ACKNOWLEDGEMENTS We thank Francis-Yan Cyr-Racine, Giulia Despali, Chuck Keeton, Stacy Kim, Alex Kusenko, Leonidas Moustakas, Annika Peter, and Simona Vegetti for helpful suggestions and interesting discussions throughout the course of this project. We also thank the anonymous referee for comments that improved the quality of this work. DG, TT, and SB acknowledge support by the US National Science Foundation through grant AST-1714953. DG, TT, SB and AN acknowledge support from HST-GO-15177. Support for Program number GO-15177 was provided by NASA through a grant from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Incorporated, under NASA contract NAS5-26555. AN acknowledges support from the NASA Postdoctoral Program Fellowship. This work used computational and storage services associated with the Hoffman2 Shared Cluster provided by the UCLA Institute for Digital Research and Education’s Research Technology Group. This work also used computational and storage services associated with the Aurora and Halo supercomputers. These resources were provided by funding from the JPL Office of the Chief Information Officer.


We thank the anonymous referee for her/his helpful and thorough reading of the manuscript, as well as for suggestions that improved the paper. B.G., E.A.C., and I.R.S. acknowledge support from the ERC Advanced Programme DUSTYGAL (321334) and STFC (ST/P0000541/1). I.R.S. also acknowledges support from a Royal Society Wolfson Merit Award. J.L.W. acknowledges support from a European Union COFUND/Durham Junior Research Fellowship (EU grant agreement number 609412) and from STFC (via an Ernest Rutherford Fellowship: ST/P004784/1, and additionally ST/P0000541/1) E.I. acknowledges partial support from FONDECYT through grant N° 1171710. This paper makes use of the following ALMA data: ADS/JAO.ALMA#2015.1.00456.S ALMA is a partnership of ESO (representing its member states), NSF (USA), and NINS (Japan), together with NRC (Canada), MOST and ASIAA (Taiwan), as well as KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO, and NAOJ.


ACKNOWLEDGEMENTS We would like to thank the referee, Artie Hatzes, for carefully reading the manuscript and supporting its conclusions. We also thank the members of the EXPRES and HARPS-N GTO teams for useful input and fruitful discussions. Our simulations involved an extensive amount of coordinate transformations made possible with the excellent astropy.coordinates module 3 (Astropy Collaboration et al. 2013 ; Price-Whelan et al. 2018 ). All figures were prepared with matplotlib 4 (Hunter 2007 ). The Center for Exoplanets and Habitable Worlds is supported by the Pennsylvania State University, the Eberly College of Science, and the Pennsylvania Space Grant Consortium.


ACKNOWLEDGEMENTS This work is supported by the Simons Foundation. JA was partially supported by the research project grant ‘Fundamental Physics from Cosmological Surveys’ funded by the Swedish Research Council (VR) under Dnr 2017-04212. BW acknowledges support by the Labex Institut Lagrange de Paris (ILP) (reference ANR-10-LABX-63) part of the Idex SUPER, and received financial state aid managed by the Agence Nationale de la Recherche, as part of the programme Investissements d’avenir under the reference ANR-11-IDEX-0004-02. TC is supported by the ANR BIG4 grant ANR-16-CE23-0002 of the French Agence Nationale de la Recherche and would like to thank NVIDIA for the donation of the Quadro P6000 used in building and testing pydelfi .


ACKNOWLEDGEMENTS It is a pleasure to thank David Alonso, Philip Bull, and Laura Wolz for very useful discussions and feedback. We also extend our gratitude to the referee whose report improved the quality of this paper. SC is supported by the University of Portsmouth. AP’s work for this project was partly supported by a Dennis Sciama Fellowship at the University of Portsmouth. DB is supported by STFC consolidated grant ST/N000668/1.


The authors thank Julian Carlin for assistance with the preparation of Figures 2 and 4 . This research was supported by the Australian Research Council Centre of Excellence for Gravitational Wave Discovery (OzGrav), grant number CE170100004. G.H. is the recipient of an Australian Postgraduate Award. This work was performed in part at the Aspen Center for Physics, which is supported by National Science Foundation grant PHY–1607611.


The authors acknowledge the use of the Wind MFI magnetic field and SWE proton data. This work is supported by the Czech Grant Agency under contracts 19-18993S. A.P. thanks the Charles University Grant Agency, project No. 1484217. We appreciate the fruitful discussions with Owen Roberts, Simone Landi, Peter Hellinger, and Honghong Wu. This research was partially supported by the UK Science and Technology Facilities Council (STFC) grant ST/P000622/. Facilities: Wind , Spektr-R .


We thank the staff of the Giant Metrewave Radio Telescope (GMRT), who have made these observations possible. The GMRT is run by the National Centre for Radio Astrophysics of the Tata Institute of Fundamental Research. This research was partially supported by the grant DEC-2013/09/B/ST9/02177 of the Polish National Science Centre.


Phoenix and Aquarius are projects of the Virgo Consortium. Most simulations were carried out on the Lenova Deepcomp7000 supercomputer of the Supercomputing Center of Chinese Academy of Sciences, Beijing, China, and on Cosmology machine at the Institute for Computational Cosmology (ICC) at Durham. The Cosmology machine is part of the DiRAC facility jointly founded by STFC, the large facilities capital fund of BIS, and Durham University. LG acknowledges support from NSFC grants (nos. 11133003 and 11425312), MPG partner Group family, and an STFC Advanced Fellowship, as well as the hospitality of the Institute for Computational Cosmology at Durham University.


Based on observations obtained with Planck and Herschel , ESA science missions with instruments and contributions directly funded by ESA Member States, NASA, and Canada. This research has made use of NASA’s Astrophysics Data System. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France. This research has made use of the VizieR catalogue access tool, CDS, Strasbourg, France. This research has made use of Astropy, a community-developed core Python package for Astronomy ( Astropy Collaboration et al. 2013 ). This research has made use of TOPCAT, an interactive graphical viewer and editor for tabular data ( Taylor 2005 ).


The scientific results reported in this article are based on observations obtained with the Chandra X-ray Observatory and XMM–Newton , an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA. This research has made use of software provided by the Chandra X-ray Center (CXC) in the application package ciao , and of softwares and tools provided by the High Energy Astrophysics Science Archive Research Center (HEASARC), which is a service of the Astrophysics Science Division at NASA/GSFC and the High Energy Astrophysics Division of the Smithsonian Astrophysical Observatory. This research is based on observations with the NASA/UK/ASI Swift mission. We thank N. Schartel for approving the XMM–Newton 2014 November observation through the Director's Discretionary Time program and the staff of the XMM–Newton Science Operation Center for performing the Target of Opportunity observations. Similarly, we thank B. Wilkes for approving the Chandra 2014 August observation through the Director's Discretionary Time program and the Chandra staff for performing the Target of Opportunity observations. We thank the Swift duty scientists and science planners for making these observations possible. The Parkes radio telescope is part of the Australia Telescope which is funded by the Commonwealth of Australia for operation as a National Facility managed by CSIRO. The authors warmly thank Phil Edwards for the prompt scheduling of the observations and John Reynolds for releasing part of the telescope time of his project. We thanks Jules Halpern for useful comments. NR is supported by an NWO Vidi Grant, and by grants AYA2012-39303 and SGR2014-1073. This work is partially supported by the European COST Action MP1304 (NewCOMPSTAR).


We are grateful to Stephen Justham at National Astronomical Observatories, Chinese Academy of Sciences (CAS), for discussions. R.X.X. acknowledges the support of National Key RD Program of China (No. 2017YFA0402602), National Natural Science Foundation of China (NSFC) 11673002 and U1531243. W.Y.W. and X.L.C. acknowledge the support of MoST 2016YFE0100300, NSFC 11473044, 11633004, 11373030, CAS QYZDJ-SSW-SLH017. R.L. and K.J.L. are supported by NSFC U15311243 National Basic Research Program of China, 973 Program, 2015CB857101, XDB23010200, 11690024, 11373011, and funding from the Max-Planck Partner Group.


We thank Kevin Schlaufman, Saul Rappaport, Jens Jessen-Hansen, and the anonymous referee for helpful comments and suggestions that have significantly improved this manuscript. Part of this manuscript was written at MIT and V.V.E. appreciates the hospitality of the researchers and staff at the MIT Kavli Institute for Astrophysics and Space Research. Work by J..N.W. was partly supported by funding from the NASA Origins program (grant ID NNX11AG85G). Funding for the Stellar Astrophysics Centre is provided by The Danish National Research Foundation (grant agreement No. DNRF106). The research is supported by the ASTERISK project (ASTERoseismic Investigations with SONG and Kepler ) funded by the European Research Council (grant agreement No. 267864). We acknowledge ASK for covering travels in relation to this publication. Part of this work was supported by the Danish Council for Independent Research, through a DFF Sapere Aude Starting grant No. 4181-00487B.


The authors thank J. Zibin for his useful comments on the letter. Partial financial support from the Spanish Ministerio de Economía y Competitividad Projects AYA2012-39475-C02-01 and Consolider-Ingenio 2010 CSD2010-00064 is acknowledged.


We thank the authors of the atlas9 , marcs , phoenix and drift-phoenix model atmosphere grids to allow us to use their model results for this comparison study, and for their helpful suggestions. We thank Dr Tim-Oliver Husser (Institut für Astrophysik, Georg-August-Universitat Göttingen) for his support with the phoenix models. We also thank Sören Witte and our referee for constructive feedback. ChH highlights financial support of the European Community under the FP7 by an ERC starting grant. IB thanks the Physics Trust of the University of St Andrews for supporting her summer placement. Most literature search was performed using the ADS. Our local computer support is highly acknowledged.


The authors thank the anonymous referee for constructive comments on the manuscript. The numerical simulations were performed on facilities hosted by the CSC-IT Center for Science in Espoo, Finland. A.R. acknowledges support from the MPA Garching Visitor Programme. A.R. is funded by the doctoral program of Particle Physics and Universe Sciences at the University of Helsinki. P.H.J. and A.R. acknowledge the support of Academy of Finland grant 274931. T.N. acknowledges support from the DFG Cluster of Excellence “Origin and Structure of the Universe.”


The authors would like to thank Scott Tremaine for helpful discussions.


ACKNOWLEDGEMENTS This work is supported by the Natural Sciences and Engineering Research Council of Canada through a Discovery Accelerator Supplement under Grant RGPAS-493042-2016.


ACKNOWLEDGEMENTS We thank Volker Springel for helpful comments, and Dylan Nelson for providing videos of the merging histories of galaxies in Illustris to help us understand the processes better. LW acknowledges support from the National Natural Science Foundation of China grants program (No.11573031), and the National Key Program for Science and Technology Research and Development (2017YFB0203300). QG is supported by two National Natural Science Foundation of China grants (Nos 11573033 and 11622325).


