Zeeman splitting is based on the works of Landi Degl’Innocenti (1976) , Schadee (1978) , Rees et al. (1989) , and Larsson et al. (2014) . For each considered Zeeman split spectral line, ZRAD requires the following precalculated quantities: the energy levels and transitions taken from the Leiden Atomic and Molecular DAtabase (LAMDA; Schöier et al. 2005 ) or JPL spectral line catalog ( Pickett et al. 1998 ), Landé factors of the energy levels used, line strengths of the allowed transitions between Zeeman sublevels, and the radius of the gas species used. For the line shape, ZRAD includes the natural, collisional, and Doppler broadening (line shape: Voigt profile) and the magneto-optic effect (line shape: Faraday-Voigt profile; Larsson et al. 2014 ). The Voigt and Faraday-Voigt profiles are obtained from the real and imaginary part of the Faddeeva function, respectively ( Wells 1999 ). In ZRAD, a fast and precise solution of the Faddeeva function is realized with the Faddeeva package ( Johnson 2012 ). 3. Zeeman splitting We consider the Zeeman splitting theory as outlined in Sect. 3 of our previous work ( Brauer et al. 2017 ). In the following, we provide a brief description of the most important physical quantities. By assuming that the Zeeman shift is negligible when compared to the line width , the circularly polarized fraction can be written as a function of the derivative of the net flux as (see Crutcher et al. 1993 ; Brauer et al. 2017 ) whereas the frequency shift owing to Zeeman splitting can be calculated with Here, is the Bohr magneton, the Landé factor, and the total angular or atomic momentum quantum number projected on the magnetic field vector . A single prime denotes the upper level; a double prime denotes the lower level of the line transition. Following Eqs. ( 1 ) and ( 2 ), the magnetic field strength in the LOS direction can be obtained by fitting the derivative of the net flux profile to the circularly polarized fraction of a Zeeman split spectral line. The derived LOS magnetic field strength converges toward a reference magnetic field strength if the assumption of Eq. ( 1 ) is valid and the LOS is optically thin ( Brauer et al. 2017 ). The reference magnetic field strength can be calculated by averaging the LOS magnetic field strength weighted with the spectral line net flux along the LOS to the observer as follows: Here, is the magnetic field strength at a certain position, is the unit vector in the LOS direction, and is the path length along the LOS. 4. Spectral lines of CN at 113 GHz Zeeman observations of CN are usually performed by observing seven of the nine hyperfine transitions at ( Falgarone et al. 2008 ; Pillai et al. 2016 ). However, we limit ourselves to the spectral lines at and since they represent two extreme cases (see Table 1 ; Crutcher et al. 1999 ; Falgarone et al. 2008 ). The line at has the largest Zeeman shift and one of the highest relative sensitivities to compared to the other lines. In contrast, the


We are very grateful to the referee, Anthony Brown, for a constructive and thorough report that improved the manuscript substantially. We are also very grateful to Frédéric Arenou for enlightening explanations regarding the treatment of H ipparcos parallax measurement errors, and to Michail Vidiassov and David Barnes for their help with R, rgl and 3D PDF figures. We acknowledge the help of the anonymous specialists who provided their assistance on various StackExchange.com forums. H. Bouy is funded by the Ramón y Cajal fellowship program number RYC-2009-04497 and by Spanish Grant AYA2012-38897-C02-01. J. Alves acknowledges travel support from the ESAC Faculty council. This research has made use of the VizieR and Aladin images and catalog access tools and of the SIMBAD database, operated at the CDS, Strasbourg, France. This research has made use of Topcat ( http://www.starlink.ac.uk/topcat/ , Taylor 2005 ). This research made use of Astropy, a community-developed core Python package for Astronomy ( Astropy Collaboration et al. 2013 ). We acknowledge the use of the Legacy Archive for Microwave Background Data Analysis (LAMBDA), part of the High Energy Astrophysics Science Archive Center (HEASARC). HEASARC/LAMBDA is a service of the Astrophysics Science Division at the NASA Goddard Space Flight Center. Using observations obtained with Planck ( http://www.esa.int/Planck ), an ESA science mission with instruments and contributions directly funded by ESA Member States, NASA, and Canada.


The authors thank the French CNRS/INSU program PCMI for their partial support of this work. V.W. and F.H. research is funded by the ERC Starting Grant (3DICE, grant agreement 336474). The authors also thank the referee for suggestions which helped to improve this paper.


available.) CBP1 showed a lying J-shaped structure consisting of simple potential loops, while CBP2 looks like a minisigmoid structure composed of two evident sigmoidal strands (see Figures 1 (A)–(C)). A line-of-sight (LOS) magnetogram is displayed in Figure 1 (D) to show the magnetic field in the eruption source region, in which the white (black) patches represent positive (negative) polarities. The purple curve outlines the shape of CBP1, which connects opposite magnetic polarities of P1 (positive) and N1 (negative), while the green and orange curves outline the two strands of CBP2 linking opposite polarities of P2 (positive) to those of N2 (negative). It is noted that a negative magnetic polarity (N) was located in between P1 and N1. The overall eruption process can be divided into three stages: the formation of the first jet (jet1: 11:10 UT—11:30 UT), the interaction of jet1 with CBP2 (11:30 UT—11:37 UT), and the formation of the second jet (jet2: 11:37 UT—12:00 UT). In the following subsections, we discuss the eruption characteristics in association with those stages in more detail. 3.1. Formation of Jet1 and Its Interaction with CBP2 Figure 2 shows the formation of jet1 and its interaction with CBP2, in which the first, second, and third rows are XRT Al_Poly, AIA 211 Å, and AIA 171 Å time sequence images, respectively. In the bottom row, the left panel shows the magnetic flux variations (measured from the HMI LOS magnetograms) within the eruption source region of CBP1, while the right panel shows the corresponding relative intensity curve (measured from XRT Al_Poly, AIA 211 Å, and AIA 171 Å images) within the same region. The left column of Figure 2 shows CBP1 and jet1. The rising of the lying J-shaped CBP1 caused the collimated jet1, and the jet spire showed an obvious westward lateral sweeping motion as indicated by the arrows in Figures 2 (A) and (B). In the meantime, a bright patch around the eastern end of CBP1 appeared, which has a typical inverted-Y (or cusp) shape and can be regarded as the post-flare loop (PFL1) caused by the reconnection between CBP1 and its ambient open field lines (see the upward arrows in Figures 2 (A)–(I) and the inset in Figure 2 (G)). With an overall consideration of the appearance locations of the jet, PFL1, and the magnetic polarities as shown in Figure 1 (D), the magnetic reconnection should occur between CBP1 and the open field lines rooted in the negative magnetic region N, and this can also explain the westward lateral motion of the jet spire. From the EUV and soft X-ray intensity lightcurves in Figure 2 (K), one can identify that the start of jet1 was about 11:18 UT (see the vertical black line in each panel). For the magnetic flux variations (Figure 2 (J)), both the positive and absolute value of the negative magnetic fluxes showed obvious rising (decl.) before (after) the start of the jet. Such a variation pattern of the magnetic fluxes suggests the first emerging and then cancellation of the


to study time variations in the outer heliosphere and its interaction with the VLISM over more than half a solar cycle. They found that the globally distributed flux (GDF) and Ribbon evolved differently, with the GDF, which mostly arises from charge exchange in the heliosheath, exhibiting a leveling off and partial recovery of ENAs consistent with the prior output flattening and recovery of the solar wind output. In contrast, the ribbon showed a greater time delay and loss indicating a source of the Ribbon beyond the heliopause, most likely as a secondary ENA source—one of the six original ideas suggested by the IBEX team at the time of the discovery (McComas et al. 2009c ). Since then, a variety of more detailed physical processes for various types of secondary sources have been proposed (Chalov et al. 2010 ; Heerikhuisen et al. 2010 ; Schwadron McComas 2013 ; Isenberg 2014 ; Giacalone Jokipii 2015 ; Zirnstein et al. 2018a ). As also pointed out by McComas et al. ( 2017 ), in the second half of 2014 the dynamic pressure increased by ∼50% from ∼1.6 to ∼2.4 nPa and remained that way for at least the following couple of years. These authors discussed how such a persistent increase in the solar wind output and dynamic pressure should have a continuing major impact on evolution of the structure of the outer heliosphere and the returned ENAs. Specifically, they predicted that the ENA response should be (1) seen first from the direction of maximum heliosheath pressure ∼20° south of the upwind direction (McComas Schwadron 2014 ), (2) observed first in the highest energy ENAs, which travel back fastest and then extending to lower energies over time, and (3) followed a couple years later by changes from the Ribbon and back along the flanks of the heliosphere. IBEX observations generally bore out these predictions and McComas et al. ( 2018b ) showed that this large increase in solar wind dynamic pressure observed in the second half of 2014 at 1 au had begun to modify the heliosheath and produce enhanced higher energy ENA emissions observed near Earth by IBEX starting in late 2016. As predicted, the enhanced emissions were centered south of the upwind direction and were seen first in the higher energy ENAs. McComas et al. ( 2018b ) also combined the observations with MHD simulations to show that the heliosphere was re-expanding from this persistent pressure enhancement after at least a decade of diminished size. McComas et al. ( 2018b ) further connected the IBEX observations with simulations to show that this pressure enhancement also very likely produced the largest enhancement in heliosheath dynamic pressure seen at Voyager 2, which was observed in late 2015 (Richardson et al. 2017 ). The roughly one year between the Voyager 2 observation and pressure enhancement beginning at 1 au in late 2014 indicated that Voyager 2 observed a transient pressure wave in the heliosheath, which was launched by the supersonic solar wind reaching the termination


is ∼92.5 per cent, and improves as the offset distance becomes closer to zero. Ching et al. ( 2017 ) provided optical identifications using data from Sloan Digital Sky Survey (SDSS) of 19 179 of radio sources from FIRST using over an area of 800 deg 2 . They obtain a reliability of 93.5 per cent using a rule-based methodology with visualization inspection of complex FIRST sources. We generalize this analysis to all collated groups and investigate any second-order effects as functions of collated number of FIRST components, maximum distance ( D ) and curliness ( Q ). The R was evaluated across a range of separations (spaced from 0 to 10 arcsec in steps of 1 arcsec) after dividing our collated groups into meaningful subsets. For the subsets in the D and Q dimensions, we established boundaries at the 20th, 40th, 60th, 80th, 85th, 90th, and 95th percentiles, where finer bins were used in regions of the parameter space with rapid variations identified after inspection of the distribution. Otherwise, we created boundaries based on the number of associated FIRST components in each collated group. We interpolate between R measures across these dimensions to create a set of reliability curves, which we present as in Fig. 5 . Broadly speaking, these curves show that as measures of complexity increase, judged either by the number of collated FIRST components or Q , the infrared predicted position becomes less reliable. At a threshold of 3.4 arcsec, these R are above 80 per cent with significant spreads of upwards of ∼12 per cent between the simple and complex groups. However, the reliability curves in Fig. 5(c) suggest groups across all D have about the same degree of reliability. We use these interpolated reliability curves to provide a measure of reliability for all collated groups in our catalogue data products for each of these dimensions. For groups outside the range of these reliability curves, we set the R = 0.5 across all dimensions. Of the 24 reliability curves in Fig. 5 , 6 have fewer than 20 genuine matches with separations 1 arcsec and are the most susceptible to small number statistical effects. Since increasing separations accumulate counts from smaller separations (i.e. bins are not exclusive), the number of genuine matches very quickly grows so that all other curves and separation bins have at least 20 genuine matches. Figure 5. Panel (a): the reliability curves of the cross-matched infrared predicted positions against AllWISE as a function of number of collated FIRST components. Panel (b): the reliability curves of the cross-matched infrared predicted positions made against AllWISE as a function of the parameter. Boundaries of the were spaced to contain roughly the same number of groups to maximize the clarity of the different reliability trends. All groups included in this figure contain three or more FIRST components. Panel (c): the same as panel (b) except as a function of D . All groups included in this figure contain two or


