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

stellar mass growth that for individual massive galaxies. At a fixed space density threshold of density of , the most massive blue galaxies are ∼0.3 dex lower in stellar mass than the most massive red galaxies (i.e., half the mass). While we expect the most massive red galaxies to remain on the red sequence and increase in mass via mergers, it is likely that the most massive blue galaxies have star formation quenched and then move onto the red sequence. The rate at which massive red galaxies increase in stellar mass through mergers with smaller galaxies appears to slow somewhat from ∼0.4 dex per unit redshift for z = 1.1 to z = 0.7 to ∼0.2 dex per unit redshift for z = 0.7 to z = 0.3. We know that massive early-type galaxies must have grown in stellar mass because observations clearly show them experiencing mergers sufficient in frequency and mass ratio to give rise to a significant increase in stellar mass. In fact, merger studies have produced a range of estimates of stellar mass growth. For example, van Dokkum ( 2005 ) found a stellar mass increase due to mergers in massive red galaxies of per Gyr, which implies a stellar mass increase over the 4.7 Gyr from z = 1.1 to z = 0.3 of ×∼1.4. Similarly, López-Sanjuan et al. ( 2012 ) found stellar mass growth in massive early-type galaxies due to mergers of ×∼1.3 from z = 1 to the present. On the other hand, Masjedi et al. ( 2008 ) found that luminous red galaxies were growing due to merger activity at a much slower rate: at least per Gyr on average at redshift ∼0.25, implying at least 8% growth from z = 1.3 to z = 0.3. The lack of evolution (in comoving coordinates) of the spatial correlation function of massive red galaxies also clearly indicates that the most massive red galaxies must be undergoing mergers. White et al. ( 2007 ) used observations of the clustering of luminous red galaxies to show that about one-third of the most luminous satellite galaxies appear to have undergone merging or disruption with massive halos between z = 0.9 and z = 0.5, while Brown et al. ( 2008 ) found that massive red galaxies grew by ×1.3 from z = 1.0 to z = 0. As with SMD evolution, our stellar mass growth measurements for massive red galaxies based on SMF evolution (×1.7) are comparable with the those implied by comparison of the K -band LF with passive evolution (×1.4). 10.4. Stellar Mass Evolution—Errors In addition to the sources of error inherent in measuring K -band luminosity evolution (Section 9.4 ), we have one very significant additional source of error in measuring stellar mass evolution—namely, uncertainty in stellar mass-to-light ratios M / L K —and we include this in Table 5 for red galaxies. M / L K uncertainties arise from the evolving M / L K –rest-frame ( B − V ) relationships in Equations ( 3 ) and ( 5 ). We take the intrinsic random variation in between galaxies to be 0.1 dex (Section 5 ). Systematic uncertainties arise from the fact that Equations ( 3 ) and ( 5 ) are derived from SPS


O B-Observatory I-Observatory O O O B-Organization I-Organization O O O O O O B-Organization I-Organization I-Organization B-Grant O O O O B-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization O B-Telescope I-Telescope I-Telescope O O O O O O B-Observatory I-Observatory O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O O O O B-Organization I-Organization O B-Location O O O O O O O B-Database I-Database O B-URL O O B-Database I-Database I-Database B-Database O O O O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Survey I-Survey I-Survey I-Survey O O O O O B-Mission I-Mission I-Mission O O O O

The Arecibo Observatory is operated by SRI International under a cooperative agreement with the National Science Foundation (AST-1100968), and in alliance with Ana G. Méndez-Universidad Metropolitana, and the Universities Space Research Association. The Nançay Radio Telescope is operated as part of the Paris Observatory, in association with the Centre National de la Recherche Scientifique (CNRS) and partially supported by the Région Centre in France. This research has made use of the HyperLeda database ( http://leda.univ-lyon1.fr ), the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration, and the Sloan Digital Sky Survey which is managed by the Astrophysical Research Consortium for the Participating Institutions.


B-Citation I-Citation I-Citation I-Citation O O O O O B-Dataset I-Dataset O O O O O O B-Dataset I-Dataset O O O B-Dataset I-Dataset O O O B-Formula O O O O O B-CelestialObject I-CelestialObject O O B-Dataset I-Dataset O O O O O O O O O O O O O O O O O O O O O O O B-Software B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O B-Software O O O O B-Model I-Model I-Model B-Model B-Citation I-Citation I-Citation O O O B-Model I-Model I-Model B-Model B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Dataset I-Dataset O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O B-Dataset I-Dataset O O O B-CelestialObject I-CelestialObject O B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O B-Citation I-Citation I-Citation I-Citation O


O O O O O O O B-Observatory O O O O O O O O B-Observatory O B-Telescope O B-Organization O O O B-Grant I-Grant I-Grant I-Grant B-Grant O B-Grant I-Grant B-Grant O O O O O O O O O O B-Telescope O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O

The authors would like to thank the SDO and RHESSI teams for their open data policy. SDO and RHESSI are NASA’s missions under the Living With a Star (LWS) and SMall EXplorer (SMEX) programs, respectively. The authors would also like to thank the NICT team for providing the HiRAS dynamic spectrum. The authors acknowledge the constructive comments and suggestions of the anonymous referee, which improved the presentation and scientific content of the article.


O O O O O B-Person I-Person O O O O O O O O O O B-Person O O O O B-Organization I-Organization

Acknowledgments We are grateful to Georg Horedt for his comments on the first version of this article. AO was supported by the Kosciuszko Foundation.


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

companions in the disk. Huang et al. (2018) and Dullemond et al. (2018) show that the rings frequently seen in continuum emission from (sub)millimeter grains are likely caused by dust trapping, perhaps due to embedded planets carving gaps in disks as opposed to being related to snow lines. In the case of SR 21 the possibility of a low-mass companion being responsible for carving out this cavity is further supported by the small grains seen in scattered light. These are expected to be closely coupled to the gas, tracing spiral arms confined to the millimeter cavity, as is frequently seen in hydrodynamical models. Azimuthal asymmetries in the outer ring. It is hard to tell from scattered light alone whether the asymmetry of the outer ring is caused by azimuthally localized overdensities in the gas and dust or if they are the product of shadowing by the inner spiral arms. This asymmetry looks different in all three ALMA bands available: Band 9 shows an asymmetry in the south, while Bands 7 and 3 show a ring-like structure with a bright asymmetry to the north. Pinilla et al. (2015b) have already suggested that the southern bright spot seen in Band 9 may be the result of a hotter region in the southern side of the disk. This is supported by Band 9 being optically thick (peak optical depth of τ ∼2.0, assuming a physical temperature of 20 K). Therefore, continuum emission in this band is not only sensitive to density variations, but also to temperature variations, which can produce structure in the emission. In Band 3, where the disk is optically thin (peak optical depth of τ = 0.17 assuming a physical temperature of 20 K), the asymmetry is reversed, with the southern bright spot disappearing and the northern one becoming prominent. This asymmetry, at this low optical depth, suggests that the northern bright spot seen in SPHERE and ALMA Bands 7 and 3 probably corresponds to a dust overdensity at this location of the ring. Band 7, with an intermediate estimated peak optical depth of τ = 0.5, shows both the overdensity and the hot region in the south. Such an overdensity could, for example, be produced in the apastron location of a slightly eccentric disk, where the lower velocity at apastron leads to higher gas densities that can also slow down drifting grains and replicate the overdensity in large grains ( Ataiee et al. 2013 ). The spiral arms pointing to the likely position of the planet. The “kinked spiral” feature we see to the north in the saturated cut of the H -band data (Fig. 1 ) is strongly reminiscent of the spirals arising in hydrodynamical models of planet-disk interaction (see, e.g., Nelson et al. 2000 ; Sándor et al. 2007 , or Pinilla et al. 2015b ). The position of the kink in the spiral, indicating the exact location of the planet in these hydrodynamical models, is found inside of the ALMA ring and in the gap between this ring and the two brighter inner spirals seen with SPHERE (Fig. 1 , right panel). This is consistent with a


O O O O B-Database I-Database I-Database B-Database O O O O O B-Organization I-Organization I-Organization B-Organization O O O B-Organization O O O O O O O O

ACKNOWLEDGEMENTS We used the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, Caltech, under contract with NASA. We acknowledge useful comments by an anonymous referee.


