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

for EW 0 (Ly α ) and β in A370-L57, and the gray areas represent the 1 σ confidence interval. In the right panel, the same information is represented by the filled star with error bars. The dependence of β on the age and metallicity of the population (middle panel) is more complex. At very young age ( Myr), β is almost independent of t and higher at lower metallicity (due to increased nebular emission). However, as the population ages and the nebular emission decreases, β increases in the Z > 0 populations but decreases for PopIII. By t ∼ 10 Myr the nebular emission has become negligible and β is monotonously higher for higher metallicity. The observed value for β in A370-L57 is consistent with almost any metallicity at some age. However, since t > 3 Myr is ruled out for Z > 4 × 10 −4 by EW 0 (Ly α ), the observed β requires Z ≲ 4 × 10 −4 . The right panel rules out a PopIII-dominated SED for A370-L57, because for the observed β the required EW 0 (Ly α ) would be ∼1000 Å. Despite this, our single population delayed exponential model is likely a gross oversimplification of the actual SFH of the galaxy. While the currently available data do not allow us to test more complex SFHs, a wider range of stellar ages and metallicities may be present. If older or more metallic stars contribute significantly to the UV continuum emission, younger and/or less metallic ones are required to compensate for their lower production rate of LyC photons in order to reproduce the observed Ly α luminosity. A conclusive diagnostic of the source of the Ly α emission in A370-L57 requires the determination of UV emission line ratios. Recently, Vanzella et al. ( 2016 ) measured line ratios C iv /Ly α = 0.25, He ii /Ly α = 0.067, and O iii ]/Ly α = 0.16 in the spectrum of a lensed z = 3.11 LAE with comparably low luminosity ( M UV = −17.0). If A370-L57 has similar line ratios, the C iv λ 1550, He ii λ 1640, and O iii ] λλ 1660, 1666 lines, among others, would be detectable with deep near-IR spectroscopy on current 10 m class telescopes. 9. Conclusions In this work we have taken advantage of strong lensing by the Abell 370 galaxy cluster in combination with deep imaging from the Hubble Frontier Fields and SHARDS Frontier Fields programs and MUSE spectroscopy to perform a detailed analysis of an Ly α emitter. This source would be fainter than magnitude 30 in the continuum if it were not magnified by the gravitational lens. The source, A370-L57, is a z = 5.75 galaxy with a low Ly α luminosity ( L (Ly α ) ∼ 10 42 erg s −1 ), which, however, implies an extreme Ly α EW of ∼420 Å. This value of the EW is exceptional among known galaxies in this luminosity range and redshift. The even fainter source B2, with similar properties and confirmed spectroscopically to be at the same redshift, is just ∼1 kpc away in projection and could be another star-forming region in the same galaxy or a close neighbor. The physical properties of A370-L57 are similar to those of galaxies with


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-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 I-Citation I-Citation O O O B-URL 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 B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey I-Survey I-Survey B-Survey B-Citation I-Citation O O O B-Telescope I-Telescope I-Telescope I-Telescope B-Telescope B-URL O O B-Survey O O O O O O B-Wavelength O O O O O O O O B-Citation I-Citation I-Citation O B-Citation I-Citation O O B-Telescope O O O O O O B-Wavelength O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O B-Formula I-Formula I-Formula B-Citation I-Citation I-Citation I-Citation 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 B-Telescope O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula B-Formula I-Formula I-Formula I-Formula 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-Survey O O O O O B-Instrument O B-Instrument O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula 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 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 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 B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Mission O B-Mission O O O O O O O O O O O O O O O O O O O O O O O O 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

how the fitted magnetic field inside MEs and the radial size of MEs vary with distance and discussed the implications of their study for the self-similar expansion of MEs. They concluded that, for individual cases, reconnection between the ME and the solar wind and/or pancaking of the ME cross section is necessary to understand the evolution of the ME size as compared to the evolution of the magnetic field. In a previous work, Leitner et al. ( 2007 ) noted that the expected difference in the decrease rate with the distance of the axial and azimuthal components of the magnetic field may create differences in the trend found for the inner and outer heliosphere. Good et al. ( 2019 ) discussed the change in orientation of the 18 CMEs measured in conjunction that they studied, finding a tendency toward lower-inclined MEs at the outer spacecraft compared to the first spacecraft. This implies a (small) difference in the way different magnetic-field components change with distance. We note that for a force-free field with self-similar expansion, the axial magnetic field is expected to vary with distance as r −1 , whereas the poloidal field should vary as r −2 . In Lugaz et al. ( 2020 ) for the 2013 July 10–13 CME, we found that a uniform decrease of the magnetic-field components as r −1.6 was a better fit to the data than a separate fit for the y (axial) or z (poloidal) components of the magnetic field. Here, we continue this analysis for the 42 CMEs measured in conjunction between two spacecraft. Because MESSENGER and VEX were planetary missions, there are significant “data gaps” in the interplanetary magnetic field measurements corresponding to the time when the spacecraft were in the planetary magnetospheres. In addition, the magnetic fields inside MEs have been reported to significantly rotate in the inner heliosphere in some cases (e.g., see Nieves-Chinchilla et al. 2012 ; Winslow et al. 2016 ) and it is unclear how this should be considered when comparing the axial or poloidal fields measured by these spacecraft with those measured near 1 au. As such, we compare the tangential and normal components of the magnetic field measured at the two spacecraft in the RTN coordinate system. We focus on the extrema of the variation of the magnetic-field components. For an ME that has a clear low (respectively high) inclination, the B T (respectively B N ) component typically keeps the same sign throughout the ME interval. In addition, the expansion of the front and back half of the ejecta may occur at different rates. For example, in event 21-2013, discussed in Lugaz et al. ( 2020 ), B T is always positive, while B N varies from positive to negative (North–West–South ME following the classification of Bothmer Schwenn 1998 ). For this event, as shown in Table 1 , the B N positive component (at the front) decreases with an index of −1.4, whereas the B N negative (at the back) decreases with an index of −1.1. We therefore calculate the average of the indices


