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

at 10 to 20%. However, a much larger bias has been invoked to reconcile cosmological parameters derived from the cosmic microwave background and cluster counts (Planck Collaboration XX 2014 ), although the calibration of the bias by Planck team has been amply discussed (von der Linden 2014 ; Andreon 2014 ; Smith et al. 2016 ). Caustic masses can provide an alternative calibration of the bias of hydrostatic masses. They are almost unused for this purpose (we are only aware of Maughan et al. 2016 ) and we exploit a new method for using this type of masses: if there is a relative bias between caustic and hydrostatic masses then there should be an offset in gas mass derived using the two masses. Throughout this paper, we assume , , and km s Mpc. Results of stochastic computations are given in the form , where and are the posterior mean and standard deviation. The latter also corresponds to 68% intervals because we only summarize posteriors close to Gaussian in this way. Logarithms are in base 10. 2. Sample selection, cluster masses, and X-ray data Sample selection, halo mass derivation, and X-ray data are presented and discussed in Andreon et al. ( 2016 , Paper I), and gas masses are derived in Andreon et al. ( 2017 , Paper II), to which we refer for details. We summarize here the work done. We used a sample of 34 clusters in the very nearby universe (, XUCS, for X-ray Unbiased Cluster Sample) extracted from the C4 catalog (Miller et al. 2005 ) in regions of low Galactic absorption. There is no X-ray selection in our sample, meaning that 1) the probability of inclusion of the cluster in the sample is independent of its X-ray luminosity (or count rate), and 2) no cluster is kept or removed on the basis of its X-ray properties, except for two clusters for which we cannot derive gas masses. The impact of this selection is discussed in Sect. 3.3. We collected the few X-ray observations present in the XMM-Newton or Chandra archives and we observed the remaining clusters with Swift (individual exposure times between 9 and 31 ks), as detailed in Table 1 of Paper I. Swift observations have the advantage of a low X-ray background (Moretti et al. 2009 ), making it extremely useful for sampling a cluster population that includes low surface brightness clusters (Andreon Moretti 2011 ). Caustic masses within 1 , , have been derived following Diaferio Geller ( 1997 ), Diaferio ( 1999 ), and Serra et al. ( 2011 ), then converted into and assuming a Navarro et al. ( 1997 ) profile with concentration . Adopting would change mass estimates by a negligible amount; see Paper I. The median number of members within the caustics is and the interquartile range is . The median mass of the cluster sample, , is and the interquartile range is 0.4 dex. The average mass error is 0.14 dex. Gas masses are derived by projecting a flexible radial profile, fitting its projection to the unbinned X-ray data, and propagating all modeled sources of uncertainties (e.g., spectral


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 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 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 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 B-CelestialObject I-CelestialObject O O O O O O O B-Formula I-Formula I-Formula 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 B-Telescope O O B-CelestialObject I-CelestialObject O B-Citation I-Citation I-Citation I-Citation O O B-CelestialObject I-CelestialObject O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O 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-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 B-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O B-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion O O O O O B-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion O B-CelestialObject I-CelestialObject O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O 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 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 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 O O O O O O O O O O O O O O O B-Model O O O O B-Model O B-Citation I-Citation I-Citation I-Citation O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O B-Observatory O O B-Formula I-Formula I-Formula O B-Formula I-Formula I-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

et al. 1993 ; Steiner et al. 2010 ), which is determined by black hole mass and spin. In the case of non-rotating black holes, ISCO is equal to three times the Schwarzschild radius. Thus, from the average innermost radius of the disk, km, the black hole mass M BH is estimated to beThe expected distance–mass relation in i = 0° and 60° are shown in Figure 5 . Figure 5. Observational constrains on the distance–mass diagram. The two solid colored lines represent Equation ( 3 ) when i = 0° (blue) and 60° (cyan). The dashed lines with the same colors denote the error region due to systematic error. The gray curves give the empirical relation that the luminosity after the soft-to-hard transition ( T = 96) is 0.01–0.04 L Edd . The shaded region represents the plausible mass and distance range. In addition, BHBs are known to show similar luminosity dependence of the spectral states. For instance, in the current case of MAXI J1348–630, the flux at the soft-to-hard transition ( T = 91) is ∼10% of the peak flux in the high/soft state ( T = 14); this value is consistent with those of other BHBs discovered by MAXI, such as MAXI J1820+070 (∼12%; Shidatsu et al. 2019 ) and MAXI J1910−057 (∼10%–15%; Nakahira et al. 2014 ). Furthermore, it was pointed out that the soft-to-hard transition typically occurs at 1%–4% of the Eddington luminosity ( L Edd ; Maccarone 2003 ). Namely, the bolometric luminosity soon after the soft-to-hard transition is expected to be 0.01–0.04 L Edd . The gray curves in Figure 5 give the distance–mass relation of L trans / L Edd = 0.01 and 0.04, where we employed the bolometric flux at the soft-to-hard transition ∼1.7 × 10 −8 erg s −1 cm −2 on T = 96 and L Edd = 1.3 × 10 38 ( M/M ⊙ ) erg s −1 . Next, we try to constrain the source distance. The galactic coordinate of the source is ( l, b ) = (309.3, −1.1), which is tangential to the Galactic Scutum–Centaurus arm. If MAXI J1348−630 locates in the Scutum–Centaurus arm, the distance is estimated to be ∼4–8 kpc (e.g., Xu et al. 2018 ). However, the value of N H = 8.6 × 10 21 cm −2 implies that the source is located in front of the arm at ∼3–4 kpc. If we adopt the most likely index L trans / L Edd ≈ 0.02 (Vahdat Motlagh et al. 2019 ), the distance becomes ∼3.8 kpc for the face-on disk. It is consistent with the estimates from optical observations (Charles et al. 2019 ; Russell et al. 2019b ). In order to estimate the black hole mass more precisely, taking account of the relativistic effects, we tried the kerrbb model instead of the diskbb model (Li et al. 2005 ). The kerrbb model gives relations among the spinning parameter a , inclination angle i , and black hole mass M under a given source distance, mass accretion rate, and spectral hardening factor ( κ in Equation ( 2 )). We carried out a joint fit to the MAXI/GSC and Swift/XRT spectra at T = 85 fixing D = 4 kpc and κ = 1.7 for several discrete a and i values, only allowing the black hole mass and mass accretion rate to be free.


