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

maps (intensity maps) of both CO and CO. For each target we show the direct comparison of the images of the intensity map of the best-fit model and the constraint on both and through spectra and intensity cuts through the major and minor axis of the zero-moment map. In three of the four targets an inner gas cavity (smaller than the dust cavity) was required to fit the data. In SR21 the 7 AU cavity previously derived from rovibrational emission was adopted, but no gas cavity is resolved at the spatial resolution of (24 AU) in our observations. In all disks, the depth is constrained to within an order of magnitude and the cavity size to within 5 AU, mainly through the comparison of the spatially resolved emission, but further confirmed by the line wings in the spectra. In the intensity cuts in Fig. 5 the parameter is varied. The comparison shows that the uncertainty on the density drop is lower than an order of magnitude. In Appendix C we show the intensity cuts for larger and smaller gas cavity radii, respectively. These plots show that the uncertainty on the gas cavity radius is typically 5 AU and the uncertainty on the depth is lower than one order of magnitude. Furthermore, in both SR21 and DoAr44 an additional drop between and is required to fit the data. The models of the CO fits of van der Marel et al. (2015b) match the isotopolog data in the outer disk remarkably well. Only minor corrections in surface density and gas-to-dust ratio were required to fit the new data. However, inside the cavity the previously derived results for the gas surface density were found to be inconsistent. A modest drop in the gas density inside the dust cavity radius was sufficient to explain the CO data, but no gas cavity was seen. Since the gas cavity becomes visible in the isotopolog data and turns out to be smaller than the dust cavity radius, the gas cavity radius could be fit independently of the depth. 4.1. Results for individual targets HD 135344B HD 135344B shows a clear gas cavity, both in CO and CO images, which is significantly smaller than the dust cavity (see top two panels of Fig. 1 ). The modeling constrains the gas cavity radius to 30 AU (dust cavity radius is 40 AU), and the drop is (top right panels in Fig. 5 ). Previously, the model based on the CO data required of for a cavity radius of 40 AU. A 30 AU gas cavity was also derived in van der Marel et al. (2015b) considering the inner radius of the small dust grains derived from the scattered-light emission ( Garufi et al. 2013 ), but a value as low as underproduces the CO emission inside the cavity. As the CO is optically thick and mainly traces the temperature at the surface, this new result suggests that the temperature structure is somewhat higher than in our model, perhaps because of some residual dust in the cavity (increasing the CO abundance by its shielding and changing the heating-cooling balance) or the vertical structure (shadowing on the outer disk; see Bruderer 2013 , for a


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

considered (see Table 1 ). Most of the population of H 2 will be in these ( v , j ) states under the conditions of ISM where radiative cooling of H 2 can dominate. When a bulk system of hydrogen molecules is thermally equilibrated, over 99% of the population is in these states at 1000 K and over 50% of the population is in these states at 5000 K. Table 1 Energy Levels of Selected ( v , j ) States in eV Note. a Energy relative to potential energy minimum of H 2 . For comparison, the energy at the dissociation limit is 4.74825 eV. The collision systems He + H 2 , H + H 2 , and H 2 + H 2 are among the most widely studied systems in reaction dynamics. For the electronic ground states of these systems, the interaction potentials are known to chemical accuracy (within 0.04 eV) and, in some cases, to spectroscopic accuracy (within 0.001 eV). This means that it is possible to simulate, to a high degree of precision, collisions within each of these collision systems. Exact quantum calculations are restricted to reduced dimensionality or to the lower energy states. For full-dimensional calculations involving dissociation, quantum calculations are not always feasible and quasiclassical trajectory (QCT) methods may be used. The development of ab initio potentials for the computational study of H 2 + H 2 paralleled the availability of computational resources. Schwenke ( 1988 ) developed a H 2 + H 2 potential to study the recombination of H atoms in the presence of H 2 using QCTs. The global H 2 + H 2 potential of Boothroyd et al. ( 1991 ) was developed with the intention of permitting full-dimensional calculations of energy transfer and dissociation to be carried out. The functional forms have derivatives that are evaluated analytically. The van der Waals well was fitted empirically. This is in contrast to earlier calculations which had been focused on those parts of the potential relevant to van der Waals interactions of H 2 molecules with low internal energy. Aguado et al. ( 1994 ) fitted the points of Boothroyd et al. ( 1991 ) to a functional form that was particularly convenient for quantum calculations. Although not spectroscopically accurate, these global potentials were deemed to be close to chemically accurate (Aguado et al. 1994 ). Diep Johnson ( 2000a , 2000b ) developed a potential for H 2 + H 2 which was focused on the (H 2 ) 2 dimer where each H 2 was treated as a rigid rotor in the ground vibrational state. Boothroyd et al. ( 2002a ) refined their earlier H 2 + H 2 potential with over 40,000 additional ab initio points. Like the earlier potential from this group, this BMKP2 potential also had analytical derivatives and an empirically fitted van der Waals region. The potential of Hinde ( 2008 ) was determined to spectroscopic accuracy for the (H 2 ) 2 dimer. Particular attention was paid to the van der Waals well for atomic separations within H 2 corresponding to low ( v , j ) states. The availability of these potentials permitted detailed


