We thank the anonymous referee and the MNRAS editorial staff for their comments on this paper. The Australian SKA Pathfinder is part of the Australia Telescope National Facility which is managed by CSIRO. Operation of ASKAP is funded by the Australian Government with support from the National Collaborative Research Infrastructure Strategy. Establishment of the Murchison Radio-astronomy Observatory was funded by the Australian Government and the Government of Western Australia. ASKAP uses advanced supercomputing resources at the Pawsey Supercomputing Centre. We acknowledge the Wajarri Yamatji people as the traditional owners of the Observatory site. This work was supported by resources provided by the Pawsey Supercomputing Centre with funding from the Australian Government and the Government of Western Australia. Parts of this research were conducted by the Australian Research Council Centre of Excellence for All-sky Astrophysics (CAASTRO), through project number CE110001020. This research made use of Montage. It is funded by the National Science Foundation under Grant Number ACI-1440620, and was previously funded by the National Aeronautics and Space Administration's Earth Science Technology Office, Computation Technologies Project, under Cooperative Agreement Number NCC5-626 between NASA and the California Institute of Technology. This research has made use of NASA's Astrophysics Data System. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. IH acknowledges many useful discussions with Jan Noordam, Rick Perley and Oleg Smirnov.


This work was supported by the Planetary Sciences and Exploration Programme, Indian Space Research Organization (ISRO), PRL, Ahmedabad under the sanctioned project scheme. Calculations reported in the present work were carried out at the Computer Centre, Banaras Hindu University.


of these values, with discrepancies too large to be explained by instrumental errors (e.g. NGC 2509, Fig. 6 ). We also remark that on average, our distances estimated from parallaxes tend to agree more often with the more distant literature value. We suggest that the isochrone fitting procedure from which most photometric distances are estimated might be biased in many of those instances, as they might be affected by field contamination, as well as the degeneracies between distance, reddening, and metallicity. The strength of the Gaia data does not only reside in parallaxes from which distances can be inferred, and in precise and deep photometry, but also in our ability to obtain clean colour-magnitude diagrams from which astrophysical parameters can be infered. Fig. 6. Sky distribution ( top left panel ), colour-magnitude diagram ( top right panel ), and parallax as a function of magnitude ( bottom panel ) for the members of NGC 2509. The median parallax is 0.36 mas. Available literature distances for this cluster are 912 pc (DAML, blue), 1700 pc (MWSC, green) and 2900 pc ( Carraro Costa 2007 , red), which correspond to parallaxes of 1.09 mas, 0.59 mas, and 0.35 mas (respectively). 5. Specific remarks on some clusters It would be lengthy and impractical to devote a Section to every object under analysis in this study, but we provide additional comments on the specific cases of two clusters classified as OCs that are likely globular clusters, and on the previously unreported OCs discovered in this study. 5.1. BH 140 and FSR 1758 are globular clusters The colour-magnitude diagrams of BH 140 and FSR 1758 (shown in Fig. 7 ) present the typical aspect of globular clusters, with a prominent giant branch and an interrupted horizontal branch displaying a gap in the locus occupied by RR Lyrae. They are also clearly seen as rich and regular distributions on the sky. These two objects, located near the Galactic plane ( b = −4.3° and −3.3° for BH 140 and FSR 1758, respectively) also exhibit small parallaxes ( π = 0.16 mas and 0.09 mas), so their distances cannot be estimated accurately from parallaxes alone. FSR 1758, with a Galactic longitude l = 349.2°, seems to be located deep in the inner disk, as the distance estimated from its parallax yields a Galactocentric radius R GC = 1560 pc, and altitude Z = −470 pc. Fig. 7. Top left panel : colour-magnitude diagram for BH 140. Middle left panel : distribution on the sky for the same stars. Bottom left panel : proper motion diagram showing the field in light grey, and the cluster stars as black dots. Right column panel : same for FSR 1758. The broad appearance of the CMD of BH 140 can be explained by blended photometry in the inner regions. As discussed in Evans et al. (2018) and illustrated in Arenou et al. (2018) , the G BP and G RP fluxes of Gaia DR2 sources might be overestimated as a result of background contamination, and the effect is especially relevant in crowded fields such as the core of globular


We thank Andrew Hearin for help in using his mock catalogue, Yu Lu for using his semi-analytical data, and Zhankui Lu for helpful discussion and the anonymous referee for helpful comments that greatly improved the presentation of this paper. HJM acknowledges the support from NSF AST-1109354. This work is also supported by the 973 Programme (nos 2015CB857002, 2015CB857005).


Batalha et al. 2013 ; Petigura et al. 2013 ). Radial velocity measurements (Weiss Marcy 2014 ) and transit timing variations (Wu Lithwick 2013 ) manifest that the masses of these super-Earths are in the range of 2–20 M ⊕ . The abundance of super-Earths presents a puzzle for the core instability theory. This theory indicates that when a protoplanet reaches super-Earth size, two physical processes make the survival of super-Earths difficult, leading to a planetary “desert” in this size range (Ida Lin 2004 ). Super-Earths excite density waves in protoplanetary disks (PPDs) and give rise to rapid type I migration. This type of migration causes the planet to be engulfed by its host star if the disk inner edge touches the stellar surface. Recent studies have sought various remedies for type I migration (Yu et al. 2011 ; Fung Chiang 2017 ). PPDs are expected to have an inner edge at the stellar magnetosphere (e.g., Long et al. 2005 ). For planets undergoing disk-driven migration, they are expected to pile up near this edge. They stay either at the edge because the gas runs out, inside the edge down to 2:1 resonance because that is where the tidal torque tapers off, or outside the edge because the standing waves generated by wave reflection off the inner edge stall planet migration (Tsang 2011 ). In this paper, we focus on another threat for super-Earths. Super-Earths have low mean density, which suggests that they must be surrounded by gas envelopes (Rogers Seager 2010 ). Since these observed super-Earths are in the range of critical mass, they trigger efficient gas runaway and accumulate massive gas envelopes. They become gas giants. As a result, super-Earths are supposed to be rare. However, Kepler ’s discovery wrecks these predictions. Lee et al. ( 2014 ) proposed a metallicity gradient inside the PPDs or the late assembly of cores to resolve the puzzle of super-Earth formation. Lee Chiang ( 2016 ) stressed that the late core assembly in transitional PPDs is more consistent with observations. In gas-poor environments, gas dynamical friction has weakened to allow proto-cores to stir one another and merge. In addition, this formation scenario ensures that super-Earth cores accrete mass with a few percent envelope mass fraction (EMF). Guillot Showman ( 2002 ) argued that the dissipation of the kinetic energy of the atmospheric wind, driven by intense irradiation, could bury heat inside the planet. Many studies extend this idea to explain the radius anomaly of hot Jupiters (Youdin Mitchell 2010 ; Ginzburg Sari 2015 ; Komacek Youdin 2017 ). These investigations focus on the late evolution after the disk dispersal. Unfortunately, this is invalid for the early evolution of super-Earths because they are still embedded within disks. The irradiation may not penetrate the disk and is not able to bury heat in the exoplanets. However, we note that tidal interactions between the host star and planet can periodically perturb the planet and generate mechanical


TIM is supported by an appointment to the NASA Postdoctoral Programme at the Goddard Space Flight Center, administered by Oak Ridge Associated Universities through a contract with NASA.


A.-M.M. is supported by the National Aeronautics and Space Administration through Einstein Postdoctoral Fellowship Award Number PF2–130095 issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of the National Aeronautics Space Administration under contract NAS8–03060.


the deeper optical potential of antikaons , the earlier onset of K − and condensations in NS matter. Moreover, condensation in comparison with K − condensation always occurs at a higher density. It can be seen from equation ( 10 ) that the threshold condition for condensations is more difficult to fulfill compared with the threshold condition for K − condensation in NSs. In our model, condensations only appear in stable NSs when the optical potential of antikaons = −100, −110, −120 and −130 MeV, and the presence of them suppresses the increase of the fraction of K − mesons as indicated in Fig. 2 (a) and Table 1 . Besides, it can be also seen from Figs 2(b) and (c) that the increase of K − mesons makes the dramatical decrease of e and μ fractions in NSs. It is because that K − meson is boson in the lowest energy state, replacing negatively charged particles, makes the system energy lower. In order to keep the conditions of the electrical neutrality, the proton fraction grows faster and then the growth is suppressed when mesons appears in NSs. Eventually, the proton fraction turns out to be almost identical neutron fraction in NS matter. Therefore, according to equation ( 15 ), the Fermi momenta of neutrons decrease and the corresponding values of protons increase including K − and condensations in NS matter, which are displayed in Fig. 3 (a). Figure 1. EOSs and NSs masses as a function of nucleon density n N . In the paper, the black, red, blue, dark cyan, magenta, dark yellow and green lines represent the seven cases of = −80, −90, −100, −110, −120, −130 and 0 MeV, respectively. The dots stand for the maximum masses of NSs for the seven cases. Figure 2. Composition of NSs as a function of nucleon density n N with and without antikaon condensations. We take the optical potential of antikaons = −80, −90, −100, −110, −120, −130 and 0 MeV. Figure 3. The nucleon Fermi momentum, the effective mass and the single particle energy E N ( p F ) at the Fermi surface versus nucleon density n N in npeμ and npe matter. We take the optical potential of antikaons = −80, −90, −100, −110, −120, −130 and 0 MeV. Table 1. Maximum masses m max = M max /M ⊙ , and the corresponding radii R and the centre densities n C as well as the threshold densities and of K − and condensations for the optical potential of antikaons = −80, −90, −100, −110, −120, −130 and 0 MeV, respectively. Fig. 3 gives the nucleon Fermi momentum p FN , the effective mass and the single particle energy E N ( p F ) at the Fermi surface as a function of nucleon density n N including and not including K − and condensations in npeμ matter. We could see that the nucleon effective mass with K − and condensations is smaller than the corresponding values without K − and condensations, and it gradually declines along with the optical potential of antikaons growth in npe matter in Fig. 3 (b). The individual single particle energies of neutrons and protons in npe matter are all much less than their values in


Acknowledgments This work was partially supported by the Consejo Nacional de Investigaciones Cientficas y Tcnicas (CONICET), and the Secretara de Ciencia y Tecnologa, Universidad Nacional de Crdoba, Argentina. Plots were made using r software and post-processed with inkscape . This research has made use of NASAs Astrophysics Data System. The authors would like to thank the anonymous reviewer for their valuable suggestions. Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the US Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society and the Higher Education Funding Council for England. The SDSS web site is http://www.sdss.org/ . The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions. The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, the Ohio State University, the University of Pittsburgh, the University of Portsmouth, Princeton University, the United States Naval Observatory and the University of Washington.


