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

II stars (as modelled in Delphi ). Indeed, a larger contribution from Pop III stars would lead to a faster coupling between the spin and CMB temperatures, resulting in a higher redshift at which the signal would tend to 0. Finally, in all panels, we also show by the grey shaded regions the models that are consistent with the EDGES data. As expected, while the range of histories naturally shows a dispersion, their redshift-evolution remains unaffected. The Pop III SFRD and the radio emissivity show the least dispersion (since they effectively govern the brightness temperature from Pop III stars) while, given their negligible contribution to the X-ray emissivity, the value of shows the largest dispersion. It is worth pointing out here that the depth of the EDGES signal is highly controversial (see, e.g. Hills et al. 2018 ; Sims Pober 2020 ). In case the amplitude of the signal turns out to be much smaller than what is assumed in this work (say |δ T b | ≲ 100 mK), then the Pop II stars with conventional choice of efficiency parameters are sufficient to explain the observations. Hence our conclusions on the Pop III stars hold only in the case where the amplitude and redshift extent of the 21-cm signal are similar to those reported by the EDGES experiment. Finally, we compare our predicted redshift evolution of the Pop III SFRD with some theoretical models in Fig. 3 . Most models predict a Pop III SFRD that either rises between z ∼ 22 and 13 (Jaacks et al. 2018 ; Sarmento et al. 2019 ) or shows a relatively constant behaviour for z ∼ 20 − 13 (Johnson et al. 2013 ). The only exceptions are the predictions by Valiante et al. ( 2016 ), Valiante et al. ( 2018 ), whose amplitude and redshift dependence are very similar to our predicted shape. Interestingly, the Valiante et al. ( 2016 ), Valiante et al. ( 2018 ) models aim to describe the formation histories of z ∼ 6–7 quasars and their host galaxies. They therefore describe rapidly evolving and biased regions of the Universe. In these models, Pop III stars (and their black hole remnants) start to form at z > 20 in dark matter mini-haloes with mass [10 6 –10 7 ]M ⊙ . However, their formation efficiency is small, as Lyman-Werner radiation limits gas cooling due to H 2 photo-dissociation. Because of this, the bulk of Pop III stars form at redshift 15 z 20 in metal poor ( Z Z cr = 10 −3.8 Z ⊙ ) Ly α-cooling haloes, with mass [10 7.5 − 10 8.5 ] M ⊙ that are able to self-shield and cool the gas more efficiently (see the top panel of Fig. 1 in Valiante et al. 2018 ). At z ≤ 15 Pop III star formation is suppressed by metal enrichment, as Z Z cr = 10 −3.8 Z ⊙ star forming regions become increasingly rare. Hence, the shape of the EDGES signal suggests that the rapid coupling between the spin temperature and the gas kinetic temperature is driven by Ly α photons produced by Pop III stars that form in relatively massive and rare haloes, whose abundance grows fast, due to the exponential growth of the massive-end


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Acknowledgments This paper is based on observations collected at the La Silla Observatory (ESO, Chile) with the FEROS spectrograph at the 2.2-m telescope under programme 088.C-0892(A). This paper includes data collected by the K2 mission. Funding for the K2 mission is provided by the NASA Science Mission directorate. The authors acknowledge the support of the UK Science and Technology Facilities Council (STFC). Funding for the Stellar Astrophysics Centre is provided by The Danish National Research Foundation (Grant DNRF106). DV received funding from the European Research Council under the European Unions Seventh Framework Programme (FP/20072013)/ERC Grant Agreement n. 320964 (WDTracer). TM acknowledges financial support from Belspo for contract PRODEX GAIA-DPAC. DH acknowledges support by the Australian Research Councils Discovery Projects funding scheme (project number DE140101364) and support by the National Aeronautics and Space Administration under Grant NNX14AB92G issued through the Kepler Participating Scientist Programme. MNL acknowledges the support of The Danish Council for Independent Research Natural Science (Grant DFF-4181-0415). TSR acknowledges the support from CNPq-Brazil and PRIN INAF 2014 CRA 1.05.01.94.05. This research has made use of the SIMBAD data base, operated at CDS, Strasbourg, France.


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

different ZDI observations of the same star. We compare the complexity derived from the observations to the magnetic complexity function in CG18 , , in Figure 1 . Here, Ro is the commonly used Rossby number for stellar magnetic dynamo activity representing the ratio Ro = τ c / P rot of rotation period, P rot , and convective turnover time, τ c . This complexity function was derived by matching the evolution of rotation periods of stars in young open clusters using the relationship between magnetic complexity and angular momentum loss derived by CG16 . The function shown in Figure 1 that provides a good match to the data corresponds to a convective turnover time τ c = 100 and value a = 0.005. The former is appropriate for the spectral types of the secondary stars considered here (Morin et al. 2010 ; Wright et al. 2011 ). The value of a is four times smaller than the one used by CG18 , though we note that this quantity only affects the most rapidly rotating stars with the smallest Rossby numbers and was not well constrained in that study that only dealt with stars with masses greater than 0.3 M ⊙ . In our CV orbital evolution model (Section 3 ), we adopt an intermediate value a = 0.01. The shape of the complexity function, n , which dictates the change in angular momentum loss with changing rotation period, remains the same. It should also be kept in mind that, while n av was shown to work reasonably well for parameterizing real magnetograms (Garraffo et al. 2016 ), there is some arbitrarity in its definition and it should strictly be interpreted only as a relative measure of complexity. The spatial resolution of ZDI-reconstructed magnetic fields is also limited by the rotation-induced velocity shift of surface magnetic features and the deconstructed complexity is inevitably going to be a lower limit to the true complexity. 3. Magnetic Disruption of Angular Momentum Loss 3.1. Angular Momentum Loss Here, we simulate the orbital evolution of CVs, including, for the first time, the magnetic complexity modulation and its effect on angular momentum loss. We use the same spin-down model as presented by CG18 . As systems evolve and lose angular momentum, the orbits shrink and periods decrease. Efficient spin–orbit coupling means that the secondary stars spin up, maintaining synchronicity between their rotation and orbital periods. Figure 1 indicates that their magnetic complexity will also increase as they spin up. The data show a somewhat steeper increase in complexity for the stars with the shortest rotation periods, although data are lacking for periods less than 10 hr. We proceed by adopting the CG18 spin-down model and complexity function, taking Figure 1 as offering some empirical support (with the function reproducing well the data on average), but recognizing that it still represents somewhat of an extrapolation to reach the CV period gap. The spin-down model can then be described by the following equations (see CG18 for further details):


