O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Tag

different dependencies on the three stellar parameters. We chose the molecular TiO bands around and Å (- and - electronic transitions, respectively) since these oxide bands are very sensitive to effective temperature, but almost insensitive to surface gravity (Fig. 1 ). For cooler stars, as shown here, a dependence on surface gravity is introduced by the increasing micro-turbulent velocities, which enhance the line width towards lower values (see Wende et al. (2009) for FeH as an example). More sensitive to surface gravity are alkali lines (Fig. 1 ), which show large alterations of their line wings that are due to pressure broadening (in case of the K lines it is more pronounced towards cooler temperatures). We chose the K- and Na-line pairs at around Å and Å, respectively. To determine the metallicity, we can use all these regions as well because the -TiO band and the alkali lines are strongly dependent on this quantity (see Fig. 2 ). Rajpurohit et al. (2014) also used the K- and Na-line pairs because of their sensitivity to gravity and metallicity, as well as several TiO-bands for temperature determination. They also illustrated the dependency on the different stellar parameters. The chosen spectral regions are also affected by lines of the Earth’s atmosphere. Especially the K- and Na-line pairs are contaminated by O2 and H2O bands, respectively. We used masks to exclude the atmospheric lines from the fit. The contamination of the TiO bands around and Å is very weak and can be neglected. The degree of sensitivity on a certain parameter for a particular line (band) also varies. In Fig. 3 we show how the width of a -level in a -map changes with varying effective temperature (i.e. the of the synthetic spectrum from which the -map is produced is varied) for a fixed surface gravity of cgs and metallicity of cgs. The change is also measured in terms of discretion elements in the -maps, since this determines the given resolution (left axis). All investigated regions become less gravity sensitive towards higher , which is probably due to the increasing thermal broadening, which becomes stronger than the pressure broadening (see also Sect. 3.3 ). At this point we have to keep in mind that the sensitivity curves only represent the behaviour for the chosen parameter values. They look different for other metallicities or surface gravities, which are not shown in detail here. Nevertheless, it becomes clear that the combined -map of all regions is the best choice for most temperatures and provides the highest sensitivity. Even though the sensitivity of the K lines is better for most temperatures than the combined one, we would not suggest to use only these lines because the results would then only depend on two lines. Experience in fitting real observations showed that the results deduced from the K lines alone can differ from the combined solution where the latter matches the actual parameters to a higher accuracy. 3.2. <inline-formula


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Acknowledgements The authors are grateful to the anonymous referee for careful and critical comments, which helped to improve the manuscript substantially. HVŞ acknowledges support from the Scientific and Technological Research Council of Turkey (TÜBİTAK) through the project grant 1001 - 115F033. EI acknowledges support from the Young Scientist Award Programme BAGEP-2016 of the Science Academy, Turkey, and is grateful to T. Reinhold and R. H. Cameron for useful discussions. GAJH would also like to acknowledge the IDEX initiative at Université Fédérale Toulouse Midi-Pyrénées (UFTMiP) for funding the STEPS programme that enabled regular research visits. This work has made use of the VALD data base, operated at Uppsala University, the Institute of Astronomy RAS in Moscow and the University of Vienna.


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We would like to thank the reviewer for comments that improved the clarity of the presentation. DF was supported by the DoD SMART Scholarship. TP was partially supported by the NSF grant AST-1109113 and the DOE grant DE-FG52-09NA29548. This research used resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the US Department of Energy under Contract No. DE-AC02-05CH11231, and the Air Force Research Laboratory. The software used in this work was in part developed by the DOE Flash Center at the University of Chicago. The data analysis was performed in part using the yt Project (Turk et al. 2011 ), and VisIt (Childs et al. 2012 ). This research has made use of NASA's Astrophysics Data System Bibliographic Services.


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I thank Long Wang for his interest. The status of the initial conditions in the N -body model emerged after a check instigated by an enquiry from him.


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We thank Drs D. Koester and R. D. Rohrmann for the enlightening discussions and useful suggestions throughout this work. IP and SO Kepler are supported by CNPq and FAPERGS-Pronex-Brazil.


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We acknowledge the anonymous referee for helpful comments and suggestions. This work made use of data supplied by the UK Swift Science Data Centre at the University of Leicester. Our study was supported by the National Basic Research Program of China with Grant No. 2014CB845800 and by the National Natural Science Foundation of China with Grants No. 11473012, No. 11475085, and No. 11275097.


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ACKNOWLEDGEMENTS We thank the anonymous referee for insightful comments and constructive suggestions. This research has made use of data, software, and/or web tools obtained from NASAs High Energy Astrophysics Science Archive Research Center ( heasarc ), a service of the Goddard Space Flight Center and the Smithsonian Astrophysical Observatory. This research has made use of the XRT Data Analysis Software ( xrtdas ) and the NuSTAR Data Analysis Software ( nustar-das ) jointly developed by the ASI Science Data Center (ASDC, Italy) and the California Institute of Technology (Caltech, USA). PG would like to thank IUCAA and BARC for their hospitality. RG would like to thank the IUCAA associateship programme and CSIR, New Delhi (03(1412)/17/EMR-II) for the financial support.


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We are grateful to Daisuke Nagai and Fang Peng for giving us a copy of their Fortran code that we used to reproduce the data in their sedimentation model. We are grateful to the anonymous referee for a thoughtful and detailed report. The suggestion to make a more comprehensive comparison between a homogeneous and a heterogeneous ICM inspired us to produce several new figures and helped us to significantly improve the final version of this manuscript. We acknowledge useful discussions with Daisuke Nagai, Matthew Kunz, Prateek Sharma, Ellen Zweibel, and Ian Parrish during the 3rd ICM Theory and Computation Workshopheld at the Niels Bohr Institute in 2014. We also thank Sagar Chakraborty and Henrik Latter for valuable comments. The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP/2007-2013) under ERC grant agreement 306614. T.B. also acknowledges support provided by a Lørup Scholar Stipend and M.E.P. also acknowledges support from the Young Investigator Programme of the Villum Foundation.