The authors appreciate the enlightening suggestions from the anonymous referee, which helped to improve the quality of this paper. This work is supported by National Basic Research Program of China (973 Program, grant No. 2015CB857005, grant No. 2013CB834905), the NSFC grant (grant No. 11233002, 11203022, 11421303, 11473025, 11033007), and the SOC program (CHINARE2015-02-03). Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and the U.S. Department of Energy Office of Science. The SDSS-III web site is http://www.sdss3.org/ . SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, Carnegie Mellon University, University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofisica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington, and Yale University.


ACKNOWLEDGEMENTS Parts of this research are supported by the Australian Research Council Centre of Excellence for Gravitational Wave Discovery (OzGrav) (project number CE170100004).


sets of transits were found in the Kepler light curve of the target star KOI-1574: one giant-planet candidate at 114 days ( Borucki et al. 2011b , KOI-1574.01), one Saturn-size candidate at 574 days ( Burke et al. 2014 , KOI-1574.02), and two Earth-size candidates at 5.8d and 9d (KOI-1574.03 and KOI-1574.04, respectively; Rowe et al. 2015 ). Only the EGP at 114 days is within our selection criteria. The two large and long-orbital periods objects have already been confirmed thanks to the transiting timing variation analysis performed by Ofir et al. (2014) . However, they reported a different period for the outermost planet of 192 d, i.e. one third of the period found by Burke et al. (2014) . They reported planetary masses for the two giant objects of and . We secured five observations of KOI-1574 with SOPHIE HE. The data have a rms of 12 m s which is compatible with the uncertainties. The bisector and FWHM have rms of 44 m s and 38 m s, respectively. We fitted four circular orbits to the data fixing the orbital ephemeris to the transit ones. For KOI-1574.02, we choose the period of 572 days. We detect a hint of variation for the EGP at 114 days, with an amplitude of m s, and an upper limit of m s within the 99% confidence interval. For the other planets, we find upper limits at the 99% level on their amplitudes of m s, m s, and m s. Assuming a stellar host mass of ( Ofir et al. 2014 ), it gives a mass constraint for the EGP in our sample of ( at the 99% level). This value is fully compatible with the one derived by the transit timing analysis of Ofir et al. (2014) . For the other planet candidates, we find upper limits on the mass at the 99% level of , , and . Assuming that KOI-1574.02 orbits with a period of 192 d, as stated by Ofir et al. (2014) , does not change significantly our constraints on the mass of KOI-1574.01. For the other planets, the upper limits at 99% change to , , and . We conclude that none of these transiting candidates is an eclipsing brown dwarf or low-mass star eclipsing the target star. We confirm they have a mass within the planetary range. Appendix A.35: KOI-1645.01 The giant-planet candidate KOI-1645.01 was found by Burke et al. (2014) with an orbital period of 41 days. We observed it twice with SOPHIE HE and find a clear SB2. We fitted the cross-correlation function with a two-Gaussian profile to derive the RV of both stars. We call star A the one with the deepest line profile and star B the one with the shallowest line profile. The variation of both stars is anti-correlated, which gives a mass ratio of 87.6%. The star A exhibits a RV variation in anti-phase with the Kepler ephemeris, revealing that the secondary eclipse was detected in the light-curve. This candidate is not a transiting planet but a secondary-only EB. Appendix A.36: KOI-1783.01 A giant-planet candidate was found to transit the host star KOI-1783 with a period of 134d by Batalha et al. (2013) . We observed it twice with SOPHIE HE and find no


ACKNOWLEDGEMENTS The authors HB, DB, MM, AK, SBP, and PW acknowledges support through the National Research Foundation of South Africa. AK acknowledges the Russian Science Foundation (project no. 14-50-00043). VL and EG acknowledges support of the Development Program of M.V. Lomonosov Moscow State University and the Russian Science Foundation 16-12-00085. MASTER-SAAO is supported by the Russian Foundation for Basic Research (RFBR) 17-52-80133. Some observations reported in this paper were obtained with the South African Large Telescope under programme 2014-2-DDT-002. We thank Prof. Jules Halpern of Columbia University, who kindly obtained a short time series in 2017 March from MDM. We also thank the students of the 2015 Dartmouth Astronomy Foreign Study Program for assistance at the telescope; they are MacKenzie Carlson, Z. Edrei Chua, Robert Cueva, Natalie Drozdoff, John French, Emma Garcia, Zoe Guttendorf, Rachel McKee, Krystyna Miles, Jack Neustadt, Samuel Rosen, Marie Schwalbe, and Nicholas Suntzeff, and graduate assistants Erek Alper and MacKenzie Jones. Finally, we thank the anonymous referee, whose comments and suggestions have lead to greater understanding, and significantly improved the quality of this work.


The low-mass inner planets of the 11 archival solar system analogues discussed in Sect. 1 are shown as white circles. It is therefore clear that to achieve higher detection frequencies for terrestrial and super-terrestrial planet at all periods, expecially shorter ones, it is necessary to obtain a higher number of observations per target star and ensure a higher-density sampling. Our observing programme, as noted in Sect. 3 , originally foresaw about 40 measurements per star, a much higher number than the average 27 per star we actually obtained; it can be argued that a number of observations closer to the one originally proposed could push the survey’s detection limits to lower planetary masses, ensuring a better coverage and higher detection frequencies for terrestrial and super-terrestrial additional planets. In fact, analytical expressions for close-in low-mass exoplanets detection threshold found in Narayan et al. (2005) show such a dependence on the number of radial velocity measurements. It will also be important in the near future comparing our results with the similarly produced detection map for the parallel HARPS-N survey mentioned in Sect. 1 . From the overall survey detection map one can finally obtain an estimate for the planetary occurence frequency f p in the presence of a giant outer planet; the probability of obtaining m detection out of a sample of size N is given by the binomial distribution: The choice of distribution is dictated by the small size of our sample (at most N = 20) and has been originally justified in Burgasser et al. (2003) and successfully used in Sozzetti et al. (2009) and Faria et al. (2016) , to name a few. During the analysis of our sample, as detailed in Sect. 4 , we found a single new candidate planet, namely the gas giant HD 50499 c, which due to its estimated minimum orbital period P ≥ 8265.51 days lies outside our considered period range of P ≥ 1 yr. Following a section of the analysis reported in the work of Mayor et al. (2011) , in which the authors estimated the occurrence frequency of stars with at leats one planet in given regions of orbital period and planetary mass, we focus our interest on sub-giant planets with orbital period less than 150 days and M sin i between 10 and 30 M ⊕ , a region for which we are conservatively sensitive to only 50% of our 20-stars sample. Having found no candidate planet falling within this mass-period space, we can only obtain a lower limit of 1− γ for the occurence frequency of low-mass planets in the presence of a known outer giant planet of f p 9.84%, a value we note to be much lower than the 38.8 ± 7.1% reported in Mayor et al. (2011) for stars hosting at least one planet in the same period-mass region. 6. Summary and discussion In this work we report the results of an intense observational campaign conducted using the high-precision HARPS spectrograph on 20 stars, obtaining an average of 27 datapoints per star. The stars in the sample were selected in


Table A.1 Linelists for the synthesis of Sr. Notes. The lists include atomic data for Sr from Bautista et al. (2002) and additional lines nearby. Columns represent element line, wavelength, and log() values. Table A.2 Linelists for the synthesis of Zr. Notes. The lists include atomic data for Zr from Ljung et al. (2006) and additional lines nearby. Columns represent element line, wavelength, and log() values. Table A.3 Linelists for the synthesis of La. Notes. The lists include the hfs (when available) of the La in question taken from Ivans et al. (2006) and additional lines nearby. Columns represent element line, wavelength, and log() values. Table A.4 Linelists for the synthesis of Ce. Notes. The lists include atomic data for Ce from Lawler et al. (2009) and additional lines nearby. Columns represent element line, wavelength, and log() values. Table A.5 Linelists for the synthesis of Nd. Notes. The lists include the hfs (when available) of the Nd in question taken from Roederer et al. (2008) and additional lines nearby. Columns represent element line, wavelength, and log() values. Table A.6 Linelists for the synthesis of Sm. Notes. The lists include the hfs (when available) of the Sm in question taken from Lawler et al. (2006) and Roederer et al. (2008) , as well as additional lines nearby. Columns represent element line, wavelength, and log() values. Table A.7 Linelists for the synthesis of Eu ii . Notes. The lists include the hfs of the Eu ii in question taken from Lawler et al. (2001) and additional lines nearby. Columns represent element line, wavelength, and log() values. Appendix B: Solar abundance plots Figures B.1 – B.5 show the synthesis for all the lines analyzed in this work for the solar spectrum from Vesta observed at Magellan in January 2006. Each plot shows (in the bigger panel) the line fitting with the best fit to the observed one and the different abundances in steps of 0.04 dex. In the lower panel, the differences between the observed spectrum and the synthetic one are shown, with the difference with the best fit highlighted. In the small square panel, the values for the different abundances are represented, with the red dot representing the minimum, hence the best fit value for the elemental abundance. Fig. B.1 Solar spectrum taken using asteroid Vesta during the run at Magellan in January 2006. Spectral lines are listed in order of element and wavelength. Chemical elements with all the hfs lines are indicated inside the lines. The different colored lines represent the different synthetic spectra with different abundances in steps of 0.04 dex, while the dots are the observed spectra. The lower panels show the values of differences between the real and synthetic spectra for the synthetic spectra plotted above. The red lines represent the best fit derived from un-normalized , visible in the small plot as a red dot. Here the fits for the Sr line and the five Zr lines are shown. Fig. B.2 As in Fig. B.1 but for the four


We thank the Wind/ WAVES, SDO /AIA, and STEREO /SECCHI teams for providing data. This research was done as part of the LWS Focused Science Topic, “SEP Variability” supported by NASA grants NNX10AL50A and NNG11PL10A. SOHO is a project of international cooperation between ESA and NASA. The authors thank the anonymous referee for helpful comments.