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

of the outer star forming rings in visually unbarred galaxies are shown in Fig. 1 . This figure presents a particular class of ring galaxies, those with accreted star forming rings in axisymmetric S0s which are especially suitable to host a dynamo process. The class is however far from being homogeneous. Figure 1 illustrates that the ring galaxies of interest can vary considerably in appearance. This is why we have to consider a variety of possible dynamo effects that might contribute to magnetic field formation in such scenarios and experiment with the dynamo numbers that estimate the strengths of the effects. A particular challenge is that NGC 4513, shown in the first panel of Fig. 1 , has a counter-rotating ring. IC 5285, UGC 5936, and UGC 9980 do not demonstrate observable radial gas velocities, thus ruling out a collisional origin for their rings ( Ilyina Sil’chenko 2011 ; Ilyina et al. 2014 ; Katkov et al. 2015 ). In fact, to discriminate between the origin scenarios for an outer ring in a particular galaxy, kinematical data are necessary, and 3D (two spatial coordinates on the plane of sky and one along the wavelength axis Courtes 1995 ); spectral data are especially useful ( Moiseev Bizyaev 2009 ). The collisional rings and OLR (Outer Lindblad Resonance) rings generate radial gas outflow while accreted gaseous rings rotate circularly, although sometimes outside the main galactic plane. In addition, the optical spectral data provide the possibility of determining the excitation mechanism for the ionized (warm) gas. The flux ratios of strong emission lines discriminate easily between the mechanisms of shock excitation and of ionization by UV radiation of young stars ( Baldwin et al. 1981 ; Veilleux Osterbrock 1987 ). To facilitate the action of a dynamo in magnetic-field generation, we need long-lived (order of Gyrs) rings; hence collisional rings, with their lifetimes of a few hundred Myr, are unlikely to be candidates; a supply of free electrons, hence an ionized state of the gas that can be provided and supported by continuous star formation in the rings; regular circular gas rotation in the main galactic planes, presumably with a flat rotation curve, to provide a differential character for the gas rotation. In some ways rings, generated by accretion may be be the most favourable for our investigation, with estimated lifetimes possibly approaching the Hubble time ( Buta Combes 1996 ). Based on the results of Ilyina Sil’chenko (2011) , Ilyina et al. (2014) and Katkov et al. (2015) we select a small sample with the properties mentioned above and present it in Fig. 1 . The typical properties of these galaxies will be used in the further theoretical consideration of the dynamo magnetic-field generation in ring galaxies. Some extension of the typical picture can be also considered, by taking into account possible cases of the outer gas counter-rotation, as in NGC 4513 ( Ilyina et al. 2014 ), or strong flaring of the gas layer in the


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

We would like to acknowledge the developers of crpropa for making the code publicly available. The cosmological simulations presented in this work were performed using the enzo code ( http://enzo-project.org ), and were partially produced at Piz Daint (ETHZ-CSCS, http://www.cscs.ch ) in the Chronos project ID ch2 and s585, and on the JURECA supercomputer at the NIC of the Forschungszentrum Jülich, under allocations no. 7006 and 9016 (FV) and 9059 (MB). We also acknowledge the use of the Golem Cluster at Hamburger Sternwarte for analysis. FV acknowledges personal support from the grant VA 876/3-1 from the Deutsche Forschungsgemeinschaft (DFG). FV and MB also acknowledge partial support from the grant FOR1254 from DFG. This work was supported by the DFG through collaborative research centre SFB 676, by the Helmholtz Alliance for Astroparticle Physics (HAP) funded by the Initiative and Networking Fund of the Helmholtz Association and by the Bundesministerium für Bildung und Forschung (BMBF). We thank R. Clay, R. Alves Batista and J. Devriendt for useful comments on the manuscript.


O O O B-Person I-Person O B-Person I-Person O O O O O B-Software I-Software I-Software B-Person I-Person O O O O O O B-CelestialObject I-CelestialObject O B-Instrument O O B-Person I-Person O O O O O B-CelestialObject I-CelestialObject B-Person O O O O B-Organization I-Organization O B-Grant I-Grant O O O O O O B-Telescope I-Telescope I-Telescope I-Telescope O O O B-Archive I-Archive O O B-Proposal O O B-Organization I-Organization I-Organization I-Organization B-Organization O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization O B-Grant I-Grant O O B-Archive O B-Telescope O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Grant O O O O O O O O B-Instrument O O O B-Telescope O O O O O O B-Observatory O O O B-Observatory I-Observatory I-Observatory I-Observatory O O B-Grant O O O O O O O B-Archive I-Archive I-Archive B-Archive O O O O O B-Observatory I-Observatory I-Observatory O O B-Organization I-Organization I-Organization I-Organization B-Organization O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O O O O O O O O B-Organization I-Organization I-Organization B-Organization O B-Telescope O B-URL O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization B-URL O O O O B-Organization O O O O O O O O O O O O O B-Collaboration I-Collaboration I-Collaboration O B-Software O O B-URL O O O O O O O O O O O O O O B-Observatory I-Observatory I-Observatory I-Observatory O O O O O O B-Dataset I-Dataset I-Dataset O B-URL O O O O O O B-Person I-Person I-Person O O O O


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

; Margutti et al. 2013 ; D’Avanzo et al. 2014 ; Zaninoni et al. 2016 ). In order to check whether XRFs, XRRs, and C-GRBs in our sample follow this correlation, respectively, we collect the E γ ,iso and E X ,iso data of the GRBs in our sample from Amati et al. ( 2008 ), Margutti et al. ( 2013 ), and Liang et al. ( 2015 ). First, the relation between E X ,iso and E γ ,iso is shown in Figure 9 . We perform the maximum likelihood method and obtain the fitting of with the extrinsic scatter of σ = 0.57 ±0.04. The E X ,iso – E γ ,iso relation is consistent with that derived by Margutti et al. ( 2013 ). Second, we also investigate the correlation between E peak, z and E γ ,iso . The result is shown in Figure 10 . The correlation fitted by the maximum likelihood method is (keV) = (2.17 ± 0.04) + (0.46 ± 0.03) with the extrinsic scatter of σ = 0.26 ± 0.02. Our result is consistent with the correlation reported by Amati ( 2006 ). Third, in Figure 11 , we present the relation between E X ,iso and E peak, z by the maximum likelihood method with the fitting of = (49.69 ± 0.27) + (0.75 ± 0.11) , and the extrinsic scatter is σ = 0.73 ± 0.04. Our result is consistent with that of Margutti et al. ( 2013 ). Finally, the E X ,iso – E γ ,iso – E peak, z relation is shown in Figure 12 . The result with the fitting of = (4.78 ± 2.79) + (0.92 ± 0.06) and the extrinsic scatter of σ = 0.44 ± 0.04 produced by the maximum likelihood method is consistent with that of Margutti et al. ( 2013 ) as well. Figure 9. Correlation between E X ,iso and E γ ,iso in the Swift -BAT3 sample. The green solid line is the best fit with the function of ( E X ,iso ) = (13.31 ± 2.73) + (0.73 ± 0.05) log( E γ ,iso ), and the extrinsic scatter is σ = 0.57 ± 0.04. The green dashed lines are marked for the 2 σ regions. The pink dashed–dotted line is the best-fitting function of log( E X ,iso ) = (10.0 ± 20.6) + (0.79 ± 0.01) log( E γ ,iso ) reported by Margutti et al. ( 2013 ). XRFs, XRRs, and C-GRBs are marked as black squares, red dots, and blue triangles, respectively. The GRBs labeled as outliers in the figure are L-GRBs, and the exception is short GRB 090510. Figure 10. Correlation between GRB peak energy E peak, z in the rest frame and GRB isotropic-equivalent energy E γ ,iso . The green solid line is the best fit with the function of log( E peak, z ) (keV) = (2.17 ± 0.04) + (0.46 ± 0.03) , and the extrinsic scatter is σ = 0.26 ± 0.02. and the green dashed lines are marked for the 3 σ regions. The pink dashed–dotted line is the best fit with the function of E peak, z = 95 keV( E γ ,iso /10 52 erg) 0.49 reported by Amati ( 2006 ). XRFs, XRRs, and C-GRBs are marked as black squares, red dots, and blue triangles, respectively. Figure 11. Correlation between GRB X-ray energy E X ,iso and GRB peak energy E peak, z . The green solid line is the best fit with the function of , and the extrinsic scatter is σ = 0.73 ± 0.04. The green dashed lines are marked for the 1 σ regions. The pink dashed line