O O O O O O O O O O O O O O O O O O B-Person O O O O B-Person I-Person I-Person O B-Organization I-Organization I-Organization O O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O B-Survey O O O O O B-Organization I-Organization I-Organization I-Organization O B-Collaboration I-Collaboration O B-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Survey O O O B-URL O B-Survey O O O O B-Collaboration I-Collaboration I-Collaboration O O O O O O B-Collaboration I-Collaboration O O B-Organization I-Organization I-Organization O B-Collaboration I-Collaboration I-Collaboration B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O B-Collaboration I-Collaboration I-Collaboration O B-Collaboration I-Collaboration I-Collaboration B-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Collaboration I-Collaboration I-Collaboration I-Collaboration I-Collaboration B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization O B-Collaboration I-Collaboration I-Collaboration B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O B-Organization I-Organization

ACKNOWLEDGEMENTS We would like to thank the anonymous referee for the suggestions that helped to improve this paper. GVC acknowledges technical support from Dr Rodrigo Romero and Estudio Conturso Asoc. This work was supported in part by the Consejo Nacional de Investigaciones Científicas y Técnicas de la República Argentina (CONICET), the Consejo Nacional de Investigaciones Científicas, Técnicas y de Creación Artística de la Universidad Nacional de San Juan (CICITCA) and the Secretara de Estado de Ciencia, Tecnología e Innovación del Gobierno de San Juan (SECITI). Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the participating institutions, the National Science Foundation, and the US Department of Energy Office of Science. The SDSS-III web site is http://www.sdss3.org/ . SDSS-III is managed by the Astrophysical Research Consortium for the participating institutions of the SDSS-III Collaboration, including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, Carnegie Mellon University, University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofisica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington and Yale University.


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

of a WD (e.g. Shen Bildsten 2007 ; Nomoto et al. 2007 ). The presence of the shell burning prior to the outburst was also suggested by Ramsay et al. (2016) . However, the high accretion rate requires a high mass transfer ratio (i.e. the mass accretion rate divided by the mass-loss rate from the donor). A very efficient wind mass transfer was suggested, for example, by Mohamed Podsiadlowski (2012) , for symbiotic stars with slow and dense winds. Skopal Cariková (2015) suggested that the high wind-mass-transfer efficiency in symbiotic stars can be caused by compression of the wind from their slowly rotating giants. Direct indication of wind focusing was found by Shagatova et al. (2016) for the symbiotic binary SY Mus. To increase the luminosity of the burning WD by a factor of 10, to values observed around the maximum of the 2015 outburst, a transient increase of the accretion rate to is needed to generate the luminosity due to hydrogen burning, where erg g is the energy production of 1 gram of hydrogen due to the nuclear fusion of four protons, and is the hydrogen mass fraction in the accreted matter. The required exceeds the stable-burning limit, which leads to blowing optically thick wind from the WD ( Hachisu et al. 1996 ). The enhanced wind is ionised by the hot WD’s pseudophotosphere, and thus converts a fraction of its stellar radiation to the nebular emission. The corresponding increase of the EM (Fig. 4 ) then causes a relevant brightening in the LC, which we indicate as the outburst (Fig. 2 ). However, the principal question remains as to the origin of this material. Probably, the red giant is responsible for a transient increase of the mass transfer ratio, which temporarily enhances . In general, Bisikalo et al. (2006) found that variations in the velocity of the wind from the giant can cause a disruption of the accretion disk, leading to the infall of a considerable amount of matter ( ) onto the WD surface, thus inducing the outburst. For Z And, Sokoloski et al. (2006) suggested that its 2000-02 outburst was triggered by the influx of hydrogen-rich material from a dwarf-nova-like disk instability at its start that consequently enhanced nuclear shell burning on the WD. 5. Summary We analysed primarily high cadence optical spectroscopy and multicolour photometry obtained prior to and during the first Z And-type outburst of the symbiotic nova AG Peg that began in June of 2015. We determined the fundamental parameters , and of the WD’s pseudophotosphere and its mass-loss rate, , in the course of the outburst (Fig. 7 ). Monitoring the evolution of the He ii 4686 Å, H and the Raman-scattered 6825 Å line profiles allowed us to suggest the ionisation structure of the active hot component in AG Peg (Fig. 12 ) and to outline the nature of its outburst. The main results of our analysis may be summarised as follows. 1. The nova-like outburst of AG Peg terminatedaround 1997 when a wave-like orbitally-related variation in theLC reached its


O O B-Person I-Person O O O O O O O O O O B-Software O O O O O O O O O O O B-Organization O O B-Grant O B-Grant O O B-Organization O O B-Grant O B-Grant O O O O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization

We thank James Stone for helpful discussions and comments, as well as for making Athena++ publicly available. Financial support for this study has been provided by NSF via grants AST-1409524 and AST-1515763, and by NASA via grants 14-ATP14-0059 and 15-XRP15-2-0139. All simulations were carried out using facilities supported by the Princeton Institute of Computational Science and Engineering.


O O O O O O B-Archive I-Archive I-Archive I-Archive O O O O O O B-Organization I-Organization I-Organization I-Organization B-Organization O B-Organization I-Organization I-Organization B-Organization O O O O O O O O O O O O O O O O B-Archive I-Archive I-Archive I-Archive I-Archive B-Archive B-Organization O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization O B-Grant O O B-Archive O O B-Telescope O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Grant O O O O O O O B-Software B-Citation I-Citation I-Citation I-Citation O B-Citation O B-Software B-Citation I-Citation O B-Software B-Citation I-Citation I-Citation O B-Software B-Citation I-Citation O B-Citation I-Citation I-Citation O B-Software I-Software

This research has made use of NASA’s Astrophysical Data System. We would like to thank the Space Telescope Science Institute (STScI) and High Point University (HPU) for facilitating this research. Some/all 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. Software: gPhoton (Million et al. 2016a , 2016b ), FaRVaE (Boudreaux 2017 ), SExtractor (Bertin Arnouts 1996 ), Scipy (Oliphant 2007 ; Millman Aivazis 2011 ), SAOImage ds9.