D. Berdichevsky provided support in the difficult and lengthy process of calibrating the data. N.F.N. and L.F.B. were supported by the NASA Voyager Project under a cooperative agreement to the University of Maryland, Baltimore County. V.F. was supported by NASA grants NNX113AF99G and NNX17AB85G. He also acknowledges support from the International Space Science Institute in Bern in the framework of the team “The Physics of the Very Local Interstellar Medium.”


Acknowledgements This work was supported by the Labex P2IO project A-JWST-01-02-01+LABEXP2IOPDO and the Programme National de Physique Stellaire (PNPS) of CNRS/INSU co-funded by CEA and CNES. This research has made use of the VizieR catalogue access tool, CDS, Strasbourg, France. The original description of the VizieR service was published in Ochsenbein et al. (2000) .


Acknowledgements The authors wish to thank Jan-Uwe Ness, Karl Foster, Ignacio de la Calle and the rest of the XMM-Newton and NuSTAR scheduling teams for the support that made the coordinated observations possible. We would like to thank the referee for the helpful comments and careful reading of the paper. The GC XMM-Newton monitoring project is supported by the Bundesministerium für Wirtschaft und Technologie/Deutsches Zentrum für Luft- und Raumfahrt (BMWI/DLR, FKZ 50 OR 1408 and FKZ 50 OR 1408) and the Max Planck Society. SB acknowledges financial support from the Italian Space Agency under grant ASI-INAF I/037/12/0. TMD acknowledges support via a Ramón y Cajal Fellowship (RYC-2015-18148). BDM acknowledges support from the European Union's Horizon 2020 research and innovation programme and the Polish National Science Centre grant Polonez 2016/21/P/ST9/04025. These results are based on observations obtained with XMM-Newton , an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA. This work made use of data from the NuSTAR mission, a project led by the California Institute of Technology, managed by the Jet Propulsion Laboratory and funded by the National Aeronautics and Space Administration. We thank the NuSTAR Operations, Software and Calibration teams for support with the execution and analysis of these observations. This research has made use of the nustardas jointly developed by the ASI Science Data Centre (ASDC, Italy) and the California Institute of Technology (USA). We thank the staff of the GMRT who have made these observations possible. The GMRT is run by the National Centre for Radio Astrophysics of the Tata Institute of Fundamental Research. Part of the funding for GROND (both hardware as well as personnel) was generously granted from the Leibniz-Prize to Prof. G. Hasinger (DFG grant HA 1850/28-1).


The author is supported by the Royal Society as a Royal Society University Research Fellow at the University of Cambridge, UK.


ACKNOWLEDGEMENTS We are grateful for a careful reading of our paper and many helpful comments from an anonymous referee. The authors would like to thank Jay Lockman, Andrew Robinson, and Jeyhan Kartaltepe for helpful discussions. AL is supported by the National Radio Astronomy Observatory under the Student Observing Support program project GBT 16B-285. SC acknowledges support from National Science Foundation grant number 1517488. YS is partially supported by the National Natural Science Foundation of China (NSFC) grant 11603032. The authors would like to thank the Sloan Digital Sky Survey for making all their data public and easily accessible and Barbara Catinella and the GASS collaboration for making their data public. The National Radio Astronomy Observatory and the Green Bank Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. Some of the data presented in this paper were obtained from the Mikulski Archive for Space Telescopes (MAST). STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. Support for MAST for non- HST data is provided by the NASA Office of Space Science via grant NNX09AF08G and by other grants and contracts.


We sincerely thank Dr. Clara Froment for her constructive comments that improved the paper significantly. We would like to thank Dr. Bart De Pontieu (LMSAL) for helpful comments on a previous version of the paper. IRIS is a NASA small explorer mission developed and operated by LMSAL with mission operations executed at NASA Ames Research center and major contributions to downlink communications funded by ESA and the Norwegian Space Centre. S.K.T. gratefully acknowledges support by the NASA contract NNG09FA40C (IRIS). AKS and MM acknowledge the support of the UGC-UKIERI grant to support the present research.


We thank Yehuda Hoffman for making the CLUES initial conditions available. IMS-S, CBB and GY thank the MINECO (Spain) for the financial support through the AYA2012-31101 grant. CBB is funded through the Ramon y Cajal programme of the MINECO. The CLUES simulations were performed and analysed at the High Performance Computing Center Stuttgart (HLRS). We thank DEISA for access to computing resources through DECI projects SIMU-LU and SIMUGAL-LU and the generous allocation of resources from STFC's DiRAC Facility (COSMOS: Galactic Archaeology), the DEISA consortium, co-funded through EU FP6 project RI-031513 and the FP7 project RI-222919 (through the DEISA Extreme Computing Initiative), the PRACE-2IP Project (FP7 RI-283493).


We thank Bill Paxton, Josiah Schwab, Pablo Marchant, Rich Townsend, Matteo Cantiello, and Lars Bildsten for engaging conversations about the MESA project. We also thank Michael Wiescher for initial discussions about this paper. This project was supported by NASA under the Theoretical and Computational Astrophysics Networks grant NNX14AB53G and the Astrophysics Theory Program grant 14-ATP14-0007, and by NSF under the Software Infrastructure for Sustained Innovation grant 1339600, and grant PHY 08-022648 for the Physics Frontier Center “Joint Institute for Nuclear Astrophysics—Center for the Evolution of the Elements” (JINA-CEE). C.E.F. acknowledges support from Arizona State University under a 2015 CLAS Undergraduate Summer Enrichment Award, a 2015-2016 Norm Perrill Origins Project Undergraduate Scholarship, and a ASU/NASA Space Grant award. F.X.T. acknowledges sabbatical support from the Simons Foundation.


The authors acknowledge the contribution of the FP7 SPACE project ASTRODEEP (Ref. No: 312725), supported by the European Commission. We thank the anonymous referee for the useful comments and suggestions that greatly helped us to improve the paper.


The Liège team acknowledges support from the Fonds de la Recherche Scientifique (F.R.S/FNRS) including especially an F.R.S/FNRS Research Project (T.0100.15), as well as through an ARC grant for Concerted Research Actions financed by the French Community of Belgium (Wallonia-Brussels Federation), and an XMM PRODEX contract (Belspo). We are particularly grateful to Reinhold Haefner for having made his IBVS data available and to Ella Antokhina and Igor Antokhin for discussions on the photometric solution. EG is greatly indebted to Stephanie Wachter and Suzanne Tourtelotte for having spared no pains in facilitating the interaction with the YALO archives. We are grateful to I. Stevens, H. Sana, Y. Nazé, J.-M. Vreux, and M. da Silva Pires for taking some of the spectroscopic data or for discussions on earlier versions of this work. We thank John Hillier for making his code available.


ACKNOWLEDGEMENTS DLL thanks the Robert A. Welch Foundation of Houston, Texas for support through grant F-634. We thank the referee for a constructive report.


K.S.R. acknowledges the financial support from the Science Engineering Research Board (SERB), Department of Science Technology, India (PDF/2015/000393). K.S.R. acknowledges N. G. Kantharia and Eric Greisen for valuable suggestions related to AIPS and M. S. Santhanam for valuable data analysis advice. P.S. acknowledges support from ISRO RESPOND program. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. We thank the staff of the Gauribidanur observatory for their help with the observations and maintenance of the antenna and receiver systems there. We thank the anonymous referee for an insightful report that has helped us improve the paper substantially.


H.J.Z. gratefully acknowledges the generous support of the Clay Postdoctoral Fellowship. M.J.G. and D.G.F. are supported by the Smithsonian Institution. We thank Scott Tremaine for carefully reading the manuscript and providing many useful comments. This work benefited from discussions with Ken Rines, Antonaldo Diaferio, Neta Bahcall, Mark Vogelsberger, and Paul Torrey. Masato Onodera kindly pointed out a mistake in Equation ( 5 ). This research has made use of NASA’s Astrophysics Data System Bibliographic Services. Observations reported here were obtained at the MMT Observatory, a joint facility of the University of Arizona and the Smithsonian Institution. 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, University of Cambridge, 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.


We thank the galform team for making the code publicly available. The work of ID and JS was supported by the ERC Project No. 267117 (DARK) hosted by Université Pierre et Marie Curie (UPMC) – Paris 6, PI J. Silk. JS acknowledges the support of the JHU by NSF grant OIA-1124403. The work of KAO was supported in part by DOE grant DE-SC0011842 at the University of Minnesota. This work has been carried out at the ILP LABEX (under reference ANR-10-LABX-63) supported by French state funds managed by the ANR within the Investissements d'Avenir programme under reference ANR-11-IDEX-0004-02.


Acknowledgements We thank Paul Benni and Tom Kaye for providing a few of the light curves and for helpful discussions. SR and BLG acknowledge partial support from National Aeronautics and Space Administration (NASA) Chandra grant GO7-18008X. AV was supported by the National Science Foundation (NSF) Graduate Research Fellowship, grant no. DGE 1144152, and also acknowledges partial support from NASA’s Transiting Exoplanet Survey Satellite (TESS) mission under a sub-award from the Massachusetts Institute of Technology to the Smithsonian Astrophysical Observatory, Sponsor Contract Number 5710003554. This work was performed in part under contract with the California Institute of Technology (Caltech)/Jet Propulsion Laboratory (JPL) funded by NASA through the Sagan Fellowship Program executed by the NASA Exoplanet Science Institute.


