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.


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.


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).


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.


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


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


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.


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.


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 (


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


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


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).


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


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


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)


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.,


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


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


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


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,


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


within the time span of 21–39 days after the latest outburst onset (in the absence of intense bursts), Younes et al. ( 2020b ) precisely measured a much higher spin-down rate of 3.9 × 10 −11 s s −1 . This might suggest a hysteresis in the dynamical response in these highly magnetized systems that is accompanied by changes in burst activation. The polar magnetic field strength inferred for a vacuum dipole approximation (i.e., ) of SGR J1935+2154 is about 4.4 × 10 14 G. However, our X-ray spectral modeling of the persistent emission with the STEMS3D model, which includes radiative propagation in extremely magnetized settings, yielded a local surface magnetic field strength of 9.6 × 10 14 G. This difference is not surprising since the spin-down estimate applies to the global field configuration, and can be modified by plasma loading of the magnetosphere (Harding et al. 1999 ). Nevertheless, the surface magnetic field strength being considerably larger than the inferred value suggests that there may be multipolar magnetic topology, where local field strengths are much larger than the dipolar ones. Such a circumstance was observed in SGR 0418+5729, the first “low-dipole field” magnetar. Its magnetic field strength inferred from its spin parameters is 6 × 10 12 G (Rea et al. 2010 ). Güver et al. ( 2011 ) modeled the XMM-Newton spectrum of SGR 0418−5729 with the STEMS atmospheric emission model and obtained ∼ 10 14 G for the surface magnetic field strength. They proposed a dominant nondipolar magnetic field structure for SGR 0418−5729, a picture that is consistent with the discovery of a variable proton cyclotron absorption feature in later XMM-Newton observations (Tiengo et al. 2013 ). A significant multipolar magnetic configuration for SGR J1935+2154 is also supported by the complexity of its energy-dependent pulse profiles. Its low-energy X-ray pulse profile is dominated by a broad structure with a phase width of around 0.7–0.8. However, minor structures become pronounced above ∼3 keV, in the absence of bright persistent X-ray emission ( kT = 0.5 keV) from the surface of the neutron star. The BB+BB spectral fits indicate that this putatively hotter portion emanates from smaller regions, less than ∼0.2 km in size, and perhaps analogous to multipolar field components that are observed from small regions on the Sun. These structured pulse profiles contrast the comparatively simple two-peaked forms observed for active outburst phases in another magnetar, 1RXS J170849.0−400910, which can be attributed to antipodal polar hot zones in a dipole field configuration (Younes et al. 2020a ). Extension of the pulse profile analysis of Younes et al. ( 2020a ) to treat broader surface temperature profiles in magnetic colatitude is unlikely to generate the abrupt rises and falls in consecutive phase bins evident above ∼3 keV in Figure 1 . We suggest that strong temperature gradients in magnetic longitude are also required to reproduce the observed


We thank the referee, Hiroyuki Hirashita, for his insightful comments, Laura Pentericci and Daniel Schaerer for their kind clarifications. The research leading to these results has received funding from the European Research Council under the European Union (FP/2007-2013)/ERC Grant Agreement no. 306476. PD acknowledges the support of the Addison Wheeler Fellowship awarded by the Institute of Advanced Study at Durham University. UM has been funded through a Marie Curie fellowship by the European Union (FP/2007-2013), grant agreement no. 267251.


We thank the HET resident astronomers and telescope operators for continuous support. A.N., M.o.A., B.D.-S., M.i.A. and K.K. are currently supported by NCN grant 2012/07/B/ST9/04415. M.o.A. also acknowledges the “Mobility + III” fellowship from the Polish Ministry of Science and Higher Education. A.W. was supported by the NASA grant NNX09AB36G. G.M. acknowledges the financial support from the Polish Ministry of Science and Higher Education through the Iuventus Plus grant IP2011 031971. The HET is a joint project of the University of Texas at Austin, the Pennsylvania State University, Stanford University, Ludwig-Maximilians-Universität München, and Georg-August-Universität Göttingen. The HET is named in honor of its principal benefactors, William P. Hobby and Robert E. Eberly. The Center for Exoplanets and Habitable Worlds is supported by the Pennsylvania State University and the Eberly College of Science. This research has made extensive use of the SIMBAD database, operated at CDS (Strasbourg, France) and NASA’s Astrophysics Data System Bibliographic Services.


This work has made use of the C2PAP cluster at the Leibniz-Rechenzentrum. NP is supported by the DFG cluster of excellence “Origin and Structure of the Universe”. GL acknowledges financial support from the ILP LABEX (under reference ANR-10-LABX-63) and from “Programme National de Cosmologie et Galaxies” (PNCG) of CNRS/INSU, France, and the ANR BIG4, under reference ANR-16-CE23-0002. This work was carried out within the Aquila Consortium.