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Acknowledgements OSIRIS was built by a consortium led by the Max-Planck-Institut für Sonnensystemforschung, Göttingen, Germany, in collaboration with Centro di Ateneo di Studi ed Attivit'a Spaziali ‘Giuseppe Colombo’ (CISAS), University of Padova, Italy; the Laboratoire d’Astrophysique de Marseille, France; the Instituto de Astrofísica de Andalucia, Consejo Superior de Investigaciones Científicas (CSIC), Granada, Spain; the Science Support Office of the European Space Agency, Noordwijk, the Netherlands; the Instituto Nacional de Técnica Aeroespacial, Madrid, Spain; the Universidad Politéchnica de Madrid, Spain; the Department of Physics and Astronomy of Uppsala University, Sweden and the Institut für Datentechnik und Kommunikationsnetze der Technischen Universität Braunschweig, Germany. Rosetta is an ESA mission with contributions from its member states and NASA. The support of the national funding agencies of Germany (DLR), France (CNES), Italy (ASI), Spain (MEC), Sweden (SNSB) and the ESA Technical Directorate is gratefully acknowledged. We thank the Rosetta Science Ground Segment at ESAC, the Rosetta Mission Operations Centre at ESOC and the Rosetta Project at ESTEC for their outstanding work enabling the science return of the Rosetta Mission.


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distance between the points on a zenith angle circle being ∼ R / N μ ) and equally spaced points on the dayside from terminator to disc edge (Fig. 1 ) with the same approximate separation. Our computed disc-averaged radiance was thus calculated as where μ i are the Gaussian quadrature points, Δμ i are the Gaussian weights, φ ij are the azimuth angles (which are different for different μ i ), and ij are the azimuth angle trapezium-rule integration weights. To ensure correct normalization, ∑ j ij = 1.0 and (i.e. ). In addition, we assumed that the exoplanet had a transit with low impact parameter such that northern and southern hemispheres were observed at the same emission angle and we also assumed north/south symmetry such that we only had to integrate over half the disc. Figure 1. Example of disc-averaging quadrature points chosen for N μ = 2, 3, 4, and 5 and phase angle ζ = 45° (where 0° is nightside and 180° is dayside). The daylight side of the planet is coloured light grey, while the nightside is dark grey. The zenith angles of the chosen Gauss–Lobatto quadrature scheme are shown by the dotted white lines. The azimuth points along each zenith angle line (indicated by the asterisk symbols) are chosen to coincide with the terminator for zenith angles that intersect the terminator and be roughly equally spaced with a fractional disc distance of 1.0/ N μ . As we assume north–south symmetry, only points on or above the equator are needed for disc-integration. An example of the chosen quadrature points for our scheme using N μ = 2, 3, 4, or 5 zenith angles is shown in Fig. 1 for a phase of 0.125 (i.e. a phase angle ζ = 45°). Here we can see that as we add more zenith angles, the number of sampled points on the disc is greatly increased. In our scheme if a given zenith angle circle intersects the day–night terminator, one azimuth quadrature point is placed on that terminator and the remaining azimuth points are chosen to be roughly equally spaced on the day and nightside, as noted above. The reason for doing this is that if we were to observe a planet where the reflected starlight is strong, we would expect that contribution to fall rapidly towards the terminator. By making sure we place a quadrature point at the terminator, we can thus ensure a better estimate of the azimuthal average of the radiance at a given zenith angle. Although in this study we have not included reflected starlight in our models, the disc-integration scheme we have defined means that we well be able to seamlessly and accurately incorporate this in future. 2.1 Computation of contribution of reflected starlight Assuming a Lambertian reflecting surface, the scattered radiance at any point on the disc is equal to α F star /π, where α is the reflectivity and F star is the local stellar irradiance (i.e. W m −2 ), calculated as F star = P cos θ/(4π d 2 ), where P is the total power of the star, d is the distance of the planet from the star, and θ is the local stellar zenith


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C.C. and A.K. were supported in part by the Kavli Institute for Cosmological Physics at the University of Chicago through grant NSF PHY-1125897 and an endowment from the Kavli Foundation and its founder, Fred Kavli. E.B. and B.J. are partially supported by US Department of Energy grant DE-SC0007901. T.N.V. was supported by the SFB-Transregio 33 The Dark Universe by the Deutsche Forschungsgemeinschaft (DFG) and the DFG Cluster of Excellence “Origin and Structure of the Universe.” The weak lensing boost factors were calculated and calibrated using the computing facilities of the Computational Center for Particle and Astrophysics (C2PAP). D.R. is supported by a NASA Postdoctoral Program Senior Fellowship at the NASA Ames Research Center, administered by the Universities Space Research Association under contract with NASA. The CosmoSim database used in this paper is a service by the Leibniz-Institute for Astrophysics Potsdam (AIP). The MultiDark database was developed in cooperation with the Spanish MultiDark Consolider Project CSD2009-00064. The authors gratefully acknowledge the Gauss Centre for Supercomputing e.V. ( www.gauss-centre.eu ) and the Partnership for Advanced Supercomputing in Europe (PRACE; www.prace-ri.eu ) for funding the MultiDark simulation project by providing computing time on the GCS Supercomputer SuperMUC at the Leibniz Supercomputing Centre (LRZ; www.lrz.de ). The Bolshoi simulations have been performed within the Bolshoi project of the University of California High-Performance AstroComputing Center (UC-HiPACC) and were run at the NASA Ames Research Center. Funding for the DES Projects has been provided by the U.S. Department of Energy, the U.S. National Science Foundation, the Ministry of Science and Education of Spain, the Science and Technology Facilities Council of the United Kingdom, the Higher Education Funding Council for England, the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign, the Kavli Institute of Cosmological Physics at the University of Chicago, the Center for Cosmology and Astro-Particle Physics at the Ohio State University, the Mitchell Institute for Fundamental Physics and Astronomy at Texas AM University, Financiadora de Estudos e Projetos, Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro, Conselho Nacional de Desenvolvimento Científico e Tecnológico and the Ministério da Ciência, Tecnologia e Inovação, the Deutsche Forschungsgemeinschaft, and the Collaborating Institutions in the Dark Energy Survey. The Collaborating Institutions are Argonne National Laboratory, the University of California at Santa Cruz, the University of Cambridge, Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas-Madrid, the University of Chicago, University College London, the DES-Brazil Consortium, the University of Edinburgh, the Eidgenössische Technische Hochschule (ETH) Zürich, Fermi National Accelerator Laboratory, the University of Illinois at Urbana-Champaign, the Institut de Ciències de l’Espai (IEEC/CSIC), the Institut de Física d’Altes Energies, Lawrence Berkeley National Laboratory, the Ludwig-Maximilians Universität München and the associated Excellence Cluster Universe, the University of Michigan, the National Optical Astronomy Observatory, the University of Nottingham, The Ohio State University, the University of Pennsylvania, the University of Portsmouth, SLAC National Accelerator Laboratory, Stanford University, the University of Sussex, Texas AM University, and the OzDES Membership Consortium. Based in part on observations at Cerro Tololo Inter-American Observatory, National Optical Astronomy Observatory, which is operated by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation. The DES data management system is supported by the National Science Foundation under grant Numbers AST-1138766 and AST-1536171. The DES participants from Spanish institutions are partially supported by MINECO under grants AYA2015-71825, ESP2015-66861, FPA2015-68048, SEV-2016-0588, SEV-2016-0597, and MDM-2015-0509, some of which include ERDF funds from the European Union. The IFAE is partially funded by the CERCA program of the Generalitat de Catalunya. Research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Program (FP7/2007–2013), including ERC grant agreements 240672, 291329, and 306478. We acknowledge support from the Australian Research Council Centre of Excellence for All-sky Astrophysics (CAASTRO) through project number CE110001020. This manuscript has been authored by the Fermi Research Alliance, LLC, under contract No. DE-AC02-07CH11359 with the U.S. Department of Energy, Office of Science, Office of High Energy Physics. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. This paper has gone through internal review by the DES collaboration.


