These differences reflect the different topologies of the H 2 O and H 2 S PES. By contrast, for H 2 S–H 2 transitions with smaller rate coefficients, i.e. those lying on the left-hand side of the plots in these figures, are larger than the rate coefficients for the corresponding transitions in H 2 O–H 2 . It should be noted that the energy spacings in H 2 S are smaller than in H 2 O since the rotational constants for the


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ACKNOWLEDGEMENTS We thank the anonymous referee for the valuable comments and suggestions. We thank Andre Izidoro for the discussions concerning our findings during the participation in the ‘Protoplanetary Disks and Planet Formation and Evolution’ programme organized by the Munich Institute for Astro-and Particle Physics (MIAPP). R.A.M. thanks financial support from Fundação de Amparo à Pesquisa do Estado de São Paulo (Grants: 2011/08171-3, 2013/24281-9 and 2016/12113-2).


O O O O O O O O O O O O O O B-Person I-Person I-Person O B-Person I-Person O O O O B-Person O O O O B-Fellowship I-Fellowship O O O O O O O B-Organization O B-Organization O O O B-Grant I-Grant I-Grant I-Grant B-Person O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Grant I-Grant O O O O O O O B-Organization I-Organization I-Organization O O B-Organization I-Organization B-Grant I-Grant I-Grant B-Grant I-Grant I-Grant I-Grant I-Grant B-Person O B-Person O O B-Location O B-Grant I-Grant I-Grant I-Grant I-Grant B-Grant O O O O O O O O O O B-ComputingFacility O O O B-Location I-Location I-Location I-Location O O B-Grant I-Grant B-Grant I-Grant O O B-Grant I-Grant I-Grant O O O B-Organization I-Organization I-Organization I-Organization I-Organization

We thank the anonymous referee for the critical reading and valuable comments. We thank J. Le Bourlot and B. Godard for the insightful discussions. V.V. acknowledges support from a CNRS-CONICYT scholarship. This research has been partially funded by CONICYT and CNRS, according to the December 11, 2007 agreement. P.H. acknowledges the financial support of the Agence National pour la Recherche through the COSMIS project. This research has received funding from the European Research Council under the European Community’s Seventh Framework Program (FP7/2007-2013 Grant Agreement No. 306483). M.G. and P.L. thank the French Program “Physique Chimie du Milieu Interstellaire” (PCMI). This work was granted access to the HPC resources of MesoPSL financed by the Region Ile de France and the project Equip@Meso (reference ANR-10-EQPX-29-01) of the programme Investissements d’Avenir supervised by the Agence Nationale pour la Recherche


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

in the formation of van der Waals complexes. The heat of evaporation of a single He atom is about 5 cm −1 (Toennies Vilesov 2004 ). Assuming an extra 7% depletion when Ar gas is replaced with dihydrogen, we can estimate the lower limit of the energy released in the droplets to be about 4200 cm −1 . The real reaction energy is expected to be much higher because not all helium droplets contain both reactants. Additionally, an ejection of the hot reaction products from the helium droplets, as well as a dissipation of the reaction energy by photon emission, are expected (Krasnokutski Huisken 2010b ). This estimate is only consistent with the reaction leading to the formation of the HCH molecule becuase the formation of the CH 2 molecule would lead to the release of only a small amount of energy ∼600 cm −1 (Harding et al. 1993 ). The high rate of this reaction found at ultra-low temperature, assumes no energy barrier in the reaction pathway. Therefore, our experiment is in line with the results of quantum chemical computations that predict the barrierless reaction C + H 2 → HCH (Harding et al. 1993 ). In the case of doping of helium droplets by more than a single dihydrogen molecule, the formed HCH molecule can also further react with a H 2 molecule leading to the formation of methane. However, the quantum chemical computations predict the presence of a barrier for this reaction (Ge et al. 2010 ; Lu et al. 2010 ). Therefore, we expect that this reaction should not proceed inside the helium droplets and that the reactions of carbon atoms are terminated after the formation of HCH molecules. 3.2. Mass Spectrometry In the next step, we applied mass spectrometry for the characterization of products of chemical reactions. In this experiment, larger helium droplets (up to 10 5 He atoms) were used. The droplets were first doped with multiple dihydrogen molecules and, in the second pick-up chamber, one or a few carbon atoms were added. We used two different conditions for the doping with dihydrogen. The helium droplets picked up about 10 and 100 dihydrogen molecules on average at low and high doping conditions, correspondingly. Although, even at the high doping conditions, the C/H ratio is much higher than that present in the ISM, it is low enough to saturate the chemistry with hydrogen (i.e., more than five hydrogen atoms per carbon atom). The doped helium droplets were ionized by electron impact in the head of the TOF mass spectrometer. The collision of a doped helium droplet with an electron, having energy larger than 25 eV, results in the formation of He + . This positive hole migrates within the droplet until it becomes localized either at a dopant or at a helium dimer to form (Scheidemann et al. 1993 ). Therefore, the cations of dopants and helium clusters as well as their complexes are produced. Figure 2 shows the mass spectra of helium droplets doped with dihydrogen alone and together with carbon atoms. Both mass spectra were recorded one after