pCO 2 case for a single multi-epoch case. 1 σ and 2 σ contours are included. 5. Atmospheric Retrievals To perform our retrievals we use the open-source radiative transfer and retrieval framework CHIMERA (Line Yung 2013 ; Line et al. 2013 ). It previously has been used to study the atmosphere of TRAPPIST-1e to determine the resolution that a future instrument needs to have in order to detect and constrain the abundances of molecules in the atmospheres of temperate terrestrial planets to high precision (Tremblay et al. 2020 ). Our retrieval setup is similar to that presented in Tremblay et al. ( 2020 ). For each of the combined spectra we fit for six parameters: an isothermal temperature profile ( T iso ), a radius scaling factor (x R p ), the cloud top pressure (), the mean molecular weight of the atmosphere, and the volume mixing ratio of H 2 O and CO 2 . We use the mean molecular weight (MMW) as a proxy to effectively fill the rest of the atmosphere with N 2 as this molecule is inert. 6. Results Each spectra that we retrieved had a different underlying cloud configuration, hence we wanted to determine if these physical processes impact the retrieved CO 2 abundance. The histograms presented in Figure 5 show that the retrieved abundances are consistent for each of the combined spectra, suggesting that the impact of cloud variability is not detectable with the resolution provided by JWST NIRSpec PRISM. This is further verified by the third panel, which shows consistent retrieved cloud top pressure for each spectra. While the cloud top pressure can be seen to vary in our models, this consistency in the retrieved cloud top pressures demonstrates that the precision of JWST NIRSpec PRISM will not be able to differentiate variable cloud spectra at any level of confidence. It can be seen from Figure 5 that for the CO 2 partial pressure greater than 10 −1 bars the posterior tends toward the upper prior, which is set by the physical limit of the volume mixing ratio, with the true value lying outside 1 σ . The lower partial pressures are not prior dominated and we are able to retrieve the correct volume mixing ratios within 1 σ . Further, the 10 cases for each partial pressure are consistent, suggesting that the variable clouds are not affecting the retrieved values. We are unable to constrain a water abundance due to its lack of strong spectral features in our models. Figure 5. Retrieved posterior distributions for four of the key parameters explored in this study. From top to bottom the four panels are: CO 2 abundance, H 2 O abundance, cloud top pressure, and temperature. Each colored histogram represents the retrieved parameter for one of the combined spectra (representing 10 different “observed” epochs), for a total 10 different combined spectra, each with different underlying cloud assumption. The thick solid vertical lines show the terminator-average abundance of CO 2 and H 2 O from the input models, while the dotted vertical lines represent


MVdV acknowledges CNPq / Twas for financial support. EMdGDP acknowledges partial support from the Brazilian agencies FAPESP (grant no. 2013/10559-5 ) and CNPq (grant no. 300083/94-7 ). GK acknowledges support from FAPESP (grants no. 2013/04073-2 and 2013/18815-0 ) and PNPD/CAPES (grant no. 1475088 ). MVdV thanks Reinaldo Santos-Lima for fruitful discussions on different topics addressed in this paper. The authors also acknowledge the anonymous referee for a careful review. This work has made use of the computing facilities of the Laboratory of Astroinformatics (IAG/USP, NAT/Unicsul), whose purchase was made possible by the Brazilian agency FAPESP (grant 2009/54006-4 ) and the INCT-A. MVdV is grateful for the great hospitality of the Instituto de Astronomia, Geofísica e Ciências Atmosféricas (São Paulo University), where part of this work was developed.


ACKNOWLEDGEMENTS Part of this work is based on archival data, software, or online services provided by the Space Science Data Center – ASI. We would like to thank the Instituto de Astrofísica de Canarias for the excellent working conditions at the Observatorio del Roque de los Muchachos in La Palma. The financial support of the German BMBF and MPG, the Italian INFN and INAF, the Swiss National Fund SNF, the ERDF under the Spanish MINECO (FPA2015-69818-P, FPA2012-36668, FPA2015-68378-P, FPA2015-69210-C6-2-R, FPA2015-69210-C6-4-R, FPA2015-69210-C6-6-R, AYA2015-71042-P, AYA2016-76012-C3-1-P, ESP2015-71662-C2-2-P, and CSD2009-00064), and the Japanese JSPS and MEXT is gratefully acknowledged. This work was also supported by the Spanish Centro de Excelencia ‘Severo Ochoa’ SEV-2012-0234 and SEV-2015-0548, and Unidad de Excelencia ‘María de Maeztu’ MDM-2014-0369, by the Croatian Science Foundation (HrZZ) Project IP-2016-06-9782 and the University of Rijeka Project 13.12.1.3.02, by the DFG Collaborative Research Centers SFB823/C4 and SFB876/C3, the Polish National Research Centre grant UMO-2016/22/M/ST9/00382, and by the Brazilian MCTIC, CNPq, and FAPERJ. The Fermi -LAT Collaboration acknowledges generous ongoing support from a number of agencies and institutes that have supported both the development and the operation of the LAT and scientific data analysis. These include the National Aeronautics and Space Administration and the Department of Energy in the United States, the Commissariat à l’Energie Atomique and the Centre National de la Recherche Scientifique/Institut National de Physique Nucléaire et de Physique des Particules in France, the Agenzia Spaziale Italiana and the Istituto Nazionale di Fisica Nucleare in Italy, the Ministry of Education, Culture, Sports, Science and Technology (MEXT), High Energy Accelerator Research Organization (KEK), and Japan Aerospace Exploration Agency (JAXA) in Japan, and the K. A. Wallenberg Foundation, the Swedish Research Council, and the Swedish National Space Board in Sweden. Additional support for science analysis during the operations phase is gratefully acknowledged from the Istituto Nazionale di Astrofisica in Italy and the Centre National d’Études Spatiales in France. This work performed in part under DOE Contract DEAC02-76SF00515. The OVRO 40-m monitoring program is supported in part by NASA grants NNX08AW31G, NNX11A043G, and NNX14AQ89G, and NSF grants AST-0808050 and AST-1109911.