We thank the anonymous referee for careful reading and offering constructive comments for improving the paper. S.K. thanks Masanori Nakamura and Keiichi Asada for helpful comments and encouragement. This paper is based on observations carried out with the VLBA. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. This work made use of the Swinburne University of Technology software correlator (Deller et al. 2011 ), developed as part of the Australian Major National Research Facilities Programme and operated under license. This work was done with the contribution of the Italian Ministry of Foreign Affairs and University and Research for the collaboration project between Italy and Japan. This work is partially supported by JSPS KAKENHI grant Nos. 18K03656 (M.K.), 18H03721 (K.N., M.K., K.H.), 24340042 (A.D.), and 25120007 (M.H., K.H., K.A.). K.A. is a Jansky Fellow of the National Radio Astronomy Observatory. The Black Hole Initiative at Harvard University is financially supported by a grant from the John Templeton Foundation. K.A. is financially supported in part by a grant from the National Science Foundation (AST-1614868). G.Y.Z is supported by the Korea Research Fellowship Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (NRF-2015H1D3A1066561). Facility: VLBA.


Support for this work was provided by NASA grant NNX15AW31G. R.M.W. acknowledges support from NASA grants NNX15AW31G and 80NSSC19K0914, and NSF grant AGS1622352. N.L. acknowledges support from NASA grants NNX15AB87G and NNX13AP52G. C.J.F. was partially supported by the NASA STEREO Quadrature grant. C.L.J., M.A.A., and L.P. acknowledge support from the Natural Sciences and Engineering Research Council of Canada. We would like to thank the STEREO PLASTIC PI for the STEREO He/H data provided for this study. All the data analyzed in this study are publicly available. MESSENGER data are available on the Planetary Data System ( https://pds.jpl.nasa.gov ), while STEREO data are available on the Space Physics Data Facility’s Coordinated Data Analysis Web ( https://cdaweb.sci.gsfc.nasa.gov ).


Acknowledgements We acknowledge Cloud Academy I 2018 at the Les Houches School of Physics, France, during which this project was kicked off. We thank Maria Steinrueck for the constructive discussions and contribution. Part of this work was supported by the German Deutsche Forschungsgemeinschaft, DFG project number Ts 17/2–1. We are grateful to the anonymous referee for helpful comments and constructive criticism of the manuscript.


This research was supported by the European Commission funded Research Training Network SOLAIRE. It was also supported by the Research Council of Norway through grants of computing time from the Norwegian Programme for Supercomputing and by the Swiss National Science Foundation under grant No. 153302. The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement No. 291058 and support by NASA grants NNX08AH45G, NNX08BA99G, NNX11AN98G, NNM07AA01C ( Hinode ), and NNG09FA40C ( IRIS ). To analyze the data we have used IDL and Vapor ( http://www.vapor.ucar.edu ).


To compute the cross-covariance matrix more accurately, we compute the BFD moments for each image of empty sky. Using the BFD software enables us to properly account for the differing PSFs and world coordinate systems (i.e. registration) of each image. We then compute the empirical cross-covariance matrix of BFD moments, : where ( i, j ) are indexes of the moment element of the covariance matrix, and α and β index are the exposures of this sky patch. The summation is performed over all combinations of images where α ≠ β . We combine data from all 39 Balrog-variant tiles to compute a global cross-covariance matrix for the DES data from empty sky regions. Finally, we test how using the new cross-covariance matrix affects the noise tests described in Section 2.4 . Analogous to χ M , we now define χ MX , which is now calculated using the sum of the shot/read-noise covariance and : where σ M is from the shot/read-noise covariance matrix and σ X is from the cross-covariance matrix . Generalizing to the χ 2 test using arbitrary moments, we have For these tests, we combine moments from all 48 Balrog-injection tiles, and compute the μ and σ of the normalized histogram (as in Fig. 1 ) for each band. We have subtracted the local sky estimate for each postage stamp and included the variance due to that local sky in the flux moment variance term of . In Fig. 6 , we show the σ value for each band/moment combination using and using + . We find general improvement using our globally defined cross-covariance term, with σ lowering from ∼1.12 to ∼1.01 for the flux moment, and dropping to similar levels for the other moments ( σ = 1.026 in the worst case). We report the σ and μ values for all bands in Table 1 . Figure 6. σ of χ M distribution (blue) and χ MX distribution (red) for each BFD moment from all 48 Balrog-injection tiles. Including the cross-covariance matrix brings the σ of the distribution closer to the expected value of 1. The values of σ for each band/moment combination are given in Table 1 . Furthermore, in Fig. 7 , we show the full χ 2 test for M F only and for all four moments of a given band across all 48 Balrog tiles and we report the value in Table 2 . In all bands, we find that when including the cross-covariance matrix that characterizes the US noise, the CDF of the data more closely approaches the χ 2 distribution with the appropriate number of degrees of freedom. The values also reflect the improvement, as they approach the expected value of 1 for M F only and 4 when looking at the vector of four moments. Figure 7. CDF of (blue/light blue) and (red/pink) for the single BFD M F moment and for the four M F , M R , M 1 , and M 2 moments for each band over all 48 Balrog-injection tiles. The χ 2 CDFs with 1 (black dotted line) and 4 degrees of freedom (black dashed line) are plotted for reference. Again, we show that including the cross-covariance term brings the moment distribution closer to expectations. Mean χ 2 values for each


We thank the anonymous referee for a helpful report, which greatly improved this manuscript. The primary data for this work were obtained with the Hubble Space Telescope operated by AURA, Inc. for NASA under contract NAS5-26555. Furthermore, 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. This work is supported by NASA grant HST-GO-13871. Facilities: HST (ACS, WFC3), Spitzer (IRAC).


The authors would like to thank Vasilis Archontis for his insightful comments and the referee for their comments and suggestions. S.D. acknowledges STFC for support via her studentship. L.v.D.G. is partially funded under STFC consolidated grant number ST/H00260X/1 and the Hungarian Research grant OTKA K-109276. J.E.L. and M.G.L. were funded by NASA’s Heliophysics Supporting Research and Living With a Star Program, and the Chief of Naval Research’s 6.1 program. The cylindrical flux rope simulations we analysed were performed with a grant of computational time from the DoD’s High Performance Computing Program.


We thank Tirthankar Roy Choudhury, Adam Amara, Phil Bull, Girish Kulkarni, Supratik Pal, Sebastian Seehars and Ali Rahmati for useful discussions and comments on the manuscript, and Joel Akeret for help and support with the cosmohammer package. We thank the anonymous referee for a detailed and helpful report that improved the content and presentation. The research of HP is supported by the Tomalla Foundation.


ratio with a different method that is not affected by the neglected terms in the Poisson equation and accounts for the DM close to the disk. The influence of the DM component on the stellar mass-to-light ratios of the DiskMass Survey galaxies was previously investigated by Swaters et al. (2014) . There, the correction for DM followed the strategy of Bottema (1993) , which depends on the estimated DM density in the mid-plane, which is not ideal. It also relies on an incomplete estimation of the stars+DM surface density from Eq. ( 6 ). They found that accounting for DM reduced their original average mass-to-light ratio from 0.3 to a stellar mass-to-light ratio of 0.24, but expect a larger decrease if a more rigorous approach was applied. The approach used here is to compute the expected contribution to the stellar velocity dispersion from the DM halo gravity and the disk gravity, respectively. This is done using the Jeans equation, Eq. ( 4 ). We note that the contribution of the gravitational field generated by each matter type to the stellar velocity dispersion is modulated by the vertical range of the old disk stars, , in Eq. ( 4 ). Fig. 2 Vertical gravitational field modulated by the vertical stellar density profile as a function of the height above the disk at . The solid lines correspond to UGC 3091 and the dashed lines to UGC 3140. The red lines reflect the stellar gravitational field, the black lines reflect the DM, and the blue lines are the sum of the black and red lines. Although the stars typically outweigh the DM in the mid-plane, the vertical component of the DM gravitational field can often reach parity at about one scale height. Obviously, this will be even more severe when the stellar mass-to-light ratio is low. This is illustrated in Fig. 2 , which shows the weighted vertical force for the stellar disk and DM halo components. For the stellar contribution, the from M13a is used (and hence is most often sub-maximal) and the DM halo is the pseudo-isothermal sphere fitted by M13a to the rotation curve (see their Table 6, Cols. 4 and 5). This is given for one of the more DM-dominated galaxies, UGC 3091, and one of the most disk-dominated galaxies, UGC 3140. In Fig. 3 the contribution to the stellar vertical velocity dispersion profile from the DM gravitational field is compared with the stellar contribution. They are computed using the DM and stellar vertical gravitational field profile as the input to Eq. ( 4 ), respectively. For UGC 3091, the DM gravitational field dominates the induced stellar vertical velocity dispersion at all radii, and thus should certainly not be ignored. We recall that the DiskMass strategy was to measure the stellar mass-to-light ratio by assuming a negligible contribution of the DM gravitational field to the velocity dispersion. On the other hand, for UGC 3140 the DM gravitational field contribution to the stellar velocity dispersion is irrelevant at most radii. Fig. 3 Contribution from different