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

overall He spread in 47Tuc is small, a small population of extreme chemistry stars may exist, which is also supported by the fact that only a handful of stars with such strong oxygen depletion has been found by e.g. Cordero et al. (2014) . The AGB polluters in Ventura et al. (2014) are in a mass range where the stars experience a mild Hot Bottom Burning, which is where the Mg-Al burning chain is activated. Their models predict an enhancement of the AGB surface abundances of Al of up to +0.5 dex, whereas the overall Mg abundances are only barely touched, with a depletion of at most 0.04 dex. Considering that the pure AGB ejecta need to be diluted with gas of pristine composition, no detectable variation in the Mg abundance is expected, consistent with our results. On the other hand, one would expect a small variation in [Al/Fe] in the polluted stars, which has indeed been reported by both Carretta et al. (2013) and Cordero et al. (2014) . That we do not see any statistically significant variation in [Al/Fe] in our sample of stars is likely a consequence of our small sample size, as discussed in Paper I. In Fig. 19 , we show the dilution curve for Mg/Mg vs. Mg/Mg, using the same AGB models as in Ventura et al. (2014) . The amount of AGB material increases from left to right in the plot, with the leftmost point giving the pristine composition assumed in their models. Clearly, the bulk of our measured isotopic ratios fall well below the predicted value, even when considering a composition of purely pristine material. However, if one started from a composition with a lower abundance of heavy Mg isotopes, the curve would shift to the left, and show much better agreement with the observations. We note here that the pristine composition assumed by Ventura et al. (2014) starts out with a higher initial fraction of the heavy Mg isotopes, which would explain this offset. During the burning chain that creates the Al enhancement in AGB stars, production of primarily Mg, but also Mg is occurring, and one would thus expect a change in the isotopic distribution between the pristine and polluted populations. Indeed, the AGB models of Ventura et al. (2014) predict a strong decrease of Mg whereas Mg should increase by almost an order of magnitude. Thus, one would expect the Mg abundances to correlate with [Al/Fe] for the polluted population. As discussed earlier, our analysis does not give any indication of such a correlation being present. This is further illustrated in Fig. 20 , where we plot the dilution curve (solid line) for the Mg isotopic fraction vs. [Al/Fe], using the models of Ventura et al. (2014) . The maximum allowed fraction of AGB material is 0.3, as imposed by the constraints from the He abundance variation measured from the extent of the Horizontal Branch in the cluster. Whereas our [Al/Fe] values are within the model prediction, we see no evidence for a strong increase in Mg. Thus, our observations are somewhat in disagreement with the


O O O O O O O B-Survey O O O B-Wavelength I-Wavelength O O O O O O O O O B-Software B-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Wavelength O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O B-Wavelength O O O B-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O B-Dataset O B-Citation I-Citation I-Citation I-Citation O O B-Survey O O O O O O O O O O O O O B-Dataset O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O B-Dataset O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O B-Survey O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O B-Survey I-Survey I-Survey O O B-Wavelength O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O B-Wavelength I-Wavelength O O O O O O B-Wavelength I-Wavelength O O O O O O B-Wavelength I-Wavelength O O O O O O O B-Wavelength O O O O O O O B-Survey O B-Instrument O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O B-Wavelength O O O O O O B-Instrument O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O B-Survey O O O O B-Wavelength O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O B-Wavelength O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O B-Wavelength O O O O O O O B-Survey O O O O O O O O O O O O O B-Survey O B-Instrument O

sources due to a bias from the FIRST sensitivity. The rest-frame g -band absolute magnitude was estimated by the SED template fitting Mizuki (Tanaka 2015 ; Tanaka et al. 2018 ). There may be two sequences of the g magnitude along the redshifts. The bright sequence with M g ≲ −21 does not strongly depend on the redshift. On the other hand, the number of sources belonging in the faint sequence seems to dramatically increase with increasing redshifts. The sources with faint absolute magnitudes are also faint in apparent magnitudes ( i > 24), and the optical SEDs of the HSC-SSP bands show that some sources on the faint sequence have a flat SED without distinct features. Thus, the redshifts of these sources are probably estimated incorrectly. In fact, the comparison of M g and redshifts with the COSMOS2015 catalog (Laigle et al. 2016 ) in UD-COSMOS shows the underestimated redshifts of the faint sequence sources, and the redshifts of COSMOS2015 indicate that most sources in the faint sequence should be at z L16 > 1.5. In this comparison, a source at z = 0.5 on the faint sequence was found to have redshift and M g consistent with the COSMOS2015 catalog. This source is really a local source with a faint optical luminosity. The faint sequence could be an apparent one due to both the effects of the underestimated redshifts and the Malmquist bias of the HSC-SSP sensitivity limits. Some sources at z ≲ 0.5 may be local galaxies with strong radio radiation from active star formation. Figure 13. Rest-frame 1.4 GHz radio luminosity (upper panel) and the absolute g -band magnitude at the rest frame (lower panel) as a function of photo- z . Only RG sources with reliable photometric redshifts, with z photo > 0, , and , are shown. The black circles and red circles denote the Wide and UD-COSMOS RGs, respectively. Radio loudness at the rest frame was estimated and is defined here as a ratio of the rest-frame 1.4 GHz flux to the rest-frame g -band flux. The wavelength of the rest-frame g -band flux is close to the rest-frame B -band, which is typically used for calculating the radio loudness. The rest-frame radio loudnesses of the SDSS- and HSC-level sources as a function of the apparent i -band magnitude are shown in Figure 14 . We found that RGs with high radio loudness () are found in the HSC-level subsample. Certainly, there are likely also low radio-loudness RGs in the HSC-level regime, but such sources are not included due to the sensitivity limit of the FIRST survey. Note that the radio loudness we use here is underestimated, because HSC band flux could be dominated by stellar light from host galaxies of RGs, and the rest-frame g -band flux is derived from the SED templates of galaxies. Figure 14. Radio loudness at the rest frame as a function of the apparent i -band magnitude. The RG sources with reliable photo- z in the Wide (black) and the UD-COSMOS (red) layers are shown. The blue dotted line is the border separating the SDSS-level and HSC-level samples


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

binary components are not hidden in the glare of an accretion disk. Hence, the short-period hot subdwarf binaries represent an important progenitor channel of CVs. In fact, Schenker (2005) postulates that the CVs below the period gap are the product of post-subdwarf binary evolution. On the other hand, the hot subdwarfs with massive WD companions are potential progenitors of Type Ia supernovae (see Iben Tutukov 1984 ; Webbink 1984 , and for the most recent candidates see Geier et al. 2013 ; Vennes et al. 2012 ). Therefore, they are an important ingredient in understanding Type Ia supernovae. Establishing the accurate masses of both components of post-common-envelope binaries (PCEBs) is the only empirical way to constrain the efficiency parameters of the CEE phase. Furthermore, detailed investigation of hot subdwarf binaries is crucial when determining their masses for comparison with their theoretically proposed evolutionary channels, as well as to test the binary-population synthesis models. However, most of the hot subdwarf binary systems with known orbital periods are single-lined spectroscopic binaries, making it impossible to reliably determine the absolute masses of their components. Among the PCEBs, 15 eclipsing binary systems have been found to date, which are comprised of a hot subdwarf primary (sdO or sdB star) and a low mass secondary, either a late dM or a brown dwarf (BD) (for the most recent discoveries see Schaffenroth et al. 2013 ; Barlow et al. 2013 ; Schaffenroth et al. 2014 , 2015 ). Such eclipsing systems are known as HW-Vir-type binaries after the prototype. In addition to eclipses, HW-Vir systems are notorious for having a very strong “reflection effect”. This reflection effect, characteristic for all close binaries that comprise a very hot primary and much cooler secondary, is due to the high contrast in the temperatures between the heated and unheated hemisphere of the secondary star. As the secondaries in these systems are supposed to be orbiting synchronously, one side of the cool secondary star is constantly being irradiated by the strong ultraviolet (UV) flux of the hot-subdwarf primary. The light-curve solutions of HW-Vir-type systems imply that the temperature of the cool companion around the substellar point is increased up to 10 00020 000 K ( Hilditch et al. 2003 ; Kiss et al. 2000 ). However, the detection of spectral features from the irradiated secondary in HW-Vir-type systems is hampered by the contamination from the much hotter subdwarf primary. Recently, the eclipsing PCEBs gained even more attention, because nearly all systems with accurate eclipse-timing measurements, which have long enough data sets, are found to show apparent orbital-period changes ( Kilkenny 2014 ) that might indicate the presence of circumbinary planets (see Beuermann et al. 2010 , 2012a , b , for the most convincing cases). The claims of circumbinary planets in short-period sdB+dM/BD systems, as well as various planets in close