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described in Section 3.2 , 417 out of 47,125 galaxies have AGN-like variability, for an overall variable AGN fraction of 0.9%. In Figure 3 , we show the light-curve standard deviation versus the PTF R -band magnitude for the full sample. In general, the scatter about the median magnitude for a given light curve increases as the magnitude increases, i.e., there is increased scatter in light curves of fainter objects. The sample of low-mass galaxies from the NSAv0 with AGN-like variability is presented in Table 3 . Three examples of low-mass galaxies with AGN-like variability are shown in Figure 4 . Figure 3. Light-curve standard deviation vs. PTF R -band nuclear magnitude. The shaded gray contours show the full population of galaxies from the NSAv0. The blue circles show galaxies we identify as having AGN-like variability. The orange points show the variable AGN from our ancillary samples (described in Section 2.2 ). The typical scatter in a light curve increases toward fainter galaxy nuclei. Figure 4. Three low-mass galaxies with star formation-dominated narrow emission lines and AGN-like variability. These galaxies span from 5 × 10 7 to 2 × 10 9 M ⊙ in stellar mass. The images cutouts (left) are from the DECaLS Legacy Survey browser and are 30′′ on each side. The black circles are the measured PTF R -band magnitude values measured within a 3′′ nuclear aperture. The light curves (right) give the PTF R -band nucleus magnitudes over 5.5 yr. In the light curves, the gray circles are data, the blue line represents the best-fit damped random walk model, and the shaded blue region shows the range of model uncertainties. Table 3 237 Low-mass Galaxies with AGN-like Variability Note. Variability-selected AGNs with M * 10 10 M ⊙ , in order of R.A. NSA ID refers to the ID given in the NSAv0. σ var , σ QSO , and σ notQSO refer to the significance that the given light curve is variable, an AGN, or a false alarm, respectively. Details on these parameters can be found in Section 3.2 . A full version of this table is available in the online version. (This table is available in its entirety in machine-readable form.) Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available. We explore the fraction of variable AGNs as a function of galaxy and light-curve properties. Uncertainties are binomial limits computed following Gehrels ( 1986 ). In Figure 5 , we show the fraction of variability-selected AGNs as a function of host galaxy stellar mass; we find that the AGN fraction increases toward higher stellar masses. In Figure 6 , we show histograms of stellar mass for the full sample and for variable AGNs. The sample of variable AGNs skews toward higher stellar masses; the median stellar mass of the overall sample is , while the median stellar mass of the variability-selected AGN is 8.3 × 10 9 M ⊙ . The pink shaded region in Figures 5 and 6 denote the region , where our sample is


O O O O O O O O O B-Organization I-Organization I-Organization O O B-Grant O O B-Person I-Person O O O B-Person I-Person O O O B-Instrument O O B-CelestialObject I-CelestialObject O B-Person I-Person O B-Person 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 B-Person O O O O O O B-Organization B-Fellowship I-Fellowship B-Person O O O O O B-Organization O O O B-Grant O O O O O O B-Archive I-Archive I-Archive I-Archive I-Archive I-Archive B-Instrument O O O O O O B-Organization O B-Grant O B-Person I-Person B-Person I-Person O B-Person I-Person O O O O O O O O B-Person I-Person O B-Person I-Person I-Person I-Person O B-Instrument O O O O O O O O O O O O B-Person I-Person O B-Person I-Person O O O O O O B-Organization O B-Grant B-Person O B-Grant B-Person O O O O O B-Instrument O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O B-Observatory I-Observatory O O O B-Survey O O O O O O B-Location B-Organization I-Organization I-Organization O B-Location B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Location O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Location I-Location O B-Organization I-Organization I-Organization I-Organization O B-Location O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility O O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization O O B-Organization I-Organization O O B-Survey I-Survey I-Survey O B-Survey O O O O O O O B-Organization I-Organization I-Organization O O O B-Grant O B-Survey O O B-Location O O O O O B-Organization O O B-Grant B-Grant B-Grant O B-Organization I-Organization I-Organization I-Organization I-Organization B-Grant O O O O B-Organization O O O B-Location I-Location O B-Organization I-Organization O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O B-Organization I-Organization O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization B-Organization B-Location B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O O O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O B-Observatory I-Observatory I-Observatory I-Observatory O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O B-Telescope I-Telescope I-Telescope B-Instrument O B-Telescope B-Instrument O B-Telescope B-Instrument O

This publication is based upon work supported by the National Science Foundation under grant AST-1108811. We thank Dan Kelson for helpful conversations, Anna Frebel for providing the MIKE spectrum of HD 122563, and Becky Canning and Jimmy for helpful conversations on the reduction of VLT spectra. We also thank the anonymous referee for suggestions that improved the presentation of the paper. A.C.R. acknowledges financial support provided by the PAPDRJ. CAPES/FAPERJ Fellowship. F.S. acknowledges financial support provided by CAPES under contract No. 3171-13-2. This research has made use of NASA’s Astrophysics Data System Bibliographic Services. M2FS was built through partial support via NSF/MRI grant AST-0923160 to Mario Mateo, Ian Thompson and Steven Shectman as co-PIs and its construction was assisted by Jeffrey Crane and John I. Bailey III. The M2FS observations used in this paper were carried out on our behalf by Mario Mateo and Matthew Walker, who were supported in part by NSF grants AST-1312967 (MM) and AST-1313045 (MW). Additional partial operational support of M2FS has been provided by the Department of Astronomy of the University of Michigan and by Carnegie Observatories. Funding for the DES Projects has been provided by the U.S. Department of Energy, the U.S. National Science Foundation, the Ministry of Science and Education of Spain, the Science and Technology Facilities Council of the United Kingdom, the Higher Education Funding Council for England, the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign, the Kavli Institute of Cosmological Physics at the University of Chicago, the Center for Cosmology and Astro-Particle Physics at the Ohio State University, the Mitchell Institute for Fundamental Physics and Astronomy at Texas AM University, Financiadora de Estudos e Projetos, Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro, Conselho Nacional de Desenvolvimento Científico e Tecnológico and the Ministério da Ciência, Tecnologia e Inovação, the Deutsche Forschungsgemeinschaft and the Collaborating Institutions in the Dark Energy Survey. The DES data management system is supported by the National Science Foundation under Grant Number AST-1138766. The DES participants from Spanish institutions are partially supported by MINECO under grants AYA2012-39559, ES2P2013-48274, FPA2013-47986, and Centro de Excelencia Severo Ochoa SEV-2012-0234, some of which include ERDF funds from the European Union. The Collaborating Institutions are Argonne National Laboratory, the University of California at Santa Cruz, the University of Cambridge, Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas-Madrid, the University of Chicago, University College London, the DES-Brazil Consortium, the University of Edinburgh, the Eidgenössische Technische Hochschule (ETH) Zürich, Fermi National Accelerator Laboratory, the University of Illinois at Urbana-Champaign, the Institut de Ciències de l’Espai (IEEC/CSIC), the Institut de Física d’Altes Energies, Lawrence Berkeley National Laboratory, the Ludwig-Maximilians Universität München and the associated Excellence Cluster Universe, the University of Michigan, the National Optical Astronomy Observatory, the University of Nottingham, The Ohio State University, the University of Pennsylvania, the University of Portsmouth, SLAC National Accelerator Laboratory, Stanford University, the University of Sussex, and Texas AM University. Facilities: Magellan : Clay (M2FS) , VLT:Kueyen (GIRAFFE) , Gemini:South (GMOS) .