Acknowledgments We thank C. Lang and D. Ludovici for sharing their reduced, high resolution VLA data covering the position of PSR J17462850, and G. Desvignes, R. Eatough, P. Esposito, D. Schnitzeler and A. Siemion for useful discussions. JD was supported by a Sofja Kovalevskaja Award from the Alexander von Humboldt Foundation of Germany. N. Degenaar acknowledges support via a Vidi grant from the Netherlands Organization for Scientific research (NWO) and a Marie Curie fellowship from the European Commission under contract no. FP-PEOPLE-2013-IEF-627148. J. Deneva was supported by the NASA Fermi program. MK and RK acknowledge the financial support by the European Research Council for the ERC Synergy Grant BlackHoleCam under contract no. 610058. The Parkes radio telescope is part of the Australia Telescope, which is funded by the Commonwealth Government for operation as a National Facility managed by CSIRO.


and wiggles a few times before ending at a hotspot 15′′ from the core. No corresponding features are detected in the X-ray band. Similarly, there are no clear knot associations in the HST image. 1116+128 (4C+12.39). The extended radio emission consists of a single knot at 25 northwest of the core. The knot is not detected in the Chandra data. No features are apparent in the HST image at the radio knot. 1303−827 (PKS 1302−82). The extended radio emission consists of a single knot at 65 southeast of the core and a knot pair about 16′′ north-northwest of the core. The X-ray jet searched was set to the southeast to include the closest knot. No knots are detected by Chandra . In the HST image, there is faint, resolved flux from the closer of the north-northwest knot pair, shown in a inset in Figure 6 . 1502+106 (B2 0954+25A). The VLBI jet is oriented at a PA of 120°, while the kpc-scale jet is at a PA of 160° (see Table 10 ) and is marginally detected. The VLA image of the jet published by Cooper et al. ( 2007 ) shows a continuous jet all the way to the termination, about 9′′ from the core. Lister et al. ( 2013 ) found a maximum apparent speed of VLBI knots of 17.5 c . The HST image shows no clear detection of any part of the kpc-scale jet. 1622−297 (PKS B1622−297). The kpc radio jet is weak and not detected with Chandra . There is a pc-scale jet at a PA of −70°, with a maximum apparent speed of 18.6 c (Lister et al. 2013 ). There are no apparent features in the HST image that are associated with radio or X-ray emission. 1823+568 (4C+56.27). There is a pc-scale jet at a PA of −160° with a maximum apparent speed of 26.17 c (Lister et al. 2013 ). The kpc-scale jet is first oriented almost due south, but bends about 1′′ from the core to the east, where it is clearly detected in the Chandra image at 25 from the core. There are no apparent features in the HST image that are associated with radio or X-ray emission, although the southern portion lies along a diffraction spike. 2201+315 (4C+31.63). The X-ray image was first published by Hogan et al. ( 2011 ). This quasar has VLBI components with apparent velocities up to 8.3 c along a PA of −145° (Lister et al. 2013 ). In the VLA image, the jet is −37′′ long at a PA of −110°, terminating in a hotspot (Cooper et al. 2007 ). To the northeast, there is a lobe about 45′′ from the core. The radio jet is detected in the Chandra data only out to about 4′′ from the core. The quasar was not part of our observing program, so we do not have an HST image of it. 2230+114 (CTA 102, 4C+11.69). There is a pc-scale jet at a PA of 160° with a maximum apparent speed of 8.6 c (Lister et al. 2013 ). There are radio-emitting knots to the northwest and southeast sides of the core but no clear association with X-ray emission. There are no apparent features in the HST image that are associated with the radio knots. 4. Discussion 4.1. Detection Statistics We detected 9 X-ray emitting jets among the 17 sources that complete our


form the Herschel maps, into radio signal at this frequency using the Bonzini et al. (2015) relation after scaling for the magnification factor does not discard the possibility that an AGN contribution might be responsible for the remaining emission. 3 <italic>Chandra</italic> X-ray observations The galaxies SDP.9 and SDP.11 were observed by Chandra in Cycle 16, with the ACIS-S3 CCD at the aimpoint, for a total exposure time of 55.3 ks (on January 10, 2015) and 19.8 ks (on February 28 and March 23, 2015), respectively. Very faint mode was used for the event telemetry format, and ASCA grade 0, 2, 3, 4, and 6 events were used in the analysis, which has been carried out using the ciao v4.7 software. Both sources are clearly detected, with 14 counts each in the 0.5–7 keV band within a circular region of 2 ′′ radius centered on the positions reported in Sect. 2 , and 8 counts in the observed 2–7 keV band. The 0.5–7 keV Chandra images of SDP.9 and SDP.11, centered on these positions, are shown in Fig. 1 . Remarkably, the 0.5 arcsec Chandra on axis resolution is able to resolve the X-ray emission from the lensed components. The X-ray emission better matches in position the SMA data than the HST images. Fig. 1 HST/WFC3 lens-subtracted F160W images (brightness scale in μ Jy arcsec −2 , left panel ) and Chandra 0.5/7 keV images ( right panel ) of SDP.9 and SDP.11, overlaid with signal-to-noise ratio (S/N) contours at 880 μ m from the SMA (in steps of 3, 6, and 9, Bussmann et al. 2013 ; Negrello et al. 2014 ). The lownumber of detected photons significantly limits the spectral constraints that can be obtained from the X-ray analysis. To provide basic information for both sources, however, we fit the spectra extracted from the Chandra data using simplemodels (within xspec v.12.9, Arnaud 1996 ) and the Cash statistics ( Cash 1979 ), which is appropriate for low-count spectra. Fitting the spectrum of SDP.9 with a power law provides Γ = 1.1 ± 1.0, which is suggestive of obscuration. When we fixed Γ to 1.8, as is typically observed in AGN and quasars (e.g., Piconcelli et al. 2005 ), we obtained a column density of ≈ 5.2 × 10 22 cm −2 at the source redshift (3 σ upper limit of ≈ 3.3 × 10 23 cm −2 ). The observed 2–10 keV flux is ≈ 3.6 × 10 −15 erg cm −2 s −1 , and the derived apparent rest-frame 2–10 keV luminosity (corrected for absorption but not for magnification) is ≈ 3.7 × 10 43 erg s −1 . The faint flux of SDP.9 explains the non-detection of the source (with an upper limit of ≈ 10 −14 erg cm −2 s −1 in the 0.5–8 keV band) in the XMM-ATLAS survey ( Ranalli et al. 2015 ). This survey covers a 6 deg 2 area with an average exposure of 3 ks. The non-detection of the AGN in XMM-Newton suggests that it is obscured, with an estimated column density of at least 10 23 cm −2 , as observed in other bright submm galaxies ( Johnson et al. 2013 ). For SDP.11, we combined the photons of the two observations into a single spectrum. As for SDP.9, a power-law model


values at the reference epoch at which the two timing models of Table 4 are defined, MJD 55655. The fit to the position at the median MJD of each aeon (the finely dotted orange line) returns μ α = 5.63 ± 0.10 mas yr − 1 and μ δ = 2.34 ± 0.28 mas yr − 1 while the dashed lilac line represents the values obtained from the BTX model, shown in Table 4 . Using an estimated distance of ≃1040 pc (from the NE2001 model of free-electron distribution in the Galaxy; Cordes Lazio 2003 ) and a total proper motion , a 2D transverse velocity of ν t = 30 ± 9 km s − 1 was calculated. This assumes an uncertainty of 30 per cent 4 in the DM-derived distance mentioned above. The measurement is in agreement with the value of 30 ± 20 km s − 1 measured by Stappers et al. ( 1998 ) and represents a twofold increase in precision, even though the uncertainty of the DM-derived distance is assumed to be much greater. It should be noted that this is significantly lower than the average value of 93 ± 13 km s − 1 reported in Desvignes et al. ( 2016 ) for the transverse velocities of binary MSPs. However, it agrees well with the value of 56 ± 3 km s − 1 reported for the binary MSPs with distance measurements from parallaxes. The proper motion values obtained from the BTX model appear to be inconsistent with those obtained from fitting to position measurements for every aeon using the respective ELL1 models. This is because the proper motion terms and the OFDs are strongly covariant and therefore the uncertainties in the values obtained from the BTX model are heavily underestimated, reinforcing the need for cautious usage of this model. 3.2 DM variations Since the DM is a measure of the density of the ionized interstellar medium (IISM) along the line of sight to the pulsar, both the motion of the pulsar and the dynamical evolution of the IISM affect this value. While it is possible to obtain the DM from timing, ‘JUMPS’ or instrumental offsets introduced to align the ToAs from the different backends are fully covariant with the DM and prevent an accurate measurement directly from the data set presented above. Therefore, a DM value of 20.7299(17) cm − 3 pc is adopted from the LOFAR measurements of Kondratiev et al. ( 2016 ). When simultaneous dual (or multi-) frequency observations are available, it is, however, possible to accurately estimate the variation in the DM. The WSRT PuMa-II backend provides observations centred at 345 and 1380 MHz, with a cadence of roughly three weeks. Observations between the two frequencies are sequential, which are separated by, at most, a few days and available for the MJD range ∼54600–56800. Since low-frequency observations are more sensitive to the DM variations, these are utilized to measure them instead of the two frequency-band observations of the PSRIX backend. To measure DM variations, the PuMa-II ToAs were fitted for DM using the ELL1 model presented in Table 4 . The ToAs were then split into 100 d long intervals, to ensure that enough


shorter than the radiative length-scale, over which substantial radiative energy losses would occur. These results are independent of black hole mass. Figure 5. Figures (a–f) show the distance travelled by the jet before reaching equipartition for a range of values of the reconnection parameters A rec and d , from ( 97 ) and fractional Eddington jet power f Edd . We stop integration of the jet evolution equations at a distance of 10 8 r s if the jet plasma has not yet reached equipartition, since radiative energy losses at larger distances than this are insignificant. The jet parameters used to obtain these results are shown under Model C in Table 2 and the radiative losses corresponding to these models are shown in Fig. 4 . We find that the dimensionless distance to equipartition, X equi = z equi / r s , depends weakly on the fractional Eddington accretion rate, f Edd . The distance to equipartition decreases slowly with increasing f Edd . These results are independent of black hole mass, M . Figure 6. The desirable region of parameter space for jets with different fractional Eddington luminosities and reconnection parameters from Figs 4 and 5 . Here, ‘desirable’ means that the jet reaches equipartition at a distance, z equi , between 100 and 10 8 r s , whilst not radiating more than 95 per cent of its initial energy in reaching this point. The unfavoured regions of parameter space which do not fulfill these criteria are coloured in black. The jet parameters used to obtain these results are shown under Model C in Table 2 . Due to more severe radiative losses at higher fractional Eddington jet powers ( f Edd ), the desirable region becomes more restrictive for higher values of f Edd . This means that lower power jets are able to reach equipartition at smaller distances whilst retaining at least 5 per cent of their initial energy. For jet powers close to the Eddington luminosity ( f Edd > 0.1), the strong radiative losses essentially prohibit the jet from coming into equipartition at a distance smaller than ∼10 4 r s , since otherwise, the jet radiates away more than 95 per cent of its initial power in the compact base region with high magnetic field strengths. This is consistent with our earlier results in Fig. 3 , in which we found that the base of the jet must be highly magnetized in order not to suffer from devastating radiative energy losses. We also see that large negative values of the reconnection power-law d are effectively prohibited, since reconnection occurring predominantly at the base of the jet will result in heavy radiative losses in the strong magnetic fields. These results are independent of black hole mass. In terms of the equipartition fraction or magnetization, which we define as σ = U B / U e ± , the equation becomes It can be more convenient to use this expression when solving the evolution equations numerically, if U B / U e ± becomes very large. 8.1 Constraining the rate of reconnection in the jet Finally, we try to