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

the CH features and C i lines in metal-poor dwarfs with [Fe/H] –3.0 (see Fabbian et al. 2009 ; Jacobson Frebel 2015 ; Placco et al. 2016a ), in what follows we shall assume that this correction is not well-determined below [Fe/H] ≲ −3.0, and make the conservative assumption that A (C i ) 3D,NLTE – A (CH) 3D,LTE = 0.0, for all [Fe/H], and hence A (CH) 3D,NLTE = A (CH) 3D,LTE . The reader should bear in mind that the 3D,NLTE corrections we shall present in what follows are most likely less extreme than would be obtained by adoption of the equation in the previous paragraph. 4. Revised <italic>A</italic>(C) versus [Fe/H] and [C/Fe] versus [Fe/H] Diagrams 4.1. The Yoon et al. (<xref ref-type="bibr" rid="apjab1f84bib113">2016</xref>) Sample of CEMP Stars With the 3D–1D and NLTE–LTE corrections in hand, we now investigate their effect on the distribution of the CEMP-no stars in the ( A (C), [Fe/H]) and ([C/Fe], [Fe/H]) planes. Figure 4 presents the data for the CEMP-no and CEMP-s objects compiled by Yoon et al. ( 2016 ), 7 7 We used only stars in the Yoon et al. ( 2016 ) catalog for which the [C/Fe] values were based on the CH G -band. While this does not affect the CEMP-no stars, it excludes some 15 CEMP-s objects. We also required the presence of [Ba/Fe] to identify membership of the CEMP-no and CEMP-s subclasses, except for stars with [Fe/H] −3.3, where in the absence of detected [Ba/Fe] we assume CEMP-no status. together with those for an additional recently reported eight CEMP-no stars presented in Table 4 , and four stars identified in Table 6 . The effects of the corrections to A (C), [C/Fe], and [Fe/H] are presented in the three rows of the figure. The uppermost row, panels (a) and (b), show data obtained using 1D,LTE for A (C) 1D,LTE and [C/Fe] 1D,LTE versus [Fe/H] 1D,LTE , respectively. Also shown in the top left panel (a) are the the ellipses containing the Groups I, II, and III of Yoon et al. ( 2016 ), together with the “high-carbon band” (horizontal orange line) and the “low-carbon band” (horizontal light blue line) of Spite et al. ( 2013 ), Bonifacio et al. ( 2015 , 2018 ), and Caffau et al. ( 2018 ) (truncated on the right by the [C/Fe] = +1.0 locus). 8 8 We draw the reader’s attention to the fact that the Yoon et al. ( 2016 ) model contains three components, while that of Caffau et al. ( 2018 ) has only two. The question one might ask is: how many components are required to best describe the stellar distribution? We shall discuss this further in Sections 7.1 and 8 . In these panels, (a) and (b), red and gray symbols refer to CEMP-no stars on the one hand, and CEMP-s stars on the other, and in what follows in the middle and bottom rows the symbol for each star will retain the same color as adopted in these uppermost panels. The full and dotted lines in all panels represent the loci of the [C/Fe] > +0.7 divide between C-normal and CEMP stars, and [C/Fe] = 0.0, respectively. Figure 4. Carbon vs. iron abundances for CEMP-no (red symbols)