the component CO lines in a merger model, measured in km s 1 . The HST images (Rix etal. 2004 ) show various clumps that indicate ALESS 122.1 and ALESS 67.1 could be mergers (Fig. 3 ). Taking the merger model and R to be 0.5arcsec (4.2kpc at z 2), which is the approximate separation of the clumps in HST optical counterparts (Fig. 3 ), the dynamical mass, M dyn sin 2 i , is 510 11 M for both ALESS 122.1 and ALESS 67.1. Figure 3. The CO(10) velocity structure of ALESS 122.1 (left) and ALESS 67.1 (right), overlaid on HST z band ( F 850 LP ) images from Rix etal. ( 2004 ) 3 . Both optical counterparts are clumpy or complex in the rest-frame UV, indicating either structured dust or a possible merging system. Blue contours indicate the CO(10) emission integrated from 300 to 0kms 1 at 3, 5, 7.... Red contours indicate the CO(10) emission integrated from 0 to 300kms 1 at 3, 5, 7.... Red and blue crosses mark the centroid of the blueshifted and redshifted emission, respectively. The images are 2020arcsec. However, the HST image does not reveal whether or not the systems contain a gaseous disc. In the presence of a gas disc, the dynamical mass can be estimated from the CO line kinematics, by comparing the spatial offset between the redshifted and blueshifted components of the CO line. This was determined by making 300kms 1 wide channel maps centred at 300 to 0kms 1 and 0 to 300kms 1 (Fig. 3 ). The centroid of the CO emission was determined for the maps, and we derive a spatial offset between the redshifted and blueshifted emissions of 1.20.6arcsec (10.25.1kpc) and 1.8 0.5arcsec (15.24.2kpc) for ALESS 122.1 and ALESS 67.1, respectively. This is comparable to CO(10) sizes observed in other SMGs by Ivison etal. ( 2011 ). Assuming this spatial offset represents rotating gas, then the dynamical mass M dyn sin 2 i = (2.11.1)10 11 M and (3.20.9)10 11 M for ALESS 122.1 and ALESS 67.1, respectively. These estimates are consistent with the dynamical masses derived from using the CO line FWHM and optical size from HST imaging. For a rotating model, Bothwell etal. ( 2013 ) found their sample of SMGs to have a median dynamical mass of (1.60.3)10 10 R M , where radius R is in kpc. Using the measured spatial offsets of 10 and 15kpc for R , the dynamical masses of ALESS 122.1 and ALESS 67.1 are consistent with the median dynamical mass of their SMG sample. The total baryonic mass can be calculated by combining the gas and stellar mass estimates for the SMGs. The stellar masses of ALESS 122.1 and ALESS 67.1 have been estimated by Simpson etal. ( 2014 ), who used absolute rest-frame H -band magnitudes from best-fitting SEDs to multiband photometry and a model mass-to-light ratio. They estimate ALESS 122.1 has a stellar mass of 5.210 10 M and ALESS 67.1 has a stellar mass of 4.410 10 M . These estimates are uncertain by a factor of at least a few, due to the difficulty in distinguishing between different model SF histories to predict an accurate mass-to-light ratio


We thank Tony Piro for his encouragement, Stefan Taubenberger for providing access to data, and Carles Badenes, Stéphane Blondin, Hector Martínez-Rodríguez, Alison Miller, Rüdiger Pakmor, Stuart Sim, and Frank Timmes for helpful discussions. K.J.S., D.M.T., and B.J.M. received support from the NASA Astrophysics Theory Program (NNX15AB16G and NNX17AG28G). D.K. is supported in part by a DOE Office of Nuclear Physics Early Career Award, and by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Divisions of Nuclear Physics, of the US DOE under Contract No. DE-AC02-05CH11231. This research used the Savio computational cluster resource provided by the Berkeley Research Computing program at the University of California, Berkeley (supported by the UC Berkeley Chancellor, Vice Chancellor of Research, and Office of the CIO), high-performance computing resources provided by the University of Alabama, and resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the US DOE under Contract No. DE-AC02-05CH11231. Software: MESA (v8845; Paxton et al. 2011 , 2013 , 2015 ), FLASH (v4.2.2; Fryxell et al. 2000 ; Dubey et al. 2009 ), SEDONA (Kasen et al. 2006 ).


giant component fractions imply the fundamental difference in the pathway topology between Snap100 and Lévy fractals; Snap100 has more efficient pathways to connect all galaxies at a shorter linking length than Lévy fractals. Very likely, this is due to the filamentary structures in Snap100, lacking in Lévy fractals. The middle panel of Fig. 2 shows the diameters. We can again see clear separations of Snap100 from the Lévy walk models. Snap100 reaches the maximum diameter, 300, at the linking length, 1.1 h −1 Mpc, while Lévy walk models reach the maximum diameters around 200 for linking lengths near 2.0 h −1 Mpc. Even for 100 Lévy walk realizations, none of the Lévy walk models can match the diameter measurements of Snap100. Hence, both the size of the giant component and diameter are network measures that discriminate the Lévy walk topologies from the Illustris simulation, despite the data sets being constructed to have matching abundance and two-point correlation statistics. The linking length for maximum diameter is related to the inflection point of the growth curve of giant component fractions; the rate of growth of the giant component decreases after reaching the maximum diameter. This transitioning feature occurs due to the ‘saturation’ of connecting edges. At first (i.e. small linking length values), increasing the linking length results in adding new vertices and increasing the size of the connected network components. However, once the largest diameter is reached, increasing the linking length tends to form new pathways within the existing structure between more far-flung members and only slowly increases the overall size of the connected structure. Therefore, the diameter is maximized at this critical scale, transitioning from ‘growing phase’ to ‘saturating phase’. The previous percolation studies are closely related to this maximum diameter scale, though they have not measured these specific diameters. If the system size is infinite, the diameter measurements transit from finite values to an infinity near this scale. The bottom panel of Fig. 2 shows transitivity results. Again, none of Lévy walk models mimics the transitivity curve of Snap100. We note that the statistical variances of transitivity measurements are much smaller than the other measurements as shown in Fig. 2 , since a single realization of the network is statistically large enough for counting triangles. Hence, the difference of transitivities between Snap100 and Lévy fractals also suggests that Snap100 is topologically very different from Lévy fractals. An interesting feature is the difference of convexities between Snap100 (concave or ‘cup’) and Lévy fractals (convex or ‘hat’). The transitivities of Snap100 are high for small linking lengths, then decrease to a minimum transitivity at 0.4 h −1 Mpc as the linking length increases. After this, the transitivities slowly increase to 0.8. This transitivity trend of Snap100 is related to the transition between the