ACKNOWLEDGEMENTS The authors wish to thank Kathryn Johnston and Douglas Boubert for stimulating discussions that helped to improve this paper. VB is grateful to Natàlia Mora-Sitjà for the careful proofreading of the manuscript. The authors thank the anonymous referee for thorough reading of the paper. 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. AJDe is supported by a Royal Society University Research Fellowship. AJDe also acknowledges support from the STFC grant ST/P000451/1. NWE thanks the Center for Computational Astrophysics for hospitality during a working visit. The authors gratefully acknowledge support by CONICYT/RCUK’s PCI program through grant DPI20140066 (‘Newton Funds’). MC is additionally supported by the Ministry for the Economy, Development, and Tourism's Millennium Science Initiative through grant IC 120009, awarded to the Millennium Institute of Astrophysics (MAS); by Proyecto Basal PFB-06/2007; and by FONDECYT grant #1171273.


than the RM of the low- z DLA sample. Such a probability indicates no significant effect. Any additional RM contribution from the plasma of the intragroup medium (see Section 3.7 ) must be low, indicating either low electron density, a weak magnetic field, or field reversals along the line of sight. The most likely scenarios are either that there is a (1 + z ) 2 dilution in the RM of background quasars, or that the Galactic RM foreground varies substantially between samples. There is no evidence for a (1 + z ) 2 dilution in the RM of the DLAs themselves, which do not show a marked difference from the control samples. Previous attempts to observe the former scenario of an evolving background quasar, e.g. Hammond, Robishaw Gaensler ( 2012 ), find that any (1 + z ) 2 dilution in RM due to cosmological expansion is weak out to z ∼ 3.5 (see also Xu Han 2014 ). If our data do therefore show an evolution in the background quasars, it may be due to a low-redshift selection effect on, for example SDSS quasars relative to high-redshift SDSS quasars, or possibly a low-redshift evolution in the magnetoionic environment surrounding the quasars themselves. To constrain the latter scenario of a varying Galactic RM foreground between samples, we use the best available model from Oppermann et al. ( 2015 ). A plot of the distribution of Galactic RMs (GRMs) towards each source is shown in Fig. 9 . There is again no difference between specific samples. We calculate a Bayesian probability of 61.5 per cent that the GRM towards J1243+4043 is greater than the GRM towards the low- z DLA sample based on 21-cm absorption measurements. This is again consistent with no effect. The combination of no difference in RM, together with no difference in GRM, means that we are consequently unable to draw conclusions about the coherent magnetic fields in the DLA in J1243+4043 itself. The only difference between the data sets is the distributions of the high- versus low-redshift RMs, which display no subsequent difference in the GRMs. This is consistent with our earlier interpretation of either an uncontrolled selection effect or an evolution of the quasar magnetoionic environment at low redshifts. Figure 9. The distribution of GRMs for high- z DLAs (top panel) and low- z 21-cm absorbing QGPs (bottom panel). The ‘control’ refers to sight lines with no DLA ( top ) and no 21-cm absorption ( bottom ), respectively. In terms of J1243+4043, the magnetic field properties do not allow us to distinguish between different scenarios in order to place strong constraints on this source. Future broad-band spectropolarimetric observations of this source will enable improved tests that can attempt to determine where this sight line fits within the greater source population. 3.7 H <sc>i</sc> emission from the associated galaxy group: the environment of the foreground galaxy In the WSRT data, we serendipitously detect H i 21-cm emission associated with other members of the galaxy group. The group


we have optimistically ignored flux and noise from unsubtracted host-galaxy light that will be there as a consequence of not having a galaxy template at the time of classification. Even if a spectrum of the host galaxy does exist (e.g., from a ground-based spectrograph), the exact galaxy SED at the position of the SN will not be accurately measured. The SN Ia efficiency for a given selection cut (see Section 3.1 ) is shown in Figure 6 . Efficiency is defined as the number of SNe correctly identified as Type Ia and passing each cut, divided by the number of SNe Ia that pass Cut 0. This calculation is per 0.1 redshift bin. SNe that pass Cut 4 have short-, medium-, and deep-exposure IFC-S spectra, in addition to the six short follow-up spectra. Figure 6. SDT and SDT* (left and right panels, respectively) SN Ia selection efficiency as a function of redshift. Efficiency is defined as the number of SNe correctly identified as Type Ia within each cut, divided by the number of SNe Ia that pass Cut 0 (see Section 3.1 ). The efficiency is calculated per 0.1 redshift bin. The gold squares, green diamonds, blue triangles, and black circles represent the efficiency of SNe Ia that pass Cuts 1, 2, 3, and 4 respectively. Lines connect data from the same tier of the survey. The large drop in efficiency from the first to the second cut at z 0.8 for the SDT strategy is caused primarily by the SDT requirement that the SN flux rises between each epoch. Comparison of the two strategies suggests that the looser selection criteria of the SDT* strategy is significantly more efficient than that of the SDT. The efficiency is low at particular redshifts, 0.3 z ≤ 0.4 and 0.7 z ≤ 0.8. This efficiency gap is partially the result of the survey design producing insufficient SN discoveries at the high- z end of each tier. However, photometric selection criteria that require the color to be consistent with an SN Ia at their host-galaxy redshift, and that the flux rise between epochs, are the main contributors to the low efficiency. For the shallow imaging tier, which covers 0.1 ≤ z 0.4, these criteria are problematic due to the tier’s short 13 s exposure, which results in noisy light curves and an undetectable rise value. The large reduction in the number of SNe between Cuts 1 and 2 is also caused by the required increase in flux between epochs. In many cases, statistical noise causes a candidate to appear to fade between two successive epochs. To reduce this selection artifact, this criterion is loosened via the iterative examination of a range of measured rise values (including negative values) for the simulated SNe Ia as a function of redshift for each tier, and a looser cut is applied. The requirements on the discovery colors ( Y − J for shallow, J − H for medium and deep) are also tightened, excluding some of the most extreme SNe Ia and significantly reducing the number of CC SNe at each step. The effect of these improved selection criteria is to increase the SN


data. We assumed radial expansion, one of the simplest laws for the velocity. Radial expansion is a simple definition and the expected case if launching takes place along the force lines of a (locally) radial magnetic field. A linear variation of the absolute value is in general expected if most accelerations take place at the beginning of the process; in our case, variation depending on the latitude and – (as for the density, see Appendix A.1) leads to somewhat better predictions than dependence on the distance to the center. We can exclude some other simple cases, such as constant velocity modulus, expansion in the axial direction, and expansion parallel to the equator, for which the predictions do not match the observations. However, other velocity laws, such as that found for the outflowing gas in Red Rectangle by Bujarrabal et al. (2016), which is more complex, would lead to results compatible with the data (although involving a higher number of parameters). We stress that the launching mechanism itself is obviously very uncertain and its possible nature is a weak argument to support any velocity field; a theoretical discussion on such processes is beyond the scope of this letter. The total size, general shape, and overall velocity of the outflowing gas are however relatively well constrained, since they are given by the observed structure at several km s from the central velocity and the total velocity extent of the emission. As mentioned in Sect. 3.1, the assumption of LTE level population simplifies a lot our analysis. Nevertheless, we must keep in mind that the rotational temperatures we use in our calculations may only represent -averaged excitation temperatures and not true kinetic temperatures. Since high- levels can obviously be less populated in reality than for LTE, these rotational temperatures are probably a lower limit to the actual ones in the outflowing, relatively diffuse gas. Another consequence of the assumption of thermalized level populations is that it is not possible to distinguish the effects of the density and the relative CO abundances, (CO, CO). Fortunately, seems relatively well constrained in the best studied objects, particularly (CO), which is the basic parameter to determine the total density and mass because of the lower opacity of CO lines. Our previous works always yielded (CO) ranging between 10 and , both for post-AGB disks and for young PNe in general. We will adopt (CO) to ease the comparison with previous results on this object (Bujarrabal et al. 2013a ). In order to match the relatively low CO/CO intensity ratio, we need a relatively low abundance ratio. We adopt (CO) 10; similar low ratios are often found in similar objects. CO is weaker than CO , confirming that the CO emission is not very opaque. Our model yields typical values of the optical depth (CO ) 3 in the disk (for the representative velocities), while we typically find (CO ) 0.2 in the outflow emission. For CO , we find optical


prior odds ( Jeffreys 1998 ): Here, and denote the hypothesis of validity of the direct and non-direct abundance proxy, respectively, and the probability represents how well some data are explained under the assumption of a hypothesis . Instead of the Bayes factor integral we use the maximum likelihood estimate. We obtain -values around , except for Kepler-93b and Kepler-10b with -values of . This means that only for Kepler-93b and Kepler-10b, there is a strong evidence that the direct abundance proxy better explains the planetary mass and radius. Generally, it will be very difficult to study the validity of a direct correlation of relative bulk abundances between star and hosted exoplanet given usual data uncertainties. Further studies on solar system objects are needed to improve our understanding of such abundance correlations and their dependence on planet formation history. 5. Discussion of the assumptions The success of an inference method is subject to the limitations and assumptions of the forward function . Firstly, we consider pure iron cores, which may lead to a systematic overestimation of core density and thus an underestimation of core size, if volatile compounds in the core are significant. The trade-off between predicted and independently inferred core sizes can be on the order of few to tens of percents, as shown for the terrestrial solar system planets in Dorn et al. (2015) . Secondly, our approach assumes sub-solidus conditions for core and mantle as well as a perfectly known EoS parameters for all considered compositions. For the six exoplanets considered here, their pressures and temperatures exceed the ranges for which these parameters can be measured in the laboratory. Clearly, extrapolations introduce uncertainty. Thirdly, we have assumed pure water composition of the ice layer, but other compounds such as CO, CO, CH, NH, etc. are also possible since the additional elements are relatively abundant. We have used water as a proxy for these volatiles in general because (1) oxygen is more abundant than carbon and nitrogen in the universe, and (2) water condenses at higher temperatures than ammonia and methane. Fourthly, our atmospheric model uses prescribed opacities of Jin et al. (2014) , which is suitable for solar abundances. In this aspect, the prescription is therefore not self-consistent with the non-solar metallicity cases we present in this work. We have checked that using different infrared and/or visible opacities can introduce errors in radius of 5%. Models that compute line-by-line opacities with their corresponding atmospheric abundances should be performed in the future to compute planetary radii in a self-consistent way. Another aspect is our assumption of ideal gas behavior. We have checked that for atmospheric mass fractions (/) of up to 1%, the difference in the radius between using the Saumon et al. (1995) EOS and ideal gas (for H-He atmospheres) can reach 10%. For the vast majority of our results,


We thank Hendrik Hildebrandt, Douglas Applegate, and Reiko Nakajima for useful discussions. We also thank Violeta Gonzalez-Perez and the anonymous referee for fruitful comments. Hananeh Saghiha gratefully acknowledges financial support of the Deutsche Forschungsgemeinschaft through the project SI 1769/1-1. Stefan Hilbert acknowledges support by the DFG cluster of excellence “Origin and Structure of the Universe” ( http://www.universe-cluster.de ).


