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


O O B-Person I-Person O O O O B-Software O O O O O O O O O O O O O O O O B-Organization O B-Fellowship I-Fellowship I-Fellowship I-Fellowship O O B-Person O O B-Organization I-Organization I-Organization I-Organization O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization O O B-Grant I-Grant B-Person O B-Person O O O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O O O B-Organization I-Organization B-Organization B-Grant I-Grant O O B-Grant I-Grant O O O B-Organization O O O O O B-Organization I-Organization I-Organization I-Organization O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization O B-Grant I-Grant O O O O O O O B-Database I-Database I-Database B-Database O O O O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Telescope B-Instrument O B-Software B-Citation I-Citation O B-Software B-Citation I-Citation O B-Software B-Citation I-Citation I-Citation I-Citation O

We thank Peter Stetson for a copy of DAOPHOT as well as his helpful engagement on its usage. Support for this work was provided by NASA through Hubble Fellowship grant #51386.01 awarded to R.L.B. by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS 5-26555. M.G.L. and I.S.J. were supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (MSIP) No. 2017R1A2B4004632. Support for program #13691 was provided by NASA through a grant from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. 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. Facility: HST (ACS/WFC). Software: DAOPHOT (Stetson 1987 ), ALLFRAME (Stetson 1994 ), TinyTim (Krist et al. 2011 ).


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We thank the anonymous referee for his/her constructive comments that helped improve the paper. P.T. acknowledges support from NASA grant 80NSSC18K0408 (solicitation NNH17ZDA001N-ADAP). This work made use of data from the NuSTAR mission, a project led by the California Institute of Technology, managed by the Jet Propulsion Laboratory and funded by the National Aeronautics and Space Administration. This research made use of the NuSTAR Data Analysis Software (NuSTARDAS) jointly developed by the ASI Science Data Center (ASDC, Italy) and the California Institute of Technology (USA). This research has made use of data obtained from the Suzaku satellite, a collaborative mission between the space agencies of Japan (JAXA) and the USA (NASA). Facilities: Suzaku , NuSTAR .


O O O O O O B-Database I-Database I-Database B-Database O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization I-Organization I-Organization

ACKNOWLEDGEMENTS This research has used 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.


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We thank the referee for useful comments that helped to improve the manuscript. We also thank Prof. R. A. Chevalier and Dr D. Caprioli for critically reading the manuscript. MP acknowledges support for this work by NASA through Einstein Post-doctoral Fellowship grant number PF3 140113 awarded by the Chandra X-ray Center, which is operated by the Smithsonian Astrophysical Observatory for NASA under contract NAS8-03060.


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

that the outburst ejecta are comprising small and bright particles. The decrease of the colour temperature and colour shortly after the peak brightness suggests an increase of the mean particle size with time for the particles crossing VIRTIS FOV. The presence of silicatic grains devoid of organic material could be explained by the high grain temperatures causing sublimation of the organics. Quantitatively, the September 13 outburst data are consistent with the silicatic grain hypothesis. However, large colour temperatures (>600 K) are measured at the peak brightness of the September 14 outburst, whereas computed temperatures are 530 K for olivine grains. Several explanations are possible. First, we did not consider grains smaller than 100 nm in radius, whereas we cannot exclude their presence. These grains might reach higher temperatures than 100 nm grains, though this is not expected from model calculations (Lasue et al. 2007 ). In our model, 100 nm grains are compact ( P = 0). Considering instead that these grains are aggregates, their temperature would be higher than the temperature of the equivalent sphere (Xing Hanner 1997 ). Another possibility is that the spectral indices of amorphous olivine differ significantly from those of the refractory material of cometary grains. We performed Mie calculations with inclusions of FeS within an olivine matrix. For a volume fraction of 6 per cent of FeS consistent with the suggestion of Fulle et al. ( 2016a ) for 67P grains, the colour temperature reaches 575 K (Fig. 12 ), which is not far from the extremum values measured during the September 14 outburst. Could fractal agglomerates explain the outburst spectra? For carbon/amorphous olivine mixtures, the colour and colour temperature of their infrared spectrum match the measurement, but this is not the case for the bolometric albedo (Fig. 10 ). Calculations made for units of amorphous olivine provide a bolometric albedo 0.4, i.e. a factor of 2 below the measured values. During 67P outbursts, MIDAS collected a high amount of micrometric grains (Bentley, personal communication), in agreement with an ejecta population dominated by compact grains rather than aggregates. We performed calculations setting the maximum size of the fractal aggregates to a max = 1 μm, and the bolometric albedo is still 0.4. Finally, the main contributors to the scattered and thermal parts of the spectrum could be distinct populations of grains. Cold and bright grains would essentially contribute to scattered light, whereas this is the opposite for warm and dark grains made of strongly absorbing material. These two populations of grains were found in the outburst ejecta of the extraordinary outburst of comet 17P/Holmes in 2007 October ( r h = 2.45 au) (Yang et al. 2009 ). The near-IR spectra of the outburst ejectas showed strong absorption bands at 2 and 3 μm related to water ice (Yang et al. 2009 ). Infrared signatures of ice are not detected in the VIRTIS-H outburst


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NS thanks J. S. Gallagher for discussions regarding binary evolution and LBVs, and in particular for drawing our attention to previous work by N. King. We benefitted from discussion about SN host environments with P. Crowther, J. Anderson, and P. Kelly, and from further discussions concerning binary evolution with S. de Mink. We also thank the referee (J. Eldridge) for a careful reading and thoughtful comments that improved the paper. Partial support was provided by NSF award AST-1312221. This research has made use of the SIMBAD data base, operated at CDS, Strasbourg, France.