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

ACKNOWLEDGEMENTS ND is supported by a Vidi grant awarded by the Netherlands organization for scientific research (NWO). LO, RW, and AP are supported by an NWO top grant, module 1, awarded to RW. DP is partially supported by the Consejo Nacional de Ciencia y Tecnologíaa with a CB-2014-1 grant #240512. DA acknowledges support from the Royal Society. JMM and JH acknowledge support from Chandra grant GO7-18031B. This work made use of data supplied by the UK Swift Science Data Centre at the University of Leicester. We also made use of MAXI data provided by RIKEN, JAXA, and the MAXI team, and public light curves from the Swift /BAT transient project.


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

is not excluded when taking into account the noise level, but we do see a systematic trend across the velocity: a dip in the estimated α + around the [C II ] peak at position 1 and a gradient at 235–240 km s −1 at position 5. In addition, the estimated α + of 20–30 is lower than the measured 12 C/ 13 C in N159 ( Johansson et al. 1994 ). Therefore, the scenario of optically thick [ 12 C II ] discussed in Sect. 4.1 is more likely. Fig. 3. Estimate of α + = 12 C + / 13 C + when assuming [ 12 C II ] is optically thin. Asterisks indicate the derived α + together with the error bars. Blue lines show the [C II ] emission profiles. 4.3. Fractionation Because the fractionation reaction from 13 C + to 12 C + is an exothermal reaction (the exothermicity is 35 K; Langer et al. 1984 ), 13 C + tends to be underabundant with respect to 12 C + at low temperatures, namely at higher A V in a PDR. Röllig Ossenkopf (2013) calculated the fractionation in the clump integrated intensity of [ 12 C II ] and [ 13 C II ], and showed that only models with low UV fields ( χ ≤ 100) and high densities ( n ≥ 10 5 cm −3 ) trace the chemical fractionation, which would result in α α + , and that the derived [ 12 C II ] optical depth is a lower limit. On the other hand, it is unlikely that the fractionation is significant in the regions in this study because the estimated PDR properties are either low density and low UV field, or high density and high UV field ( Okada et al. 2019 ). 4.4. Metallicity effect Model predictions do not indicate a clear metallicity dependence of the [C II ] optical depth. For a high density PDR clump where the C + layer consists of a thin surface, the surface brightness of the [C II ] emission is almost constant with the metallicity ( Röllig et al. 2006 ) because the surface brightness is proportional to the thickness of the layer and the density of C + ions, with the former being proportional to the inverse of the metallicity due to the dust extinction and the latter being proportional to the metallicity as a first-order approximation. The derived optical depths in the LMC regions are similar to those of some Galactic regions (M 43 and Horsehead measured by Guevara et al. 2019 ); however, this study does not provide enough statistics to conclude that we do not see a metallicity dependence in the [C II ] optical depth. 4.5. Implications for the interpretation of the [C II] intensity The impact of the optical depth effect depends strongly on the actual geometry of the sources. Most PDR models compute the [C II ] intensity emerging from the surface of an externally illuminated clump or a face-on plane-parallel structure. For this geometry the radiative transfer computation takes the optical depth correctly into account. However, when the [C II ] emission stems from a mixture of components including surfaces illuminated from the back (negative temperature gradient toward the observer) or an ensemble of clumps we can no longer simply sum up the intensity


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

ACKNOWLEDGEMENTS The research leading to these results has received funding from the European Union Seventh Framework Programme FP7/2007-2013/ under grant agreement number 607254. This publication reflects only the author’s view and the European Union is not responsible for any use that may be made of the information contained therein. KJD and HJAR acknowledge support from the ERC Advanced Investigator programme NewClusters 321271.


O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O B-Location O O

Support by the Natural Sciences and Engineering Research Council (NSERC) of Canada is acknowledged.


O O O B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person O B-Person I-Person O O O O O O O O O O O O B-Person O O O O B-Organization I-Organization O B-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship B-Fellowship B-Person O O O O O B-Organization I-Organization I-Organization B-Organization O B-Grant O B-Organization I-Organization O B-Grant O O O O O O B-Database I-Database I-Database B-Database O O B-Person I-Person O O O O B-Organization I-Organization I-Organization I-Organization O B-Person I-Person B-Person I-Person O B-Person I-Person O O O O O B-Organization I-Organization I-Organization I-Organization B-Organization O O B-Organization I-Organization I-Organization B-Organization O O O O O O B-Software O B-Citation I-Citation I-Citation O O O O O O O O O O B-Organization I-Organization I-Organization B-Organization O B-Telescope O B-URL O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization B-URL O O O O B-Organization O O O O O O O O O O O O O B-Collaboration I-Collaboration I-Collaboration O O O O O O O O O B-Telescope I-Telescope I-Telescope I-Telescope O O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O B-Mission O O O O O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Telescope O B-Mission O O O O B-Organization I-Organization I-Organization I-Organization I-Organization


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

We are very grateful to P. Jofre, A. Casey and C. Tout for fruitful discussion. This work was partly supported by the European Union FP7 programme through ERC grant number 320360.


O O O O B-Person I-Person I-Person O O O O O O O O O O O O O O O O O O O B-Person I-Person I-Person O B-Person I-Person 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 B-Database I-Database O O O O O B-Survey O B-Citation I-Citation I-Citation I-Citation O O B-Survey O O O O B-Organization O B-Grant O O B-Observatory O O O O B-Organization I-Organization I-Organization O O O O O O O O B-Organization B-Grant I-Grant I-Grant B-Grant B-Grant O B-Grant O B-Organization O B-Grant B-Person O B-Person O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Grant O B-Grant I-Grant I-Grant I-Grant O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O O O B-Location I-Location O B-Grant B-Person O O O O B-Organization I-Organization I-Organization O B-Grant O B-Grant O O O O O O O O O B-Organization I-Organization I-Organization I-Organization O O O O O O O B-Organization I-Organization I-Organization I-Organization B-Software I-Software O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O

We thank the referee, D. C. Gabuzda, for a thorough reading of the manuscript and for many suggestions that improved the paper. We are grateful to D. E. Homan and S. Kiehlmann for reading the manuscript and making useful suggestions, and to the entire MOJAVE team for their years of work in assembling the data used here. This research has made use of data from the MOJAVE database that is maintained by the MOJAVE team (Lister et al. 2009 ); the MOJAVE program is supported under NASA-Fermi grant NNX15AU76G. Operations at UMRAO were supported by the University of Michigan, and research there was funded in part by NASA-Fermi GI grants NNX09AU16G, NNX10AP16G, NNX11AO13G, and NNX13AP18G and NSF grant AST-0607523. Y.Y.K. and A.B.P. were supported by the Russian Foundation for Basic Research (project 17-02-00197), the Basic Research Program P-28 of the Presidium of the Russian Academy of Sciences, and the government of the Russian Federation (agreement 05.Y09.21.0018). T.S. was funded by the Academy of Finland projects 274477 and 284495. This research has been supported in part by the Alexander von Humboldt Foundation, and it has made use of the Swinburne University of Technology software correlator, developed as part of the Australian Major National Research Facilities Programme and operated under license (Deller et al. 2007 ).