0.02, respectively. These values are also within the typical range obtained in the study of GRB afterglows (Medvedev 2006 ). We note that different values of ε e and ε B will only change the normalization, but not the slope, of the η jet – relationship (cf. equation 3 below). We then calculate the synchrotron emission from these accelerated electrons. Like any other jet models in literature, our jet model is phenomenological. Besides, we assume that all the jet parameters remain unchanged for different sources and accretion rates, which is certainly a strong assumption. This is partly because we still do not have good constraint on them. To conclude, the only free parameter in our jet model is its mass-loss rate . We note that the L R is found to be a power-law function of (see also Heinz Sunyaev 2003 ). 2.2 Hot accretion flow model Depending on the accretion rate, two types of hot accretion flow exist. They are the advection-dominated accretion flow (ADAF; Narayan Yi 1994 , 1995 ; Abramowicz et al. 1995 ) below certain critical accretion rate and the luminous hot accretion flow (LHAF; Yuan 2001 ) above it (see review by Yuan Narayan 2014 ). LHAF is thermally unstable (Yuan 2003 ). But if accretion rate is relatively low, , the growth time-scale of the thermal instability is larger than the accretion time-scale, so the gas can remain hot throughout the flow. We call it type-I LHAF. Above , the growth time-scale of the thermal instability is shorter than the accretion time-scale thus some cold dense clumps should be formed, embedded in the hot phase medium. We call it type-II LHAF or two-phase accretion flow. We follow the standard approach to calculate the dynamical structure and the emitted spectrum of ADAFs and type-I LHAF (e.g. YCN05 ). The L X at 3–9 keV band is then derived from the spectrum. For the two-phase accretion flow, optical/UV radiation from cold clumps will provide additional (likely dominant) seed photons for the inverse Compton scattering process, to generate the X-ray emission. The whole process is obviously complicated, depending on the detailed dynamics of the two-phases accretion flow such as the filling factor and temperature of clumps and so on. Following Yuan Zdziarski ( 2004 ), we simplify the problem by replacing the electron energy equation with the Compton y -parameter. With the assumption that the electron advection term is zero in the two-phase flow, we can calculate the radiative cooling rate. The bolometric luminosity can then be derived (Xie Yuan 2012 ). In order to derive 3–9 keV L X , we assume the spectrum to be a simple power law with exponential cutoffs at both the high and low ends, i.e. F E ∼ E 1−Γ exp (− E min / E )exp (− E / E max ), where the photon index Γ is constrained by the Compton y -parameter. E min is set arbitrarily to be 0.02 keV. E max is numerically determined by the electron temperature, i.e. E max = kT e , at the location where most of the radiation comes out (Yuan Zdziarski 2004 ).


γ-ray telescopes, and, possibly, by some of the currently operating ones. To our knowledge, these results have never been reported before. We have discussed how different choice of parameters (such as source redshift, primary proton energy and angular distribution, extragalactic magnetic field, and extragalactic background light models) would change the observable spectra. We have also provided a qualitative discussion of the main stages of cascade development and the effects of additional processes. This study could significantly facilitate future axion-like particle searches in the optically thick region of blazar spectra. In addition, our work might be useful in extreme TeV blazar studies as well as in several related branches of γ-ray astronomy, including extragalactic background light and extragalactic magnetic field measurements. APPENDIX A: THE IMPACT OF FLUCTUATIONS ON THE OBSERVABLE SPECTRA The observable spectrum in the framework of the MHCM depends on the EGMF structure, in particular, on the number of proton trajectories used in our study. In Fig. A1 , we show the observable SEDs averaged over various numbers of proton trajectories. We conclude that the statistics of 10 2 trajectories is sufficient to obtain a stable enough average observable spectrum for E 10 TeV, and the use of 10 3 trajectories already allows one to robustly determine the shape of the spectrum for E 30 TeV. Figure A1. Average observable SEDs for the KD10 EBL model option and the following numbers of trajectories: 10 (black curve), 100 (red curve), 10 3 (green curve), and 10 4 (blue curve). In addition, we have calculated the observable SEDs for 10 2 individual proton trajectories to demonstrate the impact of fluctuations on the shape of the observable spectrum (see Fig. A2 ). The blue-to-red gradient of colours gives a visual representation to the values of the ratios of different individual SEDs at two benchmark energies: 10 TeV and 100 GeV. Blue colours represent lower ratios, while red colours – higher ones. We note that at E = 5 TeV, the maximal difference between the flux corresponding to 95 per cent of the trajectories is limited to the factor of 2.5. Figure A2. Observable SEDs for the KD10 EBL model option and 10 2 individual trajectories; colours represent the ratios of individual SEDs at 10 TeV and 100 GeV. APPENDIX B: DISTRIBUTION OF THE CRITICAL DISTANCE In Fig. B1 , we present a histogram of a distribution on ‘the critical distance’ L cr (see Section 4.1 for definition of this parameter). The normalization of this histogram corresponds to the case of discrete probability density function, i.e. with summation over the bins of the histogram, with the N th bin containing the largest value of L cr . Figure B1. Histogram of the critical distance L cr distribution (red curve). APPENDIX C: SPECTRA WITH AND WITHOUT TPP, URB, and DPP In Fig. C1 , we present histograms of the observable spectra of γ-rays and electrons calculated with the CRPropa3 code for