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We are very grateful for the warm reception and skillful help we have received from the staff of the Dominion Radio Astrophysical Observatory, which is operated by the National Research Council Canada. The CHIME/FRB Project is funded by a grant from the Canada Foundation for Innovation 2015 Innovation Fund (Project 33213), as well as by the Provinces of British Columbia and Quebec. Additional support was provided by the Canadian Institute for Advanced Research (CIFAR) Gravity Extreme Universe Program, McGill University and the McGill Space Institute, University of British Columbia, and University of Toronto Dunlap Institute. The Dunlap Institute is funded by an endowment established by the David Dunlap family and the University of Toronto. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Research Innovation. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. J.C. was supported by a Natural Sciences and Engineering Research Council of Canada (NSERC) Undergraduate Student Research Award. P.C. is supported by a Mitacs Globalink Graduate Fellowship. M.D. is supported by an NSERC Discovery Grant, CIFAR, and Fonds de Recherche du Québec—Nature et technologies Centre de Recherche en Astrophysique du Québec (FRQNT/CRAQ). B.M.G. is supported by an NSERC Discovery Grant and the Canada Research Chairs program. M.H. and G.H. are supported by CIFAR. V.M.K. is supported by a Lorne Trottier Chair in Astrophysics Cosmology, a Canada Research Chair, CIFAR, an NSERC Discovery Grant and Herzberg Award, and FRQNT/CRAQ. U.-L.P. is supported by CIFAR. K.W.M. is supported by the Canadian Institute for Theoretical Astrophysics National Fellows program. S.M.R. is supported by CIFAR and the NSF Physics Frontiers Center award 1430284. I.H.S. is supported by CIFAR and an NSERC Discovery Grant. P.S. is supported by a DRAO Covington Fellowship from the National Research Council Canada. Software: CHIME/FRB pipeline, alpenhorn (Hincks et al. 2015 ), bonsai (K. M. Smith et al. 2018, in preparation), Grafana ( grafana.com ), Prometheus ( prometheus.io ), RRATTrap (Karako-Argaman et al. 2015 ), PRESTO ( github.com/scottransom/presto ).


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Acknowledgements The authors thank the anonymous referee for his or her thorough review and comments, which contributed to improving the manuscript. The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013) / ERC Grant agreement No. 291058. This research was supported by the Research Council of Norway through the grant “Solar Atmospheric Modelling”. This research was supported in part with computational resources at NTNU provided by NOTUR, http://www.sigma2.no . Some computations were performed on resources provided by the Swedish National Infrastructure for Computing (SNIC) at the High Performance Computing Center North at Umeå University and the PDC Centre for High Performance Computing (PDC-HPC) at the Royal Institute of Technology in Stockholm. CHIANTI is a collaborative project involving George Mason University, the University of Michigan (USA) and the University of Cambridge (UK).


O O O O B-Wavelength B-Wavelength O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O B-Wavelength O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O B-Wavelength B-Wavelength O O B-Survey B-Wavelength I-Wavelength O O O O B-Wavelength O O O O O O O O O O O O B-Wavelength O O B-Survey B-Wavelength I-Wavelength O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O B-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-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O B-Telescope B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O B-Model I-Model I-Model B-Model O O O O O O O O O O O O B-URL O O B-Model I-Model O O O O O O O O O O O O O B-Model I-Model I-Model B-Citation I-Citation I-Citation I-Citation O O O O

occupy distinct regions of NUV– r space, and all share some overlap with SPOGs, suggesting that SPOGs are a heterogeneous group comprised of galaxies with different mechanisms for UV emission. In FUV–NUV (bottom panel of Figure 6 ), we find a similar trend, with SPOGs displaying a larger range in FUV–NUV colors compared to the star-forming sample. Once again the E + A, AGN, and interacting samples all share a similar color distribution as SPOGs, but seem to occupy distinct subregions. These plots suggest that UV emission in SPOGs may be an amalgam of the mechanisms that the comparison samples represent in different proportions. Future multiwavelength and high-resolution morphological analyses will clarify which individual SPOGs exhibit similar UV emission mechanisms to each comparison group. Figure 6. Top: k -corrected NUV– r color vs. SDSS i -band absolute magnitude ( M i ) of SPOGS (gray contours) and all comparison samples. Bottom: k -corrected FUV–NUV color vs. SDSS i -band absolute magnitude ( M i ) of SPOGS (gray contours) and all comparison samples. In both plots, the black stars are SPOGs that fall outside the outer contour. While most of the comparison samples fall within the color–magnitude space occupied by SPOGs, no single sample fully covers the SPOGs parameter space, suggesting that SPOGs may be composed of a combination of these samples. All contours are in increments of 10 percentiles of the maximum density. Figure 7 shows the cumulative distribution of FUV–NUV colors for SPOGs compared to each of the comparison samples. We used AD tests to compare the shapes of these 1D UV color distributions. For samples in the full range of masses, all samples, except the AGN sample, have statistically distinct color distributions from SPOGs with greater than 99% significance. The AGN sample is distinct from SPOGs at the 78% significance level. When restricting the comparison to a specific range of masses (−23 M i −21), all samples, except the interacting sample, have statistically distinct color distributions from SPOGs with greater than 99% significance. The interacting sample is distinct from SPOGs at the 85% significance level. This test shows that the differences in UV colors are not attributable to differences in stellar mass distribution. Figure 7. Cumulative distributions of GALEX FUV–NUV color for SPOGs and each of our comparison samples. With Anderson–Darling tests, we show that SPOGs are a distinct distribution from all other comparison samples, except AGN (see Section 3.1 ). 3.2. Mixture Models To further test which of the comparison samples contribute to the FUV–NUV colors of SPOGs and in what fractions, we used the method of Gaussian mixture models (GMMs) 20 20 We provide an example of our code and method at https://github.com/f-ardila/SPOGs-GMMs . . GMM models some underlying distribution whose true probability density function is unknown as the sum multiple Gaussian distributions (Ivezic et al. 2014 ). Here, we first


