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 B-CelestialObject O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O B-Telescope I-Telescope I-Telescope O B-Telescope 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-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O B-Telescope O O O B-Formula I-Formula I-Formula I-Formula 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 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 B-Formula I-Formula I-Formula 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 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 B-Telescope O O B-Formula I-Formula I-Formula O O O O O O O O O O O B-Formula I-Formula I-Formula O O O B-Model I-Model 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-CelestialObject O O B-Telescope 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 B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O B-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 B-CelestialObject 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 B-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula O O O O O O O O B-Formula I-Formula I-Formula 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

quasar proximity zone (e.g., Eilers et al. 2017 ) allow an estimate of the intrinsic luminosity of the quasar. However, it is crucial to note that the maximum image separation for J0439+1634 is ∼02 (Fan et al. 2018 ), close to the highest-resolution limit obtainable with the Hubble Space Telescope ( HST ; see Figure 2 ). Therefore, it is a clear possibility that many of the detected z > 6 quasars are actually lensed, with image separations below the resolution threshold. Following Barkana Loeb ( 2000 ), in Figure 2 we show the distribution in angular separations of lensing images for z = 6.51, , where is the angular diameter distance between source and observer. The distribution indicates that a fraction of the lensed sources at z > 6 have image separations ≲01. Thus far, no multiple images have been detected with the HST in samples of ∼10 z > 6 quasars (e.g., Kim et al. 2009 ; McGreer et al. 2013 ). This is equivalent to stating that the fraction of μ > 2 magnified quasars at z > 6 is ≲10% in current samples, leading to an upper limit of β ≲ 3.1 (see Figure 1 ). It is worth noting that, while the diffraction limit for the HST is ∼01, its point-spread function (PSF) is very well characterized and stable. This would, in principle, allow to discern a point-source quasar from a multiply imaged one well below the diffraction limit, possibly at a level ∼0001. For example, Libralato et al. ( 2018 ) measured proper motions of stars by identifying the centroid of the PSF with a precision ∼00003. This remark could foster a re-examination of the HST images of z > 6 quasars thus far detected. Figure 2. Distribution of image separations at z = 6.51, obtained assuming a Press–Schechter distribution of galaxies, following Barkana Loeb ( 2000 ). The shaded area indicates the 1 σ uncertainty due to the distribution of velocity dispersion in galaxies σ v . The angular separation for J0439+1634 (∼02), the HST angular resolution (∼01), and the typical angular size of lens galaxies at z ∼ 1 (∼1′′) are also shown for reference. Additionally, as originally suggested by Fan et al. ( 2018 ), the current selection criteria might have missed an important fraction of the quasar population at z > 6 because a lens galaxy in the same line of sight might have contaminated the drop-out band of the spectrum, leading to a misclassification of the source. It is remarkable to note that, if we de-magnified J0439+1634 by a factor ∼5, reducing its total magnification to μ ∼ 10, its flux would have been comparable to the one from the foreground lens galaxy and, thus, the quasar would have been misclassified. This situation could be occurring systematically for z > 6 quasars with μ ≲ 10. As the typical image separation for strongly lensed z > 6 quasars is ≪1′′ and the typical angular dimension of a z ∼ 1 lens galaxy is ∼1′′ (see Figure 2 ), the probability of lensing is equivalent to the probability of having the lens galaxy and the quasar images within the same photometric aperture.


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

model that simulates moist convection and cloud formation across various planetary conditions. Using a regional nonhydrostatic model to study moist convection is standard practice for Earth’s atmosphere, and many numerical models—named cloud-resolving models (CRMs) or large eddy simulations (LES)—have been developed accordingly (Pielke et al. 1992 ; Bryan Fritsch 2002 ; Khairoutdinov Randall 2003 ; Pressel et al. 2015 ). Similar nonhydrostatic models have been developed for Mars (Rafkin et al. 2001 ), Jupiter (Hueso Sánchez-Lavega 2001 ; Sugiyama et al. 2014 ), and Saturn (Hueso Sánchez-Lavega 2004 ), but they lack a well-documented comparison against an accepted nonlinear solution, which seems to be the first step in developing a robust numerical model. Because there are no standard tests of nonhydrostatic models for planets other than Earth, we will primarily perform simulations against standard tests for Earth-like conditions. Then, we perform an idealized simulation of the Jovian atmosphere in radiative-convective equilibrium (RCE) to study moist convection in hydrogen atmospheres. The structure of this work is organized as follows. Section 2 is devoted to the equation of motion, which includes dry air, vapors, clouds, and precipitation. Section 3 discusses the basic microphysics scheme employed in the model. Section 4 describes the numerical schemes that are designed for simulating atmospheric flows. Section 5 provides a series of benchmark tests against known solutions in the literature. Section 6 performs an idealized RCE simulation of the Jovian atmosphere. Section 7 concludes and outlines the future applications. To make the notations consistent and clear, major symbols used in this article are summarized in Appendix A for reference. 2. Equation of Motion We solve the most generic form of the equation of motion, the fully compressible Euler equations, to avoid unnecessary assumptions that are valid only for a particular type of planet. Though Euler equations can be written in many mathematically equivalent forms, they are different when discretized and implemented in a numerical model. Bryan Fritsch ( 2002 ) have compared five different ways of implementing the Euler equations, using potential temperature, equivalent potential temperature, and liquid water potential temperature. They concluded that the form of governing equations used in a numerical model has a profound effect on the simulation of a warm rising bubble. Satoh ( 2002 ) pointed out that in a model with diabatic forcing, the change in the domain integral of total energy is generally different from energy gain/loss from the boundaries if the potential temperature is used as the prognostic variable, which causes an error of the energy budget that accumulates with time. Furthermore, the expressions of potential temperature and equivalent potential temperature become complicated when the heat capacity of the atmosphere varies with temperature or when multiple condensing


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 B-Software B-Software I-Software I-Software I-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 B-Wavelength I-Wavelength 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 B-Wavelength I-Wavelength 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 B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength 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 B-CelestialObject I-CelestialObject O B-Citation O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O B-CelestialObject 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 B-CelestialObject O O O O B-CelestialObject O B-CelestialObject O O O O O O O B-CelestialObject O O O O O B-Wavelength O B-Wavelength O O O O O O B-Wavelength I-Wavelength 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-Wavelength I-Wavelength O O O O O O O O B-CelestialObject O O O O B-CelestialObject O O O O B-CelestialObject O O O O B-CelestialObject O O O O O B-CelestialObject O O O O O O O O O B-CelestialObject O O O O B-CelestialObject O O O O B-CelestialObject O O O O O B-CelestialObject 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 I-Wavelength B-Observatory O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-CelestialObject O O O O O O O O B-Observatory O O O O O O O B-Wavelength I-Wavelength B-Telescope 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 O O O O B-Formula I-Formula I-Formula I-Formula O B-CelestialObject O O O B-CelestialObject O O O B-CelestialObject O O O B-CelestialObject O O O B-CelestialObject O O O B-CelestialObject O O O B-CelestialObject