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the limit in local color was slightly larger than the median value at U − V ~ 0.65 with a magnitude step significant at 7.4 σ . On the other hand, maximizing the mass step significance led to a mass limit of about , corresponding to a magnitude step of 7.2 σ significance.In this case, the separation does not lie close to the median value, since 31% of our sample is found below the new mass limit, and 69% above. This new limit is closer to the mass bin separation of , chosen in allprevious studies on host galaxies. In particular, Childress et al. (2013) found an apparent Hubble residual transition between 10 9.8 and . Choosing this mass separation yields comparably significant mass and color steps. The top and bottom panels of Fig. 19 show the evolution of step significance as a function of the cut position when local U − V colors and host stellar masses are used as a third standardization parameter. The sample median lies close to the maximum local color step significance, whereas the most significant mass step implies a bin separation at . Table 10 Summary of all tests performed throughout the paper with the corresponding number of SNIa in the sample, the local U − V color step, the host stellar mass step, and step values when corrected for one or the other effect. However, the correlations between the Hubble diagram residuals derived from a three-parameter standardization and our host variables yield additional information. When residuals are corrected for local U − V color, the remaining maximum mass step significance is of 3.8 σ (i.e., the maximum correlation between stellar mass and corrected Hubble diagram residuals using the most significant local step). Conversely, the remaining maximum local color step after mass correction as a third variable is of 5 σ (i.e., the maximum correlation between local U − V color and corrected Hubble diagram residuals using the most significant mass step). Hence, maximizing the significance still shows that scatter in the Hubble diagram is better accounted for when the supernova brightness is corrected for local environment. It is also worth noting that the local U − V color does not fully account for the remaining scatter either. A better proxy, or a combination of proxies, linked to properties of the local environment of SNIa, is yet to be found. 7 Summary and perspectives As elaborated in Sect. 1 , many studies in the literature have found compelling proof of a dependence of Type Ia supernovæ properties on their close or distant environment, concerning a few hundred events at most that exploded in the nearby Universe. In this work, we measured the photometry of the host galaxy and local fluxes in regions with a radius a 3 kpc for 882 supernovæ that are distributed in a wide redshift range, from z = 0.01 to z = 1.1. We consistently measured photometry from SNLS and SDSS images, and gathered additional photometry from the 2MASS catalog when needed, in order to complete our sample of host galaxy


O O B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject I-CelestialObject 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 B-Software B-Model O O O O O O O O O O O O O B-Model 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 B-Model O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Identifier I-Identifier I-Identifier O O O O O B-Observatory B-Telescope O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O O O 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 B-Telescope O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O B-Model I-Model I-Model 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 B-Citation O O B-Identifier I-Identifier B-Identifier B-Identifier O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Citation O O O O O O O O O O O O O O O O

spectrum, using tbnew with the spectral fit parameters. Plainly this severely limits the sensitivity of these data, but we note that lower absorption columns for other objects may make this more visible [e.g. MAXI J1820 + 070 in Kara et al. ( 2019 ), where the column is only 1.5 × 10 21 cm −2 ]. Figure 11. The effect upon the overall thermal spectrum of considering the additional emission produced by the turbulent disc region. The red solid line denotes the xspec diskbb spectrum using parameters of Table 1 . The blue solid line denotes a bbodyrad spectrum with the same temperature as the diskbb component, but with of the power, inferred from the fit parameter of . The black solid line denotes the sum of these two components. The black dashed line denotes the absorbed total spectrum. We see that, when absorption is accounted for, the difference in shape arising from the bbodyrad component is inconsequential for the observable energy range. Placing our resultant truncation radius in the context of other studies, the same NuSTAR data set is fit by Wang-Ji et al. ( 2018 ) as ‘Obs 1 2015’, though they use the simultaneous Swift XRT data to extend this down to lower energies rather than the higher signal-to-noise ratio (but possibly worse cross-calibrated) XMM–Newton data. They fit the time-averaged spectrum with a simpler continuum model, with only a single-Compton component (rather than two as used here). Their derived relativistic smearing requires a disc with extreme iron overabundance that extends down to around 2.5 R g , an order of magnitude smaller than the radius derived here. If we remove one of our Compton continua, we find a similar fit from our XMM–Newton data, which also requires an extreme iron overabundance of A Fe = 8.67, and a small innermost disc radius of 2.69 R g (for details see Appendix B ). This fit is considerably worse (combined Δχ 2 > 300) than the two-Compton continuum model used in our spectral fits, where the reflection spectrum is solar abundance, and arises from a disc with an inner radius of 30 R g . This shows that the inferred relativistic smearing is highly sensitive to the assumed continuum shape. Here, we model only the first observation of this observing run (O1), and we set the spectral components in the timing section from fitting to the time-averaged spectral data alone. In future work, we will extend the modelling framework to fit to the later observations in this run (O2, O3, O4 of DM17 , with ObsIDs 0760646301, 0760646401, 0760646501, respectively), where the source has declined further into the hard state. To this end, we aim to develop a fully integrated fitting procedure, in which the spectral data are fit iteratively with the cross-spectrum, in order to close the loop when determining the shape of the underlying spectral components of the timing model. 11 CONCLUSIONS In MD18a / b , we developed a model for the spectral-timing properties of accreting hard-state black hole binaries, whereby


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ACKNOWLEDGEMENTS CG and SC acknowledge support from the Natural Science and Engineering Research Council (NSERC) of Canada through a PGS D scholarship and a Research Discovery Grant, respectively. This work also benefited from enlightening discussions with Peter Erwin, Jairo Méndez-Abreu, Sebastian F. Sánchez, and Jakob Walcher. Our referee's comments contributed to a leaner presentation of this paper. Funding for the SDSS IV has been provided by the Alfred P. Sloan Foundation, the U.S. Department of Energy Office of Science, and the Participating Institutions. SDSS-IV acknowledges support and resources from the Center for High-Performance Computing at the University of Utah. The SDSS web site is www.sdss.org . SDSS-IV is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS Collaboration including the Brazilian Participation Group, the Carnegie Institution for Science, Carnegie Mellon University, the Chilean Participation Group, the French Participation Group, Harvard-Smithsonian Center for Astrophysics, Instituto de Astrofísica de Canarias, The Johns Hopkins University, Kavli Institute for the Physics and Mathematics of the Universe (IPMU)/University of Tokyo, Lawrence Berkeley National Laboratory, Leibniz Institut für Astrophysik Potsdam (AIP), Max-Planck-Institut für Astronomie (MPIA Heidelberg), Max-Planck-Institut für Astrophysik (MPA Garching), Max-Planck-Institut für Extraterrestrische Physik (MPE), National Astronomical Observatory of China, New Mexico State University, New York University, University of Notre Dame, Observatário Nacional/MCTI, The Ohio State University, Pennsylvania State University, Shanghai Astronomical Observatory, United Kingdom Participation Group, Universidad Nacional Autónoma de México, University of Arizona, University of Colorado Boulder, University of Oxford, University of Portsmouth, University of Utah, University of Virginia, University of Washington, University of Wisconsin, Vanderbilt University, and Yale University. This work has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.


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The authors would like to thank the reviewer for drawing their attention to the recent work of Fivet et al. ( 2016 ) and suggesting the comparison. PJS acknowledges financial support from the Atomic Physics for Astrophysics Project (APAP) funded by the Science and Technology Facilities Council (STFC). The collision strength data, as a function of electron energy, for the lowest 15 levels of Co + and Co 2+ can be obtained in electronic format with full precision from the Centre de Données astronomiques de Strasbourg (CDS) data base.