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

This paper makes use of the following ALMA data: ADS/JAO.ALMA#2012.1.00453.S. ALMA is a partnership of ESO (representing its member states), NSF (USA), and NINS (Japan), together with NRC (Canada) and NSC and ASIAA (Taiwan), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO, and NAOJ. S.A. acknowledges support from the Swedish National Science Council grant 621-2011-4143. K.S. was supported by MOST grant 102-2119-M-001-011-MY3. E.G.-A. is a Research Associate at the Harvard-Smithsonian Center for Astrophysics, and thanks the Spanish Ministerio de Economía y Competitividad for support under project FIS2012-39162-C06-01 and NASA grant ADAP NNX15AE56G. F.C. acknowledges support from the Swedish National Science Council grant 637-2013-7261. J.M.-P. acknowledges partial support by the MINECO under grants AYA2010-2169-C04-01, FIS2012-39162-C06-01, ESP2013-47809-C03-01 and ESP2015-65597-C4-1.


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

selected from an ensemble of similar objects. Light curves were constructed by taking one of the observable parameters from the formal solutions and computing its response to the driving in depth from equation ( 8 ). In detail, this was carried out by fitting a cubic natural spline through the parameter values at the known depths. 4.4 Variable background radiation The operations for variation of the background radiation follow a broadly similar approach to those used in Section 4.3 . However, there are important differences. First, we apply only the default sinusoid and function D 6 as driving functions, since only D 6 is based on a model where the background, rather than the pump, is varied. The process is easier in the sense that the parameter that is varying in time is simply a parameter in equation ( 4 ), and no complicated justification is required for its use. A significant complication in the variable background case, however, is that the driver in the background analogue of equation ( 8 ) now demands a response from a number of different models, each computed with a different value of i BG . Therefore, modelling flares from background variation is computationally considerably more expensive. 5 VARIABLE PUMPING RESULTS We plot, in Fig. 3 , the flare light curves, over one period, that result from driving with pump functions D 0 – D 5 for a prolate cloud with Γ = 0.6, with the observer placed in the optimum position (viewing the cloud along the z -axis close to the long axis of the cloud). The cloud style is uniform in unsaturated inversion. The parameters of equation ( 8 ) in this case are τ min = 10.0 and Δτ = 5.0, corresponding to a regime that is already characteristic of quite strong saturation. Throughout Section 5 , the y -axes of graphs are shown in flux density, based on a background specific intensity that is scaled to the saturation intensity of the maser transition. Flux density is likely the best parameter to plot in view of the prominent role of single-dish monitoring in repetitive flare studies. An explanation of the flux-density scale appears in Appendix A . Owing to the nature of the saturation intensity, and particularly the fact that this quantity may itself depend on the energy density of pumping radiation, a conversion formula to units of Jy at a typical source distance, and for a particular maser transition, for example, is not trivial. Such a conversion is also discussed in detail in Appendix A . The variability index of the maser light curve, defined as in the Introduction as F pk / F qui is 1.74 in Fig. 3 . The same parameter for the driving functions, replacing flux densities with values of the depth multiplier, is 1.5. Although the variability index of the maser is significantly larger here, the light curve in Fig. 3 demonstrates the smoothing effect of saturation: as exponential growth gives way to a functional form that is closer to linear at high flux density, the maser responds more weakly to the driving


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

to study the reactions of carbon atoms with anthracene and coronene. In our computational study, we were mainly interested in the investigation of the pathways found previously for the reaction of carbon with benzene (Krasnokutski Huisken 2014c ) and naphthalene. Hence, we focused on the formation of seven-membered carbon rings. Our computations predict the barrierless reaction of carbon atoms with anthracene molecules and the possibility of a ring opening for all three aromatic cycles, i.e., the formation of seven-membered carbon rings in the center as well as on the sides of the molecule. Thus, the calculations reveal the possibility of the same reaction pathways as observed for benzene and naphthalene. This is in line with the experimental results obtained for benzene, naphthalene, and anthracene molecules. However, similar to the case of naphthalene, the carbon atom cannot be inserted into the CC bond shared by two aromatic rings. Figure 8 shows the molecular structures of the initial associative complexes between coronene and the carbon atom. It can be seen from this figure that, similar to the cases of the other PAHs studied, the carbon atom lands on the top of the CC bonds. The binding of the carbon atom to the bonds of the central ring is the weakest, and increases when the carbon atom moves to the side of the coronene molecule. Similar to the previously studied PAH molecules, the carbon atom cannot be inserted into the CC bond shared by the two aromatic rings. Therefore, the formation of a seven-membered ring in the center of coronene is not possible. Such a structure was found to be a transition state, with negative binding energy of the carbon atom. The binding of the carbon atom to the coronene molecule was enhanced going from the initial triplet state to the singlet state of the system. The highest binding energy (186.2 kJ mol −1 ) was found for the carbon atom on top of the peripheral CC bonds in the singlet state. With a relatively small energy barrier, the carbon atom can be inserted into the peripheral CC bonds of the coronene molecule. In this case, the reaction pathway is the same as for the other molecules studied. However, in the case of coronene, there is a considerable increase in the number of CC bonds, which cannot be opened. Therefore, landing of carbon atoms on these sites would not lead to the formation of a seven-membered ring. Two of the four complexes shown in Figure 8 , namely complexes 1 and 2, have rather low binding energy. Moreover, the energy barrier for the formation of a seven-membered carbon ring was computed to be a little higher compared to the case of benzene and naphthalene molecules. Therefore, there is a higher chance that the initial associative complexes 3 and 4 could also be frozen inside the liquid helium droplets. This explains the results of the calorimetric measurements showing only low energy released in the reaction of carbon atoms with coronene molecules. Figure 8. Molecular