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

in the two transitions. There is no known maser association with this core but the two are both associated with H 2 O (clusters 1 and 2, respectively), and CH 3 OH masers (Slysh etal. 1999 ). Based on our detections of two bipolar outflows in Sh2-76E, we can confirm the presence of at least two YSOs. This does not rule out the possibility of the presence of a much earlier stage YSO that is not yet driving maser emissions. However, we have explore the infrared point source catalogue to verify the nature of the possible driving sources of the outflows. We have selected infrared source with 1arcsec from the cluster positions and used them to construct the spectral energy distribution (SED) of the driving sources using Robitaille etal. ( 2006 ) SED fit tool while adopting our parallax distance. We found Two Micron All Sky Survey (2MASS) and Wide-field Infrared Space Exploration ( WISE ) points sources associated with Sh2-76EMM1 but only 2MASS point source for Sh2-76EMM2. Fig. 6 shows the SED of Sh2-76EMM1 (left-hand panel) and Sh2-76EMM2 (right-hand panel). The SED of Sh2-76EMM1 corresponds to that of a class I YSO. In the case of Sh2-76EMM2, only three data points from 2MASS was used and the error in the fitting is large. We cannot conclude on the class of the YSO/driving source Sh2-76EMM2. However, the 2MASS K -band and H -band magnitude were very similar, thus we speculate that the YSO could be a class II object. Figure 6. P(top) SED of Sh2-76EMM1 and (bottom) SED of Sh2-76EMM2. 4.2 A Plausible Probe for Binary/Multiplicity Along Same Line of Sight Line-of-sight effect on the observed properties of an object can be influenced strongly by the interception effect of another object. This could be in the form of strong absorption of the molecular line emission from the background source. With a reasonable angular resolution, the nature of molecular line emission could reveal the presence of more than one source within a region. The two driving sources of Sh2-76Eare located along the same line of sight with V LSR difference of 5kms 1 . Zinchenko etal. ( 1994 ) reported an unusual HCN emission spectrum with a missing main component, which they argued may have been caused by a foreground, 5kms 1 blue-shifted cloud. Zinchenko etal. ( 1997 ) also reported two core components based on their NH 3 (1,1) spectra, which showed additional component after a single Gaussian fitted component was subtracted. In the case of the HCN emission, it is imperative that only a very dense core could have completely absorbed the main component of the line emission. Self-absorption could have affected only the emissions around the systemic velocity of the central source, leaving a fraction of the emission to be detected. The NH 3 line observational results of Zinchenko etal. ( 1997 ) support the existence of a second component. We propose the Sh2-76EMM2 is responsible for the absorption of the HCN main component. MM2 is only 0.5arcsec from MM1 and will provided 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 B-CelestialObject I-CelestialObject 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 B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation O O O O O O O O O O O O O B-Citation I-Citation O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O B-CelestialObject I-CelestialObject O O B-Citation I-Citation 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 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 B-Dataset I-Dataset O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-Dataset I-Dataset I-Dataset I-Dataset I-Dataset B-Dataset O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Dataset I-Dataset O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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-Citation I-Citation I-Citation O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O 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

indicated by an arrow. We note, however, a group of six stars located within 2.6 core-radii of the center (red circles in Fig. 2 ) that show very similar kinematic properties, clustering around a mean velocity of km s. Likewise, as we will show in Sect. 4, their the metallicities are in excellent agreement with each other. While the presence of a secondary plume of stars at km s could in principle be identified with an underlying cluster population as well, these stars have markedly different metallicities (Sect. 4) and we rather deem these foreground objects. The same holds for those stars outside of the cluster boundary of , Thus we identify the innermost six stars at the higher velocity peak with members of FSR 1716. Their individual properties are listed in Table 2 . Table 2 Derived properties of the FSR 1716 member candidates. Thereby, we establish the mean systemic velocity of FSR 1716 as km s with a velocity dispersion of km s, a moderately low value typical of a low-to-intermediate mass Galactic star cluster (e.g., Pryor Meylan 1993 ; Koch et al. 2012 , 2017b ). Using this information and the cluster morphology in terms of its characteristic King (1966) radius ( Froebrich et al. 2008 ; Bonatto Bica 2008 ; Minniti et al. 2017 ), we can estimate the dynamical mass of FSR 1716 as ( Spitzer 1987 ), which is a factor of 70 larger than the low-mass estimate of Bonatto Bica (2008) , albeit based on their premise of a significantly lower distance. Upon a typical stellar mass-to-light ratio of 1.5, this would place FSR 1716 at an approximate absolute magnitude of mag, without doubt in the regimen of a GC. Ideally, the kinematic information should be coupled with accurate proper motions, allowing for an orbital computation that could hint at this cluster’s origin. Unfortunately, none of the member stars had a cross-match in the UCAC5 catalog ( Zacharias et al. 2017 ), and only three stars could be identified in the Hot Stuff for One Year (HSOY) proper motion catalog ( Altmann et al. 2017 ), which used the most recent positions from Gaia -DR1 ( Prusti et al. 2016 ). However, the respective proper motions are highly inconclusive, leading to a broad variety of possible orbits, from thick disk to outer halo; therefore, we do not pursue the orbital analyses any further. 4. Calcium triplet metallicities The three near-infrared CaT lines are a powerful indicator of stellar metallicities, [Fe/H], for RGB stars near and above the horizontal branch ( Armandroff Zinn 1988 ). In the following, we adopted the calibrations of line strength with metallicity from Vásquez et al. (2015) , which are applicable into the metal-rich regime up to 0.7 dex, and which employ the infrared magnitude above the red clump (). The latter is highly advantageous in population studies towards low latitudes, compared to the traditional use of the visual magnitude above the horizontal branch (), which is more sensitive to reddening. In practice, these calibrations are


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ACKNOWLEDGEMENTS This work was supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. EdUHK 28300518).