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Acknowledgments We thank the referee, Dr Wendy Lane, for her useful comments. We thank the staff at GMRT for their help during the observations. GMRT is run by the National Centre for Radio Astrophysics of the Tata Institute of Fundamental Research. RS and NG acknowledge the support from the IndoFench Centre for the Promotion of Advanced Research (IFCPAR) under Project No. 5504-2. This research has made use of the NASA/IPAC Extragalactic Database (NED) that is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation and the U.S. Department of Energy Office of Science. The SDSS-III website is http://www.sdss3.org/ . SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration including University of Arizona, Brazilian Participation Group, Brookhaven National Laboratory, Carnegie Mellon University, University of Florida, French Participation Group, German Participation Group, Harvard University, Instituto de Astrofisica de Canarias, Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington and Yale University.


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ACKNOWLEDGEMENTS We thank Sasha Philippov and Deepto Chakrabarty for helpful discussions and valuable comments on the manuscript. We gratefully acknowledge support from NASA grant NNX16AC56G and NSF grant PHY-1752809.


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Acknowledgments This research made use of data from the NuSTAR mission, a project led by the California Institute of Technology, managed by the Jet Propulsion Laboratory, and funded by NASA, XMMNewton , an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA, and the Hale Telescope at Palomar Observatory. 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). We like to acknowledge S.G. Djorgovski for providing the Palomar observations. We thank the anonymous referee for comments and suggestions, which significantly contributed to improving the quality of the manuscript. EB received funding from the European Union Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement no. 655324. Facilities: NuSTAR , Palomar: DBSP, XMMNewton .


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GALC acknowledges the support of an STFC PhD studentship. This research utilised Queen Mary's MidPlus computational facilities, supported by QMUL Research-IT and funded by EPSRC grant EP/K000128/1.


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

based on color to focus for example on red galaxies. We explored making cuts based on color like focusing on red galaxies; however, these cuts reduced the galaxy samples too much and did not allow one to obtain sufficient statistics. Hopefully with other incoming larger surveys we can explore those kinds of selections and their effects on the self-calibration. We find here a negative IG intrinsic alignment signal using the self-calibration method in the third and fourth bins. This is in agreement with the negative IA amplitude of found by KIDS450 team in Hildebrandt et al. ( 2017 ) from using the marginalization method and the linear tidal alignment model (Catelan et al. 2001 ; Hirata Seljak 2004 ; Bridle King 2007 ). In brief, this model is physically motivated by the concept that large-scale correlations between intrinsic ellipticities of galaxies are related linearly to perturbations in the primordial gravitational tidal field where these galaxies formed, leading to galaxy linear alignment with large-scale structure. The IG type of IA comes from the fact that a structure of matter aligns radially its close galaxies and shears tangentially background galaxies creating a correlation between these two as shown in Figure 1 (left panel). Our results are also consistent with the further findings of the KiDS+Gamma results of Johnston et al. ( 2019 ) where a negative amplitude also was found using the same model. We do not use any IA model in the self-calibration, but for comparisons we plotted the theory curves from this linear tidal alignment model with the IA amplitude as found in the in KIDS450 paper (Hildebrandt et al. 2017 ). Some overall consistency is good to find, but it is not surprising that some discrepancies would be present—IA modeling is an active area of work and self-calibration offers the opportunity to test such models once the signal is extracted. Although we are limited here in pursuing such a task, we expect in future work to pursue such an endeavor using more and better quality data from ongoing and planned surveys to constrain models using this approach. This will also allow one to compare to models like the Halo model introduced in Piras et al. ( 2018 ), or the higher-order nonlinear model of Blazek et al. ( 2019 ). 4. Conclusion A first detection of intrinsic shape–gravitational shear (IG) and the intrinsic shape–galaxy density (Ig) in a photometric redshift survey using the self-calibration method is reported. The IG cross-correlation between the third and fourth bins of the KiDS-450 data set is measured with a significance of 3.51 σ . The Ig correlation is measured in the third bin with a 3.65 σ significance. The negative IA signal we find here from the self-calibration method in the third and fourth bins, using the BPZ-determined best redshift estimate of Hildebrandt et al. ( 2017 ) is in agreement with the negative sign IA amplitude found there using the marginalization approach and the BPZ method and also is


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We would like to thank K. Abazajian, G. Bertone, A. Geringer-Sameth, M. Lovell, M. Walker, C. Weniger for collaboration, discussion and useful comments. EB acknowledges support by NASA through grant no. NNX123AE77G. The work of DI has been partially supported from the Swiss National Science Foundation grant SCOPE IZ7370-152581, the grant no. F64/42-2015 of the State Fund for Fundamental Research of Ukraine, the Program of Cosmic Research of the National Academy of Sciences of Ukraine, and the State Programme of Implementation of Grid Technology in Ukraine. The Draco dSph observations were performed as a part of AO-14 Very Large Programme obtained with XMM–Newton , an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA.