may be that star formation is more burst-like (e.g., higher specific SFR; Schreiber et al. 2015 ) at higher z . Intense short-duration starburst episodes may be capable of clearing sightlines through the local ISM, resulting in increased ionizing escape during periods of lower activity, giving rise to the trend in Figure 8 . 5. SUMMARY We present intermediate-resolution absorption-line spectroscopy for four new gravitationally lensed sources, which, together with our earlier work (Jones et al. 2013 ), provides a total sample of seven star-forming galaxies in the redshift interval 4 z 5. Our S/N in all cases is adequate to sample the depth of absorption in low-ionization species, which can act as a valuable indicator of the covering fraction of neutral hydrogen. We describe two methods to convert this covering fraction into estimates of the fraction of LyC photons that are capable of reaching the IGM and undertake a critical analysis of possible uncertainties in our results. Our enlarged sample strengthens the trends discovered in our earlier work. In particular, we find the following: 1. The amount of absorbing gas varies significantly from galaxy to galaxy across our sample. However, only two systems are consistent with a complete coverage of low-ionization gas. The median observed covering fraction is 66%. Following a correction for reddening based on a dust-in-cloud model, we infer a median absolute escape fraction of LyC photons of 19% ± 6%. 2. We discuss various uncertainties in this estimate, including the possibility that the stellar radiation has different covering fractions depending on its ionizing capability, as well as scattered photons that could fill in the absorption-line profiles, mimicking a reduced covering fraction. We demonstrate that, even in the extreme case, these issues would only lower the escape fraction to no less than 11%, a value in broad agreement with independent estimates based on recombination studies of the IGM probed by QSO absorption lines. Further study of low-ion absorption lines in nearby galaxies with recent LyC detections will help determine the degree to which covering fractions may overestimate f esc . 3. For one of our lensed sources, MS 1358, we demonstrate that the low-ionization gas is clearly spatially inhomogeneous, with covering fractions ranging from 40% to 100% across various star-forming clumps. Although our sample generally strengthens the correlation we found earlier whereby the escape fraction increases with the equivalent width of Ly α emission, the scatter increases when we consider trends in the individual star-forming clumps in MS 1358, consistent with recent numerical simulations. As the escape fraction is anticorrelated with the local SFR, this suggests a time delay between a burst and the emergence of leaking LyC photons. 4. Overall, our observations indicate significant variations in the escape fraction, both from galaxy to galaxy and spatially within an individual galaxy.


B.D. thanks the University of Exeter for support through a Ph.D. studentship. N.J.M. and J.G.’s contributions were in part funded by a Leverhulme Trust Research Project Grant, and in part by a University of Exeter College of Engineering, Mathematics and Physical Sciences studentship. We acknowledge use of the MONSooN system, a collaborative facility supplied under the Joint Weather and Climate Research Programme, a strategic partnership between the Met Office and the Natural Environment Research Council. This work also used the University of Exeter Supercomputer, a DiRAC Facility jointly funded by STFC, the Large Facilities Capital Fund of BIS and the University of Exeter. We thank an anonymous reviewer for their thorough and insightful comments on the paper, which greatly improved the manuscript.


giant branches and computed the difference between the obtained interpolated [Fe/H] values and those given by the respective isochrones ([Fe/H] = −2.0, −1.5, −1.0, −0.5, and 0.0 dex). We repeated this procedure for log(age/yr) = 9.4 and 9.8. By using these theoretical points and the general trend observed in Fig. 11 , we adopted weighted mean [Fe/H] values for each cluster (see Table 1 ). Figure 13 depicts the resulting distribution using the adopted mean metallicities. Fig. 11. Metallicity difference as a function of the star cluster’s age. Filled circles, squares, and triangles correspond to high-resolution spectroscopy, low-resolution spectroscopy, and photometry reference values, respectively. Open magenta diamonds represent metallicity differences derived from theoretical isochrones (see text for details). Fig. 12. Theoretical red giant branches for log(age/yr) = 9.0 (dotted lines) and 10.10 (solid lines); [Fe/H] = −2.0, −1.5, −1.0, −0.5, and 0.0 dex shown with blue, magenta, green, orange, and red, respectively. With the aim of providing an expression for the metallicity correction that covers a wide age range, we added ten LMC old globular clusters studied by Piatti Koch (2018) from Strömgren photometry. We took from that study the star clusters’ ages as well as both reference and Strömgren metallicities, with their respective uncertainties. They are represented in Figs. 11 and 13 with open circles. When performing a least square fit to all the data points, we obtained the following expression: Fig. 13. Same as Fig. 11 for adopted weighted mean [Fe/H] values. The solid line represents the least squared fit obtained (see text for details). with a standard deviation, a correlation factor, and an F-test coefficient of 0.05, 0.98, and 0.97, respectively. Strömgren metallicities calculated from Eq. ( 4 ) should be corrected by an amount equal to −Δ[Fe/H]. 5. Summary Based on our previous knowledge that metallicities derived from standard giant branches in several photometric systems are affected by the age-metallicity degeneracy for star clusters younger than the old globular clusters, and bearing in mind the fundamental role that metallicities play in our understanding of the formation and chemical evolution processes at different universe scales, we decided to investigate metallicities for the Strömgren v b y bandpasses. Until now, it has been straightforward to compute [Fe/H] values from the Strömgren reddening free ( v − y ) 0 and m 1 0 indices, the latter being a metallicity-sensitive index. In general, they have been used for the study of globular cluster metallicity distributions (e.g., Calamida et al. 2014 ; Frank et al. 2015 ) to unveil multiple stellar populations (e.g., Carretta et al. 2011 ; Massari et al. 2016 ) rather than estimate the metal content of intermediate-age star clusters. In order to probe whether such an age dependency also affects the Strömgren metallicities, we made use of unexploited publicly available


We thank the anonymous referee for comments. We would also like to thank Andy Gould for comments on an earlier version of the manuscript. This paper includes data collected by the Kepler mission. Funding for the Kepler mission is provided by the NASA Science Mission directorate. This paper also uses data from the LAMOST survey. Guoshoujing Telescope (the Large Sky Area Multi-Object Fiber Spectroscopic Telescope, LAMOST) is a National Major Scientific Project built by the Chinese Academy of Sciences. Funding for the project has been provided by the National Development and Reform Commission. LAMOST is operated and managed by the National Astronomical Observatories, Chinese Academy of Sciences. C.P. acknowledges support from the Jeffrey L. Bishop Fellowship and from the Gruber Foundation Fellowship. S.D. acknowledges Project 11573003 supported by National Natural Science Foundation of China (NSFC).


2–8 minutes. Figure 2. Same as Figure 1 , but P 0 = 80 s and σ 0 = 30 s. Green dashed lines label the prominent quasi-periodic oscillations in the range of 2–8 minutes. The cone-of-influence is cross-hatched; within it the spectrum should be considered unreliable. 3. NUMERICAL EXPERIMENTS In order to explore how stochastic transients affect the upper atmosphere, we create a set of numerical experiments and investigate how the power spectrum is altered observationally throughout its propagation in a stratified atmosphere. We do not attempt to model realistic transients at photospheric temperature and density, but only demonstrate what response could be observed if this sort of perturbation was triggered in the lower atmosphere. 3.1. Empirical Model of the Atmosphere Figure 3 plots the one-dimensional model of the atmosphere used in this study. Below z = 2.22 , we implemented the mid-age sunspot umbra model of Maltby et al. ( 1986 ); close to the bottom boundary ( z 1.2 ), we set a constant temperature (6471 ). Above z = 2.22 , we adapted the C7 model of Avrett Loeser ( 2008 ); near the upper boundary (), we set a constant temperature of 1.3 . This kind of model of temperature has been used in a number of previous studies, e.g., Heggland et al. ( 2007 ), Botha et al. ( 2011 ), and Snow et al. ( 2015 ). Figure 3. Empirical model of the atmosphere used in this study; the inset enlarges the temperature profile at z 2.5 . In hydrostatic equilibrium, the pressure is obtained by integrating the gravitational force ρg , where p , ρ , and T are the plasma pressure, density, and temperature, respectively, is the gravitational acceleration at the surface of the Sun, k B is the Boltzmann constant, and m p is the mass of a proton. We choose a base density of at z = 0 , so at coronal height the density is of the order of , see Figure 3 . In one-dimensional MHD simulation, the magnetic field decouples from hydrodynamic equilibrium; we used B = 10 , in line with the z -axis, in our simulations. The plasma parameters were normalized by choosing a set of three to be constant: the length L 0 = 1.0 , the density , and the magnetic field strength B 0 = 10 . Then the normalization factor for the velocity is , the time t 0 = 31.7 s, the gravitational constant , and the temperature T 0 = 0.06 . So the variables become dimensionless by using , , , , , , , etc., where symbols with a hat are dimensionless variables. 3.2. Magnetohydrodynamic Simulation We used the AMRVAC package (Keppens et al. 2012 ; Porth et al. 2014 ) to solve the ideal MHD equations with the finite-volume method: where is the fluid velocity, the magnetic field vector, the solar gravity vector, the unit tensor, the total energy density, the total pressure, γ the adiabatic index, and μ 0 the magnetic permeability of free space. The AMRVAC code was configured to solve Equations ( 6 )–( 10 ) in Cartesian coordinates [ x , y , z ]. The physical quantities were assumed to be invariant along the x - and


The authors would like to thank Elliott Horch, Steve Howell, and Suvrath Mahadevan for several useful discussions. Thanks are also due to the anonymous referee whose helpful comments improved the manuscript. D.H. acknowledges support by the Australian Research Council's Discovery Projects funding scheme (project number DE140101364) and by NASA under Grant NNX14AB92G issued through the Kepler Participating Scientist Program. E.V.Q. is supported by a NASA Senior Fellowship at the Ames Research Center, administered by Oak Ridge Associated Universities through a contract with NASA. This work made use of the Digitized Sky Survey (DSS) hosted by the Mikulski Archive for Space Telescopes (MAST). This work was supported by a NASA Keck PI Data Award, administered by the NASA Exoplanet Science Institute. Data presented herein were obtained at the W. M. Keck Observatory from telescope time allocated to the National Aeronautics and Space Administration through the agencys scientific partnership with the California Institute of Technology and the University of California. 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 Mauna Kea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain.