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But, under a simplistic steady state assumption, our results do not favour the surface density thresholds required for star formation commonly adopted in Galactic studies that assume a certain magnetic field strength (Heiderman et al. 2010 ). However, low-density gas in the Magellanic Bridge has been evolving into denser molecular gas, from which stars form, and the lower densities of the molecular gas in this region may signal the exhausting of the latter. The density of YSOs and PMS stars in the subregions ranges in a continuum from moderately clustered to relative isolation, reminiscent of star formation in the Milky Way (e.g. Bressert et al. 2010 ). However, low number statistics precludes us from defining a surface density for each subregion. Our results suggest that star formation observed in MB -C is underway in localized regions depending on the density inhomogeneities within an initial cloud, and is intimately linked with the presence of dense molecular gas. 5.2 Molecular gas structure in the Magellanic Bridge In Section 2 , we have investigated the properties of the molecular clumps in MB -C. The clumps were gravitationally stable, and very similar to clumps related to star formation in the Milky Way. Their densities, radii, masses, and linewidths do not differentiate them from clumps previously identified in the intermediate to low-density regimes of star formation in the Milky Way (Kennicutt Evans 2012 ). The clumps are related to star formation, as seen by their proximity to YSOs and PMS stars. The properties of YSOs and PMS stars show no remarkable differences compared to the Galaxy on account of their metallicities, except lower extinctions towards them. Overall, this suggests that even though the CO has lower filling factors in the Magellanic Bridge than found in solar metallicity molecular clouds, the actual star formation process proceeds similarly once cold molecular gas is formed, and differences may arise due to the conversion of atomic to molecular gas. The lower dust-to-gas ratio results in lower extinction towards the line of sight of protostars, which affects similarly the X CO factor, but the formation of molecular gas is the unifying factor between star formation. The effect of the lower self-shielding by CO on its durability is unclear, since the incident radiation field in MB -C is not particularly strong only containing early B-type stars. Recent observations from the Herschel space telescope at far-infrared wavelengths have suggested a common unifying factor between star formation and the formation of filamentary structure in the cold interstellar medium (André 2017 ), ubiquitous in star-forming regions. Unfortunately, the FWHM of Herschel imaging (∼5–10 pc) at the distance to MB -C is more than an order of magnitude larger than the average width of filaments detected in the Milky Way (∼0.1 pc) therefore it is currently not possible to identify filaments in the Magellanic Bridge. Instead, we simply overplot YSOs


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We thank the anonymous referee for helpful comments and suggestions. This work is partly supported by the National Natural Science Foundation of China (Grant No. U1431126; 11263002; 11311140248; 11203026) and Guizhou Natural Science Foundations (201519; 20134021; 20117006). HYC was supported by BK21 Plus of the National Research Foundation of Korea and a National Research Foundation of Korea Grant funded by the Korean government (NRF-2015M1A3A3A02009155).


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

For example, at the 0.75 bandwidth, the average depth of Night 1 and Night 3 in W2015 is 0.40% while it is 0.512% in our work. Barnes et al. (2016) also calculated the Na i D lines’ absorption depth and their result is 0.45% (average of Night 1 and Night 3) which is also larger than in W2015 but smaller than ours. The differences are probably due to the data reduction method, however, these differences are not significant considering the measurement uncertainties. When fitting the Na i absorption, we used light curve models which include the limb-darkening within the bandwidths while the other two papers use a box light curve model. As for the CLV effect, there is no obvious CLV feature in the light curve in W2015 (Fig. 3 of their paper), while the light curve in Barnes et al. ( 2016 , Fig. 6 of their paper) shows a similar CLV feature to that in our work. In general, the light curves in Barnes et al. (2016) and our work agree more closely than with W2015. Fig. 4 Observed light curves for the Mg i line (red lines). The black line is the CLV model. 4. Comparison of the CLV effect for HD 189733b and HD 209458b The actual CLV effect varies between different exoplanet systems. In order to illustrate and study the different manifestations of the CLV effect, we present the CLV of the HD 209458b system and compare it with the HD 189733b system. These two transiting exoplanet systems have bright host stars and have been extensively studied, thus they serve as typical samples for the study the CLV effect. We modelled the CLV effect of HD 209458b using the parameters shown in Table 2 . In order to compare the strengths of the CLV effect with the Na i absorption, we adopted the measured planetary absorption values from ( Snellen et al. 2008 , S2008). The results are shown in Fig. 5 and Table 4 . We note that the calculation in S2008 does not correct for the CLV effect. However, since the overall CLV contribution is relatively small (the value is at the noise level of their observation data), adopting the S2008’s value as the Na i absorption is justified in our study. Table 2 Parameters of the HD 209458b system. Notes. The transit epoch and the period are from Knutson et al. (2007) and all the other values are from Torres et al. (2008) . Fig. 5 Comparison of the CLV effect between HD 189733b and HD 209458b. Here the calculations are for the Na i D lines (average of and ). The first row is for HD 189733b and the second row is for HD 209458b. The three columns are for the bandwidths of 0.75, 1.5 and 3.0. The green lines are the modelled CLV light curves while the red lines are the Na i absorption light curves, and the black lines are the combination of the two. We note that the y axis scales are different for the two rows: the values for HD 189733b are significantly larger than for HD 209458b. In order to compare the two systems, we plot their CLV models together with the Na absorption at three different bandwidths in Fig. 5 . There are several


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ACKNOWLEDGEMENTS This research has made use of data obtained from the High Energy Astrophysics Science Archive Research Center (HEASARC), provided by NASA’s Goddard Space Flight Center. This research has made use of the NuSTAR Data Analysis Software ( nustardas ) jointly developed by the ASI Science Data Center (ASDC, Italy) and the California Institute of Technology (USA). RS and AJ acknowledge the financial support from the University Grants Commission (UGC), India, under the SRF and MANF-SRF schemes, respectively.


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

could be inaccurate if the system inclination is low or the pulsar’s companion is rapidly rotating (Freire et al. 2008 ). In sum, it is not clear if GW190814's secondary is a BH or an NS. GW190814 poses a challenge for our understanding of the population of merging compact binaries. In what follows, we estimate the merger rate density of the compact binary subpopulation represented by this source, investigate the nature of its secondary component and possible implications for the NS equation of state, discuss how the system may have formed, and study its implications for cosmology. 6.1. Merger Rate Density Given the unprecedented combination of component masses found in GW190814, we take the system to represent a new class of compact binary mergers, and use our analysis of its source properties to estimate a merger rate density for GW190814-like events. Following a method described in Kim et al. ( 2003 ), we calculate a simple, single-event rate density estimate according to our sensitivity to a population of systems drawn from the parameter-estimation posteriors. As in Abbott et al. ( 2020a ), we calculate our surveyed spacetime volume semianalytically, imposing single-detector and network S/N thresholds of 5 and 10, respectively (Tiwari 2018 ). The semianalytic for GW190814 is then multiplied by a calibration factor to match results from the search pipelines assuming a once-per-century FAR threshold. The sensitivity of a search pipeline is estimated using a set of simulated signals. For computational efficiency, this was done using preexisting search pipeline simulations and the mass properties were not highly optimized. However, given that we are estimating a rate based on a single source, the calibration errors are much smaller than the statistical errors associated with the estimate. The simulated sources were uniformly distributed in comoving volume, component masses, and component spins aligned with the orbital angular momentum. For O1 and O2, the simulated BH mass range was 5–100 M ⊙ , but for the first part of O3 we are analyzing here, the injected range was 2.5–40 M ⊙ (following our updated knowledge of the BH mass distribution); the NS mass range was 1–3 M ⊙ , and component spins are 0.95. As GW190814 occurred when LIGO Hanford was not in nominal observing mode, it is not included in the production P y CBC results, and we use G st LAL results to calculate the merger rate. We assume a Poisson likelihood over the astrophysical rate with a single count and we apply a Jeffreys prior to obtain rate posteriors. The analysis was done using samples from the Phenom PHM posterior and separately from the EOBNR PHM posterior, producing the same result in both cases. We find the merger rate density of GW190814-like systems to be . As a consistency check, we used the P y CBC search results to calculate an upper limit. Repeating the rate calculation with a P y CBC-based calibration and zero event count, we obtain an upper limit consistent (to