and calibrated with the use of miriad (Sault, Teuben Wright 1995 ). miriad was also used to perform phase and target self-calibration as well as final imaging of each configuration. The images were then primary beam corrected and exported to casa (Common Astronomy Software Applications) for processing. The 6 km and 750 m images were analysed within casa to determine flux densities and ejecta dimensions. The final set of images created had varying resolutions. The 6 km pointing at 5.5 GHz had a beam size of 2.92 × 1.54 arcsec (PA −2.50°) and at 9 GHz, a beam size of 1.71 × 0.99 arcsec (PA 0.79°). Images created from the 750 m pointing had a beam size of 13.79 × 6.98 arcsec (PA 5.04°) at 5.5 GHz, and 6.98 × 4.44 arcsec (PA 6.28°) at 9 GHz. Calibration and imaging is still on-going for the 1.5 km pointings at both spectral windows. A full combination of all the data is underway, with results from the concatenated data set to be provided in a future work (Andrews, in preparation). In this letter we focus on the presence of asymmetric spatially extended emission associated with all but one of the cool super/hypergiants, seen in the 5.5 GHz observations at the 6 km pointing. Clark et al. ( 1998 ) previously identified a cometary nebula around the RSG Wd1-26, with D10 confirming similar nebulosity around a second RSG Wd1-20, and an elliptical structure around a third RSG, Wd1-237, as well as more compact but still extended emission around three of the YHGs, Wd1-4a, -12a, and -265. The greater sensitivity of our new observations reveals striking additional detail for these structures, while resolving the nebulae associated with the last RSG, Wd1-75 and two further YHGS, Wd1-16, and -32. This leaves only a single cluster YHG, Wd1-8, with no detection at any mm or radio frequency. In Fig. 1 we present 5.5 GHz maps of these six stars, while Fig. 2 presents an optical/radio montage indicating the nebulae location and orientation. Figure 1. Shown are images of the YHGs and RSGs and their associated extended emission, from the 5.5 GHz observations at 6 km. Sources are the YHGs Wd1-4a (top − left) , Wd1-12a (top − centre) , Wd1-265 (top − right) , Wd1-16a (middle − left) , and Wd1-32 (centre) . These images are followed by the RSGs, Wd1-20 (middle − right) , Wd1-26 (bottom − left) , Wd-237 (bottom − centre) , and Wd1-75 (bottom − right) . The colourscale shows the hypergiants from the 5.5 GHz observations at the 6 km pointing, with the overlaid contours from 100 GHz ALMA observations of the cluster with a resolution of 750 × 570 mas (Fenech et al. 2018 ). W265 was out of the field of view for ALMA, so is overlaid with contours of the 9 GHz ATCA observations from the 6 km pointing. The contour levels of the ALMA observations are −1, 1, 1.414, 2, 2.828, 4, 5.656, 8, 11.31, 16, 22.62, 32, 45.25, 64, and 90.50 × 3σ (σ = 52.4 Jy for Wd1-4a, 40.0 Jy for Wd1-12a, 24.3 Jy for Wd1-16a, 28.1 Jy for Wd1-32, 30.5 Jy for Wd1-20, 63.7 Jy for Wd1-26, 31.9 Jy for Wd1-237


O O O O O O O O O O O O O O O O B-Person O O O B-Organization B-Grant I-Grant I-Grant I-Grant B-Person O O O O O O B-Grant I-Grant O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O B-Grant I-Grant I-Grant B-Person O O O O O O B-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship B-Person O O O B-Organization I-Organization I-Organization O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant B-Person O O O O B-Organization I-Organization I-Organization O B-Organization B-Person O O O O O B-Grant I-Grant O O B-Grant I-Grant I-Grant I-Grant O O O O O O O O B-Observatory B-Grant I-Grant I-Grant I-Grant I-Grant O O O B-Telescope O O O O O B-Organization I-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization I-Organization B-Grant O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Grant O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Person O O O O B-Organization O B-Grant I-Grant I-Grant I-Grant I-Grant B-Person O O O B-Organization O O B-Grant O B-Grant O O O O O O B-Database B-Database O B-Software I-Software I-Software O O O O B-Organization B-Observatory I-Observatory B-Location O O O O O O O B-Archive I-Archive I-Archive I-Archive

We thank the anonymous referee for the very useful suggestions that helped us improve this work. R.H.B. acknowledges support by FONDECYT Regular project No. 1120668. A.R.L. is grateful for financial support from ALMA-CONICYT Fund, and Dirección de Investigación of Universidad de La Serena through project DIULS REGULAR PR13144. J.L.N.C. also acknowledges financial support from the ALMA-CONICYT postdoctoral program No. 31120026. M.S. acknowledges support from ESO-Chile Joint Committee and “Becas Chile de Postdoctorado en el Extranjero” project No. 74150088. V.F. acknowledges support from the ESO-Chile Joint Committee and DIULS. M.H. acknowledges the support of the Basal PFB-06 and the Milenio Milky Way Nucleus. We gratefully acknowledge use of data from the ESO Public Survey programme ID 179.B-2002, taken with the VISTA telescope, data products from the Cambridge Astronomical Survey Unit, and funding from the FONDAP Center for Astrophysics 15010003, the BASAL CATA Center for Astrophysics and Associated Technologies PFB-06, and the Millennium Institute of Astrophysics MAS. D.M. acknowledge financial support from CONICYT by Proyecto FONDECYT Regular No. 1130196. R.K.S. acknowledges support from CNPq/Brazil through projects 310636/2013-2 and 481468/2013-7. This research has made use of SIMBAD, VizieR, and “Aladin sky atlas” operated and developed at CDS, Strasbourg Observatory, France. Also, this research has made use of NASA’s Astrophysics Data System.


O O O O O O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O B-Person I-Person O O B-Organization I-Organization I-Organization I-Organization B-Organization O O O 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 I-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O O O O O O O O O O O B-URL O O O O O O B-Software O O O O O B-Telescope I-Telescope I-Telescope I-Telescope O O O O O B-Software O O O O O O O O O B-Wavelength O O O O O O O O B-Model I-Model I-Model I-Model O O O B-Observatory I-Observatory I-Observatory I-Observatory O B-URL B-Identifier I-Identifier O O O O O O O O O O O O B-Collaboration I-Collaboration


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

Several molecular clouds and two star formation regions, Sgr B1 and Sgr B2, have been marked in the top panel. In the bottom panel, H ii regions in the GC are labelled, such as H1-8 (Yusef-Zadeh Morris 1987 ). In addition, new H ii regions, identified from our HST /NICMOS Paschen- survey, are outlined in an ellipse, two circles and boxes. Besides H2, several well-known H ii regions, as well as newly discovered ones (Wang etal. 2010 ), fall on to the orbit of molecular clouds and could represent the star formation induced by their pericentre passages. First, we consider H3, H4, H6 and H7, among the eight H ii regions (H 18) identified by Yusef-Zadeh Morris ( 1987 ) in the region between the Arches cluster and Sgr A*. Dong etal. ( 2015 ) show the presence of a single evolved massive star in each centre of H5 and H8. They find that the radial velocities of these stars are significantly different from those of nearby ionized and neutral gas. This indicates that the stars are likely interlopers and did not form in situ . In the other four H ii regions, H3, H4, H6 and H7, no evolved massive stars have been found, although the possibility exists that there are still embedded massive main-sequence stars in these H ii regions. The massive main-sequence stars normally have hydrogen or helium absorption lines. Therefore, they cannot be identified by their Paschen- emission lines in the work by Dong etal. ( 2012 ). Another possibility is that the hydrogen emission lines from the central evolved massive stars are diluted by the emission from the surrounding dust, like the dusty WC stars (Dong etal. 2012 ). Furthermore, H6 and H7 with a size of 0.1pc could be ultracompact H ii regions. Compared to H2, the embedded stars could be less massive and therefore neither have enough ionization luminosities nor have they had time to disperse the surrounding dense molecular gas. Secondly, let us consider several new H ii regions identified by our HST /NICMOS Paschen- survey in the region Galactic West to Sgr A* (see the circles, ellipse and boxes in the bottom panel of Fig. 14 ). The detailed Paschen- image of the H ii region enclosed by the ellipse can be found in fig. 3 of Wang etal. ( 2010 ). All of these regions contain evolved massive stars, such as WN, Ofpe/WN9, WC9d, B supergiant and their candidates (Muno etal. 2006 ; Cotera etal. 1999 ; Mauerhan etal. 2010a , b ; Dong etal. 2012 ). Some of them are close to the molecular cloud orbit, which include those marked by the ellipse and the two circles. Therefore, they may be molecular clouds that have experienced star formation induced by the pericentre passage around Sgr A*. The two regions marked by the boxes are somewhat off the orbit and may have different origins. In conclusion, we have demonstrated that star clusters associated with the H ii regions, aided by the CMD analysis, could help us constrain their ages and the star formation history in the GC. 5 SUMMARY In this work, we have mapped the radial