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

of different values of N and α. The 20 main simulations are divided into four sets with different orbital parameters e and Ω * . For each of these four sets, we have performed five simulations with different values of R * . We have performed the O1R39 simulation with N = 500 000 twice to investigate an unexpected effect of the numerical error in the angular momentum (see Section 4.3 ). The age at which the star reaches the desired radius is also included in Table 3 . Table 2. The initial parameters that we did not vary between the main simulations used in this work. The initial parameters that we did vary between simulations can be found in Table 3 . Table 3. The 20 main simulations used in this work and the initial parameters that were varied between them. For the three simulations in bold font, we also performed eight additional test simulations varying N and α (below table). 4.1 Tidal dissipation Before investigating the combined effects of tidal dissipation and mass-loss on the stellar orbit, we isolate the effect of tidal dissipation. We choose a simulation in which the stellar radius R * R Roche (model O0R37, see Table 3 ) so that mass-loss is negligible. In the absence of mass-loss, the change in the orbital parameters is dominated by the effects of tidal dissipation. In Fig. 5 we present the evolution of Ω * , a and e over a period of 5000 d (∼13 orbits). All simulations use the initial conditions of model O0R37 while we varied N (left-hand figure) and α (right-hand figure). It can be seen that for different values of these SPH parameters we find different values of . Figure 5. The long-term evolution through tidal dissipation of Ω * , a and e for model O0R37 with varying values of N and α. Dotted lines show the analytical solution for tidal dissipation (Hut 1981 ) with k / T ≈ 3( k / T ) Rasio . Different values of N and α result in a different radius of the relaxed SPH realization of the star. The analytical solution matching each simulation is therefore calculated with the effective radius of the SPH realization of the star in that simulation. The simulations with N = 100 000 and 200 000 are more computationally expensive and we have therefore decided to run them for only 2000 d. Note that the blue line in both plots is the same simulation. The difference in can be understood by taking the radius of the star into account. Because of the quantization approximations inherent to SPH, a different value of N can result in a slightly different hydrodynamical balance within the star. This difference, or even a different value of α, can result in variation of the radius of the SPH realization of the star after relaxation. Even a small change in R * can account for the differences in because (Hut 1981 ). While we do not include the physical processes that regulate tidal damping in our simulations, the artificial viscosity in SPH can cause dissipation. To interpret the results of our simulation, it is good to know how the time-scale of


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O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 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

i.e., . The relative plasmoid distances in a string vary depending on their different speeds along the jet, with the leading one significantly slowed down primarily by snow-plow effects against jet material, in particular, BLR clouds. This constitutes an interesting condition as the leading member in a string can reprocess and partially reflect some of the primary S radiation emitted by the trailing members (photons “mirrored” by slow clouds in the BLR were originally proposed by Ghisellini Madau 1996 ). Shrinking mirror-plasmoid gaps so produced provide compact sites with high seed photon densities for intense IC to take place. In a scenario with multiple emitting plasmoids (see Figure 1 ), the primary S flux in the optical–UV bands is emitted by a plasmoid like H starting within the BLR, that is, in the range . The S flux is emitted forward and mirrored backward by the leading plasmoid M toward an incoming plasmoid K . The whole process is subject to a “causality condition” (Böttcher Dermer 1998 ); the mirrored photons are received by an incoming plasmoid when the latter is at the receiving point that we denote with (cf. Figure 1 ). Figure 1. Schematic picture of the source structures we expect at and beyond the BLR. S radiation (orange dashed line) is emitted by inner plasmoids such as H at a radius r h and is reflected back (violet dotted lines) by the outermost mirror-plasmoid M at a radius toward an incoming plasmoid K : the encounter occurs at a radius . Dense seed photons build up in the gap between the approaching plasmoid K and the mirror, where they are IC upscattered to gamma-ray energies (green dotted lines) by electrons accelerated in and around plasmoids. The condition is easily evaluated when the same plasmoid moving with radial coordinate and boost Γ first emits at r , and then receives the radiation reflected backward by the mirror moving with coordinate and boost . The receiving point reads in the AGN frame, for primary photons emitted in the named range and reflected back at /. Here and correspondingly are the relative velocity and boost between the receiver and the mirror (note that /). Moreover, is the receiving point for primary photons emitted at and reflected at /. Note that for small values of r 0 the approximation holds; so the factor makes it possible to have relevant reflections beyond R BLR . The IC radiative event is completed when the plasmoid K crosses the effective gap defined byand lasts for an observer time /: this turns out to be about 2 minutes when, e.g., , , and hold. In the initial stage, the primary emitter radiates from an inner position and the mirror surface is small relative to the cross section of the emission beam as to reduce the effective power received by the mirror to in the head-on approximation and with . A fraction thereof is reflected back and is received by the incoming plasmoid when the latter is close to the reflection point, that is, in a cone of a cross section of order . Then,


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We thank Chris Flynn for carefully reading this manuscript and for providing valuable comment and suggestions. We also thank the participants of the 2017−2019 FRB meetings for the useful discussions. Thanks additionally go to Sarah Burke-Spolaor for initial survey parameter data. DWG acknowledges travel support from the Research Corporation for Scientific Advancement to attend the Aspen FRB meeting in 2017. 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)/ERC Grant Agreement n. 617199 (“ALERT”); from Vici research programme “ARGO” with project number 639.043.815, financed by the Netherlands Organisation for Scientific Research (NWO); and from the Netherlands Research School for Astronomy (NOVA4-ARTS). EP further acknowledges funding from an NWO Veni Fellowship. This research has made use of numpy ( van der Walt et al. 2011 ), scipy ( Oliphant 2007 ), astropy ( Astropy Collaboration 2018 ), matplotlib ( Hunter 2007 ), bokeh ( Bokeh Development Team 2018 ) and NASA’s Astrophysics Data System.


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GHz transition under study belongs to the A series. Maser emission in transitions of this series was not observed or theoretically predicted. However, qualitative considerations show that this transition probably belongs to Class II. Observations show that the strongest Class II maser occurs in the A transition, while the strongest Class I maser occurs in the A transition. Class II methanol masers are therefore characterized by overpopulation of A levels of the ladder with respect to the A levels of the ladder, while for Class I masers the situation is opposite. Model calculations for Class II methanol maser conditions by Cragg et al. (2005) show that A levels of the ladder tend to be overpopulated with respect to A levels of the ladder. This means that the 349.1070 GHz transition from A series most probably belongs to the Class II family. Strong support for this conclusion comes from the observational evidence that emission in the newly discovered maser transition covers the same velocity range and shows a similar position-velocity dependence as the strongest Class II methanol maser at 6.7 GHz ( Moscadelli et al. 2017 ). The spectra and the peak locations of the new maser may not coincide with those of the 6.7 GHz masers because of the different sensitivity to the physical conditions, which is usual for Class II methanol maser transitions ( Cragg et al. 2005 ). The A line series contains transitions with frequencies starting from 303.37 GHz. Many of them can be observed with the same instrument, which allows avoiding calibration problems in determining the relative line intensities. The lower levels of these transitions cover a rather wide range of energies from 2.32 K for the A level to 243.45 K for the A lower level of the transition under study and higher. It is worth mentioning that in our SMA data obtained in December 2010, the CHOH A line at 342.729796 GHz was detected in quasi-thermal emission ( Zinchenko et al. 2015 ). This may indicate that the discovered maser is related to the accretion burst in 2015, but additional modeling and monitoring of these lines is needed for an exact answer. Observations of the methanol line series proved to be a good tool for the physical parameter diagnostics both in maser and quasi-thermal cases ( Voronkov et al. 2006 ; Menten et al. 1988 ; Salii Sobolev 2006 ). This is very important because the new maser line was detected toward positions that are spread over the disk. An inspection of our channel maps shows that the peaks of the maser emission at different velocities lie on a curve that resembles an arc (Fig. 3 c). This can be part of a ring in the disk or on the surface of the disk at a substantial distance of several hundred AU from the star. Taking into account the disk orientation, which follows from the outflow data ( Zinchenko et al. 2015 ; Burns et al. 2016 ), it becomes clear that the brightest emission comes from the part of the disk that is closer to us. For the lower brightness