left-hand panel of Fig. 3 ). Despite such significant perturbations, the presence of a DM filament potential well coupled to the relatively high density of the gas ensures that the cooling time within the filament remains short. As a result, the filament is still visible as a cold stream cutting through the hot superbubble in the middle right-hand panel of Fig. 3 . Due to these consequent perturbations induced by the stellar feedback, we cannot use either the temperature or vorticity to define the gas filament truncation radii in the feedback run. It should also be noted that our assumption of isothermality of the filaments becomes less valid than in the no stellar feedback case as stronger temperature gradients develop between core and outer envelope. To be more specific, in the no feedback case, the temperature varies between core and truncation radius by about a factor of 2, but in the feedback case in can reach an order of magnitude. However, most of this gradient is localized in the outer parts of the filament, so that the central region retains a significantly large isothermal core. This can be understood by performing the following simple calculation. Neglecting the presence of the wall, we may integrate both the gas and DM density profiles (from equation 4 ) to obtain the filament mass per unit length, μ , and its half-mass radius The fact that the (small) core radius contains half of the mass makes the filamentary material relatively impervious to the stellar feedback/filament interaction: provided the core is shielded from it, there can only be a minor change in the amount of gas mass that the filament carries. It has been suggested in the literature that Kelvin–Helmholtz instabilities could be triggered at the interface between cold filament gas and the feedback powered, hot, galactic wind (e.g. Mandelker et al. 2016 and subsequent work). These will depend non-trivially on redshift and the distance of a filament segment to the central galaxy, so it is quite difficult to define a unique characteristic time-scale, t KH . Nevertheless, writing , where v w is the relative velocity between the wind and the gas filament and ρ w the density of the wind, we can see that given the steepness of the filament density profile that we measure, t KH becomes larger as the perturbation progresses deeper in the filament. This means that the time-scale is ultimately set by t KH ( r 0 ). Plugging in typical numbers for our feedback run at z = 4, i.e. r 0 ∼ 5 kpc, ρ ( r 0 ) ∼ 3 × 10 −27 g cm −3 , v w ∼ 100 km s –1 , and ρ w ∼ 3 × 10 −28 g cm −3 , we, thus, get t KH ∼ 20 Myr which is about an order of magnitude shorter than the infall time from the virial radius of the embedded halo. The conclusion is, thus, that our gas filaments should not survive the interaction. Notwithstanding that this does not happen in our simulations, which might admittedly be of too low a resolution to capture the instability properly, the calculation ignores both the


nearby neighbors or from morphologically different galaxies. If we ignore the contamination (which is significant), the SFR efficiencies determined in Section 3.2.3 would be increased by a factor of about two. This sets an upper limit on the any potential biases in sample selection on the radial surface brightness and the resultant SFR efficiencies. 2.5. Effects of Ly<italic>α</italic> on the Surface Brightness Profiles The Ly α emission line falls into the rest-frame FUV bandpass and could potentially contaminate the measured flux. We consider whether Ly α could be contaminating our stacks, and thereby the resulting surface brightness profiles. Previously, Rafelski et al. ( 2011 ) conducted a test to see whether a typical SFG Ly α line would significantly affect the measured photometry by using the stacked LBG spectrum from Shapley et al. ( 2003 ) to estimate the effect, and found it to be negligible. However, it is possible that a subset of our sample has much stronger Ly α emission than a typical LBG, such as the green peas (Henry et al. 2015 ), which could bias the SFRs obtained from the rest-frame FUV continuum high. To test for this possibility, in particular in the galaxy outskirts, we conduct the following tests. First, for the and samples we create a smaller sample including about half of the galaxies for which Ly α does not fall in the FUV bandpass by constraining the redshift, and compare the radial surface brightness profile of that stack to the full subsample stacks. We find no evidence of a decrease in the flux in the outskirts of the galaxies within their uncertainties. Second, we compare the radial surface brightness profiles for the FUV and NUV bands, since the NUV bands will not include the Ly α line. Again, we find no evidence of a change in the radial surface brightness profile in the outskirts. The fact that the galaxies have the same radial surface brightness profile shapes in both bands suggests that the Ly α line has little to no effect on the radial surface brightness profiles. We note that this is not in conflict with the results by Steidel et al. ( 2011 ), who find extended Ly α halos around SFGs. First, that study samples a different galaxy population of brighter SFGs. Second, the Steidel et al. ( 2011 ) study goes out to ∼80 kpc using ground-based observations, while we limit ourselves to the central ∼10 kpc, which is barely resolved in that ground-based study. Third, Steidel et al. ( 2011 ) use narrowband filters to find the Ly α , while our stacks are in very broad filters, and thus the Ly α would not contribute except in the extreme emitter cases, and then only in the FUV bands for part of the redshift range. 3. SFR EFFICIENCY The radial surface brightness profiles of the SFGs show spatially extended star formation in the galaxy outskirts. Star formation is expected in the outskirts of high-redshift galaxies, as it is measured in atomic-dominated hydrogen gas at low redshift (Thilker et al. 2007 ; Boissier et


(5) predicted H i mass derived using equation ( 1 ); and (6) calculated H i deficiencies. 3.2 H <sc>i</sc> kinematics of the NGC 7232/3 triplet Although the coarse velocity resolution of our observations does not allow for the detailed analysis of the kinematics of the triplet galaxy group and its surroundings, it is clear from the Fig. 5 that NGC 7232B has higher velocities and is kinematically different from NGC 7232 and NGC 7233 (velocity difference of up to 400 km s −1 ). The H i debris appears to have similar velocities to NGC 7233 and NGC 7232 within ∼200 km s −1 , which could indicate that most of this gas is coming from the interaction between the galaxy pair and not NGC 7232B. Figure 5. MeerKAT-64 H i velocity field map of the NGC 7232/3 triplet. The black stars indicate the optical centres of the triplet galaxies. 3.3 H <sc>i</sc> deficiency equation of the NGC 7232/3 triplet We determine the H i deficiency of each galaxy in the NGC 7232/3 triplet group to determine if the group spirals are H i -deficient or H i -rich. The H i deficiency is derived by comparing the observed H i mass to the expected H i mass for an isolated galaxy. The expected H i masses () are derived from the absolute B -magnitudes obtained from HyperLeda 4 (Makarov et al. 2014 ). We have used the scaling relation derived in (Jones et al. 2018 ) based on measurements or constraints on the H i masses of 844 isolated galaxies compiled by the AMIGA project (Analysis of the interstellar Medium in Isolated GAlaxies; Verdes-Montenegro et al. 2005 ): where log [ L B / L ⊙ ] is derived by where M bol, ⊙ is the Sun's bolometric absolute magnitude, we adopt M bol, ⊙ = 4.88 (Lisenfeld et al. 2011 ), D is the distance in Mpc, and B c is the absolute B -magnitude corrected for extinction. The H i deficiency is then defined by where is the H i mass derived from the observations. Positive values of DEF indicate H i deficiency while negative values indicate H i excess. We compare the expected H i mass for each galaxy to its H i mass derived from our observations (see Table 2 ). NGC 7232 and NGC 7233 are H i -deficient while NGC 7232B is found to have excess H i . Taking into account the uncertainties in B -magnitudes and the scatter in the scaling relation, we consider a galaxy to be H i -deficient when DEF > 0.2 and H i excess if DEF −0.2. The total H i mass of the NGC 7232/3 triplet including all the H i debris (i.e. H i streams and clouds) is ] = 9.84 ± 0.002. Comparing the total derived H i mass to the expected H i mass of , we find a total DEF of −0.23 ± 0.11, which indicates that the NGC 7232/3 galaxy triplet has an overall H i excess compared to field galaxies. 4 DISCUSSION One of the questions coming from our data is the possible origin of the H i debris observed. In this work, we search for signs of interaction within the NGC 7323/3 galaxy triplet and its surrounding environment. The detection of wide-spread H i debris around the galaxy triplet demonstrates the need for


degrees of freedom. The nonrelativistic Model 1 already gives a good fit to the X-ray spectra of Fairall 9. In addition, we do not clearly detect the signature of a broad iron line in Figures 1 and 2 . All these considerations lead us to conclude that the relativistic reflection component in the spectra of Fairall 9, if present, is weak. To constrain possible deviation from Kerr spacetime around the black hole in Fairall 9, we replace the component relxill in Model 3 with its non-Kerr extension relxill _ nk v1.3.2 (Bambi et al. 2017 ; Abdikamalov et al. 2019a ). Similar to the results with relxill , we also find three solutions. The best-fit parameters are shown in Table 5 and the constraints of the deformation parameters in Figure 6 . We only show the results corresponding to solution 1 (Model 3.1) because the deformation parameters are totally unconstrained in the other two solutions. This is easy to understand since both negative spin and truncated disk result in a large distance between the black hole and the inner edge of the accretion disk. In this case, the effect on the reflected spectrum due to deviations from the Kerr background are not strong enough to be detected with current data. When assuming solution 1, we find from Figure 6 that the deformation parameters can recover 0, which means the Kerr solution is recovered. Figure 6. Confidence contour plot for spin parameter and deformation parameters. The red, green, and blue lines correspond to 68%, 90%, and 99% confidence levels respectively. The gray region is not included in our analysis because the spacetime there has pathological properties. Table 5 Best-fit Values with Model relxill_nk Note. Model: Tbabs ∗ (nthComp + relxill _ nk + xillver + zCutoffpl) . The parameters with * are fixed at given values in the fit. Uncertainties are given at the 90% confidence level. 4. Discussion and Conclusions Fairall 9 has a number of interesting properties (listed at the beginning of this paper) that make it a promising source for testing the Kerr black hole hypothesis using X-ray reflection spectroscopy. Unfortunately, the relativistic reflection component, if present, is weak, which makes the selection of the correct astrophysical model with the available data challenging. However, we should stress that the ideal source with all the nice properties for testing general relativity and no bad properties probably does not exist, so we have to try to do our best with the available sources and data. Moreover, in the case of Fairall 9 we can expect (see Section 4.3 below) that future observations with a higher energy resolution near the iron line can solve the degeneracy and be capable of selecting the astrophysical model and the physical best-fit solution. 4.1. General Considerations We studied a simultaneous XMM+NuSTAR observation of Fairall 9. The soft excess in the spectra can be described by a Comptonization component (Model 1) and the fit is already good. When we add a blurred reflection