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

K1 (with PA 145 with respect to the core component), of the peak of the B3 component as observed in total intensity images. The polarization morphology resembles a limb-brightened structure. At 15GHz, the two polarized components are resolved from 2016 March, whereas in the first three epochs they are blended together, in agreement with what is found by Lister etal. ( 2018 ). At 43GHz, polarized emission from component K1 is detected during all epochs with the exception of 2015 October, whereas significant polarized emission from component K2 is detected sporadically. Polarized flux density of the sub-components of S50836710 are reported in Table 4 , while the full set of polarization images are presented in Appendix C (Fig.C1) . In the core component, we observe very high values of RM, which may exceed 5000radm 2 . The RM is highly variable with sign changes and its structure is patchy, indicating either opacity gradients and/or different components that evolve with time, expected in the case of a perturbed flow, which is moving along the jet. In the last epoch, when the radiation is optically thin at all three frequencies, we observe an RM of 1400500 rad m 2 , and an RM-corrected magnetic field direction of 585, roughly parallel to the jet direction. RM images and the associated error images at each observing epoch are presented in Fig. 11 . Figure 11. Rotation measure images (colour scale) for S50836710 overlaid with total intensity contours (left-hand column), and the associated rotation measure error images (colour scale; right-hand column). Vectors represent the RM-corrected magnetic field ( B ) vectors. Figure 11. continued. During the epochs in which component K2 has significant polarized emission at the three frequencies the RM is about 1950150 rad m 2 in 2015 August, and 1200400 rad m 2 in 2015 October and 2016 March. The RM-corrected magnetic field direction ranges between 160 and 175. Component K1 has RM values between 850120 and 180120 rad m 2 , with a tentative sign change observed in the last epoch, while the RM-corrected magnetic field direction ranges between 60 and 75, roughly parallel to the jet direction. We perform the analysis of the jet transverse structure using the data taken in March 2016, i.e. when polarized emission from both K1 and K2 components is clearly visible at all frequencies. Fig. 12 indicates the RM image and the slice considered for the analysis. A transverse RM gradient is clearly visible with K1 component showing positive RM values, while K2 component has negative RM values (Fig. 12 ). The shaded area marks regions with low polarization levels consistent with noise, where no reliable RM could be estimated. Total intensity and polarization profiles on the same transverse slice show a ridge-brightened profile and a limb-brightened profile, respectively. The transverse spectral index profile between 15 and 24GHz indicates a smooth flattening of the spectrum towards the ridge of the jet, with the


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

reduce the in equation ( 60 ). Thus, it can achieve arbitrary precision by increasing the bit length. However, the round off error will also propagate and accumulate through the extrapolation table in Table 1 . As the order of the GBS extrapolation increases, the round off will accumulate faster and faster. Thus the additional mantissa bits becomes less and less efficient in increasing the integration accuracy. Therefore, reducing the round off error in GBS extrapolation is also important in order to achieve the same precision with less mantissa bits and less CPU time. 3.1.1 Improvement on GBS extrapolation In the BS extrapolation, higher order methods can be obtained from lower order methods by extrapolation, as described in equation ( 52 ). However, the round off error will also propagate and accumulate through the extrapolation table. If the round off error from the base integration method is ε, −ε, ε, ... in the first column, then the round off error propagation with the extensively used step sequence n i = 2 i suggested by Deuflhard ( 1983 ) will behave as in Table 2 . As shown in the table, T 8, 8 with 16th order precision magnified the round off error to become 100 times larger. Thus, we will lose at least 2 significant digits from the extrapolation. This becomes more problematic for higher order extrapolations, as required by arbitrary precision integration methods with extremely low tolerance. Table 2. Round off error propagation in the Bulirsch–Stoer extrapolation with step sequence n i = 2 i . To reduce the round off error in the extrapolation process, there are two fine-tunings that can be performed on the extrapolations. The first is a step sequence choice. The step sequences n i = 1, 2, 3, 5, 8, 12, 17, 25, 36, 51, 73, ...(Fukushima 1996 ) is better than the extensively used sequence n i = 2 i , where the extrapolation coefficient reduces the round-off error propagation. Table 3 shows the error propagation with the new step sequence. We see that it performs much better than the original sequence suggested by Deuflhard ( 1983 ). Table 3. Round off error propagation with optimal step sequence in the BS extrapolation. The second method to reduce the round off error in the extrapolation process is to extrapolate the raw increment dξ of the integration instead of the integrated result ξ. Since the GBS extrapolation is linear, it is possible to do the following Because the raw increment dξ is usually tiny compared to the integrated results, the round of error in the first column of Table 1 is ∼eps × |dξ| instead of ∼eps × |ξ|. Then, the round off error accumulated from the extrapolation table will be smaller than the error accumulated from the direct extrapolation. We note, however, that the initial Δ T i , 1 should be the raw increment evaluated from the basic integrator, not from the subtraction of T i , 1 ( H ) − T i , 1 (0). The close value subtraction will introduce additional round off errors and will significantly degrade the


O O O B-Person I-Person O B-Person I-Person O O O O O O O O O O O B-Grant I-Grant I-Grant I-Grant O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O O O B-Grant B-Grant B-Grant O B-Grant B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O B-Grant B-Grant B-Grant O B-Grant B-Organization B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization B-Grant I-Grant I-Grant I-Grant O O O O O O O O B-Database I-Database O B-Database I-Database I-Database I-Database B-Observatory I-Observatory I-Observatory I-Observatory I-Observatory

ACKNOWLEDGEMENTS We thank Elisabeth Krause and Fabian Schmidt for their useful discussions. This work was in part supported by Grant-in-Aid for Scientific Research from the Japan Society for the Promotion of Science (JSPS) Promotion of Science (No. 23340061, 26610058, 15H03654, and 17H01131), Ministry of Education, Culture, Sports, Science and Technology (MEXT) Grant-in-Aid for Scientific Research on Innovative Areas (No. 15H05887, 15H05893, 15K21733, and 15H05892), JSPS Program for Advancing Strategic International Networks to Accelerate the Circulation of Talented Researchers, and Japan Science and Technology Agency (JST) CREST Grant Number JPMJCR1414. Numerical computations were in part carried out on Cray XC30 at Centre for Computational Astrophysics, National Astronomical Observatory of Japan.