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

of higher frequency as well as others due to nonlinear interactions of the flows. Our present simulations indeed show complex timing properties of the radiation as well as the flow dynamics. For this, we chose the flow to have an accretion rate () below the Eddington limit for all of the cases we studied. The exponent α in the cooling rate was varied from 0.5 (bremsstrahlung) to 0.6 to observe the effects of the strength of cooling on the oscillation of shocks. The specific angular momentum λ was chosen based on the recent study by Deb et al. ( 2017 ), where an onset of vertical oscillation was seen between the two values chosen here. The variation of the radius of the neutron star had a more complex effect as it controlled the effects of radiation pressure on the hydrodynamics through the parameter when a self-consistent variation is chosen. Note also that for the timescales of simulations C1 to C5, the mass and momentum deposited on the star were negligible as compared to the star’s mass and spin. This accumulation of mass and momentum would become significant for timescales of the order of years or more, which is outside the purview of the current paper. However, the energy release at the surface was found to be significant, resulting in a measurable change of T NS . We show, among other things, that the simulations produce both low- and high-frequency QPOs, and the oscillations last during the whole simulation period (more than 200 dynamical timescales measured at the injected flow radius, i.e., 30 r S ). This suggests that the QPOs are formed from a part of the flow dynamics and are not a transient effect, as inferred by others (e.g., Barret et al. 2005b ). We measure the QPO frequencies and find that both the centroid frequencies and Q factors match well with the observed results of neutron stars such as GX17+2, 4U 1728-34, and Cir X-1. We believe that the advective flow suggested in the literature, while explaining the behavior of the source Cir X-1 (Boutloukos et al. 2006 ), may be the same as the dynamic transonic flow solution we discuss here. We showed that the presence of angular momentum itself can generate multiple modes of oscillation in CENBOL and NBOL, manifesting as QPOs in the PDS, in the presence of cooling. In Figures 1 (b), 2 (c)–(d), and 3 (a), we see different types of shocks are being formed. The outer shock was found to be vertical near the equatorial plane and oblique away from the plane, very similar to what was seen for simulations around black holes ( MLC94 ). The bending instabilities reported in M01a are also found here and correspond to the hectohertz oscillations found in the PDS. So far, in the literature, a model that appears to be capable of phenomenologically addressing both timing and spectral properties is the TL model of TLM98 , who assumed the disk to be Keplerian to begin with. The viscosity was also assumed to be high enough to maintain a Keplerian distribution. The QPOs are then explained as the


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

g is a binary loss function and s j the scorefor learner j . The predicted class for x 0 is associated with the index k for which the vector Δ is minimal. Appendix C Description of classification algorithms: SVM – Ensemble methods Support-machine vectors The SVM method classifies the data by finding the best hyperplane separating the datapoints of one class from those of another category. Given a training set of M datapoints , where x i refers to the P-dimensional feature vector and y i the associated label that indicates whether the datapoint belongs to the positive class ( y i = +1) or the negative class ( y i = −1), the objective of SVM is to separate the data into distinct classes using a separating rule in form of a parametrized function f ( x ). For linearly separable data, the equation of the hyperplane is: where the scalar product w . x is equivalentto w ⊤ x . An infinity of hyperplanes verify Eq. ( C.1 ), but only one hyperplane maximizing the margins between the observationsand the hyperplane exists. This optimal hyperplane verify: To find the“best” linear hyperplane minimizing the margins , the SVM algorithm consists in solving a quadratic problem: For non-linearly separable data, the use of a kernel φ trick enables to map the distribution of the datapoints x into a projected space where φ ( x ) can be linearly separable, and defines, in the same approach as in Eq. ( C.2 ), a quadratic problem: where f ( x ) = f W , B ( x ) = W . φ ( x ) + B = 0. The selection of an adequate kernel K is determined by a list of criteria. By definition, a kernel must be symmetric, definite positive, square integrable and satisfy: Among commonly used kernels: Linear: K ( x i , x j ) = x i . x j Power: Gaussian (rbf): Further details about the SVMs are available in Vapnik (2000) and Cristianini Shawe-Taylor (2000) . C.2: Ensemble classifiers The principle of ensemble methodology is to combine a set of predictions from different learners in order to improve the accuracy of a single learner. Among the ensemble methods, two distinct approaches are identified: 1. Averaging methods: Bagging/ Random forests... 2. Boosting methods: AdaBoost/GentleBoost/RSBoost/... – AdaBoost AdaBoost, known also as “Adaptive Boosting” refers to a specific algorithm of boosted classifier defined as the sum of individual predictions from T weak learners. The algorithm aims to minimize the (weighted) classification error at each iteration: where: x i is the feature vector of the i th observation. y i is the true label of the i th observation. h t is the prediction of learner t . 1 is the indicator function. is the weight of the i th observation at step t . t the iteration step from 1 to T . At the first iteration, the weights are initialized (e.g., ) and the weak learner h t is obtained by minimizing the error ε t . For the next iteration, the weights of the learner ( t + 1) are adjusted according to the performance of the previous one ( t ): whether increase for misclassified


O O O O O O B-Model I-Model O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O B-Model I-Model O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model B-Model B-Citation I-Citation I-Citation O B-Model B-Model B-Citation I-Citation I-Citation O B-Model B-Model B-Citation I-Citation O O B-Model B-Model B-Citation I-Citation I-Citation O O O O O O O O O O B-Model I-Model O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O B-Model O B-Citation I-Citation I-Citation O B-Model O B-Citation I-Citation O O B-Model O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O B-Model O B-Model O O O O O B-Model O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O B-Citation I-Citation I-Citation O O O O O O O O O O O B-Model O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O B-Citation I-Citation I-Citation O B-Model O B-Citation I-Citation I-Citation O B-Model O B-Citation I-Citation O O B-Model O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O B-Instrument I-Instrument I-Instrument O O O O B-Wavelength O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O