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

Distances for each of these endpoints are reported explicitly, as well as the stream width. A5 Hermus We base our endpoints for the Hermus stellar stream on the galstreams footprint, which is based on the discovery paper (Grillmair 2014 ). One endpoint is computed using the galstreams algorithm, while the other does not match with an end of the stream and is identified separately. Distances for each of these endpoints are reported explicitly in Grillmair ( 2014 ), as well as the stream width. A6 Hyllus We base our endpoints for the Hyllus stellar stream on the galstreams footprint, which is based on the discovery paper (Grillmair 2014 ). Both endpoints computed using the galstreams algorithm do not match with the ends of the stream footprint and were identified separately. Distances for each of these endpoints are reported explicitly in Grillmair ( 2014 ), as well as the stream width. A7 Kshir Discovered using Gaia DR2 and confirmed spectroscopically by Malhan et al. ( 2019 ), the Kshir stream is distinct from but highly correlated in phase space with GD-1. We use two spectroscopic member stars as anchor points, corresponding to the highest φ 1 overall and the lowest φ 1 star from SDSS. These stars were chosen due to how close they are to the best-fitting orbit of Kshir and their high separation from each other. We assume both anchors are at the uncertainty-weighted distance of the stream (10 kpc) with ±1 kpc uncertainty, while the angular uncertainties are both assumed to be 0.5 deg. A8 Kwando We base our endpoints for the Kwando stellar stream on the galstreams footprint, which is based on the discovery paper (Grillmair 2014 ). Both endpoints computed using the galstreams algorithm do not match with the ends of the stream footprint and were identified separately. Grillmair ( 2017b ) reports the FWHM of the stream as 22 arcmin (Gaussian σ = 0.16 deg) and a physical width of 130 pc, corresponding to a heliocentric distance of 20.3 kpc. We assume both anchor points are at this distance and that the distance uncertainty is 20 per cent. A9 Magellanic Stream While the Magellanic Stream has been studied with great detail in recent years (Nidever, Majewski Butler Burton 2008 ; Nidever et al. 2010 ), its sheer size and complexity does not easily lend to being described by anchor points. We opt for the anchor points adopted by Pawlowski et al. ( 2012 ), which correspond to overdensities identified by Brüns et al. ( 2005 ). We adopt the same 55 kpc distance for both anchor points, with a 20 per cent distance uncertainty and an angular uncertainty of 2 deg. A10 Murrumbidgee We base our endpoints for the Murrumbidgee stellar stream on the galstreams footprint, which is based on the discovery paper (Grillmair 2014 ). Both endpoints computed using the galstreams algorithm do not match with the ends of the stream footprint and were identified separately. Grillmair ( 2017b ) quotes a heliocentric distance of 20 kpc. We assume both anchor points are at this


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

ACKNOWLEDGEMENTS The authors thank Yun-Young Choi, Harshil Kamdar, Juhan Kim, Joel Primack, and the anonymous referee for insightful discussion and feedback on our research. J.-h. K. acknowledges support by Research Start-up Fund for the new faculty of Seoul National University (SNU), and by Creative-Pioneering Researchers Program through SNU. This work was also supported by the National Institute of Supercomputing and Network/Korea Institute of Science and Technology Information with supercomputing resources including technical support, grants KSC-2018-S1-0016 and KSC-2018-CRE-0052. The CosmoSim data base used in this paper is a service by the Leibniz-Institute for Astrophysics Potsdam (AIP). The MultiDark data base was developed in cooperation with the Spanish MultiDark Consolider Project CSD2009-00064.


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

ACKNOWLEDGEMENTS We thank A. El-Zant for his careful reviewing, F. Combes, A. Nusser, F. van den Bosch, O. Ginzburg, T. Nussbaum, Y. Birnboim, and M. Kretschmer for stimulating discussions and physical insights. This work was partly supported by the grants France-Israel International Projects of Scientific Collaboration (PICS), Israeli Centers of for Research Excellence (I-CORE) Program of the Planning and Budgeting Committee(PBC)/Israel Science Foundation (ISF) 1829/12, U.S-Israel Binational Science Foundation (BSF) 2014-273, National Science Foundation (NSF) AST-1405962, German-Israeli Foundation for Scientific Research and Development (GIF) I-1341-303.7/2016, and Deutsch-Israelische Projektkooperation (DIP) STE1869/2-1 GE625/17-1. NIHAO simulations were carried out at the Gauss Centre for Super-computing e.V. (GCS, www.gauss-centre.eu ) at the GCS Supercomputer SuperMUCat Leibniz Supercomputing Centre ( www.lrz.de ) and on the High Performance Computing resources at New York University Abu Dhabi.


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We thank Professors M-D Ding, H-M Wang, and Y-N Su for very helpful discussions. This work is supported by NSFC grants 11790304 (11790300), 11125314, 11773016, and 11533005, No. U1531247 and 41574166, the Recruitment Program of Global Experts of China, the Key Laboratory for Modern Astronomy and Astrophysics (Nanjing University), and the Max Planck Partner Group program. H.T. thanks ISSI and ISSI-BJ for the support to the team “Diagnosing heating mechanisms in solar flares through spectroscopic observations of flare ribbons.”


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The Liège team acknowledges support from the Fonds de Recherche Scientifique (FRS/FNRS) including especially an FRS/FNRS Research Project (T.0100.15), as well as through an ARC grant for Concerted Research Actions financed by the French Community of Belgium (Wallonia-Brussels Federation), and an XMM PRODEX contract (Belspo). Anthony Hervé is supported by grant 14-02385S from GA ČR.