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

decrement, the flattest BLR decrements (lowest-ratio) are similar to the narrow-line decrement; i.e. the lower envelope is a 45-deg line parallel to the reddening vector. The null hypothesis, that the minimum BLR decrement is independent of the NLR decrement (see for example, Fig. 2 , panel VI), is excluded at a probability p = 0.002. There is a lack of AGNs with NLR decrements steeper than the BLR decrement. Points to the right of the 45-deg line are consistent with measuring errors. Only one point lies more than two standard deviations to the lower right of the red line. For the majority of AGNs, the BLR decrement is steeper than the NLR decrement. There is no significant difference in the median NLR decrement for the AGNs with very steep BLR Balmer decrements compared with those with very flat BLR Balmer decrements. These results are consistent with the earlier findings of De Zotti Gaskell ( 1985 ) and Glikman et al. ( 2007 ). De Zotti Gaskell ( 1985 ) found that Balmer decrements for nearby AGNs were steeper for the broad lines than the narrow lines, and Glikman et al. ( 2007 ) found that, for the FIRST–2MASS red quasar survey, broad lines seem to be reddened more than the sum of broad and narrow lines. Our results strongly imply that: the dust that reddens the NLR also reddens the BLR, but most of the dust reddening the BLR lies between the BLR and the NLR. The dust causing the common reddening of both the NLR and BLR could be associated with the NLR or it could be dust in the host galaxy. De Zotti Gaskell ( 1985 ) studied nuclear continuum colours and both broad- and narrow-line Balmer decrements of nearby AGNs as a function of the orientation of the host galaxy. They found that for more highly inclined disc galaxies, the nuclear colours were redder and the Balmer decrements steeper. Since the axis of symmetry of an AGN is not necessarily aligned with the rotation axis of the galaxy (see for example, Tohline Osterbrock 1982 ; Valtonen 1983 ; Battye Browne 2009 ), the greater nuclear reddening of inclined galaxies must be due in part simply to dust in the plane of the galaxy. 4 THE RELATIVE STRENGTH OF [O <sc>iii</sc>] VERSUS THE BLR REDDENING As noted above, intervening dust not only causes reddening, but also extinction. If the dust is located between the NLR and the BLR, we would expect higher extinction of the BLR and AD to make [O iii ] stronger relative to the BLR and the continuum. 4.1 Selection of objects [O iii ] λ5007 is the strongest narrow line in the optical and the Balmer lines are the strongest broad lines. Therefore, a very large number of measurements are potentially available in the Sloan Digital Sky Survey (SDSS). Dong et al. ( 2008 ) have carefully measured Hα/Hβ ratios after subtraction of narrow lines and Fe ii , etc. Comparison of their ratios with the simple Gaussian fits of the SDSS pipeline reveals quite a few very discrepant measurements in the SDSS data base and that the difference between the Dong et al. (


O B-Telescope O O B-Organization B-Grant I-Grant I-Grant O O O O B-Organization O O O O O B-Organization I-Organization I-Organization I-Organization O O O O O O O O O B-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization B-Grant O O B-Observatory I-Observatory I-Observatory B-Observatory O O O O O O O O B-Organization O O B-Telescope I-Telescope I-Telescope O B-Telescope I-Telescope I-Telescope I-Telescope O O O O O O O O O O O B-Person I-Person B-Person I-Person B-Person I-Person O B-Person I-Person O O O O O O B-Organization I-Organization O O O B-Organization O O B-Grant B-Grant B-Grant B-Grant B-Grant B-Person I-Person O O O B-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship O B-Fellowship B-Person I-Person O O O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant B-Person I-Person O O O B-Organization O O B-Grant O B-Grant

Acknowledgements IRIS is a NASA Small Explorer mission developed and operated by LMSAL, with mission operations executed at NASA Ames Research Center and major contributions to downlink communications funded by the Norwegian Space Centre through a European Space Agency PRODEX contract. The Solar Dynamics Observatory (SDO) data that we used are provided courtesy of NASA/SDO and the Atmospheric Imaging Assembly and Helioseismic and Magnetic Imager science teams. The authorsthank the anonymous referee for suggestions. We thank Y. Chen, Z.J. Ning, Y. Li, and L.P. Yang for valuable discussions. The work at Peking University is supported by NSFC under contracts 41574168, 41231069, 41274172, 41474148, 41421003. LM Yan is supported by National Postdoctoral Program for Innovative Talents (grant BX201600159). J.S. H.E. is also supported by “National Youth Talent Support Program” of China. L.D. Xia is supported by NSFC under contracts 41274178 and 41474150.


O O O O 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 B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-ObservationalTechniques I-ObservationalTechniques O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-ObservationalTechniques I-ObservationalTechniques O O O O O O O O O O O O O B-ObservationalTechniques I-ObservationalTechniques O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-ObservationalTechniques I-ObservationalTechniques 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

model. This is partially caused by the inner region of the circumbinary disk ( ), which is thinned out by the gravitational forces of the two stars (e.g., Avramenko et al. 2017 ). However, this effect only occurs if the separation between the two stellar components is on the order of . A smaller separation would lead to a behavior that is similar to circumstellar disks around a single star. If the separation is significantly larger, the dust and gas around the binary can no longer be described with a single circumbinary disk. In circumstellar disks with a single star, the inner region has the highest density and usually the highest magnetic field strength (see Fig. 1 in Sect. 5.4 ; Flock et al. 2017 ). Therefore, as mentioned in Sect. 6.3 , circumbinary disks lack a significant fraction of circularly polarized emission if the inner high magnetic field region is missing. In addition, the different directions of circulation of the toroidal magnetic field decrease the circularly polarized emission from regions with similar velocities relative to the observer if not spatially resolved. Furthermore, the estimation of the LOS magnetic field strength from circumstellar disks with a single star is dominated by the inner region characterized by high magnetic field strength. In contrast, a Zeeman observation of a circumbinary disk is able to provide information about the magnetic field farther out in the disk if the requirements for such an observation are fulfilled. However, this requires that a significant part of its innermost region be depleted by the gravitational forces of both stellar components. 7. Conclusions We studied the requirements to observe the Zeeman splitting of the CN lines in circumstellar disks and their dependence on selected disk parameters. Such observations can be used to resolve degeneracies and obtain complementary information about the magnetic field if combined with polarimetric continuum observations. However, this is only applicable, if the polarimetric continuum observations are mainly caused by elongated aligned dust grains. In particular, we evaluated whether Zeeman observations of circumstellar disks should be performed spatially resolved or unresolved. With spatially resolved Zeeman observations, the strength and structure of the magnetic field in the LOS direction can be reconstructed for most regions in circumstellar disks. Only the region close to the star cannot be traced. However, the required sensitivity (, if ) is far beyond the capabilities of recent and upcoming instruments/observatories. For spatially unresolved Zeeman observations, we obtained different results. Under the assumption of Keplerian rotation and a toroidal structure of the magnetic field, two independent average magnetic field strengths can be obtained from the circularly polarized fraction. These average values are sensitive to changes in the strength and structure of the magnetic field inside the disk. In addition, they can be used to


