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

variables to their conservative form and back (using the Newton–Raphson-based root-finder of Noble et al. 2006 for the conservatives-to-primitives step, as described next). The detailed Jupyter notebook used to generate needed GRHD equations in MANGA may be found in the NRPy+ github repo 4 or be viewed directly via nbviewer . 5 Before proceeding, we note two important points. Previously, MANGA used only cgs units, but for GR, G = c = 1 units are superior so the code was extended to support them. Second, although our MM code is limited to periodic boundary conditions, no boundary conditions are applied to the metric (as it is static and known), so there is no ‘periodic gravity.’ We simply ensure that the outer boundaries of our numerical domain are sufficiently far away from regions of interest, so that as outer (periodic) boundary conditions are applied to the hydrodynamic variables, they have little to no effect on the simulation. In future work, we may as needed adopt radiation inflow and outflow boundary conditions as described in Chang et al. ( 2020 ) to the hydrodynamic variables on the boundary, to produce arbitrary boundary conditions. We note that this implementation would be similar to the boundary conditions for a ‘sphered cube’ (Burns et al. 2020 ). 3.1 Time-stepping We time integrate equation ( 9 ) as follows: Estimate the Courant-limited time-step Δ t for each cell, as described in Chang et al. ( 2017 ). The time-step can either be an individual time-step in a multistep algorithm (Prust Chang 2019 ) or a global time-step (Chang et al. 2017 ). Estimate the half time-step state of the cell using the second-order van Leer scheme described in Chang et al. ( 2020 ). In brief, we solve the RHS of equation ( 9 ), but with the replacement of Δ t → Δ t /2 and use piecewise continuous reconstruction to get face values. We then solve for the fluxes following the methodology described next and include the source terms on a half-time-step. Drift the mesh generating points by a half-time-step and recompute the half-time-step tessellation to provide second order convergence in time (e.g. provide an estimate for ). Use the half-time-step states and use full linear reconstruction to derive face values to compute the half-time-step fluxes, (described next). Then, apply the full step including the source terms (using the half-step values), e.g. . Update the state of the cell to the full step. As stated in Chang et al. ( 2020 ), the use of the van Leer half-step prediction allows the source terms to be automatically included at second order. It also simplifies the code as the equations are only written once. Moreover, the van Leer method can be easily adapted to multistepping schemes as we have done here. The only change is that the half-time-step estimate must be taken from the cell’s initial state. MANGA was originally designed to reconstruct the conserved values at cell faces. For Newtonian codes, this is a reasonable choice, but modelling


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

−1 , with an average value of 0.2 eV molecule −1 . For crystalline ice the energy needed to convert it into compact amorphous ice is higher. For instance, Leto Baratta ( 2003 ) estimated that this energy ranges between 0.59 and 1.42 eV molecule −1 for pure crystalline water ice and for various projectiles. Famá et al. ( 2010 ) obtained an energy of eV molecule −1 for a pure crystalline water ice impacted by H + ions with an energy of 225 keV. Note that Raut et al. ( 2008 ) suggested the existence of a stopping power threshold of 4 eV Å −1 to trigger the destruction of the open porosity of the ice. However, the presence of such a threshold in compaction at low stopping power was not confirmed for the high-energy cosmic rays encountered in interstellar space (Dartois et al. 2013 ). These results are not surprising since every molecule is coordinated with the neighbors in the lattice. The photodissociation of a single water molecule, breaking and reformation of bonds, and formation of radicals or other species such as H 2 O 2 affect the unit cell of the crystalline structure, and hence a larger number of molecules are affected (Leto Baratta 2003 ). Figure 8 shows the impact of the energy needed to compact ice on the depth down to which cometary ice inside the nucleus is fully converted into compact amorphous ice. For an energy varying between 10 −2 and 10 eV molecule −1 , this depth varies between ∼28 and ∼8 m. The depth down to which the ice structure is fully changed by irradiation is not strongly dependent on the energy needed to compact ice but is rather controlled by the sharp drop of the deposited energy by GCRs inside the nucleus. Figure 8. Maximal depth until which the cometary ice is completely converted into compact amorphous ice as a function of the energy required to convert the ice into amorphous ice. One important implication of this result is that, regardless of the water ice structure inside the cometary nucleus, its outer layer (the first ∼10–20 m) consists of compact amorphous ice and is not necessarily representative of the whole nucleus. This has strong implications for dynamically new comets (i.e., a comet that is approaching the Sun and outgasses for the first time). For instance, recent observations by Meech et al. ( 2009 ) showed that the activity at large heliocentric distances of comets passing through the solar system for the first time may be caused by the annealing of amorphous water ice. According to our results, such observations of the altered outer layers of a cometary nucleus cannot be taken as a proof that comets as a whole are composed of amorphous ice and cannot be used to infer the temperature and region where comets have formed in the protosolar nebula. 5. Discussion and Conclusion In this paper we analyzed the effects of GCRs on the isotopic composition, chemical composition, and ice structure inside a cometary nucleus. We did not consider surface effects such as sputtering, which leads to erosion of the