taking its place. It is only when m 3 ∼ m 2 that genuinely chaotic dynamics can take place, in some cases leading to coalescence. Finally, Fig. 5 shows the merger fraction as a function of the initial eccentricity of the inner and outer binary. We note that the merger fraction increases with increasing e in , while it decreases with increasing e out . The dependence upon e in is readily understood, since highly eccentric inner binaries are closer to the efficient GW-emission stage and can easily be driven to coalescence by a relatively mild perturbation from a third body. The dependence upon e out is likely due to the fact that quasi-circular outer binaries form a stable hierarchical triplet for a comparatively longer time during the inspiral of m 3 , hence leaving more room to the development of K–L resonances, which are efficient at driving the inner binary to coalescence. Conversely, in very eccentric outer binaries, m 3 soon interacts with the inner binary at pericentre, entering the chaotic phase. Chaotic interactions are more likely to result in ejections rather than mergers, hence suppressing the overall merger fraction. Figure 5. Merger fraction (colour coded) as a function of the initial inner ( e in ) and outer ( e out ) binary eccentricities. 3.1.1 Importance of PN corrections As pointed out in the previous section, the K–L mechanism can be suppressed by general relativistic effects. In particular, relativistic precession tends to destroy the coherent pile-up of the perturbation that the third body induces on the inner binary, hence effectively damping the K–L resonances. 5 In order to quantify the impact of the relativistic precession on the merger fraction and to compare our results with previous work that neglected this effect (e.g. Iwasawa, Funato Makino 2006 ; Hoffman Loeb 2007 ), in Table 3 and in Fig. 6 we compare, only for the case m 1 = 10 9 M ⊙ , the merger fraction obtained with and without 1PN corrections. Overall, the merger fraction is substantially higher in the case without 1PN terms (right-hand panel of Fig. 6 ). As can be seen, the largest differences compared to the full case occur for q in ≪ 1, where, because of octupole-order terms, the K–L mechanism is maximally effective. On the contrary, for large q in the merger fractions with or without 1PN corrections are similar, because, as previously discussed, coalescences are mainly due to chaotic strong encounters, rather than to K–L oscillations. Our results highlight the importance of K–L resonances in inducing MBH mergers in triple systems, and the need to account at least for 1PN corrections. Figure 6. Comparison between the merger fraction in the case m 1 = 10 9 M ⊙ , when the dynamics is evolved with (left-hand panel) and without (right-hand panel) 1PN term. The suppression of the merger fraction for low q in , due to 1PN precession, is clearly visible (see discussion in the main text). Table 3. Comparison of the merger fraction from the simulations with m 1 =


tips of the H 2 bow shocks, where the shock velocities are high and the gas will be dissociated, rather than behind the H 2 bow shocks (e.g., Davis et al. 1999 , 2000 ; López et al. 2010 ; Lee et al. 2014 ; Bally et al. 2015 ). Detection of further [Fe ii ] emission in G53.11_MM1 with high signal-to-noise ratio requires deeper imaging observations, although the marginal detection of [Fe ii ] emission can be interpreted as intrinsically fainter or absent [Fe ii ] emission compared to H 2 emission. In the outflows from high-mass YSOs, the [Fe ii ] detection rate with respect to the H 2 detection rate tends to be low, ≲50% or much less (Cooper et al. 2013 ; Wolf-Chase et al. 2013 ; Caratti o Garatti et al. 2015 ). The brightness of the [Fe ii ] lines also tend to be weaker than the brightness of the H 2 lines (Caratti o Garatti et al. 2015 ). This can be attributed to the different extinction effect between the two lines but it is more likely to happen because H 2 and [Fe ii ] emission arise from different physical conditions, such as gas density, temperature, or shock velocity. In the G53.11_MM1 outflow, the strong, extended H 2 emission with very weak or negligible [Fe ii ] emission may imply that slow, C-type shocks are dominant in G53.11_MM1. Further spectroscopic observations will be necessary to derive the physical conditions of the environment and confirm the shock’s properties. 5. Central YSOs The core G53.11_MM1 is bright from IR to millimeter, with a large IR-excess emission. The central star (YSO1) was previously identified in the Red MSX Source survey with a bolometric luminosity of (3–4) × 10 3 L ⊙ (G053.1417+00.0705; Mottram et al. 2011 ; Lumsden et al. 2013 ); however, it is in fact composed of two sources, YSO1 and YSO2, which are separated by ∼8′′ in the Spitzer mid-IR images with higher spatial resolution. Both YSOs are saturated in the MIPS 24 μ m image but their SEDs with strong excess in mid-IR and spectral indices derived by using the available photometry from the GLIMPSE and MSX catalogs classify them as Class I YSOs that have a dusty envelope infalling onto a central protostar (Kim et al. 2015 ). The two YSOs are also observed in near-IR wavebands. Both are fairly bright in the K -band, marginally detected in the H -band and are not observed in the J -band, which indicates that they are deeply embedded. The evolutionary stages of the YSOs, with the proximity to the center of the outflow (see Figure 2 ), suggest that one or both can be the driving source of the G53.11_MM1 outflow. The coordinates of YSO1 and YSO2 are ( α 2000 , δ 2000 ) = (19 h 29 m 1760, +17°56′233) and ( α 2000 , δ 2000 ) = (19 h 29 m 1726, +17°56′173), respectively. In the following, we will discuss their photometric variability in near-IR and physical parameters constrained from SED analysis. 5.1. Near-IR Photometric Variability YSOs are known to commonly show variability (e.g., Carpenter et al. 2001 , 2002 ; Morales-Calderón et al. 2011 ; Johnstone et


as well (see, e.g., Gromadzki et al. 2013 , for more details about light curves of S-type symbiotics). 3.4. Hot component and outburst activity The most prominent features in the light curves of Gaia18aen (Fig. 7 ) are the outbursts observed in 2018. In Fig. 8 , the part of the light curve showing the active stage is depicted. For clarity, the light curves in various filters were shifted to the same level to study the structure of the active stage. Individual brightenings are labeled by the numbers 0−5. Fig. 7. Light curves of Gaia18aen. Individual light curves in various filters were shifted to the level in the OGLE V filter for clarity; values of shifts are shown in the figure legend. Different colors denote different filters. Fig. 8. Outbursts of Gaia18aen. The colors are the same as in Fig. 7 . The vertical dotted lines indicate the individual brightenings (denoted by numbers 0−5). The arrows show the times when the two spectra were obtained. Fig. 9. Light curves in selected filters phased with the period of P = 486.9 d. Individual datasets were shifted to the level in the OGLE I filter. The first small pre-outburst of about 0.5 mag in V filter (denoted 0) was detected at JD 2 458 089. It was followed by more prominent outburst (1) after approximately 27 d (JD 2 458 116) of gradual decline. The maximal brightness during this outburst was ≈11.2 mag in V filter (JD 2 458 119), thus the amplitude was about 3.3 mag in comparison with the quiescent V magnitude (OGLE V ∼ 14.5). The analysis of the combined light curves constructed from the observations in various filters revealed the complex structure of this outburst with at least two another re-brightnenings that followed the first maximum. Approximately after 47 d (JD 2 458 163) after the first maximum Gaia18aen reached the magnitude similar to the brightness of the pre-outburst 0. The outburst denoted in this paper as 2 started after 57 d of a quasi-steady period (JD 2 458 220) and lasted for 35 d (until JD 2 458 255). The maximal brightness in V filter during this period was ≈12.5 mag. A third, small-scale outburst was detected at JD 2 458 357. The amplitude of the outburst was much smaller than in the previous cases, however, the approximate duration was similar to the outburst 2. Up-to-now, the last two increases in brightness (denoted 4 and 5) were detected at JD 2 458 470 and JD 2 458 503. It is worth noting that both brightenings were much shorter than the previous events, at 12 and 15 d, respectively. Moreover, the shape of at least the first event (4) looks as thought it was suddenly interrupted, which may indicate that both brightenings are part of a single outburst that is apparently interrupted by some obscuration process. Since JD 2 458 518, there were no other significant brightenings detected in the case of Gaia18aen. The amplitude of the outbursts and their duration resemble the behavior of typical classical symbiotic stars (e.g., AG Dra, Z And; see, e.g., Mikołajewska et al.


galaxies. These objects were used to draw conclusions about the AGN population that would be missed in optical and X-ray surveys. Of the 30 AGN candidates using the Jarrett et al. ( 2011 ) selection box and presented in Satyapal et al. ( 2014 ), only one object is in the mass and redshift range probed by our analysis here (the others are either at higher masses or higher redshifts), and it is found in our sample of star-forming dwarfs in the Jarrett et al. ( 2011 ) box (NSA ID 93798). Secrest et al. ( 2015 ) measured an X-ray luminosity from XMM-Newton observations (extracted with a ∼15′′ aperture) of L 2–10 keV = 2. 4 × 10 40 erg s −1 for this object, and claim that the W1 − W2 color is strongly indicative of AGN activity. While this object is indeed in the Jarrett et al. ( 2011 ) selection box, given the median uncertainties on the WISE photometry, its infrared colors are consistent with this object potentially being scattered from the primary locus of star-forming galaxies and it does not have a strong power law to longer infrared wavelengths as expected for an AGN. Sartori et al. ( 2015 ) presented a sample of 83 objects with photometry placing them in the Jarrett et al. ( 2011 ) selection box, using data from the older WISE All-sky data release. These authors only required S/N > 2 for detections in the W1 , W2 , and W3 photometric bands. We cross-matched against the more up-to-date AllWISE selection, and using a S/N cut of 3.0, we find that only 34 objects (∼41%) continue to fall inside the Jarrett et al. selection box. 9 9 All 83 of the objects in the Sartori et al. ( 2015 ) sample have updated AllWISE W1 and W2 photometry with S/N > 3.0, but 26 of the objects have W3 photometry with S/N 3, only 10 of which have 2 S/N 3. Of these 34 objects, only 15 are in our parent sample of dwarf galaxies. The remaining 19 objects are either not in the NSA because their redshifts are greater than 0.055, or are in the NSA but not classified as dwarf galaxies by our mass criterion. Looking closer at these 15 dwarf galaxies, 10 are found in Table 1 (NSA IDs 4610, 6205, 10311, 53934, 57649, 93798, 109919, 117162, 118025, and 118523), 4 of the 15 are BPT-selected AGNs or composite galaxies (NSA IDs 10779, 79874, 124050, and 125318), and one is the previously discussed quasar contaminant (NSA ID 110100). One object that was listed as a Stern et al. ( 2012 ) candidate but not a Jarrett et al. ( 2011 ) candidate in Sartori et al. ( 2015 ) moved into the Jarrett et al. ( 2011 ) selection box with the updated AllWISE photometry (NSA ID 98135), and one object we have listed in Table 1 does not appear in Sartori et al. ( 2015 ) (NSA ID 151888). 3.5. The Feasibility of Detecting Supermassive Black Holes in Dwarf Galaxies with WISE Finding evidence for AGNs in dwarf galaxies is challenging as AGNs at a given accretion rate have lower bolometric luminosities due to the smaller masses of the central black holes, making them harder to observe above the emission due


