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

B ), which can be used not only to capture complicated patterns between variables and to keep a good balance between bias and variance, but also to identify the most important variables that explain model predictions. We address the second problem by using a linear dimension reduction algorithm, the principal component analysis (PCA; see Appendix A ), which can effectively reduce the dimension of the halo AH and the galaxy SFH and yet retain large amounts of information of the histories for the empirical modelling. Finally, we address the third problem by building a deep model that incorporates components of both dimension reduction and ensemble regressor and classifier. Each component in the model is motivated physically and can be optimized separately. This approach makes the model capable of dealing with complex patterns in parameter space, and yet transparent to interpret. The ensemble regressor and linear dimension reduction method has already been used to study the relationship among halo properties in Chen et al. ( 2020 ). Here, we extend it to studying the galaxy–halo connection. As the first in a series, this paper focuses on central galaxies in dark matter haloes. We identify important ingredients that should be included in an empirical model, and demonstrate the limit such a model can reach in describing the stellar masses and SFHs of individual galaxies. Our model is built on the inferences from two hydrodynamic simulations, the Illustris-TNG (e.g. Nelson et al. 2019 ) and EAGLE (e.g. The EAGLE team 2017 ). This paper is organized as follows. In Section 2 , we describe the simulation data we use, and define the halo properties and samples used in our analysis. In Section 3 , we use both the GBDT and PCA to study the relations of galaxy stellar mass and SFR with halo properties for both star-forming galaxies and quenched galaxies. We also identify halo properties that cause a galaxy to quench. In Section 4 , we build an empirical model that predicts the SFH of galaxies in dark matter haloes, testing its performance in several steps. We summarize and discuss our results in Section 5 . 2 THE DATA 2.1 The Illustris-TNG and EAGLE simulations The Illustris-TNG simulation (Marinacci et al. 2018 ; Naiman et al. 2018 ; Nelson et al. 2018 , 2019 ; Springel et al. 2018 ; Pillepich et al. 2018b ) is a suite of cosmological, hydrodynamical simulations implemented with the moving-mesh code Arepo (Springel 2010 ). The cosmological parameters are taken from the Planck 2015 results (Planck Collaboration XIII 2015 ): Hubble constant with h = 0.6774, cosmological constant Ω Λ,0 = 0.6911, matter density Ω M,0 = 0.3089, baryon density Ω B,0 = 0.0486, and initial power spectrum with normalization σ 8 = 0.8159 and index n s = 0.9667. The simulated physical processes for galaxy formation include gas cooling, star formation, stellar feedback, metal enrichment, black hole feedback, and so on. The details can be found in the two method papers, Weinberger


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

We want to thank Chris Carilli for assistance on the simulations of the ngVLA observations and for providing us with the ngVLA antenna position files, and Giovanni Dipierro for helpful comments on the manuscript. This work was supported in part by the ngVLA Community Studies program, coordinated by the National Radio Astronomy Observatory, which is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. A.I. and L.R. acknowledge support from NSF grant No. AST-1535809. A.I., S.L., and H.L. acknowledge the support from the Center for Space and Earth Sciences at LANL, and H.L. acknowledges the support from the LANL/LDRD program. ALMA is a partnership of ESO (representing its member states), NSF (USA), and NINS (Japan), together with NRC (Canada) and NSC and ASIAA (Taiwan) and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO, and NAOJ. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.


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

very well separated components () and with marginal distributions and pairwise scatter plots as shown in the diagonal and lower triangle of the matrix of plots in Fig. 3(a) . The upper triangle of the matrix displays the correlation between each pair of variables. Thus, the first two of the three variables have a very high (almost linear) pairwise correlation of 0.98, while the other two pairs have little to modest correlations between them. It is tempting to surmise that one of the first two dimensions are nearly redundant and that dropping one of them would not have much effect on the quality of clustering. We test this assertion by performing GMMBC (with BIC used to determine the optimal number of groups) on the dataset using each of the three distinct pairs of variables. Figs 3(b) –(d) display the results of clustering each pair of coordinates, with colours representing the obtained clustering and character denoting the true grouping. Including either one of the two seemingly redundant variables with the third variable identifies only two groups and a partitioning (Figs 3b and c ) that hardly matches the true with an adjusted Rand index of 0.37. Interestingly, clustering the two seemingly redundant variables (and ignoring the third) does better, identifying four groups and with . However, this is still a far cry from the perfect partitioning that is obtained when all three coordinates are used in GMMBC with BIC to determine the optimal number of groups. Therefore, it is important to consider the relevant variables in clustering. This fact becomes more important in the light of attempts by many researchers to cluster GRBs using, for instance, only the duration variables. This example also demonstrates that two variables having correlations even as high as 0.98 are not necessarily redundant and should be carefully analysed before arriving at decisions on their inclusion or exclusion in analysis. Raftery Dean ( 2006 ) proposed a method for selecting variables containing the most relevant clustering information by recasting the variable selection problem in terms of model selection where comparison of the models is done via BIC (refer to Chattopadhyay Maitra 2017 for a thorough review on variable selection). Figure 3. Result of clustering (a) data simulated from a three-dimensional five-component GMM , using (b, c, d) two and (e) all three variables. 2.3 Measuring distinctiveness of partitioning through the overlap Chattopadhyay Maitra ( 2017 ) explain that an overlap measure can be used to indicate the extent to which clusters obtained through a method are distinct from one another. We refer to that paper for further details, but note that they adopt Maitra Melnykov ( 2010 )’s definition of the pairwise overlap between two groups as the sum of their misclassification probabilities. To provide a sense of these pairwise overlap measures, we illustrate three two-dimensional examples in Fig. 4 . (For ease of display and understanding, we use two