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Because complete atomic line lists for these heavy species are not available (Kasen et al. 2013 ), we have simply assumed that the energy integral of the full radiative spectra of r -process material is similar to that of Fe. Under these conditions, we find that metal cooling from r -process material is not expected to influence the dynamics of NSBM remnants expanding into an ambient medium with . The resulting NSBM remnant evolution in these environments should solely be determined by the metal cooling of the swept-up material. However, the mass fraction of r -process material at shell formation within the remnant is expected to be severely enhanced to about , assuming a solar abundance ratio and . In contrast, with a total r -process mass per supernova of (Shen et al. 2015 ), we expect a local enhancement of only about when a Type II SNR attains shell formation in similar external conditions. Of particular relevance in this case is the heavy element composition of galactic halo stars with the metallicity regime , which has been found to have pure r -process products with a distribution that is characteristic of solar system matter but with a large star-to-star scatter in their r -process concentrations (Sneden et al. 2008 ). In some stars with , the r -process enrichment can be as large as 10 2 , assuming a solar abundance ratio. The presence of r -process material in these stars with a distribution that is characteristic of solar abundance ratios illustrates that r -process enrichment has operated in a fairly robust manner, while their abundance dispersions further suggest that r -process production sites must be rare and locally very enhanced, as expected from NSBM enrichment (e.g., Shen et al. 2015 ). These localized inhomogeneities would then be smoothed out as more NSBMs take place and r -process material is given more time to be transported and mixed throughout the early Milky Way. Metal feedback from NSBM remnants is thus essential to understand the formation of r -process enhanced stars in galaxies. Despite the initial differences, our conclusions regarding the efficacy of the transport and mixing of r -process material by NSBM remnants in a cosmological context should be similar to that expected from single SNRs. APPENDIX RESOLUTION CONVERGENCE Here we describe the results of our resolution study. Simulations are initialized with a static AMR and with a maximum level of refinement of 10 within a sphere enclosing all of the tail material. In all cases, we reduce the refinement by two levels after the size of the tidal remnant reaches 1/20 of the size of the computational box. The grid mesh refinement is then based on the value of the density. To test how our results are sensitive to the refinement criteria and resolution, we run two more simulations using the initial fiducial model parameters but subtracting three and one level(s) of refinement, respectively. We compare the different simulations in Figure 8 with final


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We are very grateful to Mirko Boezio and Marius Potgieter for providing the Voyager data for protons, He nuclei, and electrons and to Gabriela Castelletti and Gloria Dubner for providing us with the radio data points from the region coincident with the AGILE ray detection. This work was partially funded through Grant PRIN-INAF 2012.


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

the fit is repeated; the uncertainty on each RV is taken to be the standard deviation of the best-fitting velocity at each epoch when this procedure is repeated many times. Fitting a Keplerian orbit amounts to simultaneously maximizing the likelihood of the RV curves of the primary and secondary, where the model RV for a given set of orbital parameters is obtained by solving the two-body problem (Murray Correia 2010 ). We use a custom python implementation of the adaptive simulated annealing algorithm (Iglesias-Marzoa, López-Morales Jesús Arévalo Morales 2015 ) to obtain an initial maximum-likelihood estimate of the best-fitting orbital parameters and then sample the parameter space in the vicinity of the maximum likelihood with emcee (Foreman-Mackey et al. 2013 ) to estimate parameter uncertainties. We use non-informative, flat priors throughout. In addition to the seven standard Keplerian orbital parameters, 10 we fit a ‘jitter’ term, s 2 , to allow for the possibility of intrinsic scatter in the RVs due to e.g. stellar pulsation or underestimated RV uncertainties (see e.g. Baluev 2009 ; Price-Whelan et al. 2017 ). The effective total uncertainties in the RVs used in fitting are then , where σ i are the RV uncertainties at each epoch found from bootstrapping. Explicitly, the log-likelihood function isHere, the sum is over N epochs at times t i , represents the predicted RV at time t for a system with orbital parameters (Murray Correia 2010 ), and and are the orbital parameters for each component. For most systems, the best-fitting jitter is small ( s 2 ∼ 0.1 km 2 s − 2 ), indicating that our estimates of σ i are reasonably accurate. However, for stars with large v macro , which indicates significant rotation, jitter is sometimes of order 1 km s − 1 . This suggests that our velocity measurements are less accurate for rapidly rotating stars, which is also supported by our experiments with semi-empirical binary spectra (Appendix B1 ). For some systems with mass ratios near 1, we found that it was initially impossible to obtain a good fit to the measured RVs because the velocity assignments of the two stars were switched in the fits for one or more visits. We attempted to fit these systems by allowing the fitting algorithm to switch the assigned velocities for individual visits if doing so would improve the fit. In most cases, this solved the problem. A few systems (∼5 per cent of those with sufficient coverage) remained with RV curves that could not be well fitted by a Keplerian orbit, even with the possibility of switching the assigned velocities; these systems may have poorly measured RVs or contain an unseen component. Fig. 10 (a) shows an example orbital solution for a system with typical phase coverage, RV errors, and number of epochs. This system has the lowest mass ratio, q = 0.44, of the systems for which we derive orbital solutions. Because of the system’s low mass ratio, the secondary contributes only a small fraction (∼3 per cent)