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O B-Instrument O O O O O O O O O O O O O O O O O B-Instrument O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

spectroscopic analysis. Results for 11 SB1 are shown as open circles. The atmospheric parameters we determined for 402 GK stars are presented in Table 1 (Cols. 69), where the numerical values of , , , and [Fe/H] are presented together with their intrinsic uncertainties. The values of resulting atmospheric parameters generally remain within the range of the TGVIT model grids. Figure 5 shows the relations between the atmospheric parameters presented in Table 1. We note that the results obtained for single-line spectroscopic binaries (SB1) agree very well with those for apparently single stars. The effective temperature lies between 4398 K and 6394 K with a median value of 5167 K. The distribution of , presented in Fig. 6 a, shows two maxima, one for giants (cooler) and one for subgiants (warmer), which are the two most numerous groups of stars in our sample. The intrinsic uncertainty distribution in is presented in Fig. 6 e. The gravitational accelerations for our sample range between 1.49 and 4.72 with a median of 3.65. The distribution of is presented in Fig. 6 b. We found that 5 stars have , 60 have , 277 have and 60 stars have . Most of our stars (194) have of which means that generally they are subgiants. The uncertainty distribution in is presented in Fig. 6 f. The microturbulence velocity, , reaches values from to and has a median at . Most of our stars have between and (Fig. 6 c). The uncertainty distribution in is presented in Fig. 6 g. The metallicity of the stars in our sample, [Fe/H], remains within the limit of to with a median value at . Most of our objects have [Fe/H] in the range of to . Figure 6 d presents the distribution, which clearly shows that our stars are mostly less metal abundant than the Sun. The uncertainty distribution in [Fe/H] is presented in Fig. 6 h. Fig. 6 Histograms of of , , , and [Fe/H] obtained for 402 stars with complete spectroscopic analysis. Results for 11 SB1 are shown in black. 3.6. Uncertainy estimates of the atmospheric parameters The mean intrinsic uncertainties of our determinations, that is, those delivered by TGVIT, are K, , , and [Fe/H] . Figure 7 shows the intrinsic uncertainties of these three parameters as a function of . No correlation exists between the uncertainties and the obtained parameter values for any of the atmospheric parameters in the wide range of between 4500 K6000 K. The scatter of the uncertainties is uniformly distributed over the whole range of resulting parameters. We note, however, that for stars with below 4500 K or above 6000 K the uncertainties are slightly higher, especially in and [Fe/H]. To test the effect of the shift in EWs between DAOSPEC and ARES measurements presented in Sect. 3.4 , we calculated stellar atmospheric parameters for the same five stars using DAOSPEC and ARES EWs separately. We obtained agreement within 1 intrinsic in all parameters except for the microturbulence velocity, in which the results differ by 23 intrinsic . We therefore assume that


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 changing our results. We stop our pure infall models earlier than , as these runs require much more computing time than our standard runs. However, this should not greatly affect our analysis, as the behaviour of these runs is clear and is unlikely to change significantly in the period between t final and 1000 yr. In the pure infall realizations only one sink forms and grows rapidly via accretion, reaching a mass of over in only ∼100 yr. In contrast, all of the other runs show considerable fragmentation within the first 1000 yr, forming anywhere between 15 and ∼120 sinks. The total mass in sinks (M tot ) and the total number of sinks (N tot ) in each realization at the final output time is listed in Table 3, and time evolution of these quantities is shown in Figs 2 and 3 , respectively. In addition, Fig. 4 shows some illustrative examples of the evolution of some of our realizations. The difference in behaviour that we see between the pure infall runs and the other runs occurs because the pure infall runs are the only ones in which no disc forms over the course of the simulations. Some non-zero angular momentum arises during the gravitational collapse but is too small to trigger the formation of a disc. In all of the other runs 3 a dense, gravitationally unstable accretion disc forms which soon fragments. Figure 2. Total mass in sinks as a function of time after the first sink is created. Each panel shows the results for the five different realizations of each setup. Increasing the initial turbulent or rotational energy tends to systematically decrease the total mass in sinks at any given time. We also see that there is significant variation from simulation to simulation for all of the setups with non-zero initial turbulence, but not for the setups with non-initial turbulence. Figure 3. Total number of sinks as a function of the time elapsed after the formation of the first sink. The colour scheme is the same as in Fig. 2 . We see that the number of sinks that form varies substantially from simulation to simulation for all of the setups. A colour version is available online. Figure 4. Column density plots (two top rows: x – y plane of the simulation box; two bottom rows: x – z plane of the simulation box) of the evolution of realization β01 – 1, α005 – 5, and α025β001 – 3. In the purely rotational runs, the protostellar disc lies in the geometrical x – y plane of our simulation box during the whole of the simulation, as demonstrated here for run β01 – 1. In all runs including turbulence, however, the orientation of the disc varies strongly over time. The projections are centred on the centre of mass of both sink particles and gas within a 500 AU radius around the most massive sink particle at the time of the snapshot considered. The projection thickness is about half the size of our simulation box (), the distance between the position of the first sink and the edge of the simulation box. In our plots of the evolution of the total mass


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

ACKNOWLEDGEMENTS This work is based on observations obtained with the Southern African Large Telescope (SALT), programmes 2010-1-RSA-OTH-001 and 2018-1-MLT-008, and supported by the Russian Foundation for Basic Research grant 19-02-00779. AYK acknowledges support from the National Research Foundation (NRF) of South Africa. LMO acknowledges partial support by the Russian Government Program of Competitive Growth of Kazan Federal University. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France.