A.C.C. acknowledges the support of the UK Science and Technology Facilities Council, as well as the Scottish Universities Physics Alliance. J.L. is supported by an NSF Astronomy and Astrophysics Postdoctoral Fellowship under award AST-1701487. GAMA is a joint European-Australasian project based around a spectroscopic campaign using the Anglo-Australian Telescope. The GAMA input catalog is based on data taken from the Sloan Digital Sky Survey and the UKIRT Infrared Deep Sky Survey. Complementary imaging of the GAMA regions is being obtained by a number of independent survey programs, including GALEX MIS, VST KiDS, VISTA VIKING, WISE , Herschel -ATLAS, GMRT, and ASKAP, providing UV to radio coverage. GAMA is funded by the STFC (UK), the ARC (Australia), the AAO, and the participating institutions. The GAMA website is http://www.gama-survey.org/ . Based on observations made with ESO telescopes at the La Silla Paranal Observatory under program IDs 179.A-2004 and 177.A-3016.


There are no noteworthy objects adjacent to IMS J2204+0112, and we found no spectral features with respect to the velocity as one can expect from its redshift. 3 3 At z = 5.926, the prominent [C ii ] 158 μ m line is located at the band gap between bands 6 and 7. In the defined spectral windows, there could be a highly excited CO( J = 21–20) line and several H 2 O lines, but they are expected to be weak and/or rare at z ∼ 6 (Narayanan et al. 2008 ; Bañados et al. 2015 ). Using the IMFIT task of the CASA package, we fitted the source on each continuum map with a simple 2D Gaussian model, resulting in the integrated flux densities at 250 and 343.5 GHz being f 250 GHz = 1.474 ± 0.023 and mJy, respectively. Note that the peak flux densities are 1.289 ± 0.020 and 2.966 ± 0.027 mJy beam −1 , respectively. These flux densities are higher than the value expected from the relation between and of other high-redshift quasars (Equation (2) in Venemans et al. 2016 ; see details in Section 4.1 ) by a factor of six, although there has been a recent suggestion that there is no correlation between and (Venemans et al. 2018 ). Assuming that the FIR flux is dominated by the host galaxy, no features in the residual maps after the point source model subtraction (right panels of Figure 1 ) is consistent with its host galaxy being as compact as (or about 4 kpc in physical scale at z ∼ 6), like those of other high-redshift quasars (Wang et al. 2013 ; Willott et al. 2015 , 2017 ; Venemans et al. 2016 , 2017a ; Mazzucchelli et al. 2017 ; Decarli et al. 2018 ). The central positions of the ALMA detection are offset by only about 02 from the z -band position (see crosses in Figure 1 ). These small offsets between the optical and submillimeter detections are in agreement with the previously reported uncertainties of ALMA astrometry (Capak et al. 2015 ; Willott et al. 2015 ; Pentericci et al. 2016 ), disfavoring the possibility that the submillimeter flux comes from a neighboring or foreground galaxy. Figure 2 shows the spectral energy distribution (SED) of IMS J2204+0112 in the observed frame. The black filled circles represent the flux densities of IMS J2204+0112 from Kim et al. ( 2015b , 2018 ) and the values derived from the archival data (see Section 2.2 ), while the red filled circles are from our ALMA observation. Also plotted are the composite quasar spectrum (gray line; Selsing et al. 2016 ), the intrinsic SED of a type 1 quasar (green line; Lyu Rieke 2017 ), and the empirical SED of ULIRGs hosting AGN at z ∼ 2 (purple line; AGN4 of Kirkpatrick et al. 2015 ). The ULIRG AGN template is consistent with the submillimeter data, which suggests that the host of IMS J2204+0112 is ULIRG-like, similar to the hosts of other high-redshift quasars (Wang et al. 2013 ; Willott et al. 2013 , 2015 , 2017 ; Venemans et al. 2016 ; Decarli et al. 2018 ; Izumi et al. 2018 ). Note that the templates were redshifted to the observed frame using z = 5.926 (Kim et al. 2018 ), including


They used an automated search, applying a ‘friends-of- friends’ algorithm to find groups in the magnitude-limited Center for Astrophysics 2 redshift survey (CfA2; de Lapparent, Geller Huchra 1986 ) and Southern Sky Redshift Survey (SSRS2; da Costa et al. 1991 ) catalogues. This algorithm used projected distances between galaxies (ΔD ≤ 50 kpc), and their line-of-sight velocity differences (Δv ≤ 1000 km s −1 ) to determine whether two galaxies belong to a group. This methodology was adopted in order to eliminate biases as a function of distance which are introduced by visually selecting groups, as Hickson ( 1982 ) had done. Selecting CGs based on their redshift reduces the possibility of chance projections, however the isolation criterion was not rigorously satisfied and therefore many RSCGs are actually components of larger structures. Because of this, RSCGs 21, 67 and 68 are excluded from our analysis as they are part of clusters, thus reducing our sample to 46 CGs (Walker et al. 2012 ). The RSCGs in our sample were therefore selected to have properties similar to HCGs. In addition, Walker et al. ( 2010 ) chose to include only CGs that are at a sufficiently low redshift ( z 0.035) that the polycyclic aromatic hydrocarbon features do not shift out of their rest-frame IRAC bands to maintain their rest-frame positions in mid-IR colour space. The 46 remaining CGs in our sample satisfy this requirement. The coordinates and group velocities of each CG are given in Table 1 , as well as the breakdown of group properties such as group H i content. Table 1. HCG and RSCG sample. Notes . a Position data taken from Hickson ( 1982 ) for HCG sample. b Position data taken from Barton et al. ( 1996 ) for RSCG sample. c Velocities corrected to CMB taken from http://ned.ipac.caltech.edu/ for all CGs in our sample. d CMB corrected values from http://ned.ipac.caltech.edu/ with a cosmology of H 0 = 70 kms −1 Mpc −1 , Ω M = 0.3, Ω Λ = 0.7. e Values taken from http://ned.ipac.caltech.edu/ with a cosmology of H 0 = 70 kms −1 Mpc −1 , Ω M = 0.3, Ω Λ = 0.7. f SDSS Optical r -band Data from Walker et al. ( 2013 ). g Group types as defined by J07 . h Walker et al. (submitted). i These CGs are part of clusters. Their photometry is presented in Table 5 , but they are not included in the subsequent analysis. 2.2 UV data Swift is a multiwavelength observatory (Gehrels et al. 2004 ) whose primary goal is to study gamma-ray bursts. When Swift is not following gamma-ray burst targets, there is a fill-in program of other observations. The UVOT (Roming et al. 2005 ) instrument is a 30 cm telescope with a 17 × 17 arcmin 2 field of view that provides UV and optical coverage (1600–8000 Å) with a spatial resolution of ∼ 2.5 arcsec. It uses a micro-channel-plate, intensified photon- counting CCD detector. It has 256 × 256 active pixels, each of which is subdivided into 8 × 8 pixels using a centroiding algorithm (Breeveld et al. 2010 ). The data used in this study originated from


This paper used data from the JCMT Survey M16AL001 awarded by the East Asian Observatory. We thank the JCMT staff for carrying out the observations and contributions to the data reduction. We greatly thank K. Hodapp for help with the ephemeris for EC 53. We also thank S. Lee for help with the SED fitting. The authors appreciate valuable comments by A. Pon, A. Scholz, H. Kirk, Y. Aikawa, V. Chen, and C. W. Lee. This research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) (grant No. NRF-2015R1A2A2A01004769) and the Korea Astronomy and Space Science Institute under the RD program (Project No. 2015-1-320-18) supervised by Ministry of Science and ICT. G.J.H. is supported by general grant 11473005 awarded by the National Science Foundation of China. D.J. is supported by the National Research Council of Canada and by an NSERC Discovery Grant. S.M. is partially supported by an NSERC graduate scholarship. M.K. was supported by by Basic Science Research Program through the National Research Foundation (NRF) of Korea funded by the Ministry of Science and ICT (No. NRF-2015R1C1A1A01052160). The JCMT is operated by the East Asian Observatory on behalf of The National Astronomical Observatory of Japan, Academia Sinica Institute of Astronomy and Astrophysics, the Korea Astronomy and Space Science Institute, and the National Astronomical Observatories of China and the Chinese Academy of Sciences (Grant No. XDB09000000), with additional funding support from the Science and Technology Facilities Council of the United Kingdom and participating universities in the United Kingdom and Canada. This research has made use of the Canadian Astronomy Data Centre operated by the National Research Council of Canada with the support of the Canadian Space Agency. This research used the services of the Canadian Advanced Network for Astronomy Research (CANFAR, specifically VOSpace), which in turn is supported by CANARIE, Compute Canada, University of Victoria, the National Research Council of Canada, and the Canadian Space Agency. 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. Facility: JCMT (SCUBA-2) (Holland et al. 2013 ). Software: Starlink (Currie et al. 2014 ), Astropy (Astropy Collaboration et al. 2013 ), Python version 2.7, APLpy (Robitaille Bressert 2012 ).