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

), Since Δ ν is expected to scale as (e.g., Ulrich 1986 ; Brown Gilliland 1994 ) we can substitute Δ ν in Eq. (7) . Assuming Γ 0 ( ν max ) ∝ M c T eff d we can then write, From this development, it can clearly be seen that the b exponent, which represents the Δ ν dependence (Eq. (7) ), does not produce an important influence in the departure from the L / M power law. On the contrary, the influence of the c exponent, introduced by Γ, amplifies the departure from a power law in L/M . In order to simplify the approach, we consider that the relative variation of the effective temperature on the RGB and in the clump is so small compared to the variation in luminosity that we can neglect the T eff dependence. Therefore, we performed a fit of A 0,bol as power law of L and M only. We find a variation in L 0.77±0.06 M −1.25±0.14 with the FREQ method, and in L 0.70±0.06 M −1.40±0.13 with the PROB method. In order to evaluate the validity of the previous hypothesis leading to neglect the T eff influence, the variation of the mode amplitude with L , M and T eff was also measured. We find a variation in L 0.70±0.07 M −1.03±0.15 T eff −4.79±1.36 with the FREQ method, and in L 0.61±0.06 M −1.14±0.14 T eff −5.48±1.18 with the PROB method. The dependence in L and M are less important, as expected, but consistent with the ones we previously found, considering the error bars. In contrast to these results, we can see that the measured T eff dependence is very important. However, the large error bars on the exponent and the lack of important impact on the other dependencies lead us to confirm the simplification hypothesis and neglect the T eff dependence. To assess the impact of the clump stars on the fits, we also consider the RGB stars alone and find significant differences: A 0,bol varying as L 0.84±0.08 M −1.34±0.27 with the FREQ method, and in L 0.82±0.07 M −1.61±0.27 with the PROB method. As stated above, seismic and stellar parameters of stars do not evolve much during the helium burning phase, on the contrary to the RGB phase. It follows that clump stars with similar masses will have similar A 0,bol values, thus making it difficult to disentangle the luminosity and mass dependence for these stars. The fit performed only on RGB stars allows us to get rid of a possible influence of one dependence on the other, and is therefore the one considered throughout the rest of the article. The exponents we find for the luminosity are slightly larger than the ones theoretically predicted ( Samadi et al. 2012 ), but agree with previous measurements ( Mosser et al. 2010 , 2012a ; Huber et al. 2011 ; Stello et al. 2011 ; Corsaro et al. 2013 ; Kallinger et al. 2014 ). A possible explanation for the difference between the predicted and observed exponents is the strong influence of non-adiabatic effects on the mode driving in red giants. Indeed, the theoretical predictions previously mentioned do not rely on fully non-adiabatic models. This type of modeling has not yet


O B-Observatory I-Observatory I-Observatory I-Observatory O O O O O B-Organization I-Organization I-Organization O O O O O B-Organization I-Organization I-Organization

The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.


O O O O O O O O O B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person O B-Person I-Person B-Person B-Person O B-Person O O O O B-Organization O O O O O O O O O O O O O O B-Organization O O O O O B-Grant I-Grant I-Grant I-Grant I-Grant O B-Grant I-Grant I-Grant I-Grant

We are grateful for stimulating and helpful discussions with Piero Madau, Monica Colpi, Mitch Begelman, Francesco Haardt, Ralph Pudritz, Chris McKee, Mike Fall, Elena M. Rossi, Melvyn Davies, Milos Milosavljevic, Kevin Schawinski, Luciano Rezzolla, Pedro Montero, Richard Larson, and Christian Reisswig. L.M., D.F., and S.B. acknowledge the hospitality of KITP, where crucial phases of this work were conceived and carried out in two different KITP programs in 2013 and 2014 (“A universe of Black Holes” and “Feedback: Gravity’s Loyal Opposition”).


B-Person O O O O B-Grant I-Grant I-Grant O B-Organization I-Organization I-Organization O O O O B-Organization

J.P.U.F. acknowledges support from the ERC-StG grant EGGS-278202. The Dark Cosmology Centre is funded by the DNRF.


O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O O O O O O O B-Dataset O O O O O O O O O O O O O B-Dataset O B-Wavelength O O O O O O O O O O O O O O B-Software B-Survey O B-Wavelength O O O O O O O O O O O O O B-Software O O B-Wavelength O O O O O O O O O O O O O O O O O O O O B-Software O O O O O O O O O B-Wavelength O O O O O B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Dataset O B-Survey O O O O O O O O B-Dataset O O O O O O O O O O O O O O O B-Survey O O O O O O O O O O O O O O O O O O B-Software O O O O O B-Survey B-Dataset O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey O O O O B-Software O O B-Survey O O O O O O B-Survey O O O O O O B-Software O O O B-Survey O O O O O B-Software O O O O B-Dataset I-Dataset O O O O O O O O O O O O B-Software O O O O O O O B-Software O O O O O O O O O O O O O O O O O O O B-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

see that the optical analyses have larger scatter by a factor of ≳2 in T eff , ≳4 in log g , and ≳4 in [Fe/H]. The larger scatter suggests that our simplified derivation of statistical uncertainties is sufficient until we can calibrate stellar parameters for a larger set of more homogeneous benchmark stars. Well-calibrated stellar parameters would require a more thorough probabilistic model of both StarNet training and StarNet predictions. Therefore, we consider this very good agreement and do not investigate these intrinsic dispersions further at this time. A comparison of Figs 10 and 13 reveals that, when StarNet is trained on synthetic spectra and compared to DR12, the scatter is a factor of ∼2 lower than the residuals between the DR13 and optical analyses. However, due to the different input physics, analysis techniques, spectral resolution, etc. between StarNet, APOGEE, and optical analyses, we cannot directly compare the precision of the stellar parameters returned by StarNet and an optical analysis at this time. Rather, this similar degree of scatter in the residuals indicates that the systematic errors intrinsic to StarNet are comparable to the systematic errors expected from an optical analysis. This indicates that the StarNet model is sufficient for a single survey analysis and can provide a new and exciting tool for the efficient analyses of spectroscopic surveys. 5.2 M dwarfs in DR13 While APOGEE has primarily observed red giant and sub-giant stars, DR13 includes spectra for known M dwarfs. These stars are accompanied with a specific Target Flag: ‘APOGEE MDWARF’. Initially, we had not removed these stars from the data set and found obvious discrepancies between the StarNet results and those provided by ASPCAP DR13. On closer inspection, we found 5900 stars that resembled the known M dwarfs, but that had not been flagged as M dwarfs. Those stars were removed from our data sets, using one of the following cuts: Metallicity parameters of −0.9 (ASPCAP [Fe/H]) 1.0, and where (StarNet [Fe/H] − ASPCAP [Fe/H]) −0.4, or Gravity parameters of (ASPCAP log g ) >3.6, and where (StarNet log g − ASPCAP log g ) −0.3 The ASSET grid provided with the APOGEE DR12 data release does not include synthetic spectra for M dwarfs, and therefore, StarNet cannot be trained on those stars. Furthermore, StarNet cannot be trained on the observed spectra at this time since there are too few M dwarfs in the APOGEE data set (1000 flagged). Our method for flagging M dwarfs is not robust, e.g. some RGB stars may have been removed, while other M dwarfs were not. 5.3 NN considerations One limitation of a deep NN is the necessity of large training sets spanning a wide range of the parameter space. The distribution of the stellar parameters in the training set for StarNet (when trained on observed spectra) are shown in Fig. 14 . From these plots, it is evident that there are fewer spectra for stars at high temperatures, low metallicities, and low gravities. As seen in


