O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-Telescope I-Telescope I-Telescope B-Telescope B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O B-Observatory I-Observatory I-Observatory O B-Observatory O B-Citation I-Citation I-Citation I-Citation O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O B-Wavelength B-Wavelength O B-Wavelength I-Wavelength O O O O O O O O O O O

of magnetohydrodynamic (MHD) waves with observations of solar atmospheric waves and oscillations gives information on the physical parameters of medium (e.g., Nakariakov et al. 2016 ), including sunspots (e.g., see Snow et al. 2015 ; Sych 2016 for recent results). Moreels van Doorsselaere ( 2013 ) designed a method for deriving the temperature of plasma confined in photospheric magnetic flux tubes by using the intensity, velocity, and magnetic field strength fluctuation amplitudes. Reznikova et al. ( 2012 ) estimated the inclination angle of umbral magnetic field, based on the interpretation of umbral oscillation as a slow magnetoacoustic gravity (MAG) wave in an inclined magnetic field. Yuan et al. ( 2014 ) established that the magnetic inclination angle derived seismologically was 30%–40% larger than that given by the magnetic field extrapolation. Roberts ( 2004 ) reviewed the analytical expressions for the cutoff frequency as a function of observable parameters for different solar atmospheric models. Roberts ( 2006 ) provided an analytical form of angular cutoff frequency of a slow magnetoacoustic wave in a non-isothermally stratified atmosphere with a uniform vertical magnetic field. The cutoff frequency not only prescribes the lowest frequency of a propagating wave, but also acts as a natural frequency of a medium (e.g., Roberts 2004 ). It suggests that the atmosphere should be observed to oscillate at the frequency equal or higher than the cutoff frequency in response to an external broadband excitation (Botha et al. 2011 ; Chae Goode 2015 ; Kwak et al. 2016 ). Thus, the cutoff frequency is always below the detected frequency (e.g., Tziotziou et al. 2006 ; Yuan et al. 2014 ). Thus, the cutoff frequency involves the physical parameter of the medium, independently of the specific excitation mechanism of atmospheric oscillations. In this work, we determine the cutoff frequency of umbral oscillations by using the weighted frequency, , where P ( f ) is the power spectrum (Takahashi et al. 2015 ), for 478 sunspots observed in the continuum with the Heliospheric Magnetic Imager (HMI; Scherrer et al. 2012 ; Schou et al. 2012 ) on board the Solar Dynamics Observatory ( SDO ; Pesnell et al. 2012 ). Using the theory given by Roberts ( 2006 ), we determine the Alfvén speed, plasma-beta ( β ), and mass density inside umbrae. In Section 2 , we describe the method used to obtain the weighted frequency and its link with the Alfvén speed, plasma- β , and mass density. In Section 3 , we provide maps of those quantities as well as their average behavior for the 478 analyzed sunspots. Finally, we summarize and discuss our results. 2. Method: Seismology We derive the physical parameters of an umbra by using the seismology, developing the approach designed by Yuan et al. ( 2014 ), who estimated acoustic cutoff frequencies of umbral oscillations at the heights of 1700, 1600, and 304 Å line formation. The authors found that the acoustic cutoff frequency is


O B-Person O B-Person O O O O B-Organization I-Organization I-Organization B-Organization O O B-Location I-Location B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O O O B-Grant O B-Observatory I-Observatory O O O O B-Organization I-Organization O O O O O B-Location I-Location I-Location O O O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O O O O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O O B-Grant O O O O B-Survey O O O O O O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility B-ComputingFacility O O B-Organization I-Organization O O O O O O O B-Organization I-Organization I-Organization B-Organization O O O O O B-Person I-Person O O O O O O O B-Observatory O O O O O O B-CelestialObject O O O O O O O O O O O O B-Person I-Person O O O O