O O O O O O O B-Wavelength I-Wavelength O B-Wavelength I-Wavelength O B-Wavelength I-Wavelength O O B-Wavelength I-Wavelength O O O O O O O B-Wavelength I-Wavelength O O O O O O B-Wavelength I-Wavelength B-Wavelength B-Wavelength B-Wavelength O O O O O O O O O O O O O B-Wavelength I-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 B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength O O O B-Citation I-Citation I-Citation I-Citation 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 B-Instrument 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 B-Model I-Model I-Model 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 O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O B-TextGarbage I-TextGarbage O O O O O O O O O O O O O O O O O O O O O O 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 B-CelestialObject I-CelestialObject 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 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 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

part. The short-wavelength region contains the strong Balmer lines of H γ , H δ , and H ε , while the long-wavelength section only contains H β and weaker lines of He i λλ 4387, 4471, 4713, 4921. The difference in the CCF strength for the two regions suggests that the H Balmer lines are the dominant contributor to the CCF amplitude. In the similar, lower-mass binary, EL CVn, evidence suggests the presence of a thick hydrogen envelope even after extreme mass loss (Maxted et al. 2014 ), and the spectrum of the companion in EL CVn shows strong H Balmer lines with narrow cores (Wang et al. 2020 ), consistent with their appearance in the model CCF template spectra for solar abundances that we use here. Thus, the companion of Regulus probably has a photosphere with a significant hydrogen abundance. 4. Discussion The cross-correlation analysis of the large set of high-S/N spectra from ESPaDOnS/NARVAL reveals a weak signal that has all the properties expected for the spectral signature of the pre-white dwarf companion of Regulus. The CCF peak only appears using model spectra for a hot object, and it attains the strongest and narrowest morphology for a secondary semiamplitude that is consistent with the predicted extreme mass ratio and low mass of the pre-white dwarf remnant. The narrow appearance of the peak agrees with expectations of a low projected rotational velocity for synchronous rotation that is predicted in models of binary evolution. The mass and radius implied by the observations lead to a predicted small gravitational redshift that is consistent with the measured peak velocity. Taken together, these results indicate that the CCF peak marks the first detection of the spectral features of the pre-white dwarf companion of Regulus. The stellar masses we derive from the CCF analysis are similar to those proposed in earlier work (Gies et al. 2008 ). Che et al. ( 2011 ) used the stellar temperature and luminosity and the Yale–Yonsei evolutionary tracks to find a primary mass of M 1 = (4.15 ± 0.06) M ⊙ . This agrees within uncertainties with our result, M 1 = (3.7 ± 1.4) M ⊙ . The pre-white dwarf star has a low mass, , which represents the mass of the surviving core after completion of mass transfer. There is a close relationship between core mass and the properties of the former, Roche-filling red giant, and this implies that the core mass is related to the orbital period of the system. Rappaport et al. ( 2009 ) describe how the relation applies to the Regulus system and how the orbital period leads to a predicted pre-white dwarf mass of M 2 = (0.28 ± 0.05) M ⊙ , and this estimate agrees within uncertainties with the measured mass. The evolution of the stellar core after envelope removal was investigated by Istrate et al. ( 2016 ) using MESA models to study the internal structure and tracks in the plane. We show in Figure 8 one example for a pre-white dwarf with an He core and a mass of 0.305 M ⊙ from the basic set they present, i.e.,


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

statistical studies that can identify correlations over longer time-scales, and more accurately measure the scatter between gas reservoirs and black hole growth. It is thus interesting to make predictions for the connection between H i and black hole properties. Fig. 9 shows how black hole properties depend on the H i content of galaxies in simba , specifically the total H i mass M H i (left column), and the H i mass fraction f H i = M H i / M * (right column). The rows show various black hole properties, from top to bottom: M BH , , M BH / M ⋆ , and f Edd . All galaxies are colour coded by sSFR. The running median at z = 0 is shown as the black line with 1σ uncertainties from jackknife resampling. The blue and turqoise lines show the running medians at z = 1, 2 respectively; the individual galaxy points are not shown at those redshifts. Figure 9. Black hole properties as a function of H i content in simba . Each galaxy at z = 0 is colour coded by sSFR and the black line is the running median at z = 0. The blue and cyan lines show the corresponding medians at z = 1, 2, respectively. There is a strong anticorrelation between M BH and f H i , as well as a correlation between f Edd and f H i , both reflecting a tight M BH – M ⋆ relation. The top left panel shows that the black hole mass is essentially uncorrelated with H i mass, and there is little evolution in this relation. More interestingly, at a given H i mass, larger black holes populate more quiescent galaxies. This shows that there is a strong connection between black hole growth and gas removal in galaxy outskirts, likely owing to suppression of cooling to feed the H i reservoir. The most star-forming galaxies primarily have the lowest M BH , but there is also a weaker trend that they have the highest M H i . Hence star formation is enhanced in galaxies that have both small black holes and high gas content. The top right panel shows M BH versus f H i , which displays a strong anticorrelation, reflecting a tight M BH – M ⋆ relation at late times, with the most star-forming galaxies having concurrently the smallest black holes and highest gas fractions. There is modest evolution upwards in this relation with time, such that galaxies at a given black hole mass have higher f H i at earlier times, reflecting the overall increase in gas content in galaxies at earlier epochs (Davé et al. 2019 ). The second row shows the dependence of BHAR on H i content. At z = 0, BHAR shows little correlation with H i mass, but there is an evident correlation at such that black hole accretion is stronger for higher H i masses. At these earlier epochs, the accretion is dominated by the torque-limited mode, which depends on gas fraction. Even though torque-limited accretion is computed within the core of the galaxy while the H i is more diffusely distributed, the overall enhanced gas content appears to drive black hole accretion. By z = 0, in contrast, the emergence of quenched galaxies dominated by Bondi