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

of the Ramaty ( 1969 ) model fit to the radio spectra. Both spectral indices are listed on Table 2 . As can be seen from these results, the spectral indices of the energy distribution of the radio emitting electrons agree reasonably well with that of the hard X-ray producing electrons, when considering photons with energies higher than 400–700 keV or, conversely, electrons with energies ≥1 MeV. The reconstructed energy spectra of the accelerated electrons can be represented by a broken power law with break energy around 500 keV, and spectral index δ = 4 below this energy and δ = 2 above (see Figure 6 ). The photons detected below energies of ∼500 keV (representing E 2 ) are produced by lower-energy electrons with an energy distribution index of δ ≈ 4, whereas the higher-energy hard X-rays and radio emission (microwaves and millimeter waves) are generated by electrons with energies ≥1 MeV and δ ≈ 2. Previous works, such as Silva et al. ( 2000 ), showed that the spectral indices for the population of accelerated electrons emitting the radio and the X-rays do not match, with the radio index being harder than that of the X-rays by approximately 2 units. The authors explained this discrepancy by the fact that the radio emission is produced by higher-energy electrons than the X-rays, and that the common accelerated electron population has a power-law energy distribution that breaks up above 300 KeV. Since the hard X-rays analyzed in Silva et al. ( 2000 ) had energies lower than ∼200 keV, the results are in agreement with those presented here for the SOL2013-05-13 flare, as well as the two discrepancies in the spectral indices of hard X-rays and radio. Moreover, Vestrand ( 1988 ) and Dennis ( 1988 ) report giant flares observed in hard X-rays with energies larger than 1 MeV that showed a breakup in their photon spectra at ∼300 keV. More recently, from the analysis of an X8.2 solar flare detected in hard X-rays by RHESSI, Ning et al. ( 2019 ) found a broken-up power-law spectra originating from a coronal source. However, the break energy was only about 50 keV and the harder spectral photon index was ∼3. There are basically three possible explanations for electrons to exhibit such a broken-up power-law energy distribution. The first is that there are two components, or sources, of energetic electrons that were produced by two different acceleration mechanisms (Silva et al. 2000 ; Krucker et al. 2008 ). However, to produce a similar temporal evolution in radio and hard X-ray emission, there must be a close link between these two acceleration mechanisms. Alternatively, the second possibility is that the difference in spectral indices is due to physical characteristics of a certain acceleration mechanism and/or a transport process of electrons such as diffusive shock acceleration (Li et al. 2013 ), where a hardening of the spectrum occurs around 500–600 keV, or stochastic acceleration due to wave–particle interactions in the presence of Coulomb collisions


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

cube is the removal of the continuum and determination of the stellar kinematics. Because both the MUSE and SINFONI spectral resolutions are only moderate, we only fit for the stellar velocity and velocity dispersion. We also included an additive fourth degree polynomial in the fit to model any emission from the central AGN. To create the continuum-subtracted MUSE cube, we renormalized the best-fitting binned spectra to the median continuum level of each individual spectrum before subtraction. Fig. 4 shows the results of our ppxf fits for the MUSE cube. Figure 4. Results from fitting the MUSE cube with ppxf . The top row plots the stellar velocity ( left ) and dispersion ( right ). The bottom row plots the mean light-weighted stellar population age ( left ) and mean light-weighted metallicity ( right ). In all frames, North is up and East is to the left. 2.6.2 Emission line fitting To measure the bulk distribution and kinematics of the molecular and ionized gas in NGC 5728, we fit single Gaussians to the relevant emission line tracers of the gas. In particular, we fit the CO (2–1) line (ν rest = 230.538 GHz) in the ALMA cube; the H β, [O iii ] doublet, [O i ], [N ii ] doublet, H α, and [S ii ] doublet lines in the MUSE cube; and the [Fe ii ]λ1.64 m, [Si vi ], H 2 (1–0) S(1), and Brγ lines in the SINFONI cube. This set of lines represent the strongest emission lines observed in nearby galaxies and AGNs and provide diagnostic power into the state of gas in a range of phases from cold molecular gas [CO (2–1)] to warm molecular gas [H 2 (1–0) S(1)] to hydrogen recombination lines (H β, H α, Br γ) and forbidden lines ([O iii ], [O i ], [N ii ], [S ii ], [Fe ii ], [Si vi ]) from ionized gas in a range of ionization levels. For each line, we cut out the relevant sections of the continuum-subtracted spectra that contain the single line or multiple lines in the case of the [O iii ] doublet, H α and [N ii ] blended region, and [S ii ] doublet. We fixed the velocity and velocity dispersion to be the same for all doublets and fixed the intensity ratio to the expected theoretical value of 3 for the [O iii ] and [N ii ] doublets. For the fit of the [Si vi ] line, we also included Gaussian components for the nearby H 2 (1–0) S(3) and Br δ lines. As an estimate of the local noise around each line, we measured the root mean square (RMS) of the line-free regions. Using the RMS, we produced 100 simulated spectra for every emission line by randomly perturbing the original spectra assuming a Gaussian distribution with a standard deviation equal to the RMS. Each of the simulated spectra were fit in the same way as the original spectra and uncertainties on the integrated flux, velocity, and velocity dispersion were calculated from the standard deviation of the best-fitting values from the simulated spectra. Finally, all velocity dispersions derived from MUSE and SINFONI data were corrected for instrumental broadening. For lines from MUSE, we assumed an


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We would like to thank the anonymous referee for the useful comments and suggestions which helped improve this paper. NPM and FAG would like to thank Monica Valluri for the very interesting discussion and useful comments that help to improve this manuscript. NPM, FAG, PMC and CMG are grateful to Carles Simó for his illuminating discussions, comments and suggestions. We are also grateful to Volker Springel, Simon White and Carlos Frenk for generously allowing us to use the Aquarius simulations. Finally, NPM wants to thank D. D. Carpintero, F. Bareilles and E. Suárez for their assistance with the lp-vicode as well as with the pre-processing of the data. NPM, PMC and CMG were supported with grants from the Consejo Nacional de Investigaciones Científicas y Técnicas (IALP UNLP–CONICET) de la República Argentina (CCT-La Plata) and the Universidad Nacional de La Plata (FCAG UNLP). FAG and BWO acknowledge support from the US NSF Office of Cyberinfrastructure by grant PHY-0941373 and by the Michigan State University Institute for Cyber-Enabled Research (iCER). BWO was supported in part by NSF grants PHY-0822648 and 1430152: Physics Frontiers Center/Joint Institute for Nuclear Astrophysics (JINA). APC is supported by a COFUND/Durham Junior Research Fellowship under EU grant [267209].