AW acknowledges support by Polish Ministry of Science and Higher Education in Mobility Plus Program and Polish National Science Centre for supporting this work through grant DEC-2011/03/N/ST9/01867. Support from the German Ministry for Education and Research (BMBF) through the Verbundforschung Astroteilchenphysik grant 05A11VH2 is gratefully acknowledged. This research was supported in part by PLGrid Infrastructure.


respect to the geometric centre, with a sinusoidal function was derived by Williams et al. ( 2016 ). Fig. 5 shows the resulting expansion velocity of the forward shock as a function of the position angle for Model B at t = T age = 450 yr; the detected velocities of the proper motion from the X-ray and the radio in Williams et al. ( 2016 ) for a distance of 2.3 kpc are also indicated. The velocities from the simulation for Model B at different position angles of the forward shock range from 3000 to 4000 km s −1 . For the shock velocities from the simulation and the ones derived from X-ray/radio observations according to the position angle, a significant deviation exists between 50° and 100°. In particular, the detected velocity at θ = 80° is about 1000 km s −1 smaller than the simulation value. Moreover, the velocities from θ = 200° to 250° are about 500 km s −1 smaller than the detected ones. Apart from this variation, at θ = 15° and 30°, the resulting velocities are consistent with those detected in the radio. From 120° to 150°, coincident with the protrusion to the south-east, the detected values of velocities and the decreasing trend are reproduced. The increasing trend, which is indicated in both the X-ray and the radio observations, is also consistent with the simulation of the velocities for the position angle from 150° to 180°. Moreover, except for 276°, the simulated velocities from 250° to 350° are about 3500 km s −1 , which is in agreement with the averaged values of the detected ones in the radio and the X-ray band. Figure 5. The distribution of the speed of the forward shock in relation to the position angle in the plane x = 0 for Model B at t = T age = 450 yr. The detected velocities at different positions on the periphery of Tycho's SNR for a distance of 2.3 kpc based on the radio and the X-ray observations are also indicated for comparison (Williams et al. 2016 ). 4 DISCUSSION AND CONCLUSIONS A series of 3D MHD simulations have been performed both to investigate the formation mechanism of the peculiar morphology of Tycho's SNR and to derive the ambient material distribution prior to the supernova. These simulations are based on the assumption that the progenitor is imbedded in a bubble that is blown by the wind, which has a latitude-dependent density distribution. Moreover, the inclination angle between the pole axis of the wind and the north direction, and the spatial motion of the progenitor are included in order to reproduce the asymmetry of the profile of the SNR shock. With a pole velocity of v p = 100 km s − 1 , ξ = 20 and a duration of T w ∼ 10 5 yr, an inclination angle of ∼50° between the pole of the wind and the north direction and a spatial velocity of v s ∼ 0.3 v p are derived based on the simulation to reproduce the detected profile of the outer border of the remnant. Furthermore, because a wind with a velocity greater than 100 km s −1 can be produced as a result of accretion onto a WD, an SD scenario for the


H.J. acknowledges support from the Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Education (NRF-2013R1A6A3A04064993).


mass) of the ejecta are mainly associated with the observational data near the peak time (∼1 day) and the optimal pulsar luminosity mainly depends on the late observations (i.e., a few days after the peak time). If a high ejecta mass is adopted in the fittings, the contribution of the PWN emission to the late phase may be low. Then, a low pulsar luminosity may be found if a high ejecta mass is adopted in the fittings. Figure 4. Fitting result (solid lines) of AT 2017gfo, where the observational data are described with circles and the upper limits are represented with triangles. Figure 5. Posterior probability density functions for the physical parameters of AT 2017gfo from MCMC simulations. Table 1 Fitting Result from MCMC Fitting In order to test our fits result, we confront our result with HST observations (left panel), Swift observations (middle panel, UVW1 , UVW2 , and UVM2 bands), MASTER optical observations (middle panel, W band), and Spitzer Space Telescope observations (right panel) in Figure 6 . We add the observational data of HST at >100 days (Lyman et al. 2018 ; Margutti et al. 2018 ; Lamb et al. 2019 ; Piro et al. 2019 ). It is found that the model curve is lower than data points, which suggests the late time observation is dominated by the afterglow of GRB 170717A. The observational data of the Spitzer Space Telescope is from Villar et al. ( 2018 ). This figure reveals that our result is consistent with the data from HST , Swift , MASTER , and Spitzer Space Telescope , which were not used in our MCMC fits. In observations, it is found that the observed radiation spectrum of AT 2017gfo gradually deviates from the thermal radiation spectrum over time (Troja et al. 2017 ). Then, we plot the radiation spectrum from 11.5 to 19.5 days after trigger based on our fits result. The radiation spectra are shown in the left panel of Figure 7 , where the circles and triangles are the observational data laying closest to our selected time. One can find that our fits result describes the observed radiation spectra nicely. It is interesting to point out that the spectral peak of the thermal component moves from ∼10 14 Hz at t = 10.5 days to the very low frequency at t = 19.5 days. Moreover, the thermal component is comparable to the nonthermal component at t ≲ 19.5 days. This behavior suggests that the bolometric luminosity at t ≲ 19.5 days can be well described with the thermal emission from the ejecta. In the right panel of Figure 7 , we compare the thermal luminosity based on our fitting result with the observed bolometric luminosity (Waxman et al. 2018 ). One can find that our thermal luminosity describes the observed bolometric luminosity very well. Figure 6. Confronting our fitting result with HST observations (left panel), Swift observations (middle panel, UVW1 , UVW2 , and UVM2 bands), MASTER optical observations (middle panel, W band), and Spitzer Space Telescope observations (right panel). Figure 7. Comparison of radiation spectra


since the LC acts as a pin-hole, as well as due to their rareness. Single scattering, which leads to angular momentum change of ∼ j lc , is associated with impact parameter ∼( m * j cir / M bh j lc ) r . This impact parameter has to be ≳ R * , and in terms of r, m * , and M bh , strong scattering is relevant if This condition is easily satisfied for TDEs of main-sequence stars, and even for TDEs of red giants or binary break-ups, which leads to HVSs’ production, 3 it is satisfied for apoapsis distances r ∼ r h , which dominates the rate of TDEs and hyper velocity stars’ production. 6 SUMMERY AND DISCUSSION In this work, we have discussed the statistical properties of the pre-TDE dynamics and its correlations with the properties of the TDEs. In general, empty LC ( j d / j lc ≪ 1) is associated with non-violent TDEs of disrupted stars, in which stars that have already experienced significant tidal interaction with the SMBH experience TDE with marginal periastron (β − 1 ∼ j d / j lc ≪ 1). Similarly, full LC is associated with violent TDEs [] of non-disrupted stars. As for minority populations, different behaviour occurs for empty LC and full LC while considering single value of j d / j lc . In empty LC, a significant fraction () of the TDEs are non-typical being violent and involve mostly non-disrupted stars. This population of TDEs relates to the logarithmic fraction of stars that have been scattered into the LC by single large scatterings rather than by a large number of small scatterings. In the case of full LC, the fraction of non-violent TDEs of disrupted stars drops to zero for j d / j lc ≳ 0.3. However, significant minority population does arise for full LC, while assuming realistic j d / j lc distribution that arises due to the apoapsis distribution of the stars in the galaxy (Section 4 ). In this case, stars in orbits of marginal LC dominate the rate of TDEs, and as a result even if the LC is extremely full at the radius of influence [ j d, h = j d ( r h ) ≫ j lc ], an asymptotic fraction of of the TDEs involve stars in empty LC. Therefore, for any value of j d, h , at least a significant fraction () of the events are non-typical. Finally, in Section 5 , we discuss the value of j d, h / j lc in realistic astrophysical systems and find it to be ≫1 for red giants and for main-sequence stars. The physical consequences of previous interactions with the SMBH were not in the focus of the current work, and therefore are only briefly presented in the current section. For red giants, the role of previous interactions was already presented by MacLeod et al. ( 2013 ). According to this model, due to their inflated structure, red giants tend to ‘graze’ the LC, loose small amount of mass in each passage, and get back to equilibrium as an object of lower mass. This picture gives rise to ‘spoon feeding’ TDE instead of the violent typical TDE. This picture agrees perfectly with our expectation that most of the TDEs of red giants are expected to be


review by Somerville Davé 2015 ). At z ∼ 5–7, the excess of bright sources compared to the semi-analytical predictions appears to be even more pronounced than at lower redshifts but we caution that the most constraining measurement is based on a small number of sources only, and thus needs to be put on a firmer statistical footing. Meanwhile, the observations at z ∼ 2–3 appear to be consistent with Vallini et al.’s ( 2016 ) empirical predictions, and thus with what is expected from estimates of dust-obscured star formation activity at high redshift based on infrared luminosity functions. 4.2.2. Cold Gas Density of the Universe The observational constraints on the evolution of the cold gas density with redshift remain in agreement with both semi-analytical (Obreschkow et al. 2009 ; Lagos et al. 2011 , 2012 ; Popping et al. 2014a , 2014b ) and empirical (Sargent et al. 2012 , 2014 ) model predictions at z ∼ 2–3. Since most of the semi-analytical models include a varying α CO between individual galaxies, a simple interpretation of the consistency—despite the disagreement in the luminosity function estimates—remains challenging. In addition, the predictions do not account for the sensitivity limits of the CO surveys, or uncertainties due to cosmic variance. Given the differences in the CO luminosity functions between models and observations at high z , this effect could in principle lead to up to a factor of a few difference in the corresponding gas densities at high redshift. However, as discussed in Section 3.4 , the impact of the sensitivity limits, which would bias the measurements toward lower values, appears to be relatively minor based on the preferred model Schechter function fits to the COLDz data. Meanwhile, cosmic variance due to large-scale structure in the distribution of gas-rich galaxies (which is assumed to be uniform in our analysis) could bias the measurements either low or high. To obtain an approximate estimate of systematic uncertainties introduced by cosmic variance, we follow the prescription by Driver Robotham ( 2010 ), based on the distribution of galaxies near the characteristic stellar mass at a given redshift. 40 40 This method is based on a generalized expression (their Equation (4)) calibrated through an examination of galaxies within ±1 mag of the characteristic optical magnitude out to z ∼ 0.1 in the Sloan Digital Sky Survey (SDSS), which represent the most common galaxies at a given redshift. See cosmocalc.icrar.org for additional details. The field sizes and CO( J = 1 → 0) redshift ranges in Table 1 are used for all calculations. Including both Poisson uncertainty and cosmic variance scaled to the volume of the COLDz survey, we find a sample variance uncertainty of ∼30%–40% and ∼25% for the COSMOS and GOODS-North fields, respectively. Alternatively, adapting results based on models of the evolution of the most massive galaxies (i.e., M ⋆ > 10 11 M ⊙ ) by Moster et al. ( 2011 ) 41 41 For our estimate, we have made


We thank Don Melrose for introducing us to key references in the quantum plasma literature, notably including BM07 . We also thank Bryn Haskell, the first reviewer Taner Akgün, and the anonymous second reviewer for their insightful comments, which have significantly improved the quality and clarity of this paper. This work was supported by an Australian Research Council Discovery Project Grant (DP110103347) and an Australian Postgraduate Award.