of C 6+ . However, the Ecker–Kröll model ( Ecker Kröll 1963 ) predicts a much higher population fraction of C 6+ compared with that obtained using our model. This differs from the conclusion drawn using the solid-density Mg, Al, and Si plasma ( Ciricosta et al. 2012 , 2016 ; Zeng et al. 2020 ), where the IPDs determined by the Ecker–Kröll model were in much better agreement with the experimental results than those of the SP model. Fig. 4. Charge-state distribution of C plasma as a function of the plasma temperature at mass densities of 2.25 g cm −3 ( a ), 3.75 g cm −3 ( b ), and 5.0 g cm −3 ( c ). Our results are compared with the Debye–Hückel (DH; Debye Hückel 1923 ), Stewart–Pyatt (SP; Stewart Pyatt 1966 ), ion-sphere (IS; Rozsnyai 1972 ), and Ecker–Kröll (EK; Ecker Kröll 1963 ) analytical models. We obtained the best agreement with the Ecker–Kröll model ( Ecker Kröll 1963 ) for the CSDs at a mass density of 3.75 g cm −3 . The SP ( Stewart Pyatt 1966 ), IS ( Rozsnyai 1972 ), and Debye-Hückel ( Debye Hückel 1923 ) models predicted a higher population fraction for C 5+ and a lower fraction for C 6+ than those predicted by our model and the Ecker–Kröll model. With the increasing mass density up to 5.0 g cm −3 , our theoretical IPDs and those of the IS and Ecker–Kröll models exhibited good agreement. The SP and Debye–Hückel models predicted a higher population fraction for C 5+ and a lower fraction for C 6+ . The aforementioned results can be seen in Fig. 5 , which shows the average ionization degree of C plasma as a function of the plasma temperature (100–500 eV) at mass densities of 2.25, 3.75, and 5.0 g cm −3 . Our predicted average ionization degree is consistent with those of the Ecker–Kröll model ( Ecker Kröll 1963 ) at a density of 3.75 g cm −3 and the IS and Ecker–Kröll models at a density of 5.0 g cm −3 , which is completely in accordance with the features observed with respect to CSDs (Fig. 4 ). Fig. 5. Average ionization degree of C plasma as a function of plasma temperature at mass densities of 2.25 g cm −3 ( a ), 3.75 g cm −3 ( b ), and 5.0 g cm −3 ( c ). Our results are compared with the Debye–Hückel ( Debye Hückel 1923 ), Stewart–Pyatt ( Stewart Pyatt 1966 ), ion-sphere ( Rozsnyai 1972 ), and Ecker–Kröll ( Ecker Kröll 1963 ) analytical models. 3.3. Analysis and explanation of a recent experiment Here, we verify the validity of our proposed model of screening potential by comparing its predictions with the results of a recent experimental measurement of the average ionization degree of C in a CH-mixture plasma ( Kraus et al. 2016 ). In this experiment, a highly compressed CH-mixture plasma (polystyrene) was created via spherically convergent shocks at the National Ignition Facility. Then, the spectrally resolved X-ray scattering of line radiation at 9.0 keV was recorded. The experiment measured an average ionization degree of 4.92 ± 0.15 for C at an average temperature of 86 ± 20 eV (radiation–hydrodynamics simulations show that


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

to first order with b – which is degenerate with the function of σ n e – and the only way to break the degeneracy is to have enough variation in the secant of the zenith angle. In a sparse and noisy observation of ΔTEC, the secant variation is poor and it is expected that this degeneracy exists. Therefore we also show the product b σ n e , and we see that this compound value discrepancy is smaller by approximately 35%. Table 2. Average and standard deviation, over all experimental conditions, of the difference between the learned physical hyperparameters and the true hyperparameters. In Table 3 we summarise the performance of the physical kernel against each competitor kernel. We display the mean of ΔLPO C ( η ), and ΔLPH C ( η ) over all experimental conditions, as well as their values at the nominal experimental conditions of 30 directions per 12.6 deg 2 , and ΔTEC noise of 1 mTECU, which is indicated with η nom . We use bold font in Table 3 to indicate the best competitor model. Table 3. Probability ratio FOMs (see text) averaged over experimental conditions and at nominal conditions. Notes. Larger values indicate that the physical model is more probable. Bold face indicates the best performing competitor model (lower number). We first consider the ability of each model to represent the observed data. For the dawn ionosphere, the M52 competitor kernel has the best (lowest) ⟨ΔLPO C ⟩ η = 1.55 and , implying that the M52 kernel model is 55% and 46% less probable than the physical kernel model on average over all experimental conditions, and at nominal conditions, respectively. We note that the M32 kernel produced similar results. For the dusk ionosphere, the EQ kernel model is likewise the best among all competitors, being only 73% and 54% less probable than the physical kernel model on average over all experimental conditions, and at nominal conditions, respectively. In all experimental conditions, the physical model provides a significantly more probable explanation of the observed data. We now consider the ability of each model to infer the held-out data. For the dawn ionosphere, the M52 competitor kernel has the best (lowest) ⟨ΔLPH C ⟩ η = 1.49 and = 1.31, implying that the M52 kernel prediction is 49% and 31% less probable than the physical kernel model on average over all experimental conditions, and at nominal conditions, respectively. We note that the M32 kernel produced similar results. For the dusk ionosphere, the EQ kernel model is likewise the best among all competitors, with predictions only 16% and 12% less probable than the physical kernel model on average over all experimental conditions, and at nominal conditions, respectively. In the case of the rougher dawn ionosphere, the physical model provides a significantly more probable prediction of the held-out data in all experimental conditions. However, for the smoother dusk ionosphere at nominal conditions, the physical model is only 12% more probable than the EQ kernel model,


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

et al. 2013 ). Moreover, Cleeves et al. ( 2015 ) show that reduced cosmic ray ionization (a consequence of exclusion by disc winds) produce disc chemistry features in agreement with TW Hya observations. Our population results showing that X-ray ionized models produce populations that better reproduce observational features are in agreement with these results. One key difference in our super Earth populations and the observations is that our model produces fewer close-in super Earths. When comparing the direct population outputs (Fig. 10 ) with the populations that account for observational biases (Fig. 9 ), we see that a portion of the zone 5 planets in our model are filtered out as they have low observation probabilities. Additionally, our model does produce a large number of failed cores, but a significant fraction of these orbit just outside the defined outer observable limit of 2 au, and are situated on orbits out to 5 au. The range of radii between 1 and 5au is the most common region for super Earths to form in our model as this is the region where the ice line, heat transition, and cosmic ray dead zone traps converge to. Thus, our model predicts there to be a significant population of super Earths with orbital radii of 1–5 au. Our planet formation model does not produce low mass super Earths that migrate into short-period orbits. We noted this several times throughout Section 4 and refer to this as a zone of avoidance of our model within zone 5 of the mass-semimajor axis diagram. The lowest mass super Earths formed in our model that populate zone 5 are ∼3 M ⊕ and orbit outside of 1 au. This feature of our populations is tied to the evolution of the traps that evolve from orbital radii outside ∼8 au to within ∼1 au on disc evolution time-scales. This prevents ∼Earth-mass planets from migrating to short period orbits in our model as they evolve with the trap they are forming within. Planets can, however, become liberated from their host planet traps at the onset of type II migration. In this case, planets must exceed their gap opening mass (equation 17 ) of ∼10 M ⊕ to type II migrate separately from their trap. Initially, type II migration takes place on shorter time-scales than trapped type I migration, so these planets can, in some cases, migrate to short period orbits during their slow gas accretion phase before their accretion is terminated at the disc lifetime. Thus, the lowest mass zone 5 planets orbiting between 0.01 and 0.1au formed in our model have masses ≳10 M ⊕ . Hasegawa ( 2016 ) also found that a core accretion model involving trapped type I migration could not form a failed core population consistent with observations. In particular, this model could only form super Earths more massive than ∼4–5 M ⊕ , similar to the results found in this work. Based on the results of our constant dust-to-gas ratio model, one might suggest that formation scenarios in addition to the failed core scenario are necessary to explain the observed