ACKNOWLEDGEMENTS VM and BWS acknowledge funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 694745). The Parkes Observatory is part of the Australia Telescope which is funded by the Commonwealth of Australia for operation as a National Facility managed by the Commonwealth Scientific and Industrial Research Organisation (CSIRO). This work was supported by the Australian Research Council Centre for Excellence for All-sky Astrophysics (CAASTRO), through project number CE110001020. The re-processing of the HTRU survey made extensive use of the GPU Supercomputer for Theoretical Astrophysics Research (gSTAR) hosted at Swinburne University, and funded by a grant obtained via Astronomy Australia Limited (AAL). We extend our gratitude to Craig Heinke for greatly helping the writing of the Swift proposal for the confirmation attempt of J1618–36, and for performing the subsequent data analysis. Finally, we thank the referee Scott Ransom for providing valuable comments.


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The authors thank the anonymous referee for the careful reading and useful comments, Nicolas Billot for his support and help in the data reduction process, the IRAM 30 m staff, and Jonathan C. Tan and Silvia Spezzano for their useful suggestions. A.C.T., P.C., and J.E.P. acknowledge the financial support of the European Research Council (ERC; project PALs 320620).


O O O O O O O B-Wavelength O O O B-Wavelength I-Wavelength B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength B-ObservationalTechniques I-ObservationalTechniques O O O B-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O B-Wavelength O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength O O B-Telescope B-Wavelength I-Wavelength I-Wavelength O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O B-Survey I-Survey I-Survey I-Survey I-Survey I-Survey I-Survey B-Survey B-Citation I-Citation I-Citation I-Citation O B-Survey O O O O B-Wavelength O O O O O O O O O O O B-Telescope I-Telescope I-Telescope I-Telescope I-Telescope I-Telescope I-Telescope B-Telescope O O O O O O B-Survey O O O O O O O O O B-Wavelength B-ObservationalTechniques I-ObservationalTechniques O O O O O O O O O O O O O O B-Survey O O B-Telescope O O O O B-Wavelength I-Wavelength I-Wavelength O B-Wavelength O O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model O O O O O O O O O O O O O B-Wavelength B-ObservationalTechniques O O B-Survey I-Survey I-Survey I-Survey I-Survey I-Survey I-Survey I-Survey B-Citation I-Citation I-Citation I-Citation O B-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O B-Survey I-Survey B-Citation I-Citation I-Citation I-Citation O O B-Citation O O O O O O B-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey O O B-Wavelength B-Instrument I-Instrument I-Instrument B-Instrument O O B-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey O O O O O O O O O O O O O O O O O O

(measured either by stellar light absorption A V or gas absorption H α/H β) and H 2 is due to the correlation between dust and H 2 . This method is convenient since spatially resolved extinction maps are available for large samples of galaxies thanks to optical integral-field spectroscopy surveys. However, unlike 12 μ m, extinction as measured by the Balmer decrement is only valid over a range that is limited by the signal-to-noise ratio of the H β emission line. With extreme levels of extinction, e.g. in local ultraluminous infrared galaxies, the H β line becomes invisible, so this method cannot be used. It is not yet known whether the correlation between 12 μ m and CO holds at subgalaxy scales, or how it compares with the resolved SFR–H 2 and A V –H 2 correlations. Comparing these correlations at resolved scales may give insight into the factors driving the 12 μ m–CO correlation. The WISE 12 μ m beam full width at half-maximum (FWHM) is 6.6 arcsec (Wright et al. 2010 ), which corresponds to ≤1 kpc resolution for galaxies closer than 31 Mpc. This resolution and distance range is well matched to the Extragalactic Data base for Galaxy Evolution survey (EDGE; Bolatto et al. 2017 ). EDGE is a survey of CO(1–0) in 126 nearby galaxies with 4.5 arcsec spatial resolution using the Combined Array for Research in Millimeter-wave Astronomy (CARMA). One of the main goals of EDGE was to allow studies of resolved molecular gas and optical integral-field spectroscopy data in a large sample of nearby galaxies. In this study, we use the EDGE CO and WISE data to measure the 12 μ m and CO(1–0) correlation within individual galaxies. We find that the best-fitting parameters describing this relation vary significantly among galaxies. We perform multivariate linear regression using a combination of global galaxy measurements and quantities derived from spatially resolved optical spectroscopy from the Calar Alto Legacy Integral Field Area Survey (CALIFA; Sánchez et al. 2012 , 2016 ; Walcher et al. 2014 ). This yields a set of linear functions with log Σ(H 2 ) as the dependent variable that can be used as spatially resolved estimators of H 2 surface density. These estimators can predict H 2 surface density with a root-mean-square (RMS) accuracy of ≃0.2 dex in galaxies for which 12 μ m data are available. 2 DATA AND DATA PROCESSING 2.1 Sample selection The sample is selected from the EDGE survey (Bolatto et al. 2017 , hereafter B17 ). The typical angular resolution of EDGE CO maps is 4.5 arcsec, and the typical H 2 surface density sensitivity before deprojecting galaxy inclination is 11 M ⊙ pc −2 ( B17 ). Every EDGE galaxy has optical integral field unit (IFU) data from CALIFA, allowing joint studies of the content and kinematics of cold gas (H 2 ), ionized gas, and stellar populations, all with ∼kpc spatial resolution. We processed the CO data for all 126 EDGE galaxies, and as a starting point we selected the 95 galaxies which had at least one detected pixel