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

types is generally similar throughout. That said, we note two small biases: (i) cool stars (K stars and the only M star of the sample) have in general a small presence in the subsamples; and (ii) when the density is in the relation, there is a larger contribution of F-stars and G-stars, since asteroseismology provides most of its data for these stellar types. Table 8 Percentage of Stars in the Different Subsets Used for Obtaining the Regressions with Different Spectral Types 5.2. Linear Regression Consistency In addition to using R 2 , relative accuracy, and relative precision as the main statistics for studying the quality of the regressions, we have also developed additional consistency tests to ensure that the linear regressions are representative of the observational data. In Figure 7 , we show q – q plots of the 38 selected relations selected in a form to show whether the standardized residuals are normally distributed. The ordered standardized residuals are plotted on the ordinate of each plot, while the expected order statistics from a standard normal distribution are on the abscissa. Points close to the straight line are consistent with a normal distribution. In this figure we can see that all the relations do in general follow this straight line. Therefore, the use of linear regression is justified. Only in a few cases are there extreme departures from this straight line, but in general the departures are not statistically significant. Figure 7. q – q plots of the 38 relations. See the text for details. In Figure 8 we present the residuals as a function of the fitted values of these 38 relations. Any clear trend in these residuals can be a signature of inaccurate or inefficient regression. We have also added a LOESS (local polynomial regression) curve to guide the eye. In this figure we can see that, in general, there are no clear trends in the distributions of the residuals. In every plot, the main body of points is randomly distributed around the value zero. There are a few extreme cases, but they contain only a small percentage of the observational set. The impact of these values on the regression coefficients is analyzed in the next figure. Figure 8. Residuals vs. the fitted values of the 38 relations. The line is a LOESS curve to guide the eye. See the text for details. In Figure 9 we present a final and more complex consistency test. Here, we analyze the influence of every observational point in the regression coefficients. This influence is calculated using the Cook's distance (Sheather 2009 , D i ). This distance is calculated as a combination of the residual and the leverage (or how isolated a value is) for every point. The plots of Figure 9 show the standardized residuals as a function of the leverage, and the Cook's distance is represented by the size of the points. According to Weisberg ( 2005 ), “... if the largest value of D i is substantially less than one, deletion of a case will not change the estimate ... by much.”


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

We thank the referee for the helpful suggestions. We acknowledge the use of the public data from the Fermi data archives. This work is supported by the National Basic Research Program (“973” Program) of China (grant No. 2014CB845800), the National Natural Science Foundation of China (grants No. 11725314, 11673068, 11433009, 11543005, 11603076, 11573014, 11533003, 11473012, 11722324, 11603003, 11633001, and 11690024), the Youth Innovation Promotion Association (2011231 and 2017366), the Key Research Program of Frontier Sciences (QYZDB-SSW-SYS005), the Strategic Priority Research Program “Multi-waveband gravitational-wave Universe” (grant No. XDB23000000) of the Chinese Academy of Sciences, and the Natural Science Foundation of Jiangsu Province (grant No. BK20161096). J.J.G. is supported by the National Postdoctoral Program for Innovative Talents (grant No. BX201700115) and China Postdoctoral Science Foundation funded project (grant No. 2017M620199). B.B.Z. acknowledges the support from the National Thousand Young Talents program of China.


B-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 B-CelestialObject 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 B-CelestialObject I-CelestialObject O B-Formula I-Formula I-Formula 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 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 B-Citation I-Citation O B-Citation I-Citation O B-Citation I-Citation I-Citation O B-Citation I-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 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 B-Citation I-Citation I-Citation I-Citation O O O O 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 B-CelestialObject B-Citation I-Citation I-Citation O O B-Person B-Model I-Model B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation O B-Citation I-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 O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O 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 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 B-Citation I-Citation I-Citation I-Citation 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 B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O O O O O O B-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 B-Citation I-Citation I-Citation I-Citation O O O B-Survey I-Survey I-Survey I-Survey I-Survey B-Survey O O B-Telescope 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 B-Telescope O O O O B-Wavelength O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O

et al. 2007 ; Thornton et al. 2013 ; Petroff et al. 2015 , 2016 ). Although the progenitors of these events are debated, the large values of the dispersion measure (DM) in excess of the Galactic value of these events (Dolag et al. 2015 ) suggest they are extragalactic or even cosmological in origin. The localization of the repeating burst FRB 121102 at z ∼ 0.19 has firmly established the cosmological origin of at least this event (Scholz et al. 2016 ; Spitler et al. 2016 ; Chatterjee et al. 2017 ; Marcote et al. 2017 ; Tendulkar et al. 2017 ). The observed DM of an FRB therefore should at least have a significant contribution from the intergalactic medium (IGM). Based on the average DM– z relation, one can estimate that the FRBs are typically at distances of the order of a gigaparsec (Ioka 2003 ; Inoue 2004 ; Deng Zhang 2014 ; Zheng et al. 2014 ; Zhang 2018 ). The cosmological origin of FRBs allows them to become promising tools to study the universe and fundamental physics, e.g., probing baryon density and spatial distribution (Deng Zhang 2014 ; Mcquinn 2014 ), constraining the dark energy equation of state (Gao et al. 2014 ; Zhou et al. 2014 ; Weltman et al. 2018 ), probing the ionization history of the universe (Deng Zhang 2014 ; Zheng et al. 2014 ), tracing the large-scale structure of the universe (Masui Sigurdson 2015 ), testing Einstein’s equivalence principle (Wei et al. 2015 ; Nusser 2016 ; Tingay Kaplan 2016 ), constraining the rest mass of the photon (Wu et al. 2016 ; Shao Zhang 2017 ), measuring the cosmic proper distance (Yu Wang 2017 ), as well as constraining the magnetic fields in the IGM (Akahori et al. 2016 ). Thanks to another two properties of these mysterious transients, i.e., narrow durations (∼(1–10) ms; Lorimer et al. 2007 ; Keane et al. 2011 ; Thornton et al. 2013 ; Spitler et al. 2014 ; Petroff et al. 2015 ; Ravi et al. 2015 ; Champion et al. 2016 ; Petroff et al. 2016 ; Spitler et al. 2016 ) and a high event rate (∼10 3 –10 4 per day all sky; Thornton et al. 2013 ; Champion et al. 2016 ), lensed FRBs have been proposed as a probe of compact dark matter (Muñoz et al. 2016 ; Wang Wang 2018 ), motion of the FRB source (Dai Lu 2017 ), as well as precision cosmology (Li et al. 2018 ). In practice, there are some issues that hinder the application of FRBs for cosmological purposes. First, it is not easy to measure the redshifts of most FRBs. Localizing them is possible if they repeat, but it is possible that only a fraction of FRBs repeat (Palaniswamy et al. 2018 ). Recently, the Canadian Hydrogen Intensity Mapping Experiment (CHIME; using the CHIME/FRB instrument) has reported detections of 13 FRBs during a precommissioning phase (The CHIME/FRB Collaboration 2019a ). It is more exciting that 1 of the 13 FRBs is a second source of repeaters, which suggests that CHIME/FRB and other wide-field sensitive radio telescopes will find a substantial population of repeating FRBs (The CHIME/FRB Collaboration 2019b ). The second