which indicates the importance of non-equilibrium chemistry in the inner wind. Moreover, as the initial HCN abundance of R Dor and IK Tau lie within a factor of 2 of each other, quite similar physical and chemical conditions are likely present in their inner winds independent of mass-loss rate. The factor of 2 difference might be due to the lower mass-loss rate of R Dor or different pulsation characteristics. Fig. 8 Black: integrated line strengths of HCN modelled using a Gaussian abundance profile characterised by = with respect to H and cm. Overplotted are the integrated line strengths measured with APEX (red circles), SEST (blue circles), and HIFI (purple circles). The error bars for the resolved molecular lines correspond to an absolute error of 20%. Fig. 9 Range in abundance profiles found for HCN throughout the CSE. The molecular transitions probe the region marked between dashed vertical lines. 6. Conclusions We have constrained the radial abundance profile of SiO and HCN in the stellar wind of the low mass-loss M-type AGB star R Dor using a non-LTE extended atmosphere model that accounts for the interaction between gas and dust. Our analysis used the integrated line intensity and line profile shapes of a set of lines obtained with both ground- and space-based instruments. For SiO, we used 42 molecular transitions, of which 16 are spectrally resolved. The molecular data are sensitive to the region between approximately 5 and 100 . The initial abundance of SiO lies between and with respect to H. The abundance profile is constant up to , after which it follows a Gaussian profile with an e-folding radius between cm. The decline in SiO abundance near 60 might be due to condensation onto dust grains or photodissociation. We are unable to unambiguously determine the mechanism at work. For HCN, we used five resolved molecular transitions. The molecular data are sensitive to the region between approximately 7 and 40 . The initial abundance of HCN lies between and with respect to H. The abundance profile is a Gaussian profile centred on the star with an e-folding radius between cm. The initial abundances found are higher than those reported in previous studies (with the exception of the study by Khouri 2014 , for SiO). This might be due to our inclusion of higher- molecular lines. Compared to results for IK Tau, a high mass-loss rate M-type AGB star, the onset of photodissociation occurs closer to the star for both SiO and HCN. This can be explained by their difference in mass-loss rate. The R Dor initial abundance of SiO is also higher than those found for IK Tau. This might be due to different pulsation characteristics of the central stars and/or a difference in dust condensation physics. It is not connected to a differing sensitivity to non-equilibrium chemistry in the inner wind, as this molecule is unaffected by such processes ( Cherchneff 2006 ). For both stars, we find roughly similar HCN abundances, though both are five orders of


We acknowledge the anonymous referee for many useful suggetions. We are grateful to the ASTE team for making the observations possible. We thank M. Béthermin and I. Shimizu for making the model number counts available. The study is partially supported by KAKENHI (No. 25103503). Y.S. and K.T. are supported by the JSPS Research Fellowship for Young Scientists (Nos. 09J05537 and 09J00159, respectively). This work is based on observations and archival data made with the following telescopes and facilities. The ASTE telescope is operated by National Astronomical Observatory of Japan. The Australia Telescope Compact Array is part of the Australia Telescope National Facility, which is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO. Herschel is an ESA space observatory with science instruments provided by European-led Principal Investigator consortia and with important participation from NASA. NRAO is a facility of the NSF operated under cooperative agreement by Associated Universities, Inc. The 45 m radio telescope and the Nobeyama Millimeter Array are operated by Nobeyama Radio Observatory, a branch of National Astronomical Observatory of Japan. The Submillimeter Array is a joint project between the Smithsonian Astrophysical Observatory and the Academia Sinica Institute of Astronomy and Astrophysics and is funded by the Smithsonian Institution and the Academia Sinica. The Spitzer Space Telescope is operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA. The Subaru Telescope is operated by National Astronomical Observatory of Japan. The United Kingdom Infrared Telescope is operated by the Joint Astronomy Centre on behalf of the Science and Technology Facilities Council of the U.K. This publication makes use of data products from the 2MASS, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation. Facilities: ASTE (AzTEC) , ATCA , Herschel (SPIRE) , VLA , NoMA , Nobeyama 45 m (T100, BEARS) , SMA , Spitzer ( IRAC , MIPS ), Subaru (MOIRCS) , UKIRT (WFCAM) , WISE .


ACKNOWLEDGEMENTS We acknowledge the use of public data from the Fermi data archive. This work is supported by the National Natural Science Foundation of China (grant nos 11922301, 11603006, 11851304 and 11533003), the Guangxi Science Foundation (grant nos 2017GXNSFFA198008, 2018GXNSFDA281033, AD17129006 and 2018GXNSFGA281007), and also by the One-Hundred-Talents Program of Guangxi colleges, the Bagui Young Scholars Program (LHJ), and special funding for Guangxi distinguished professors (Bagui Yingcai Bagui Xuezhe).


We gratefully acknowledge the ALMA, IRAM, CARMA, and MOPRA facilities and thank the M33 and MAGMA teams for making their data public. This paper makes use of the following ALMA data: ADS/JAO.ALMA#2011.0.00876.S, ADS/JAO.ALMA#2012.00650. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), NSC and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO, and NAOJ. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. Based on observations carried out with the IRAM 30 m telescope. IRAM is supported by INSU/CNRS (France), MPG (Germany) and IGN (Spain). A.E. acknowledges partial support from grants PFB #06, FONDECYT #1130458, and ACT #1101. A.H. acknowledges support from the Centre National d’Etudes Spatiales (CNES). A.U. acknowledges support from Spanish MINECO grants AYA2012-32295 and FIS2012-32096. J.M.D.K. gratefully acknowledges financial support in the form of a Gliese Fellowship and an Emmy Noether Research Group from the Deutsche Forschungsgemeinschaft (DFG), grant number KR4801/1-1. J.P. thanks the CNRS/INSU program PCMI for support. M.Q. and S.E.M. acknowledge funding from the Deutsche Forschungsgemeinschaft (DFG) via grants SCHI 536/7-2, SCHI 536/5-1, and SCHI 536/7-1 as part of the priority program SPP 1573 “ISM-SPP: Physics of the Interstellar Medium.” M.Q., S.E.M., and E.S. acknowledge financial support to the DAGAL network from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme FP7/2007-2013/ under REA grant agreement number PITN-GA-2011-289313. E.R. is supported by a Discovery Grant from NSERC of Canada. G.B. is supported by CONICYT/FONDECYT, Programa de Iniciacion, Folio 11150220.


We are grateful for the referee for constructive comments that have helped us to improve our paper. This work is supported in part by a Grants-in-Aid for Scientific Research from the Japan Society for the Promotion of Science (JSPS; No. 27-2450 for D.T.) and by a Grant-in-Aid for Scientific Research (25287062) of the Ministry of Education, Culture, Sports, Science and Technology in Japan.


has most of its high energy distribution below 10 keV, above which the cross section limits the charge-exchange rate. More specifically, from Figure 1 we can see that the multicomponent model has significantly more particles with 8–10 times the thermal speed compared to the kappa-distribution, and close to the TS where the total proton temperature is just over 1 MK this corresponds to protons in the 6–10 keV range. As expected, Case IV has significantly stronger source terms in the heliosheath, compared to the other three cases. As explained in Section 3.2 , in this case the electron temperature close to the TS is low, allowing for a PUI pressure that is enhanced compared to the other three cases in which the electron and proton pressures are assumed equal. Figure 2 (C) shows that case IV is about twice as efficient at removing energy from the plasma as case I (note the larger range on the color scale than in Figures 2 (A) and (B)). This has a dramatic effect on the size of the heliosphere, so that the heliopause for case IV is approximately the inner edge of the saturated blue region (see also Figure 5 ) where the source term ratio is in fact negative because the energy sources change sign at the heliopause. Figure 3 shows the ratio of the momentum source term magnitude to the magnitude of the momentum source term for a single Maxwellian. While the MHD code works with the momentum source term vector, the magnitude used in the Figure 3 can be thought of as indicating where the plasma is slowed down by charge-exchange. For the single kappa-distribution (Figure 3 (A)), the source term ratio is lower close to the TS, indicating less momentum transfer away from the plasma. The reasoning is similar to that discussed above for the energy transfer, and is a consequence of the energy-dependent cross section reducing the charge-exchange rate with the high energy wings of the distribution. Interestingly, as the plasma flows toward the heliotail, it eventually cools sufficiently for the wings of the distribution to participate in the charge-exchange process. At this point we can see an abrupt increase in the momentum source term that corresponds to a significant slowing of the plasma in the tail (this slowing of the heliotail flow is discussed in more detail in Section 3.4 ). In the more distant heliotail the source terms are similar (see also Figure 4 ), indicating that the flow speeds are similar in both the Maxwellian and kappa-distribution cases. Figure 4. Plasma (solid lines) and neutral bulk (dashed lines) properties along the line through the Sun and parallel to the direction the LISM flows from. Figure 3 (B) shows that momentum source for the multicomponent model (case III) is slightly lower than the Maxwellian case close to the TS, but similar elsewhere. Figure 3 (C) shows that in the region where the energy source for case IV greatly exceeds the corresponding source in the Maxwellian case (Figure 2 (C)), the momentum sources for case I and


ACKNOWLEDGEMENTS The authors are grateful to Rien van de Weygaert, Shy Genel, Marta Volonteri, and Christophe Pichon for useful discussions. This work has made use of the Rusty Cluster at the Center for Computational Astrophysics (CCA) of the Flatiron Institute. The Flatiron Institute is supported by the Simons Foundation. AP is supported by NASA grant 15-WFIRST15-0008 to the WFIRST Science Investigation Team ‘Cosmology with the High Latitude Survey’. RSS is grateful for the generous support of the Downsbrough family.


This work has been supported by the Academy of Finland Centre of Excellence ReSoLVE (NO, MJK, JP), Finnish Cultural Foundation grant no. 00170789 (NO) and Estonian Research Council (Grant IUT40-1; JP). We thank Aki Vehtari for useful discussion and comments on GP related questions. MJK and JL gratefully acknowledge discussions with Petri Käpylä, Andreas Lagg, and Jörn Warnecke on the theoretical interpretation of the observational data. We also thank Katalin Olah for sharing insight into some questions related to MW dataset, as well as Matthias Rheinhardt and Axel Brandenburg for comments on the manuscript. The HK_Project_v1995_NSO data derive from the Mount Wilson Observatory HK Project, which was supported by both public and private funds through the Carnegie Observatories, the Mount Wilson Institute, and the Harvard-Smithsonian Center for Astrophysics starting in 1966 and continuing for over 36 yr. These data are the result of the dedicated work of O. Wilson, A. Vaughan, G. Preston, D. Duncan, S. Baliunas, and many others.


Acknowledgments We would like to thank our referee, Roberto Soria, for useful comments on this paper. We gratefully acknowledge support from the Science and Technology Facilities Council (HE through studentship grant ST/K501979/1 and TR as part of consolidated grant ST/L00075X/1). The scientific results reported in this paper are based on data obtained from the Chandra Data Archive, and on archival observations obtained with XMMNewton , an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA.