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We thank Seshadri Nadathur, András Kovács and Juan García-Bellido for correspondence and discussion. Some of the results in this Letter were derived using the healpix (Górski et al. 2005 ) package. ABL thanks CNES for financial support through its post-doctoral programme. This work was supported in part by the Kavli Institute for Cosmological Physics at the University of Chicago through grant NSF PHY-1125897 and an endowment from the Kavli Foundation and its founder Fred Kavli. OL acknowledges support from a European Research Council Advanced Grant FP7/291329, which also supported ABL and KN.


O O O O O O O O O O O O O O O O O O O B-Location B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Person O O O O O B-Organization I-Organization O O O O O O B-Database O O O O B-Organization B-Location I-Location

Acknowledgements We would like to thank the anonymous referee for many helpful comments. This work is supported by the Canadian Natural Sciences and Engineering Research Council. TAAS also gratefully acknowledges support from Western University. This research made use of the SIMBAD data base, 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 B-Telescope B-Instrument O B-CelestialObject O O O B-Instrument O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O B-Instrument O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-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 B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength O B-Wavelength I-Wavelength O O O O O O O O O B-Instrument O O O O O O O O O B-ObservationalTechniques I-ObservationalTechniques I-ObservationalTechniques O O O B-Instrument I-Instrument B-Instrument O O B-Instrument I-Instrument B-Instrument O O O O O B-Instrument 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 B-Instrument O O O O O O O O B-Software I-Software I-Software O O B-Software I-Software I-Software I-Software I-Software B-Software B-Citation I-Citation O O O O O O B-Software I-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 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 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 B-Instrument O O O O O O O O B-Instrument O O O O B-CelestialObject O O O B-CelestialObject O O O O O B-CelestialObject O O B-CelestialObject O O O O O B-Telescope O O O O O O O O B-Instrument O O O O O O

for the water production rate of both asteroids. In Section 5 , we calculate the fraction of ice coverage required to achieve this upper limit, discuss our results, and present our conclusions. 2. Observations and Data Analysis 2.1. Herschel HIFI Observations Themis was observed with HIFI on Herschel on 2012 January 30 (see Table 1 ). The asteroid was traveling inbound (2.92 au) and close to perihelion (2.75 au) when the observation was carried out. Cybele was observed with HIFI on 2012 December 21 (see Table 1 ) when the asteroid was 3.52 au from the Sun and inbound, having already passed aphelion (3.8 au). It is important to highlight that with the low escape velocity from these asteroids, any escaping water vapor would have been visible to Herschel independent of its source location, as the footprint of the telescope was much larger than the asteroids themselves. Table 1 Observations and Observing Conditions for the Previously Unpublished Measurements Used in This Paper Note. Columns: target (the two asteroids), observatory and instruments used, ObsID (observation ID reference number), date and time in UT, rh (heliocentric distance), Δ (Earth to asteroid distance), α (phase angle). The line emission from the fundamental ortho-H 2 O 1 10 –1 01 line at 556.936 GHz was searched for in the lower sideband of the HIFI band 1b mixer. The observations were performed in the frequency-switching observing mode using both the wide-band spectrometer (WBS) and the high-resolution spectrometer (HRS). The spectral resolution of the WBS is 1 MHz (0.54 km s −1 at the frequency of the observed line), while the HRS was used in its high-resolution mode with a resolution of 120 kHz (0.065 km s −1 ). Initial processing of the HIFI data set was carried out using the standard HIFI processing pipeline of the Herschel Interactive Processing Environment v15.0.1 (HIPE; Ott 2010 ), followed by processing with the GILDAS CLASS software. In CLASS, vertical and horizontal polarizations were folded and averaged. The frequency-switching observing mode introduces quite a strong baseline ripple, which was removed through a polynomial baseline correction performed on the final spectra. The averaged and baseline-corrected HRS spectra of the two asteroids are shown in Figures 1 (a) and (b). The pointing offset of both the vertical and the horizontal polarization spectra is 35 in band 1b with respect to the target position. The half-power beam width is 381 at 557 GHz. The main beam brightness temperature scale was computed using a forward efficiency of 0.96 and a beam efficiency of 0.62. The output line area rms values are provided in Table 2 . Figure 1. Averaged HIFI spectra and thermophysical modeling output. Shown are the HRS-averaged spectra for (a) asteroid Themis and (b) asteroid Cybele with TPM outputs (c) for Themis (left) and Cybele (right). These outputs represent the Herschel view with orientation “ecliptic sky” at the specific HIFI observing start epochs. The plots in