We are grateful to the anonymous referee for a number of helpful suggestions. Support for this work was provided by the National Research Foundation of Korea to the Center for Galaxy Evolution Research, and by KASI under the RD program (Project No. 2014-1-600-05) supervised by the Ministry of Science, ICT and future Planning. M.P. acknowledges support from Mid-career Researcher Program (No. 2015-008049) through the National Research Foundation (NRF) of Korea. Software: IRAF, DAOPHOT II/ALLFRAME (Stetson 1987 , 1994 ).


The authors thank the anonymous referee for the useful comments and suggestions, which helped to improve the paper. We are grateful to Emanuele Daddi for useful discussion, Maria Cebrián for providing the effective radii from the NYU-VAGC catalogue and Helena Domínguez-Sánchez, Kenneth Duncan, Andrea Grazian, Chiara Mancini and Adam Muzzin for providing their mass functions. A.C. is also gratetful to Alfonso Veropalumbo for helpful discussion. We also acknowledge the support of the grant PRIN MIUR 2010 The dark Universe and the cosmic evolution of baryons: from current surveys to Euclid. 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.


Hinode is a Japanese mission developed and launched by ISAS/JAXA, with NAOJ as domestic partner and NASA and STFC (UK) as international partners. It is operated by these agencies in cooperation with ESA and the NSC (Norway). CHIANTI is a collaborative project involving the following Universities: Cambridge (UK), George Mason, and Michigan (USA). This work was partially supported by the JSPS Core-to-Core Program 22001. The work of D.H.B. was performed under contract with the Naval Research Laboratory and was funded by the NASA Hinode program.


E.D.M., V.Zh.A., N.C.S., and S.G.S. acknowledge the support from Fundação para a Ciência e a Tecnologia (FCT) through national funds and from FEDER through COMPETE2020 by the following grants UID/FIS/04434/2013 POCI–01–0145-FEDER–007672, PTDC/FIS-AST/7073/2014 POCI–01–0145-FEDER–016880, and PTDC/FIS-AST/1526/2014 POCI–01–0145-FEDER–016886. E.D.M. acknowledges the support from the fellowship SFRH/BPD/76606/2011 funded by FCT (Portugal) and from the Investigador FCT contract IF/00849/2015/CP1273/CT0003. V.Zh.A., N.C.S., and S.G.S. also acknowledge the support from FCT through Investigador FCT contracts IF/00650/2015/CP1273/CT0001, IF/00169/2012/ CP0150/CT0002, and IF/00028/2014/CP1215/CT0002 funded by FCT (Portugal) and POPH/FSE (EC). J.I.G.H. acknowledges financial support from the Spanish Ministry of Economy and Competitiveness (MINECO) under the 2013 Ramón y Cajal program MINECO RYC–2013–14875, and the Spanish ministry project MINECO AYA2014–56359-P. We thank Sara Bisterzo and Donatella Romano for kindly providing their GCE models. This research has made use of the SIMBAD database operated at CDS, Strasbourg (France), the IRAF facility, and the VALD3 database. Finally, we are sincerely grateful to the anonymous referee, whose careful review helped to improve this paper.


be given elsewhere (D. Radice et al. 2017, in preparation). A summary of the simulations is given in Table 1 . Table 1 Gravitational and Baryonic Masses, Compactnesses, Tidal Deformability Parameters, BH Formation Time, and Disk and Ejecta Masses Notes. Disk and ejecta masses are given at the final simulation time. a NS gravitational mass. b NS baryonic mass. c NS compactness, . d Dimensionless quadrupolar tidal parameters, Equation ( 2 ). e Dimensionless tidal parameter, Equation ( 1 ). f Gravitationally bound material with outside of the apparent horizon. g Dynamic ejecta mass, computed as from the flux of unbound matter through the coordinate-sphere . h BH formation time, in milliseconds after merger. i Final simulation time, in milliseconds after merger. We compute the mass of the dynamic ejecta and of the remnant accretion disk for each model. Our results are shown in Table 1 and Figure 1 . The typical dynamic ejecta masses in our simulations are of the order of , in good qualitative agreement with previous numerical-relativity results. We do not find any clear indication of a trend in the dynamic ejecta masses as a function of the binary parameters or EOS. However, we find a clear correlation between the disk masses and the tidal parameter . According to our simulations, binaries with inevitably produce BHs with small accretion disks. These cases are incompatible with the infrared data for AT2017gfo, even under the assumption that all of the matter left outside of the event horizon will be ejected. Figure 1. Remnant disk plus dynamic ejecta masses (upper panel) and BH formation time (lower panel) plotted against the tidal parameter (Equation ( 1 )). For models that do not collapse during our simulation time, we give a lower limit. The horizontal dashed line shows a conservative lower limit for AT2017gfo, , obtained assuming that the entire disk is unbound. The vertical dotted line is . Errors on and are estimated following Equation ( 3 ) and are added in quadrature. The reason for this trend is easily understood from the lower panel of Figure 1 . The NS dimensionless quadrupolar tidal parameters depend on the negative-fifth power of the NS compactness ( Equation ( 2 )). Consequently, small values of are associated with binary systems having compact NSs that result in rapid or prompt BH formation. In these cases, the collapse happens on a shorter timescale than the hydrodynamic processes responsible for the formation of the disk. Consequently, only a small amount of mass is left outside of the event horizon at the end of the simulations. Binaries with larger values of produce more massive disks, up to , and longer lived remnants. In these cases, neutrino driven winds and viscous and magnetic processes in the disk are expected to unbind sufficient material to explain the optical and infrared observations for AT2017gfo (Perego et al. 2014 ; Wu et al. 2016 ; Siegel Metzger 2017 ). 4. Discussion On the basis of our simulations and the