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

leads to the inclusion of a number of RGB stars that are located close to the selection boundary, while retaining the color selection in ( m F435W − m F555W ) will still lead to rejection of RC stars. The RGB sample resulting from this updated selection run includes 207 stars. We repeated all of our subsequent analysis and found a new C index value of 0.063 mag, which is almost the same as our initial result, C index = 0.062 mag. We therefore conclude that the potential loss of a small number of genuine RGB stars by our initial selection method does not significantly influence our measurement of the cluster’s RGB broadening, nor our final results. 4. Discussion Our results show that the artificial stellar population is characterized by a similar dispersion in C F336W,F435W,F814W as the observed RGB sequence of NGC 1783. This demonstrates that the photometric uncertainties fully account for the RGB’s broadening in NGC 1783. The color index used, C F336W,F435W,F814W , is sensitive to the stellar N and He abundances, which are two of the most representative elements that exhibit large abundance variations in star clusters (Gratton et al. 2004 ). The consistency of the observed RGB’s width with that defined by our artificial SSP therefore indicates that our RGB sample is best represented by single-valued N and He abundances. There are a small number of outliers in the observed RGB distribution, in particular two stars at the far left (see the top panel of Figure 6 ). These objects are unlikely statistical fluctuations, given that they deviate by >5 σ from the Gaussian peak. Alternatively, they might be field stars that have not been properly removed by our field star decontamination algorithm. If they were cluster members, they would need to have unrealistically extreme metallicities. Note that these two data points appear both in the scatter diagram in the top panel of Figure 6 and in the observed histogram in the figure’s bottom panel. We suspect that these two stars might result from stochasticity in the field’s RGB sample (see Figure 5 ), rather than from random effects associated with our field star decontamination. We explored whether these objects might be binary systems instead. If we assume that the primary components ( M 1 ) of such binary systems are genuine RGB stars, the secondary components ( M 2 ) must have lower masses. We tested the appearance of binary systems with different mass ratios, M 2 / M 1 . For very low-mass companions, the change in color is almost negligible, while for equal-mass binaries no color difference is expected, compared with the single-star case. The top panel of Figure 6 includes binary sequences for M 2 / M 1 = 0.7, 0.8, and 0.9. It is clear that the outliers at the far left cannot be binary systems. An intermediate-age cluster with an age of 1.8 Gyr and a mass of 1.8 × 10 5 M ⊙ , NGC 1783 is comparably as massive as other star clusters that show clear evidence of MSPs (e.g., Martocchia et al. 2018 ). If


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

Acknowledgements We would like to thank John Helly for technical assistance during the course of this work and Spoorthy Raman for reading the manuscript and providing useful suggestions for improving the text. This work was supported by the Science and Technology Facilities Council [ST/L00075X/1]. This work used the DiRAC Data Centric system at Durham University, operated by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC Facility ( www.dirac.ac.uk ). This equipment was funded by BIS National E-infrastructure capital grant ST/K00042X/1, STFC capital grant ST/H008519/1, and STFC DiRAC Operations grant ST/K003267/1 and Durham University. DiRAC is part of the National E-Infrastructure.


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

which both β and IRX have been measured (Capak et al. 2015 ), but the galaxies with from Capak et al. ( 2015 ) and the galaxy presented by Watson et al. ( 2015 ) lie outside the region spanned by the simulated galaxies. Because our simulations and theirs cover disjoint regions of parameter space in terms of redshift and mass, it is not possible to make detailed comparisons between our results and theirs. However, their results highlight the potential importance of dust destruction for accurately predicting the UV properties of simulated galaxies and provide motivation for future studies that include more complex treatments of dust production, growth, and destruction. 9. Implications for Observations Our simulation results suggest that there is not a tight relation between IRX and β that applies to all galaxies at all redshifts. The simulated galaxies tend to lie near the M99 relation, which was determined based on observations of galaxies in the local universe. However, during merger-induced starbursts, even the galaxies can depart significantly from the relation: because IRX increases significantly but β is almost unaffected, the merger-induced starbursts, such as that shown in Figure 3 , tend to lie above the M99 relation. The simulations—of both disk galaxies and mergers—deviate more significantly from the M99 relation: even when they are not undergoing starbursts, they tend to lie above the relation. These results are consistent with observational works that have demonstrated that some classes of galaxies deviate significantly from the M99 relation. As already discussed above, observed DSFGs tend to lie above the M99 relation and do not exhibit any relationship between IRX and β (e.g., Bell et al. 2002 ; Goldader et al. 2002 ; Howell et al. 2010 ; Casey et al. 2014 ). Conversely, some galaxies lie significantly below the M99 relation (i.e., have lower IRX than expected from the relation given their β ). This was demonstrated for the lensed galaxies cB58 at (Pettini et al. 2000 ) and the Cosmic Eye (Smail et al. 2007 ) at . Similarly, Reddy et al. ( 2012 ) found that young systems (age Myr) at lie below the M99 relation. Moreover, we have demonstrated that the dust composition—specifically the strength of the 2175 Å feature—can have a very dramatic effect on the UV slope. Consequently, extrapolation of the locally calibrated relation to regimes for which it is not observationally constrained may be problematic if, e.g., the dust composition of high-redshift galaxies is significantly different from that of galaxies. How the strength of the UV bump varies with galaxy properties and redshift is still poorly understood, but there are some useful observational constraints. The commonly employed Calzetti et al. ( 1994 ) attenuation law, which was defined based on observations of local-universe starburst galaxies, does not exhibit a UV bump. Based on a study of ∼10,000 star-forming galaxies, Battisti et al. ( 2016 ) derived an average attenuation


O O O O O O O O O O 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 B-CelestialObject 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 B-CelestialObject O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-CelestialObject O O O O B-Wavelength 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 I-Formula O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O B-CelestialObject O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-CelestialObject O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-CelestialObject O O O O O O O B-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O B-CelestialObject O O O O O O O O O B-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion 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 B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O B-Model O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O