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

for the sample of velocity-selected clusters. As in Fig. 5 , θ is the acute angle between the projected major axis of each galaxy and that of the cluster in which it resides. Cluster position angles were determined from moments of inertia of the projected galaxy distribution. The Kuiper V, Rao, and binomial statistical tests all indicate a probability that the observed distribution of angles is consistent with random BCG orientations. Figure 9. BCG alignments as a function of peculiar velocity. Here, Δ V BCG /σ is the absolute difference between the BCG’s velocity and the mean cluster velocity, and σ is the cluster velocity dispersion. 4 DISCUSSION The main findings of this paper are: A significant fraction of BCGs have spatial offsets of a few tens of kpc or more from the centroid of the X-ray light distribution that presumably traces the centre of the DM halo and reflects the cluster’s dynamical state. Compared with theoretical models, these offsets are much larger than the expected ‘wobble’ around the centre of a standard CDM halo (2 kpc versus a few tens of kpc) as in the simulations of Kim, Peter Wittman 2017 ; Harvey et al. 2017 ). However, the X-ray gas may not trace the DM halo distribution (e.g. by gas sloshing, etc.) A significant number of BCGs also have significant line-of-sight peculiar velocities relative to the cluster. These observations suggest that many BCGs are not currently at rest in the potential well of their host cluster. Despite the prevalence of BCG displacements, these galaxies still show a strong tendency to share the same orientation as the cluster in which they reside (cf. Tempel, Stoica Saar 2013 , a remarkably robust coherence of structures over scales from tens to thousands of kpc, as suggested by the simulations of Rhee et al. 2017 ). 4.1 Comparison of observations with simulations The computation of the cluster and BCG elongation axes is done as in Ragone-Figueroa et al. ( 2020 ). They are obtained from the principal axes of the ellipsoids that best describe the corresponding distribution of matter. For the purposes of this work cluster principal axes and centre of mass are obtained using DM particles within r 200 . While for obtaining BCG principal axes we use star particles inside 0.1 r 500 . Fig. 10 shows the distributions of BCG offsets in position and velocity as well as their correlations with the BCG–cluster alignment angle, in full 3D space (four left-hand panels) and in projection and radial velocity (four right-hand panels). We find in simulations galaxies with significant offsets, in projected space the mean(median) offset is ∼53 kpc(78 kpc), which is larger that the mean found in the observational data (∼15 kpc). Conversely, the mean(median) normalized 1D BCG velocity | V BCG /σ| (with respect to the cluster mean) is ∼0.09(0.07), which is lesser than in the data (0.26). The maximum Δ V /σ in these simulations is lower than that observed because of the smaller number of simulated cluster samples.


O O O O O O O O O O O O O O O O O O O O O O B-Person I-Person O O O O O B-Person O O O O O B-Grant O O O O B-Organization O O O O O B-Organization I-Organization I-Organization I-Organization O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization O B-Grant O O O O O O B-Organization I-Organization I-Organization O O O O O O O B-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O O O O O O O O O O O O O B-Survey I-Survey O O O O O B-Organization I-Organization I-Organization I-Organization O B-Location B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O O B-Survey O O O O O O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility O O B-Organization I-Organization I-Organization O B-Survey O O O B-URL O B-Survey O O O O B-Collaboration I-Collaboration I-Collaboration O O O O O O B-Collaboration I-Collaboration O O B-Collaboration I-Collaboration I-Collaboration O B-Organization I-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 I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization B-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 B-Organization B-Organization I-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization B-Organization I-Organization I-Organization B-Organization B-Location B-Organization I-Organization I-Organization B-Organization B-Location B-Organization I-Organization I-Organization I-Organization B-Organization B-Observatory I-Observatory I-Observatory I-Observatory I-Observatory B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization B-Observatory I-Observatory B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Observatory I-Observatory I-Observatory B-Collaboration I-Collaboration I-Collaboration I-Collaboration B-Organization I-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 I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization O B-Organization I-Organization

Acknowledgments We thank the reviewer for their valuable and constructive feedback which greatly contributed to the quality of this paper. We thank Greg Snyder for useful discussions and input. PT acknowledges support for Program number HST-HF2-51384.001-A that was provided by NASA through a grant from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Incorporated, under NASA contract NAS5-26555. This research made use of a University of Victoria computing facility funded by grants from the Canadian Foundation for Innovation and the British Columbia Knowledge and Development Fund. We thank the system administrators of this facility for their gracious support. Funding for the SDSS IV has been provided by the Alfred P. Sloan Foundation, the US Department of Energy Office of Science, and the Participating Institutions. SDSS-IV acknowledges support and resources from the Center for High-Performance Computing at the University of Utah. The SDSS web site is www.sdss.org . SDSS-IV is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS Collaboration including the Brazilian Participation Group, the Carnegie Institution for Science, Carnegie Mellon University, the Chilean Participation Group, the French Participation Group, Harvard-Smithsonian Center for Astrophysics, Instituto de Astrofsica de Canarias, The Johns Hopkins University, Kavli Institute for the Physics and Mathematics of the Universe (IPMU)/University of Tokyo, Lawrence Berkeley National Laboratory, Leibniz Institut fr Astrophysik Potsdam (AIP), Max-Planck-Institut fr Astronomie (MPIA Heidelberg), Max-Planck-Institut fr Astrophysik (MPA Garching), Max-Planck-Institut fr Extraterrestrische Physik (MPE), National Astronomical Observatory of China, New Mexico State University, New York University, University of Notre Dame, Observatrio Nacional/MCTI, The Ohio State University, Pennsylvania State University, Shanghai Astronomical Observatory, United Kingdom Participation Group, Universidad Nacional Autnoma de Mxico, University of Arizona, University of Colorado Boulder, University of Oxford, University of Portsmouth, University of Utah, University of Virginia, University of Washington, University of Wisconsin, Vanderbilt University and Yale University.


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 O O O B-Location B-Organization B-Organization O B-Organization B-Person O B-Organization O O B-Fellowship I-Fellowship I-Fellowship I-Fellowship O O B-Organization O B-Grant O O O O O O O O O B-Organization I-Organization I-Organization B-Organization O B-Telescope O B-URL O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization B-URL O O O O B-Organization O O O O O O O O O O O O O B-Collaboration I-Collaboration I-Collaboration O O O O O O O O O O B-ComputingFacility I-ComputingFacility I-ComputingFacility B-Organization B-Organization O O B-Organization O B-Grant O B-Organization


O O O O O O O O O O B-Software B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Dataset I-Dataset O O O O O O B-Dataset I-Dataset O O O O O O O B-Software O B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O B-Survey B-Citation I-Citation O B-Citation I-Citation O O O O O O O B-Software B-Citation I-Citation I-Citation I-Citation O O O O O O B-Software B-Citation I-Citation I-Citation I-Citation O O B-Formula I-Formula I-Formula O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O B-Dataset I-Dataset O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O B-Software O O O O O O O B-Formula I-Formula I-Formula O B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O O O O O B-Wavelength O B-Wavelength O B-Wavelength O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey O O O B-Wavelength O O O B-Instrument O O O B-Database I-Database I-Database I-Database I-Database O O O O O B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O B-Software O O B-Survey O O O O O O O O O O O O O B-Dataset I-Dataset O O O O O O O B-Identifier O B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-URL O O O O O O O O B-Software O O B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O B-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-Dataset I-Dataset O O O O O O O O O O O O O O O O O O B-Software O O O


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

We thank M.M. Romanova for valuable discussions and an anonymous referee for valuable comments. This work was supported in part by NASA grants NNX11AF33G and NSF grant AST-1211318.