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

speed projected onto the beam direction. A.2. Plasma Instability A multipeaked electron distribution function , such as that shown in Figure 2 with the addition of the thermal electron peak at small velocity (not in the figure, that only shows the scattering source) is unstable to the electrostatic “bump-on-tail” instability. This instability is essentially inverse Landau damping, and occurs whenever the derivative of the distribution function with respect to some component of electron velocity is positive. Electron plasma waves with phase velocities ( ω and k are the plasma wave frequency and wave vector, related by the dispersion relation , where is the plasma frequency and the Debye length) for which grow at a rate of (Chen 1974 )where is the normalized one-dimensional electron distribution function of a density n beam of high velocity (Compton recoil) electrons and n e is the background electron density. If the fast electrons are only a small fraction of the total electron density and their speeds are much greater than the electron thermal velocity, conditions that are generally met, then for waves excited by the fast electrons and , where v is a velocity on the rising part of the electron distribution function. Then the growth rate becomeswhere is not normalized to n beam , but is the full electron distribution function. The rapid decrease of drag deceleration with increasing speed, shown by the factor in Equation ( 27 ), acts to create a minimum in (the large peak in from thermal electrons at very small velocity is not shown in Figure 2 ) even when S ( v ) is a monotonically decreasing function, as it can be for power-law photon spectra or a mixture of two- and three-photon annihilation (not shown). For example, if , making the non-relativistic approximation , then . For all but the most steeply decreasing S ( v ), and for v exceeding a few thermal velocities, and the plasma is unstable. In the opposite limit of scattering by very energetic gamma-rays , , and again the plasma is unstable (for quantitative growth rates Equations ( 28 ) and ( 29 ) need to be corrected for the relativistic increase in electron mass). This mechanism of producing unstable electron distributions may operate anywhere an intense flux of gamma-rays, not necessarily from positron annihilation, whose spectrum is not too steep, is incident upon a non-relativistic plasma. The required intensity is determined by the competition between the growth rate γ (Equations ( 28 ) and ( 29 )), proportional to the gamma-ray flux, and the collisional damping rate of the plasma wave that depends on the plasma density and temperature. For a plasma frequency comparable to the frequencies MHz of observed FRBs, is sufficient to grow the instability by ∼10 e -folds to saturation in the sub-millisecond timescale of FRBs. A.3. Energetic Failure This apparently attractive model fails on energetic grounds. The total Klein–Nishina cross-section for a 511 keV photon is cm 2 , so that


O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O O B-Grant O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Person O O O O B-Organization B-Grant B-Person O O O O O B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization

This research was supported by the Korea Astronomy and Space Science Institute under the RD program, Development of a Solar Coronagraph on International Space Station (Project No. 2017-1-851-00), supervised by the Ministry of Science, ICT, and Future Planning. R.-Y.K. acknowledges the support from NASA NNX13AG54G. R.-Y.K. is also supported by the Office of Naval Research and George Mason University.


O O O B-Person I-Person I-Person O O O B-Person O O O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O B-Grant B-Person O O O B-Organization O O B-Grant B-Person B-Person O B-Person O O O O B-Organization I-Organization I-Organization I-Organization B-Organization O O B-Grant O O O O O O O O O B-Archive I-Archive I-Archive I-Archive I-Archive I-Archive I-Archive B-Archive O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Location O

ACKNOWLEDGEMENTS We thank D. González Caniulef for helpful discussions. SWKE acknowledges support from the Science and Technology Facilities Council (STFC; grant number ST/N504488/1). MJP acknowledges support from STFC (grant number ST/N000811/1). MJP, AAB, and NPMK acknowledge support from the United Kingdom Space Agency (UKSA; grant number ST/P002323/1). This research has made use of data from the High Energy Astrophysics Science Archive Research Center (HEASARC) and the UK Swift Science Data Centre, provided by NASA’s Goddard Space Flight Center and the Department of Physics and Astronomy, Leicester University, UK, respectively.


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

where each DLA is detected. The purity of the catalogue should increase with CNR, so any effect of impurities should decrease rapidly with the threshold we impose on CNR. We show this in Fig. 4 , where we see again an increased variation of DLA bias with metal strength as the minimum required CNR is increased. Figure 4. Bias of the DLAs against S (left-hand panel) and (right-hand panel) for different cuts in CNR. Red squares (CNR > 4) and blue triangles (CNR > 2) have been horizontally shifted to avoid overlap. Furthermore, in this case we see a larger variation of the bias for the smallest value of S : a higher threshold in CNR results in a lower bias factor for the DLAs with the smallest metal strength. The variation is highly significant: taking into account that the sub-samples with CNR > 4 contain 70 per cent of the same DLAs in the sub-samples with CNR > 2, the expected statistical fluctuation in the difference of bias factors is 0.4σ, where σ stands for the error in the largest sample, with CNR > 2 (indicated by the blue error bar in the figure). The expected fluctuation comes from the fact that the sub-sample with CNR > 2 can be considered as the combination of two independent samples (one with CNR > 4, and another one with 2 CNR ≤ 4) that are combined with weight to construct the final estimator. This implies that the typical fluctuation is δσ CNR > 2 , where . This variation is opposite to our expectation if impurities caused only by noise were present in the catalogue, in which case false DLAs would have metal strength and bias consistent with zero. Our interpretation of this result is that the contaminants that are included in the catalogue as the CNR threshold is lowered are mostly regions of broad Ly α absorption in the forest, which correspond to absorbers of lower column density than DLAs but with sufficiently broad velocity dispersions to create a broad absorption line that is consistent with a DLA in the most noisy spectra. These absorbers generally have weaker associated metal lines because of their lower column densities and higher ionization level (most of the lines used to measure the metal strength are of low-ionization species; see Arinyo-i-Prats et al. 2018 ), and they are more highly biased than the DLAs with the weakest metal lines because they are associated with collapsed regions, or regions in the process of collapsing, with high velocity dispersion. This can explain why the presence of contaminants increases the bias factor, and actually decreases the variation we measure of the bias factor with metal strength. These type of absorbers and their average metal lines are likely similar to the systems studied by Pieri et al. ( 2014 ); a detailed study of the bias factor of these strong Ly α absorbers is separately being done (Blomqvist et al. in preparation). 4.3 Correction for the effect of metal strength measurement errors The errors in the measurement of mix the samples , and , as each DLA is classified to one of