of mag, with mag. The power law removes any degeneracy in the slope of the dust extinction law, and thus excludes the possibility of significant grey dust. Another example is GRB 120815A , whose SED is fit by a power law and SMC-like extinction to give an value of 0.08 mag, which is significantly smaller than the of 0.44 mag. We find that GRB 121024A is also best fit with a power law. Indeed, Fig. 9 shows that only one object that has an overpredicted was fit with a broken power law. Although there is strong evidence for dust destruction caused by the GRB itself ( Morgan et al. 2014 ), this would not cause a discrepancy between and . Any dust that extinguishes the GRB would also be visible in depletion, so if that dust is destroyed it is no longer visible in depletion or extinction. Fig. 9 as measured directly from the SED against that calculated from the DTM. The green line indicates a 1:1 conversion between the two. Blue circles represent SEDs best fit with a simple power-law, whereas red triangles are used for broken power-law fits. Empty points refer to depletion measured from low-resolution spectra. Large error bars are due to significant errors in several measured parameters being combined in quadrature. Intervening systems such as absorbers are known to contain similar quantities of dust as galaxies (e.g. Ménard Fukugita 2012 ), although QSO-DLAs tend to show very little reddening ( Krogager et al. 2016 ; De Cia et al. 2016 ). For the group (2) objects, we notice that 050820A , 100219A , 111008A , and 130408A all have intervening absorbing systems. Should these objects have a high dust content, they could significantly affect the SED of the GRB afterglow, such that the reddening caused by dust in the host galaxy itself is indeed smaller, and thus pushes these objects towards the 1:1 line. However, for these intervening systems to be the reason for a much higher than from DTM, they would need to contribute around 80% of the extinction along the line of sight, whereas the systems in our sample are much weaker in metal line absorption than the host DLA (e.g. in GRB 100219A, Thöne et al. 2013 ). We therefore find it unlikely that a significant amount of the extra extinction is caused by intervening systems. 6.5. Equivalent dust column density Having established that depletion is a good tracer of the dust, and with being accurate and reliable, we look to the relation used to calculate , Eq. ( 10 ). This is based upon the relation between hydrogen and dust in the Galaxy, where a column of cm results in an of 0.45. We note that the value of the Galactic gas-to-dust ratio varies depending on the sample and technique used to measure it. We use the result of Watson (2011) . Measurements of this value have been consistent over the past few decades, and include those by Bohlin et al. (1978) , Predehl Schmitt (1995) , and Güver Özel (2009) . The value used does not alter the fact that a significant discrepancy is observed. In DLAs, the hydrogen


This work was performed using HPC resources from GENCI-IDRIS (grant 2017-040219). It has been supported by Programme National Soleil-Terre (PNST/INSU/CNRS).


E.Z. and J.H. acknowledge support from NASA grant NNX16AG83G. R.K. was partially supported by the Max-Planck/Princeton Center for Plasma Physics and NSF grant AST-1517638. This work was also carried out as part of the IBEX mission, which is part of NASA’s Explorer program. The work reported in this paper was performed at the TIGRESS High Performance Computing Center at Princeton University, which is jointly supported by the Princeton Institute for Computational Science and Engineering and the Princeton University Office of Information Technology’s Research Computing department.


We would like to thank the staff of the East Asian Observatory for their invaluable support in the completion of the BISTRO survey. We also wish to thank the people of Hawai’i for granting us access to the unique geographical site of the Maunakea observatory. Furthermore, we are grateful to the GAS Consortium for generously granting us access to their spectroscopic data. We also thank the anonymous reviewer for their helpful and detailed comments. Finally, we thank B.-G. Andersson, Kelvin Au, Jordan Guerra Aguilera, James Lane, Anna Ordog, Amélie Simon, Ian Stephens, and Julien Vandeportal for helpful discussions. This research was conducted in part at the SOFIA Science Center, which is operated by the Universities Space Research Association under contract NNA17BF53C with the National Aeronautics and Space Administration. The James Clerk Maxwell Telescope is operated by the East Asian Observatory on behalf of the National Astronomical Observatory of Japan, Academia Sinica Institute of Astronomy and Astrophysics, the Korea Astronomy and Space Science Institute, and the Center for Astronomical Mega-Science (as well as the National Key RD Program of China with No. 2017YFA0402700). Additional funding support is provided by the Science and Technology Facilities Council of the United Kingdom and participating universities in the United Kingdom and Canada. SCUBA-2 and POL-2 were built through grants from the Canada Foundation for Innovation. This research used the facilities of the Canadian Astronomy Data Centre operated by the National Research Council of Canada with the support of the Canadian Space Agency. This research has also made use of the simbad database and of NASA’s Astrophysics Data System Bibliographic Services. The Starlink software (Currie et al. 2014 ) is currently supported by the East Asian Observatory. M.K. was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT Future Planning (NRF-2015R1C1A1A01052160). W.K. was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF-2016R1C1B2013642). C.W.L. was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (NRF-2016R1A2B4012593). D.L and K.Q. are supported by National Key RD Program of China No. 2017YFA0402600 and acknowledge the support from the National Natural Science Foundation of China (NSFC) through grants U1731237, 11473011, 11590781, 11629302, and 11725313. Software: S tarlink (Currie et al. 2014 ; Parsons et al. 2017 ; Chapin et al. 2013 ), The IDL Astronomy User’s Library (Landsman 1993 ).