ACKNOWLEDGEMENTS The authors thank Lars Bildsten, Jared Brooks, Sterl Phinney, Evan Kirby, Selma de Mink, Thomas Tauris, and Onno Pols for useful discussion. IK is supported by the DOE NNSA Stockpile Stewardship Graduate Fellowship Program. This research is also funded in part by the Gordon and Betty Moore Foundation through Grant GBMF5076. DK is supported in part by a Department of Energy Office of Nuclear Physics Early Career Award, and by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Divisions of Nuclear Physics, of theU.S. Department of Energy under Contract No. DE-AC02-05CH11231.


on the individual galaxies. We derived the source counts using a circular aperture with 13′′ radius, which, at a distance of 65 Mpc, corresponds to 4 kpc. To account for the background emission, we used annuli with 60′′–120′′ radii. We did not obtain statistically significant detections for any of the individual galaxies. To increase the signal-to-noise ratio, we co-added the X-ray emission associated with the individual galaxies. For the full sample of 51 LSBGs, this resulted in a total exposure time of 381.1 ks. We did not detect statistically significant emission from the stacked data, implying that the X-ray brightness of LSBGs remains below the detection threshold. We also stacked the subset of 17 UDG candidates and the 17 LSBGs as well as the subset of blue and red galaxies in our sample. We did not detect X-ray emission in any of the subsets. In the absence of detections, we set upper limits on the average luminosity of galaxies by calculating the confidence bounds of the stacked signal. We defined the 95% confidence region of the distribution, and used the upper confidence bound of the count rate as an upper limit. To convert the count rate to flux, we assumed that the emission from the hot gas can be described with an optically thin thermal plasma model. Specifically, we assumed a gas temperature of kT = 0.2 keV and a metallicity of 0.2 solar, which are typical in low-mass elliptical galaxies (e.g., Boroson et al. 2011 ; Goulding et al. 2016 ). Based on the resulting count rate upper limit of , we estimate the upper limit on the flux of for the full sample of 51 galaxies, which corresponds to a luminosity of , where d represents the average distance of the sample in Mpc. We obtained similar upper limits for the subset of UDG candidates and LSBGs and for the blue and red subsamples, which are listed in Table 1 . Table 1 X-Ray Upper Limits on the Stacked LSBGs 5. Discussion 5.1. Constraining the Halo Masses The prototypical UDG, Dragonfly 44, has a virial mass of (van Dokkum et al. 2016 , 2017 ). Using its effective radius of 4.6 kpc and assuming a Navarro–Frenk–White (NFW) dark-matter halo profile, we estimate that it has a total mass of . Based on the L X – M (5 r eff ) scaling relation, this total mass is linked with an X-ray luminosity of L 0.3–8 keV ≈ 2.4 × 10 39 erg s −1 in the 0.3–8 keV band. However, the luminosity upper limit measured for the sample of 51 field LSBGs, with an assumed distance of 65 Mpc, is in the 0.3–1.2 keV band. After converting the X-ray upper limit luminosity to the 0.3–8 keV band, we obtain . This value is ∼40 times lower than that expected for a galaxy with a massive dark-matter halo (see Figure 2 ). A similar conclusion is obtained for the subset of 17 UDG candidates and the subset of 17 LSBGs with 0.3–8 keV, as well as for the blue and red galaxy subsets. Figure 2. Empirical relation between the 0.3−8 keV band X-ray luminosity of hot diffuse gas and the total gravitating mass within 5 r eff (red


of the new fitting functions are shown in the second and fourth columns of Fig. 4 . In this case, the measurements of P θ θ are reproduced with a maximum systematic error of 3% on all scales below k = 0.7 h Mpc −1 , and for all redshifts and neutrino masses considered. We therefore use a total of only five free parameters k δ , b , a 1 , a 2 and a 3 to mimic, with a 3% level accuracy at k 0.7 h Mpc −1 , the nonlinear effects on both the auto- and cross-spectra P θ θ and P δ θ . Let us now focus on the sensitivity of these parameters to cosmology and specifically to the overall amplitude of the matter power spectrum. From our set of four simulations at four different redshifts we are able to span a large range of possible values of σ 8 , which we use as a proxy for the amount of nonlinearities. Regarding neutrino cosmologies it is necessary to choose whether we use the σ 8 defined for cold dark matter only, σ 8, c , or the one defined for the total matter, σ 8, m . It has been shown ( Castorina et al. 2015 ) that regarding the bias or the nonlinear effects on the density power spectrum P δ δ , what matters is the amplitude of the cold dark matter clustering and not the total one. We have analyzed the dependency of the fitted parameters with respect to both amplitudes σ 8, c and σ 8, m and we found that one should use the total matter σ 8, m parameter in order to assess the correct values of k δ , b , a 1 , a 2 and a 3 ; at least, this choice is the one that lowers the residual dependency with respect to the neutrino mass. Figure 5 shows that the cosmological dependance of the fitting parameters can be mostly encapsulated into the σ 8, m parameter evaluated at the corresponding redshift. The most relevant example is the good match at redshift 1.5 of the ΛCDM simulation with the M ν = 0.53eV simulation at redshift 1; these simulations share almost the same value of the total matter σ 8, m , while differing significantly in the power spectrum shape. For the two cases, we obtain the same values for the fitted parameters k δ and k θ . Fig. 5. Top panel : dependence of the fitting parameters k δ , b , k θ , a 1 , a 2 and a 3 on the total matter clustering amplitude σ 8,m at each redshift, in the corresponding simulation (symbols). Lines are showing the fit of the dependance. Bottom panel : residual between the fitted σ 8,m dependance and the measured one. On the contrary, when using the cold dark matter σ 8,c parameter (see Table 1 ) the residuals are increasing because of spurious neutrino mass dependence when going from one cosmology to another. This effect can be explained by the fact that if massive neutrinos have a weak effect on the dark matter clustering in the nonlinear regime, they add, instead, a relevant contribution to the velocity field which is felt by dark matter particles. As a result, it seems that the preferred dependence on the total matter σ 8,m comes from the fact that nonlinearities in the velocity field are generated by the


ACKNOWLEDGEMENTS NN and EJ acknowledge financial support from the International Science Program (ISP). BB thanks the European Research Council (ERC Starting Grant 757448-PAMDORA) for their financial support.


(by ∼400 km s −1 ) than in Cano et al. ( 2018 ). Figure 9. Time evolution of the pEWs for features 1, 3, 4, 7, and 8 together with the Si ii expansion velocity evolution (bottom right panel). Black circles are the measured pEWs after lens- and host galaxy subtraction and de-reddening. Transparent points and shaded bands are individual measurements and the binned mean (±1σ) of low-redshift SNe from Folatelli et al. ( 2013 ), for all (red) and ‘Normal’ (blue) SNe Ia in their sample. The black and red dashed lines shows the pEW and velocity evolution of the Hsiao template and SN 2007le, respectively. Turning to the pEW measurements, we do not see any significant deviations from the time-evolution of SNe Ia in Folatelli et al. ( 2013 ). In Fig. 9 , the black points show the pEW measurements of iPTF16geu compared to all (red points) or ‘normal’ (blue points and blue shaded region) SNe Ia in Folatelli et al. ( 2013 ). However, we note that some measurements are outside the 1σ range, e.g. late-time pEW1 (likely due to improper lens and host galaxy removal), pEW3 and pEW7 (where the telluric corrections are imperfect). 5 TIME-DELAY MEASUREMENTS FROM SPECTRA OF SPATIALLY RESOLVED LENS IMAGES In our single epoch of HST spectroscopy, we can spatially resolve two spectra: one spectrum corresponding to Image 2 and one spectrum corresponding to Images 1, 3, and 4. However, Images 3 and 4 are subdominant, contributing with 7 per cent and 5 per cent to the total flux in F 814 W at this epoch, respectively. Hence, we will treat this spectrum as stemming from Image 1. By comparing the time evolution of spectral features between the spectra, we can in principle provide an independent measurement of the time delays between the SN images. However, in our case we are limited by the coarse ( R ∼ 210) spectral resolution. To complicate things further, at the epoch (+29 d) the Si ii absorption feature is no longer well-defined, displaying two or more local minima. Age dating of SN spectra is routinely done using cross-correlation techniques (e.g. snid ; Blondin Tonry 2007 ), and have been successful in measuring cosmic time-dilation (Blondin et al. 2008 ). We construct a simple χ 2 -statistic, fitting Hsiao template spectra (Hsiao et al. 2007 ) at different phases to the spectra of the spatially resolved SN images. This allows us to simultaneously fit for residual lens and host galaxy contamination using our template spectrum, and subtract a fraction of that flux (0.80 ± 0.03 and 0.19 ± 0.02 for Images 1 and 2, respectively) from the resolved SN spectra, so that the subtracted SN spectra and Hsiao templates at each phase match the host subtracted F 814 W photometry (see upper panel of Fig. 10 ). Figure 10. Top panel: HST spectra of the spatially resolved Images 1 + 3 + 4 (blue line) and Image 2 (green line). The summed spectra (red line) show very good agreement with the ground-based Keck spectrum (black line), observed at the same time. Bottom panel: χ 2 minima of


star discovered by Caffau et al. (2011a ). The other symbols are literature data. The black and yellow dashed lines delimit the low-carbon band. Details can be found in Bonifacio et al. (2018) . 6.3 <italic>α</italic> and neutron-capture elements Figure 6 shows the abundance ratios of [Mg/Fe] and [Ca/Fe] as a function of [Fe/H] for our sample of stars using the solar abundances from Lodders et al. (2009) . Literature data from Roederer et al. (2014) are also shown, which contain results from a rather large sample of evolved and main sequence stars. We were able to measure magnesium in the five stars. Among them, SDSS J081554.26+472947.5 seems to have a rather low [Mg/Fe] abundance ratio and a subsolar [Ca/Fe] upper limit abundance. This is due to our high upper limit of [Fe/H]. In fact, by adopting the very low [Fe/H] determined by González Hernández et al. (2020) , we obtain [Mg/Fe] = 1.62 dex in excellent agreement with the [Mg/Fe] = 1.66 dex abundance that these latter authors obtained. The stellar parameters we adopted for SDSS J081554.26+472947.5 are close to those used by González Hernández et al. (2020) with a difference of 15 K on the temperature, a difference of 0.6 dex in log g that has no strong effect (typically 0.1 to 0.15 dex on the neutral Ca and Mg) on the determination of the abundance of neutral species, and the same micro-turbulent velocity. We found three stars with subsolar values for calcium, confirming the existence of stars with low [ α /Fe] ratios as already suggested by Bonifacio et al. (2018) . However, we reiterate the fact that in very metal-poor stars, under the LTE hypothesis, the resonance line that we used to determine the abundance of calcium leads to an underestimation of the calciumabundance ( Spite et al. 2012 , and references therein). For turnoff stars, the amplitude of the effect is rather small. Spite et al. (2012) computed a correction of the order of +0.1 dex in a turnoff star with [Fe/H] = −3.2 dex. Figure 7 shows the [Mg/Ca] ratio as a function [Fe/H] (upper panel) and as a function of [Mg/H] (lower panel). We have added the literature data from Roederer et al. (2014) for comparison. The [Mg/Ca] ratio found in our sample of stars ranges from +0.2 to +0.5 dex. This ratio is slightly higher than the abundance ratio found in the [Fe/H] range of –2 to –3 dex. At lower metallicities, the results from Roederer et al. (2014) show that the spread in the [Mg/Ca] ratio increases as [Fe/H] decreases with values ranging from negative abundance ratios to highly enhanced [Mg/Ca] ratios. From our measurements, the [Mg/Ca] ratio seems to increase as [Fe/H] decreases. The result for SDSS J081554.26+472947.5 found by González Hernández et al. (2020) seems to corroborate this point. The increase of the [Mg/Ca] ratio is also visible when the ratio is plotted as a function of [Mg/H]. However, a high value of [Mg/Ca] at very low [Mg/H] is not found in all the stars. In particular, SDSS J102915+17292, the normal