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

(top) WC/WN versus metallicity. Blue lines correspond to BPASS binary models and red dashed lines the single models. The black star shows the averaged WC/WN estimation for the Antennae. For comparison, we also show the values for the Magellanic Clouds and the Milky Way taken from Rosslowe Crowther ( 2015 ), shown with open stars. (bottom) WR/O versus metallicity. The upside down arrow represents an upper limit for the Antennae, since we only computed the number of O-type stars in the SSCs with WR stars. Finally, the template-fitting method has been used in several works to classify WR stars (e.g. Hadfield Crowther 2006 , 2007 ; Kehrig et al. 2013 ; Gómez-González et al. 2020 ). However, it is still not clear how representative a template spectrum is for a given subtype. That is, what is the dispersion in the strengths of different lines in the individual spectra used for obtaining the template. An in-depth study of line strengths of WR stars in the Galaxy updated with new astrometric and photometric information from Gaia would be required to address this question. 5 SUMMARY AND CONCLUDING REMARKS We have used VLT MUSE data cubes from the ESO archive to search for WR stars in star-forming complexes of the Antennae galaxies. We reported their number, classification, and distribution. Our results can be summarized as follows. We detected 38 WR SSC complexes with 4053 ± 84 WR stars, out of which 2021 ± 60 are WNL, 2032 ± 59 WC-types. We cannot uncover a plausible presence of WO-type stars given the limited spectral range covered by the observations used for this study. Further observations that covering the VB could confirm or rule out this population, the rarest type of WR stars. However, thanks to the GTC spectrum of WR 1, we can rule out the presence of WO-type stars in this SSC complex, the one with the highest number of WR stars in the Antennae. Galactic WR templates of WNL, WCE, and WCL subtypes were appropriate to classify and quantify the WR stars of each SSC complex, given the metallicity of the Antennae, with an oxygen abundance 12 + log(O/H) ≈ 8.9. We analysed the observed WR blue and red bumps using multiple-component Gaussian fitting in order to recover the ionic transitions responsible for the bumps and report their main parameters. In all cases, the recovered ions are consistent with those expected for the inferred subtype using the templates. Avoiding any nebular contamination, we evaluated the contribution for each broad emission line to the entire luminosity of the BB and the RB of the entire WR sample. We do not find any evidence of the nebular He ii emission line. This is explained by theoretical models, as discussed, given the high metallicity of the Antennae. We estimated the main physical properties of the WR nebular environments, oxygen abundances, and presented information regarding their kinematics. We derive a global WC/WN ratio ∼1, which, according to predictions of the current BPASS models is consistent with the


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

Larson core. We focus on niMHD calculations; iMHD calculations are discussed in Sect 5 . Fig. 8 Visualisation of the disk structures. Top row : panels a) and b) show side and top views, respectively, of the disk density (orange), with the velocity vectors superimposed for . Panels c) and d) are the same side and top views, but showing the plasma parameter (colour map), over which we plot the magnetic field direction for the side view c) and the velocity vectors for the top view d) . Bottom row : same as for the top row , but for the simulation. Each row has a different spatial scale. 4.1. Aligned case Conservation of angular momentum during the collapse yields a very high specific angular momentum close to the protostar, which eventually leads to the formation of rotationally dominated structures with a strong toroidal velocity component and in some cases to genuine disks with Keplerian velocity profiles. To define a “disk” in the simulations, we used the criteria defined in Joos et al. (2013) . Structures in which the magnetic pressure either dominates or is at least not negligible, however, may satisfy these criteria while being very different from the flat rotationally supported structures characteristic of Keplerian disks. It is important to clearly identify and distinguish these two types of structures, since the existence of flat disks around Class-0 objects remains a subject of heated debate, and this issue is addressed below. Following Joos et al. (2013) , a piece of fluid belongs to the disk if it fulfils all the following constraints (using ): it is close to hydrostatic equilibrium:; it has strong rotational support: ; its rotational support is stronger than the thermal support: ; it has a high density: . In our fiducial aligned case with , we do observe the formation of a disk according to the above criteria that strongly resembles a Keplerian disk. Its characteristic properties are given in Table 3 and the results of the simulations are shown in Fig. 8 (top row). The disk is well defined in density, beginning just at the edge of the core and exhibiting sharp edges at its periphery. The breaking of symmetry observed in the top view (Fig. 8 b) is due to the evolution over several orbital periods at the core radius, with small numerical errors leading to a bar-like instability that evolves into two spiral arms. The disk then grows to a radius of au and is flat. The velocity profile in the disk is displayed Fig. 9 and is very close to a Keplerian one, with an estimated mass for the central object of compared to (Table 3 ) (see Appendix C for an important remark about assuming a Keplerian profile to estimate the mass of the central object). Table 3 Properties of the disks that are formed in the non-ideal MHD simulations. The evolution of the disk for our two values of magnetisation is displayed in Fig. 10 (solid lines for , dashed lines for ). In niMHD, the pinching of the field lines the midplane is greatly reduced and the radial


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 B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Mission O O O O O O O O B-Survey O O O B-Wavelength O O O O O O O O O O O O O B-Wavelength O B-Wavelength O B-Wavelength O B-Wavelength I-Wavelength 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Wavelength O B-Wavelength I-Wavelength 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

software based on the analytical equation applied to spot modeling by Budding (1997) , assuming circular spots. Fixed parameters were the effective wavelengths of the filters used, linear limb darkening coefficients ( Howarth 2011 ) taking into account the stellar parameters, and the unspotted brightness in all bandpasses. We note that there is no way to deduce the true unspotted brightness of an active star showing the usual rotational and long-term light variations. On the other hand, one would expect a higher brightness level and smaller rotational variation with fewer and fewer spots. Therefore, we took the observed maximum magnitude as the unspotted reference brightness level. The rest of the activity is supposed to be distributed evenly and/or remain on the poles. We note that we have observed only two rotations of the star in a standard photometric system, and the archival and K2 data were obtained in different, non-standard bandpasses (except ASAS which has a V magnitude bandpass), and therefore cannot be compared quantitatively. We modeled in parallel the B − V , V − R C , V − I C color observations, assuming that there are just two circular starspots. The parallel modeling of each of these colors results in spot coordinates (longitudes, latitudes), sizes, and a single spot temperature. For EPIC 211759736 we have a high rotational inclination angle (81.85°), and thus the two stellar hemispheres are nearly interchangeable (supposing that the rotational axis is perpendicular to the orbit, the star is seen nearly edge-on), that is, approximately invariant under inversion. Therefore, in the course of the modeling, the spot latitudes were kept fixed at the equator; generally, it is not possible to obtain reliable spot latitudes from photometric data. In this way we had five free parameters to fit for: two longitudes and sizes, and the spot temperature. The results show that in early 2018 there were two cool spots (active regions) on the stellar surface, one facing the secondary component and the other on the opposite side, covering altogether about 10% of the total stellar surface, with a temperature of 3960 ± 300 K, or about 800 K below the surface temperature of 4750 K. The individual results of the spot temperature modeling from the three different color indices are as follows: B − V : 3968 ± 305, V − R C : 3936 ± 364, and V − I C : 3978 ± 215. Although the spot temperatures from the three color indices have substantial uncertainties, their values are remarkably close to each other. The resulting spot longitudes and sizes from the three color indices are within their mutual 1- σ uncertainties. The four-color light curves and the fitted color indices are plotted in Fig. 6 . (We note that experiments allowing the spots’ latitudes to also be free parameters gave essentially the same results for the longitudes, sizes, and temperature, but with much higher uncertainty due to the error propagation.) By contrast, the average stellar