O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model B-Identifier B-Model B-Identifier B-Model B-Identifier O O O O O O O O O O O O O O O B-Model B-Identifier B-Model B-Identifier O O O O O O O O O O O O O O O O B-Model 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model B-Model 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 B-Model O O O O B-Model B-Identifier B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O B-Model O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model B-Identifier O O O O B-CelestialRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

profiles are extrapolated beyond the edge of the grey area, since no hard strong-lensing constraints are found at these distances. Here, a clear separation between models appears: Bradac (v2), CATS (v3.1), Zitrin-NFW (v3) and our fiducial model profiles tend to keep a high density at large radii, while glafic (v3), Sharon (v3) and our external-shear model generate a lower mass profile. At very large distances, the profile from Williams (v3) drops considerably lower than all others. These effects are seen in both panels of Fig. 12 . Figure 12. The integrated (upper panel), differential (middle panel) and ratio (lower panel) mass profiles of the cluster from different studies. The ratio is computed over our fiducial model, the one with clumps in the outskirts and only gold sample. The black line surrounded by the blue-shaded region represents the mass profile for the external shear and 3 statistical uncertainties. The black line surrounded by the shaded orange region represents mass profile for the fiducial model and the 3 statistical uncertainties. The grey area represents the region where multiple images used as constraints are located. The discrepancies in the inner core could be due to the new hard constraints we add to our mass models, while the discrepancies outside the multi-imaged region may be related to different aspects of the modelling technique and their sensitivity to environmental effects. By probing the overall discrepancies in the mass profiles between different analyses, we can begin to understand the magnitude of systematic uncertainties and their overall effects on the modelling. Compared to other parametric models (v3 from CATS, glafic and Sharon), our fiducial model reaches a similar, or slightly higher rms (0.6arcsec). The main difference is a higher ratio between the number of constraints ( k ) and the number of free parameters ( n ), which can be used as a metric on the level of constraints available. Thanks to the large number of spectroscopic redshifts available for the gold systems, we obtain k / n 134/304.5 compared to 70/302.33 for CATS (v3), and 146/1001.46 for glafic (v3) (Kawamata etal. 2016 ). The ratio between constraints and free parameters in our model is comparable to the Sharon (v3) model ( k / n 108/274, Sharon private communication), but they use multiple emission knots in each galaxy as constraints, making them not strictly independent. We note that our current model is able to accommodate a large number of constraints with only a small number of free parameters, which means that we are reaching a limit (in rms) with this method. 6.4 Estimating the level of systematics in mass models Our fiducial model, containing mass clumps in the outskirts, constrained with the gold set of multiple images and released as CATS (v4) as part of the FFs model challenge, shows a statistical error of stat 1percent on the mass density profile in the cluster core (see Fig. 12 and Section 6.3 ). This error is comparable to


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ACKNOWLEDGEMENTS We thank the anonymous referee for providing useful suggestions that improved the paper. This research was supported in part by Lilly Endowment, Inc., through its support for the Indiana University Pervasive Technology Institute and for the Indiana MAETACyt Initiative. This work was also supported in part by the NASA Origins of Solar Systems grant NNX08AK36G. This material is based on work supported by the National Science Foundation under Grant No. CNS-0521433 and CNS-0723054.


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DF acknowledges support from the Italian Ministry of Science and Education (MIUR), project SIR (RBSI14ZRHR). The authors would like to thank the WISH team and L. Podio for providing the HIFI CO and CO –9 spectra of TW Hya and HD 163296. We are also grateful to the DIGIT and GASPS teams for providing the PACS spectra of CO. Astrochemistry in Leiden is supported by the Netherlands Research School for Astronomy (NOVA), by a Royal Netherlands Academy of Arts and Sciences (KNAW) professor prize, and by the European Union A-ERC grant 291141 CHEMPLAN.


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T.J.M. is supported by the Grants-in-Aid for Scientific Research of the Japan Society for the Promotion of Science (JP17H02864, JP18K13585). This work was supported by the Australian Research Council through ARC Future Fellowships FT160100035 (BM), Future Fellowship FT120100363 (AH), and by STFC grant ST/P000312/1 (BM). C.C. was supported by an Australian Government Research Training Program (RTP) Scholarship. Sergei Blinnikov is supported by RSCF 19-12-00229 on the development of the STELLA code. Numerical computations were in part carried out on PC cluster at the Center for Computational Astrophysics, National Astronomical Observatory of Japan. This research was undertaken with the assistance of resources obtained via NCMAS and ASTAC from the National Computational Infrastructure (NCI), which is supported by the Australian Government and was supported by resources provided by the Pawsey Supercomputing Centre with funding from the Australian Government and the Government of Western Australia. A.H. has been supported, in part, by a grant from the Science and Technology Commission of Shanghai Municipality (grants No. 16DZ2260200) and the National Natural Science Foundation of China (grants No. 11655002). Software: Kepler (Heger Woosley 2010 ), Arepo (Springel 2010 ), STELLA (Blinnikov et al. 1998 , 2000 , 2006 ), CoCoNuT-FMT (Müller et al. 2010 ; Müller Janka 2015 ).


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The authors thank Peter Berhoozi, Ferah Munshi, and Aldo Rodriguez for providing the stellar mass–halo mass tables. We thank Marla Geha for valuable discussions and ideas. Support from NSF grants AST-1312376 and AST-1613582 is gratefully acknowledged.


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ACKNOWLEDGEMENTS We thank J. Stott, M. Swinbank, C. Mason, O. Turner, and N. Leethochawalit for kindly sharing their measurements of galaxy properties. We thank the referee for her/his constructive comments that have helped us to improve the quality of this paper. C-LH acknowledges support from the Harlan J. Smith Fellowship at the University of Texas at Austin. The Flatiron Institute is supported by the Simons Foundation. TY acknowledges fellowship support from the Australian Research Council Centre of Excellence for All Sky Astrophysics in 3 Dimensions (ASTRO 3D), through project number CE170100013. CAFG was supported by NSF through grants AST-1412836, AST-1517491, AST-1715216, and CAREER award AST-1652522, by NASA through grant NNX15AB22G, and by a Cottrell Scholar Award from the Research Corporation for Science Advancement. Support for PFH was provided by an Alfred P. Sloan Research Fellowship, NASA ATP Grant NNX14AH35G, and NSF Collaborative Research Grant #1411920 and CAREER grant #1455342. DK was supported by NSF grant AST-1715101 and the Cottrell Scholar Award from the Research Corporation for Science Advancement. AW was supported by NASA through grants HST-GO-14734 and HST-AR-15057 from STScI. The numerical calculations were run on the Caltech compute cluster ‘Zwicky’ (NSF MRI award #PHY-0960291), allocations TG-AST120025 and TG-AST130039 granted by the Extreme Science and Engineering Discovery Environment (XSEDE) supported by the NSF, and allocation PRAC NSF.1713353 supported by the NSF. The authors acknowledge the Texas Advanced Computing Center (TACC) at The University of Texas at Austin for providing HPC resources that have contributed to the research results reported within this paper. URL: http://www.tacc.utexas.edu.