The authors thank S. Gunar, B. Gelly, and the team of THEMIS for assisting with the observations. We would like to thank Jean-Marie Malherbe and Thierry Roudier whoco-aligned the SOT frames. They tested, up to now unsuccessfully, the CST and LCT methods to derive the flow pattern in the plane of the sky. We thank J. Dudik who provided the time-distance code to track the knots in the SOT cube of data, and G. Aulanier and P. Démoulin for fruitful discussions. This paper was discussed during the ISSI workshop (PI N. Labrosse) on “Solving the prominence paradox”. P.J.L. acknowledges support from an STFC Research Studentship. N.L. acknowledges support from STFC grant ST/I001808/1. Hinode is a Japanese mission developed and launched by ISAS/JAXA, with NAOJ as domestic partner and NASA and STFC (UK) as international partners. It is operated by these agencies in co-operation with ESA and NSC (Norway). IRIS is a NASA small explorer mission developed and operated by LMSAL with mission operations executed at NASA Ames Research Centre, and major contributions to downlink communications funded by the Norwegian Space Center (NSC, Norway) through an ESA PRODEX contract. The AIA data are provided courtesy of NASA/ SDO and the AIA science team. M.Z. acknowledges support from the project RVO:67985815 of the Czech Academy of Sciences.


of a disc and also contributed to the increase of the central BH mass. The analysis of the formation histories of eagle galaxies and its connection to the scatter of the MZR will be the subject of a forthcoming article (Zenocratti et al., in preparation). Sharma Theuns ( 2019 ) propose a model of self-regulated galaxy formation, in which the SFR, stellar mass, gas mass, and metallicity depend on halo mass, cosmological accretion rate, and redshift, but regulated by feedback. In their ‘Iκεα’ model, the main astrophysical parameter ε is a dimensionless measure of the efficiency of stellar feedback: a large value of ε implies efficient feedback and low SFR, while feedback is inefficient and the SFR is high for a small ε. This leads to the following scaling for Z and f g with M ⋆ and efficiency ε: where n ≈ 1.4 is the slope of the Kennicutt–Schmidt star formation law. These relations show that when feedback is efficient (meaning ε is large, ε ≈ 1), Z is low and f g is high, whereas, inefficient feedback (ε ≪ 1) implies Z is high and f g low. We can connect this to the morphology of the galaxy by speculating that feedback in a thin disc – corresponding to a galaxy with high κ co – is more efficient than when κ co is low (a more spheroidal gas distribution). High-resolution simulations that resolve individual supernova energy injections in gas columns suggest this type of relation between feedback efficiency and disc morphology. For example, the simulations by Creasey, Theuns Bower ( 2013 ) show that supernova explosions that occur above or below the disc are more efficient at driving winds, because cooling loses are suppressed when the explosion occurs at the lower densities that prevail there (see also Girichidis et al. 2016 ). Thus, in eagle , accretion of metal-poor gas seems to trigger the formation of a disc but, once the disc has already been formed, feedback effects would play a role in regulating the subsequent metallicity evolution. We leave the analysis of feedback effects on eagle disky galaxies for a future work. 5 CONCLUSIONS We analysed the MZR as a function of morpho-kinematical parameters in the eagle cosmological hydrodynamical simulations. At z = 0, we found new secondary dependences of metallicity on the internal kinematics and morphology of galaxies. At low masses (), higher metallicities are found for more spheroidal and lower rotation-supported galaxies. A preliminary analysis of the star formation histories of low-mass galaxies indicates that late accretion of metal-poor gas dilutes the metal content of galaxies, triggers their star formation activity, and contributes to the formation of the galaxy disc. When the gas is in a thin, rotationally supported disc, feedback may be more efficient, which results in lower O/H and a higher gas fraction (Sharma Theuns 2019 ). The trends in more massive galaxies are generally less strong, with lower metallicities found in more prolate galaxies with lower levels of rotational


of hydrogen was switched on at s and for the first published snapshot, at s. The non-equilibrium hydrogen ionization leads to much higher electron density in the cool pockets at 0.5–2 Mm and also higher electron densities up to 3.5 Mm height. There is not much change with time of this probability density function after s. 3.6. Velocity field Spectral lines are normally observed to be broader than what the thermal broadening of the opacity profile would give. An extra free parameter, called microturbulence, is often introduced in 1D semi-empirical models to account for this broadening. The “micro” in the name comes from the fact that this parameter is introduced as an extra broadening of the opacity profile, acting in exactly the same way as thermal broadening. This would be a physically correct description in the limit of zero length-scale for the velocity field. It is also often necessary to introduce a second free parameter to account for the observed lineshape. This is called macroturbulence and is equivalent to a Gaussian convolution of the emergent intensity profile (rather than a convolution of the opacity profile as is the case for microturbulence). Realistic 3D radiation hydrodynamic simulations of the solar photosphere give line profiles that are close to the observed profiles without the addition of extra free parameters – the non-thermal broadening comes from Doppler shifts arising from the convective flows and oscillations (e.g., Asplund et al. 2000 ). Also spectral lines formed in the outer atmosphere are broader than what thermal broadening alone predicts. The nature of this non-thermal broadening in the outer atmosphere is still unclear, but the presence of strong shocks ( Carlsson Stein 1992 , 1997 ; De Pontieu et al. 2015 ), torsional motions ( De Pontieu et al. 2014a ), and Alfvén wave turbulence ( van Ballegooijen et al. 2011 ) are some of the candidates. Fig. 14 Average non-thermal velocity calculated over 1 dex in (column mass) (red, left scale) and average temperature (blue, right scale) as function of logarithmic column mass for the simulation snapshot at s. There is no simple way to characterize the macroscopic velocities in the simulation that give rise to non-thermal broadening. The effect of a given velocity field on the spectral line width depends on whether the spectral line is optically thick or optically thin, where in the atmosphere the line is formed and the width of the contribution function to intensity. One possible way of quantifying the velocity field is the standard deviation of the vertical velocity over a given height range as function of height and horizontal position. At each column of the simulation box at s we calculate the column mass scale (which is more closely related to line formation quantities like optical depth than a geometric height) and take the standard deviation of the vertical velocity over a range of 1 dex in (column mass). We multiply the standard deviation by the square root


tend to have the steepest radio spectra (), pointing to another possible bias against finding fast-spinning MSPs in ongoing surveys, which focus on central observing frequencies around 350 MHz (Deneva et al. 2013 ; Stovall et al. 2014 ) and 1.4 GHz (Cordes et al. 2006 ; Keith et al. 2010 ; Barr et al. 2013 ). As a result, radio pulsation searches at frequencies below 300 MHz have the potential of opening up a so far largely unexplored parameter space, in the cases where IISM scattering is low and eclipsing does not hinder detection either. Here, we present the discovery of PSR J0952−0607, a very-steep-spectrum MSP, which is now the fastest-spinning neutron star known in the Galactic field (outside of a globular cluster). PSR J0952−0607 was found in a radio pulsation survey using the Low-Frequency Array (LOFAR; Stappers et al. 2011 ; van Haarlem et al. 2013 ) to target unassociated Fermi γ -ray sources. This Fermi -targeted approach has been successful in finding many new MSPs (Ray et al. 2012 ), but our survey is the first to use LOFAR to survey at observing frequencies of 135 MHz (see also Pleunis et al. 2017 ). To enable this survey, a combination of coherent and incoherent dedispersion has been employed to limit the effects of dispersive smearing (Bassa et al. 2017 ). In Section 2 , we will highlight the discovery and multi-wavelength follow-up, with the results being presented in Section 3 . We discuss the broader implications of PSR J0952−0607's discovery and conclude this manuscript in Section 4 . 2. Observations and Analysis 2.1. Radio PSR J0952−0607 was discovered as part of an ongoing LOFAR survey at 135 MHz, continuing on the pilot survey by Pleunis et al. ( 2017 ). Unassociated γ -ray sources were selected from an all-sky source list based on seven years of Fermi -Large Area Telescope (LAT; Atwood et al. 2009 ) Pass 8 data. That list resulted from a preliminary version of the procedure that will be used to produce the next public release LAT source catalog. Among these is a new γ -ray source that has a test statistic of and a relatively small error radius of . The source’s γ -ray spectrum is strongly curved, peaking at 1.4 GeV, and no significant γ -ray emission is detected above 10 GeV. As the source lies well out of the plane (), these characteristics made it a prime millisecond pulsar candidate. The γ -ray source was observed for 20 minutes on 2016 December 25 with LOFAR. The high-band antennas (HBAs) from the innermost 21 LOFAR core stations (longest baseline of 2.3 km) were used to form seven tied-array beams ( FWHM), each covering a 39 MHz wide band centered at 135 MHz. This setup is identical to that of Pleunis et al. ( 2017 ). The complex voltage output for each tied-array beam—in the form of 200 Nyquist-sampled, dual-polarization subbands of 195 kHz each—was processed using GPU-accelerated software to perform coherent dedispersion and channelization with cdmt (Bassa et al. 2017 ) at steps of 1 pc cm −3 between dispersion