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ACKNOWLEDGEMENTS We thank Alis Deason, Kathryn Johnston, and Wyn Evans for insightful comments that helped to improve the quality of the paper. A special thanks to the anonymous referee who carefully read our manuscript and provided useful comments. The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013), ERC Grant Agreement no. 308024, and PIFI Grant no. 2018PM0050. ITS and SEK thank the Center for Computational Astrophysics for hospitality.


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This paper is based on data collected at Subaru Telescope, which is operated by the National Astronomical Observatory of Japan. GM and II are supported by Japan Society for the Promotion of Science KAKENHI Grant number: 24244018. GM acknowledges support by the Swedish Research Council (Vetenskapsrådet). AKI is supported by JSPS KAKENHI Grant number: 26287034. A part of this research has made use of the NASA/IPAC Infrared Science Archive, which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with NASA. We extend a warm thank you to Yuichi Matsuda, Katsuki Kousai, Elisabeta Lusso, Cristian Saez, and Alice Shapley for providing us with their spectra, and with some clarifications on their work and helpful advice. We also thank Andrea Grazian for useful suggestions and comments on this work.


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 B-Observatory B-Telescope O O O O O O O O O O B-Telescope 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 B-Observatory B-Telescope O O O B-Wavelength O O O B-Observatory B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion B-Citation I-Citation I-Citation I-Citation O O O O O B-Telescope O O O O B-Observatory B-Telescope O O O O O O O O O O O B-Telescope O O O O O B-Telescope O O O O O O B-Tag O O O B-Observatory B-Telescope B-Wavelength O O O O O O O O O O O O B-Observatory B-Telescope 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 B-Telescope 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 B-Telescope O O B-Telescope O O O O O B-Telescope 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 B-Telescope O B-Telescope O O O O O O O O O O O O O O O O O O B-Identifier I-Identifier O O O O O O O O O O O O B-Observatory B-Telescope O O O O O O O O O O O O O O B-Observatory B-Telescope O O O O O O O B-Telescope 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

two consecutive timesteps, it was flagged as cosmic-ray pixel and its value was substituted with the median value from the two previous and two posterior timesteps. This rather conservative approach made sure that we did not filter long-lasting events (more than two timesteps), but some cosmic rays remain, as can be seen in the figures. The left panel of Figure 2 shows the temporal evolution of the flare loops during the gradual phase between 16:01 and 16:47 UT when the WL continuum emission enhancement is observed by HMI. In the right column, we can see the variation of the specific intensity of the WL continuum radiation along the horizontal cut marked by a red dotted line through the flare loop after subtraction of pre-flare images. We later convert these intensities into electron densities and can thus also determine the maximum electron density n e in the flare loops. Figure 2. Temporal evolution of SDO /HMI WL loops and their intensity. The left panel shows the HMI WL image with a cut through the flare loop (dotted red line). The solid line in the right panel shows calibrated intensities with the pre-flare subtracted in CGS units along the marked red dotted line. The dashed line shows the pre-flare intensity divided by 10. We further coaligned the SDO /HMI data with all EUV channels of the SDO /AIA data. These channels cover the temperature range between 5 × 10 4 and 2 × 10 7 K by observing the transition region and corona (Lemen et al. 2012 ). The spatial resolution of AIA is 12, while for SDO /HMI it is 1′′ and the temporal resolution is 12 s for AIA images and 45 s for HMI observations. 3. Multi-thermal Loops Seen by <italic>SDO</italic>/AIA Apart from the SDO /HMI WL evolution, we also examine the behavior of the flare loops in various SDO /AIA channels. The AIA images clearly show a multi-thermal nature of the observed loop arcade and we can deduce spatial correlations between loops in different AIA channels and those detected by HMI in the WL. In this section, we provide a qualitative description of the multi-thermal behavior and discuss possible mechanisms responsible for the formation of AIA diagnostics. Most AIA channels and a pre-flare subtracted HMI image are shown in Figure 3 . In this HMI image, the cosmic rays were intentionally not removed to show their prevalence. We also plot the intensity variations along one cut through the loop system (red dotted line in Figure 3 ). The absolute intensity on the y axis refers only to HMI, all AIA signals were scaled to have their maximum at an arbitrary value. Figure 3. Example of flare loops of AR 12673 on the west limb on September 10, 2017 at 16:20:03.8 UT in SDO /HMI (upper left plot, in this case without a correction for cosmic rays) and various SDO /AIA passbands (labeled in their titles). In the HMI panel, a pre-flare image from 15:35:48.8 UT was subtracted. HMI loop contours (marked in blue) are overlaid on all images. The emission along the red dotted line is shown for all


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 I-Wavelength B-Wavelength I-Wavelength I-Wavelength B-Wavelength I-Wavelength I-Wavelength O B-Wavelength I-Wavelength I-Wavelength I-Wavelength 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 I-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 B-Wavelength I-Wavelength I-Wavelength I-Wavelength O O O O O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength O B-Wavelength I-Wavelength I-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 B-Wavelength I-Wavelength I-Wavelength I-Wavelength 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 I-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 B-Wavelength I-Wavelength I-Wavelength I-Wavelength 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 B-Wavelength I-Wavelength I-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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 far off-limb region but give a hint of slight increase in the velocity up to 1.3 R ⊙ . Fig. 12. Effective velocity (combined thermal and non-thermal velocity) obtained along the coronal loop from various spectral lines as labelled. In Fig. 13 , we plot the non-thermal velocities ( ξ ) obtained from Fe X 184.54, Fe XI 188.23, Fe XII 193.51, and Si X 258.37 Å spectral lines. For this purpose, we incorporated electron temperature T e obtained in Sect. 3.3 to calculate the thermal velocity. Again Fe XII 193.51 Å, the strongest line, shows almost constant non-thermal velocity with height. Other lines show some increasing trend in the non-thermal velocity with height, however, the data points are highly scattered. The average non-thermal velocity, as obtained from Fe XII 193.51 Å is ≈23 km s −1 . Si X 258.37 Å shows an average value of ≈30 km s −1 with some increase with height. However, non-thermal velocities from Fe X 184.54, and Fe XI 188.23 Å show relatively lower values. Interestingly, Del Zanna et al. (2018b) have noted that the instrumental width for Fe XII 193.5 Å line appears to be constantly larger than that of the other lines. They also noticed the overestimation in line widths from Fe XII 193.51 Å line, which is partly due to instrumental issues and partly due to opacity effects in the stronger lines of Fe XII based on line ratio of Fe XII λ 193.51/ λ 195.12. However, in our coronal loop, deviation of line ratio is within 10% (see Fig. 6 ). Thus, non-thermal velocity estimation from Fe XII 193.51 Å is mildly affected. Fig. 13. Non-thermal velocity obtained along the coronal loop from various spectral lines as labelled. 3.6. Alfvén wave energy flux The Alfvén wave energy flux density is given by where ρ is mass density ( ρ = m p N e , m p is proton mass, and N e is electron number density), ξ is Alfvén wave velocity amplitude, 2 for two degrees of freedom, and V A is Alfvén wave propagation velocity given as . Therefore, the total Alfvén wave energy crossing a surface area A per unit time is given by Henceforth, the total Alfvén wave energy propagating along the loop depends on the electron number density, wave amplitude, magnetic field, and area of cross section. However, the product of magnetic field B and cross-section area A is always a constant along the loop owing to magnetic flux conservation. Therefore, the total Alfvén wave energy propagating along the loop is always proportional to . The product of is expected to be constant with height if the total Alfvén wave energy is conserved as wave propagates along the loop. Thus, we obtain the proportional Alfvén wave energy () along the loop using the N e (see Sect. 3.2 ) and ξ (see Sect. 3.5 ) obtained from Fe XII spectral lines. In Fig. 14 , we plot variations of with height. The plot shows that decreases with height. Thus this provides evidence of damping of Alfvén wave energy with height along the coronal loop, although associated error bars are very large on individual data