O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O B-Model I-Model 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 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 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 B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation 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 B-Citation I-Citation I-Citation O O O O B-Person B-Citation I-Citation O O O O O O O O O O O O O B-Model I-Model I-Model O B-Observatory O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O B-Telescope O O O O O B-Telescope O B-Telescope O O O O O O O O O O O O O B-Telescope B-Telescope 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

in Table 2 . For an easy display, only the deviations of the parameters ( a , e , i , ω , Ω, and w ) from the true values (6922.8781 km, 0.00181017, 429715, 2070229, 1169049, and 225215) are listed. Table 2 The Orbit Parameter Spaces Note. “Δ a ,” “Δ e ,” “Δ i ,” “Δ ω ,” “ΔΩ,” and “Δ w ” are the deviations for the semimajor axis, eccentricity, inclination angle, RAAN, argument of perigee, and mean anomaly, respectively. First, the orbit determination method is demonstrated with LE. At each grid point of the parameter space, the “predicted” profile is folded and its significance is obtained. As shown in Figure 3 , the significance of the profile varies significantly with the deviation of the orbital parameters and has a maximum around the true value (zero deviation). Then, the maxima obtained by fitting a Gaussian function curve give the optimal values for the six orbital parameters separately, i.e., each time one parameter is free with the other five fixed, and the results are shown in Table 3 . The process obtaining the best parameters is very similar to that used by Sheikh et al. ( 2007 ) to get the TOAs from the observed pulse profiles (Sheikh 2005 ). Therefore, the uncertainties of these parameter values can be obtained in a similar way as follows:where W is the FWHM, and S/N is the signal-to-noise ratio obtained by the bootstrap method (Diaconis Efron 1983 ). As mentioned by Sheikh (Sheikh 2005 ), the S/N is limited to a maximum of 1000 by Figure 3. Orbit determine result with Insight/LE: χ 2 of the orbit elements of calculations (blue squares) and fitted results (red lines). “Δ a ,” “Δ e ,” “Δ i ,” “Δ ω ,” “ΔΩ,” and “Δ w ” are the deviations for the semimajor axis, eccentricity, inclination angle, RAAN, argument of perigee, and mean anomaly, respectively. Table 3 Best Estimated Value of the Elements and Errors (3 σ ) Then, similar demonstrations are also done for HE and ME, as shown in Table 3 . It shows that the errors for HE are less than those for ME and LE, because it has collected more pulsed photons. By combining all the data from HE, ME, and LE, the errors become smaller. By transferring the orbit elements to the cartesian parameters, we obtain the 3 σ errors of the current position and velocity, which are 3.15 km, 6.61 km, and 4.46 km for x, y, and z ; and 0.0073 km s −1 , 0.0033 km s −1 , and 0.0042 km s −1 for v x , v y , and v z , respectively. In short, the position and velocity are pinpointed within 10 km (3 σ ) and 10 m s −1 (3 σ ). 5. Discussions Conventionally, a minimum of three pulsars are required to get the absolute navigation. Considering the clock time-offset on the spacecraft, another pulsar is needed. Thus, at least four pulsars should be observed simultaneously, which would require at least four detectors, increasing the technical complexity and the cost of the mass, energy, and money. An alternate choice is to observe different pulsars sequentially using a single detector, which would increase the risk of the