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Members of the CAGE team (Cosmochimie, astrophysique et géophysique expérimentale) at IPGP are thanked for insightful discussions. G.A. acknowledges funding from the Région Ile-de-France through the DIM-ACAV+ program. J.D.G. acknowledges funding from the Science and Technology Facilities Council (STFC) grant No. ST/R000751/1. This study contributes to the IdEx Université de Paris ANR-18-IDEX-0001. This is IPGP contribution #4092.


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This paper has benefitted from discussions in depth with the referee J. Th. van Loon. This work was partially funded by the Spanish MICINN under the Consolider-Ingenio 2010 Program grant CSD2006-00070 First Science with the GTC 6 , and through grants AyA2011-24052. This work has been supported by the CoSADIE Coordination Action (FP7, Call INFRA-2012-3.3 Research Infrastructures, project 312559). F.J.E. acknowledges financial support from the ARCHES project (7th Framework of the European Union, No. 313146). Support was also granted by Deutsche Forschungsgemeinschaft through grant EN 176/30.


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We acknowledge the insightful discussions and useful comments of A. de Ugarte-Postigo and C. Thöne. We acknowledge the support from the European Research Council (Starting Independent Researcher Grant CAMAP-259276), and the partial support of grants AYA2010-21097-C03-01, CSD2007-00050 and PROMETEO-2009-103. CC-M also acknowledges the support of ACIF/2013/278 fellowship, and the partial support of UV-INV-PREDOC13-110509 fellowship. We thankfully acknowledge the computer resources (‘Lluís Vives’ and ‘Tirant’ supercomputers), technical expertise and assistance provided by the Servei de Informatica at the University of Valencia.


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O O O O B-Location O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Location O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O B-Location O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Location B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Location B-Location B-Location B-Location O B-Location O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Location O B-Location O B-Location O B-Location O O B-Location O O O O O O O O O O O O O O O O O B-Location O B-Formula I-Formula I-Formula B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula B-Location O B-Formula I-Formula I-Formula B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula B-Location O B-Formula I-Formula I-Formula B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula B-Location O B-Formula I-Formula I-Formula B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula O B-Location O B-Formula I-Formula I-Formula B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O B-Location O B-Location O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

Lake Meteorite. The first specimen of 131 g was discovered on 2000 September 17. Later investigations on 2006 November identified additional 526 fragments with total mass of 8991 g, i.e. 900 per cent of increase of the total known weight (Verish 2009 ). The distribution of Antarctic ordinary chondrites and elsewhere present similar entropic indices (2.12 and 2.18) what suggests equivalent mechanisms that yield the observed distributions. On the other hand, β q present a variation of the order of 10 times between the distributions. This result confirms the tendency identified by Huss ( 1990 ); the Antarctic meteorites present mean mass smaller than those found in the rest of the Earth. The combined sample is modeled by a q -stretched exponential, most probably due to the influence of the larger mean mass of non-Antarctic meteorites. These results, and the great dispersion of the entropic indices, suggest that the observed distributions, more properly modeled by q -stretched exponential, are more influenced by the ‘gathering bias’. 4.3 Findings/fall location sites Halliday, Blackwell Griffin ( 1989 ) suggested an overall rate of 83 falls of meteorites every 10 6 km 2 /yr. Considering this estimate, it would be expected 85 events per year in Brazil (de Carvalho 2010 ). This amount exceeds the number of meteorites collected in the last two centuries in the country. This suggests the occurrence of a gathering bias on the observed distribution. When meteorites are separated by regions with large territorial areas (Russia, Canada, USA, China, and Brazil), we verified that the distributions are described by q -stretched exponential with a P value ≥0.95 (Fig. 6 ). Figure 6. Inverse cumulative distributions of mass for some types of meteorites found in Brazil (circles), Canada (diamonds), China (squares), Russia (crosses), and USA (plus). The red solid lines represent the fitting of q -stretched exponentials for the meteorites found in Brazil ( q = 1.87, β q = 5.43 × 10 −3 g −1 , N t = 74, and γ = 0.57), Canada ( q = 1.47, β q = 5.08 × 10 −3 g −1 , N t = 65, and γ = 0.61), China ( q = 1.64, β q = 7.48 × 10 −2 g −1 , N t = 359, and γ = 0.39), Russia ( q = 1.91, β q = 4.20 × 10 −3 g −1 , N t = 144, and γ = 0.61), and USA ( q = 1.43, β q = 2.60 × 10 −2 g −1 , N t = 1816, and γ = 0.48). The average γ = 0.53 ± 0.08 overlaps with the value found on sub-Section 4.2. This result may be understood if the fraction of meteorites by mineralogical type is also valid for national (local) samples. This hypothesis is reasonable, since the weight average shape parameter of the total sample of meteorite types modeled by q -stretched exponential is γ = 0.65. The values of β q for China and USA are about 10 times smaller than the other national samples. This implies a smaller number of meteorites of large mass for these two countries. The origin for this may be due to the fraction of iron meteorites in the samples. Iron meteorites are heavier in all national samples, but


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We thank Dr. Jan Robrade of Hamburger Sternwarte for his help in data analysis of the XMM-Newton data. This work was carried out as part of Project A16 funded by the Deutsche Forschungsgemeinschaft (DFG) under SFB 963. AAV acknowledges support from an Ambizione Fellowship of the Swiss National Science Foundation. C.P.F. was supported by the grant ANR 2011 Blanc SIMI5-6 020 01 “Toupies: Towards understanding the spin evolution of stars”. Part of the work was also supported by the COST action MP1104 “Polarisation as a tool to study the Solar-system and beyond”. Finally, we thank the anonymous referee for their detailed and constructive comments.