O O O O O O O O O O O O O O B-Person O B-Person O B-Person I-Person O B-Person I-Person O O O O O B-Telescope O O B-Person I-Person O B-Person I-Person O O O O O B-Telescope O B-Person O O B-Organization I-Organization I-Organization I-Organization I-Organization O O O O O O O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant B-Person O O B-Grant I-Grant I-Grant I-Grant O O B-Location B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Grant O O B-Location B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O O B-Grant O O O O O O O B-Database I-Database I-Database I-Database O O O O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Survey O O O O O B-Organization I-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization O O B-Location B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Survey O O O B-URL O B-Survey O O O O B-Organization I-Organization I-Organization O O O O O O B-Collaboration I-Collaboration O O B-Organization I-Organization I-Organization O B-Collaboration I-Collaboration I-Collaboration B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O B-Collaboration I-Collaboration I-Collaboration O B-Collaboration I-Collaboration I-Collaboration B-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Collaboration I-Collaboration I-Collaboration I-Collaboration I-Collaboration B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization O B-Collaboration I-Collaboration I-Collaboration B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O B-Organization I-Organization O B-Survey I-Survey I-Survey O O B-Archive I-Archive I-Archive I-Archive O O O O O O O O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O B-Organization I-Organization O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Location O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Location B-Organization I-Organization I-Organization B-Organization I-Organization O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization O B-Observatory I-Observatory I-Observatory I-Observatory I-Observatory I-Observatory I-Observatory O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization O O O B-Grant O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O O B-Grant O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization

We thank the referee for the constructive comments that helped to clarify the text. DH and BAG thank Marie Hrudkova and Raine Karjalainen for their help during the WHT observations, and Elyar Sedaghati and Boris Haeussler for their help during the VLT observations. FM thanks the Centre national d’études spatiales (CNES) who funded his research through the post-doctoral grant “Probing the geometry and physics of active galactic nuclei with ultraviolet and X-ray polarized radiative transfer”. CRA acknowledges the Ramón y Cajal Program of the Spanish Ministry of Economy and Competitiveness through project RYC-2014-15779 and the Spanish Plan Nacional de Astronomía y Astrofisíca under grant AYA2016-76682-C3-2-P. This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and the U.S. Department of Energy Office of Science. The SDSS-III web site is http://www.sdss3.org/ . SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, Carnegie Mellon University, University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofisica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, The Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington, and Yale University. The Pan-STARRS1 Surveys (PS1) and the PS1 public science archive have been made possible through contributions by the Institute for Astronomy; the University of Hawaii; the Pan-STARRS Project Office; the Max-Planck Society and its participating institutes, the Max Planck Institute for Astronomy, Heidelberg, and the Max Planck Institute for Extraterrestrial Physics, Garching; Johns Hopkins University; Durham University; the University of Edinburgh; the Queen’s University Belfast; the Harvard-Smithsonian Center for Astrophysics; the Las Cumbres Observatory Global Telescope Network Incorporated; the National Central University of Taiwan; the Space Telescope Science Institute; the National Aeronautics and Space Administration under Grant No. NNX08AR22G issued through the Planetary Science Division of the NASA Science Mission Directorate; the National Science Foundation Grant No. AST-1238877; the University of Maryland; Eotvos Lorand University; the Los Alamos National Laboratory; and the Gordon and Betty Moore Foundation.


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ACKNOWLEDGEMENTS The authors are supported by the project grant 2014.0017 ‘IMPACT’ from the Knut and Alice Wallenberg Foundation. AJ was supported by the European Research Council under ERC Consolidator Grant agreement 724687-PLANETESYS, the Swedish Research Council (grant 2014-5775), and the Knut and Alice Wallenberg Foundation (grants 2012.0150, 2014.0017, and 2014.0048). The simulations were performed on resources provided by the Swedish National Infrastructure for Computing (SNIC) at Lunarc. This research has made use of the Exoplanet Orbit Database and the Exoplanet Data Explorer at exoplanets.org . We thank the referee, John Chambers, for a careful and insightful referee report.


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

This paper is based on observations collected at the European Southern Observatory Very Large Telescope, Cerro Paranal, Chile – Programs 166.A-0106, 079.B-0469, 185.A-0745, 092.A-0170. We are indebted to an anonymous referee for helpful comments that clarified several points in the paper. VD is grateful to Gwen Rudie for sharing and adapting her results on the KBSS for Fig. 9 . MV is supported by the ERC Starting Grant ‘cosmoIGM’ and PD51 INDARK grant. TSK acknowledges funding support from the ERC Starting Grant ‘cosmoIGM’, through grant GA-257670. MH was supported by the ERC Advanced Grant 320596 ‘The Emergence of Structure during the epoch of Reionisation’. PB is supported by the INAF PRIN-2014 grant ‘Windy black holes combing galaxy evolution’. Parts of this research were conducted by the Australian Research Council Centre of Excellence for All-sky Astrophysics ( CAASTRO ), through project number CE110001020 .


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Acknowledgements We thank G. Dashyan, M. Lemoine, C. Pfrommer, R. Teyssier, and A. Wagner for enlightening discussions. We warmly thank S. Rouberol for smoothly running the Horizon cluster on which several simulations were run. This work was supported by the ANR grant LYRICS (ANR-16-CE31-0011) and the CNRS programs “Programme National de Cosmologie et Galaxies” (PNCG) and “Physique et Chimie du Milieu Interstellaire” (PCMI).