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forbidden line emission such as [O i ] lines (Appenzeller, Oestreicher Jankovics 1984 ; Hartigan, Edwards Ghandour 1995 ). Our spectra show that the EW of the [O I] (6300 Å) line increases by a factor of 10 after the eclipse (Figs 6 and 7 ). The observed EW increase is in agreement with measurements by Petrov et al. ( 2015 ) and Takami et al. ( 2016 ). Petrov et al. ( 2015 ) attribute the change in the forbidden line's EW to a drop in the photospheric continuum, as reported by the resolved photometry of RW Aur A by Antipin et al. ( 2015 ). Petrov et al. ( 2015 ) further imply that the obscuring body must be blocking the inner parts of the system while the outflow remains visible. The He i (6678 Å) and Hα emission lines remain clearly visible in our spectra after RW Aur enters the eclipse. This again indicates that at least part of the accretion flow is still visible. The He i EW remains constant (Fig. 8 ), implying the He-emitting regions are obscured in the same way as the photosphere. The Hα EW decreases after the eclipse (Fig. 7 ). Our EW measurements show lower values for the line during the dimming compared to the values reported by both Petrov et al. ( 2015 ) and Takami et al. ( 2016 ). We attribute this to the fact that our spectroscopy does not resolve the A and B components, hence we get an additional flux in the continuum from RW Aur B, resulting in a lower EW value. The Hα line profiles show a suppressed blueshifted peak after the start of the dimming (Fig. 5 ). This can also be seen in the Hα profiles from Takami et al. ( 2016 ) from both the 2010 and 2014 dimmings. This blueshifted absorption can be interpreted as the presence of an absorbing material moving towards the observer's line of sight, i.e. an outflow. 4.3 Origin of the eclipse In Section 1 , we introduce two possible explanations for the long dimming event observed in RW Aur. The obscuring screen could either be a tidal arm in the outer disc, as suggested by Rodriguez et al. ( 2013 , 2016 ), or a wind emanating in the inner disc, suggested by Petrov et al. ( 2015 ). Our observations provide new evidence to support the occultation by a wind. In particular, we show that the blueshifted portion of the Hα line is suppressed since the beginning of the eclipse, indicating the presence of outflowing and thus blueshifted gas with velocities of 100–200 km s −1 in the occulting screen. This scenario is further supported by the increase in the mid-IR fluxes of the system in eclipse, reported by Shenavrin et al. ( 2015 ) and visible in archive NEOWISE data in the W 2 band (Fig. 4 ). Shenavrin et al. ( 2015 ) fit a blackbody to the spectral energy distribution of RW Aur in its faint state and find that the excess IR emission is plausibly explained by the presence of hot dust with temperature around 1000 K along the line of sight. Thus, the occulting body is outflowing and contains hot dust, which fits with a scenario where a wind emanating from the inner disc eclipses the


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We thank Peter Goldreich, Phil Hopkins, Christine Moran, Evan Kirby, and Sterl Phinney for useful discussions. We acknowledge stimulating workshops at Sky House where these ideas germinated. JF acknowledges support from NSF under grant no. AST-1205732 and through a Lee DuBridge Fellowship at Caltech. CDO acknowledges support from NSG through grants PHY-1151197 and AST-1205732.