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(SLAC) lenses for a substructure mass function slope α = 0.90 () (Vegetti et al. 2014 ). Thus, as long as baryonic physics does not significantly affect the result, it is reasonable to conclude that CDM substructures are not the entire reason for the flux anomaly problem. On the other hand, our result for line-of-sight lensing significantly differs from the result that was obtained using R cusp and R fold (Xu et al. 2012 ). The difference may come from the typical source redshift z S = 2 assumed in Xu et al. ( 2012 ). In fact, our result indicates that for z S 2, the ratio of the strength of the convergence perturbation from subhaloes to that of the total value is 30 to 40 per cent. For higher source redshifts, however, the ratio becomes much smaller. Moreover, the two lens systems B2045+265 and B1555+375 used in Xu et al. ( 2012 ) (the latter was excluded in our analysis), which have a relatively large R cusp = 0.4–0.5, show another source of anomaly: B2045+265 has a secondary lens (McKean et al. 2007 ) and B1555+375 has an edge-on disc component that can account for the anomaly (Hsueh et al. 2016 ). Excluding these complex lenses would surely weaken the discrepancy with our result. Complex lens environments, such as secondary lenses and disc components and neighbouring groups and clusters, should be taken into account properly. Our result indicates that a secondary lens can reside in the intergalactic space and is not necessarily a companion of the primary lens. Furthermore, the previously claimed subhalo with a mass of (1.9 ± 0.1) × 10 8 M ⊙ discovered from the residual image of an Einstein ring in B1938+666 (Koopmans 2005 ; Vegetti et al. 2012 ) may not be the subhalo of the primary lensing galaxy halo. It may be isolated from any haloes or belong to another distant one. To measure the redshift of a secondary or that of a third lens, we can use the distortion pattern of an extended source and future submillimetre observations would be able to detect such small signals (Inoue Chiba 2005a , b ). Using ALMA, the detection of other anomalous anomalies in lensed quadruple SMGs could be achieved by increasing the number of anomalous targets to ≳10, which would test our findings. In our analysis, we assumed that primary lenses are described by SIEs as indicated by the surface brightness of the lensing galaxies. This assumption may be too simple. We did not take into account the slight smooth distortion of the lens potential, such as low-order multipoles m 3 and m 4, or a deviation from an isothermal profile. As long as these complexities are related with the fluctuations of the first derivatives on scales comparable to or larger than the Einstein radius of the primary lens, we expect that our result would not change significantly. This is because the anomaly in the flux ratios is caused by a perturbation of the second derivatives of the gravitational potential rather than the first derivatives. However, to obtain more accurate results, we do


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M.P. and F.M. acknowledge financial support from the University of Trieste (FRA2016). F.C. acknowledges funding from the INAF PRIN-SKA2017 program 1.05.01.88.04 and from grant PRIN MIUR 2017 - 20173ML3WW_001. The authors thank an anonymous referee for careful reading of the manuscript and useful suggestions.


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We are very grateful to the entire NuSTAR , INTEGRAL , Swift , XMM-Newton , VLA, and VLBA teams for making this observing campaign possible. We thank R. Lunnan, A. Suzuki for their feedback on the first version of the paper that appeared on the archive. Some of the observations reported here were obtained at the MMT Observatory, a joint facility of the University of Arizona and the Smithsonian Institution under programs (2018A-UAO-G15, 2018B-SAO-21, 2018B-UAO-G16; PIs Fong, Patnaude, Terreran). 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 under program NW254 (PI Miller). 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. The Keck and MMT observations were supported by Northwestern University and the Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA). This paper includes data acquired with UKIRT under program (U/18A/UA01, PI Fong). UKIRT is owned by the University of Hawaii (UH) and operated by the UH Institute for Astronomy; operations are enabled through the cooperation of the East Asian Observatory. This paper includes data gathered with the 6.5 m Magellan Telescopes located at Las Campanas Observatory, Chile. Based in part on observations at Cerro Tololo Inter-American Observatory, National Optical Astronomy Observatory (NOAO Prop. 2018A-0343, 2018B-0210; PI: G. Terreran), which is operated by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation. Based in part on observations obtained at the Southern Astrophysical Research (SOAR) telescope, which is a joint project of the Ministério da Ciência, Tecnologia, Inovaçãos e Comunicaçãoes (MCTIC) do Brasil, the U.S. National Optical Astronomy Observatory (NOAO), the University of North Carolina at Chapel Hill (UNC), and Michigan State University (MSU). This paper uses data products produced by the OIR Telescope Data Center, supported by the Smithsonian Astrophysical Observatory. Support for this work was provided to MRD by NASA through Hubble Fellowship grant NSG-HF2-51373 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS5-26555. Partly based on observations with INTEGRAL , an ESA project with instruments and science data center funded by ESA member states (especially the PI countries: Denmark, France, Germany, Italy, Switzerland, Spain) and with the participation of Russia and the USA. Partly based on observations obtained with XMM-Newton (IDs: 0822580401, 0822580501, AO-17, program #82258; PI Margutti), an ESA science mission with instruments and contributions directly funded by ESA member states and NASA. R.M. acknowledges partial support from NASA XMM-Newton Guest Investigator program grant 80NSSC19K0384. We acknowledge the use of public data from the Swift data archive. This work made use of data from the NuSTAR mission (IDs 90401327002, 90401327004, 90401327006, 90401327008), a project led by the California Institute of Technology, managed by the Jet Propulsion Laboratory, and funded by the National Aeronautics and Space Administration. This research has made use of the NuSTAR Data Analysis Software (NuSTARDAS) jointly developed by the ASI Science Data Center (ASDC, Italy) and the California Institute of Technology (USA). Observations taken with the VLA (program 18A-123; PI Coppejans) were used in this research. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. B.D.M. acknowledges support from NSF grant AST-1615084, NASA Fermi Guest Investigator Program grants NNX16AR73G and 80NSSC17K0501, and through the Hubble Space Telescope Guest Investigator Program grant HST-AR-15041.001-A. P.U. and S.M. acknowledge financial support from ASI under contracts ASI/INAF 2013-025-R0. D.G. acknowledges the financial support of the UnivEarthS Labex program at Sorbonne Paris Cité (ANR-10-LABX-0023 and ANR-11-IDEX-0005-02). K.D.A. acknowledges support provided by NASA through the NASA Hubble Fellowship grant HST-HF2-51403.001 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS5-26555. I.C. acknowledges support by the Telescope Data Center, Smithsonian Astrophysical Observatory and the Russian Science Foundation grant 17-72-20119. D.J.P. acknowledges support through NASA Contract NAS8-03060. L.D. acknowledges support by the Bundesministerium für Wirtschaft und Technologie and the Deutsches Zentrum für Luft und Raumfahrt through the grant FKZ 50 OG 1602. N.R. acknowledges the support from the University of Maryland through the Joint Space Science Institute Prize Postdoctoral Fellowship as well support from the Center for Research and Exploration in Space Science and Technology II. M.R.D. acknowledges support from the Dunlap Institute at the University of Toronto. D.D.F. and A.V.K. gratefully acknowledge support from RFBR grant 18-02-00062. Facilities: Swift , XMM , NuSTAR , INTEGRAL , Odyssey , WIND (Konus) , Fermi , Magellan:Baade (LDSS2 imaging spectrograph, Boller Chivens spectrograph), Magellan:Clay (LDSS2 imaging spectrograph) , SOAR , Keck:I , Keck:II , WIYN , CTIO:0.9m , UKIRT , MMT , VLA , VLBA . Software: BOXFIT (Version 2; van Eerten et al. 2010 , 2012 ), CASA (McMullin et al. 2007 ), CIAO (Fruscione et al. 2006 ), HEAsoft (Version 6.24), HOTPANTS (Becker 2015 ), INTEGRAL Off-line Scientific Analysis (OSA), IRAF (Tody 1986 , 1993 ), pwkit (Williams et al. 2017 ), SNOoPY ( http://sngroup.oapd.inaf.it/snoopy.html ), XMM-Newton SAS (Version 17.0), XSPEC (Arnaud 1996 ).