A.R.G.S. acknowledges the support from FCT (Portugal) through the grant reference SFRH/BD/88032/2012. M.S.C. and P.P.A. are supported by FCT through the Investigador FCT contracts of reference IF/00894/2012 and IF/00863/2012 and POPH/FSE (EC) by FEDER funding through the program COMPETE. Funds for this work were provided also by the EC, under FP7, through the projects FP7-SPACE-2012-31284 and PIRSES-GA-2010-269194. T.L.C. acknowledges the support of the UK Science and Technology Facilities Council (STFC).


n s is the number density of the s th species of the fluid. The mass density is given by Chattopadhyay ( 2008 ) and Chattopadhyay Ryu ( 2009 ), where , is the composition parameter and . The electron and proton masses are and , respectively. For single-temperature flow, the isotropic pressure is given by The EoS for multi-species flow is (Chattopadhyay 2008 ; Chattopadhyay Ryu 2009 ) The non-dimensional temperature is defined with respect to the electron rest mass energy, . Using equations ( 19 ) and ( 20 ), the expression of the energy density in equation ( 21 ) simplifies to where The expressions of the polytropic index, the adiabatic index and the sound speed are given as Integration of first law of thermodynamics (equation 13 ) by assuming adiabatic flow ( Q + = 0) and using the EoS (equation 22 ) gives us the adiabatic relation of multi-species relativistic flow (Chattopadhyay Kumar 2013 ; Kumar et al. 2013 ), where k 1 = 3(2 − ξ)/4, k 2 = 3ξ/4 and and is the constant of entropy. Equation ( 24 ) is the generalized version of . Combining equations ( 24 ) and ( 14 ), we get the expression of entropy accretion rate, Re-arranging equations ( 10 )–( 14 ) with the help of equations ( 9 ), ( 7 ), ( 19 ), ( 20 ) and ( 22 ) in geometric units, we present the spatial derivative of flow variables v , l and Θ, where Here, contains an extra term l 2 v /( r 2 γ 2 ) compared to the inviscid case (Chattopadhyay Chakrabarti 2011 ). There is γ φ term in the expression of disc height (equation 12 ). The radial derivative of equation ( 14 ) implies that the radial derivative of the specific angular momentum will be non-zero, which causes the extra term to appear. There are many height prescriptions (Lasota 1994 ; Riffert Herold 1995 ; Peitz Appl 1997 ), and choice of any one of them apart from the one used will not affect the result qualitatively. Then, Moreover, These differential equations are integrated by using fourth-order Runge–Kutta numerical method with the help of using critical point conditions and l′Hospital rule at critical point. 2.2.1 Sonic point equations Mathematical form of critical point equation is , which gives two equations as and Here, the subscript ‘c’ denotes the same physical quantities described in equations ( 26 )–( 28 ), but evaluated at the location of the critical point. The velocity gradient on the sonic point, i.e. (d v /d r ) c , is obtained by employing l′Hospital rule. 2.2.2 Relativistic shocks for viscous flow The relativistic shock conditions were first obtained by Taub ( 1948 ), which for viscous flow in the presence of mass-loss are where . We have solved four shock conditions ( 31 )–( 34 ) simultaneously, where viscous shear tensor () is continuous across the shock and we obtained the relation between pre-shock (suffix ‘−’) and post-shock (suffix ‘+’) flow variables, where . Here, , . From equation ( 11 ), viscous shear tensor can be written as . 2.3 Outflow equations The jet being tenuous, we idealize it to be