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ACKNOWLEDGEMENTS Data analysis was performed using the high performance computing cluster POLARIS at the Korea Astronomy and Space Science Institute. This research made use of topcat and stil : Starlink Table/VO Table Processing Software developed by Taylor ( 2005 ) and also the Code for Anisotropies in the Microwave Background ( camb ; Lewis, Challinor Lasenby 2000 ; Howlett et al. 2012 ). Srivatsan Sridhar would also like to thank Sridhar Krishnan, Revathy Sridhar, and Madhumitha Srivatsan for their support and encouragement during this work.


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D.M., H.V., and B.P. acknowledge a postdoctoral fellowship by grant CONACyT Ciencia Básica 255167. H.M.V. acknowledges grant DGAPA-PAPIIT IN109116; O.V. and S.R.-F. acknowledge grant DGAPA-PAPIIT IN112518, Fronteras de la Ciencia CONACyT 281; D.M.C. acknowledges grant DGAPA-PAPIIT IN105916, etc. We acknowledge the use of the Atocatl supercomputer at the Instituto de Astronomía of the Universidad Nacional Autónoma de México (UNAM) and DGTIC-UNAM for the use of Miztli, as well as the ABACUS supercomputer, where the simulations were performed. This paper is dedicated to the loving memory of our friend and colleague, Dr. Bárbara Pichardo, who first triggered the dynamical study of spiral arms in Mexico.


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We acknowledge the support of the staff of the Lijiang 2.4 m telescope. Funding for the telescope has been provided by Chinese Academy of Sciences (CAS) and the People’s Government of Yunnan Province. This research is supported by the Strategic Priority Research Program—the Emergence of Cosmological Structures of the Chinese Academy of Sciences, grant No. XDB09000000, by the NSFC through NSFC-11173023, -11133006, -11233003, -11473002, and by the Israel–China ISF-NSFC grant 83/13.


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ACKNOWLEDGEMENTS I thank Charlie Conroy and Dan Weisz for insightful comments on earlier versions of this paper, Michael Fall, Kristian Finlator, Oleg Gnedin, Pawan Kumar, Smadar Naoz, Eliot Quataert, Charli Sakari, Chris Sneden, and Eros Vanzella for helpful discussions, and Tom Petty for aural support. Support for this work was provided by The University of Texas at Austin, the National Science Foundation (grant AST-1517226), and NASA through grant NNX17AG29G and HST grants AR-12836, AR-13888, AR-13896, GO-14191, and AR-14282 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. Much of the analysis in this paper relied on the python packages NumPy (Van Der Walt, Colbert Varoquaux 2011 ), SciPy (Oliphant 2007 ), Matplotlib (Hunter 2007 ), and iPython (Pérez Granger 2007 ); I am very grateful to the developers of these tools. This research has made extensive use of NASA’s Astrophysics Data System ( http://adsabs.harvard.edu/ ) and the arXiv eprint service ( http://arxiv.org ).


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The authors would like to thank Prof. A. Gould for consultation. The OGLE project has received funding from the National Science Centre, Poland, grant MAESTRO 2014/14/A/ST9/00121 to A.U. OGLE Team acknowledges Profs. M. Kubiak and G. Pietrzyński, former members of the team, for their contribution to the collection of the OGLE photometric data over the past years. J.P.B. and J.B.M. gratefully acknowledge support from ESO’s DGDF 2014. C.C. was supported by an appointment to the NASA Postdoctoral Program at NASA Ames Research Center, administered by Universities Space Research Association under contract with NASA.


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We acknowledge insights and assistance with data provided by Drs. Philip Best, Annalisa Bonafede, George Contopoulos, Federica Govoni, Christian Kaiser, and Preeti Kharb. We especially thank Annalisa Bonafede and Federica Govoni for presenting us with the calibrated data for A2142A and 5C4.152. We also acknowledge the assistance of Antonios Nathanail in the preparation of Fig. 2 . This work was supported by the General Secretariat for Research and Technology of Greece, the Irish Research Council (IRC) and the European Social Fund in the framework of Action Excellence. We thank the referee whose comments have led to an expansion of the paper that helped improve the clarity and significance of our results.


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S.B., D.R.G.S., and R.B. are thankful for funding through the DFG priority program “The Physics of the Interstellar Medium” (projects BO 4113/1-2, SCHL 1964/1-2, and BA 3706/3-2). T.G. acknowledges the Centre for Star and Planet Formation funded by the Danish National Research Foundation. D.R.G.S. is thankful for funding through Fondecyt regular (project code 1161247) and through the “Concurso Proyectos Internacionales de Investigación, Convocatoria 2015” (project code PII20150171). D.R.G.S. would also like to thank Basel PFB-06 CATA for funding. S.B. also acknowledges the kind hospitality of the Kavli Institute for Theoretical Physics (KITP), where this work has been completed, and Andrea Ferrara, Troels Haugbølle, and Raffaella Schneider, for fruitful discussions on this topic. We are indebted to Hiroyuki Hirashita for the derivation of the equations reported in the Appendix. This research was supported in part by the National Science Foundation under Grant No. NSF PHY11-25915. The plots of this paper have been obtained by using the YT tool (Turk et al. 2011 ). The simulations have been performed on the German HLRN cluster under the project nip00035.