O O O O O O O B-Person I-Person O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O B-Person O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization

ACKNOWLEDGEMENTS The authors would like to thank Jim Hinton for useful discussions and help during the production of the paper. The authors would also like to thank the HAWC collaboration for useful discussions. The research of GG was supported by a Grant from the GIF, the German-Israeli Foundation for Scientific Research and Development.


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

Again we note that has a small constant component, , in the direction of the body frame and a big one of modulus describing a circle in the plane of the body frame. The angular velocity in the body frame is given by It follows from Eqs. ( 3 )and ( 5 )that . Since the main axis, , of the ellipsoid is much greater than the other axes, and , we find that . Moreover, for low values of , , and therefore is also small. Finally let us note that when , then and both, angular momentum and the angular velocity are aligned on the axis. Since the angular momentum, , is preserved in an inertial reference frame, we take the inertial system so that the axis is aligned with . The major axis of the bar has to keep an angle with respect to , and then also measures the angle between the main axis of the bar and the plane of the inertial reference system. For this reason, from now on, it will be referred to as the tilt angle of the motion of the bar (see bottom panel of Fig. 2 ). In the inertial frame the major axis of the bar describes a cone about the axis, while and are slightly misaligned since the bar is also rotating about its major axis. When , the major axis of the bar rotates inside the plane, there is no rotation of the bar about its major axis, and and are again aligned. We define now a new non-inertial reference frame henceforth called the precessing reference system. In this reference frame, the axis is aligned with the major axis of the bar, but the bar is not fixed as in the body frame but rotating around the axis. In the body reference system, the angular momentum and angular velocity vectors rotate around the main axis of the bar ( axis in the body frame) with angular speed . The precessing reference frame rotates with respect to the body frame about the axis they share. This is, these frames are related by means of a time-dependent rotation of axis and angular velocity , in such a way that and are constant in the precessing reference system, with values of We are interested in the equations of motion of our galactic model in the precessing reference frame. To compute them, we need the angular velocity of the precessing frame with respect to the inertial one. This angular velocity, , is the sum of the angular velocity of the body, , and the angular velocity of the body axes in the precessing frame. Therefore, and taking the value of into account, we obtain where (see Chapter 2 of Sánchez-Martín 2015 for more details about the rotations). Finally, as a complement, we briefly discuss the motion of the bar in the inertial frame. According to Poinsot’s theorem (see Arnold 1989 ), the bar, which is described by an ellipsoid, rolls without slipping on a fixed plane normal to the angular momentum . If the ellipsoid has axial symmetry, as in our case, this motion is the superposition of a rotation of the ellipsoid along its symmetry axis with constant angular velocity, , and a precession with constant pattern speed around the axis of the angular momentum.


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


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

It is our pleasure to thank Rich Plotkin, Eric Bell, Kayhan Gültekin, and Jenny Greene for very helpful discussions. We also thank the anonymous referee for useful comments and suggestions. Support for AER was provided by NASA through Hubble Fellowship grant HST-HF2-51347.001-A awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS 5-26555. M.V. acknowledges funding from the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013 grant agreement No. 614199, project “BLACK”).


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

Since the Monte Carlo simulations described in step (2) are time consuming, we first constrained the parameter space of interest by testing a wide range of (⟨ β ⟩, rms( β )) values on a coarse sampling of the ranges ⟨ β ⟩ = − 2.2, − 1.0 and rms( β ) = 0.1, 1.5. We then accurately constrained their best-fit and confidence range through the analysis of a 35 × 35 grid in the range ⟨ β ⟩ = − 2.0, −1.4 for both the Gaussian and log-normal distributions, and rms ( β ) = 0.4, 0.8 (for the Gaussian distribution) and rms( β ) = 0.4, 1.0 (log-normal). For each position in the grid and for each magnitude bin, we extracted 25 000 objects from the CB07 library and perturbed magnitudes in all bands as described in 3). We note that the estimate of L in step (4) requires the observed and simulated UV slopes distributions to be binned: the choice of the bin widths was tailored to ensure that the extended but poorly populated tails in the observed distributions are efficiently sampled by the simulations. As shown in Fig. 5 , different bin widths were thus set depending on the 1, 2, 3 σ ranges of the observed distribution so as to reduce numerical noise in our procedure. The best-fit parameters of the Gaussian and log-normal PDF( β ) in each magnitude bin are reported in Table 2 . Confidence regions for the PDF( β ) are shown in Fig. 6 , together with observed and best-fit distributions. It is also highlighted how the latter (blue lines) are reshaped by observational effects (red): only a full modelling approach such as presented in C12 and adopted in this work allows us to recover the intrinsic slope distributions from observations. Table 2. UV slope distribution: best-fit parameters and 68% c.l. uncertainties. Fig. 6. Simulation results for the Gaussian ( left panel ) and log-normal ( right panel ) fit in the two different magnitude bins. In the leftmost column , we show maximum likelihood contours at 68%, 95%, and 99% c.l. in green, blue, and red, respectively; the red cross indicates the position of the best fit parameters. The rightmost column shows the histogram of the observed data and the relevant best-fit distribution. The red continuous line is the intrinsic PDF( β ), which is transformed into the blue continuous line by observational effects. We find that L > L * objects at z ∼ 3 have typical, average UV slopes ∼ − 1.7. No significant variation with UV magnitude is found in the Gaussian case. The log-normal best-fit distributions point to a slightly redder average (∼ − 1.5) in the fainter bin, although with large correlated uncertainties between the parameters. The absence of a strong correlation between UV slope and magnitude is in agreement with what was found by C12 at z ∼ 4, but it disagress with the previous analysis of z ∼ 3 objects by Bouwens et al. (2009) . While it is not possible to determine whether the best assumption is the Gaussian or the log-normal shapes, we note that the latter does not seem to accurately recover objects in the (poorly