O O O O O O O O O O O O O B-Archive I-Archive I-Archive I-Archive I-Archive I-Archive I-Archive B-Archive O O O O O O B-Organization I-Organization I-Organization O B-Organization O O B-Organization I-Organization I-Organization I-Organization O O B-Observatory I-Observatory I-Observatory O O O O O O O O O B-Archive I-Archive I-Archive I-Archive I-Archive O O O O O O O O B-Telescope O O B-Organization O O O O O O O O O B-Organization O O O O O O B-Location B-Location B-Location B-Location B-Location B-Location O O O O O B-Location O O B-Location O O O O O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength B-Wavelength O O O B-Database I-Database I-Database O O B-Organization B-Location I-Location O O B-Person I-Person I-Person O O O O B-Observatory B-Telescope O O O O B-Person I-Person I-Person O O B-Wavelength O O O B-CelestialObject I-CelestialObject

ACKNOWLEDGEMENTS This research has made use of data and/or software provided by the High Energy Astrophysics Science Archive Research Center (HEASARC), which is a service of the Astrophysics Science Division at NASA/GSFC and the High Energy Astrophysics Division of the Smithsonian Astrophysical Observatory. We acknowledge the use of public data from the Swift and Fermi data archives. In this work, we analysed observations performed with INTEGRAL , an ESA project with instruments and science data centre funded by ESA member states (especially the PI countries: Denmark, France, Germany, Italy, Switzerland, Spain) and with the participation of Russia and the USA. We also acknowledge the use of NASA’s Astrophysics Data System (ADS) and of the SIMBAD data base, operated at CDS, Strasbourg, France. We thank Dr. David Smith for useful discussions on Fermi LAT pulsar timing issues, and Dr. Matthew Kerr for providing radio pulsar ephemerides for PSR B1509−58.


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We thank Bill Paxton for making the MESA code publicly available, as well as Aaron Dotter for the valuable assistance in the construction of the stellar isochrones with the MIST package. We also thank the anonymous referee for the useful comments that have contributed to the discussion of our results. J.L. acknowledges financial support by Fundação para a Ciência e Tecnologia—FCT grant No. PD/BD/128235/2016 in the framework of the Doctoral Programme IDPASC—Portugal.


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 B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O B-Telescope O O B-Telescope O O O O O O O O O B-CelestialRegion O B-CelestialRegion I-CelestialRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Dataset I-Dataset I-Dataset I-Dataset I-Dataset B-Dataset B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software I-Software I-Software I-Software B-Software B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O B-Software B-Citation I-Citation I-Citation O O B-Software O O O O O O O O O O O O O O O O O O O O B-Software O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O B-Software I-Software O B-Software I-Software I-Software I-Software O B-Citation I-Citation O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope I-Telescope I-Telescope I-Telescope I-Telescope B-Telescope B-Citation I-Citation I-Citation I-Citation O O B-Survey I-Survey I-Survey I-Survey B-Survey B-Citation I-Citation O B-Citation I-Citation O O O O O O O O B-Telescope I-Telescope I-Telescope I-Telescope B-Telescope B-Citation I-Citation I-Citation I-Citation O O B-Survey I-Survey I-Survey I-Survey I-Survey I-Survey B-Survey 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 B-Model I-Model O O O O B-Telescope B-Citation I-Citation I-Citation I-Citation O O B-Telescope I-Telescope I-Telescope I-Telescope B-Telescope B-Citation I-Citation O O O O O O O O O O O O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O

a new era of research on eclipsing binary systems (EBs). The mission was designed with the main objective of searching for transiting planets (Borucki et al. 2011 ). As a by-product, the Kepler satellite provides the detection and monitoring of variable stars, most of which are EBs. This is an interesting fact, because EBs are important astronomical targets for determining the orbital and physical parameters of component stars from the geometry of their light curves (LCs) (Deb Singh 2011 ). The Kepler space mission Kepler was originally designed to investigate a region located between Swan and Lyre constellations, having a telescope with an aperture of 0.95 m and a field of view of 115.6° squares. Equipped with a photometer containing 42 CCDs with 2200 × 1024 pixels, where each pixel covers a region of 4 s of arc, Kepler provides unprecedented quality and quantity photometric data (e.g. Thompson et al. 2016 ). Details on the instrumentation of the mission can be found in Koch et al. ( 2010 ). The Kepler Eclipsing Binary Catalog 1 (KEBC; Prša et al. 2011 ; Slawson et al. 2011 ; Kirk et al. 2016 ) is an excellent bridge between the eclipsing binary data of the mission and the scientific community. In the catalogue versions, the parameters of the systems were determined by the method of Eclipsing Binaries via ArtificialIntelligence (EBAI; Prša et al. 2008 ), a computational tool for data mining of large volumes of data. Trained with synthetic LCs generated by the PHOEBE (Prša Zwitter 2005 ), the EBAI uses polynomial adjustment and does not aim at the precise and individual adjustment of LCs. On the other hand, the JKTEBOP code (Southworth, Maxted Smalley 2004a ; Southworth et al. 2004b ), based on the EBOP code ( Eclipsing Binary Orbit Program ; Etzel 1981 ; Popper Etzel 1981 ), is an efficient alternative for individual and precise analysis of LCs, obtaining more exact adjustments by allowing the parameters of interest to be free. The larger Kepler data set is a challenge for analysis tools. Consequently, a test of the fidelity of data mining tools for different processes is crucial, since the large observational programme such as Convection, Rotation and planetary Transits (CoRoT; Baglin et al. 2006 ) and All Sky Automated Survey (ASAS; Pojmanski 1997 ; Pojmański 2001 ), and in the future, programs such as Transiting Exoplanet Survey Satellite (TESS; Ricker et al. 2014 ) and PLAnetary Transits and Oscillations of stars (PLATO; Catala et al. 2010 ) will discover a lot of EBs and surely have data studied by powerful instruments such as neural networks. Furthermore, missions such as Gaia (Perryman et al. 2001 ) and Large Synoptic Survey Telescope (LSST; Tyson 2002 ) will discover millions of EBs but obtain LCs with few points (Southworth 2012 ), requiring more accurate and appropriate analysis tools. In this paper, we present the orbital and physical parameters of 78 EBs and investigate possible discrepancies between the results found by EBAI and