It is defined as the standard deviation of the differential light curve over each of the five rotations (Mathur et al. 2014 ). In the analyses below, all three of these measures were tried and found to be essentially equivalent for the purpose of correlating brightness with variability. The method actually employed in this paper is the re-sampled fit to the smoothed R loc ; we will call this R smo . This leads to a set of both absolute brightness and variability measurements at the same 45 time points in each light curve. A few illustrations of these sets are provided in the upper panel of Figure 11 . A linear fit is made to each set of points, and both the slope and Pearson-r correlation coefficient are computed. For the small and large red asterisks, the [slope, Pearson-r] values are [−0.14, −0.91] and [−0.92, −0.84]; for the small and large pluses, they are [0.16, 0.87] and [0.59, 0.53]; and for the small and large black diamonds, they are [0.00, 0.01] and [−0.20, −0.30]. The KIC numbers for the stars shown (in the same order) are 5302725, 9334867, 8078753, 11014223, 2694810, and 11299398. Shown in aqua in the lower panel are the 12 stars that MTF17 identified as exhibiting clear activity cycles over 4 years of observations (their Figure 5 ). Four of these are very clear-cut cases of spot dominance (those with the most negative r coefficients and slopes), two are unclear (those above the lower dotted line), and the rest are distributed along a continuum of spot dominance. Figure 11. Upper panel: five illustrative sets of brightness vs. variability. They have been scaled and shifted to fit on the plot. Color and symbol size are related to slope (see text). Lower panel: slopes of the linear fits to the brightness vs. variability points for all stars; the ordinate is the Pearson-r coefficient for each star. The colors indicate the designations from MTF17 based on the sign of their correlation slopes (see text). Green points are stars with clear brightness cycles in MTF17. MTF17 divided the sample into three cases: anti-correlated (red), correlated (blue), and not clear (black); the colors in Figure 11 correspond to their classification. As explained in Section 2.1 , the “anti-correlated” label is used for stars that become brighter as they become more variable; they are generally interpreted to be faculae-dominated. The points for such stars have a positive slope, so they should lie in the upper right quadrant of the lower panel of Figure 11 , which shows the results for the full sample. Similarly, the blue (correlated) stars get darker as they get more variable (spot-dominated) and are in the lower left quadrant. Most stars from the sample (320 in MTF17; 322 for us) are in this category. In most cases (310 stars), their sense agrees with ours, although there are a few red points in the lower left quadrant, and stars that they did not classify in either category (black) are found in both quadrants for us. The most likely source of discrepancies


of the solar wind at 1au is a few km s −1 ( Němeček et al. 2020 ), which is small compared to the average radial wind speed of 400–600 km s −1 . Despite this, attempts to constrain the solar wind AM flux have been made in the past (e.g. Lazarus Goldstein 1971 ; Pizzo et al. 1983 ; Marsch Richter 1984 ; Finley et al. 2019 ). Though each of these studies suffered from uncertainty, either due to the precision of the spacecraft pointing or the ability of the plasma instruments to detect the small tangential flows. These uncertainties are lessened with Parker Solar Probe (PSP) which samples the solar wind within 0.25 au, where the signal to noise on the tangential wind speed measurements should be increased and the influence of wind-stream interactions reduced. However, during its first few encounters, PSP detected tangential solar wind speeds of up to ~ 50 km s −1 ( Kasper et al. 2019 ). These speeds are far greater than expected from magnetohydrodynamic (MHD) modelling (e.g. Réville et al. 2020 ) and, if they were prevalent throughout the corona, would be incompatible with the AM-loss rate implied by the slope of the rotation-age relation. Finley et al. (2020) analyse the data from the first two orbits of PSP and show these flows to be localised, existing along with wind streams that have large negative tangential speeds. Therefore, the average equatorial solar wind AM flux measured by PSP is similar to observationsfrom previous spacecraft. At present, the mechanism(s) that generate these large tangential solar wind speedshave yet to be determined. One possibility is the motion or circulation of open magnetic flux at the base of the wind ( Crooker et al. 2010 ; Fisk Kasper 2020 ; Macneil et al. 2020 ), though this is also not well understood. During PSP’s first two perihelion passes (E01 and E02, respectively), neither the Solar Probe Cup (SPC, Case et al. 2020 ) or the Solar Probe ANalysers (SPAN; Whittlesey et al. 2020 ; Livi et al. 2020 ) were able to confidently measure the properties of the alpha particles in the solar wind. Previously, Pizzo et al. (1983) used Helios observations to show that the alpha particles contain a large negative contribution to the total AM flux (see also Marsch Richter 1984 ). Though, due to an error in spacecraft pointing, the data from Helios required a significant correction, and more recent measurements of the alpha particle AM flux using the Wind spacecraft at 1au instead suggest a much smaller (but still negative) contribution ( Finley et al. 2019 ). As the alpha particles carry roughly 15− 40% of the linear momentum in the solar wind, it is vital that their contribution to the total solar wind AM flux is better understood in order to further constrain the slope of the rotation-age relation for Sun-like stars. In this work, we analyse more recent SPAN-Ion observations from the third and fourth encounters of PSP (hereafter E03 and E04), which we use to determine the mechanical AM flux of both the solar wind


equation of state (EOS) has been studied for hydrodynamic turbulence and for a polytropic EOS (Federrath Banerjee 2015 ) or an adiabatic EOS (Nolan et al. 2015 ; Mohapatra Sharma 2019 ), indicating additional dependencies, on (for example) the adiabatic index γ , the relation between density fluctuations and . In the magnetized case the majority of studies focus on the isothermal case , finding an additional dependency on the ratio of thermal to magnetic pressure (e.g., Kowal et al. 2007 ; Padoan Nordlund 2011 ; Molina et al. 2012 ). Overall, a highly dynamic picture of turbulence has been found, challenging our ability to examine the general case. In this paper, we present adiabatic magnetohydrodynamic simulations of stationary turbulence in the subsonic ( to 0.6), super-Alfvénic (), and high (ratio of thermal to magnetic pressure with ) regime. This regime approximates the turbulent intracluster medium (ICM; Brunetti Lazarian 2007 ; Brüggen Vazza 2015 ) even though our magnetohydrodynamics (MHD) model neglects effects stemming from low collisionality (Schekochihin Cowley 2006 ; Schekochihin et al. 2008 ). However, studies including effects from low collisionality, e.g., through the Chew–Goldberger–Low MHD model, found that they generally introduce only small differences compared to the MHD model, e.g., a small increase in density fluctuations (Kowal et al. 2011 ; Santos-Lima et al. 2017 ), but leave imprints on Faraday rotation maps (Nakwacki et al. 2016 ). Here, we specifically focus on the effects of departure from an isothermal equation of state by varying the adiabatic index γ and the cooling function between simulations. The rest of this paper is organized as follows. In Section 2 , we introduce the numerical setup and the simulations conducted. In Section 3 , we present results from analyzing the simulations starting with a high-level overview of the energy spectra, to correlations in the stationary regime, to statistics of distribution functions that can potentially be used to break degeneracies between the thermodynamics and sonic Mach number. The results are discussed in Section 4 , and we conclude with a brief outlook in Section 5 on how our findings point the way to future measurements that can be used to better diagnose the properties of turbulence in astrophysical plasmas. 2. Numerical Details In this work we utilize the equations of compressible, ideal MHD equations that are closed by an ideal equation of state , with γ as the ratio of specific heats. The symbols have their usual meaning, i.e., density ρ , velocity , total pressure consisting of thermal pressure and magnetic pressure , and magnetic field , which includes a factor . Cooling is included via and is the total energy density with specific internal energy e . Vector quantities that are not in boldface refer to the L 2 norm of the vector and ⨂ denotes the outer product. The details of the acceleration field that we use to mechanically drive our simulations are


again. The velocity is calculated by dividing the distance that the center of the BD moved by the time between recordings. The image was then advanced again and this process is repeated until the BD disappears or merges with another BD. Because the lifetime of the BDs is variable, the time between recordings varies, but as a general rule the number of recordings is maximized (minimizing the time between each recording) but there are at least 11 s between each recording. The average velocity of a BD is the average of these multiple velocity measurements. The speed was measured for only 25 BDs because there were not enough data points for five of the BDs. Figure 3 (i) is a scatterplot between the speed and the ratio of length-to-width of the BDs. We plot this figure in an attempt to find a correlation between how long a BD is relative to how fast it is moving (the thought being that faster BDs might be elongated in the radial direction), but evidently there is no clear relationship; there is perhaps a slight tendency for faster BDs to have less elongation. To investigate the formation mechanism and temperature of these BDs, we obtained their light curves from five AIA channels. Figure 4 shows the light curves of four of our BDs. These light curves are made by tracking the BD from when it first begins to brighten, through peak intensity, and ending when it fades from view or gets dim enough. To measure the intensity, we first find the target BD using the Hi-C 193 Å images and then match the location to the AIA 193 Å images. We center a circle on the BD's brightest part and measure the intensity inside. The frame is advanced and the intensity is measured for the new time, again with the circle centered on the brightest part of the BD. In this way, we track the BD's peak brightness over its lifetime or over its brightest peak during its lifetime. This intensity is then normalized to the highest intensity over the period. Figure 4. Normalized light curves for four example BDs from a set of five AIA bands. Each set of light curves is from tracking the brightest part of the BD as it drifts laterally during its peak brightening. As denoted in each panel by different colored lines, orange is for 193 Å, pink is for 211 Å, yellow is for 171 Å, green is for 1600 Å, and red is for 304 Å. Please note that the time on the x -axis is based on the AIA 193 Å channel; the closest available data in time for other channels is taken at each time step. Therefore, a few seconds’ difference in the observation of different channels is not seen. Asterisks on the 193 Å light curves mark data points. We use four AIA wavelengths in addition to the 193 Å: 211, 171, 1600, and 304 Å. The AIA 171, 193, and 211 Å channels are typically coronal, as their response functions peak at temperatures of roughly 1, 1.5, and 2.5 MK, respectively (Lemen et al. 2012 ). However, all of these channels have cooler-TR lines in the passband and hence have some response in the cooler-TR