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

14 for components A, B, C, and D, respectively. In light of the large core radii of most of the four components (21, 28, 21, and 5 for A, B, C, and D, respectively); however, these offsets are not necessarily significant. Specifically, our analysis does not support the hypothesis advanced by Diego et al. (2015b) that component A is significantly offset from the closest light peak. These authors argued that this offset is probably due to the lack of lensing constraints in that area. Since three of the four components have core radii larger than 15, i.e., larger than 100 kpc at the redshift of MACS J0717, their superposition leads to a relatively flat mass distribution. In the following, this model is referred to as the cored mass model. Various mechanisms that could lead to such large cores have been proposed (see also Diego et al. 2015b , a , for a thorough discussion). Large cores in massive central galaxies are thought to be caused by massive black holes that clear the centre of galaxies of stars (see, e.g. López-Cruz et al. 2014 ). This may affect dark matter as well, but the scales on which this mechanism can be expected to be effective (less than 10 kpc) are smaller than the scale we are interested in here (100 kpc). Actif galactic nucleus feedback can also contribute to the flattening of the central region ( Martizzi et al. 2012 ), but once again this mechanism is efficient only on small scales (up to 10–15 kpc). On scales of 100 kpc, large cores may result from violent interactions related to merging events in this actively evolving cluster, although several studies find that DM profiles are not strongly altered by a collision ( Ricker Sarazin 2001 ; Dekel et al. 2003 ; Molnar et al. 2010 ). Finally, heating of massive galaxies by dynamical friction against the diffuse dark matter distribution of the cluster can flatten the slope of the DM density profile, and sometimes even dominate over adiabatic contraction (see, e.g. El-Zant et al. 2001 , 2004 ). Another explanation might be self-interacting dark matter particles ( Natarajan et al. 2008 ; Rocha et al. 2013 ), known to flatten the cusps of cluster scale haloes on scales up to 100 kpc, or the multi-coupled Dark Energy scenario ( Garaldi et al. 2016 ). Given the implications of a flat mass profile for MACS J0717, we investigate its mass distribution further by testing whether large-core components are really required by the data. To this end, we explore in the next subsection a peaky, non-cored mass model. Table 2 Same as Table 1 for the non-cored mass model. Table 3 NFW parameters inferred for the four large-scale dark matter clumps (A, B, C, D) and the dPIE parameters for the galaxy-scale component (core radius fixed to 0.3 kpc). Notes. These parameters correspond to the NFW mass model. Coordinates are given in arcseconds with respect to . The ellipticity is for the mass distribution. Error bars correspond to confidence level. Concerning the scaling relations, the zero point is set