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

Zr The neutron-capture element Zr is predominately produced by AGB stars and is a first s -process peak element. The s -process contribution to Zr in the Solar system is 80percent (e.g. Simmerer etal. 2004 ; Sneden, Cowan Gallino 2008 ; Bisterzo etal. 2014 ). By determining the abundance of Zr, we expand on the measurements of Y, another first s-process peak element whose abundances were previously obtained by NS11 . Fig. 3 (a) shows [Zr/Fe] as a function of [Fe/H]. The dispersion in [Zr/Fe] is 0.12dex, which is larger than the error of 0.04dex. When considering the two populations, the scatter in [Zr/Fe] is smaller for the low- stars with a dispersion of 0.06dex compared to a dispersion of 0.13dex when combining the high- and TD stars. In addition to the difference in the dispersion of [Zr/Fe], the low- stars have a systematically lower [Zr/Fe] abundance compared to the high- and TD stars. Figure 3. Four s -process elements (Zr, La, Ce and Nd) versus [Fe/H]. The red circles indicate low- stars, the blue open circles indicate high- stars and the plus signs indicate TD stars. The 1 error is shown in the bottom left of each plot. This possible separation in the high- and low- populations is in agreement with the slight separation in abundance measurements of [Y/Fe] for the two populations seen in NS11 . As Zr and Y are both first-peak s -process elements, they are expected to follow the same trend. Fig. 4 demonstrates the difference in the Zr abundance for a low- star (HD 194598) and a high- star (HD 111980) at nearly the same metallicity (see Table 1 ). The low- star has a weaker Zr ii line than the high- star. While the effective temperature differs between these two stars by approximately 150K, all other lines in this region exhibit very similar strengths. Figure 4. MIKE spectra around the Zr line at 4208.98 for a low- star (HD 194598) and a high- star (HD 111980). A comparison between [Y/Fe] as measured by NS11 and [Zr/Fe] is presented in Fig. 5 . The abundance of Zr follows the abundance of Y, which is expected if Y and Zr have a common origin. While there is a systematic offset between [Y/Fe] and [Zr/Fe] that may be due to errors in the gf values of the lines, the important point is that the slope of the data is close to 1. The high- stars have a tighter correlation between [Y/Fe] and [Zr/Fe] compared to the low- stars. Figure 5. Comparison of [Y/Fe] (taken from NS11 ) and [Zr/Fe]. The red circles indicate low- stars, the blue open circles indicate high- stars and the plus signs indicate TD stars. The dashed line shows the one-to-one correspondence line. The 1 error is shown in the top left. 3.2 La, Ce and Nd We extend upon the Ba measurements of NS11 by determining abundances for other elements belonging to the second s -process peak, namely La, Ce and Nd. The s -process contribution to La in the Solar system is 75percent and there are a number of advantages with using La as an s -process indicator compared to Ba (e.g. Simmerer etal.


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We thank the anonymous referee for a thorough report and many constructive comments, which helped us improve the presentation of this work. This work is supported by the 973 program (2015CB857005, 2012CB821804), the NSFC (11522324,11421303), the Strategic Priority Research Program “The Emergence of Cosmological Structures” of the Chinese Academy of Sciences, grant No. XDB09010400 and the Fundamental Research Funds for the Central Universities. H.J.M. would like to acknowledge the support of NSF AST-1517528. The numerical calculations were done on the supercomputing system in the Supercomputing Center of the University of Science and Technology of China.


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λλ1907, 1909, C iv 1548, 1551, and He ii λ1640. They find seven objects with [C iii ], C iii ] λλ1907, 1909 emission, some of them reaching extremely high equivalent width values (). Finally, they find that C iv 1548, 1551 and He ii λ1640 have equivalent widths below 2 Å and conclude that the detection of C iv 1548, 1551 atÅ may require extremely metal poor stars and gas. In SBS 0335−052E, which is more metal-poor that the previous sample, C iv 1548, 1551 shows a weak P-Cygni profile and nebular components. The EWs of the nebular [C iii ], C iii ] λλ1907, 1909 and C iv doublet emissions are 5 and 1.7 Å, respectively. The largest C iv 1548, 1551 EW which has been reported for a nearby starburst galaxy is Å. This is for galaxy J104457, which has 12+log(O/H) = 7.45 (Berg et al. 2019b ) and is at a very similar redshift (0.013) compared to SBS 0335−052E. Senchyna Stark ( 2019 ) present HST COS UV observations of six star-forming XMPs with 12+log(O/H) between 7.4 and 7.7, i.e. lower than in the work of Senchyna et al. ( 2017 ). They find stellar C iv 1548, 1551 in five of the galaxies and high [C iii ]+C iii ] equivalent widths (Å) in two objects. The highest EWs of C iv 1548, 1551 and He ii which they find are 4.4 and 1.7 Å, respectively. For SBS 0335−052E we find EWs of 1.7 Å for C iv 1548, 1551 and He ii λ1640. Although nebular C iv 1548, 1551 emission is present in some very high sSFR nearby systems, nearby systems do not reach the equivalent widths of C iv which are observed in individual lensed systems at z >6. Undisputed detections of nebular emission in He ii in predominantly star-forming systems at z >6 remain elusive (Senchyna Stark 2019 ). Objects located at z = 2-4 with high values of EWs(C iii ]), i.e. ≥10 Å, are analysed in Nakajima et al. ( 2018 ), who find that EWs(C iii ])>20 Å can only be modelled with a combination of photoionization by stars and an AGN. 6.2 C/O Berg et al. ( 2016 ) and Berg et al. ( 2019a ) studied the C/O ratio derived via UV collisionally excited emission lines of a sample of 12 low metallicity galaxies with significant detections of carbon and oxygen lines. At low metallicity, (12+log(O/H)8.0), they find that no clear trend is evident in C/O versus O/H. We find log(C/O) ∼ −0.45 via tests 2 and 3, and 12+log(O/H) = 7.48 / 7.42 via tests 4/5, respectively. This is very similar to what Berg et al. ( 2016 ) report for galaxy J120122, which is log(C/O) ∼ −0.45 and 12+log(O/H) = 7.45. 6.3 JWST observation As a simple exercise, we placed SBS 0335−052E at redshift z = 10, and used the COS G130M + G160M + G185M spectrum to simulate an observation of this galaxy with the near-infrared spectrograph (NIRSpec) onboard JWST . For this purpose, the spectrum’s flux was diluted using the luminosity distance for cosmological parameters H 0 = 69.6, Ω M = 0.286, and Ω vac = 0.714. In addition, we accounted for IGM absorption of UV photons using Madau ( 1995 ) attenuation. We degraded the spectrum to match NIRSpec’s prism


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DKG acknowledges the support of an Australian Research Council Future Fellowship (project FT0991598 ). This paper utilizes preliminary analysis results from the Multi-INstrument Burst ARchive (MINBAR), which is supported under the Australian Academy of Science's Scientific Visits to Europe program, and the Australian Research Council's Discovery Projects funding scheme. This research has made use of data and software provided by the High Energy Astrophysics Science Archive Research Center (HEASARC), which is a service of the Astrophysics Science Division at NASA/GSFC and the High Energy Astrophysics Division of the Smithsonian Astrophysical Observatory.