We thank M. J. Irwin for allowing us to use his observational data. We are also grateful to an anonymous referee for providing useful information and comments. The computations were performed on the FIRST cluster at the Center for Computational Sciences, University of Tsukuba. This work was supported in part by JSPS Grants-in-Aid for Scientific Research: (A) (21244013), (C) (25400222), and (S) (20224002), and Grants-in-Aid for Specially Promoted Research by MEXT (16002003).


Acknowledgements This research has made use of the SIMBAD data base operated at CDS, Strasbourg, France and NASAs Astrophysics Data System (ADS) Bibliographic Services. ADU gratefully acknowledges the support of the Fonds qubcois de la recherche sur la nature et les technologies . GAW is supported by an Natural Science and Engineering Research Council of Canada Discovery Grant. JOS acknowledges funding from the European Unions Horizon 2020 research and innovation programme under the Marie SklodowskaCurie grant agreement no. 656725. ADU also warmly thanks Alex Fullerton and Vronique Petit for their helpful comments and kind guidance. We also wish to thank the anonymous reviewer who provided very useful observations and suggestions which contributed to improve this paper and its impact.


which the sample was selected, i.e., all objects with significant C iv BLR size measurements. For five of the six Seyfert AGNs in Table 6 there are BH mass estimates from H β RM. In Table 7 we list these BH mass estimates as given in the database of Bentz Katz ( 2015 ). 14 14 http://www.astro.gsu.edu/AGNmass/ From a comparison of these mass estimates to our estimates from the C iv line in Table 6 , we find that for NGC 7469 and 3C 390.3, the BH mass estimates from the two lines are within the 1 σ uncertainties (i.e., the 1 σ uncertainties overlap). For NGC 3783 and NGC 4151, the BH mass estimates are within the 1.5 σ uncertainties (if we add the σ from both measurements), and for NGC 5548, they are within 2 σ . This resemblance in the mass estimates for the two emission lines increases the confidence in these results and in the ability of the RM method to give consistent mass estimates. Table 7 Black Hole Mass Estimates from H β Reverberation Mapping Note. Measurements from the database of Bentz Katz ( 2015 ) in units of . Note that the front page of the database lists the averaged mass measurements from all lines, and here we list the mass measurements from the H β line alone. 5. Summary We have reported the final results from a 13 yr spectrophotometric RM campaign on high-luminosity quasars. The spectrophotometric observations were supplemented by 18 yr of photometric monitoring, which improved the cadence and the accuracy of the spectrophotometric continuum light curves by adding to them the photometric light curves. All 11 objects with photometric light curves display continuum variability of 10%–70% over about six years in the rest frame. This value is similar to that reported in Paper I with data over a period that was about one-third of the current one. Six of the 11 objects were monitored spectroscopically. We identified C iv emission-line time lags for 3 objects, indicating C iv emission-line region sizes of about 100 to 250 light days. Together with data from previous studies, we have constructed a C iv BLR size–UV luminosity relation over eight orders of magnitude in UV luminosity; the slope of 0.45 ± 0.04 is consistent with previous studies and with photoionization theory. Although all our monitored AGNs show significant continuum variation, only in about half of them did we measure C iv time lag (the same fraction was also was found by Lira et al. 2018 ). This may indicate that the ionizing continuum behaves differently from the 1350 Å continuum we measured in this study. Although C iv is not a preferred line for the central BH mass determination, we derive the mass for the 19 objects with proper C iv RM data. We find that the mass scales approximately as the square root of the UV luminosity, but with a large scatter. The scatter probably results at least partly from the drawbacks of the C iv line for BH mass measurement, but probably also includes an intrinsic scatter in that relation for AGNs, e.g., different velocities for


Observatory Ultraviolet Optical Telescope. A large uncertainty in the bolometric luminosity in the first epoch is due to the fact that ultraviolet images were obtained four hours after the first optical and infrared ones—a delay comparable to the predicted evolution timescale of the emission at that time. Therefore the bolometric luminosity at the epoch is calculated in two different ways: 1. By fitting a blackbody only to the simultaneous optical and infrared data (blue fit in Figure 2 ). 2. By fitting a blackbody to the optical, infrared, and (four-hour later) ultraviolet data (red fit in Figure 2 ). Figure 2. Blackbody fits to the optical and infrared SED at discovery (black points; blue fit) and to the ultraviolet, optical, and infrared (the ultraviolet data are from four hours after discovery; gray points; red fit). Including the ultraviolet data reduces the inferred blackbody temperature by ∼1500 K, resulting in a lower bolometric luminosity at discovery (Figure 5 ). Optical and infrared magnitudes interpolated to the ultraviolet epoch are shown in purple empty circles for comparison and demonstrate the rapid evolution of the SED at these times. The insets show the corner plots for each MCMC fit, with contour lines denoting 50% and 90% bounds, red and blue solid lines (overplotted on each histogram) denoting the mean and median of each parameter distribution (on top of each other in most cases), and dashed lines denoting 68% confidence bounds. The bandpasses of the different filters used are shown at the bottom of the main plot. Both fits for the discovery epoch are presented in Figure 2 . They each match the data well and converge cleanly on a set of blackbody parameters. Including the ultraviolet data from four hours after discovery in the discovery epoch lowers the best-fit temperature by about 1500 K, compared to not having any ultraviolet constraints. A total of 21 additional epochs are fit. All fits converge onto single-peaked radius and temperature distributions except in five epochs where a small number of walkers converged on disjointed local likelihood maxima, leading to a >15% relative error in the radius, temperature, or deduced bolometric luminosity. These epochs were removed. The resulting bolometric light curve is presented and compared to other published light curves in Figure 3 . Figure 3. Bolometric light curve of the GW170817 kilonova derived here compared to those from Cowperthwaite et al. ( 2017 ), Drout et al. ( 2017 ), and Waxman et al. ( 2017 , SED integration method). After the first day, the bolometric light curve declines at an initial rate of ∼ t −1 followed by a steeper ∼ t −1.3 decline at later times, consistent with the expected radioactive heating rate. It is possible that the true SED of the kilonova cannot be described by a single blackbody in all epochs. However, the good fits in most epochs suggest that the blackbody approximation is reasonable. In addition, the bolometric values derived here are


abundances in Paper III ( Rab et al. 2015 ). We intend to offer our modelling tools and collected data sets to the community at the end of the FP7 DIANA project 12 . Appendix A: Stellar parameters and irradiation Appendix A.1: Stellar parameters The photospheric component of the stellar emission is characterised by the effective temperature , the surface gravity , and the stellar (photospheric) luminosity . Since these properties are fairly well-known for most of our target objects in the literature, we have decided not to put too much efforts into this issue. Assuming solar abundances for the star, we use standardPHOENIX stellar atmosphere models ( Brott Hauschildt 2005 ) to fit , and the interstellar extinction , to our photometric and spectroscopic data (see Fig. A.1 ). A thorough determination of requires to fit high-resolution optical spectra. For most target objects, this has been done already in the literature, so we can pick from the literature and only fit and for the assumed distance , using at first an estimate of the surface gravity . Once and are determined, we involve pre-main sequence stellar evolutionary models ( Siess et al. 2000 ) to find the stellar mass and the age. The stellar radius and surface gravity are then given by and . We use the resulting value for to redo the fitting above. This procedure is found to converge very quickly, and – thanks to having fixed from the literature – gives quite unambiguous results, see examples in Table A.1 . Fig. A.1 Fitting stellar parameters, and compilation of the stellar irradiation for two examples, TW Hya ( left ) and AB Aur ( right ). The upper plots show measured photometric fluxes (coloured symbols) as function of wavelength , in comparison to our best fitting, reddened Phoenix stellar atmosphere model spectrum (black), and the averaged observed FUV data (orange). The lower plots show the de-reddened surface intensities (black), and the averaged, de-reddened FUV data ( nm, red). The blue lines show fits to de-absorbed X-ray data, using a two-component X-ray gas emission model (energy keV). The dashed grey line marks the EUV regime in between, which is assumed to be absorbed by neutral hydrogen between the star and the disk and hence disregarded in the disk model. The dashed magenta lines show quick parametric fits to the UV and X-ray data, see Eqs. ( A.1 ) and ( A.2 ) and text, not used for the TW Hya and AB Aur models. Appendix A.2: Stellar UV irradiation The UV irradiation by the central star is much more difficult to determine, and hampered by the lack of high-quality UV data, especially in the hard FUV region (130 nm), and for Ly. We have systematically scanned and collected UV data from IUE, FUSE, HST/STIS, HST/COS, and HST/ACS. These data have been re-binned and collated, using the inverse square of the flux uncertainties as weighting factors, following the idea used by Valenti et al. (2000 , 2003) . The results of this data collection will be described elsewhere


avoid the Galactic disk where a fraction of the dust is farther than 4.5 , and therefore, traced by dust in emission, but not present in the SGF absorption map. Fig. 10 Comparison between the renormalized DL estimates (), and those derived from optical stellar observations (). The top row shows the maps derived from optical stellar observations. The lines have been added for reference. The bottom row left panel compares the renormalized estimates with those derived from optical stellar observations in the sky. The agreement of these independent estimates is a successful test of our empirical renormalization. The bottom row right panel show the histogram of the difference of the two estimates, also in the sky. Figure 10 shows the comparison between the renormalized DL estimates () with the stellar observations based estimates in the sky. The agreement between both estimates is remarkable. The difference between the estimates () has a mean of 0.02 mag and scatter (variance) of 0.12 mag. This comparison validates our renormalized DL estimates as a good tracer of the dust optical extinction in the sky. Our optical extinction estimate () was tailored to match the QSOs estimates. QSOs were observed in diffuse diffuse Galactic lines of sight (most of the QSOs have ). The agreement of the and estimates extends the validity of the DL renormalized estimate () to greater column densities. The scatter of – provides an estimate of the uncertainties in the different estimates. 7. FIR SEDs per unit of optical extinction The DL model parameter and the QSO data are used to compress the FIR IRAS and sub-mm Planck observations of the diffuse ISM to a set of 20 SEDs normalized per , which we present and discuss. The parameter is mainly determined by the wavelength where the SED peaks; as a corollary, SEDs for different values of differ significantly. The values obtained from the QSO analysis,, allow us to normalize the observed SEDs (per unit of optical extinction) and generate a one-parameter family of . This family is indexed by the parameter; the QSO lines of sight are grouped according to the fitted Galactic value. We divide the sample of good QSOs in 20 bins, containing QSOs each 15 . To obtain the values we proceed as follows. For each band and , we would like to perform a linear regression of the values as a function of. The large scatter and non-Gaussian distribution of and the scatter on make it challenging to determine such a slope robustly. Therefore, we smooth the maps to a Gaussian PSF with FWHM to reduce the scatter on , redo the dust modelling (to obtain a coherent estimate), and perform the regression on the smoothed (less noisy) maps. The non-Gaussian distribution of do not introduce any bias in the slope found 16 . Figure F11 presents the set of SEDs. The left panel shows the SEDs for the different values. The right panel shows each SED divided by the mean to highlight the differences between the individual SEDs. The complex statistics of the


DB and AG acknowledge ICRANet for partial support. All the authors thank Professor L. Stella for useful discussions at the beginning of the present project. AP acknowledges support from the European Union Seventh Framework Programme (FP7/2007-2013) under grant agreement no. 267251 ‘Astronomy Fellowships in Italy (AstroFIt)’.