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

not removed, but their orbits were significantly changed due to a significant perturbation caused by an encounter with a giant planet. In Figure 2 , we present an example of the effects of such an encounter with Jupiter. The plots show the maximum final variation in semimajor axis and eccentricity among the hundred particles that share the same initial radial position. As expected, the values increase with the radial distance. In the region of the rings (indicated by the vertical lines) the semimajor axis changes by more than 30 km and the eccentricity grows up to more than 0.5. Figure 2. An example of a disturbing close encounter caused on the ring by a close encounter with Jupiter. (a) Maximum final change in eccentricity. (b) Maximum final change in semimajor axis (km). The plots show the maximum final changes among the hundred particles that share the same initial radial position. The vertical lines indicate the boundary of the ring region. The encounter was performed with a minimum distance of 6.6 planet radii, with a relative velocity of km s −1 . The encounter resulted in a critical radius of R C = 460 km, meaning that no particles in the region of the rings were removed. The results of the encounters that produced at least some noticeable variations (Δ e ≥ 0.01) on the orbits of the rings are presented in Table 4 for backward and forward integrations, excluding the encounters followed by ejection. Table 4 List of Significant Disturbing Encounters (Δ e ≥ 0.01) with the Giant Planets for both Forward and Backward Integration within the Time Span of 10 Myr Notes. The immediate ejection cases were excluded. a The minimum encounter distance given in terms of the radius of the planet in question. b Survival time after a disturbing encounter. For the forward integration, we observed only five encounters with Jupiter and two with Saturn that resulted in eccentricities larger than 0.1 for the ring particles. None of the encounters with Uranus or Neptune showed significant orbital variation of the particles of the rings. Similarly, if we look backward, we see fewer close encounters that could have increased the eccentricity of the particles of the rings for values larger than 0.1 (five with Jupiter, one with Saturn, and one with Uranus). Since Chariklo, as observed now, has well-defined narrow circular rings (Braga-Ribas et al. 2014 ), this might mean that it did not suffer any of these disturbing encounters or, if they did occur, it was so long ago that the rings had time to evolve, damping the eccentricity and reshaping the rings. Both possibilities are compatible with our results and, as shown in Table 3 , the probability of catastrophic or disturbing encounters is very low, and probably occurred several million years ago. 7. THE EJECTION CASES The close encounters of Chariklo with any of the giant planets followed by ejections are particularly interesting. If we look forward, these would be the encounters responsible for removing Chariklo


ACKNOWLEDGEMENTS We thank an anonymous referee for the helpful suggestions.


O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Grant B-Grant B-Grant O B-Grant B-Grant O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant B-Person O O O O O B-Fellowship I-Fellowship O O B-Organization I-Organization O B-Location I-Location B-Person O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O B-Grant B-Person O O O O O B-Organization O B-Grant O B-Grant O O O O O O O O O B-Organization I-Organization I-Organization I-Organization O O O B-Grant I-Grant

The work is jointly supported by the National Natural Science Foundation of China (41231068, 41304137, 41531073, and 41504132, 11575203) and the Specialized Research Fund for State Key Laboratories. X.L. acknowledges the support of the post-doctoral programme of the North-West University in South Africa. M.S.P. acknowledges the financial support of the South African National Research Foundation (NRF) under the Incentive and Competitive Funding for Rated Researchers, grants 87820 and 68198. M.Z. was supported in part by NASA Grants NNX14AJ53G and NNX15AN72G. This material is based upon work supported by the US National Science Foundation under Grant No. CNS 09-23050.


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O B-Survey I-Survey I-Survey I-Survey B-Survey B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

other secondary biases, since it shows that the fact that it increases with mass was an artefact of the mass scales that were being probed. Our results place updated constraints to models addressing the connection between galaxies and haloes. The wide dynamical range that we probe encompasses haloes hosting from emission-line galaxies at the low-mass end to massive quiescent galaxies and clusters at the high-mass end. In the context of the halo-galaxy connection, it has become an observational challenge to prove the existence of galaxy assembly bias , a hypothesis that states that the clustering properties of galaxies, at fixed halo mass, depend on secondary halo properties such as the accretion history (or age) of haloes (see e.g. Lin et al. 2016 ; Miyatake et al. 2016 ; Montero-Dorta et al. 2017 ; Niemiec et al. 2018 ). For luminous red galaxies (LRGs), indications of the existence of galaxy assembly bias have been reported by Montero-Dorta et al. ( 2017 ) and Niemiec et al. ( 2018 ), from a sample extracted from the Baryon Oscillation Spectroscopic Survey (BOSS; Dawson et al. 2013 ). The typical mass of the haloes inhabited by these galaxies is estimated in ∼10 12.7−13 h −1 M ⊙ (Niemiec et al. 2018 ), but a large scatter is expected, so that the most massive LRGs could inhabit haloes above ∼10 14 h −1 M ⊙ . These results are, in principle, compatible with both the halo assembly bias and the concentration bias signal reported in Fig. 4 . Our measurement of halo assembly bias at the high-mass end can be properly connected to the results presented in Montero-Dorta et al. ( 2017 ) and Niemiec et al. ( 2018 ) through the technique of ‘age matching’ (Hearin et al. 2016 ). In addition, the large scale of the spin bias signal for cluster-size haloes, of almost a factor 2 at ∼10 14.5 h −1 M ⊙ , suggests an alternative route towards an observational proof of secondary bias. Probing the effect of spin bias requires measuring rotation, or a proxy for it, in a large sample of galaxy clusters. These measurements, which are still extremely challenging, might be possible in the near future thanks to techniques such as kinetic Sunyaev–Zel’dovich effect (see e.g. Baldi et al. 2018 ). We have applied, for the first time, a fully multitracer approach to the measurement of secondary bias. Here, different subsets of haloes are viewed as different LSS tracers. We show that this method is capable of reproducing all features observed from the standard measurement. In addition, we have obtained statistical uncertainties which are comparable to other bias estimates from N -body simulations that minimize cosmic variance by relying on direct knowledge of the density field, e.g. Gao White ( 2007 ); Chue et al. ( 2018 ). However, in contrast to those methods, which in effect compute δ α /δ m at each point (in configuration or Fourier space), the technique used in this work can be applied both to simulations as well as to actual data, in real or redshift space. The


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

and UV-illuminated (afterwards) gas condensation of the massive star-forming cluster that formed the Solar system. In this condensation, after a sudden decrease of the temperature due an increase in density and efficient dust cooling, PO condensed on grains along with other molecules, including complex species also detected in the comet (Goesmann et al. 2015 ; Altwegg et al. 2017b ). Under these physical conditions, deuteration increased, producing heavy water and other deuterated species detected in the comet (Altwegg et al. 2017a ). PO does not react easily with atomic H, which is the only mobile species on the dust grains at low temperature. This allowed a relatively high abundance of PO in the ices of the comet. 4.2.2 From Solar system bodies to primitive Earth: providing prebiotic P The confirmation of the presence of PO in the comet 67P/C–G has important implications for the prebiotic chemistry that occurred on the early Earth. The possible contribution of prebiotic material from comets is a long-standing topic (e.g. Chyba et al. 1990 ). Recent works have pointed out that comets could have contributed significantly to the chemical reservoir of our planet. O’Brien et al. ( 2018 ) claimed that of Earth’s water could have its origin in a cometary source, while Marty et al. ( 2017 ), based on ROSINA measurements of Xenon isotopes in 67P/C–G, showed that comets might have provided the of the Earth’s atmospheric Xe. In sight of our findings of P in 67P/C–G, we explore here the possible contribution of comets to the P reservoir on the early Earth. The amount of P in the Earth crust is 930 ppm (Yaroshevsky 2006 ), which means ∼2.6 × 10 22 g. However, most of this P is not available for biological processes, being locked in insoluble minerals. In the astrobiology community, there is an intense debate (known as the ‘phosphate problem’, see e.g. Menor-Salvan 2018 ) about the availability of inorganic phosphate at the dawn of our planet. Orthophosphate (PO), which is the most common form of P on Earth, is mainly found in apatite minerals. The insolubility of these minerals locks P, which is not available for (pre)biotic chemistry. To solve this scarcity of P, alternative sources of P should be explored. One possibility comes from meteorites. It has been measured that CI chondrites, a type of stony meteorites, contain a nearly solar P abundance (Lodders 2003 ). This suggests that an important fraction of P likely came to the Earth in rocks. However, as mentioned before, most of this P is not easily accessible to trigger prebiotic chemistry due to low solubility in water. As a possible solution, Pasek ( 2008 ) proposed that schreibersite, (Fe,Ni) 3 P, the major carrier of P in iron meteorites, which is more soluble in water, may be the main contributor of P in the early Earth. These authors claimed that that impacts of meteorites probably delivered between 10 18 and 10 21 g of P. Another extraterrestrial possibility would be the contribution from