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

material absorbs the particle and then shortly after reemits the absorbed energy isotropically. Numerically, the time step is too large for the absorption and emission processes to be resolved separately, such that they appear as one scattering process ( as ). The simulation is initially populated with Monte Carlo particles according to Equation ( 66 ). During each time step, the code creates new Monte Carlo particles to simulate the process of emission. The number of particles created depends on how many particles are already in the simulation: if there are relatively few existing particles, then many are created, but if the number of existing particles is close to the maximum allowed value then few are created. We typically set the maximum to 10 6 particles; we want enough particles to populate every cell and frequency group (Section 3.1 ), but not so many that our simulation runs slowly. For each particle, the details of its creation (location, direction, etc.) are randomly chosen. The cell of creation is randomly chosen with weighting , the amount of energy the cell emits in the time step. Using Equations ( 10 ), ( 33 ), and ( 77 ), we havewhere is the volume of the cell and is the time step for the cell (see below). For simplicity, the radius within the cell and the time within the time step are randomly chosen with uniform weighting; from Equation ( 10 ), the direction is weighted uniformly (isotropically) while the frequency is weighted by . The particle also has an energy weight, equal to the total energy of the photon packet. This is not randomly chosen; instead, all of the particles “emitted” in a time step have the same energy weight, given bywith being the number of Monte Carlo particles emitted in that step. At the end of the time step, the cell temperature is adjusted due to emission using(see below). Particles are also created at the inner boundary of the simulation, the base of the atmosphere. Here the physical process for the creation of the particles is not emission, but the escape of photons from the hot layers beneath the atmosphere. As before, the details of creation are chosen randomly; the time within the time step is chosen with uniform weighting, while from Equation ( 35 ), the direction is weighted by μ and the frequency is weighted by B ν . The energy weight for these particles iswith being the number of particles created at the base in the time step and being the energy entering the simulation from the base of the atmosphere. From Equations ( 35 ) and ( 53 ), we havewhere is the area of the base and is the time step at the base (see Equation ( 67 )). The created particles (photon packets) are transported according to the left-hand side of Equation ( 5 ). If general relativistic effects are ignored, the particles travel in straight lines. For a particle traveling a distance s from the position and moving in the direction initially defined by , where , the new radius of the particle is given by the law of cosines:The


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We thank the referee for helpful comments. MRK acknowledges support from an Australian Research Council Discovery Project (DP160100695). JMDK gratefully acknowledges financial support in the form of a Gliese Fellowship and an Emmy Noether Research Group from the Deutsche Forschungsgemeinschaft (DFG), grant number KR4801/1-1. RMC is the recipient of an Australian Research Council Future Fellowship (FT110100108). MRK and JMDK thank the Aspen Center for Physics, which is supported by NSF Grant PHY-1066293, for its hospitality during the early phases of this work.


O O B-Person I-Person I-Person O B-Person I-Person O O O O O B-Person I-Person O O O O O O O O O O O O B-Instrument I-Instrument O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Location O B-Grant O B-Organization I-Organization I-Organization I-Organization O B-Location O B-Grant B-Grant B-Grant O B-Grant O B-Software B-Citation I-Citation I-Citation I-Citation O B-Citation O O O B-URL O

We thank Profs. Hong-bo Hu and Qiang Yuan for helpful discussions. We appreciate Su-jie Lin for the discussion of the generated cross section of antiproton and provide EPOS 1.99 data. This work is supported by the National Key Research and Development Program of China (No. 2016YFA0400200), the National Natural Science Foundation of China (Nos. 11875264, 11635011, 11761141001, and 11663006). Software: DRAGON (Evoli et al. 2008 , 2017 ) available at https://github.com/cosmicrays .


O O O O O O O O B-Citation I-Citation I-Citation O B-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Software O O O O O O O O O O O O O B-Database I-Database I-Database I-Database I-Database B-Database B-Citation I-Citation I-Citation I-Citation O O B-Dataset I-Dataset I-Dataset I-Dataset O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O O O O O O O O B-Model I-Model O O B-Model I-Model O O B-Model I-Model B-Citation I-Citation I-Citation I-Citation O O B-Model O B-Model I-Model O O O O O O O O O O O O O O B-Citation I-Citation O O B-Software O O O O O O O B-Model I-Model O O O O B-Software I-Software O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O

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


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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.