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

compared with that of J1846−0258. The differences between the behaviour of J1119−6127 and J1846−0258 suggest that the peculiar spin frequency evolution of J1119−6127 reveal processes not well understood during the transition from a high- B radio pulsar to a magnetar. The net spin-down we observed following the X-ray bursts implies a release of a large amount of rotational energy. Assuming the canonical neutron star moment of inertia of I 45 = 10 45 g cm 2 , the rotational energy released can be estimated as This is ∼20 times of the total X-ray outburst energy, and in fact we did not observe obvious correlation between the X-ray light curve presented in Coti Zelati et al. ( 2018 ) and the radio flux densities nor the spin-frequency evolution. For a time span of ∼100 days, the spin-down power gives us an averaged luminosity of ∼4.4 × 10 36 erg s −1 , about two times larger than the normal spin-down luminosity. While only a small portion of the spin-down energy goes into radio and X-ray, we could expect much stronger high energy emissions from the pulsar (e.g. γ-ray) if energy loss via high energy radiation is the main energy-loss mechanism. Such a high spin-down luminosity could also power strong relativistic particle outflows that can brighten the pulsar wind nebula (Blumer et al. 2017 ). A complete picture of the PSR J1119−6127 event is likely to be that ultra-strong magnetic fields powered the X-ray bursts and triggered an additional torque that produced the peculiar spin frequency evolution. The fact that the polarization PA changed significantly following the X-ray bursts indicates that the magnetic field might have changed. If we assume that the spin-down process is dominated by dipole braking, the surface magnetic field strength can be estimated as where P and are the spin period and spin-period derivative. Applying equation ( 2 ) on our measurements of P and of PSR J1119−6127, we found that after the X-ray burst the surface magnetic field strength can reach as high as ∼9 × 10 13 G, which is more than two times stronger than the normal field strength. Under such assumptions, the fast increase and slow recovery of as shown in the third panel of Fig. 1 indicate similar evolution of the surface magnetic field strength of the pulsar. This suggests that the X-ray bursts triggered some reconfiguration of the magnetosphere of the pulsar, resulting in the increase of the apparent field strength. The energy of the global dipolar field external to the neutron star can be estimated as and in order to increase the magnetic field strength from ∼4 × 10 13 G to ∼9 × 10 13 G a total amount of energy of ∼2 × 10 45 erg is needed. This is more than one order of magnitude larger than the spin-down power released following the X-ray bursts. Energies either from multipole (and/or internal) magnetic fields or neutron star interior need to be converted to the strong dipolar field and/or distort the magnetic field. Under such a scenario, the slow recoveries of


O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O B-CelestialObject I-CelestialObject 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 O O O O O O 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 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 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 B-CelestialObject I-CelestialObject O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation O B-Citation I-Citation I-Citation I-Citation O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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-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 B-Software O B-Citation I-Citation I-Citation I-Citation O O B-Software O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O B-Software

about 200 Myr after the MS turnoff). The second phase coincides with the base of the RGB, where τ DR decreases from about 3 Gyr to about 100 Myr for both stars. These rapid changes in τ DR can be explained by departures from thermal equilibrium, which are measured by ε grav = − T ∂ s /∂ t . The bottom panel of Fig. 8 shows the variations in ε grav in the stellar core of both stars, which are clearly anti-correlated with the variations in τ DR . The forcing of differential rotation is maximal at the peaks of ε grav , that is when the core contracts on a thermal timescale. Fig. 8. Variations in the timescale τ DR over which differential rotation is forced ( top panel ) and in ε grav ( bottom panel ) along the subgiant branch for our best-fit models of KIC 8524425 (red dashed line) and KIC 5955122 (solid blue line). The filled circles correspond to the stars at current age. The stars studied by D14 all lie after the peak of ε grav corresponding to the base of the RGB except for the least evolved one (star B), which lies precisely at the maximum of the peak (see Fig. 6 of Eggenberger et al. 2019b ). As shown by Fig. 8 , the evolutionary stage of KIC 8524425 and KIC 5955122 places them well before the maximum of ε grav , which confirms that they are indeed less evolved than the sample of D14. The nearly solid-body rotation profiles that we obtained show that the internal redistribution of AM for these stars takes place on timescales lower than the current value of τ DR (about 320 Myr for KIC 5955122 and 570 Myr for KIC 8524425). 5.2. Efficiency of AM transport To estimate the efficiency of the AM transport that is required to reproduce the observed rotation profiles, we computed rotating models for the two subgiants, including an additional constant viscosity ν add in the equation for the transport of AM in radiative zones. This approach was already followed for instance by Eggenberger et al. (2012 , 2019b) , Spada et al. (2016) , and den Hartogh et al. (2019) , for more evolved subgiants and red giants. As already mentioned in these works, this is a very crude description of the AM transport in subgiants. Naturally, we do not expect whatever mechanism is at work to indeed operate like a diffusive process with constant viscosity. The main goal of this approach is to study how the mean efficiency of the unknown transport processes vary with stellar parameters, and in particular with evolution. It was shown by Eggenberger et al. (2019b) that the transport efficiency decreases during the late subgiant phase, near the base of the RGB, but must increase again as stars evolve along the RGB ( Eggenberger et al. 2017 ). We here had the opportunity to estimate the efficiency of the transport closer to the MS turnoff and compare with its value on the MS. 5.2.1. Rotating models We used two different stellar evolution codes: YREC ( Demarque et al. 2008 ) and GENEC ( Eggenberger et al. 2008 ). The two codes differ in their treatment of the rotation. GENEC


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We thank Linda Tacconi, Reinhard Genzel, Jing Wang, Richard D'Souza, Sambit Roychowdhury for helpful discussions. GALEX is a NASA Small Explorer, launched in 2003 April, developed in cooperation with the Centre National d'Etudes Spatiales of France and the Korean Ministry of Science and Technology. This research has made use of the NASA/IPAC Infrared Science Archive, which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. 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 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, Cambridge University, Case Western Reserve University, University of Chicago, Drexel University, Fermi National Accelerator Laboratory, 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), the Leibniz Institute for Astrophysics, 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 US Naval Observatory and the University of Washington.


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This work was supported by the National Science Foundation of China (11721303) and the National Key RD Program of China (2016YFA0400702). We thank Peter Erwin for the constructive discussion. M.D. is supported by the grants “National Postdoctoral Program for Innovative Talents” (No. 8201400810) and “Postdoctoral Science Foundation of China” (No. 8201400927) from the China Postdoctoral Science Foundation. V.P.D. was supported by STFC Consolidated grant ST/R000786/1. V.P.D. acknowledges support from the Kavli Visiting Scholars Program for a visit to the KIAA during this work. We utilized the High-performance Computing Platform of Peking University.