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

simulations showed similar results. However, Chambers (2013) evidenced some differences related to the masses and the time-averaged eccentricities of the final planets. We believe that a more realistic treatment of the collisions should be included in future -body simulations. Such improvements will allow us to determine the orbital and physical properties of the planets formed in the simulations in greater detail. On the other hand, Marcus et al. (2010) presented results from smoothed particle hydrodynamics simulations of impacts between differentiated water(ice)-rock planets. From this, the authors analyzed the effects of late giant impacts on the final bulk abundance of water in super-Earths. Marcus et al. (2010) derived general laws, which should be incorporated into future -body calculations of planet formation to track the composition of growing planets in more detail. In the present work, we consider a snow line with a fixed position for each star. However, several works such as Ramirez Kaltenegger (2014) and Tian (2015) , calculated how the orbital distance of the HZ and the position of the snow line change throughout the pre-main-sequence (PMS) stage of the host star. In particular, for a 0.5 star, Ramirez Kaltenegger (2014) found that the snow line in the PMS moves inwards in the protoplanetary disk from 2 AU to 0.5 AU in a period of 200 Myr. Regardless of star type, all planets located at the inner edge of the main-sequence (MS) HZ receive stellar fluxes that exceed the runaway greenhouse threshold for at least part of the PMS stage, which results in the rapid evaporation of surface water. Triggering a runaway greenhouse does not ensure that a planet could not later become habitable because water could recondense afterwards. Planets orbiting at distances corresponding to the inner and outer MS HZ around a 0.5 star would lose up to 25 EOs and 0.5 EOs, respectively, and about 0.1 EOs are lost at the MS snow line. Assuming that a HZ and a snow line evolving in time may lead to changes in the final results obtained in the present work. Future works based on -body simulations should incorporate such effects to test the sensitivity of the results concerning the physical and dynamical properties of the HZ planets. It is also important to note that all our simulations were integrated for 150–200 Myr. Thus, the planetary systems obtained in the present work should be treated as systems of potential interest. It would be very interesting to analyze the long-period dynamical stability of the planets surviving in the HZ to clarify the distribution of these kind of exoplanets around low-mass stars. We believe that the results obtained in the present work lead to a better understanding about the planetary formation processes around M3- and M0-type stars in systems without gas giants. Future observational evidence will be necessary to test our theoretical models and to strengthen our knowledge about the population of terrestrial-like planets


O O O O O O O O O O B-ComputingFacility I-ComputingFacility O O B-Organization I-Organization I-Organization B-Person O B-Person O O O O O O B-Organization O O B-Grant

ACKNOWLEDGEMENTS The calculations for this Letter were performed on the ‘Eureka’ supercomputer at the University of Surrey. RRR and JIR would like to acknowledge support from STFC consolidated grant ST/M000990/1.


O O O O O O O O O B-Observatory I-Observatory I-Observatory B-Observatory I-Observatory B-Location O O B-Telescope I-Telescope I-Telescope O O B-Proposal O O B-Proposal O O O O O O B-Instrument O O O O B-Telescope O B-Organization O O B-Telescope I-Telescope B-Telescope O O O O O B-Organization I-Organization I-Organization B-Organization O B-Location O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O B-Location O O B-Organization I-Organization I-Organization O O O O O O O O O O O B-Software O O B-Organization I-Organization I-Organization I-Organization O O O O B-Survey I-Survey I-Survey I-Survey O O O O B-Organization O B-Organization O B-Survey O O O B-URL O O O O O O O O B-Observatory O O O O O O O O O O O O O O B-Person I-Person O O O O O O O O O B-Location O O B-Survey O O O O B-Organization O B-Grant I-Grant O B-Grant O B-Person O O O O O B-Organization B-Person B-Person O B-Person O O O O B-Organization I-Organization I-Organization O O B-Grant I-Grant I-Grant I-Grant I-Grant B-Grant B-Person B-Person O B-Person O O O O O B-Organization I-Organization I-Organization O B-Grant O B-Grant O B-Collaboration I-Collaboration I-Collaboration O O O O O B-Location O O B-Location O O O O B-Location I-Location O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Person O O O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant B-Grant B-Person O O O O B-Organization I-Organization I-Organization O O B-Grant I-Grant I-Grant I-Grant I-Grant B-Grant B-Person O O O O O B-Organization I-Organization I-Organization O O B-Location I-Location B-Grant I-Grant I-Grant B-Grant O O B-Grant I-Grant B-Person O B-Person O O O O O B-Organization I-Organization I-Organization O O B-Location I-Location B-Grant I-Grant I-Grant B-Grant O O B-Grant B-Person O O O O O O O B-Location B-Organization I-Organization I-Organization I-Organization I-Organization O O O B-Grant B-Person B-Person O B-Person O O O O O B-Grant I-Grant O B-Grant I-Grant I-Grant B-Person O O O O O B-Grant I-Grant I-Grant B-Person O O O B-Organization B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O B-Grant I-Grant I-Grant I-Grant I-Grant B-Grant B-Person O O O O O O O O O O B-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization B-Person O O O O O B-Organization I-Organization B-Grant O O B-Grant I-Grant B-Grant O O O B-Grant I-Grant B-Location O O O O O B-Organization

This work is based on observations collected at the European Southern Observatory, Cerro Paranal, Chile, using the Very Large Telescope under programs 182.A-0886 and partly 070.A-9007. Also based on observations obtained with MegaPrime/MegaCam, a joint project of CFHT and CEA/DAPNIA, at the Canada-France-Hawaii Telescope (CFHT), which is operated by the National Research Council (NRC) of Canada, the Institut National des Sciences de l’Univers of the Centre National de la Recherche Scientifique (CNRS) of France, and the University of Hawaii. This work is based in part on data products produced at TERAPIX and the Canadian Astronomy Data Centre as part of the Canada-France-Hawaii Telescope Legacy Survey, a collaborative project of NRC and CNRS. The VIPERS web site is http://www.vipers.inaf.it/ . We acknowledge the crucial contribution of the ESO staff for the management of service observations. In particular, we are deeply grateful to M. Hilker for his constant help and support of this program. Italian participation to VIPERS has been funded by INAF through PRIN 2008 and 2010 programs. D.M. gratefully acknowledges financial support of INAF-OABrera. L.G., A.J.H., and B.R.G. acknowledge support of the European Research Council through the Darklight ERC Advanced Research Grant (#291521). A.P., K.M., and J.K. have been supported by the National Science Centre (grants UMO-2012/07/B/ST9/04425 and UMO-2013/09/D/ST9/04030), the Polish-Swiss Astro Project (co-financed by a grant from Switzerland, through the Swiss Contribution to the enlarged European Union), and the European Associated Laboratory Astrophysics Poland-France HECOLS. K.M. was supported by the Strategic Young Researcher Overseas Visits Program for Accelerating Brain Circulation (#R2405). O.L.F. acknowledges support of the European Research Council through the EARLY ERC Advanced Research Grant (#268107). G.D.L. acknowledges financial support from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement # 202781. W.J.P. and R.T. acknowledge financial support from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013)/ERC grant agreement #202686. W.J.P. is also grateful for support from the UK Science and Technology Facilities Council through the grant ST/I001204/1. E.B., F.M. and L.M. acknowledge the support from grants ASI-INAF I/023/12/0 and PRIN MIUR 2010-2011. L.M. also acknowledges financial support from PRIN INAF 2012. Y.M. acknowledges support from CNRS/INSU (Institut National des Sciences de l’Univers) and the Programme National Galaxies et Cosmologie (PNCG). C.M. is grateful for support from specific project funding of the Institut Universitaire de France and the LABEX OCEVU. SdlT acknowledges the support of the OCEVU Labex (ANR-11-LABX-0060) and the A*MIDEX project (ANR-11-IDEX-0001-02) funded by the “Investissements d’Avenir” French government program managed by the ANR.