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

constrained by the GW signal. We can then obtain that is . Consequently, the absolute charge Q NS is e.s.u. The dimensionless charge of an NS can be estimated as (Zhang 2019a )In order to satisfy the observational constraint, one requires . This implies that the neutron star has to be a millisecond magnetar before the merger. The condition to form such a magnetar in BNS mergers is contrived, so this scenario is disfavored. Similarly, for a charged BH–BH merger system we adopt the following two most straightforward assumptions: (1) the lighter BH has a mass of 2.8 M ⊙ , which is less than 3 M ⊙ and falls into the BH mass regime; (2) only the lighter BH carries a constant dimensionless charge (for the same absolute charge Q , a lighter BH carries a higher which is more relevant). The mass ratio q of this system should be different from the range constrained above assuming an NS–BH merger, but this ratio does not enter the problem in view of assumption (2) above. We constrain the black hole charge as and the corresponding absolute charge e.s.u. The demanded dimensionless charge is comparable to the one required to explain the putative γ -ray event (Connaughton et al. 2016 ) associated with the first BH–BH merger event (Zhang 2016 ). Contrived conditions are again needed for a BH to carry such a large charge. 4.2.2. cCBC with an Increasing Charge This scenario involves a plunging BH–NS system in which the BH is immersed in the magnetic field of the NS and gains charge via the Wald mechanism (Wald 1974 ) in an initial electro-vacuum approximation. Levin et al. ( 2018 ) suggested that the BH can be charged stably to carry the Wald’s charge quantity Q W until it could transit from the electro-vacuum state to the force-free state thanks to abundant pair production induced by the strong electric field. At this point, the BH may reach the maximal Wald charge. In this scenario, there are four possible pre-merger mechanisms (first and second magnetic dipole radiation, electric dipole radiation, and magnetic reconnection close to BH’s equatorial plane; Dai 2019 ) and two possible post-merger mechanisms (magnetic reconnection at polar regions and the BZ mechanism; Zhong et al. 2019 ) to generate γ -ray emission. Following Dai ( 2019 ) and Zhong et al. ( 2019 ), we calculate (Figure 12 ) that the subthreshold GRB could be produced by the pre-merger magnetic reconnection or the post-merger BZ mechanism if the NS surface magnetic field satisfies or , respectively, given the following conditions: the radiative efficiency η γ = 1, the mass ratio is q = 5, the minimal separation between the BH and the NS is a min = 2 GM BH / c 2 + r NS , the NS mass is M NS = 1.4 M ⊙ and its radius is r NS = 12 km. The following two points are worth mentioning in our calculation: (1) We consider that the pre-merger magnetic reconnection in Equation (19) of Dai ( 2019 ) should be the BH’s magnetic field produced by the Wald charge Q W rather than that of the NS. This is because the


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

lines available in the MUSE spectral range can be seen, and our upper limit on the C iv /Ly flux ratio seems compelling enough to exclude photoionization by the QSO as the main driver of the LAB Ly luminosity. The upper limit on the He ii /Ly ratio is just below the border mentioned, so that based on this criterion alone, our object would be on the verge of being compatible with photoionization by the central source. Interestingly, only one among the B16 radio quiet targets lies in the photoionization region in Fig. 13 , but since its position corresponds to upper limits only, it remains impossible to tell how far its luminosity can really be explained by photoionization. All other objects have a too low line ratio along either one or both axes. Table 2 Upper limits to the SB of lines due to highly ionized species. Fig. 13 Ratios of high-ionization line fluxes for our object (red) and for those of B16 (Table 2) surrounding radio-quiet QSOs (blue). The He ii line is detected in only one object of the latter sample, while the C iv line is detected in three objects. The green hatched area represents the range of line ratios compatible with photoionization models ( Arrigoni Battaia et al. 2015 ). Fig. 14 Relation size–luminosity for our object (red) and for those of B16 that are radio quiet (blue). The magenta full dots represent the 14 giant LABs discovered by Matsuda et al. (2011) . 5.3.1. Two other probable Lyman alpha emitters at the same redshift We have detected two other possible Ly emission features in the neighborhood of the QSO; their coordinates are given in Table 3 . The brighter feature (LAE1) lies away from the QSO, which corresponds to a projected distance of about pkpc, and it emits within the range Å to Å. The vicinity to the QSO and the emission at wavelengths identical to the central LAB suggest that this object is emitting in the Ly line. Figure 15 (left panel) shows the extension of this emitter as found with CubEx, which is about or pkpc in diameter; if the eastern extension is real and physically belongs to the LAE, then the major axis of the LAE would reach or pkpc. This appears very large, but is consistent with the finding of Wisotzki et al. (2016) , who found many examples of LAEs with Ly emission extending to radius at similar redshift. The emission feature of this nebula consists of two peaks, as shown in the right panel of Fig. 15 . This is very typical of some Ly emitters (LAEs). LAE 221745.3+002006, for instance, shows a very similar profile ( Yamada et al. 2012 , Fig. 2). The latter authors concluded from their observation of LAEs that more than % of them show a double peak, and that in most cases the red component is stronger than the blue one, which is naturally explained by transfer effects in expanding media, even inhomogeneous ones ( Verhamme et al. 2006 , 2008 , 2012 ; Gronke et al. 2016 , 2017 ). Fig. 15 Left : CubEx optimally extracted map of the probable Ly emitter LAE1 located away from the QSO. The key