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rates and substellar velocities. Figure 13. Mid-tropospheric atmospheric temperature ( p = 658 hPa). The temperature reference in the lower right corner of each pane indicates the value of the highest temperature contour, with successive cooler contours at 2 K intervals. The central column (tidally locked) phase-curve examples are shown in Figure 12 . At this height in the atmosphere, , there is no frictional damping. In the stratified model, we find a more complicated relationship than in the shallow-water study. At the surface, the thermal response is tightly coupled to the forcing, and at all rotation rates, the peak integrated temperature is lagging the motion of the substellar point. However, at altitude, from where observed infrared emission will originate, the temperature distribution is sensitive to the speed of the diurnal cycle. Above the boundary layer, momentum and temperature are less strongly damped, thermal advection is efficient compared to friction, and the hot spot is advected by the wind field. Figure 13 shows the horizontal temperature structure in the mid-troposphere; for both eastward- and westward-propagating substellar points, eastward and westward hot spots are observed, depending on the rotation rate of the planet. As previously demonstrated in the hot Jupiter studies of Showman et al. ( 2015 ), a quickly moving substellar point, or rapidly rotating system results in a reduction in zonal variability. At the mid-troposphere example plots shown in Figure 13, there is an ∼65 K gradient between substellar and antistellar points in the equilibrium temperature T eq ; in contrast, the atmospheric temperature varies little, with an efficient thermal transport from dayside to nightside. The efficient heat transport and zonal redistribution with a rapidly moving substellar velocity predicts relatively warm nightside temperatures and a largely isothermal distribution of temperature in the upper atmosphere; this is perhaps expected from our intuition of Earth, which has a very rapid diurnal cycle relative to atmospheric radiative timescales, . The reduction in the meridional temperature gradient is also a result of the short diurnal timescale, providing an effective relaxation profile, as shown in Figure 7 and discussed above. The phase-curve offset is found by calculating the normalized phase curve relative to the substellar point using Equation ( 22 ) and then solving for the longitude of maximum integrated thermal emission. The panels of Figure 14 show the phase-curve offset as a function of substellar velocity near the surface and at several levels in the troposphere. Phase curves near the surface are a strong function of substellar velocity, with little influence from rotation rate; in general, the faster the substellar point moves, the further the thermal hot spot has lagged behind the point of maximal heating. This is due to the short timescales of both radiative and frictional damping in the bottom boundary of 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 B-Wavelength O B-Wavelength O O B-Citation I-Citation I-Citation I-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 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-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-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 I-Citation 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 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-Wavelength O O O O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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-CelestialObject O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 I-CelestialRegion I-CelestialRegion I-CelestialRegion I-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 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

the sources H ii 1, 2 and 6 are the extrapolated thermal flux density estimated using H emission. For the sources H ii 2 and 6, comparing the best-fitting parameter m to equations ( 1 ) and ( 2 ), we estimate the thermal freefree emission to be optically thick ( ff 1) below 0.220.03 and 0.410.05GHz, respectively. Recently, Hindson etal. ( 2016 ) in a study of Galactic H ii regions, found evidence of a turnover in the freefree spectrum typically with turnover frequencies in the range 0.31.2GHz. We estimated 8 the EM to be (1.20.3)10 5 and (4.6 1.2) 10 5 pccm 6 for H ii 2 and 6, respectively which in turn is related to the average thermal electron density n e as (Berkhuijsen, Mitra Mller 2006 ): where, f is the filling factor and h HII is the size of the H ii region along the line of sight. Assuming a typical f 5percent for the clumpy star-forming disc (Ehle Beck 1993 ) and h HII 50pc, i.e. the spatial resolution of our observations, we estimate n e to be 11 and 22cm 3 for H ii 2 and 6, respectively, which are typical values for H ii regions (Hunt Hirashita 2009 ). Deeg etal. ( 1993 ) pointed out that such values of EM and n e are necessary to explain the radio continuum spectra of star-forming blue compact dwarf galaxies. To better constrain n e and the sizes of the H ii regions, high-resolution radio continuum observations at even lower frequencies with LOFAR will be necessary. The thermal emission independently estimated using extinction-corrected H emission well represents the emission in the three H ii regions (shown as black dotted lines in Fig. 6 ). This suggests that the extinction-corrected H emission is a good tracer of the thermal freefree emission on scales below 100pc. Since, the total radio continuum emission in these regions are already consistent with 100percent thermal emission, it is difficult to estimate the contribution of the non-thermal component. We have therefore blanked these pixels in our future calculations. 4.2.2 Non-thermal bubble An interesting feature observed in the maps of and nt lies towards the south-eastern edge of IC10 marked as the non-thermal bubble in Fig. 3 . The bubble was first identified in the radio continuum observations of Yang Skillman ( 1993 ). The sharp boundary of this region is distinctly visible only in the spectral index maps (see Fig. 4 ). The total intensity emission is merged with the bright H ii region H ii 1 and does not show the bubble distinctly. In Fig. 7 , we show a zoomed-in view of the spectral index map. We mark the sharp boundary of the bubble and determine its centre to be at RA = 00 h 20 m 29 s and Dec. = 591639.5. The non-thermal bubble extends 300pc in the north-east to south-west direction and 100pc in the north-west to south-east direction. Its north-western edge, where the spectrum flattens from being non-thermal with 0.6 to thermal 0.1, is bound by GMCs as observed by Leroy etal. ( 2006 ), shown as the black circles in Fig. 7 . This suggests that the GMCs likely confine


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

2019 ). Here, the uncertainty in the wavelength calibration in Doppler units is expected to be about 1 km s −1 . Information of the two target lines and their associated calibration lines is listed in Table 2 . After the wavelength calibrations, the Si iv and Mg ii k lines have redshifts of 2.3 km s −1 and 3.1 km s −1 , respectively, in the quiet Sun region. Here, the Doppler shift of Mg ii k line is obtained using the central absorption at k3, and unrelated to the spectroscopic results of coronal rain. Figure 4. Spectral information of the coronal rain observed by IRIS. Maps of intensity (a1)–(a2), Doppler shift (b1)–(b2), and line width (c1)–(c2) of Si iv (1394 Å) (a1)–(c1) and Mg ii k (2796 Å) (a2)–(c2) lines for the IRIS raster scan #3. Like in Figure 2 (a), the blue rectangles and diamond separately indicate the positions of northern and southern parts of the coronal rain, which is enclosed by the blue dashed–dotted lines. The FOV is denoted by the pink rectangle in Figure 2 (a). See Section 4.1 for details. Table 2 Lines of Interest Note. Listed are the lines, the rest wavelengths of the lines, the Doppler shifts (Δ v ) of the rest wavelengths of the lines to the Si iv (upper) and Mg ii k (lower) lines, and the absolute Doppler shifts of the lines in the spectrum averaged over a quiet Sun region after the wavelength calibrations. Positive (negative) values of the Doppler shifts correspond to redshifts (blueshifts). The rest wavelengths of the lines are obtained from the line list of Tian ( 2017 ). Similar spectroscopic results of coronal rain are obtained for the four middle raster scans of IRIS, i.e., from scans number two to five. Among them we take the results for the third raster scan for example, and display them in Figure 4 . The left and right columns of Figure 4 show the maps of intensity, Doppler shift, and line width of the Si iv and Mg ii k lines, respectively. Here, the instrumental line width of about 26 mÅ is subtracted from the Gaussian line width (De Pontieu et al. 2014 ). In these maps, the line fit parameters outside the locations of the coronal rain are not shown as they are not well-fitted because of low count rates. Therefore, we only concentrate on the coronal rain region enclosed by the blue dashed–dotted lines in Figure 4 . Same as in the IRIS 1400 Å SJIs (see Figure 2 (a)), two substructures of the coronal rain are identified, marked separately by the blue square and diamond signs in Figure 4 . This demonstrates that in our observations in the coronal rain, the 1400 Å channel is indeed dominated by the transition region Si iv line. Comparing the Si iv and Mg ii k intensity maps, we find that the coronal rain seen in the Mg ii k line is located mostly at the same locations as the Si iv coronal rain; see Figures 4 (a1)–(a2). At the north (south) coronal rain, we measure the intensity, Doppler shift, and line width, and obtain the mean values of 46 (18) DN pixel −1 , 7.5 (5) km s −1 , and 8.6 (7.3) km s −1 for the