O O O O O 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 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 B-Software O B-TextGarbage I-TextGarbage B-URL O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 O O B-Telescope B-Wavelength I-Wavelength O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Tag O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Citation I-Citation I-Citation I-Citation I-Citation O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope 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

might be candidates of prestellar cores or simply overdensities of molecular gas flows. 4.2. Gas Temperatures in Dense Cores We estimated gas temperatures in dense cores using the VLA (1, 1) and (2, 2) lines. The temperatures were then used to calculate core masses below. Line widths, column densities, and optical depths were derived at the same time. We extracted the mean (1, 1) and (2, 2) spectra within the FWHM of the 2D Gaussian fit of each core and fit them with a customized code pyAmor . 9 9 https://github.com/xinglunju/pyAmor We assumed local thermodynamic equilibrium (LTE) conditions and the same filling factor for all hyperfine components. The free parameters in the fit are the core velocity , the rotational temperature , the column density N (), the velocity dispersion , and the filling factor. The core velocity was first selected by eye and then varied within ±0.62 (one channel) of the selected value. Model spectra were constructed with these parameters. The nonlinear least-squares minimization of the difference between the model spectra and the observed spectrum was implemented with the lmfit package (Newville et al. 2014 ), and then the parameters of the best-fit model spectrum were taken to be the best-fit results. The optical depth at the line center of the main hyperfine component of (1, 1), , was derived afterward using the best-fit , N (), and . An example of the fitting is shown in Figure 6 . Figure 6. Fitting results of gas temperatures in I18308-c1 using the VLA (1, 1) and (2, 2) lines. The red curve shows the best-fit model, with the best-fit parameters displayed in the panel. Toward several dense cores, multiple velocity components in lines were found. Then we fit two independent models, each of which was constructed with the parameters listed in the previous paragraph. Two sets of best-fit parameters were derived, from which we chose the one that has similar to dense gas tracers in cores (e.g., H 2 CO, CH 3 OH) to calculate dense core properties. 4.3. Masses, Densities, NH3 Abundances, Virial States The masses of the dense cores were derived using the following equation:where is the gas-to-dust mass ratio, S ν is the dust emission flux, d is the distance, is the Planck function at temperature , and is the dust opacity. We assumed and cm −2 g −1 (MRN model with thin ice mantles, after 10 5 yr of coagulation at 10 6 ; Ossenkopf Henning 1994 ). The kinematic distances were derived using the rotation curve model in Reid et al. ( 2009 ; see Lu et al. 2014 , for details). The near distance was taken in case of kinematic distance ambiguity. Under the assumption of LTE, the dust temperatures were taken to be the gas temperatures derived from , , in Section 4.2 . We did not use dust temperatures derived from Herschel data because their angular resolution is not sufficient to resolve the dense cores, nor did we use gas temperatures based on the SMA H 2 CO or CH 3 CN lines because they usually only probe 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 B-Citation 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 B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O B-Citation O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O 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 B-Citation O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O B-Citation O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O B-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 B-Citation 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 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 B-Citation O O O O O O O O O O O O O O O B-Citation O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula 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 B-Citation O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O 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 B-Citation O O O B-Model I-Model O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O

cent confidence limits, respectively, analogous to 1σ and 2σ random experimental error bars. 2.1 The misinterpretation of the mass-error correlation The next step taken by K20 is to take the upper error bars on each MC trial’s measured M hi (i.e. the upper error bars on the data points in their fig. 3, or our Fig. 1 ), and plot them as a function of ( M hi − M hi,in ) (shown in their fig. 5). K20 name this latter quantity ‘overestimate of M hi ’, but which is equivalent to ‘ M hi /M − 18’, i.e. the difference between the output and input values of M hi . K20 observed that these two quantities are correlated, and interpreted this correlation as each randomly scattered data point being aware of how far it is from the centroid of the input distribution, and that this information is communicated back to the observer through the data point’s error bar. Continuing with this line of reasoning, K20 then claim that it is possible to transpose the results of each individual MC trial back to the input value of M hi,in with a precision of ±0.8 M. Finally, K20 then treats the analysis of the real-world sample of 24 progenitor mass estimates as though it were a single MC trial, and concludes that the best fit of M hi M should be adjusted down to M hi = 15.8 ± 0.8 M. This reduction of M hi , as well as its upper error bar, implies that the difference between M hi and the mass associated with the H–D limit is now in excess of 10σ, leading K20 to state that ‘the RSG problem remains’. In Figs 2 and 3 , we use the results of our MC experiment to make similar figures to fig. 5 in K20 , again seeing a correlation. However, in Fig. 2 , we make the same plot but for three different values of M hi,in . Were the individual data points aware of of the true input value of M hi,in , the three sets of data would be offset in the y -direction, since a different correction factor would be required for each different value of M hi,in . However, the exact same trend is seen irrespective of M hi,in . Hence, we can say that the trend seen in fig. 5 in K20 has no dependence on M hi,in . Figure 2. Our version of fig. 5 in K20 , showing the quantity ( M hi − 18 M) for each of our MC trials, as a function of the positive error bar on M hi for that trial. In addition to showing the results for the same input value as K20 ( M hi,in = 18 M), we also show the results for M hi,in = 20 and 22 M. The exact same trend is seen irrespective of M hi,in , demonstrating that the correlation seen in the plot does not depend on the input value of M hi . Figure 3. Same as our Fig. 2 , but for fixed M hi,in = 18 M, and with three different sizes of error bars on the input progenitor masses (σ M = 10, 20, and 30 per cent). Different trends are seen for each value of σ M , demonstrating that the correlation seen in fig. 5 of K20 is in fact caused by simple error propagation. Next, in Fig. 3 , we again recreate fig. 5 of K20 , but for MC experiments with fixed M hi,in = 18 M and three different values


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Acknowledgements OSIRIS was built by a consortium of the Max-Planck-Institut für Sonnensystemforschung, in Göttingen, Germany, CISAS-University of Padova, Italy, the Laboratoire d’Astrophysique de Marseille, France, the Instituto de Astrofisica de Andalucia, CSIC, Granada, Spain, the Research and Scientific Support Department of the European Space Agency, Noordwijk, The Netherlands, the Instituto Nacional de Tecnica Aeroespacial, Madrid, Spain, the Universidad Politechnica de Madrid, Spain, the Department of Physics and Astronomy of Uppsala University, Sweden, and the Institut für Datentechnik und Kommunikationsnetze der Technischen Universität Braunschweig, Germany. The support of the national funding agencies of Germany (DLR), France (CNES), Italy (ASI), Spain (MEC), Sweden (SNSB) and the ESA Technical Directorate is gratefully acknowledged. This research project also received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No. 686709. In memoriam of Mike F. A’Hearn. Much of Rosetta ’s research has been motivated by the results of the Deep Impact and EPOXI missions that were under Mike's leadership. We lost an outstanding colleague and dear friend.


O O O O O O O O O O O B-Telescope I-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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope I-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O 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 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 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 B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O