O O O O O O O O O O O O O O B-Model O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 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 B-Formula I-Formula I-Formula 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 B-Survey I-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 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 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 O O 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 B-Model 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 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 B-Wavelength O O O B-Wavelength I-Wavelength O O O O B-Wavelength O B-Wavelength O O O B-Wavelength I-Wavelength I-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 B-Wavelength O B-Wavelength O O O O O O O O O O O O B-Citation I-Citation

there is a normally distributed scatter around the mean gas metallicity given by the MZR, with the dispersion σ 0 = 0.1 dex (the intrinsic scatter in the MZR). We allow σ 0 to increase linearly with decreasing mass at M * 10 9.5 M ⊙ . 2.3.3 Distribution of metallicity within galaxies The average metallicity of a galaxy roughly corresponds to the metal content that would be measured in this galaxy at the distance of one effective radius from its centre (Kewley Ellison 2008 ). Due to metallicity gradients present within galaxies there is a certain range of metallicities with which stars can form inside their host. The azimuthal metallicity variations are typically negligible (e.g. Sánchez-Menguiano et al. 2017 ). However, typical radial abundance gradients in the local disc galaxies are around −0.1 dex/ r e (∼−0.03 dex kpc− 1 ) (e.g. Sánchez et al. 2014 ; Sánchez-Menguiano et al. 2016 ). The detailed studies of the distribution of metallicities of H ii regions within z ∼ 0 disc galaxies carried out by Sánchez et al. ( 2014 ) and Sánchez-Menguiano et al. ( 2016 ) with the CALIFA survey show that the distribution of metallicities at which the star formation proceeds is roughly symmetric with respect to the average value found at . However, the exact range of metallicities of the H ii regions and the metallicity gradient depend on the assumed metallicity calibration (see e.g. table 1 of Sánchez-Menguiano et al. 2016 ). 2 Our choice : We assume that the distribution of metallicities at which the star formation proceeds within galaxies can be represented by a normal distribution with dispersion = 0.14 dex. This particular choice of corresponds to half of the average range of metallicities of H ii regions 2 found by Sánchez et al. ( 2014 ) and Sánchez-Menguiano et al. ( 2016 ), averaged between the two studies. See Appendix E for additional discussion. 2.4 Star formation–mass relation The stellar mass and star formation rate of star-forming galaxies are strongly correlated, giving rise to the star formation–mass relation (SFMR; e.g. Brinchmann et al. 2004 ; Salim et al. 2007 ; Speagle et al. 2014 ; Tomczak et al. 2016 ; Boogaard et al. 2018 ) also called the star-forming main sequence. SFRs are measured based on the luminosities of galaxies observed in certain bands that correlate with the recent (≲100 Myr) star formation activity. Those luminosities need to be corrected for dust attenuation, which is one of the main sources of uncertainty in SFR estimation. Furthermore, conversion from luminosity to SFR is sensitive to the assumed IMF and metallicity. The most common tracers of SFR are UV luminosity (usually at ∼1500–2800 Å), certain recombination lines e.g. Hα and IR continuum emission between ∼3 and 1100 m. Different indicators are sensitive to the star formation on different time-scales: H α line typically probes short ∼10 Myr time-scales while UV and IR provide information on SFR averaged over longer ∼100 Myr time-scales (see e.g. Kennicutt Evans


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

ψ at 89°, as a function of the resonance order N for both inside (a) and outside (b) the plasmapause. Here the results are presented for the broadband MS wave model at the wave lower ( f lc ), peak ( f m ), and upper ( f uc ) frequencies, respectively. Clearly, to evaluate the resonant scattering effect for the ring current protons with energies ∼1 keV–1 MeV, the high order cyclotron resonances must be considered. As shown in Figures 1 (a) and (b), due to the variation of the k ∥ which is modified by the background plasma density, the MS waves with the given frequency distributions can cyclotron resonate with ring current protons at orders N = 3–11 inside the plasmapause, while at orders N = 4–9 outside the plasmapause. The determined resonance orders can be applied to QLT method for calculating the diffusion coefficients. Figure 1. Resonance energy of ring current protons for interactions with MS waves with different resonance orders at L = 4.5: (a) inside the plasmapause; (b) outside the plasmapause. Here the blue, green, and red lines denote the upper cutoff frequency, the peak frequency, and the lower cutoff frequency, respectively. 3.2. Scattering of Ring Current Protons In this part, we examine the MS wave-induced scattering effect of ring current protons in the form of the bounce-averaged diffusion coefficients, and compare the results obtained from both TP simulations and QLT calculations (e.g., Ni et al. 2008 ) with the given MS wave model. Figure 2 shows the 2D plots of bounce-averaged diffusion coefficients , , and as a function of equatorial pitch angle α eq and proton kinetic energy E k at L = 4.5, both inside ((a)–(c)) and outside ((d)–(f)) the plasmapause. The diffusion coefficients obtained from TP simulations, QLT calculations, and the corresponding normalized differences are presented in each column (from left to right, respectively). Here the cyclotron resonance orders discussed above are adopted for the QLT calculations. First, MS waves ∼218 pT can remarkably affect the ring current protons with the equatorial pitch angles ∼50°–90°. Specifically, the energy diffusion () dominates the wave-driven interactions with the rates at the order of ∼10 −4 s −1 for both inside and outside the plasmapause (Figures 2 (b1) and (b2), (e1), and (e2)). The pitch angle scattering () and the mixed diffusion ( ) effects are weaker than the energy diffusion effect, with the rates ∼10 −6 s −1 and 10 −5 s −1 , respectively. The results imply that the MS waves can effectively accelerate and heat the ring current protons, rather than pitch angle scattering. Clearly, the accelerating becomes more important for ring current protons at high pitch angles. Second, the maximum diffusion rates are located at several keV for ring current protons inside the plasmapause, while at several tens of keV outside the plasmapause. These differences in the diffusion rates are mainly caused by the change in the MS wave phase velocities, which are modified by the


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

the width of the frequency band, andIn our case, and , so ν 0 = 80 MHz and δ ν = 40 MHz. To seed the beam variations in our training set, we draw a 0 , a 1 , and a 2 from independent normal distributions,with the means and standard deviations μ k and σ k given in Table 3 . An extra constraint is applied to exclude FWHM( ν ) curves which dip below 15° in the 40–120 MHz band. The resulting training set of FWHM curves is shown in Figure 3 . We simulate the beam-weighted foreground temperature for ten different bins in LST by smearing the map through LST before computing the spectra. 20 20 By smearing, we refer to averaging many rotations of the foreground map corresponding to LSTs between the edges of each LST bin. The spectra from the 10 LST bins are then concatenated into the final data vector. It is important to note here that the Legendre-polynomial based toy model used to generate the beam training set in this paper is a placeholder for performing detailed electromagnetic simulations specific to the antenna used by the experiment being analyzed. Such simulations can output both antenna power patterns and S -parameters while accounting for effects such as ground plane interactions, scattering/reflections from nearby objects, and local soil properties. Since the gain, G ν , represents the instrument’s transducer gain, which includes the antenna reflection coefficient (Nhan et al. 2019 ), these simulations will also inform the model of the gain. In addition, if these simulations find that a given antenna design is sufficiently inefficient, the noise level from Equation ( 10 ) could be modified to account for the fact that the system temperature of an instrument with that antenna would not be dominated by beam-weighted foreground sources. 3. Signal training set : is formed from a training set where each curve is created by applying the turning point nonlinear signal model to a sample from the prior distribution of its parameters (see Section 4.2 , Figure 2 , and Table 2 ). Figure 3. Ten percent of the training set of 500 beam FWHM. The curves are quadratic Legendre polynomials with coefficient distributions given in Table 3 . Table 3 Parameters of Legendre Coefficient Distributions. Note: See Equations ( 14 )–( 16 ). 5. Results This section lays out the results of applying the general AMLP method described in Section 2 to the procedure put forth in Section 3 for fitting sky-averaged radio data measured with a nonideal receiver using the models laid out in Section 4 . The initial fit using the linear signal model (following Section 3.2.2 ) is shown in Section 5.1 and the final fit using the nonlinear signal model (following Section 3.2.4 ) is shown in Section 5.2 . 5.1. Fit with Linear Signal Model The signal uncertainties implied by the first MCMC fit with the linear signal model are shown in Figure 4 . The main mode of uncertainty is line-like, with a width of approximately 50 mK. This width comes from the similarity, or overlap, between the