We give a special thank to Sambit Roychowdhary, then at NCRA in Pune, for helping us carry out some of the GMRT observations. We are grateful for the tips we got from Jayaram Chengalur at NCRA and K. S. Dwarakanath at RRI in Bangalore regarding the reduction of the GMRT data. T.P.K.M. acknowledges financial support from the Spanish Ministry of Economy and Competitiveness (MINECO) under grant number AYA2013-41243-P. He is grateful to the Kapteyn Astronomical Institute for their hospitality as a long-term guest during the time much of this paper was being written. Part of this work was done at Leiden Observatory. M.A.W.V. and T.P.K.M. acknowledge financial support provided by NOVA, the Netherlands Research School for Astronomy, and travel support from the Leids Kerkhoven-Bosscha Fonds. M.A.W.V. acknowledges support from the FP7 Marie Curie Actions of the European Commission, via the Initial Training Network DAGAL under REA grant agreement 289313. M.A.B. acknowledges support from NSF/AST-1009471. K.B.W. acknowledges grants OISE-754437 (NSF) and 614.000.807 (NWO). We finally thank the referee for constructive comments and suggestions.


determine whether the remnant continues to migrate in the HR diagram towards the hotter S Dor instability strip occupied by quiescent LBVs, or if increasing extinction from ongoing dust condensation in the ejecta pushes it redwards again. Figure 10. Modification of the HR diagram for LBVs and their kin from Mauerhan et al. ( 2015 , see their fig. 8). The magenta coloured square is the previous estimate for the precursor star from Mauerhan et al. ( 2015 ), uncorrected for possible circumstellar extinction. The red square represents the revised best-matching model of the precursor SED, corrected for grey circumstellar extinction (see the text). The blue square indicates the aftermath of the eruption, a hot B4–B5 supergiant, also corrected for grey circumstellar extinction. The luminosities of the remnant and the revised precursor were calculated by integrating the UV–IR SEDs of the best-matching models shown in Figs 8 and 9 . The revised parameters of the stellar precursor warrant re-analysis of the star's initial mass as well, which was previously estimated at ∼30 M ⊙ (Mauerhan et al. 2015 ). Fig. 11 shows the data, after correcting for the purported grey circumstellar extinction parameters discussed above (for the remnant, E ( B − V ) = 0.48 mag and R V = 5.4; for the precursor, E ( B − V ) = 0.16 mag and R V = 5.4), along with evolutionary tracks from the Geneva rotating stellar models for 50 and 60 M ⊙ (Ekström et al. 2012 ); the data appear to most closely match (but are slightly below) the 60 M ⊙ model, which at the locations of both the remnant and precursor is undergoing core-He burning (Ekström et al. 2012 ). This revised initial mass is approximately twice as high as the circumstellar extinction-free estimate by Mauerhan et al. ( 2015 ). Interestingly, the photometry of the remnant and precursor, which was corrected for different values of circumstellar extinction and based on the best SED matches, is consistent with no significant change in stellar luminosity between before and after the 2014 eruption. Figure 11. The precursor (open black square) and remnant (filled black square) photometry of SN Hunt 248 on the HR diagram, after correcting for our estimated circumstellar extinction parameters (see the text, Section 4.1.2 ). The evolutionary tracks are from Geneva rotating stellar models (Ekström et al. 2012 ) at solar metallicity for initial masses of 50 M ⊙ (green curve) and 60 M ⊙ (magenta curve). 4.2 The 2014 outburst, revisited 4.2.1 Massive binary merger-burst? The energy source of the 2014 eruption is uncertain. The structure of the outburst light curve, the outflow velocity and the large-amplitude pre-outburst variability detected over prior decades might provide clues. We can speculate that the cool-hypergiant precursor was a massive interacting binary, perhaps similar to HR 5171 (Chesneau et al. 2014a ), and that its large pseudophotosphere was the signature of a common envelope. If this is the case, it is plausible that SN


We are grateful to the anonymous referee for the constructive comments that helped us improve this paper. Prof. Neal J. Evans II and Dr. Kee-Tae Kim are also acknowledged for useful discussions. This work is supported by the National Natural Science Foundation of China through grants 11503035, 11573036, 11373009, 11433008 and 11403040, 11403041, the International ST Cooperation Program of China through the grant of 2010DFA02710. T.L. is supported by the EACOA fellowship. K.W. is supported by grant WA3628-1/1 through the DFG priority program 1573 “Physics of the Interstellar Medium.”


instead. In addition, some R 50 of SLSN hosts are provided in Lunnan et al. ( 2015 ). Otherwise, we use the the half-light radius within the SDSS catalog 13 13 http://www.sdss3.org/ by matching the SN host galaxies with SDSS galaxies within 3′′. In the SDSS catalog, the half-light radius is estimated from the r -band Petrosian half-light radius R 50,petro and the Petrosian 90% radius R 50,petro following R 50 = R 50,petro /(1 – 8 × 10 −6 ( R 90,petro / R 50,petro ) 8.47 ) (Graham et al. 2005 ). We also update the offset parameters from the literatures. Lunnan et al. ( 2015 ) calculated the projected R off from HST images for SLSNe. Anderson et al. ( 2016 ) reported the projected R off from SNe II to the nearest H ii regions. Kelly Kirshner ( 2012 ) provided the deprojected r off = R off / R 50 for SNe II and SNe Ibc. Although projected offsets and deprojected offsets are statistically consistent, they are different for specific objects. Since most offsets in the literature and catalogs are projected, we use these deprojected offsets only when projected offsets are not available. We also convert them to r off when R 50 is available in our catalog. The sample sizes for SLSNe, SNe Ibc, SNe II, and SNe Ia with host galaxy properties are 107, 900, 4251, and 7221, respectively. To have a consistent z range as the FRB sample, we screen the samples with z 1. This gives sample sizes of 95, 874, 2829, and 7003 for the four types, respectively. Most SNe Ibc, SNe II, and SNe Ia have z 1. The excluded objects are mostly those without redshift information. The sample size for each parameter for each type of stellar transient is presented in Table 2 . 3. Multivariate Comparison We would like to perform a comparative study of the host galaxy properties between FRBs and other stellar transients. Since multiple parameters are involved, multivariate analysis methods are needed. We perform two tests. First, taking all the FRBs as a whole sample, we compare it with other samples using the multivariate Kolmogorov–Smirnov (KS) test. Second, we also compare each individual FRB with other samples to see which type it most likely belongs to. For easy understanding, we use the naive Bayes method to test individual FRBs in the FRB sample to see how they may be consistent with various types of stellar transients. We try to classify LGRBs, SLSNe, SNe Ib/Ic, SNe II, SNe Ia, and SGRBs with their host galaxy properties using the naive Bayes method and then apply the same method to each FRB. Galaxies evolve with redshift, and the FRBs in our sample all have redshift z 1, so to enable a direct comparison, in the following we compare the FRBs with the transients with redshifts z 1 only. 3.1. Multivariate KS Test 3.1.1. Method The classical KS test compares the cumulative distribution function (CDF) of two distributions P ( x ) and P ( x ′), which could be one data sample and one model sample, or two data samples. The largest distance between the two CDFs is defined as D


ACKNOWLEDGEMENTS We thank Arif Babul and members of the LoCuSS collaboration for their support and assistance. SLM and GPS acknowledge support from the STFC. AF and AEE acknowledge support from NASA Chandra Grant G06-17116B. AF acknowledges support from a McWilliams Postdoctoral Fellowship. GPS acknowledges support from the Royal Society. CO, DPM, ZA, JEC, and CARMA operations were supported by NSF grant AST-1140019. CPH acknowledges support from PRIN INAF 2014. This paper is dedicated to the memory of Dr. Yu-Ying Zhang.