of protons that decay into pions, f sec 0.7 is the ratio of secondary and total cosmic ray e , m p and m e are the masses of protons and electrons, and c is the speed of light. The normalization of the proton injection spectrum Q p, 0 can be directly related to the supernova rate via where 0.1 is the fraction of the supernova energy E SN 10 51 erg that is converted into kinetic energy of cosmic rays (Dorfi 2000 ). The Lorentz factor p, 0 10 9 eV/( m p c 2 ) 1 marks the low-energy end of the cosmic ray proton spectrum. When travelling through the interstellar medium, cosmic rays lose energy continuously. The total number N e () of e can be described as where the energy losses are determined by the cooling time-scale e . At steady state, we find The different energy loss channels are: ionization (ion), bremsstrahlung (brems), inverse Compton scattering (IC), synchrotron emission (synch), and galactic outflows (wind). The individual time-scales can be summarized as and result in the total cooling time-scale Here, T 6.6510 25 cm 2 is the Thomson cross-section, u B B 2 /(8) is the energy density of the magnetic field B , u ISRF is the energy density of the interstellar radiation field (ISRF), n is a gas density, H is the galactic scaleheight, v wind the velocity of the galactic wind, and is the e Lorentz factor. 2.2 Synchrotron emission in a galactic magnetic field In the presence of a magnetic field, cosmic rays perform spiral motions and hence are constantly accelerated. A single electron with a Lorentz factor results in the spectral power where K 5/3 ( x ) is the modified Bessel function of second kind and (see e.g. the review by Blumenthal Gould 1970 ). To find the synchrotron emission L , synch produced from the full population of cosmic rays, one has to integrate over the cosmic ray distribution, i.e. The last integral over the pitch angle is roughly 8.9 for a cosmic ray spectrum with a slope of 2.2 and the lower limit of the integration is e, 0 10 7 eV/( m e c 2 ) 20. We note that the synchrotron luminosity L synch, is directly proportional to the supernova rate , which determines the total number of cosmic rays (see equation 3 ). As the supernova rate is correlated with the SFR, synchrotron emission can be used to estimate a galaxys SFR. 2.3 Freefree emission and absorption At low frequencies and high gas densities, the interstellar medium is optically thick and synchrotron emission, holding the information about the SFR, is absorbed. The optically thick regime is characterized by an optical depth ff larger than 1. The value of ff depends on the electron temperature T e , the emission measure EM , and the frequency : with The number density of the free electrons n e can be related to the gas density via the ionization degree f ion : n e f ion n . The filling factor f fill describes the clumping of the medium (Ehle Beck 1993 ; Berkhuijsen, Mitra Mueller 2006 ; Beck 2007 ). Hence, the critical frequency crit at which ff 1, determining


We thank the anonymous referee for their various helpful comments and suggestions. IDR and LCP thank the National Science and Engineering Research Council of Canada for funding. We thank X. Yang et al. for making their SDSS DR7 group catalogue public, L. Simard et al. for the publication of their SDSS DR7 morphology catalogue, and the NYU-VAGC team for the publication of their SDSS DR7 catalogue. This research would not have been possible without these public catalogues. Funding for the SDSS 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 website is http://www.sdss.org/ .


The authors would like to thank the referee, John Landstreet, for useful comments that improved the manuscript. L.F. acknowledges financial support from the Alexander von Humboldt Foundation. T.M. acknowledges financial support from Belspo for contract PRODEX GAIA-DPAC. N.L. and A.R. acknowledge financial support from the DFG-CONICYT International Collaboration Project (DFG-06). S.S.-D. acknowledges funding by the Spanish Ministry of Economy and Competitiviness under the grants AYA2010-21697-C05-05, AYA2012-39364-C02-01, and Severo Ochoa SEV-2011-0187, and by the Canary Islands Governments under grant PID2010119. L.F. is greatly in debt to Oleg Kochukhov for providing most of the tools used here for reducing and analysing the HARPSpol data. L.F. also thanks Gregg Wade, John Landstreet, and Coralie Neiner for fruitful discussions. The authors thank Andreas Irrgang, Ignacio Negueruela, Henk Spruit, Gautier Mathys, and Alexander Kholtygin for useful comments. S.H. and M.S. thank Thomas Szeifert for providing the pipeline for the FORS spectra extraction.


A. Strugarek is a National Postdoctoral Fellow at the Canadian Institute of Theoretical Astrophysics, and acknowledges support from Canada’s Natural Sciences and Engineering Research Council. This work was supported by the ANR 2011 Blanc Toupies and the ERC project STARS2. We acknowledge access to supercomputers through GENCI (project 1623), Prace (8th call), and ComputeCanada infrastructures.


The Fermi LAT Collaboration acknowledges generous ongoing support from a number of agencies and institutes that have supported both the development and the operation of the LAT, as well as scientific data analysis. These include the National Aeronautics and Space Administration and the Department of Energy in the United States; the Commissariat à l’Energie Atomique and the Centre National de la Recherche Scientifique/Institut National de Physique Nucléaire et de Physique des Particules in France; the Agenzia Spaziale Italiana and the Istituto Nazionale di Fisica Nucleare in Italy; the Ministry of Education, Culture, Sports, Science and Technology (MEXT), the High Energy Accelerator Research Organization (KEK), and the Japan Aerospace Exploration Agency (JAXA) in Japan; and the K. A. Wallenberg Foundation, the Swedish Research Council, and the Swedish National Space Board in Sweden. Additional support for science analysis during the operations phase is gratefully acknowledged from the Istituto Nazionale di Astrofisica in Italy and the Centre National d’Études Spatiales in France. We made use of data products based on observations obtained with Planck ( http://www.esa.int/Planck ), an ESA science mission with instruments and contributions directly funded by ESA Member States, NASA, and Canada. This work was partially funded by NASA grants NNX14AQ37G and NNH13ZDA001N. Facilities: Fermi , Planck . Software: Astropy ( http://www.astropy.org , Astropy Collaboration et al. 2013 ), Fermipy ( http://fermipy.readthedocs.io/ ), GALPROP ( http://galprop.stanford.edu/ , Vladimirov et al. 2011 ), HEALPix ( http://healpix.jpl.nasa.gov/ , Górski et al. 2005 ), ROOT ( http://root.cern.ch/ , Brun Rademakers 1997 ), matplotlib (Hunter 2007 ).


This work is supported by the national science foundation of China (grant nos. 11025316 and 11121062), National Basic Research Program of China (973 Program) under grant no. 2009CB24901, the CAS/SAFEA International Partnership Program for Creative Research Teams (KJCX2-YW-T23) and China Postdoctoral Science Foundation (2013M531231).