imposed in each layer and the wide and position required for the transition region inside the domain. In this simulation we take a 0 = 4.9 × 10 5 K, a 1 = 2 × 10 8 cm, a 2 = 0.5 × 10 8 cm, and a 3 = 5. × 10 5 K. In Fig. 4 the temperature profile obtained for these values and the consequent hydrostatic pressure distribution are shown, for ρ 0 = 10 −11 g cm −3 at the base domain, constant gravity g = 2.74 × 10 4 cm s 2 , specific heat ratio γ = 5/3, and particular gas constant R = 16.6289196 × 10 7 erg (K mol) −1 (totally ionized hydrogen). The numerical results of the hydrostatic condition shown in Fig. 4 are presented in Fig. 5 , where the convergence curves for both the linear and the local hydrostatic reconstruction MUSCL-Hancock schemes are plotted. As expected, the results of the scheme with linear reconstruction exhibit the aforementioned third order superconvergence but they present strong errors in the hydrostatic equilibrium preservation when low resolution grids are used. On the other hand, the results corresponding to the local hydrostatic reconstruction technique show a similar convergence rate for large numbers of cells ( M ≳ 100), but with smaller errors than the standard scheme, which can be even several orders of magnitude smaller when coarse grids are used. This behavior shows the potential of the local hydrostatic reconstruction scheme, since it allows for improvement of the results for very stratified atmospheres with large temperature gradients, as found in many solar astrophysical applications. Fig. 4. Temperature distribution and hydrostatic pressure profile in the solar atmosphere model by Vernazza et al. (1981) given in Eq. ( 63 ). Fig. 5. Convergence curves for the numerical results of the hydrostatic equilibrium atmosphere shown in Fig. 4 . The blue line with circles shows the L 1 -norm of the pressure error for the standard second order MUSCL-Hancock scheme (linear reconstruction), and the red line with crosses corresponds to the MUSCL-Hancock scheme with local hydrostatic reconstruction. 6.2. Diffusion analysis In this analysis we simply study the ability of the local hydrostatic reconstruction scheme to capture a shock wave traveling in a gravitationally stratified medium. The aim of the analysis is to verify that this scheme does not introduce an excessive numerical diffusion compared to the scheme with linear reconstruction to model the shock wave. In addition, we check the behavior of the hydrostatic scheme in the default AMR module of FLASH, which uses the PARAMESH 2 package ( MacNeice et al. 2000 ). This toolkit builds a hierarchy of sub-grids blocks with identical logical structure that cover the physical domain with different resolution levels according to the gradient magnitude of the set refinement variables. Each block is treated as an independent uniform grid, so that the local hydrostatic reconstruction is directly applied on adaptive meshes without the need to modify any subroutine. For this simulation


We thank the anonymous referee for comments that have greatly improved this manuscript. The simulations were performed at the National Energy Research Scientific Computing centre (NERSC), Lawrence Berkeley National Laboratory , and at NASA Advanced Supercomputing (NAS) at NASA Ames Research centre. The analysis was performed on the Astric cluster at HU. This work was supported by ISF grant 24/12 , by BSF grant 2014-273 , by GIF grant G-1052-104.7/2009 , by the I-CORE Program of the PBC , ISF grant 1829/12 , by CANDELS grant HST-GO-12060.12-A , and by NSF grants AST-1010033 and AST-1405962 . DC has been partly funded by the ERC Advanced Grant, STARLIGHT: Formation of the First Stars (project number 339177).


We then investigated the possibility that these objects could form a cluster in some bi-dimensional projections of the parameter space. We tried all the possible magnitudes, colours, and redshifts combinations without finding any obvious clustering (some of these combinations are shown in Appendix C ). We also checked whether the group could correlate with a specific (high) error measure associated with any of the used features, but no any evident correlations were found. The nature of the objects in the overdensity region is still under further investigation. Figure 6. The scatter plot in the top left corner (a) shows the distribution of outliers in the SFRs spectroscopic versus SFRs photometric space with a superimposed density map, while the diagrams int the top right (b) and bottom left (c) corners show highlighted in orange all the objects with a density, respectively, six and eight times higher than the average point density. The histogram in the bottom right corner (d) shows the outliers density distribution. 4.7 Comparison with a recent work In order to compare our regression models with the k-NN used by Stensbo-Smidt et al. ( 2017 ) and their feature selection, we performed an experiment using the full training set and the set of 8 features found by Stensbo-Smidt et al. ( 2017 ). In Table 12 , we present the statistical results, which show a comparable performance among the three methods, although with a lower RMSE obtained by RF and MLPQNA. Using the features found by ΦLAB, the RF and MLPQNA can achieve even better performance, as shown in Table 6 . This is not surprising as k-NN is much more sensitive to the dimensionality of the parameter space (the so-called curse of dimensionality) than other two models. These latter can, therefore, take advantage of the information carried by a larger number of features than a k-NN model. Table 12. Comparison between our RF and MLPQNA against (Stensbo-Smidt et al. 2017 ) k-NN using the full train set and the best eight features found by Stensbo–Smidt. 5 DISCUSSION AND CONCLUSIONS In this work, based on our preliminary analysis of the problem presented at the ESANN-2018 conference (Delli Veneri et al. 2018 ), we estimated star formation rates for a large subset of the SDSS-DR7 and produced a catalogue of SFRs derived using photometric features only (magnitudes and colours) and the MLPQNA ML model (see Appendix B ) trained on a knowledge base of spectroscopically determined SFRs. By looking at Fig. 3 and the statistics in Table 6 , the regression results appear very promising. This is particularly true, considering that the dynamical range of SFR is between −12 and −7, and also that we have ∼5000 outliers out of the objects of the blind test set and, finally, taking into account the low percentage of outliers (∼2 per cent). However, from the results obtained by varying the size of the model training set (Tables 7 and 8 ), we think that a larger knowledge base of SFRs would further improve the


perpendicular HTS and find that the PUIs and thermal gas are more heated and energized at the parallel than the perpendicular shock. We also model a quasi-parallel HTS and a quasi-perpendicular HTS to consider the case of an oblique HTS. In the last section, we summarize our results about the structure of collisionless oblique shock waves when mediated by energetic particles. 2. Model In this section, we present a brief review of the formulation of the PUI or SEP-mediated plasma model presented by Zank et al. ( 2014 , 2016 ), Zank ( 2016 ), and Mostafavi et al. ( 2017b ). The heliosphere comprises thermal solar wind, suprathermal energetic particles such as PUIs or SEPs, and neutral atoms (beyond an ionization cavity of about 6–10 au). The charge exchange mean free path in the IHS is approximately 2500 au and greater than 200 au in the supersonic solar wind beyond 10 au (Zank 2015 ). Thus, the charge exchange mean free paths are very large, and we can ignore the coupling between neutral atoms and solar wind protons when studying the structure of shocks. Using appropriate parameters for the supersonic solar wind beyond 10 au, the IHS, and the VLISM, Zank et al. ( 2014 ) estimated the equilibration timescales of PUIs and thermal plasma in these regions. They showed that the PUIs are not equilibrated with the background thermal plasma. Zank et al. ( 2016 ) showed that SEPs with energies greater than 5 keV cannot equilibrate in the inner heliosphere. Therefore, energetic particles such as PUIs, SEPs, and ACRs are a distinct component in the plasma system. The plasma flow is described by a multi-component model comprising thermal solar wind ions and electrons with Maxwellian distributions, and an energetic ion component (PUIs, SEPs, or ACRs). The multi-component model is too complicated for most problems, but it can be reduced to a single-fluid-like model by making some assumptions (see details in Zank et al. 2014 ). The collisionless diffusion or heat flux tensor and pressure tensor for the energetic particles may be expressed, respectively, as where η ≃ P p τ s is the viscosity coefficient and τ s is PUI-scattering timescale. P p is the PUI scalar pressure and Π p a stress tensor. The assumption is that the magnetic field is along the x -axis. K ∥ and K ⊥ are diffusion coefficients parallel and perpendicular to the magnetic field. The reduced single-fluid-like model equations, together with the Maxwell equations, are given by (Zank et al. 2014 , 2016 ) where μ 0 is the permeability of free space and J is the current density. B and E denote the magnetic and electric fields, P p the PUI pressure, P g the thermal gas (sum of electrons and protons) pressure, U the bulk flow velocity, and ρ the total density. We denote all quantities pertaining to PUIs and thermal gas with the subscripts p and g , respectively. γ p/g denotes the adiabatic index for PUIs/thermal gas. The viscosity and heat flux dissipation terms introduce distinct length scales into


along an almost perfect line in the northwest–southeast direction. The centroids, however, depart from this line at high velocities, especially for the blueshifted gas (≤−8 km s −1 ), although some of the associated positional errors are large. This suggests the presence of a second kinematic component. As shown in Section 4 , this configuration is consistent with the presence of an almost edge-on ionized disk, and a disk wind. 4. Modeling of the H21<italic>α</italic> RRL Similar configurations to the RRL centroid map obtained for MonR2-IRS2 have been observed for MWC349A (Martín-Pintado et al. 2011 ; Báez-Rubio et al. 2013 ; Zhang et al. 2017 ) and MWC922 (Sánchez Contreras et al. 2019 ). This configuration has been modeled assuming that the massive star is surrounded by a (partly) ionized Keplerian disk and an ionized wind. We have thus adopted a similar physical structure to model the H21 α centroid map derived for MonR2-IRS2. The set of input parameters that best fit our ALMA observations is described below (see also Table 1 ). Table 1 Input Parameters of the Best Fit of the MonR2-IRS2 H21 α Data Note. a r is in units of au and angles are measured relative to the polar axis; θ and θ a , are in degrees. In our model, the ionized wind lies inside a double cone with a semi-opening angle of 57° (the neutral disk), while the ionized disk layer is contained within an opening angle of 65 on the surface of the double cone (Figure 4 ). The ionized wind expands radially at a constant velocity, v 0 , while the circumstellar disk rotates following a Keplerian law with the velocity rotation component being added to the expansion velocity of the wind (Martín-Pintado et al. 2011 ; Báez-Rubio et al. 2013 ). The inclination angle is measured from the direction perpendicular to the disk and is −25°. Figure 4. Sketch of the double-cone geometry used for the modeling of MonR2-IRS2 (see also Martín-Pintado et al. 2011 ; Báez-Rubio et al. 2013 ). We have used the non-LTE 3D radiative transfer code MORELI (MOdel for REcombination LInes; Báez-Rubio et al. 2013 ) and the departure coefficients of hydrogen, b n and β n , calculated by Walmsley ( 1990 ). The velocity separation between the H21 α emission peaks (blueshifted and redshifted; Figure 2 ) constrains the central mass of the MonR2-IRS2 source to 15 M ⊙ . This mass corresponds to a B0-type star on the zero-age main sequence, which is consistent with the luminosity of MonR2-IRS2 (∼0.5–1 × 10 4 L ⊙ ; Howard et al. 1994 ). The radial density distribution of electrons within the ionized double cone, N e , follows a r −2 law with an inner radius of 13 au (Table 1 ). We choose a r −2 law because it fits nicely the 1.3, 0.85 and 0.4 mm free–free continuum fluxes of MonR2-IRS2, and it allows us to simultaneously model the disk and the expanding wind in a simple way. The predicted mass-loss rate for MonR2-IRS2 is 2.8 × 10 −7 M ⊙ yr −1 , and the mass of the ionized disk is 2.4 × 10 −5 M ⊙ , a factor ≥10 lower


The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. We acknowledge the exellent commentary by two referees and the ApJ statistician on the paper’s manuscripts. This work was carried out in part at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration. Parts of this research were conducted by the Australian Research Council Centre of Excellence for All-sky Astrophysics (CAASTRO), through project number CE110001020. C.M.T. is supported by an Australian Research Council DECRA Fellowship through project number DE140100316.