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

that an analytic continuation of B ( c ) to the lower half-plane c , apart from poles of Landau quasi-modes, contains also a pole due to the damped mode c = c − , and near this pole B ( c ) has the form: where For real c , expression ( 23 ) can be decomposed, with the aid of equation ( 21 ), as follows: where Now analytic continuation is obvious, since ε ± ( c ) can be replaced by off the real axis, and g ± are replaced by where, depending on signs ‘’ or ‘’, integration contour passes below or above the singularity at u = c . Note that i.e. this is a decomposition of function g (). Since has one zero in the lower half-plane c = c − , B − ( c ) has a pole at this point leading to ∝exp (− γ k t ) contribution to density decay. Expansion near c = c − gives Finally, substitution to leads to the desired result ( 35 ), if we choose the integration contour along the real u -axis. The input from this pole gives a density decay slower that the Landau damping for k > k * ≈ 0.437, as is seen in Fig. 8 . Note that decomposition ( 37 ) is not unique. Moreover, it is possible to decompose B ( c ) so that parts of new decomposition have no singularities in the upper/lower half-planes (Appendix B ). Gaussian in time density decay occurred for Maxwell B ( c ) (Fig. 6 ) is simply a reflection of the fact that B ( c ) has no singularities in the lower half-plane. 4.3 Power-law decay To understand an appearance of the power-law term (Fig. 7 ), we should re-examine derivation of equations ( 7 ) and ( 8 ). They are obtained as a result of analytic continuation of the integrals over the real u -axis by deformation of the integration contour to the lower half-plane. Since g () is zero for || > * , the cut in the complex plane is finite (Fig. 10 ), and deformation of the contour is not needed for this integral. On the either side of the cut The cut leads to an additional input to density ( 6 ): Integrating by parts, assuming g () is even and real, one obtains for large t : Expression in the square brackets gives sinusoidal oscillations with some phase shift due to the presence of in the denominator. If g ( * ) is small, the power-law decay reveals itself only after a while. Figure 10. Integration contour in ( 6 ) in the complex -plane (blue dashes). ‘+’ signs mark the Landau-damped quasi-modes obtained as zeros of . A wavy line marks the cut on real axis c : − * c * . 5 IMPLICATIONS In this article, we analysed numerical solutions of equations describing perturbations of the homogeneous stellar medium. Although the equilibrium state is problematic in the infinite media and invokes a so-called Jeans swindle (e.g. BT ), it is a good testing ground for many phenomena in stellar dynamics (see Bisnovatyi-Kogan Zel’dovich 1971 , for example of a more realistic set-up). The unexpected behaviour of damped solutions in the unstable domain is associated with the presence of a genuine damped mode, which is complex conjugate to the unstable Jeans mode. The damped mode cannot


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

ACKNOWLEDGEMENTS We would like to thank the anonymous referee for a constructive report that helped to improve the paper. The authors would like to thank the Klaus Tschira Foundation. SJ acknowledges funding by the graduate college Astrophysics of cosmological probes of gravity by Landesgraduiertenakademie Baden-Württemberg. SJ also acknowledges support by the IMPRS for Astronomy and Cosmic Physics at the University of Heidelberg. RP, CMS and VS acknowledge support through the European Research Council under ERCStG grant EXAGAL-308037. VS also acknowledges support through subproject EXAMAG of the Priority Programme 1648 ‘Software for Exascale Computing’ of the German Science Foundation. CP acknowledges support through the European Research Council under ERC-CoG CRAGSMAN-646955.


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

of the AM CVn (= SDSS J120841.91+355024.8), two polars (AR UMa in a low state and AP CrB in a high state), and three dwarf novae of the sub-types U Gem, SU UMa, and WZ Sge (= GY Cnc, BZ UMa, and EZ Lyn, respectively) were obtained from SDSS DR16 (Ahumada et al. 2020 ). CV subtypes : The CV Gold Sample contains examples of all six major different sub-types, their respective numbers are listed in Table 4 . The different sub-types form clearly distinct clusters in the Gaia HR diagram (Fig. 8 , left-hand panel); 6 and the location of these clusters closely links to the spectro-photometric properties of each sub-type (Fig. 8 , right-hand panel). Table 4. The number of each type in the CV Gold Sample together with the range of their orbital periods. The novalike variables are characterized by stable high mass transfer rates and hot accretion discs that dominate the optical emission of these systems. Correspondingly, their cluster is located at small absolute magnitudes and blue colours. Two AM CVn stars, HP Lib and the prototype AM CVn itself (Faulkner, Flannery Warner 1972 ) are novalike variables with stable, hot helium discs that are somewhat bluer and fainter than their cousins with hydrogen-rich discs. The three sub-classes of dwarf novae exhibit clear trends in their location within the HR Diagram. The U Gem type dwarf novae have lower mass transfer rates than the novalike variables, their quiescent discs are therefore less luminous and their donor stars can contribute noticeably to the optical flux of the systems, which is reflected in the number of these systems being located close to the main sequence. The donors and accretion discs in the SU UMa systems are less luminous than those in U Gem-type dwarf novae, hence they are concentrated closer to the white dwarf cooling sequence. Finally, the WZ Sge type dwarf novae have the dimmest accretion discs and donor stars; in fact, some of them contain brown dwarf companions (GD552 Unda-Sanzana et al. 2008 ; QZ Lib (Pala et al. 2018 ), 1RXS J105010.3–140431 (Mennickent et al. 2001 ), SDSS J102905.21+485515.2 (Thorstensen, Alper Weil 2016 ), SDSS J143317.78+101123.3 (Hernández Santisteban et al. 2016 ), and SSS J122221.7–311525 (Neustroev et al. 2017 )). WZ Sge are therefore inherently the faintest CVs and merge into the white dwarf cooling sequence. A noticeable outlier among the dwarf novae is V1129 Cen, a long-period (≃21.4 h) CV that exhibits low-amplitude (≃0.6 mag) outbursts about once per year, but no emission lines are detected in its spectrum (Bruch 2017 ). The donor is a luminous F-type+ star, explaining the location in the HR diagram. Magnetic CVs have a larger spread due to their more varied spectral appearances. During states of low mass transfer they resemble the detached WD+M binaries whilst during high states, their optical spectra can contain cyclotron emission lines (Wickramasinghe 1988 ) that will affect their colour and absolute magnitude. Overall, the CV Gold Sample contains a