O O O O O O O O O O O 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 B-CelestialObject 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 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 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 B-ObservationalTechniques O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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-ObservationalTechniques O B-CelestialObject O B-CelestialObject O O O O O O O O O O O O O O B-ObservationalTechniques 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 B-ObservationalTechniques O O O O O O O O O O O O O B-ObservationalTechniques O B-CelestialObject O O O O O O O O O B-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject B-CelestialObject O O O O O O B-Formula 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 B-CelestialObject O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O B-CelestialObject I-CelestialObject O O O O O B-CelestialObject B-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O B-CelestialObject 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 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 B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation 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 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 B-CelestialObject 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

the latter. Fig. 7 shows that if one adopts a T eff lower by 100 K then nearly exact agreement between dynamical and asteroseismic numbers are reached for this star when adopting the correction from Rodrigues et al. ( 2017 ). For KIC8410637 comparisons to very similar stars in the open cluster NGC6819 (Handberg et al. 2017 ) suggests that the observed T eff , measured by Frandsen et al. ( 2013 ), could be too high. There are reasons to suspect that T eff of the binary sample measured by Gaulme et al. ( 2016 ) could be overestimated for some stars, which would cause an overestimate of mass and radius from the asteroseismic scaling relations even if appropriate corrections are applied. The way T eff was measured in that study ignored the continuum contribution from the secondary stars, which makes the spectral lines appear weaker, potentially mimicking a higher temperature. The stars that we re-measured taking into account the light ratio were found cooler, though only by 56, 16, and 12 K. However, the light ratio and therefore the potential overestimate of T eff is larger for the two stars with largest discrepancy between dynamical and asteroseismic measures, KIC5786154A and KIC4663623A, than any of the three giants in our sample. We also note that the spectroscopic log g values reported by Gaulme et al. ( 2016 ) for these two stars are larger than the dynamical and asteroseismic log g measurements by 0.25 and 0.5 dex, suggesting potential issues with the spectroscopic analysis. KIC10001167A can be compared to stars in the globular cluster 47 Tucanae (47 Tuc; NGC104) given that it has similar metallicity ([Fe/H]∼−0.7, compare Gaulme et al. 2016 and Brogaard et al. 2017 ). Since the globular clusters are almost always found to be as old or older than field stars at similar metallicity, KIC10001167A would be expected to have an age equal to or younger than 47 Tuc. A comparison to the turn-off mass of 47 Tuc determined from the eclipsing member V69 (Thompson et al. 2010 ), extrapolated to the giant phase via isochrones (Brogaard et al. 2017 ) would then suggest a mass of for KIC10001167A, about 2σ larger than the measured by Gaulme et al. ( 2016 ). Indeed, if their low mass of is correct, the corresponding age of this star would be larger than the presently established age of the Universe. This problem could be avoided if the star is an AGB star that experienced mass-loss on the RGB. However, we also note that the T eff measured by Gaulme et al. ( 2016 ) for KIC10001167B, the MS star in this binary, is very much (∼6σ) larger than would be expected for their measure of a star on the MS. This suggests that the true mass of KIC10001167B is larger. Since dynamical mass estimates of the two components of a binary system correlate strongly, this also indicates that the mass of KIC10001167A is larger than the dynamical measure. Furthermore, if KIC10001167A is an AGB star then f Δν is ∼1.005 instead of ∼0.957 and thus the seismic mass and radius would be


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 B-CelestialObject I-CelestialObject 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-Wavelength I-Wavelength 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 B-Wavelength I-Wavelength O O O O O O O O B-CelestialObject O O O O B-CelestialObject O O O O O O O O O B-CelestialObject I-CelestialObject O O O O 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 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 O B-CelestialObject I-CelestialObject O B-CelestialObject 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 B-CelestialObject 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-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 B-CelestialObject B-CelestialObject O O B-Wavelength 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-Wavelength O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O B-CelestialObject O O B-Wavelength B-Wavelength O B-Wavelength I-Wavelength 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 B-Wavelength I-Wavelength 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 O O O O O O O O B-CelestialObject O O B-Wavelength I-Wavelength O O O B-Telescope O O B-CelestialObject O O O O O O O O B-Wavelength B-Wavelength O B-Wavelength I-Wavelength