is the linear radius of the half-power beam width of the KVN telescope at the distances of two VeLLOs. On the other hand, there are other targets whose infall velocities are smaller than the freefall velocity at the distances comparable to those of these two sources. This indicates that the collapsing radius of the core may not be uniquely determined but variable depending on the physical status of the core. Any further quantitative discussion in comparison of our observations with results predicted by the various models dealing with gas infall motions is beyond the scope of this paper, and we leave this issue for future study. 4.4. Mass Infall Rates and Mass Accretion Rates toward the VeLLOs, and Their Implication In this section, we consider the mass infall rates from the envelopes of the VeLLOs and the mass accretion rates toward the VeLLOs as useful physical quantities to help us understand the physical processes involved in the formation of the VeLLOs from their parent envelopes. The mass infall rates were derived using the infall speeds obtained from our model fitting, with , where ρ 0 is the mean density of the envelope given by and R in is the half of FWHM (16′′) of our observing KVN telescope. It is assumed that the envelope has a uniform density ρ and the infall is spherically symmetric with a speed of V infall . Estimated mass infall rates range from 10 −7 to 10 −5 M ⊙ yr −1 , with a median value of (3.4 ± 1.5) × 10 −6 M ⊙ yr −1 (Table 3 ). The values of κ can be a significant contributor to the uncertainties in the mass and then the mass infall rate, which may vary within a factor of 2 owing to the uncertainty in the value of κ (Ossenkopf Henning 1994 ). We note that line profiles showing an infall asymmetry can be affected by an outflow activity in their shapes if it is strong enough, and thus the infall speed and the mass infall rate that we derived can be affected. We found that 13 out of 15 sources for which infall speeds are derived from their infall asymmetric profiles have possible outflow wings from the CO observations by Kim et al. ( 2019 ), but they are found to be all weak enough not to significantly affect the derived values of infall speed and the mass infall rate. The mass accretion rate can be obtained by using CO observations around the outflow regions. Kim et al. ( 2019 ) made a single-pointing and/or a mapping survey of 68 VeLLOs in CO lines, finding the evidence for outflows over 16 dense cores having the VeLLOs. We found that there are five outflow sources identified from the CO mapping survey for which the mass infall rates were estimated in this study. For these sources, we used the mass accretion rates given by Kim et al. ( 2019 ). We also found that there are eight more outflow sources identified from the single-pointing CO observations for which the mass infall rates were estimated in this study. For these sources we calculated the mass accretion rates using the equation given by Kim et al. ( 2019 ) with


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We thank Shoya Kamiaka and Kento Masuda for useful discussions. We are also grateful to an anonymous referee for several important suggestions that improved our earlier manuscript. This research is supported by the Grant-in Aid for Scientific Research by Japan Society of Promotion of Science No. 24340035.


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

of the star formation rate (SFR) density of the universe with time and stellar mass (e.g. Brinchmann et al. 2004 ; Bauer et al. 2005 ; Feulner et al. 2005 ; Noeske et al. 2007 ; Zheng et al. 2007 ; Chen et al. 2009 ). The Hα, [O ii ] , ultraviolet–optical spectral energy distribution fitting and infrared photometry are commonly used to estimate the SFR at different redshifts. Two major conclusions of these studies are as follows: (1) the comoving SFR density of the universe has declined by an order of magnitude since z ∼ 2 (Hopkins et al. 2006 ); (2) the SFR per unit stellar mass (SSFR) depends on both stellar mass and redshift, with massive galaxies forming most of their stars earlier than less massive systems (Heavens et al. 2004 ; Thomas et al. 2005 ). To fully understand galaxy formation and evolution, it is important to understand both how the population as a whole evolves and how SFR within individual galaxies evolves. A first step is looking at how SFR is distributed spatially in galaxies as a function of their physical parameters, such as stellar mass and environment. However, this is not an easy task, especially for high- z galaxies given their small angular size and faintness. The radial distribution of star formation in local galaxies has been analysed in individual galaxies (e.g. NGC 1566; Comte Duquennoy 1982 ) and samples of tens to hundreds of galaxies using narrow-band imaging centred on Hα which traces the ionizing photons produced by massive stars. Ryder Dopita ( 1994 ) studied the relative scalelengths of Hα, V -, and I -band emission in 34 S0-Sm galaxies, finding that the line emission had a larger scalelength than the continuum. James, Bretherton Knapen ( 2009 ) compared the Hα and R -band light profiles of 313 S0a-Im field galaxies, finding that the major central Hα deficit (relative to the continuum) happens in barred galaxies, particularly in early-type and hence high-mass barred galaxies (see also Nair Abraham 2010 ; Hakobyan et al. 2014 ). Statistical studies of larger volumes have so far been lacking due to the decrease in spatial resolution with distance, and the necessity of using multiple narrow-band filters to accommodate the redshifting of the Hα line. Sloan Digital Sky Survey (SDSS) provides the largest galaxy sample of photometry and spectra so far. It is a great data base to study all kinds of properties of local galaxies. Ge et al. ( 2012 ) select double-peaked narrow emission-line galaxy sample from SDSS DR7 and study their properties. However, due to the 3 arcsec diameter fibre, it is hard to derive any spatial information about the galaxies directly from the spectra. In this paper, we make the first attempt of getting spatial information from the structures of Hα emission lines in SDSS spectra. As we know, the Hα profile depends on the strength of emission at a given velocity, which is determined by the rotating curve and the Hα surface brightness distribution in a rotating disc. Thus, through comparing


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

a significant challenge. The initial magnetic and thermodynamic configuration (i.e., densities, pressures, and temperatures imposed on the system) is critical to the initial force balance of the system, particularly in the layers at and directly above the model photosphere. Unless this initial state is constructed in a physical way, where the pressure gradients act to balance the forces from magnetic pressures and stresses acting to push apart concentrations of field, nonphysical flows and dynamics will eventually dominate any driving forces imposed at the photosphere. This is a particular problem with the zero- β approach because the only possible restorative forces in these regions are due to Reynolds and viscous stresses. On the Sun, the observed evolution of the magnetic field in the photosphere and low atmosphere results from a complex interaction of fields and flows in a gravitationally stratified, turbulent environment. But there is insufficient observational information available to adequately specify the dynamic and thermodynamic initial state of the system. In standard ab initio models of magnetic flux emergence or magnetoconvection, one is not faced with this difficulty. Typically, field-free thermodynamic states are developed in a physical way through a dynamic and energetic relaxation process, and stratification in density, pressure, and temperature naturally results from the presence of gravity and the application of physical boundary conditions. Once this relaxation procedure is complete, only then is magnetic field introduced into the system. In the case of data driving, we are presented with the opposite scenario. We are given an initial magnetic field and an electric field to be applied to the model’s photospheric boundary, with little to no information regarding the hydrodynamic state of the plasma in the low atmosphere where such information is necessary to drive the dynamics of the system in a physical way. So how best to proceed? We find that there are two ways to address this initialization problem: the first is to simply scale the fields and place the lower boundary of the simulation in the upper transition region or corona, thereby placing the driving layer in a field-filled, magnetically dominated regime. The second is to keep the driving layer in the photosphere, generate an initial thermodynamic stratification, and artificially limit nonphysical runaway flows when necessary to mitigate dynamics unrelated to the driving forces of interest. We choose not to pursue the first approach, because we find that photospheric electric fields bear little resemblance to coronal electric fields once magnetic structures have expanded into the low-density, low- β corona. This amounts to ignoring the data in the photosphere altogether in favor of a different, more idealized problem. The second approach involves generating initial thermodynamic states and flow fields by a dynamic relaxation process that holds the initial magnetic