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R.K. acknowledges support from STFC via ST/L000709/1. J.P. and R.K. acknowledge comments from J. Anderson and C. Gutiérrez on an earlier version. L.D. acknowledges financial support from “Agence Nationale de la Recherche” grant ANR-2011-Blanc-SIMI-5-6-007-01. This work was partly supported by the EU/FP7 programme via ERC grant number 320360 awarded to G. Gilmore. AG-Y’s team is supported by the EU/FP7 via ERC grant no. 307260, the Quantum Universe I-Core program by the Israeli Committee for planning and budgeting and the ISF; by Minerva and ISF grants; by the Weizmann-UK “making connections” program; and by Kimmel and ARCHES awards. S.J.S. acknowledges funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC Grant agreement no [291222] and STFC grants ST/I001123/1 and ST/L000709/1. S.B. is partially supported by the PRIN-INAF 2014 project Transient Universe: unveiling new types of stellar explosions with PESSTO. Support for L.G. is provided by the Ministry of Economy, Development, and Tourism’s Millennium Science Initiative through grant IC120009, awarded to The Millennium Institute of Astrophysics, MAS. L.G. acknowledges support by CONICYT through FONDECYT grant 3140566. M.S. acknowledges support from the Royal Society and EU/FP7-ERC grant number 615929, and STFC via ST/L000679/1. K.T. was supported by CONICYT through the FONDECYT grant 3150473, and by the Ministry of Economy, Development, and Tourism’s Millennium Science Initiative through grant IC12009, awarded to the Millennium Institute of Astrophysics, MAS. This work is based (in part) on observations collected at the European Organisation for Astronomical Research in the Southern Hemisphere, Chile as part of PESSTO, (the Public ESO Spectroscopic Survey for Transient Objects) ESO programme 188.D-3003/191.D-0935, and as part of programme 092.D-0586. This work utilises data from the 40-inch ESO Schmidt Telescope at the La Silla Observatory in Chile with the large area QUEST camera built at Yale University and Indiana University. The Liverpool Telescope is operated on the island of La Palma by Liverpool John Moores University in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias with financial support from the UK Science and Technology Facilities Council (proposal ID: PL12B05, P.I. R. Kotak). The William Herschel Telescope is operated on the island of La Palma by the Isaac Newton Group in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias (programme W/2013A/20). 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.


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I thank M. Debruyne for many years of technical support at the Elginfield Observatory where the observations were taken and also thank the student observers who took some of the observations. I am grateful to the Natural Sciences and Engineering Research Council of Canada for financial support.


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example, Ganeshaiah Veena et al. ( 2021 ) have shown that massive haloes whose spin is perpendicular to the filament spine rotate on average faster (i.e. have higher spins) than haloes with spins along the filament spine. A similar effect has been pointed out by López et al. ( 2019 ), who have shown that the haloes which experienced the largest amount of spin growth are also more likely to have spin orientations perpendicular to the filaments surrounding them. 5.1 Net angular momentum growth of haloes Here, we follow the López et al. ( 2019 ) approach and define the net spin growth as the ratio between the present-day spin, , and the proto-halo spin, , in the initial conditions, which we take as the matter distribution at redshift z = 80. This definition is motivated by the TTT framework, in which the angular momentum at some time is the initial spin times a time-dependent growth factor (see equation 1 ). Thus, within the TTT approach, the net spin growth is basically the above growth factor. López et al. have shown that haloes with high ratios for their mass are more likely to have collapsed later and thus followed the TTT predictions for longer. This observation holds for the population as a whole, however not necessarily for individual haloes which could have a high ratio due to non-linear effects boosting their late-time spin growth. To keep the analysis simple, we follow the López et al. classification and for each narrow bin in mass we divide the halo population into three subsamples corresponding to the haloes with: highest, medium, and lowest net spin growth. We abbreviate these subsamples as H, M, and L, respectively. Each category corresponds to exactly a third of the haloes in each halo mass bin. This nomenclature is slightly different from the one used in López et al. ( 2019 ), where the same categories are referred as winner (W), median (M), and loser (L). Here, we decide to change the names of the samples (and the abbreviation of the one with the highest net spin growth, W→H) in order to better highlight their properties and the motivation of the classification. This analysis is illustrated in Fig. 8 , where the top panel show the net spin growth, , for individual haloes as a function of their mass. It shows that the ratio increases systematically with halo mass and illustrates why the H, M, and L subsamples need to be selected using narrow mass bins. The selection is further depicted in the bottom left-hand panel in Fig. 8 , which shows the distribution of net spin growth for a narrow mass bin. While most haloes have a narrow range in values, which for the given mass bin cluster around , the distribution has extended wings with a considerable fraction of haloes with ratios an order of magnitude higher or lower. The three subsamples, each containing a third of the haloes, are shown in the panel by the three shaded regions. Figure 8. Top panel: the halo net angular momentum growth (i.e. the present-day angular momentum divided by