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

models that terminate at values in agreement with the inferred luminosity and temperature for SN 2016gkg (as discussed in Section 3.4.2 ). The best-fitting model has an initial stellar mass of M 15M with a 1.5-M companion. The initial period is 1000d and the primary star explodes with M 5.2M . Two additional examples with initial masses 12M (8.4-M initial mass companion, 160-d period) and 16M (14.4-M initial mass companion, 6.3-d period) are shown with dotted and dashed lines, respectively. All of these models agree with the inferred luminosity and temperature of SN 2016gkg. We find that it is extremely unlikely that SN 2016gkg originated from a single star. Woosley Heger ( 2007 ) and Sukhbold etal. ( 2016 ) have found that, for stars with M ZAMS 30M , the pre-SN iron core is too large for an SN to be successful. Moreover, mass-loss is sufficiently strong so that most of these stars lose their entire hydrogen envelopes and are thought to end their evolution as WolfRayet stars, implying that the subsequent SN would be Type Ib or Ic. SNe IIb require progenitor stars with extended low-mass hydrogen envelopes (Podsiadlowski 1993 ; Woosley etal. 1994 ; Elmhamdi etal. 2006 ), and any single-star model for such a system would require finely tuned mass-loss that would otherwise fail to reproduce the observed range in SN IIb light curves, spectra, and progenitor stars. While the single-star scenario could describe a minority of SNe IIb, it is likely that the majority of these systems come from binary-star systems such as the one observed towards SN 1993J (Maund etal. 2004 ; Fox etal. 2014 ). 3.4.2 Binary-star models We examine evolutionary tracks involving binary stars in order to assess the plausibility of these systems as possible progenitor stars for SN 2016gkg. We obtained our binary-star evolutionary tracks from the Binary Population and Spectral Synthesis ( bpass ) code as described in Eldridge Stanway ( 2009 ). These models provide a range of metallicities ( Z 0.0010.040), primary-star masses ( M /M 0.1300), mass ratios ( q 0.10.9), and initial periods [log( P /1d)04]. We fixed the metallicity of the binary-star models to Z 0.010 in order to provide the best match to the observed metallicity of NGC 613. Otherwise, we examined the full range of parameters provided by bpass . For our fitting scheme, we looked for binary-star models that produced a primary star with terminal luminosity and temperature that minimized Overall, we found that 107 out of 5565 bpass models terminated with primary-star luminosity and temperature within our measurement uncertainties for the SN 2016gkg progenitor star. Of these models, the 2 ranged from 0.11 to 4.01 with a median value of 1.05. In Fig. 4 , we show the stellar evolution of the best-fitting binary-star model on the HR diagram along with the inferred luminosity and temperature of the SN 2016gkg progenitor star. The primary star has an initial mass of 15M while the secondary (accreting) star has an initial


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

in the strong peaks of emission towards the top and bottom of this figure, at distance of 19 arcsec or 1.8 kpc from the nucleus. The spectrum shows complex nuclear structure, with multiple components, including a very rapidly rotating structure, which we interpret as a star-forming nuclear ring. Between the nuclear and bar-end rings, diffuse emission is apparent, particularly in the upper part of Fig. A2 . Thus, in spite of its peculiarity, we do consider this an example of the SFD phenomen, and it is included as such in this paper. Figure A2. Two-dimensional optical spectrum of NGC 3729, centred on the H α and [N ii ] lines. The emission-line clump is indicated by the arrows. Comparison with the bright H ii region towards the bottom of the frame shows the extended nature of the line emission from the clump. The unusual feature seen in Fig. A2 is the peak of emission seen just below the nuclear ring, 5.7 arcsec (560 pc) from the nucleus. At first sight, this resembles an H ii region, but uniquely, in the current data set at least, it shows clear LINER-type ratios. To illustrate this point, Fig. A3 shows the extracted spectrum of this peak in the lower frame, with an H ii region spectrum from the same long-slit observation shown in the upper frame for comparison. The spectra are clearly different, and argue against ongoing SF in the near-nuclear clump. The clump has [N ii ] and H α EW values of 5.63 and 6.73 Å, respectively, similar to or slightly greater than the values for the two SFD regions in NGC 3729 (4.70 and 3.69 Å for [N ii ], 6.76 and 4.50 Å for H α). These values are all at the high end of the EW distributions for line emission from SFD regions, while the [N ii ]/Hα ratio for the clump, 0.837, is entirely consistent with the distribution of ratios for SFD regions (Fig. 1 , lower panel). Figure A3. Extracted H α and [N ii ] emission for the NGC 3729 clump (bottom) and, for comparison, an H ii region in the same galaxy (top). The high [N ii ]/H α ratio in the clump is clearly apparent. One possibility is that the near-nuclear clump could be the nucleus of the tidally shredded companion that has been drawn towards the centre of NGC 3729 through dynamical friction. One test of this is to look for spatial extent. Visual inspection of Fig. A2 indicates that the clump appears moderately extended, e.g. compared with the most compact H ii region (towards the bottom of the image). Measurements confirm this; along the spatial direction, the clump has a full width at half-maximum (FWHM) of 5.3 pixels, or 2.33 arcsec, compared to 3.7 pixels or 1.63 arcsec for the compact H ii region. As the latter may itself be somewhat extended, we also measured the FWHM of the standard star observation taken closest in time to the NGC 3729 spectra, finding values of 3.2 pixels or 1.4 arcsec. Taking either the star or (conservatively) the H ii region as a measure of the seeing broadening the clump FWHM, the true size of the clump is 1.9 or 1.7 arcsec,


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ACKNOWLEDGEMENTS Based on observations with the Atacama Pathfinder EXperiment (APEX) telescope. APEX is a collaboration between the Max Planck Institute for radio Astronomy, the European Southern Observatory, and the Onsala Space Observatory. The authors acknowledge support from the UK Science and Technology Facility Council under grant ST/L000768/1. iraf is distributed by the National Optical Astronomy Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under co-operative agreement with the National Science Foundation.