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previous snapshot. The second criterion ensures that we exclude galaxies that experienced a merger within the past 150 Myr. 4. Synthetic Observations of the Simulations: Images and Spectra To generate synthetic observations, each simulation snapshot is post-processed with the dust radiative transfer software SUNRISE (Jonsson 2006 ; Jonsson Primack 2010 ; Jonsson et al. 2010 ). Synthetic images and spectra are created from the SUNRISE output. The synthetic Hubble Space Telescope ( HST ) images used in this paper are available as a high-level science product from MAST 12 12 https://archive.stsci.edu/prepds/vela : https://doi.org/10.17909/t9-ge0b-jm58 . 4.1. Dust Radiative Transfer with <monospace>SUNRISE</monospace> SUNRISE contains two primary steps. It first generates a spectral energy distribution (SED) for each source of radiation in the simulation. It then propagates the associated polychromatic rays through the 3D gas grid of the simulation, taking into account dust absorption and scattering, toward a user-defined camera(s). For each snapshot, the ART output is first loaded into the YT analysis software (Turk et al. 2011 ) and converted into the appropriate SUNRISE format. This is carried out using an updated version of the pipeline used in Moody et al. ( 2014 ). An SED is assigned to each star particle based on its age, mass, and metallicity using STARBURST99 (Leitherer et al. 1999 ) assuming a Kroupa ( 2001 ) initial mass function. Emission lines are generated from young star particles, less than 10 Myr old, using a starburst model from the photoionization and shock modeling code MAPPINGS III (Dopita et al. 2005 ; Groves et al. 2008 ). This model includes a central massive young stellar cluster whose SED is set with STARBURST99 , a surrounding H ii region, and a photodissociation region with a covering fraction of 0.2 (Groves et al. 2008 ). To account for 10 4 K thermal broadening, we convolve the original MAPPINGS III H α emission line with a 10 km s −1 1D Gaussian kernel. The dust density is assumed proportional to the gas metal mass using a dust-to-metals mass ratio of 0.4 (Dwek 1998 ). Consequently, the dust geometry is resolved to a typical gas cell size of 17–35 pc. We adopt the dust grain size distribution from Weingartner Draine ( 2001 ) and Draine Li ( 2007 ) and set the slope of the dust extinction law, R v , to the Milky Way value of 3.1 (e.g., Gordon et al. 2003 ). SUNRISE cameras are placed at 19 positions around the galaxy. The camera parameters are user-selected and not defaulted to SUNRISE. Of the cameras, six are random but remain fixed in comoving space over time, eight are random but change from timestep to timestep, and the remaining five are fixed with respect to the net angular momentum of the galaxy and, as such, change from timestep to timestep. Those fixed to the galaxy include one that is face-on, i.e., along the gas angular momentum axis; one that is reverse face-on; two that are edge-on; and one that is


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multiple power sources. Furthermore, the presence of H α emission lines in the late-time spectrum and the rebrightening in the late-time LC show an unambiguous signature for interactions between the SN ejecta and a hydrogen-rich CSM. Hence, any model with a single power source or double power sources is challenged in explaining the LC of iPTF13ehe. A triple-power-source model should be seriously considered. In this paper, we propose a triple-energy-source model for iPTF13ehe and try to understand its explosion mechanism and LC. This paper is organized as follows. In Sections 2 and 3 , we fit the early-time and late-time LC using double and triple-energy-source models, respectively. In Sections 4 and 5 , we discuss and conclude our results. 2. MODELING THE EARLY-TIME LC We start by studying the early LC and determining the power sources of iPTF13ehe. As pointed out by Yan et al. ( 2015 ), of 56 Ni were synthesized while of 56 Ni are required to account for the LC peak. Therefore, there should be other energy sources to aid the high peak luminosity of iPTF13ehe. The early-time spectra shows no H emission lines, indicating that the ejecta-CSM interaction can be neglected in the early-time luminosity evolution. Hence, the energy source aiding the SN might be a magnetar spin-down input. The possibility that iPTF13ehe is a CCSN and can be aided by a magnetar was also pointed out by Yan et al. ( 2015 ), though they did not provide further analysis. Considering the contribution from 56 Ni, which cannot be neglected, the most reasonable model should contain contributions from both 56 Ni and a magnetar. Wang et al. ( 2015b ) have constructed such a unified model for SNe Ic and explained three luminous SNe Ic. We employ this model here to fit the LC of iPTF13ehe. Supposing that the ratio of the r -band flux to bolometric flux remains nearly constant around the peak and in the late-time, we scale the r -band luminosities to obtain the bolometric luminosities. The scaled bolometric luminosities are rough, but they can be regarded as an approximation of real values. These data are plotted in Figure 1 . In this section, we use some models to fit the early-time LC. The photospheric velocity and the optical opacity κ are fixed to ∼13,000 km s −1 (Yan et al. 2015 ) and 0.2 cm −2 g −1 , respectively. Figure 1. Modeling iPTF13ehe’s early-time LC using 56 Ni, magnetar, and hybrid ( 56 Ni + magnetar) models. Data are obtained from Yan et al. ( 2015 ). The early-time and late-time bolometric luminosities scaled from r -band ones are shown as the orange filled circles and orange unfilled circles, respectively. The dashed–dotted line is the LC powered by 19 of 56 Ni; the dashed line is the LC powered by a magnetar; the solid line is the LC powered by 56 Ni and a magnetar. The short dashed line is the LC powered by 2.5 of 56 Ni with full trapping of gamma-rays. The other model parameter values are shown in the text. 2.1. 56Ni Model The first of the models


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

analyses of the strongly depleted element Ca have demonstrated that dust commonly reaches out far beyond the stellar bodies of galaxies deep into circumgalactic and intergalactic space (e.g., Richter et al. 2011 ; Zhu Ménard 2013 ). In this broader context, additional systematic studies of metal depletion in the MW halo and in other circumgalactic environments would be very useful to better understand the large-scale circulation of dust in and around galaxies. 5.3. Origin of LA II To further evaluate whether LA II originally stems from the SMC or LMC let us first collect the main results from our absorption-line study and summarize the main conclusions from these findings. 1. LA II exhibits an α abundance and N/ α ratio that closely match those of the current-day SMC, possibly implying that the gas was recently removed from the SMC and pushed deep into the MW halo. If so, the age of LA II can be at most a few hundred Myr. If we consider only the chemical abundance pattern as age indicator, LA II could be older if the gas originates in the LMC. In that case, the observed abundance pattern in LA II would reflect that of the LMC 1–2 Gyr ago (Pagel Tautvaisiene 1998 ; Harris Zaritsky 2004 ). That the LMC had exactly the same α /N abundance pattern as the SMC today at the time when the gas was removed from the MCs is not unrealistic given the star formation history of the LMC (Pagel Tautvaisiene 1998 ), but it would be a coincidence. 2. LA II exhibits a very high thermal gas pressure of P / k ≈ 1680 K cm −3 in the molecular gas phase, suggesting that the gas is situated in the inner halo of the MW ≈10 kpc above the disk, where the gas is compressed by ram-pressure forces. LA II and the MCs then would be separated by at least 30 kpc in space, suggesting that it would have taken the gas more than 200 Myr to reach its current position after it was separated from its host galaxy (assuming a relative speed of 100 km s −1 ). This sets a minimum age of ∼200 Myr for the LA II. Yet a distance a small as 10 kpc for the LA cannot be reproduced by the most recent hydrodynamical simulations of the Magellanic System (Pardy et al. 2018 ) in a first infall scenario, where the minimum distance of the LA is found to be d ≈ 24 kpc. 3. The H 2 formation timescale in the cold gas in LA II is ∼640 Myr. If all of the H 2 had formed in situ, this sets a lower limit for the age of the LA II. However, given the fact that so much dust has survived the separation process, it is equally likely that also the H 2 (or at least part of it) had formed earlier in the LA II source galaxy. If so, the H 2 was transported together with the neutral gas into the MW halo, where the molecular gas fraction adjusted to the local conditions on much shorter timescales. 4. The very high dust-to-gas ratio in LA II suggests that the gas originally stems from an interstellar region with a neutral+molecular gas column as high as log N (H) = 21.2. Such high column densities are typical for the inner