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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.


O B-Identifier O O O O O O O O O O O B-Identifier O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Identifier O O O O O O O O O O O O O O O O O O O O O O B-Identifier O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Identifier O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Identifier O O O O O O O O O O O B-Identifier O O O O O O O O O B-Telescope B-Dataset B-Telescope B-Wavelength I-Wavelength O B-Telescope B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O B-Identifier O O O O O O O O O O O O B-Telescope B-Dataset B-Telescope B-Wavelength I-Wavelength O B-Telescope B-Wavelength I-Wavelength O O O O O O O O O O O O B-Identifier O O O O O O O O B-Identifier O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Identifier O O O O O O O O O O O O O O O O O B-Identifier O O O O O B-Identifier O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Identifier O O O O O O O O O O O O O O O O B-Identifier O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

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


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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


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

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


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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.


O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O B-Formula I-Formula I-Formula O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey O O O O B-Survey O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O B-Wavelength O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O B-Wavelength O O O O O O O O O O O O B-Wavelength O O O O O B-Wavelength O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O B-ObservationalTechniques I-ObservationalTechniques I-ObservationalTechniques O O O O O O O O O O O O O O O O O O O O O O O O B-Tag O O O O O O O O O O O O O O B-Telescope O O O O O O B-Wavelength O O O O O O O O O O O

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


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O B-Survey O B-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey O O O O O O B-Survey O O O O O O O O O O O O O O O O O O O O O O B-Survey O O O O O O O O O B-Survey O O O O O O O B-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O B-Wavelength O O B-Wavelength O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

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


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

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


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

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,


O O B-Person I-Person B-Person I-Person O B-Person I-Person O O O O O O B-Person I-Person O O O O O O O B-Person I-Person O O O O O O B-Location B-Organization O O O B-Grant I-Grant B-Person I-Person O O O O B-Organization B-Collaboration I-Collaboration I-Collaboration I-Collaboration I-Collaboration I-Collaboration I-Collaboration I-Collaboration I-Collaboration O B-URL O

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 ).


B-Person O O O O O B-Location B-Organization I-Organization I-Organization I-Organization I-Organization O O O O B-Location B-Organization I-Organization I-Organization B-Person O O O O B-Organization B-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship O O B-Fellowship B-Survey O O O B-Location O O O O O O O O B-Telescope I-Telescope O B-Survey O O O O O O O O O B-Survey I-Survey I-Survey I-Survey O O B-Survey I-Survey I-Survey I-Survey I-Survey O O O O B-Survey O O O O O O O O O O O O B-Telescope B-Survey B-Telescope B-Survey B-Telescope B-Survey B-Telescope O B-Telescope B-Survey B-Telescope O B-Telescope O B-Wavelength O B-Wavelength O B-Survey O O O O B-Organization B-Location O B-Organization B-Location O B-Observatory O O O O O B-Survey O O B-URL O O O O O O B-Observatory O O O B-Observatory I-Observatory I-Observatory I-Observatory O O O B-Proposal O B-Proposal

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.


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

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


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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


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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 ).


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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.


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

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


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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).


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O B-Model O O O O O O B-Model O O O O O O O O O O O O O B-Telescope O O O B-Observatory O O O B-Wavelength O B-Wavelength O O B-Wavelength O B-Telescope B-Wavelength O O O B-Wavelength I-Wavelength O B-Telescope I-Telescope I-Telescope O O O O O O O O O O O O O B-Telescope O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O B-Telescope I-Telescope I-Telescope O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O B-Telescope O B-Observatory O B-Telescope O O B-Telescope I-Telescope I-Telescope O O O O O O O B-Model O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O B-Observatory O O O B-Wavelength O B-Wavelength O O B-Wavelength O B-Telescope B-Wavelength O O O B-Wavelength I-Wavelength O B-Telescope I-Telescope I-Telescope O O O O O O O O O

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


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

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