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

more warm absorption or reflection modeling. We then fit all the spectra with an absorbed power-law model. The required additional absorption at a redshift of the source in Chandra spectra modeling is moderate with a fitted absorption of . The value of the inferred absorption in Suzaku is consistent with that within uncertainties (Table 2 ). The Chandra spectra are harder with a photon index of , compared to the value of in Suzaku . The two Swift spectra are even harder than that of Chandra , while the value of the photon index cannot be well constrained due to low S/N and degeneracy with absorption. Thus in the fitting of Swift spectra we tied all the parameters to those of Chandra except the normalization. The fitted parameters are shown in Table 2 , and the spectra with the fitted power-law model are shown in Figure 3 . In Figure 3 we also show the joint contours of the photon index Γ and column density N H . It is clear that the changes of photon index between Suzaku and Chandra are significant at 99% confidence. Figure 3. Unfolded X-ray spectra of SDSS J155258+273728 with absorbed power-law model fits for Suzaku and Chandra observations. Inset: contours give the joint 68%, 90%, 99% confidence for the two interesting variables, photon index Γ, and the intrinsic absorption N H . Table 2 Parameters of X-Ray Spectra Fits a Notes. a Unabsorbed flux in 2–10 keV. b The values are fixed in the fitting. There is more than a factor of 2 brightening in Chandra observation with an unabsorbed 2–10 keV flux of erg s −1 cm −2 , compared to those in Suzaku and Swift -2014 with values of erg s −1 cm −2 and erg s −1 cm −2 , respectively. The inferred flux of Swift -2018 is erg s −1 cm −2 , indicating that the X-ray emission of SDSS J155258+273728 fades back to the level of Swift -2014. 3.1. IR–Optical–X-Ray Photometry and Variability In Figure 4 we show the X-ray and broad H α line variations of SDSS J155258+273728 on a decade. The optical and mid-IR photometry from CRTS and the Wide-field Infrared Survey Explorer survey are also shown. It is clear that accompanied by the significant enhancement of broad H α emission, SDSS J155258+273728 presents increased emission in hard X-ray, optical V -band, and mid-IR. The variation timescale of this broadband brightening is ∼4 yr, in which the X-ray varied more than a factor of 2, and CRTS V -band and mid-IR W 1, W 2 bands varied with amplitudes of 0.18 ± 0.12, 0.32 ± 0.02, and 0.43 ± 0.03, respectively. Figure 4. Light curves showing the multiwavelength changes observed in SDSS J155258+273728 in the optical V -band data from CRTS (top panel), mid-IR W 1 and W 2 bands from WISE (middle panel), and hard X-ray flux along with broad H α emission (bottom panel). In the top and bottom panels, we also present the median values of each season epoch. The dotted–dashed lines mark the start/end of the significant variation timescale. 4. Discussion 4.1. Reddening Measurement from Optical Spectra The detected moderate


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

that minihalos that have been chemically enriched by supernova ejecta from prior Population III star formation can cool and form stars and, moreover, significantly contribute to the overall ionizing photon budget of reionization. We refer to this new class of halos as metal-line cooling halos, or MCs. Follow-on simulations (the Renaissance Simulations) in much larger volumes by Xu et al. ( 2016b ) provide the star formation rates (SFRs), intermittency, and ionizing escape fractions in the MCs, LMACHs, and HMACHs with extremely high resolution and good statistics. Using these results as our input, we revisit the problem: what is the role of the lowest-mass halos in the reionization process? The main improvement of our work compared with previous work is that the simulations shown here are fully coupled cosmological radiation hydrodynamic simulations, with a time-dependent treatment of the ionization kinetics and emissivities assigned to the source halos dynamically, considering the intermittency of the contribution from MCs. We find that because star formation is intermittent in MCs, the earliest phases of reionization exhibit a stochastic nature, with small H ii regions forming and recombining. Only later, after the characteristic halo mass scale has reached ∼10 9 , does reionization proceed smoothly in the usual manner deduced from earlier studies. Adopting concordance cosmological parameters and only using the galaxy properties from the Renaissance Simulations, our 1152 3 simulation in a 14.4 comoving Mpc box begins reionizing at z = 20, is 10% ionized at z = 10, and fully ionizes at z = 7.1. This paper is organized as follows. We summarize the relevant results from Xu et al. ( 2016b ) in Section 2 . The description of computational method and inputs to the simulations is provided in Section 3 . We show results in Section 4 and offer a discussion and conclusions in Section 5 . 2. Ionizing Photons from the Smallest Galaxies Unlike the previous papers in this series (So et al. 2014 ; Norman et al. 2015 ), where ionizing emissivities were calculated from a simple star formation/feedback recipe incorporated in the simulation itself, here we employ results from much higher resolution simulations that calculate the escaping ionizing photons of high-redshift galaxies directly. How this is done is described in Sections 3.2 and 3.3 . This approach enormously relaxes the spatial resolution requirement on the global reionization simulation and takes advantage of more precise simulation results. Uniform grids may be employed for the reionization simulation; however, they must have sufficient mass and spatial resolution to accurately capture the halo population of importance. In addition, we are able to use moment methods for the radiation transport, which do not get bogged down as reionization completes as some ray-tracing methods do (Norman et al. 2015 ). We draw on the results of Xu et al. ( 2016b ), who performed three high-resolution AMR


O O O O O O O O O O O O O O O O O O O O O O O O B-TextGarbage O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-TextGarbage O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope I-Telescope O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O B-Telescope I-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 B-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

of for the central beam ( top ) and an offset beam ( bottom ) with a coma lobe at a position angle of . For the correction algorithm, we averaged the previously modeled side-lobe intensities on a fixed grid containing 2160 cells in cylindrical coordinates for the inner of the antenna diagrams. The cells have an azimuthal extent of and a radial extent of , covering the radial range of (first minimum) up to . 3.5.4. The far side lobes The far side lobes are determined by details of the telescope structure. It is difficult to measure these side lobes (e.g., Higgs 1967 ; Hartsuijker et al. 1972 ), so we used ray-tracing to model them. While in the near side-lobe range, details of each of the individual antenna diagrams need to be considered, and it is sufficient to use a single common far side-lobe diagram for all of the receivers. For the subsequent discussion of far-side-lobe effects, we consider the telescope as a transmitting system. The most important side lobes that are far away from the main beam of the 100-m telescope, were determined by Kalberla et al. (1980a, see their Fig. 3) . These are the stray cones, caused by reflection of plane waves from the primary mirror at the feed support legs. The second most important structure is the spill-over at the edge of the main reflector. Its irradiation level depends on the edge taper of the primary feeds. In addition, we considered spherical waves originating in the feeds and determined their reflections at the support legs. Figure 6 shows these structures. The eightfold symmetry is caused by the four legs. Each leg consists of four main tubes; two of them, separated by 1.98 m, are visible from the feed. These side lobes have an interesting structure, but it turned out that they are rather unimportant. Fig. 6 Side lobes caused by reflections of spherical waves from the feed at the support legs of the 100-m (intensities relative to main beam). The Effelsberg 100-m telescope has a Gregorian secondary focus with several feed systems in an apex cabin. The seven-feed system is situated in primary focus, and the roof of the apex cabin is closed during EBHIS observations. This roof causes reflections that are offset from the main axis by . The side lobes are easily determined from the geometry of the apex roof. However, that these reflections are oriented in the east-west direction makes the situation very uncomfortable since it can produce multiple reflections. A part of the rays being reflected off the apex roof can hit feed support legs located east or west of the roof. This causes secondary stray cones. Only a fraction of these secondary stray cones are reflected onto the sky. The other part is reflected to the main mirror, causing caustics. A minor fraction of the secondary stray cones can hit the fence at the rim of the reflector before escaping. These features were determined by ray-tracing. Figure 7 shows the resulting pattern. We disregarded further reflections caused by support legs to the