becomes minimum at S, with the Lorentz factor reaching maximum, suggesting a highly Doppler boosting jet. Together with the fact that an active γ -ray flaring event in 1H 0323+342 coincided with the passage of a highly superluminal component through S (Doi et al. 2018 ), the recollimation shock S at the end of ACZ might be a potential site of γ -ray production as well as the jet base. The deprojected distance of this feature is ∼40–100 pc. The γ -ray production at such distances is much higher than those usually suggested in typical γ -ray blazars, while this situation is quite similar to HST-1 in the jet of M87. 6. We found that the core shift of the 1H 0323+342 jet is small between 1.4 and 43 GHz. This is consistent with the jet having a small viewing angle to our line of sight. We estimated a relative separation between the 43 GHz core and the central BH using the measured parabolic collimation profile of the inner jet, and obtained a deprojected separation of ∼(0.24–0.71)pc (or possibly shorter) for a viewing angle of 4°–12°. 7. We found various remarkable similarities in the parsec-scale jet structures between 1H 0323+342 and M87 (e.g., the collimation profile and recollimation shock). If M BH of 1H 0323+342 is ∼4 × 10 8 M ⊙ and thus follows the M BH – σ relation, we suggest that a common jet formation mechanism is at work in M87 and 1H 0323+342, where the external gas bound by the SMBH potential plays a role in collimating the jets. 8. If M BH of 1H 0323+342 is a few times (and thus close to or above the Eddington limit), which is proposed by several previous papers, the parabolic jet continues up to 10 7–8 R s from the black hole, suggesting additional large-scale structures that confine the jet. NLR outflows, which may be driven by super-Eddington accretion flows, could be responsible for the large-scale jet confinement. Appendix Calibrator 0329+3510 0329+3510 is a radio source separated by 136 on the sky from 1H 0323+342. This source is a candidate to be a high-frequency peaker, which is a subclass of young radio galaxies (Dallacasa et al. 2000 ). In Figure 9 we show self-calibrated images of 0329+3510 obtained at 15, 24, and 43 GHz. The source morphology significantly changes with frequency. At 43 GHz, where the highest angular resolution is available, the source is resolved into the core (the southernmost brightest region) and a strong knot. The core and the knot are also securely resolved at 24 GHz. However, the two features are mixed in a synthesized beam at 15 GHz and the lower frequencies. This is because the knot becomes brighter as frequency decreases (i.e., an optically thin steep spectrum), while the core spectrum is relatively flat or slightly inverted (i.e., optically thick), as well as the resolution effect. This prevents us from specifying a reliable reference position in the 0329+3510 images at ≤15 GHz. Figure 9. Self-calibrated VLBA images of 0329+3510. From left to right, the images are at 43, 24, and 15 GHz,


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

to see if the hint for high redshift contributions to is sharpened by future CMB polarization data. We eagerly await upcoming results from the new Planck HFI large-scale polarization data which is still proprietary to see if these observations strengthen the hint seen in the LFI data. Alternatively, these may reflect remaining systematics in the LFI data that do not also apply to the HFI data. Based on Fig. 5 , we expect that a future CV-limited experiment should be able to confirm or refute the high redshift contribution to , although we postpone a more detailed investigation of these prospects to future work. It will be extremely challenging to test the hint for non-negligible ionization fractions at z 15 by other means. The best alternative is likely redshifted 21cm surveys but these face challenges at high redshift owing to the bright galactic emission at the frequencies of interest. However, these surveys may find that the average neutral fraction rises more slowly towards high redshift than expected in models with Pop-II stars alone (see Fig. 1 ). There may be differences in the sizes of the ionized regions in these scenarios as well, which may provide a potential signature (Koh Wise 2016 ). However, the possibility of a significant contribution from Pop-III stars at high redshift may also somewhat complicate the interpretation of the 21cm power spectrum measurements (e.g. Fialkov etal. 2013 ). Another possibility may be to extract signatures of early phases of patchy reionization using the Kinetic SunyaevZeldovich effect, but these will have to push to smaller angular scales, which is challenging given foreground contamination. An extended self-regulated phase likely evades current constraints (Zahn etal. 2012 ; George etal. 2015 ) on the duration of reionization (Park etal. 2013 ). Finally, it is worth commenting on the implications of our findings for the goal of determining from the ionization history inferred from redshifted 21cm observations (Liu etal. 2016 ). This is an appealing idea, because the optical depth is an important nuisance parameter that can limit, for instance, inferences regarding the sum of the neutrino masses from upcoming CMB lensing measurements. However, this prospect becomes difficult if there are significant high redshift contributions to the optical depth, as hinted at in the Planck LFI data, which will be hard to extract from upcoming redshifted 21cm surveys. We hope that this work will encourage reionization modellers to adopt this PC analysis methodology of Hu Holder ( 2003 ) and effective likelihood of Heinrich etal. ( 2016 ). Here we have considered rather simple models for the ionization history in an effort to explore the broad-brush implications of the Planck data, but it would be interesting to explore more detailed reionization models and to combine the full information content of the CMB data with other reionization observables. It will also be interesting to explore whether dark matter