Y.I.I. and N.G.G. thank the hospitality of the Max-Planck Institute for Radioastronomy, Bonn, Germany. They acknowledge support from the Program of Fundamental Research of the Department of Physics and Astronomy (Project No. 0117U000240) of the National Academy of Sciences of Ukraine. Funding for the Sloan Digital Sky Survey (SDSS) has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Aeronautics and Space Administration, the National Science Foundation, the U.S. Department of Energy, the Japanese Monbukagakusho, and the Max Planck Society. The SDSS Web site is http://www.sdss.org/ . The SDSS is managed by the Astrophysical Research Consortium (ARC) for the Participating Institutions. The Participating Institutions are The University of Chicago, Fermilab, the Institute for Advanced Study, the Japan Participation Group, The Johns Hopkins University, Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, University of Pittsburgh, Princeton University, the United States Naval Observatory, and the University of Washington.


We thank Prateek Agrawal, Imre Bartos, Luke Kelley, Frans Pretorius, Jakub Scholtz, and Kip Thorne for extremely useful conversations on several aspects of our paper. L.R. is supported by NSF grants PHY-0855591 and PHY-1216270. Z.-Z.X. is supported in part by the Center of Mathematical Sciences and Applications, Harvard University.


Acknowledgments SJP is supported by a Royal Society University Research Fellowship.


More specifically, we can summarize our findings as follows: 1. Because the drag force experienced by small dust grains is very strong, a specific implicit numerical scheme was implemented in the code RoSSBi to accurately follow the dynamics of the disk. This method is very accurate for any value of the Stokes number of the pressureless dust fluid, and we use it to study the evolution a vortex model with dust characterized by Stokes numbers in the range . 2. Dust is systematically accumulated inside the vortex for every value of the Stokes number. The exponential growth rate of the dust density at the vortex center follows the analytical model we developed in our previous study. The timescale depends on the grain size, but the density enhancement reached at the end, when the gas is perturbed by the drag force, is similar regardless of the Stokes number, and produces dust-to-gas ratios of order unity. We highlight the existence of a generic capture process, characterized by a timescale that scales with the Stokes number, which allows us to compare disks with different dust sizes at an equivalent state of evolution, but corresponding to intrinsically different physical timescales. 3. The vortex instability is triggered at the end of the capture, regardless of the grain size. The growth rates of the excited modes also depend weakly on the Stokes number. This effect is highly correlated with the similarity of the dust capture, and the concept of equivalent states of evolution, producing almost the same perturbation of the gas vorticity profile. 4. A new phase of dusty vortex evolution is discovered for Stokes numbers on the order of 10 −3 and below, where a succession of vortex instabilities followed by dust capture events occurs. This period lasts several hundred of disk orbits and produces strong mixing and a fast reorganization of the dust during the relaxation of the vortex. The dust-to-gas ratio increases progressively to high values, up to 8 at the vortex center. The very dense core that forms and survives even after eventual vortex dissipation could be a preferential place for planetesimal formation. 5. When the timescale of the drag effect is too long compared to the resistance and relaxation of the vortex, the formation of a dust ring becomes unlikely. In our case, the runs with St = 10 −3 were still in the unstable phase by the end of the simulations. Even when it forms, for St 10 −2 , the dust ring produced by well-coupled grains has fewer eddies than with larger Stokes numbers. Even if the dust-to-gas ratios are comparable, they suffer diffusion, and their role in planetesimal formation is less promising than the unstable phase. There are a number of caveats to our model that need to be pointed out. First, the fact that the simulations are still only two-dimensional, which could have a relevance both for the development of two-fluid turbulence during and after the vortex instability phase (see the discussion in Surville et al. 2016


ACKNOWLEDGEMENTS We thank the anonymous referee for the detailed comments that helped to improve this manuscript. We thank Patrick Diamond, Ellen Zweibel, Michael Norman, and Todd Thompson for insightful suggestions and advice, Eve Ostriker for pointing out a typo, and Bili Dong for his help with yt . We would like to thank the Simons Foundation and the participants of the Galactic Superwinds symposia for stimulating discussions. TKC and DK were supported by NSF grant AST-1715101 and the Cottrell Scholar Award from the Research Corporation for Science Advancement. Support for PFH was provided by an Alfred P. Sloan Research Fellowship, NSF Collaborative Research Grant #1715847, and CAREER grant #1455342, and NASA grants NNX15AT06G, JPL 1589742, 17-ATP17-0214. EQ was supported in part by a Simons Investigator Award from the Simons Foundation and by NSF grant AST-1715070. The Flatiron Institute is supported by the Simons Foundation. CAFG was supported by NSF through grants AST-1517491, AST-1715216, and CAREER award AST-1652522, by NASA through grants NNX15AB22G and 17-ATP17-0067, and by a Cottrell Scholar Award from the Research Corporation for Science Advancement. The simulation presented here used computational resources granted by the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant no. OCI-1053575, specifically allocation TG-AST120025. Numerical calculations were also run on the Caltech compute cluster ‘Wheeler’, allocations from XSEDE TG-AST130039 and PRAC NSF.1713353 supported by the NSF, and NASA HEC SMD-16-7592. This work uses data hosted by the Flatiron Institute’s FIRE data hub. This work also made use of yt (Turk et al. 2011 ), matplotlib (Hunter 2007 ), numpy (van der Walt, Colbert Varoquaux 2011 ), scipy (Jones et al. 2001 ), and NASA’s Astrophysics Data System.


aberrations and we anticipate good astrometry results with the mean PSFs of each cluster. However, PSFs from stars with a magnitude of 11 have small and almost randomly distributed clusters. Although the mean PSFs of two different clusters are almost the same in Fig. 12(f) , this might be induced by the average of many different PSFs. To fully reflect the classification performance, we perform PSF-fitting astrometry in these data, using the Fourier-based registration method (Stone et al. 2001 ) with the mean PSFs obtained from our method. This method assumes that the PSFs in the same cluster are morphologically similar and only have a different subpixel shift. We can obtain this subpixel shift by maximizing the correlation coefficients between the stamp images of stars and the mean PSFs in an oversampled Fourier domain. The subpixel shift and the position of the brightest pixels in the images of the celestial objects can then be used to calculate the star's position in the image. For comparison, we also use the Gaussian function as a PSF template and we calculate the positions of stars with the least-squares fitting method (Stone 1989 ). The Gaussian function has a FWHM of 2 pixels. The positions we calculated with the above two methods are compared with the Tycho-2 catalogue (Høg et al. 2000 ) as follows. We obtain the star positions (α i , ξ i ) from the Tycho-2 catalogue as the theoretical positions of these stars and we construct the association between that position and the position of these stars in the image using as proposed in Sun, Zhao Zhang ( 2013 ). Here, (α 0 , δ 0 ) is the corresponding equatorial position of the frame centre. With this association, the observed position (α c , ξ c ) of these stars can be obtained from the pixel position ( x c , y c ), and the residual position errors of each star (α c − α i , δ c − δ i ) are obtained. The astrometry error of these two methods from the Tycho-2 catalogue is shown in Fig. 13 . The systematic errors of Tycho-2 are nearly 0.01 arcsec so this does not have an effect on the calculation. Compared with the Gaussian fitting method, we can see that stars with a magnitude of 10 have better astrometric accuracy with the mean PSF and stars with a magnitude of 11 have almost the same astrometric accuracy. Figure 13. Astrometric residuals of stars with magnitudes of 10 and 11 of telescope B. The number of stars with the magnitude of 10 is 517 and the number with the magnitude of 11 is 737. Top: the residuals of right ascension. Bottom: the residuals of declination. Crosses indicate Gaussian PSF-fitting centroid and circles indicate mean PSF fitting. It is worth noting that PSF classification is a clustering problem and for stars with the magnitude of 11, we do not know why the PSFs are not clustered distinctly. There are two possibilities: (i) these PSFs are nearly the same essentially, so applying the average of these PSFs for subsequent processing is a sound method (Sun Jia 2017 ); (ii) the


ACKNOWLEDGEMENTS VW’s research is funded by an ERC Starting Grant (3DICE, grant agreement 336474). The authors acknowledge the CNRS program ’Physique et Chimie du Milieu Interstellaire’ (PCMI) co-funded by the Centre National d’Etudes Spatiales (CNES). LM also acknowledges the support from the NASA postdoctoral program. A portion of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration.


the EUVI-A stack plot does not show any clear upward-propagating structure. The result that it was unable to be picked up in the field of view captured by EUVI-A, combined with the observation of the slow-rise phase in the COR1 field of view, suggests that the eruption was initiated from higher altitudes. The EUVI stack plot does, however, show a large brightening around the time of the rapid acceleration phase beginning, likely to be post-eruption loops associated with the stealth CME. We then fitted exponential and quadratic curves to the CME position in the COR1 field of view. The curves can give indications of what mechanisms are driving the eruption (Schrijver et al. 2008 ; D’Huys et al. 2014 ). Numerical simulations matched with observations have demonstrated that an exponential rise profile occurs when an instability is dominating the eruption, such as the torus or kink instability, while a quadratic rise profile occurs during a breakout model scenario. For this event the exponential curve produced the best fit, suggesting an instability dominating the eruption. Both the torus and kink instability require a flux rope prior to eruption, and given that the concave-up structure could be tracked for a period of hours during the slow-rise phase, it is likely that in addition to the structure being initiated at a high altitude, the flux rope was also formed at a high altitude in the corona. Figure 2. Left: EUVI/COR1 image indicating the slice used to create the stack plot (solid line). Right: EUVI-B 195 Å (lower) and COR1-B (upper) stack plots. The height–time profile of the stealth CME observed on 2009 October 27 can be determined from the COR1-B data, which show the underside (concave-up structure) of the stealth CME. Exponential (red line) and quadratic (blue line) fits have been applied to the COR1-B data. The stealth CME is not observed in the COR1-A images until ∼15:30 UT on 2009 October 27, several hours after the eruption onset time as determined by Kilpua et al. ( 2014 ). The CME is also very faint and barely visible in the images, making it difficult to pinpoint the exact time that it enters the field of view. It also emerges from a bright streamer that acts to mask the CME structure. However, the stealth CME is seen more clearly, and earlier, in COR1-B, which could suggest that the eruption is closer to the limb of STEREO-B than STEREO-A . The estimated source region from triangulation techniques is of similar distance to the nearest limbs in both spacecraft, while the decayed AR is directly on the limb in STEREO-A and on disk in STEREO-B , and AR 11029 is directly on the limb of STEREO-B and on disk in STEREO-A . Using COR1 and COR2 from the twin STEREO spacecraft, the wire frame of the GCS model (representing the flux rope) was fitted to the concave-up cavity structure in the coronagraph observations (Figure 3 ). The footpoints of the erupting structure were found to be N03E05 and N03W18 from the GCS model, illustrated by