in the W 1 and W 2 bands and are characterized by W 1 − W 2 0.5 mag. Instead, the red W 1 − W 2 > 1 of our objects imply a considerable contribution of the warm and hot dust to their mid-infrared luminosity (Izotov et al. 2014a ). Three out of five galaxies were detected by WISE in the W 4 band at 22 μm. The estimated ratio of the 22 μm luminosity, which is a characteristic of warm dust, to the luminosity absorbed at 1500 Å in these galaxies is of order of unity (Table 9 ). As the luminosity of the cold dust emitting in the far-infrared range of extreme starbursts (not accessible to WISE ) is less or comparable to the luminosity of the warm dust (Izotov et al. 2014b ), we conclude that the UV luminosity absorbed in visible star-forming regions of our galaxies is consistent with the luminosity emitted by dust in the infrared range. Optical, near- and mid-infrared observations of other low-metallicity SFGs with similar properties suggest that they are relatively transparent (Izotov Thuan 2011 , 2016 ). That there is not much dust-obscured hidden star formation is also implied by the observed thermal free–free cm radio emission in dwarf galaxies with optical and infrared observations. Its flux density is consistent with the value derived from the flux density of the H β emission line (Izotov et al. 2014b ), indicating that there is not a considerable amount of additional star formation, not seen in the UV range, in our galaxies. 10 DISCUSSION To the best of our knowledge, our experiment is the first where compact SFGs with strong emission lines and high [O iii ]λ5007/[O ii ]λ3727 ratios are observed in the LyC. Furthermore, the entire sample (five out of five) at z ∼ 0.3 is found to emit LyC radiation, with absolute escape fractions ranging between 6 per cent and 13 per cent. Our observations thus significantly expand the sample of LyC leakers at low redshift, from four previously known galaxies (Leitet et al. 2013 ; Borthakur et al. 2014 ; Leitherer et al. 2016 ) to nine. The newly discovered sources also show significantly higher LyC escape fractions, compared to f esc (LyC) ≈ (1–4.5) per cent previously found. Apparently, the selection criteria we adopted are very efficient in finding LyC leakers. As such, this finding is probably one of the most important results of our study. Compactness and a peculiar emission line ratio as selection criteria, were previously already suggested to be related to LyC leakage. Jaskot Oey ( 2013 ) and Nakajima Ouchi ( 2014 ) have proposed that extreme [O iii ]λ5007/[O ii ]λ3727 ratios may be due to high escape fractions of ionizing photons and have argued that this could be the case for some ‘GP’ galaxies at z ∼ 0.1–0.3 or in z ∼ 2–3 LAEs. For comparison, Heckman et al. ( 2011 ) examined so-called Lyman-break analogues (LBAs) and suggested that a subset of them, those with a compact massive (∼10 9 M ⊙ ) dominant central object, could be LyC leakers. The LBAs have lower excitation and higher masses compared to


and 180° to the phase space densities at 90° are greater than three. It is easy to see that strong depletions occur within the first bar, and the depletion CSE interval was removed when we estimated the percentages of CSEs. One can also see that the bars in the rear half have two short intervals, which are caused by scattering of strahl electrons. We therefore identify the two short intervals as CSE strahls, and the percentage of CSE strahls is about 35%. Fig. 1. Suprathermal electron pitch angle distributions of 272 eV, magnetic field and plasma data measured by ACE during the October 21C22, 1999 ICME passage. The two vertical dashed lines denote the boundaries of the ICME. Furthermore, this study examined all the suprathermal electron PADs of the 272 ICMEs and estimated the percentages of CSEs. The results are listed in the sixth column of Table A.1 . Only 10 (9.9%) of the 101 MCs have no CSE, and the ratio is consistent with the results of Shodhan et al. (2000) , who examined the CSE signatures of 52 MCs and concluded that 6 MCs have no CSEs. As for the other 91 MCs, the percentage of CSEs varies from 6 to 100%, with a mean value of 57%. Meanwhile, 75 of the 171 nonMC ICMEs (43.9%) do not contain CSEs. The fraction of ICMEs without CSEs is thus clearly larger in nonMC ICMEs than in MCs. The extensive difference may imply that the two groups have different magnetic structures. For the other 96 nonMC events, their mean CSE percentage is 45%, which is smaller than for the MCs (57%). Among the 96 nonMC ICMEs, 21 have greater than 70% CSEs. Examination of the magnetic field component curves of these 21 ICMEs reveals that fields of most events have neither apparent smooth rotations nor disorder, but their magnetic field component curves have only slight rotations, and they are relatively stable or even close to the line. It is well known that most MCs can be described with a constant force-free field configuration, for example, the Lundquist solution ( Lepping et al. 1990 ; Feng et al. 2006 ). According to the Lundquist solution, the shapes of measured field component curves depend on the distance d 0 between the spacecraft trajectory and the rope axis (see Figs. 2–4 of Feng et al. 2006 ). The spacecraft will measure center-enhanced and bipolar curves if the spacecraft trajectory is close to the rope axis; otherwise, the bipolar curves will disappear. Figure 2 shows the variations of the magnetic field components for the case of d 0 = 0.9 R 0 , where R 0 is the radius of the flux rope, z is the axial direction, x is the radial direction pointing to the satellite contact position, and the direction y is obtained from the cross product of z and x . In Fig. 2 , all the three magnetic field components are relatively stable and exhibit only slight rotations. These trends indicate that the spacecraft that passes through the flank of a magnetic flux rope will measure relatively stable magnetic field variations. Therefore, the 21 highest percentage (more


calculations and the applicability of their formula for C-rich AGB stars with Z ini 10 4 should be checked by using the appropriate values. Also, the dependence of the mass-loss rate on the velocity amplitude of pulsation should be investigated, since the dependence is considered to be more sensitive for stars with larger C and R . The mass-loss rate derived from the DDW model is significantly smaller than the mass-loss rate assumed in stellar evolution calculations. If we use the derived mass-loss formula after the necessary condition for the efficient DDW is satisfied on the TP-AGB, the dredged-up carbon accumulates in the surface regions; accordingly, the effective temperature decreases and the mass-loss rate could increase. Although in the present calculations the derived mass-loss rate is inconsistent with the assumed mass-loss rate, it should be recalled here again that the hydrodynamical model can derive the properties of the DDW by specifying a set of input parameters, being independent of the stellar evolution model. Thus, the derived formulae, together with a necessary condition for the efficient DDW presented in Section 5.1 , could enable us to evaluate the mass-loss rate and dust yield during the C-rich AGB phase of stars with Z ini 10 4 in a manner consistent with stellar evolution, including whether the efficient DDW can operate on the C-rich AGB. 5.3 Implication for evolution of C-rich AGB stars and the dust-driven wind in the early Universe Investigations on the formation of stars in low-metallicity environments have revealed that the critical metallicity Z cri for the transition from Population III to Population II stars is as low as 10 9 10 7.5 , depending on the depletion factor of metal into dust (e.g. Omukai etal. 2005 , Schneider etal. 2006 , Chiaki etal. 2015 ). Although there is no information available for the initial mass function at the present time, intermediate-mass AGB stars with Z ini 10 4 can contribute to the enrichment of dust in the early Universe if the condition for the efficient DDW derived in the previous subsection is satisfied during the TP-AGB phase. However, the possibility of developing dust formation and a resulting DDW on the AGB is strongly influenced by the mass-loss history during the evolution, on which the time evolution of effective temperature as well as the elemental composition and opacity in the surface layer depend strongly through the number of TDU episodes and/or the occurrence of HBB. At present, we have no knowledge of the mass-loss mechanism and mass-loss rate before the onset of the DDW for the extremely low-metallicity stars considered in this article. In recent investigations focused on low-metallicity (1.6[Fe/H] 0.5) AGB stars observed in distant galaxies, Rosenfield etal. ( 2014 , 2016 ) showed that a mass-loss rate higher than SC05 is required during the AGB phases previous to the onset of the DDW, to reproduce the observed TP-AGB luminosity function as well as the number


the tail in the velocity distribution is produced independently of η, with velocities up to ∼1000 km s −1 . However, different eccentricities do not change the shape of the distribution function with respect to the case of the circular orbit. Therefore, these results suggest that the energy exchange between the generic star of the GC and the BHB is almost independent on the eccentricity, depending only on the initial total energy of the binary. Figure 3. Comparison among the velocity distributions of escaping stars for an SMBHB with mass ratio ν = 1/4 and different eccentricities (η = 0, 0.25, 0.75). The distributions are cut on the left side at 212 km s −1 , which corresponds to the escape velocity from the system evaluated at 20 pc. For what regards the branching ratios, Table 2 shows the branching ratios as function of η. From this table, it is clear that the branching ratio remains nearly constant for different eccentricities. Therefore, not only the shape of the velocity distribution is preserved, but also the probability of star ejection. Table 2. The values of the Branching Ratios (BR) for ν = 1/4 and different BHB orbital eccentricities, η. To conclude, the BHB orbital eccentricity does not affect neither the shape of the velocity distribution nor the branching ratio of ejected stars. Therefore, the main features of the ejected stars depend on the binary mass ratio ν, but not on the binary eccentricity. 3.3 The role of the GC orbital inclination In our scattering experiments, the GC orbits are coplanar with the BHB orbital plane. This means that the angular momentum of the GC and that of the BHs are aligned. In order to explore the role of the GC orbital inclination, we performed a set of simulations in the extreme case of GC orbits perpendicular with respect to the BHB orbital plane, in the case of mass ratios ν = (1/20, 1/10, 1/5, 1/3). The results of our scattering experiments reveal that the GC orbital inclination plays an important role both for the branching ratio and the resulting velocity distribution. Fig. 2 shows the branching ratios for both the coplanar and perpendicular cases. In the perpendicular case, the branching ratios of the ejected stars are reduced. Actually, the angle between the two angular momentum vectors results to have an important role in the output of the scattering experiments, as the relative inclination of the angular momenta of the GC and of the test star has. Therefore, the actual value of the branching ratio comes from a combination of two effects due to the two-mentioned relative inclinations. Calling β and γ the angles between the pairs of (GC, BHB) and (test star, GC), respectively, the higher probabilities are obtained when β ∼ 0 and γ ∼ 0. Finally, when ν ≲ 1/20, the branching ratio tends to the value of the single BH case, for which β is not defined and consequently only γ has a role in the output. The effect of the GC orbital inclination is significant also in the velocity distribution of the


the numerical code. The second term is the source term, , which describes the injection of new power-law particles into the causal volume. In general, S ′ ( p e ) receives contributions from other processes, such as Compton scattering, pair-production and annihilation. The advection coefficient for the adiabatic cooling of particles is given by Here, we have used the scaling of particle energy with comoving volume due to adiabatic expansion, such that where is the adiabatic index for a relativistic (non-relativistic) particle distribution. In general, the advection coefficient includes contributions from other processes that change the energy of particles, e.g. Compton scattering, synchrotron cooling, Coulomb interactions, and particle heating (as described below). The adiabatic cooling timescale is obtained from the rate of volume expansion, where where ζ = 7/3 for r r s when Γ ∝ r 1/3 , and ζ = 2 for r ≥ r s when Γ = Γ ∞ . By expressing the LHS of equation ( A3 ) using the number density, we find where we have conveniently defined the comoving growth time of the causal volume, , through Next, we use equation ( A2 ) to express the rate of change of the comoving number density with comoving time in terms of and the causal volume , so that which in turn implies where the comoving particle injection time into the causal volume is defined by and is the particle injection rate per unit volume. Note that the causal comoving volume grows faster than the total comoving volume V ′ since it occupies an increasing fraction of it, , where . Now, using equations ( A3 ) and ( A6 ) lead to the equation for the number density evolution where . By integrating the above equation over p e , it can be shown that the adiabatic cooling term vanishes and , where so that the equation reads . The comoving rate of particle injection per unit volume per unit dimensionless momentum comprises of two terms, where a fraction ξ of the total is accelerated into a power-law (non-thermal) distribution and the remaining fraction (1 − ξ) forms a thermal distribution, where represents the normalized momentum distribution. The total energy density per unit rest mass energy of the injected distribution can be expressed as where 〈γ e 〉 th is the mean energy per rest mass energy of the thermal distribution and for the power-law distribution 〈γ e 〉 nth is given in equation ( 10 ). Here, we make the assumption that the injected thermal particles are cold, so that . The momentum distribution of power-law electrons is given by The normalization is obtained by equating the rate of energy injection per unit volume to that given to the electrons due to dissipation, such that which for γ M > γ m ≫ 1 gives where we take γ M = γ max , the maximum LF corresponding to the outer boundary of the particle momentum grid in the simulation. The efficiency of acceleration is controlled by the mean energy of the power-law electrons, which depends on ξ, and ultimately by the minimal energy of power-law