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

on redshift is smaller than the dependence on the dynamical state. There seems to be a slight although not very significant evolution of the sparsity with z . Higher-redshift ( z > 0.54) clusters have a slightly larger value of S 500/2500 by 18%, that is these profiles are less concentrated, which is not consistent with the low-redshift ( z 0.2) clusters at ∼1.8 σ . We found the same behaviour when excluding the outliers. There is a much stronger and significant variation of the sparsity with dynamical state: morphologically disturbed (high ⟨ w ⟩), non-CC (low C SB ), and disturbed (low M ) clusters have larger sparsity. For all parameters considered, the sparsity of the first and third bins is not consistent at more than 3 σ , and the difference between the sparsities of these bins is of the order of ∼50%. At the same time, the intrinsic scatter increases significantly, reaching ∼0.2 dex for the most disturbed or least concentrated objects. For example, the sparsity increases by 64% at a significance level of 3.4 σ between M −0.6 and M > 0.5, that is, between the one third most relaxed and the one third most disturbed as defined by this parameter. Only an upper limit on the intrinsic scatter can be estimated from the former ( 0.04 dex), while the intrinsic scatter for the latter reaches 0.25 ± 0.09 dex. There are strong outliers at high sparsity. Excluding the outliers yields the same qualitative results, although the variation between bins is weaker. This suggests a sparsity distribution skewed towards high values, with a skewness increasing with departure from dynamical relaxation. 7. Discussion 7.1. Dynamical state The first result of our study is that SZ-selected samples are dominated at all redshifts by disturbed and non-CC objects. Recent observational work on local clusters has converged to similar results (e.g. Lovisari et al. 2017 ; Rossetti et al. 2017 ; Andrade-Santos et al. 2017 ; Lopes et al. 2018 ). In particular, these works highlight the higher fraction of disturbed objects or the lower fraction of CC objects in SZ-selected samples as compared to X-ray-selected samples, a fact interpreted to be due to preferential detection of relaxed or more concentrated clusters in X-ray surveys. In contrast, there is little consensus in the literature concerning the evolution of the dynamical state, as determined from various morphological parameters. Studies of the evolution up to z ∼ 1 of the centroid shift and/or power ratios of X-ray-selected clusters indicate a larger fraction of disturbed clusters at high z ( Maughan et al. 2008 ; Jeltema et al. 2005 ; Weißmann et al. 2013 ). However, the latter study is also consistent with no evolution, and Nurgaliev et al. (2017) did not find any significant evolution in the redshift range 0.3 z 1 for the 400 d X-ray-selected clusters. These somewhat contradictory results may simply be due to selection effects: X-ray detectability is clearly not independent of cluster morphology. More peaked


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

which the excitation temperature can be found naturally depends on the number of usable lines. Typically, the excitation temperature could be constrained to better than ±150 K. Fortunately, the isotopic ratio is not highly sensitive to the excitation temperature, and uncertainties in the ±150 range have only a small effect on the resulting isotopic ratios. To reduce the uncertainty in the abundances in the case of ill-defined excitation temperatures, we investigated the relation between the excitation temperature, T exc , and the effective temperature, T eff . There is considerable basis for assuming that these quantities are related via the atmospheric structure and elemental abundances. Effective temperature is a measure of the total energy integrated over all wavelengths radiated from a unit of stellar surface area. The value is fixed by luminosity and radius and is an observable quantity. T eff is given by the relationwhere F is the bolometric flux received at Earth, σ is the Stefan–Boltzmann constant, and φ is the angular diameter (Ridgway et al. 1980 ). Most values of T eff for cool giants have been set using Equation ( 1 ) with φ determined by lunar occultations and interferometry (see, e.g., Ridgway et al. 1980 ; Richichi et al. 1999 ) and F determined from near-IR photometry. Observational limits associated with the techniques restrict the sample of objects in magnitude, diameter, and position on the sky. A second approach based on infrared flux (Blackwell Shallis 1977 ; Blackwell et al. 1990 ) also produces effective temperatures. Both techniques produce similar results. We limit our discussion to the angular diameter approach. Effective temperature is known to vary with spectral type, for the M giants nearly linearly (Richichi et al. 1999 ). Worthey Lee ( 2011 ) present a comparison of T eff versus V – K relations for cool giants. The Bessell et al. ( 1998 ) T eff versus V – K relation, derived from a compilation of occultation and interferometry diameters, is the best fit to the Worthey Lee ( 2011 ) data. Sharma et al. ( 2016 ) review a number of fits to the T eff versus M giant spectral type relation against several groups of synthetic spectra. A T eff –( V – K ) relation derived from a homogeneous set of angular diameters by Richichi et al. ( 1999 ) gives the best match and extends to the coolest non-Mira M giants. Therefore, we adopted the spectral type—effective temperature relation by Richichi et al. ( 1999 ) for our study. However, use of the Bessell et al. ( 1998 ) calibration would result in negligible change. All the calibrations show scatter around a mean relation. The Richichi et al. ( 1999 ) relation shows considerable scatter to lower temperatures. Since the sample stars are bright—in fact most (Table 1 ) are in the Yale Bright Star Catalog (Hoffleit 1964 )—there are well-determined spectral types and magnitudes. We ignore the galactic reddening of these nearby objects. Table 2 lists the parameters for the program