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also provide viable explanations. In any case, the transit of a more extended cloud of material, whether associated with a planet or not, might be more easily detectable. About 20 ks into the XMM-Newton observation (Fig. 2 ), the soft-band count rate drops by ≈35% for ≈800 s, i.e., two data points. This timescale is consistent with the occultation of a point-like source by the hypothesized planetary body of CVSO 30 b. However, the lack of an associated depression in the hard-band light curve makes an eclipse by a solid planetary disk unlikely. A temporary elevation in the absorption column by 10 21 cm −2 (e.g., caused by the transit of an extended planetary atmosphere) produces a count rate drop of 60% in the soft band with only a 10% drop in the hard band. Such a scenario would thus be compatible with the observation. By means of a Student’s t-test, we find that the mean of the two data points in question differs from that of the sample consisting of the two preceding and following points at the 2% significance level. As the ephemerides are uncertain, however, we count about ten similar opportunities during the flare where such an occultation may have happened and be interpreted in the same way. Therefore, the chance to obtain such a result by chance is about 20%, and we conclude that the data remain insufficient to produce a significant result. The hard-band light curve shows an apparent depression about 25 ks into the XMM-Newton observation (Fig. 2 ). This variation has no counterpart in the soft-band light curve, however, and might be more easily explained by the superposition of two flares or secondary heating rather than absorption or occultation of flaring material. 3.4. Planetary irradiation and mass loss Having measured the stellar X-ray flux, we now estimate the expected mass-loss rate of the candidate hot Jupiter CVSO 30 b to see whether such a configuration is physically plausible. A number of values have been proposed for the mass of CVSO 30 b (e.g., Barnes et al. 2013 ; Ciardi et al. 2015 , or Johns-Krull et al. 2016 ). These range from approximately one to seven Jovian masses. We assume here a stellar mass of 0.44 M ⊙ , a planetary mass of 3.9 M J , and a planetary radius of 1.61 R J . These values are based on those given in Table 1 . To remain on the conservative side regarding the planetary mass-loss rate, we increased the nominal mass estimate in Table 1 by its uncertainty and decreased the radius likewise. Both choices increase the assumed planetary density and inhibit mass loss. Kepler’s third law then demands a semimajor axis, a , of 0.00874 AU. The resulting Roche-lobe geometry is shown in Fig. 4 . The shape of the planetary candidate CVSO 30 b is determined by an equipotential surface, the level of which is given by the radius derived from transit modeling. The result clearly demonstrates the expected deviation from spherical geometry. Fig. 4. Roche lobe (solid line) and extent (blue shade) of planetary candidate CVSO


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first mechanism does not necessarily lead to an immediate terminal SN explosion, it may explain the three-decade-long eruptive phase of SN 2000ch ( Pastorello et al. 2010 ). The second mechanism is promising as it may reproduce the sequence of events leading to SN 2009ip and its subsequent evolution (e.g. Graham et al. 2017 , and references therein). Alternatively, mass loss, driven by waves generated in the convective core during the late nuclear burnings, has also been proposed for moderate-mass ( M ZAMS ∼ 20 M ⊙ ) stars and for very massive stars at low-metallicity regime. This would explain the violent mass ejections observed in some SNe IIn from a decade to a few months prior to core-collapse ( Quataert Shiode 2012 ; Shiode Quataert 2014 ). The modern strategy of SN searches and the availability of big data archives have increased the discoveries of pre-SN outbursts, but the number of events is still of the order of a few tens, and is limited in volume. Future SN searches with big telescopes, in particular the Large Synoptic Survey Telescope ( LSST Science Collaboration 2009 ), will enormously increase the discovery rates, and will provide us with valuable datasets of light curves with coverage of many years. Appendix A: Optical photometry of SN 2018cnf Table A.1. Optical photometry of SN 2018cnf: Johnson-Bessell B , V (Vega mag), Sloan u , g , r , i , z and PanSTARRS y (AB mag). Notes. PS1 = 1.8 m Pan-STARRS Telescope + GPC1 camera (Haleakala, Hawaii Islands, USA); ATLAS = 0.5 m ATLAS-1 Telescope + STA-1600 CCD (Haleakala, Hawaii Islands, USA); ASAS-SN-5 = 0.16 m Payne-Gaposchkin Telescope + FLI ProLine PL230 CCD (Las Cumbres Observatory – South African Astronomical Observatory); ASAS-SN-3 = 0.16 m Paczyński Telescope + FLI ProLine PL230 CCD (Las Cumbres Observatory – Cerro Tololo Inter-American Observatory, Chile); GTC = 10.4 m Gran Telescopio Canarias + OSIRIS (La Palma, Canary Islands, Spain); LT = 2.0 m Liverpool Telescope + IO:O (La Palma, Canary Islands, Spain); fl11 = 1.0 m Telescope (Dome 3) + Sinistro CCD (Las Cumbres Observatory – Siding Spring Observatory, Australia); fl16 = 1.0 m Telescope (Dome 5) + Sinistro CCD (Las Cumbres Observatory – South African Astronomical Observatory); fl03 = 1.0 m Telescope (Dome 4) + Sinistro CCD (Las Cumbres Observatory – Cerro Tololo Inter-American Observatory, Chile); fl15 = 1.0 m Telescope (Dome 2) + Sinistro CCD (Las Cumbres Observatory – Cerro Tololo Inter-American Observatory, Chile); fl06 = 1.0 m Telescope (Dome 7) + Sinistro CCD (Las Cumbres Observatory – South African Astronomical Observatory); fl12 = 1.0 m Telescope (Dome 8) + Sinistro CCD (Las Cumbres Observatory – Siding Spring Observatory, Australia); Copernico = 1.82 m Copernico Telescope + AFOSC (Mt. Ekar, Asiago Observatory, Italy); NTT = 3.58 m New Technology Telescope + EFOSC2 (ESO-La Silla, Chile); NOT = 2.56 m Nordic Optical telescope + ALFOSC (La Palma, Canary Islands, Spain). ( ‡ ) PanSTARRS w band converted to Sloan r ,


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MVCD thanks his scholarship from FAPESP (process number 2014/18632-6). LSJ acknowledges the support of FAPESP (2012/00800-4) and CNPq to his work. This work was supported in part by the Consejo Nacional de Investigaciones Científicas y Técnicas de la República Argentina (CONICET), Secretaría de Ciencia y Tecnología de la Universidad de Córdoba and Secretaría de Ciencia y Tecnologíca de la Universidad Nacional de San Juan. 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, 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. This work has made use of the computing facilities of the Laboratory of Astroinformatics (IAG/USP, NAT/Unicsul), whose purchase was made possible by the Brazilian agency FAPESP (grant 2009/54006-4) and the INCT-A.


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We thank the referee for very helpful comments to improve the presentation of the paper. Y.P.L., H.L., and S.L. gratefully acknowledge the support by LANL/CSES and NASA/ATP. Simulations of this work were performed with LANL Institutional Computing resources. H.L. gratefully acknowledges useful discussions with S. Ida, R. Miranda, and R. Rafikov. Software: Astropy (Astropy Collaboration et al. 2013 ), LA-COMPASS (Li et al. 2005 , 2009a ), Matplotlib (Hunter 2007 ), Numpy (van der Walt et al. 2011 ), RADMC-3D (Dullemond et al. 2012 ).