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

the rise time of the light curve can be also used to estimate the radius of the progenitor of type IIP supernova through the relation between the progenitor radius and the rise time of the light curve, i.e. log R(R ⊙ ) = (1.225 ± 0.178) log t rise (d) + (1.692 ± 0.490) (Morozova et al. 2016 ). For SN 2017eaw, the rise time is estimated to be t rise = 6.81 ± 0.85 d in the g band, which gives an estimate of the radius as 515 ± 180 R ⊙ . The above two estimates of the progenitor radius agree within 1σ error. Figure 6. Constraining the progenitor radius of SN 2017eaw based on the cooling of the photospheric temperature in the early phase after the explosion. The red dots are the temperatures inferred from the blackbody fit to the observed UV and optical photometry; while the red curve represents the best fit of the radius. The green and black curves show the upper and lower limits of the estimates of the radius, respectively. The blue stars show the temperature evolution of SN 1987A, and the blue dashed line shows the corresponding best-fitting radius using the theoretical model (Rabinak Waxman 2011 ). We also try to fit the observed SED of the progenitor star from the prediscovery HST and Spitzer images with synthesized spectra calculated using the stellar evolution code marcs . 4 However, the best-fitting model spectrum has an effective temperature of only about 2500 K [A similar value of 2600 K was also suggested by Kilpatrick Foley ( 2018 )] with A V = 1.83 ± 0.59 mag by including the Spitzer data (Fig. 7 ), much lower than that inferred for the HST data alone. Given the luminosity, the lower temperature would result in an effective radius of 1330 R ⊙ for the progenitor, which is inconsistent with the estimate either from the rise time or temperature evolution of the shock cooling in the early phase. Despite an overall reasonable fit, the measurements in two Spitzer bands may suffer large contaminations of the nearby red sources due to large aperture photometry and/or the presence of circumstellar dust. In the latter case, the light of the progenitor star is scattered/absorbed by the surrounding dust and re-emitted at longer wavelengths [see also the analysis by Kilpatrick Foley ( 2018 )]. We also derive the F606W-band magnitude in 2004 by assuming that the dimming behaviour in F814W-band is totally due to the CSM dust. Taking into account this speculated F606W-band magnitude and the observed F814W-band magnitude obtained in 2004, the SED of the progenitor inferred in 2004 matches with the theoretical stellar spectra model characterized by an effective temperature of 3550 ± 150 K and a radius of 636 ± 155 R ⊙ (see Fig. 7 ). As an alternative, the dimming behaviour in F814W band could be also due to the intrinsic variation of an RSG star, but this explanation is inconsistent with either the observation taken at one year to a few days before the explosion or the theoretical prediction for its final stage evolution (see discussions in


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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Tag I-Tag 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 O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O B-Wavelength O B-Wavelength O O O O O O O O O B-Telescope B-Telescope O B-Telescope 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 B-Telescope O O O O O O O O O O B-Telescope B-Telescope B-Telescope O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


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

ejects these elements into space where they are then available for the next generation of stars. Common uranium isotopes have half-life decay times of 10 8 to 10 9 years, and had been used to determine the age of the universe by observing ultra-metal-poor stars ( Frebel et al. 2007 ). Gopka et al. (2007) identified Th II 5989.045 Å in the KPNO Arcturus spectrum from Hinkle et al. (2000) . They followed this up by the identification of more such lines from the KPNO atlas ( Gopka et al. 2013 ). The most widely used line is Th II 4019.129 Å. Together with the nearby neodymium line Nd II 4018.8 Å this line is used to form the chronometric ratio Th/Nd, first suggested by Butcher (1987) as an age indicator. However, there is no systematic identification of heavy-element lines in benchmark stars. We have visually searched our library sample for the strong lines of U II at, for example 3859.57 Å and 4241.67 Å as well as Th II at 4019.129 Å and 5989.045 Å, leaning on new oscillator strengths from Nilsson et al. (2002a , b ). Some of these lines are indeed identified, for example the Th II -Nd II line pair at 5989 Å in giant stars like Arcturus, α Ari, or μ Leo or the U II transition at 4241-Å in ε Vir. Figure 7 is a comparison of above three targets with the Sun for the Th 5989-Å region. For many others there is only vague evidence due to blending. Note again that the solar spectrum in this plot was also taken with PEPSI in the same manner as the other stars. It shows a dominant telluric blend on the blue side of the expected Nd II line. Th II 5989.045 may be present in the solar spectrum with an upper limit at the 1 mÅ level. Fig. 7 Th II 5989.045-Å and Nd II 5989.378-Å lines in three RGB stars (full lines, from top to bottom in the Ti I line core; Arcturus, Hamal, Rasalas). The top spectrum shown as dots is a spectrum of the Sun. In connection with chronometry, the s-process elements Ba and Sr (a.o.) are also key elements. The most prominent barium line is the one Ba II transition at 4554.02 Å. Other comparably weaker lines are 3891.78 Å and 4130.64 Å (see, e.g., Siqueira Mello et al. 2014 ).Strontium lines are comparably more prominent than U and Th, for example Sr II at 4077.72 Å or 5215.52 Å. The 4077-Å line is commonly used in the M-K system to classify cool, low-gravity, stellar atmospheres because of its density sensitivity ( Gray Garrison 1989 ). Our library spectra may be used to investigate spectral lines from heavy elements in greater detail than before. 7 Summary We present a library of high-resolution (on average ≈220 000), high-S/N optical spectra of a sample of 48 bright reference stars. The sample includes the northern Gaia benchmark stars and a few well-known M-K standards. Deep spectra are build by average combining individual exposures and reach S/N of many hundreds and, in some cases, even thousands. Continua are set by predetermining synthetic spectra that match the target classification. Continuum adjustments of several tens


O O O O O O O O O O O O O O O O O O O O O B-Organization I-Organization I-Organization B-Location O O O B-Grant B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O B-Organization B-Grant I-Grant B-Location O O B-Grant I-Grant I-Grant I-Grant I-Grant B-Person O O O O B-Organization O B-Grant I-Grant I-Grant B-Grant B-Grant B-Grant O B-Grant B-Grant B-Person B-Person O B-Person O O O O B-Location B-Organization I-Organization I-Organization O O O B-Grant O O O O B-Collaboration I-Collaboration I-Collaboration I-Collaboration I-Collaboration B-Collaboration O O O O O O O O O B-Location B-Organization I-Organization I-Organization O O O B-Grant B-Person O B-Person O O O O O O O O O O O O O O B-Organization I-Organization I-Organization I-Organization O O B-Location B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization O O O B-Grant B-Person B-Person B-Person B-Person O O O O O O O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility B-Person B-Person O B-Software B-Citation I-Citation I-Citation I-Citation O B-Software B-Citation I-Citation I-Citation I-Citation O B-Software B-Citation I-Citation I-Citation I-Citation O B-Citation O B-Organization I-Organization B-Software I-Software I-Software I-Software I-Software B-Citation I-Citation O B-Software B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Software O B-URL O