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

that the angle between and x is . Second, we restrict to layers with the minimum variance component . This configuration restricts the analysis of the current to the cases reported in the cartoon of Figure 2 (b). These constraints ensure that the above surrogate computed from the Cluster 4 data is very close to the actual current density. The current layers detected by the PVI method under the above constraints seem to have a self-consistent shape at time lags that range from inertial to sub-proton scales, resembling equilibrium solutions of both fluid-like and kinetic plasmas. The simplest analytical model that could represent thin current layers on kinetic scales is the well-known Harris sheet (Harris 1961 ), which is widely used to describe a plasma sheath confined between two regions of oppositely directed magnetic field. It is a kinetic equilibrium and the earliest exact analytical solution of the Vlasov equation. Under some assumptions, the magnetic field follows a 1D hyperbolic-tangent profile. The number of structures selected by PVI ranges from thousands () to hundreds . Applying the geometrical restrictions of the minimum variance analysis described above, we found that the Harris profiles well describe 5% and 10% of the discontinuities. Figure 3 shows two examples of such as 1D current sheets in their local minimum variance reference frame. The time duration is (a) and (b), which correspond to 60 km and 420 km along x , respectively, assuming the validity of the Taylor frozen-in hypothesis. The maximum variance component B l performs a smooth, large-amplitude rotation, while . Note that B m , albeit very small, displays a multi-polar signature, typical of solar wind reconnection exhausts (Eriksson et al. 2015 ). B l , B m , and B n refer to the fluctuating part of the magnetic field after that the mean value, computed on the time duration of the discontinuity, is subtracted. For the above structures, the direction of the removed average field is almost aligned to and perpendicular to . Moreover, the full magnetic field component along is constant and equal to the removed average field over the interval so that the geometry corresponds to that of a common Harris sheet + guide field, as reported pictorially in Figure 2 (b). Figure 3. Fluctuations of the magnetic field (after subtracting the mean value) in the local minimum variance frame, in a discontinuity at electron (a) and sub-proton (b) scales. B l is reported with a solid (blue), B n with a dotted–dashed (green), and B m with a dashed (red) line. The thick (black) line represents the Harris profile. Panels (c) and (d) report the surrogate current density (red dashed) for the discontinuities in panels (a) and (b), respectively, together with the Harris current (black solid). The best fits from the Harris model , where and λ is the half-thickness of the layer, are also compared in the same figures (thick lines), indicating very good agreement with the plasma equilibrium theory.


B-Wavelength O O O O O O O O O O O O O O O O B-ObservationalTechniques I-ObservationalTechniques O O O O O O O O O O O O O O O O O O B-ObservationalTechniques I-ObservationalTechniques O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject O O O O O B-Instrument O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject O O O O B-CelestialObject I-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 O O O O O O O O O O O O O O O O O O O O O O O O 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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-ObservationalTechniques I-ObservationalTechniques O O O O O O O O O O O O O O

optical reflected spectra from exoplanets. The major results of this work can be summarized as follows: the CCF technique permits the recovery of the wavelength dependence of reflected spectra of exoplanets, and consequently their albedo function; the CCF technique is able to distinguish between possible albedo configurations and hint at the planetary atmosphere composition; it will be possible to probe at planetary atmospheres for planets in a vastly accessible orbital parameter range; even in cases where a low number of wavelength bins are possible, the ratio between the albedo at redder and bluer wavelengths should help constrain possible chemical and physical atmospheric configurations. as close as 2018, ESPRESSO should already be able to recover the albedo function from hot Jupiter class exoplanets with a few hours of exposure time (e.g. 51 Pegasi b with 1h); the advent of HIRES will allow to probe smaller planets (e.g. hot Neptunes and Super Earths) with just with a few hours of exposure time (e.g. HD 76700 b with around 5h and 55 Cnc e with about 4h) However, the albedo from an exoplanet is not the only factor that modulates the reflected spectrum from an exoplanet. An exciting prospect to further characterize the planet comes from the observation of the phase function of the planet and how it varies with wavelength. This function describes the light curve of a planet as a function of orbital phase. It depends not only on the fraction of the planet illuminated by the host star but also on the general scattering properties of the planet’s atmosphere. The detection of the reflected optical from exoplanets is a daunting task that requires a broad spectral coverage and a extremely high-resolution to achieve the level of S/N we require, as well as an extremely high PSF stability for long periods of time. This can be achieved with ESPRESSO@VLT, HIRES@ELT, and similar observing facilities, which will lead the way towards a more detailed characterization of exoplanets and their atmospheres. The sheer collecting power of giant telescopes, combined with the precision and stability of next-generation high-resolution spectrographs, will put researchers in a position to not only look at the reflected light from exoplanets, but use it to characterize their atmospheres in great detail. A very bright future awaits exoplanetology indeed. APPENDIX A: OPTIMAL OBSERVATION WINDOWS AND DETECTABILITY The reflected signal of the planet is small, and to detect it is essential to choose orbital phases where that signal is close to its maximum. As per equation ( 2 ), this occurs at superior conjunction (or opposition in case of a transiting planet). Unfortunately at that point of the orbit, both the planet and star will have matching radial velocities and thus be difficult – if not impossible – to separate. Even with the precise stellar template built with the CCF technique, fluctuations on the stellar flux will leave residuals in the radial velocity domain at


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after the observing sequence because of a slight saturation of the off-axis PSF obtained before the observation. An example of the output of this technique is shown in Fig 2 . Fig. 2 38th IFS spectral channel (1.63 m) with planets HR 8799 de obtained with KLIP reduction. A second approach, where ADI and SDI were used together, was then implemented. The single exposures in each of the 32 spectral datacubes were averaged. The PSF library used for the PCA fitting taking all frames into account, both along the temporal and spectral dimensions, where the PSF has moved by more than a separation criteria . In this scheme, the library is constructed using the frames spatially rescaled according to their respective wavelength. Various tests showed that a value of FWHM gives good results in terms of S/N for the detection of the planets. To account for the flux losses induced by the speckle subtraction algorithm, forward modeling is performed via the off-axis PSF of the above-mentioned star as a model for the PSF of the planet. The model is projected on the same PCA modes as the science data, and the flux loss is measured as the attenuation of the flux for the model before and after projection on the PCA modes. The fluxes of the planets are measured in the final spectral channels with aperture photometry in an aperture of diameter 0.8 (4 pixels). The flux is finally corrected for the flux loss estimated using the forward modeling. The error bars on the photometry were measured in the same way as for the IRDIS data described in Sect. 3.2 , except that we did not consider the flux variation during the exposure, as one of the two PSFs is slightly saturated. With this approach, we obtained eight spectral extractions from four independent pipelines. For each planet, a final estimate of the flux ratio between the star and planet was obtained by computing the median of the results. Astrometric measurements for planets HR 8799 de measured from the IFS are shown in Table 5 .The error budget is presented in Table 6 . The error bars are compatible with the expected ones for these targets, following the simulations of Zurlo et al. (2014) . Fig. 3 Contrastand off-axis PSFs curves for the IRDIFS_EXT data set. The 5 contrast for the two instruments are plotted as a function of the angular separation. The off-axis PSF of the star is represented as a black continuous line. Planets around HR 8799 are also shown as photometric points, the error bars are inside the dimension of the dots. The dotted vertical line indicates the coronagraph IWA. Fig. 4 Mass limits deduced from the contrast curves for the IRDIS and IFS instruments. An age of 30 Myr is assumed.Two different models are represented: the “hot-start models” BT-SETTL models, and the “warm-start models” from Spiegel Burrows (2012) . The separations where a possible planet f is expected to be (from Goździewski Migaszewski 2014 ) are shown as dashed black lines. The 5 contrast curves of IRDIS and IFS for the IRDIFS_EXT