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in the parlance of the General Catalogue of Variable Stars. 1 The first-order combination terms between the modes n and n ′ have the following frequencies: and Given negligible first-order corrections ε T f (1, 0) , equations ( 15 ) are consistent with equations ( 4 ) and ( 7 ), while equations ( 14 ) with equations ( 8 ). The referee has suggested a test that our f n ,0 and modes are indeed associated with the l = 1, m = 0 spherical harmonics and provided examples of applying the test to simulated data. The test consists in dividing the data into two parts according to the orbital phase in such a way that one part contains the data covering orbital phases from one quadrature to the other, and the second part, the remaining data, and then computing amplitude spectra for the two parts separately. Using simulated l = 1, m = 0 light curves with an assumed pulsation frequency, Reed, Brondell Kawaler ( 2005 ) found for a range of inclination of the pulsation axis to the line of sight that in the amplitude spectra of the two parts of the data there appears a peak at the assumed frequency flanked by f orb aliases, whereas in the amplitude spectrum of the complete data set the peak at the assumed frequency is missing (see their fig. 4). In addition, there is a phase difference equal to between the light curves in the two parts of the data. For the test, we used the red BRITE magnitudes because their spectral window is cleaner than that of the blue magnitudes (see the insets in the lower panels of Fig. 1 ). We removed the orbital light-variation by pre-whitening with f orb , 2 f orb , 3 f orb , 4 f orb , and 6 f orb , divided the data into two parts as described above, and computed amplitude spectra. The results are displayed in Fig. 6 . The top left-hand panel shows the amplitude spectrum of the complete data (referred to as set 1 in the caption to the figure) with the peaks at the frequencies appearing in equations ( 2 )– ( 5 ) labelled. The upper middle left-hand panel shows the amplitude spectrum of the magnitudes covering the orbital phases from the western to eastern quadrature, i.e. the phases from 0.3825 to 0.8825 in Figs 3 and 5 (set 2). The peak at f n ,0 = ( f 2 + f 4 )/2 = 0.4857 d −1 and its f orb aliases dominate the spectrum. The aliases occur at the same frequencies as the f 2 and f 4 peaks in the top left-hand panel but should not be confused with them. While the aliases reproduce the side-lobes of the spectral window seen in the top right-hand panel, the frequencies f 2 and f 4 arise as the result of a transformation of the corotating frame of reference whose polar axis coincides with the line joining the components’ mass centres to the non-rotating frame with the polar axis parallel to the pulsating component’s rotation axis (see the second paragraph of this section). The lower middle left-hand panel contains the amplitude spectrum obtained from the set 2 data pre-whitened with f n ,0 . Now, the highest peak appears at


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This paper is dedicated to the memory of our co-author James Caswell who passed away January 14th 2015. James was a leading figure in maser astronomy for more than three decades and his work in this field represents a peerless legacy to future researchers. Funding assistance was provided in part by Sigma Xi Grants-in-Aid of research, the Deutscher Akademischer Austauschdienst (DAAD), and National Natural Science Foundation of China (Grant No. 11133008). The authors would like to thank the referee for their detailed analysis and comments in reviewing this paper.


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etal. 2006 ; Hao etal. 2014 ), so one might expect that their far-IR SEDs are also unchanged. On the basis of the assumption that the intrinsic AGN emission as a function of wavelength is broadly independent of AGN luminosity [for L , 5100 or L X(210keV) 10 43.5 ergs 1 AGN] and redshift (at least up to z 3.5), my results indicate that, on average, the far-IR/submm emission in the most luminous QSOs at the tail of the 2 z 4 optical luminosity function (Richards etal. 2006 ) is primarily produced by the AGN. This implies that for such systems, the emission in the Herschel bands and longer wavelengths such as those probed by SCUBA-2 at 850m would be AGN dominated; thus, wide-area Herschel and SCUBA-2 surveys will contain a population of QSOs which are primarily powered by AGN. Moreover, the SFRs of such systems cannot be determined with X-ray to submm broad-band photometry, and other means such as IR spectral lines will need to be used. Note that this does not mean that the host galaxies of luminous QSOs do not have star formation, perhaps even a considerable amount: I calculate a 3 upper limit on the SFR of 3165 and 643M yr 1 for the two QSO samples studied here. It simply means that the contribution from star formation is not detected in the broad-band SED as it is energetically less prominent than the AGN power at all wavelengths. This conclusion is in disagreement with the work of N16 . N16 use an AGN torus template to decompose their QSO SEDs into an AGN torus component and a star-forming component. The torus template used by N16 has a steeper far-IR slope than the S16 AGN SED, falling by about 0.5dex between 50 and 70m, compared to a 0.1dex change in the S16 AGN SED. This implies that a smaller fraction of the far-IR emission is attributed to the AGN in the work of N16 , and indeed, they find that star formation is a significant contributor to emission in the Herschel bands. In S16 , however, we argued that using torus templates in SED decomposition can significantly underestimate the AGN power in the far-IR, as they often lack an extended dust component, which would, in turn, boost the contribution required from star formation. Other works which use SED decomposition to separate the AGN and star formation contributions also find that QSOs have IR luminosities systematically larger than the IR luminosity produced by a torus component (e.g. Leipski etal. 2014 ; Drouart etal. 2016 ; Gruppioni etal. 2016 ; Podigachoski etal. 2016 ). Although traditionally this has been assigned to star formation, here I argue that a significant fraction, and in some cases all, of this excess IR luminosity can be attributed to AGN-heated dust at kpc scales. Using a bolometric correction factor f = 4, where L AGN, bol f L , 5100 , and an efficiency of = 0.1 to convert AGN luminosity into black hole accretion rate (BHAR) as in N16 , I calculate a 3 upper limit on the SFR/BHAR ratio of 23 for the N16 sample and 36 for the T15 sample. However, note that higher


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We thank Deepto Chakrabarty for useful conversations and for providing input on the effective collecting area of RXTE -PCA and NICER. We are also grateful to Jean in’t Zand and the referee for valuable comments on the manuscript.