We are thankful to the anonymous referee for providing constructive feedback that improved our manuscript. This research is supported by the National Science Foundation (USA) under grant No. PHY-1430152 (JINA Center for the Evolution of the Elements) and by the ERC Consolidator Grant (Hungary) funding scheme (project RADIOSTAR, G.A. n. 724560). K.B. acknowledges support from the NCN grants Sonata Bis 2 (DEC-2012/07/E/ST9/01360), OPUS (2015/19/B/ST9/01099), and OPUS (2015/19/B/ST9/03188). M.M., N.V., and R.S. are supported by the U.S. Department of Energy under contract No. DE-AC52-07NA27344 for the topical collaboration Fission In r -process Elements (FIRE). This work was also supported in part by the U.S. Department of Energy under grant No. DE-SC0013039 (R.S. and T.S.). A portion of this work was also carried out under the auspices of the National Nuclear Security Administration of the U.S. Department of Energy at Los Alamos National Laboratory under contract No. DE-AC52-06NA25396 (C.F., O.K., R.W., M.M.). This research used resources provided by the Los Alamos National Laboratory Institutional Computing Program (O.K., R.W.). Software: OMEGA (Côté et al. 2017b ), PRISM (Mumpower et al. 2017 ), StarTrack (Belczynski et al. 2002 , 2008 ), Los Alamos suite of statistical Hauser-Feshbach codes (Kawano 2016 ), NumPy (Van Der Walt et al. 2011 ), matplotlib ( https://matplotlib.org ).


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O O O O O O O O O O O O O O B-CelestialRegion I-CelestialRegion O O O O O O O O O O O O O O O O O O B-CelestialRegion I-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 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 B-Wavelength O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation I-Citation 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 O B-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation O B-URL O O B-URL O O B-Citation I-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation O O B-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation O B-Citation I-Citation I-Citation I-Citation 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-Wavelength I-Wavelength O O O O O O O O O O O O B-Wavelength O O B-Observatory B-Telescope O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O B-Wavelength O O O O B-Wavelength O O O O O O B-Wavelength O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength 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 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 B-CelestialRegion I-CelestialRegion 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-Dataset I-Dataset I-Dataset I-Dataset 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 B-CelestialObject B-Wavelength 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 O B-Telescope O O B-CelestialObject I-CelestialObject O O O B-CelestialObject I-CelestialObject I-CelestialObject I-CelestialObject 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 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 B-Software O B-Software O O O O O O O O O O O O B-Wavelength I-Wavelength O O B-Software I-Software I-Software B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O B-CelestialObject O O B-Citation I-Citation I-Citation I-Citation I-Citation 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-Wavelength O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O O O O O O O O O B-Model I-Model I-Model I-Model O O O O O O O O O O O O O O O O B-Wavelength 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 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 B-Citation I-Citation I-Citation I-Citation O O O O O O O O O

1 bursts, and the blue-filled triangles indicate the Class 2 bursts. We find that most of the multiple-peaked bursts are located close to the vertex of the CCD. Figure 2. Colour–colour diagram (CCD) of all RXTE observations of 4U 1636-53. The colours of 4U 1636 − 53 are normalized to the colours of Crab. The grey points represent all available observations with one point per observation. The black crosses stand for all X-ray burst in this source. The red-filled circles and the blue-filled triangles represent Class 1 and Class 2 bursts, respectively. We extracted the 64-s interval spectrum prior to a burst as persistent emission. We generated the instrument response matrix using the tool pcarsp and the instrumental background using the tool pcabackest in heasoft for each spectrum. In this work, we fitted the spectrum in the 3.0−20 keV band using xspec version 12.10.1 (Arnaud 1996 ). We added a systematic error to the pre-burst spectra because of calibration uncertainties. During the fitting process, we included the effect of interstellar absorption using the cross-sections of Balucinska-Church McCammon ( 1992 ) and solar abundances from Anders Grevesse ( 1989 ), with a fixed hydrogen column density, N H , of (Pandel, Kaaret Corbel 2008 ). We used all available PCUs during the X-ray bursts to produce time-resolved spectrum. We corrected every spectrum for dead time according to the methods supplied by the RXTE team. Since the light curve of bursts decay is quite smooth, to compensate the lower count rates, we extracted spectrum over longer intervals in the tail of the bursts. For each multiple-peaked burst, we generated one instrument response matrix using the pcarsp and the instrumental background using the pcabackest in heasoft . For the burst spectral analysis, we initially used a single-temperature blackbody model, tbabs*bbodyrad , to fit the net burst spectra, which is well established as a standard procedure in X-ray burst analysis (Kuulkers et al. 2002 ; Galloway et al. 2008 ). The model provides the blackbody colour temperature, kT bb , and the normalization, K bb , proportional to the square of the blackbody radius of the burst emission surface, and it allows us to estimate the bolometric luminosity as a function of time assuming a distance of 5.95 kpc (Fiocchi et al. 2006 ). The bursts bolometric flux are calculated as where , R km is the effective radius of the emitting surface in km, and D 10 is distance to the source in units of 10 kpc. We defined r 1,2 as the ratio of the first peak to the second peak flux. We note that, to reduce the effect of the instrument, we used the bolometric flux (not the net burst count rate ratio in Fig. 1 ) from the standard approach to calculate the ratio r 1,2 . After subtracting the instrumental background for the time-resolved spectra, we used another model that allows us to vary the pre-burst spectrum by a free scaling factor (Worpel et al. 2013 ). We used two models to describe the persistent


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

The authors are grateful to Amanda Heiderman and Neal Evans for their useful collaboration and discussion on embedded protostellar environments, and to Mike Dunham for his comments on the paper. Many thanks to the referee, Charles Lada, for his very useful comments and suggestions. 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, by a Spinoza grant and grant 614.001.008 from the Netherlands Organisation for Scientific Research (NWO). The authors are indebted to the various observers who have collected data for their papers and kindly provided them to be included in the LOMASS database, as well as staff at the JAC. Acknowledgment is given to the following programs and languages for building this database: gildas-class and python for data reduction and format manipulation; python-matplotlib for plotting; MySQL for construction of the database; php and html for the web interface.