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Acknowledgements The authors thank the reviewer for a set of helpful comments, Richard Booth, Charles Gammie, Sebastien Fromang, and Ji-Ming Shi for important feedback on an earlier draft of the paper, and Kacper Kornet for advice on numerical issues. This research is partially funded by STFC grant ST/L000636/1. Many of the simulations were run on the DiRAC Complexity system, operated by the University of Leicester IT Services, which forms part of the STFC DiRAC HPC Facility ( www.dirac.ac.uk ). This equipment is funded by BIS National E-Infrastructure capital grant ST/K000373/1 and STFC DiRAC Operations grant ST/K0003259/1. DiRAC is part of the UK National E-Infrastructure.


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We thank the anonymous referee for his/her careful reading of the manuscript and the valuable feedbacks. We extend our gratitude to Jacob A. Arnold and Kristin A. Woodley regarding their help in observations. We thank Blesson Mathew and Nicola Pastorello for the careful reading of the manuscript. We also acknowledge the members of SAGES group, especially Christopher Usher, Vincenzo Pota and Joachim Janz, for the support and enlightening discussions. SSK thanks the Swinburne University for the SUPRA fellowship. DAF thanks the ARC for support via DP-130100388. This work was supported by NSF grant AST-1211995. This paper was based in part on data collected at Subaru Telescope, which is operated by the National Astronomical Observatory of Japan. This paper uses data products produced by the OIR Telescope Data Center, supported by the Smithsonian Astrophysical Observatory. This work is based on observations made with the NASA/ESA Hubble Space Telescope , and obtained from the Hubble Legacy Archive, which is a collaboration between the Space Telescope Science Institute (STScI/NASA), the Space Telescope European Coordinating Facility (ST-ECF/ESA) and the Canadian Astronomy Data Centre (CADC/NRC/CSA). Some of the data presented herein were obtained at the W. M. Keck Observatory, operated as a scientific partnership among the California Institute of Technology, the University of California and the National Aeronautics and Space Administration, and made possible by the generous financial support of the W. M. Keck Foundation. We wish to recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain. This research has made use of the NASA/IPAC Extragalactic Database (NED) operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. The analysis pipeline used to reduce the DEIMOS data was developed at UC Berkeley with support from NSF grant AST-0071048. We acknowledge the usage of the HyperLeda data base ( http://leda.univ-lyon1.fr ).


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

are dominated by dark matter halo once one goes sufficiently far out in the galaxy. What is relevant is that the halo is dense and compact and hence the dark matter dominates even at inner radii as in LSBs (e.g. Ghosh Jog 2014 ) or in dwarf galaxies like DDO 168 (Ghosh Jog 2018 ). It is this feature that influences the development of a slow bar due to dynamical friction. DDO 168 has a high central dark matter density, ρ 0 = (39.81 ± 6.37) × 10 −3 and a scale radius, r s = 2.81 ± 0.83 kpc for an isothermal dark matter halo (Oh et al. 2015 ). It has been found that the dark matter halo dominates the observed dynamics of this galaxy starting from the central region (Ghosh Jog 2018 ). Thus, the detection of a slow bar in DDO 168 supports the proposition that the dense, compact dark matter halo slows down the bar through dynamical friction. We note that all the three galaxies that so far have been seen to host an H i bar (NGC 2915, NGC 3741, and DD0 168), also have the property that the bar is slow. We further note that the H i gas is very extended (several times the optical radius) in all three galaxies, and in NGC 3741 and DDO 168 the halo is dense and compact (Ghosh Jog 2018 ). Here, it should be emphasized that now, there is evidence that slow bars are more common than what was thought before. For example, using an innovative and simple technique, Font et al. ( 2017 ) determined the corotation radius in 68 galaxies. Using the photometric data, they further determine the bar length in these galaxies and consecutively estimate the to find that almost one-third of their sample galaxies host ‘slow bars’ (i.e. ). This commonality of slow bars in galaxies can be thought of due to more effective braking by the dark matter halo than what was believed before. However, the status of the pattern speeds in dark matter dominated galaxies, especially LSBs, is not well studied as compared to the HSBs (Font et al. 2017 ; Peters Kuzio de Naray 2019 ). As shown in our works for DDO 168 and NGC 3741, the dense and compact halo might play an import role in slowing down the H i bars. Thus, though the braking of bars by dark matter halo is more common, yet the dark matter dominance from the central region might have an enhanced effect in determining the slowdown of the bar. Further, Font et al. ( 2014b ) have shown by simulation that, due to the dynamical braking by the dark matter halo, the corotation radius moves outwards, at the same time, the bar can also grow in length significantly due to accretion. This implies, even for a slow bar the ratio, can settle well below the nominal value of 1.4, thus declaring the bar to be a fast one. Hence, all the fast bars as decided by criteria might not be fast ones. However, we clarify that the traditional definition of a slow bar (i.e. ) does not change our conclusion on the existence of the slow bar in DDO 168, albeit it puts questions on its rarity. 4 CONCLUSION We have identified an H i bar in the dwarf galaxy DDO