configuration. 6. Formation of Molecular Gas Due to Jet–ISM Interactions? Figures 10 – 12 display that a wall structure is clearly seen toward the locus of the extension of the precession axis of the SS 433 jets, in which the column density of H i increased precipitously. Enhanced CO emissions are also found to be nicely associated with the wall structure seen in H i emission. MC G40.331−4.302 has the H i counterpart, which displays more extended arc-like structure nearly perpendicular to the precession axis of the SS 433 jets (Figure 12 ). The positional coincidence between G40.331−4.302 and the precession axis of SS 433, as well as their coincident kinematic features, strongly suggests the physical connection between them (see Sections 4 and 5 ). We obtain that the column density, N H = N (H i ) + 2 × N (H 2 ), is about 2.1 × 10 21 cm −2 for the cloud G40.331−4.302, which corresponds to A V ≈ 1.1 mag assuming N H ≈ 1.9 × 10 21 cm −2 mag −1 × A V . At the column density, the molecules are shielded from UV radiation, and self-shielding allows significant H 2 molecules to exist. The total mass of the main concentration of the cloud is ∼3 × 10 3 M ⊙ within a radius of ∼66 (Table 1 ). The molecular fraction / N H is about 0.87, suggesting that the dominant of the gas in the cloud is in molecular form. Table 1 Properties of Gas toward G39.315−1.155 and G40.331−4.302 Notes. a The area of the emission with I (CO)>5 K km s −1 for G39.315−1.155 and I (H i )>130 K km s −1 and I (CO)>2.5 K km s −1 for G40.331−4.302. b The effective radius is calculated from (Area/3.14) 0.5 . c The mean intensity of the H i (70–90 km s −1 ) and CO (73–88 km s −1 ) emission. d The column density of the atomic and molecular gas is calculated from 1.823 × 10 18 × I mean (H i ) and 2 × 10 20 × I mean (CO), respectively. See the text. e Parameter d 4.9 is the distance to the cloud in units of 4.9 kpc (see Section 4 ). f The volume density of the atomic and molecular gas is calculated from the mass and the effective radius of the emission. The virial mass exceeds the total mass of the cloud by more than one order of magnitude, indicating that the cloud is in a gravitationally unbound state. The fragmented subclouds (e.g., with a size of ∼1 pc) in MC G40.331−4.302 may dissipate on a timescale of several Myr (sound crossing time) without other support. Alternatively, the MC may be confined by an external pressure of ≳4.4 × 10 4 K cm −3 (e.g., ρ (H i ) σ 2 (H i )) when the magnetic pressure and the self-gravity are negligible. We emphasize that G40.331−4.302 is the only detected MC within the range of l = 349–451, −51 ≲ b ≲ −30, and V LSR ≳ 70 km s −1 . It indicates that such an MC is located about 370 pc below the Galactic plane, where a kinematic distance of 4.9 kpc is adopted. However, the MCs within the solar circle are concentrated in the Galactic plane with a Gaussian FWHM of ∼90–100 pc (e.g., see Section 4.5 and Figure 6 in Heyer Dame 2015 ). This suggests that


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

This work was partially supported by NASA grants ATP12-0139 and ATP13-0077. We thank Alessandra Buonanno, Francesc Ferrer, Ted Jacobson, Henric Krawczynski, Tzvi Piran, Laleh Sadeghian, and Joe Silk for helpful comments and discussion.


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

The research of E.C. and J.C.W. is supported by NASA grant HST-AR-13276.002-A. E.C. thanks the Enrico Fermi Institute for its support via the Enrico Fermi Fellowship.


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O B-TextGarbage I-TextGarbage O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

a stronger field provides more magnetic energy to damp. We fit the slopes of this “big trend” for all the curves by appropriately removing a few points far away from this “big trend” and taking the average of these slopes. Interestingly, both viscous and magnetic dissipations obey an identical scaling law:The dashed lines in Figures 5 (b) and (c) denote this scaling law. This scaling law for the relation of the two dissipations and magnetic fields reveals that there exists self-similarity for the magnetic effect on dynamical tide. Figure 5. (a) Kinetic energy, (b) viscous dissipation, and (c) magnetic dissipation vs. S 2 at various ω. Pm = 1.0. The two dashed lines denote the scaling law ∝ S 2 . 3.2. Investigation of Pm In this subsection we investigate Pm . Similar to Figure 2 , Figure 6 shows viscous dissipation, magnetic dissipation, total dissipation, and the ratio of magnetic to viscous dissipations versus tidal frequency at various Pm with S 2 fixed to be 0.1, namely in a strong field regime. The first three subfigures show that for all the tidal frequencies, a larger Pm leads to higher viscous dissipation and lower magnetic dissipation but total dissipation is almost independent of Pm . This is reasonable because Pm is the ratio of viscosity to magnetic diffusivity (see Equation ( 9 )) but it cannot influence the total diffusivity. More interestingly, Figure 6 (d) shows that magnetic dissipation wins out over viscous dissipation for and this ratio is approximately equal to Pm −1 . In the astrophysical situation Pm is very small, and it can be inferred that magnetic dissipation dominates over viscous dissipation with a moderate or stronger magnetic field. Note again that with a very weak field, e.g., S ≤ 10 −4 , viscous dissipation wins out over magnetic dissipation even at a small Pm , e.g., (Lin Ogilvie 2018 ). Figure 6. (a) Viscous dissipation, (b) magnetic dissipation, (c) total dissipation, and (d) ratio of magnetic to viscous dissipations vs. tidal frequency at various Pm . . To find the scaling laws for Pm , we plot the two dissipations versus Pm as shown in Figure 7 . The dependence on Pm looks more regular than the dependence on S in Figure 5 because the field strength influences the resonant frequencies, whereas diffusivities cannot. By taking the average of the slopes for different tidal frequencies, we obtain the scaling lawsThe dashed lines in Figures 7 (a) and (b) denote these two scaling laws. The ratio of magnetic to viscous dissipations is indeed close to Pm −1 , as shown in Figure 6 (d). Note that our parameter regime is not the real regime, e.g., E and Pm are not too small, so these scaling laws might not be realistic. Lacking knowledge of the physical properties in stars and planets, we do not know the real parameters, and even estimating the order of magnitude is not convincing. These scaling laws obtained in the moderate parameter regime at least give us some qualitative evidence that a moderate or stronger


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

different from those of normal SNe, and the study of the immediate environment of these events can provide important information on physical properties of their progenitors which so far have remained undetected. Fig. 1 Left panel : Pan-STARRS -band image of NGC 3191 with the PMAS (blue squares) and the MaNGA fields of view (red hexagon) superposed. Right panel : map of the H ii regions obtained with the code described in the text and applied to the PMAS cubes. The SLSN 2017egm position is marked with a red cross in both panels. The levels of the isophotes, from the outermost to the innermost, are 21.86, 21.11, 20.66, 20.22, and 19.91 mag/arcsec. Indeed, several studies of SLSN host galaxy samples have revealed significant differences in the properties of Type I and Type II hosts ( Leloudas et al. 2015 ; Perley et al. 2016 ; Lunnan et al. 2014 ; Schulze et al. 2016 ). Type I hosts are usually star-forming (SF) dwarf galaxies with low metallicities at the extreme end of the distribution in the Baldwin-Philips-Terlevich (BPT; Baldwin et al. 1981 ) diagram and likely even more extreme than gamma-ray burst (GRB) hosts (see e.g. Leloudas et al. 2015 ; Schulze et al. 2016 ; but see also Lunnan et al. 2014 ). In addition, they have been found in very young stellar populations, indicating that Type I SLSNe might be the first and most massive stars to end in a SN explosion after the onset of a new starburst episode in their galaxy or HII region ( Thöne et al. 2015 ). Type II hosts seem to be more metal rich and within the bulk of emission-line galaxies in the SDSS. At higher redshifts, Type I SLSN hosts evolve in line with the most star-forming galaxies towards higher-mass galaxies with higher absolute star formation rates (SFRs), but still seem to show a metallicity cut-off at 0.4 solar and a tendency towards low-mass hosts ( Schulze et al. 2016 ). In this paper, we present integral field unit (IFU) spectroscopic data of NGC 3191, the host galaxy of SN 2017egm, a Type I SLSN discovered by the Gaia satellite ( Delgado et al. 2017 ) on May 23, 2017. Detailed analysis of its early optical spectra revealed its Type I SLSN nature ( Dong et al. 2017 ; Nicholl et al. 2017 ). The SLSN reached its optical maximum on June 20, 2017, with an absolute magnitude of mag. As pointed out in Nicholl et al. (2017) , Bose et al. (2017) , and Chen et al. (2017b) , the host seems to be the first Type I host with super-solar metallicity. In this work, we analyse the properties of different regions in the host galaxy, and in the SLSN location, providing a more detailed analysis of the metallicity and the star formation rate distributions around the SLSN environment and several other H ii regions. Resolved spectral modelling across the host galaxy gives us important clues to the different underlying stellar populations, their ages, and their metallicities, allowing us a more detailed insight into this apparently very peculiar SLSN-I environment. 2. Observations We observed the