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Guang-Xing Li received support for this research through a stipend from the International Max Planck Research School (IMPRS) for Astronomy and Astrophysics at the Universities of Bonn and Cologne and is currently supported by the Priority Program 1573 ISM-SPP from the DFG (Deutsche Forschungsgemeinschaft). Guang-Xing Li would like to thank ISIMA (International Summer Institute for Modelling in Astrophysics, now Kavli Summer Program in Astrophysics) for facilitating collaborations, and would like to thank Nicolas Peretto and Patrick Hennebelle for discussions. Lee Hartman is acknowledged for giving a nice lecture in ISIMA, which motivates the thinking of gravity, and Di Li is acknowledged for providing references on angular momentum. Guang-Xing Li thanks Alexei Kritsuk for discussions and for his final push towards the publication of the results. Guang-Xing Li thanks Manuel Behrendt for discussions of gravitational instabilities and clumps in disk galaxies. This publication makes use of molecular line data from the Boston University-FCRAO Galactic Ring Survey (GRS). The GRS is a joint project of Boston University and Five College Radio Astronomy Observatory, funded by the National Science Foundation under grants AST-9800334, AST-0098562, and AST-0100793. This work is based in part on observations made with the Spitzer Space Telescope, which is operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA. We also would like to thank Thomas Robitaille for making his code publicly available. The research made use of the astropy package. The referee has to be acknowledged, whose comments have lead to very significant improvements in our paper.


O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O B-Software O O O B-Telescope O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O B-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

the measured Ly profiles in Fig. 4 feature a more or less pronounced inwards upturn around a radius of 1, suggesting either a superposition of a compact emission component on top of a more extended one, or alternatively a more complicated radial law. Modelling such curved profiles as single exponentials would yield spurious values for the scale lengths that strongly depended on the chosen radial range for the fitting. We adopted a two-component model as the functional form fitted to the Ly SB distributions of each object, decomposing it into two distinct components. The first was taken to resemble that of the compact UV continuum; we call it the “continuum-like” component and assume that its shape parameters are precisely known from our GALFIT modelling of the HST images (i.e. as elongated exponential discs or as point sources), except for a single flux scaling factor related to the Ly EW of this component. The Ly halo, on the other hand, was again parametrised as a single exponential. Since in this paper we only aim at obtaining robust estimates of the azimuthally averaged halo sizes, we enforced the halo model to be circularly symmetric; we also assumed both components to be concentric (see Sect. 4.4 for a brief discussion of the fitting results when these restrictions were relaxed). There were thus 3 free parameters to be optimised in each fit: The integrated fluxes and of both Ly components, and the exponential scale length of the halo. We present the results from these fits in the next subsection. Our two-component model can be seen as a minimalistic extension of the conventional single exponential profile, but it may also represent a physically meaningful hypothesis: If some fraction of the Ly luminosity produced within the star-forming regions escapes (more or less) directly – possibly suffering from dust attentuation but without large-scale spatial redistribution – then this Ly emission will roughly follow our continuum-like component. The halo component, on the other hand, describes the Ly emission more extended than the continuum, irrespective of whether it has its origin inside the galaxy and then got scattered outwards, or whether it is produced by mechanisms other than recombination in H ii regions. An alternative approach to model the Ly SB distribution would be to replace the separation into two components by a more flexible single SB law for the Ly profile such as a Sersic function. Note that a circular Sersic profile has again 3 free parameters to be fitted (total flux, half-ligh radius and Sersic index). We explored such fits as well and briefly report about the outcome below. Fig. 7 Decomposition of the observed Ly surface brightness distributions into a compact (continuum-like) and an extended exponential component (halo), as described in the text. Only the objects with detected haloes () are shown. The datapoints are the same as in Fig. 4 , but now plotted against linear radii. The green curves show the profiles of the


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V.P. and S.M. acknowledge funding by the European Research Council through ERC grant SPIRE 647383. The authors acknowledge funding by SpaceInn, PNPS (CNRS/INSU), and CNES CoRoT/ Kepler and PLATO grants at SAp and IRAP. The authors thank the anonymous referee for helping to improve the quality of the paper.


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ACKNOWLEDGEMENTS We thank U. Gorti for sharing her FUV models, as well as I. Pascucci and R. Alexander for the useful and constructive discussions. JJ thanks D. Henderson for his remarks. This research has made use of the Exoplanet Orbit Database and the Exoplanet Data Explorer at exoplanets.org. BE, JJ and GR acknowledge the support of the Munich Institute for Astro- and Particle Physics (MIAPP) of the DFG Cluster of Excellence ‘Origin and Structure of the Universe.’ BE is supported by the Deutsche Forschungsgemeinschaft - Ref no. DFG ER 685/8-1 FOR 2634/1. This work has been supported by the DISCSIM project, grant agreement 341137 funded by the European Research Council under ERC-2013-ADG.