order of Type 2, 3, and 4 successively. The Type 1 clumps are puzzling, because we would expect that they are the clumps just before the onset of cluster formation in a stage prior to the Type 2 clumps, but their chemical compositions indicate that they are older than the Type 2 clumps. We will discuss the nature and origin of the Type 1 clumps in Section 4.3 . 4.2. Velocity Structures of the Clumps The results shown in Figures 11 – 12 suggest that there are interesting systematic differences among the types of clumps. In the following, we further investigate the velocity structures of the Types 1–3 clumps. Figure 15 shows the distribution of the velocity dispersion σ obs measured with the 13 CO and C 18 O emission lines for the 24 clumps as a function of the projected distance from the cluster center (for Type 2 and Type 3 clumps) or from the clump peak (for Type 1 clumps). Values of σ obs measured with the two emission lines are shown by dots with different colors—gray and pink for the 13 CO and C 18 O emission lines. We found that σ obs at the center of the clumps differs depending on the types of the clumps; the σ obs values of Type 1 (except for clumps 3890a and 3890b), Type 2 (except for 4417b), and Type 3 are mostly ≲0.5 km s −1 , ≳1.0 km s −1 , and ≳0.5 km s −1 , respectively. This suggests that the large velocity dispersion at the clump center is a typical feature of cluster-forming Type 2 and Type 3 clumps. The velocity dispersion is particularly large in the Type 2 clumps, indicating that there must be a lot of motions around the clump center in the beginning of cluster formation. Figure 15. Variation of velocity dispersion ( σ obs ) for each clump as a function of the distance from the cluster center (for the Types 2 and 3 clumps) or the C 18 O emission peak position (for the Type 1 clumps). The different color dots represent the velocity dispersion values measured from the 13 CO (gray) and C 18 O (pink) data. Blue and red squares represent the median values of σ obs in the 0.2 pc bin for the 13 CO and the C 18 O data, respectively. The error bars show the standard deviation of each piece of data in the bins. We also investigated the C 18 O distributions based on the position–velocity (PV) diagrams for all of the clumps. In Figure 16 , we show examples of the PV diagrams measured along the major and minor axes of the clumps, which are displayed in panels (b) and (c) of the figure. As denoted by the white broken circles in panels (b), we found that the PV diagrams of some Type 2 clumps measured along the major axis show double peaks separated by ∼1 km s −1 , and they are symmetrically located with respect to the clump centers. This feature is seen only in three of the seven Type 2 clumps (4417c, 4423a, and 4753b), but not in Type 1 or Type 3 clumps. Figure 16. Distributions of the H 2 column density derived from the C 18 O integrated intensity, observed position–velocity diagram measured along the major axis (cut 1–1′) , and that


indices in the respective bands (see equation 2 ), for a large control sample of aperiodic quasars. This requires the availability of spectra in both bands, as well as optical and UV time-domain data (ideally sampled in both bands at the same time). Unfortunately, the number of quasars with such data are limited; Charisi et al. ( 2018 ) analysed a small sample of 42 quasars and found that the Doppler signature can arise by chance in (40 per cent) of the cases for the near-UV (far-UV) band. This probability reflects the limited data quality of the control sample (as is also demonstrated from the increase of chance coincidence in the lower quality far-UV data), and represents only an upper limit on how frequently quasars mimic the Doppler colour variations. A larger sample of quasars with better UV + optical is needed to assess this caveat more accurately. 4.6 Constraints from future observations An interesting question to ask is how much the evidence for or against the Doppler model may tighten with continued multiband monitoring of PG1302-102. To address this question, we generated hypothetical data representing future observations over ∼10 yr, covering two additional cycles of periodicity, and computed the p -values of the Doppler model with the extended data. For simplicity, we focused on the V and M 2 bands only. In particular, we assumed that the follow-up monitoring will continue with observations similar to those in Cycles 13 and 14. We mimicked the cadence of the existing Swift observations, by picking consecutive epochs of future observed dates that are 122 d apart (i.e. three epochs per year), and generated a total of 33 new mock observations to cover a baseline of 10 yr. We also approximated the photometric errors for the mock V - and M 2-band data by taking the average of the errors over the last seven Swift observations, which yields ∼0.03 and ∼0.01 mag, respectively. 14 Finally, we combined the additional hypothetical data with the original nine Swift points to construct the full new light curves. First, we assumed that the Doppler boost model is, in fact, correct. We simulated 50 random realizations of mock V -and M 2-band data, using the fiducial DB and DRW parameters from DHS15 . We generated continuous DB and DRW light curves for a time period of 10 yr, downsampled these at the forecast future MJDs and added photometric uncertainty. We show an example of a hypothetical light curve in the left most panel of Fig. 11 . The other two panels in Fig. 11 represent different models from the fiducial, which will be explained later in this section. We then computed the corresponding p -values of the mock data, following the method described in Section 2.2 . We generated 1000 mock light curves to assemble the reference CDF, corresponding to the ‘theoretical prediction’ for the new data in the Doppler model (see Fig. 2 ). In this analysis, we added the new mock data points one-by-one, and re-computed the p -values as each of the 1, 2,


magnitude smaller than the size of the thermal disturbance. In all cases, the back torque exerted on the planet by the perturbed disc was evaluated using the softening length ε 2 . We have found that thermal torques thus evaluated do not depend on the softening length, and that there are only minute differences in the perturbation of the density field arising from heat release. All runs with larger mass planets as well as those focused on the study of the cold torque were performed using a softening length ε 2 . 2.3 Code and mesh domain To numerically solve equations ( 1 )–( 5 ), we use the hydrodynamic public code fargo3d 1 (Benítez-Llambay Masset 2016 ) with orbital advection enabled (Masset 2000 ). We have implemented the energy diffusion equation as an additional source step corresponding to the following differential equation: where is given by equation ( 4 ). In our simulations we adopt parameters for the pressure length-scale and for the thermal diffusivity that are typical of those found at a few astronomical units in protoplanetary discs (e.g. Benítez-Llambay et al. 2015 ; Bitsch et al. 2015 ; Lega et al. 2015 ). As a consequence the size of the thermal disturbance λ c is significantly smaller than the pressure length-scale H (Masset 2017 ). This is in contrast with the work of Hankla et al. ( 2020 ), who considered a thermal disturbance comparable in size to the pressure length-scale, which allowed them to satisfy largely the scale separation between the distance x p of the planet to corotation, and λ c , i.e. they have x p ≪ λ c ≲ H , whereas in our case we have x p ≲ λ c ≪ H . Namely, we take the following values in all our runs: where Ω p is the planet’s frequency. At the planet’s location we have Resolving this length-scale over a few zones while simulating a full disc would have a prohibitive computational cost, especially for parameter space explorations such as those presented here. For this reason we restrict our computational domain in the three coordinates. In the r -direction we cover the interval [ r min , r max ] = [0.9 r p , 1.1 r p ], in the θ-direction we use (hence we simulate only one hemisphere of the disc and use reflecting boundary conditions at the mid-plane). Finally our azimuthal extent is . The cell numbers in each direction are ( N r , N θ , N φ ) = (880, 64, 1536). Recast in pressure length-scale our box size is (4 H, H , 7 H ), while its resolution is (2.3 × 10 −4 r p , 7.8 × 10 −4 r p , 2.3 × 10 −4 r p ). To avoid reflections on the radial boundaries of our computational box, we use damping boundary conditions as in de Val-Borro et al. ( 2006 ), the width of the inner damping ring being 3 × 10 −2 r p and that of the outer ring being 3.5 × 10 −2 r p , the damping time-scale at the edge of each damping ring being 1/20th of the local orbital period. The size of the box considered is too small to properly capture the Lindblad and corotation torques. However, when our focus is on the heating torque, we


The authors thank the anonymous referee and the AAS Journal statistician for useful comments, Łukasz Stawarz and Fabio R. Herpich for fruitful discussions, and Rafael Pacheco Cardoso and Graciana Brum for their help in the morphological classification. This work was carried out within the framework of the Polish National Science Centre grant UMO-2013/09/B/ST9/00026. Grażyna Stasińska was partially supported by the National Research Centre, Poland, DEC-2013/08/M/ST9/00664, within the framework of the HECOLS International Associated Laboratory. D.K.W. was partly supported by the Polish National Science Centre grant UMO-2013/09/B/ST9/00599. G.S. and N.V.A. acknowledge the support from the CAPES CSF–PVE project 88881.068116/2014-01. The Sloan Digital Sky Survey is a joint project of The University of Chicago, Fermilab, the Institute for Advanced Study, the Japan Participation Group, the Johns Hopkins University, the Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy, the Max-Planck-Institute for Astrophysics, New Mexico State University, Princeton University, the United States Naval Observatory, and the University of Washington. Funding for the project has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Aeronautics and Space Administration, the National Science Foundation, the U.S. Department of Energy, the Japanese Monbukagakusho, and the Max Planck Society.


We see that the Strang CTU algorithm achieves second order for most variables (as expected), with some quantities converging to almost third order (for smooth flows, the PPM algorithm approaches third-order accuracy in space), while having difficulty with . For SDC-2, we see second-order convergence in all the variables, including . Finally, for SDC-4, all of the variables converge at rates of ∼3.8–3.9, demonstrating the fourth-order accuracy expected for the method. This test shows that the SDC algorithm can achieve fourth-order convergence for reactive hydrodynamics problems with astrophysical networks. Figure 7. Thermodynamic, dynamic, and nuclear state at t = 0.06 s for the reacting hydrodynamics test run with SDC-4 using 128 2 cells. Table 6 Convergence ( L 1 Norm) for the Reacting Convergence Problem with the Strang CTU Solver Table 7 Convergence ( L 1 Norm) for the Reacting Convergence Problem with the SDC-2 Solver Table 8 Convergence ( L 1 Norm) for the Reacting Convergence Problem with the SDC-4 Solver 5.6. Burning Buoyant Bubble Our final convergence test problem considers a hydrostatic atmosphere with a temperature perturbuation. 11 11 This problem setup is available in Castro as Exec/reacting _ tests/bubble _ convergence . Buoyancy causes the perturbation to rise (and eventually roll up in the nonlinear phase). The presence of reactions prevents the bubble from fizzling out, keeping it buoyant via the heat deposition. In addition to looking at the convergence rate of the numerical solutions, we also consider how well we maintain hydrostatic equilibrium in an undisturbed hydrostatic atmosphere. We create an initial atmospheric model that is isentropic and in hydrostatic equilibrium by integrating the system where the relation ρ ( p , s ) is provided by our equation of state. We take gravity, g , to be constant and the composition to be uniform throughout the atmosphere (pure helium, with the other nuclei mass fractions set to the small value 10 −8 ). To integrate this system, we specify the conditions at the base of the atmosphere, which we take to be the lower domain boundary (not the center of the bottom-most cell). We specify and , and get and through the general stellar equation of state. We integrate this system using fourth-order Runge–Kutta, using a step size of Δ x /2 to get from the bottom of the domain to the first cell center, and then a step size of Δ x to integrate to each of the remaining cell centers vertically in the domain. The initial conditions are then converted to cell averages using the same transformation discussed earlier in the paper. Note that the hydrostatic model is generated specifically for the resolution of the problem, and as such, the initial atmosphere converges with fourth-order accuracy. For the boundary conditions, we use periodic conditions on the sides and reflecting boundary conditions at the top and bottom. Table 9 lists the problem setup parameters. Table 9 Hydrostatic Atmosphere