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plot the evolution of the median size of the distribution (our results in large green circles) and compare our values to those reported in the literature (in light green): square (Pirzkal et al. 2007 ), hexagon (Taniguchi et al. 2009 ), triangles (Bond et al. 2009 , 2011 ), circles (Malhotra et al. 2012 ), diamond (Kobayashi et al. 2016 ), and inverted triangle (Guaita et al. 2015 ). We show as blue squares the median size for a sample of HAEs selected at lower redshift using the same narrow-band technique (Paulino-Afonso et al. 2017 ). We complement this figure with results for UV-selected SFGs from the literature (in light blue): large diamond (van der Wel et al. 2014 ) and left-facing triangle (Ribeiro et al. 2016 ). Finally, we show the derived size evolution of LAEs (green solid line) and SFGs (blue dashed line). The inset plot shows the estimated size ratio between SFGs and LAEs. Estimates point to SFGs being ∼5 times larger at z ∼ 0 and of the same size as LAEs at z ∼ 5.5. We hypothesize that Lyα-selected galaxies are small/compact throughout cosmic time likely linked with the physical processes that drive Lyα escape. At higher and higher redshifts, typical SFGs start to have the typical sizes of Lyα emitters, which can be seen as an alternative explanation for the rise of the Lyα emitting fraction of SFGs/LBGs into z ∼ 6. 6.3 Relations between LAEs, HAEs, and UV-selected galaxies When compared to the typical sizes of SFGs (selected as Hα emitters, HAEs) that have been studied in a previous work (Paulino-Afonso et al. 2017 ), we immediately see that the two populations are not alike in terms of their extent. Despite having only one common period with observations of both populations (at z = 2.23), where HAEs are almost two times larger than LAEs, our prediction of LAE sizes at lower redshifts is consistently lower than what we report for the HAE population. This is even more contrasting if we include the sample at z ∼ 0, where almost no evolution is expected for the LAE population. This is potentially corroborated by the existence of green pea galaxies (Cardamone et al. 2009 ; Izotov, Guseva Thuan 2011 ) that are compact in nature and found to have Lyα detections and high Lyα escape fractions (e.g. Henry et al. 2015 ; Yang et al. 2016 ; Verhamme et al. 2017 ). We also use two recent and comprehensive studies on the evolution of UV-selected SFGs (van der Wel et al. 2014 ; Ribeiro et al. 2016 , see also Shibuya, Ouchi Harikane 2015 ) that overlap both HAEs and LAEs that we have studied to complement our observations. These confirm our findings that at z ∼ 2 the typical star-forming population is larger in size than the LAE population (by a factor of ∼3). However, we see that this difference fades away and, by z ∼ 5, the two populations are indistinguishable from one another, in what their median extent is concerned. These results are in agreement with previous findings where both populations are compared (e.g. Malhotra et al. 2012 ;


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ACKNOWLEDGEMENTS The authors thank the anonymous referee for the careful reading and useful feedback. These results made use of the DCT at Lowell Observatory. Lowell is a private, non-profit institution dedicated to astrophysical research and public appreciation of astronomy and operates the DCT in partnership with Boston University, the University of Maryland, the University of Toledo, Northern Arizona University, and Yale University. In addition, some of the data presented herein were obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W. M. Keck Foundation. The authors wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Maunakea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain. We also acknowledge the UoC data base for providing us the rich data set to make this study possible. TL gratefully acknowledges support for this project from the University of Toledo Graduate Fellowship. JC acknowledges support from an NSERC Discovery Grant and a Western University SERB Accelerator Award. We thank Teznie Pugh, Jason Sanborn, and Heidi Larson at Lowell Observatory for technical support during our observation. Finally, we thank Prof. Aviv Amirav for helpful communications and useful suggestions.


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These results have important implicationsfor the delivery of water to the asteroid belt and on Earth, as also suggested by previous studies focusing on the in situ formation or a more limited migration of the giant planets ( Turrini et al. 2011 ; Turrini Svetsov 2014 ; Grazier et al. 2014 ). Raymond Izidoro (2017a ) simulated both an in situ growth and a large scale migration ofthe giant planets including gas drag. They found that a fraction of objects from beyond the current position of Jupiter are implanted in the main asteroid belt during the growth of the giant planets, generating a large-scale mixing of the small bodies. The source region of implanted asteroids was from 4 to 9 au in the in situ scenario, identified as the precursors of the C -type asteroids, and from 4 to 15 when migration was taken into account. In our migration model, we also found implanted bodies from 4 to 16 au in the asteroid belt, but most of them, 96.6%, come from 4 to 5 au region (that end up piled up in the 2:1 resonance with Jupiter at about 3 au as shown in Figs. 4 and 5 ) and just 3.4% of them come from 6 to 16 au. Differently from Raymond Izidoro (2017a ), we did not simulate the preexisting asteroid belt for computational time reasons, but we can analyse our results considering a preexisting “virtual” asteroid belt composed by S- and C- type asteroids, with the S-type dominating the inner belt and C-types more common in the outer belt. Taking into account the Minimum Mass Solar Nebula, the asteroid belt mass is about 1 M ⊕ . From the same assumption, a particle in our simulations carries 5 × 10 −5 M ⊕ and thus we can make a crude estimation of the mass that is injected in the asteroid belt. From the 5 Myr snapshots we counted the particles that ended up in the asteroid belt. The results are that in the nominal model, roughly 1 M ⊕ of outer solar system planetesimals are injected into the asteroid belt. This number is to be compared to the amount of mass in the primordial asteroid belt, that is roughly 1 M ⊕ . Hence, after the migration, about 50% of the belt is composed of outer solar system planetesimals. The nominal model is the most efficient in injecting bodies into the asteroid belt and the least efficient ones are the in situ model and the growth tracks 2.0 times faster than the nominal model, both inject only ~0.2 M ⊕ . It is important to notice that, in this model, 96.6% of the mass injected in the belt resides in the 2:1 resonance and a subsequent instability of the giant planets after the disc dispersal can affect dramatically this resonant region, depleting it almost completely. We will show this result in Sect. 5 . This will reduce drastically the contamination of the belt, leaving just 10 −2 M ⊕ of P and D type asteroids in the belt to be compared with the 1 M ⊕ preexisting belt. Even though the contamination is not so important in terms of mass, secular erosion of the mass of the asteroid belt only accounts for 50% of the its mass loss (


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We thank Oleg Kochukhov and Colin Folsom for useful discussions. We acknowledge support from the ANR (Agence Nationale de la Recherche) project Imagine. This research has made use of the SIMBAD data base operated at CDS, Strasbourg (France), and of NASA's Astrophysics Data System (ADS).