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

dipolar signal exists for HD 41641, as the model fits extremely poorly, fitting extremely few of the features visible in the LSD profiles. To ensure that the fitting process had converged properly, it was repeated several times with various first guess parameters, while also rejecting the region of the main spot within the profile when fitting the Stokes I spectra prior to modelling. The results of the modelling are listed as follows. We determined two combinations of inclination and obliquity angles, which effectively corresponds to i = 70° ± 5° and β = 30° ± 5°, and i = 30° ± 5° and β = 70° ± 5°, both with χ 2 = 1.875. The model also suggests a phase shift Δψ = 0.0738 ± 0.005 and, assuming it is a dipole, a maximum polar field strength of B pol = 1880 ± 10 G. The best-fitting model is visible in Fig. 6 . We stress that the dipolar fit to the data is very poor and the above values must therefore be considered with great care and are provided here only to give an idea of the amplitude of the magnetic field signature. This model again shows that a dipolar fit is not appropriate for this star. Figure 6. Results of dipolar modelling performed on the 16 best profiles. Profiles are ordered in phase, increasing vertically first then horizontally. Model fit is displayed as red overlay. Comparing the results determined here for i , β, and B pol with those calculated in Section 3.2 , it is clear there is quite an offset, though this is expected as a result of the poor-fitting dipolar modelling. We do however see a match between the calculated values of β = 79° ± 11° and i = 22° ± 11° and the model with values of β = 70° ± 5° and i = 30° ± 5°. Finally, the error bar of the calculated B pol looks far more reasonable than the range of possible values determined by the dipolar modelling in Section 3.2 , but considering the bad fit we obtain, this error bar is not realistic. 4 CONCLUSIONS We carried out a spectropolarimetric study of the δ Sct star HD 41641, complementing the findings of E16 . We utilized data taken with the NARVAL echelle spectropolarimeter from 2015 October 21 to 2016 December 2. The spectra were used to determine the existence and possible origin of the magnetic field of HD 41641, as well as confirm some of the stellar parameters as determined by E16 . First of all, we confirm that HD 41641 is indeed magnetic, making it the fourth magnetic δ Sct star discovered to date. Through our subsequent analysis, we determined that a different rotation frequency than the one suggested by E16 fit the data more accurately. Switching from a frequency of 0.17756 to 0.3560 d −1 revealed a periodic variation in the magnetic field measurements and in the LSD Stokes I profiles. As a result, some of the other stellar parameters calculated by E16 , such as the inclination i , were no longer suitable and required recalculation. The new value for i was determined to be i = 22° ± 11° and the magnetic obliquity angle β, assuming a dipolar field, was found to be


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

ACKNOWLEDGEMENTS MRL is supported by a COFUND/Durham Junior Research Fellowship under EU grant 609412 and also by a Grant of Excellence from the Icelandic Research Fund (grant number 173929051). This work was carried out on the Dutch National e-Infrastructure with the support of SURF Cooperative. We would also like to thank Dr. Benjamin Oppenheimer for contributing his simulations of cold dark matter, without which we would not have been able to complete this project. DH is supported by the D-ITP consortium, a program of the Netherlands Organization for Scientific Research (NWO) that is funded by the Dutch Ministry of Education, Culture and Science (OCW). This work is supported by the Swiss National Science Foundation (SNSF). This project has received funding form the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation program (COSMICLENS: grant agreement No. 787886


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-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 B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O B-Telescope O O O B-ObservationalTechniques I-ObservationalTechniques O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-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 B-CelestialObject I-CelestialObject 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 B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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-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

In the second approach, as a consistency check, we performed an unconstrained fit by allowing for the bulge age to vary between 16.4 and 18.0 Gyr (on steps of 0.2 Gyr) and bulge iron abundance to vary between 0.10 and 0.16 dex (on steps of 0.02 dex) to account for the adopted uncertainties on the bulge properties. For the NSD, we explored the same ranges of age and iron abundance as for the constrained fit. The resulting best-fitting model requires a bulge with t bulge = 18.0 Gyr and [Fe/H] bulge = 0.16 dex and an NSD with t NSD = 3.2 Gyr and [Fe/H] NSD = 0.50 dex (Fig. 5 ). In both cases, we conclude that the NSD of NGC 1023 is much younger and more metal rich than the host bulge. The age of the NSD is well constrained, whereas the its iron abundance corresponds to the upper limit of the [Fe/H] range of the available SSP models. Without the knowledge of the light fraction of NSD, the age and metallicity of the NSD can be hardly recovered due to the degeneracy between these two parameters (see Sarzi et al. 2016 , for a discussion). 4 DISCUSSION AND CONCLUSIONS The structure and properties of the stellar population of the nuclear region of the interacting SB0 galaxy NGC 1023 were investigated through a detailed analysis of archival HST imaging and ground-based integral-field spectroscopy. The galaxy is known to host a highly inclined NSD (Faber et al. 1997 ; Sil'chenko 1999 ; Sarzi et al. 2006 ; Ledo et al. 2010 ). Moreover, the stars of the galaxy nucleus have significantly different chemical properties with respect to the surrounding bulge. They are younger, more metal rich, and have a higher magnesium overabundance (Sil'chenko 1999 ; McDermid et al. 2006 ; Kuntschner et al. 2010 ). In this paper, we derived the central surface brightness, scalelength, inclination, and position angle of the NSD of NGC 1023 in all the available broad-band HST images by assuming that it is an infinitesimally thin exponential disc. We applied the photometric decomposition method of Scorza Bender ( 1995 ) and adopted the algorithm by Morelli et al. ( 2004 , 2010 ), which we implemented for a better determination of the best-fitting parameters. The location and orientation of the NSD do not depend on the observed passband, as already observed for the few other NSDs for which a detailed multiband photometric analysis was performed (Krajnović Jaffe 2004 ; Morelli et al. 2010 ; Corsini et al. 2012 ) whereas the NSD appears more concentrated in the bluer image. We measured the light contribution of the NSD to the total luminosity of the galaxy L NSD / L T in the same concentric circular rings centred on the galaxy nucleus where the equivalent widths of the Lick/IDS line-strength indices were obtained from ground-based integral-field spectroscopy by Sil'chenko ( 1999 ). In the WFPC2/ F555W passband the NSD contributes a maximum of 6 per cent of the total luminosity within the innermost circular aperture ( R 0.65 arcsec), whereas all the galaxy light is given by the