O O O O O O O O B-Organization I-Organization I-Organization B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Person I-Person I-Person O B-Person I-Person I-Person O O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility O O O O O O O O O O O O O O O O O O O O B-Event I-Event I-Event I-Event O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O O O O O O O O O O B-Software B-Citation I-Citation O O O B-Software O O O O O O O O B-Software O O O O O B-Software O O O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O B-Archive I-Archive I-Archive I-Archive B-Observatory O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O O O O O B-Organization I-Organization I-Organization O O O O O O O B-Instrument I-Instrument I-Instrument B-Instrument O O O O O B-Survey I-Survey I-Survey B-Survey O O O O B-Survey O O O O O O B-Location B-Organization I-Organization I-Organization O B-Location B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Location O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Location I-Location O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility O O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization O O O O O O B-Survey I-Survey I-Survey O O O O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O B-Collaboration I-Collaboration O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization B-Organization B-Location B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O O O O O O O B-Organization I-Organization I-Organization O B-Observatory I-Observatory I-Observatory I-Observatory O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization

ACKNOWLEDGEMENTS This work utilizes resources supported by the National Science Foundation’s Major Research Instrumentation program, grant #1725729, as well as the University of Illinois at Urbana-Champaign. We thank Dr. Volodymyr Kindratenko and Dr. Dawei Mu at the National Center for Supercomputing Applications for their assistance with the GPU cluster used in this work. This work is based on projects started during the 2019 graduate-level AI seminar at the Department of Astronomy, University of Illinois at Urbana-Champaign. We thank the anonymous referees for helpful comments. We acknowledge use of matplotlib (Hunter 2007 ), a community-developed python library for plotting. This research made use of astropy , 4 a community-developed core python package for Astronomy (Astropy Collaboration 2013 ; Price-Whelan et al. 2018 ). This research has made use of NASA’s Astrophysics Data System. NOAO is operated by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation. This project used data obtained with the Dark Energy Camera (DECam), which was constructed by the Dark Energy Survey (DES) collaboration. Funding for the DES Projects has been provided by the U.S. Department of Energy, the U.S. National Science Foundation, the Ministry of Science and Education of Spain, the Science and Technology Facilities Council of the United Kingdom, the Higher Education Funding Council for England, the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign, the Kavli Institute of Cosmological Physics at the University of Chicago, Center for Cosmology and Astro-Particle Physics at the Ohio State University, the Mitchell Institute for Fundamental Physics and Astronomy at Texas AM University, Financiadora de Estudos e Projetos, Fundacao Carlos Chagas Filho de Amparo, Financiadora de Estudos e Projetos, Fundacao Carlos Chagas Filho de Amparo a Pesquisa do Estado do Rio de Janeiro, Conselho Nacional de Desenvolvimento Cientifico e Tecnologico and the Ministerio da Ciencia, Tecnologia e Inovacao, the Deutsche Forschungsgemeinschaft, and the Collaborating Institutions in the Dark Energy Survey. The Collaborating Institutions are Argonne National Laboratory, the University of California at Santa Cruz, the University of Cambridge, Centro de Investigaciones Energeticas, Medioambientales y Tecnologicas-Madrid, the University of Chicago, University College London, the DES-Brazil Consortium, the University of Edinburgh, the Eidgenossische Technische Hochschule (ETH) Zurich, Fermi National Accelerator Laboratory, the University of Illinois at Urbana-Champaign, the Institut de Ciencies de l’Espai (IEEC/CSIC), the Institut de Fisica d’Altes Energies, Lawrence Berkeley National Laboratory, the Ludwig-Maximilians Universitat Munchen and the associated Excellence Cluster Universe, the University of Michigan, the National Optical Astronomy Observatory, the University of Nottingham, the Ohio State University, the University of Pennsylvania, the University of Portsmouth, SLAC National Accelerator Laboratory, Stanford University, the University of Sussex, and Texas AM University.


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O B-Telescope O O O O O O O O O B-Telescope B-Telescope B-Telescope B-Telescope B-Telescope O B-Telescope O O O O O O O O O O O O B-Observatory O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O B-Observatory O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O B-Telescope O O B-Observatory O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O

observing epochs. Figure 5 shows that the parameter constraints are much tighter when we average over more observing epochs, emphasizing the importance of sampling the intrinsic source variability when attempting to constrain the model parameters with EHT observations. Figure 5 (a) has the poorest ( u , v ) coverage by far, but achieves the tightest constraint, while fixing both ( u , v ) coverage and sensitivity in Figures 5 (b) and (c) again show that simply sampling more epochs will tighten the parameter constraints significantly. Figure 5. Parameter estimation test with the same underlying parameters as Figure 4 . The three panels show the averaged likelihoods for 20 realizations each in three separate setups. The number of observations in each setup is chosen such that the raw overall sensitivity is held fixed across the three setups. The three panels correspond to (a) 920 epochs on the SMA–CARMA–SMT baseline, where previous EHT observations were done; (b) 61 epochs on baselines including SMA, CARMA, SMT, LMT, APEX, and SPT; (c) 4 epochs including the same baselines as panel (b) but with ALMA replacing APEX. These figures show that sampling the source variability is more important for parameter estimation than the raw sensitivity of the array or the ( u , v ) coverage. 3.4. Effect of Time Averaging In the parameter estimation test, we calculated likelihoods over parameter space with both time-dependent and averaged GRMHD images to compare the effect of time averaging. Figure 6 contrasts the likelihoods of time-resolved (black contours) and time-independent (red contours) inputs to our Bayesian method when the same number of mock observations are analyzed. Figures 6 (a) and (b) are the likelihoods assuming the early three-station baselines and the six-station EHT with ALMA, respectively. The figure shows that a much smaller region of parameter space is allowed when comparing the mock data to a time-averaged image. However, the best-fit parameters in the time-averaged case are offset from the true parameters, as is most clearly evident in Figure 6 (b). This demonstrates the false certainty implied by the small allowed parameter region. The time-resolved analysis, by contrast, delivers allowed parameter ranges that are consistent with the input simulation. Figure 6. Effect of time averaging in the parameter estimation test for (a) the early EHT baselines and (b) the full EHT baselines including ALMA. We use the identical parameters for the mock data as Figure 4 . The likelihoods of the averaged GRMHD image are overplotted in red contours. The likelihood using the averaged images underestimates the uncertainties of the inferred parameters. The best-fit parameters derived from the time-dependent and averaged images are offset from each other as well. 3.5. Model Selection We now use the Bayesian method to identify the relative posterior likelihood among several models, as discussed in Section 2.2 . For this test we generated mock visibilities