in the magnitude range where our analysis is conducted ( g 24). This procedure was repeated 10 4 times and the corresponding distributions of N syn and μ V, syn were computed. The number of stars contained within the same magnitude limits defined above was counted in the observed CMD and the density of stars per square degree Σ obs was calculated by dividing by the sampled area. The fractions f N of random extractions with N syn Σ obs and the fractions with μ V, mod > μ V, max were then computed. If the MS star density estimated around the sample of observed GCs were compatible with that predicted by models, the distribution of percentiles would be uniform. In Fig. 7 , the cumulative distributions of percentiles of the eight GCs at d ⊙ 45 kpc with respect to the N syn distribution of the five Aquarius simulations are shown. On average, the distribution of percentiles is consistent with a uniform distribution (although a vast range of lumpiness is covered by the five considered simulations), indicating a general agreement with model predictions for three out of five simulations. A Kolmogorov-Smirnov (KS) test indicates probabilities 0.1 P 0.2 for these simulations . However, the simulations Aquarius D and Aquarius E show opposite trends with distributions of percentiles that are incompatible with observations. Note that Aquarius D is the most massive halo among the five simulations of the Aquarius sample, with a virial mass M = 2.52 × 10 12 M ⊙ , exceeding the current estimate for the Milky Way (Patel, Besla Mandel 2017 ). It is therefore likely that the number density of the halo is also overestimated in this simulation. On the other hand, simulation Aquarius E is the one with the lowest fraction of stars in the diffuse halo at distances d GC > 20 kpc, with the majority of stars in this distance range contained in bound satellites. For this reason, the number density outside satellites turns out to be lower than those in other haloes. Figure 7. Cumulative distribution of percentiles in the number density domain for the eight GCs at d ⊙ 45 kpc. Different lines refer to the various cosmological simulations. The probabilities associated with the KS test are also indicated. The same conclusion can be drawn when the entire sample of 14 GCs is considered in the μ V space. The distributions of extracted surface brightness from each of the considered simulations are shown as a function of heliocentric distance in Fig. 8 . We note that the background surface brightness distribution is peaked at values in the range 30 μ V, syn 35 mag arcsec −2 following a declining trend with distance. At large distances, the surface brightness distribution becomes skewed with a tail towards bright values at μ V, syn 34 mag arcsec −2 . This is a consequence of the increasing degree of lumpiness of the halo at large distances: GCs forming within satellites in an early stage of dissolution are still surrounded by the compact remnant of their host galaxy. The upper limits


it was about 3 per cent) to about 4.5 per cent at the time of our observations. In this spectral region, we have not detected any change between 2015 and 2018, but data obtained in 1995 were in between the values measured in the two epochs. At 6800 Å, data obtained by Putney ( 1995 ) show the lowest values among all data sets (∼1 per cent). Our BBP measurements in the red (4.0 per cent integrated over a R filter) are consistent with the relatively recent BBP measurement of Butters et al. ( 2009 ), who had detected a signal of 4.06 ± 0.16 per cent. In conclusion, we have clearly detected a change of 1.5 per cent over a 40+ yr interval, but found no evidence of change over a time-scale of the order of three years. 8.3 Linear polarization No large changes of the fraction of linear polarization are detected either on a short (3-yr) or long (40-yr) time-scale. However, over a 40–45 yr interval of time, the position angle has definitely changed by more than 10° both in the blue and the red. In the following, we look at the various linear polarization spectra and their differences in more detail. On the long time-scale sampled by the difference between the 1970s data and our recent ISIS spectra (40 yr), there definitely are changes. In particular, below 4000 Å, the recent level of linear polarization sampled by Q / I seems to have decreased, while that sampled by U / I is larger. This corresponds to a very significant rotation of the position angle of the linear polarization away from the value of ∼20° found in the 1970s to about 33° in recent times. We note that the measurement by West ( 1989 ) obtained 1986 suggests also a decrease of linear polarization compared to the 1970s (3.19 per cent in the B filter, for a position angle of 19.1 ± 0.8) but as discussed in Section 4.3 , these kinds of comparison should be made with caution. It is notable that although the circular polarization is quite different from zero throughout the visible spectrum, the non-zero linear polarization is present essentially below 5500 Å, with possible low-level features suggested by the Steward spectrum, but largely absent from the lower resolution MCSP data. The position angle in the red as measured in the 1970s was around 110°, with a fair amount of scatter due to the small but not quite vanishing amplitude of Q and U in that region. In the ISIS data, both Q and U are also close to zero, therefore the position angle has a large uncertainty, but is consistent with a 10°–30° rotation from the value measured in the 1970s. We conclude that linear polarization measurements are certainly variable over a time-scale of decades, mostly in terms of a rotation, while no significant variation has been detected on time-scale of three years. A rotation constant in wavelength provides a first rough description of the change in linear polarization. 9 CONSTRAINTS ON THE ROTATION PERIOD OF Grw+70° 8247 Measurements of the position angle of the broad-band linear polarization of Grw+70°


also do not show another source within the NACO FoV, indicating that both BHB2007-2AB and VLT 171104.07-272258.8 are more evolved than BHB2007-1. In the analysis we also calculated the photometry in the K S band of BHB2007-2AB and VLT 171104.07-272258.8, listed in Table 2 . Table 1 Astrometric Measurements of the Components Measured with Respect to the Central Source [BHB2007]-1 Table 2 Apparent Magnitudes of the Components Measured with Respect to the Central Source [BHB2007]-1 3.3. Stellar Properties Here we calculate the stellar properties of [BHB2007]-1 and -2 based on the Gaia EDR3 parallax (see Section 3.2 ) and the notion that [BHB2007]-2 is a binary system. We collected the B-to-W4-band photometry of −1 and −2 from Vizier. We investigated the ASAS-SN light curves (Kochanek et al. 2017 ) finding that the visual brightness of both stars is only moderately variable ( mag over years). We adopted a Phoenix model of the stellar photosphere (Hauschildt et al. 1999 ) with the effective temperature constrained by Covey et al. ( 2010 ) ( K and K, for −1 and −2, respectively, with typical uncertainties of ±300 K) and visual extinction calculated from the observed colors between the R , I , and J bands, and stellar luminosity L * from the integrated photospheric model. For [BHB2007]-1, this yielded mag and . However, the edge-on geometry of the disk (see Section 3.4 ) may in principle yield an underestimation of the luminosity. In fact, stars with very inclined disks appear on average older (since less luminous) than the other stars (see Garufi et al. 2018 ). As for [BHB2007]-2, we first had to consider the visually triple nature of the star (see Section 3.1 ). All three stars sit within the 2MASS beam, meaning that the observed photometry is a contribution of all of them. We computed the actual J -, H -, -, and W 1-band magnitudes through the relative flux ratios measured in our NACO images. We then constrained visual extinction and stellar luminosity of [BHB2007]-2A assuming that the constrained by Covey et al. ( 2010 ) refers to this star since it is significantly brighter than the other two. We found that the is comparable with that of [BHB2007]-1 (1.5 ± 0.4 mag) while the luminosity is . Finally, we constrained stellar mass M * and age t of the two sources through multiple sets of pre-main-sequence tracks (Baraffe, MIST, and Parsec; Baraffe et al. 2015 ; Dotter 2016 ; Bressan et al. 2012 ). Bearing in mind the assumptions and the uncertainties described above, we found and Myr for [BHB2007]-1, and and for [BHB2007]-2. The stellar mass of [BHB2007]-1 is significantly smaller than what was constrained by Alves et al. ( 2020 ) from the position–velocity diagram of the CO emission (2.23 ). Such a large discrepancy cannot be explained by an erroneous estimate of the stellar luminosity alone since the evolutionary tracks corresponding to stars with K are nearly vertical, making the stellar mass only marginally impacted by the luminosity.


of 1.5. Convection sets in close to the point where the cold branch of the S-curve ends which leaves this point sensitive to α ml . This effect is even stronger on the critical point where the hot branch starts, as this is where convection is the strongest. Higher values of α ml shift both critical points at which the S-curve bends closer together, leading to a smaller Q Σ crit . This alters the global behaviour of the disc and the outburst properties: the decay from the outburst in a disc with $α ml $ = 6 starts at higher Σ and higher T eff , and less mass is accreted and accumulated in the disc during the outburst cycle. Therefore, more efficient convection produces outbursts that are more frequent and of lower amplitude, and even lack quiescent phases. While it is important to note that this lack of quiescence may be related to uncertainties in the end of the lower branch, there are other ways out. In the discussion below, we examine a few options to restore or modify quiescence. The comparison of DIMRI with $α ml $ = 1.5 and DIMa (Figs 10 and 9 c) highlights the importance of changing the dissipation profile, as this is the only difference between these two models. The main difference is that the outbursts in DIMRI with $α ml $ = 1.5 are wider and the quiescence is longer than in the DIMa light curve. Changing the mixing length parameter is not the only way to increase the outburst amplitude and restore quiescent phases to the DIMRI models. Increasing the mass transfer rate, while all other parameters are fixed, makes the disc hotter and denser. This means that the surface density everywhere in the quiescent disc is closer to the critical value and the disc luminosity is higher. The result is more frequent lower amplitude outbursts for higher mass transfer rate regardless of model, as illustrated by comparing the two mass transfer rates shown in Fig. 9 for each of our three models. Hence, merely reducing the mass transfer rate in the DIMRI model can increase the outburst amplitude and restore quiescent phases. If one sets as low as g s −1 in the DIMRI (with α ml = 6), the elapsed time between two consecutive outbursts starts to be longer and also the outburst amplitude rises (see Table 1 and Fig. 11 ). Note that for such a low , the discs in DIM and DIMa become cold and stable. There is yet another alternative way to restore quiescence in the DIMRI light curves. Observed X-ray fluxes in quiescent dwarf novae are far too large compared to what models predict. A solution to this problem is a truncation of the inner disc. Numerical calculations by Hameury, Lasota Warner ( 2000 ) and Schreiber, Hameury Lasota ( 2003 ) confirm that truncating the inner disc has substantial influence on the dwarf nova light curves and may solve the discrepancy between observations and theory. This truncation may be caused by the magnetic field of the primary white dwarf. A white dwarf magnetic field in the range 10 4 –10 7 G (which translates to a magnetic