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

Fig. 12 shows a time frame of each of the gasoline2 simulations compared to the gas surface density data of Corbelli et al. ( 2014 ) in the bottom right. Best fits were found via a combination of by eye and an automated routine using a structural similarity index (SSIM; built into python ’s scipy module) of images of the gas surface density. The simulated disc is first inclined at the orientation of M33, then rotated in increments to assess the suitability of different phase angles. These images are smoothed over a scale of 2 kpc to leave only the strongest features. The SSIM is then calculated for each time-stamp and phase angle (Δ t = 10 My, Δ θ = 10° using the time domain of 0.5–1.0 Gyr, resulting in 1800 images for each calculation). The best fitting of these low-resolution comparisons are then shown in Fig. 12 , now at their natural resolution. Figure 12. Best-fitting gasoline2 models compared to M33 gas distribution (lower right). In Fig. 12 we show one of the better-fitting snapshots of each simulation, orientated in the same manner as the observed M33. Certain features like the arms shown in Fig. 8 are seen in some of these models, with accompanying inter-arm voids. The lowest feedback model displays some very similar features; the upper-right arm structure, the irregularly shaped arm north-west of the centre, and the straight-arm segment in the edge of disc to the south-east. The nature of dynamic spiral features such as these allows for spiral arms that are less regular than the assumed fixed log-spiral features used by density wave-like potentials (Grand, Kawata Cropper 2012 ; Baba, Saitoh Wada 2013 ). Cavities in the gas seen in M33 are a simple result of inter-arm voids. However, the gas does not display the same smaller scale features, like the irregular patchy features seen in the inter-arms of M33. The 5 per cent feedback model shows a more disrupted spiral structure. Similar small arm features are seen as previously, though now the increased feedback stunts their growth considerably. This appears one of the poorer matches to the observational data, with both the feedback cavities and inter-arm regions too small to provide a good match for M33. The remaining higher feedback models provide a good match to the general structure of M33, though neither is a precise match. The 20 per cent model is very effective at creating large ISM cavities, much like the sphNG models, though this comes at the expense of creating very few strong arm features. The cavities in the 20 per cent model may even be too large and numerous, with the disc perhaps showing too great a degree of fragmentation compared to M33. The 10 per cent feedback model is a good middle ground, creating a handful of large cavities but also managing to maintain some elongated arm features. We found that many of the snapshots not shown here produced certain features very well, while missing others entirely. Enough realizations could feasibly eventually produce every feature


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

ACKNOWLEDGEMENTS We thank the referee for going through the manuscript carefully and providing constructive comments, which improved the manuscript. All the observers of the 2-m HCT (operated by the Indian Institute of Astrophysics), who kindly provided part of their observing time for observations of the supernova, are gratefully acknowledged. We thank Takashi Hattori, Ji Hoon Kim and the staff at the Subaru Telescope for their excellent support of observations under S15A-078 (PI: K. Maeda). We thank Professor David Branch for clarifying some of the issues related to the spectrum synthesis code syn++ . We also thank Dr Kuntal Mishra for providing us with the code for fitting the bolometric light-curve. This research has been supported in part by the DST-JSPS grant DST/INT/JSPS/P-211/2016, the Grant-in-Aid for Scientific Research of JSPS (15H02075, 16H02168, 26400222, 26800100) and MEXT (25103515, 15H00788), and by the World Premier International Research Center Initiative, MEXT, Japan. This work has made use of the public data in the Swift data archive and the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration (NASA).


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

panel), 95701-01-03-00 ( km, middle panel), and 91701-01-52-01 ( km, bottom panel), respectively. 3.2. Spectral Parameters The spectral fitting results are presented in Figure 5 . The unabsorbed power-law luminosity ( L PL ) and the disk luminosity increase simultaneously with the total luminosity ( L 3–30 keV ). The apparent inner disk radius ( R in ) is related to the disk normalization as , where D 10 is the distance in units of 10 kpc. Here we adopt the inclination angle θ = 66° (Fender et al. 1999 ), a color correction factor f = 1.9 (Neilsen et al. 2011 ), and a distance of 8.6 kpc (Reid et al. 2014 ) in the calculation. There are two branches shown in the diagrams of L 3–30 keV − R in and L 3–30 keV − kT : (1) The inner disk remains at a small radius ( R in ≤ 70 km, hereafter S branch), kT increases with the X-ray luminosity, and the X-ray emissions are fainter and softer (larger Γ). (2) The majority of data (189 out of 233) draw the other branch (L branch), the apparent inner edge of disk recedes, and the temperature increases slowly at high luminosity. Meanwhile, the photon index (Γ) of the nonthermal component is anticorrelated with the X-ray luminosity. Figure 5. Correlations between the spectral parameters and distribution of the reduced χ 2 with the fitting model of diskbb + powerlaw (right bottom panel). Open squares and filled cycles correspond to the data with R in being smaller and larger than 70 km, respectively. All parameters are plotted with their 1 σ errors. Intriguingly, there are the positive correlations between T rec , R in , and the X-ray luminosity as well. Additionally, T rec has an even tighter correlation with the power-law luminosity. Since the uncertainty on T rec is much larger than on L 3–30 keV , we carry out a power-law fit to the relation by taking the error on T rec into account, yielding an index of n = 1.10 ± 0.10. Meanwhile, T rec is proportional to . It is worth noting that the change of apparent inner disk radius can be interpreted as a varying color correction factor without moving the intrinsic inner disk radius (e.g., Merloni et al. 2000 ; Zoghbi et al. 2016 ). In order to check this scenario, we model the disk component with diskpn (Gierliński et al. 1999 ), in which the disk normalization is linked to the color correction factor: . The inner disk radius is fixed to the bottom limit 6 R g , although it is much smaller due to high spinning rate (McClintock et al. 2006 ). In addition, the power-law model is replaced by a physical Comptonization model ( tbabs*(diskpn + comptt) in XSPEC). We tie the seed temperature ( kT seed ) to the disk temperature and fix the plasma temperature to 50 keV because it cannot be constrained by our data. The data in the S branch are relatively soft, and the model described above cannot provide an adequate fit to them unless the kT seed varies freely and becomes hotter than the disk temperature; however, it is inconsistent. Henceforth, we only fit the data in the L