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

be derived. The symbols are the same introduced in the legend of Fig. 8 . In our case, the benefit of using instead of Δα −10, 10 to represent the MFS amplitudes consists of a larger number of useful maps. In Fig. 12 , the versus α 0 plot confirms, based on a larger sample of cases, the trends seen in Fig. 10 . The plot appears less scattered than that of Fig. 10 with regard to positions of Hi-GAL and fBm images, while the positions of the simulations cover a wide range towards larger values. The ‘solenoidal’ and the t 1 , yz maps of both the ‘quasi-hydrodynamical’ and ‘high-magnetization’ scenarios are the closest to the observational points, mostly to the ones corresponding to SPIRE maps of l224 and l217, that is to say that, from the point of view of the MFS amplitude, they show a degree of multifractality similar to that of the most actively star-forming regions in our sample. Figure 12. Plot ot the area A Φ under the MFS and above f = 1.5 versus the peak position α 0 for maps for which A Φ can be derived. The symbols are the same introduced in the legend of Fig. 8 . 4.2.4 Left versus right tail width The diagnostics used in Figs 10 , 11 , and 12 consider the MFS as a whole, neglecting information contained in possible asymmetries. In fact, the left tail of the MFS represents the heterogeneity (broad tail) or uniformity (narrow tail) of the high values distribution, as well as the right tail is related to heterogeneity/uniformity of the low values distribution (e.g. Pavon-Dominguez, Jimenez-Hornero de Rave 2013 ; de Freitas et al. 2017 ). Strong asymmetries are observed in most of the spectra analysed in this paper, with the extreme case represented by PACS 70 maps, discussed above. In order to make use of the MFS asymmetry, single values of α on the two sides of the MFS (for example, α 10 and α −10 , to follow the same approach as above) should be considered (de Freitas et al. 2017 ). In Fig. 13 , the two widths Δα L ≡ α 0 − α 10 and Δα R ≡ α −10 − α 0 , are plotted. First, a strong segregation in abscissa is visible between the group of fBm sets (which are right-skewed and for which the width of the left MFS tail α 10 remains nearly constant, see also Table 3 ) and that of Hi-GAL maps. The latter is internally more composite: the most quiescent, l215, is found on the left while the most active, l224, on the right, as a consequence of the leftward broadening of the MFS in presence of bright compact sources (cf. Fig. 5 ). Along the vertical coordinate, a systematic increase is seen from short to long Herschel wavelengths, while the column density maps appear mixed with SPIRE maps but with no specific trend. Figure 13. Plot ot the MFS left versus right tail amplitude for maps for which it is possible to derive both quantities. The symbols are the same introduced in the legend of Fig. 8 . The dotted line represents the bisector, to facilitate the distinction between left-skewed (below the line) and right-skewed (above the line) MFSs,


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The Telescope Array experiment is supported by the Japan Society for the Promotion of Science through Grants-in-Aids for Scientific Research on Specially Promoted Research (21000002) “Extreme Phenomena in the Universe Explored by Highest Energy Cosmic Rays” and for Scientific Research (19104006), and the Inter-University Research Program of the Institute for Cosmic Ray Research; by the U.S. National Science Foundation awards PHY-0307098, PHY-0601915, PHY-0649681, PHY-0703893, PHY-0758342, PHY-0848320, PHY-1069280, PHY-1069286, PHY-1404495 and PHY-1404502; by the National Research Foundation of Korea (2007-0093860, R32-10130, 2012R1A1A2008381, and 2013004883); by the Russian Academy of Sciences, RFBR grants 11-02-01528a and 13-02-01311a (INR), IISN project No. 4.4509.10, and Belgian Science Policy under IUAP VII/37 (ULB). The foundations of Dr. Ezekiel R. and Edna Wattis Dumke, Willard L. Eccles, and the George S. and Dolores Dore Eccles all helped with generous donations. The State of Utah supported the project through its Economic Development Board, and the University of Utah through the Office of the Vice President for Research. The experimental site became available through the cooperation of the Utah School and Institutional Trust Lands Administration (SITLA), U.S. Bureau of Land Management, and the U.S. Air Force. We also wish to thank the people and the officials of Millard County, Utah for their steadfast and warm support. We gratefully acknowledge the contributions from the technical staffs of our home institutions. An allocation of computer time from the Center for High Performance Computing at the University of Utah is gratefully acknowledged.


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well as the narrow range of scales involved, we are only able to claim qualitative similarity with the Mallet et al. ( 2017 ) prediction. Figure 2. Spectral index of the dissipation range binned in the (, β e ) plane. The black square marks the region with the steepest spectral indices in the range of 0.1 ≲ β e ≲ 1 and . To resolve the ambiguous results obtained with Figures 1 (d) and (e), we repeat our analysis with the subset of the data within the black square in Figure 2 , which encloses 41% of the total data and is bounded by 0.1 ≲ β e ≲ 1 and . The spectral indices are significantly steeper in this region, and if this is caused by reconnection, then may have significantly better scaling with in the marked region than with ρ c . In Figure 3 (a), the slope of the power-law fit for as a function of closely agrees with the one based on the full distribution. In contrast, in Figure 3 (b), the slope of the power-law fit for as a function of is remarkably close to 0. Based on this, we suggest that at least at low β e magnetic reconnection may control the ion-scale break of the solar wind turbulence. The intercept of the power-law fit is , implying C D = 4.7 (see Equation ( 1 )). Figure 3. (a) and (b) are identical to Figures 1 (e) and (d); however, they present the subset of measurements, which are within the black square in Figure 2 corresponding to 41% of the overall data points. Both and were close to normally distributed in our data, thus we use an F -test to investigate whether they have equal variance. The ratio of the sample variances is with 95% confidence intervals of [0.8328; 0.8468]. Thus we reject the null hypothesis and conclude that predicts the break with smaller spread than ρ c . Finally, the scaling of as a function of β i , while significant over the whole range of β i present in the data, is not particularly strong. With reference to the results of Chen et al. ( 2014 ), Mallet et al. ( 2017 ) pointed out that correlations between and β i could cause the scaling behavior of d i to mimic that of . Neglecting a nearly constant factor ,and so if were anticorrelated with β i , the ratio would scale less strongly with β i than otherwise expected. Figure 4 shows that empirically, such an anticorrelation does in fact exist in the solar wind (at least at low β i ). Assuming that the break scale (as does appear to be the case: see Figures 1 (d) and 3 (b)), this contributes to the rather shallow scaling of in Figure 1 (b). Similar consideration could contribute to the shallow scaling of with . Figure 4. 2D histogram showing the distribution of the measurements in the () plane. The least-square fit is indicated with a black line and the average and standard deviation of each 5% of the data are marked in white. 4. Conclusion In this Letter, we have presented a statistical study of the break scale between the inertial and dissipation ranges of the solar wind turbulence spectrum, and to what extent agrees with the fundamental ion length


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We thank the anonymous referee for the thorough review that helped us improve this manuscript. We are grateful to Athanasia Tsatsi for useful comments. This research was supported in part by the Polish National Science Centre under grant 2013/10/A/ST9/00023.