O O O O O O B-Organization B-Archive O O O O B-Mission B-Instrument B-Instrument O B-Instrument O O O O B-Person I-Person I-Person O B-Person I-Person I-Person O O O O O O O O O O O O O O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O B-Grant O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Grant B-Grant B-Grant B-Grant O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization

We would like to thank the NASA CDAWEB for providing the public WIND 3DP, MFI, and SWE data. We also acknowledge Dr. Lief Svalgaard and Dr. Lan Jian for providing the sector boundary list and the lists of ICMEs and CIRs. This work is jointly supported by the National Basic Research Program of China (Grant No. 2012CB825601), the National Natural Science Foundation of China (41231068, 41174152, 41374188, 41304146), and the Specialized Research Fund for State Key Laboratories.


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

of the complexity of modeling subtle variations. For example, improved modeling of spectral energy distributions of stellar populations could be accomplished with cycle-starnet . As another example, relating N -body simulations of dark matter distributions to large-scale galaxy data is an ideal candidate. For fields outside astronomy, medical imaging provides interesting opportunities for cycle-starnet because the data are highly dependent on the particular medical device that is used for data acquisition. These instrumental effects could be corrected either by combining simulations and clinical data or by learning the translation of data from one system to another. Last but not least, climate modeling is an area where efficiency could be improved by relating low-resolution models to high-resolution data, a domain-transfer problem where the difference between the domains is resolution. 5.2. Limitations and Future Implementations While cycle-starnet has many attractive properties, the training of cycle-starnet can be delicate and may still require some fine-tuning. The difficulty mainly arises from the adversarial training setup. Specifically, adversarial training provides competition between the autoencoder networks and the critic networks, making convergence not as straightforward as other machine-learning tasks such as supervised regression. We note that the other proposed methods, including The Payne (Ting et al. 2019 ), The Cannon (Ness et al. 2015 ), AstroNN (Leung Bovy 2019 ), and StarNet (S. Bialek et al. 2020, in preparation), are examples of supervised regression, and therefore are technically much easier to train. To train cycle-starnet , we have extensively explored numerous architectural choices and training details before deciding upon the final model. For instance, removing the adversarial losses leads to a smoother convergence, but without it, the latent representations are no longer shared, causing cross-domain translations to fail. Nevertheless, adversarial training is an active field of research in machine learning, with many new ideas proposed (Deshpande et al. 2018 ; Miyato et al. 2018 ; Donahue Simonyan 2019 ) since the original UNIT paper was published. Consequently, we expect that some of these advancements would benefit and stabilize the training of future versions of cycle-starnet . Besides the difficulty in training in an adversarial setting, we have made a few simplifying assumptions regarding the training spectra data sets. First, we assumed that the uncertainties provided by APOGEE are uncorrelated and accurately determined. How a mischaracterization of the noise may skew the training is yet to be studied. Additionally, the labels from both domains in this study span the same ranges. Early experiments suggest that having the two domains span a similar label space is an essential aspect of cycle-starnet . For a new survey, we might not know beforehand the range of the stellar labels. Knowing how to resolve this


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

Acknowledgements We thank the anonymous referee for the comments improving the paper. This research was supported by the project Enabling Green E-science for the SKA Research Infrastructure (ENGAGE SKA), reference POCI-01-0145-FEDER-022217, funded by COMPETE 2020 and FCT, Portugal. D.B. acknowledges support from the DeutscheForschungsgemeinschaft , DFG project ISM–SPP 1573. The calculations were carried out at the ISM – Xeon Phi cluster of the Computational Astrophysics Group, University of Évora, acquired under project “Hybrid computing using accelerators coprocessors-modelling nature with a novell approach” (PI: M.A.), InAlentejo program, CCDRA, Portugal.


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V.S. thanks DFG for financial support (grant WE 1312/48-1) and D.S. thanks RFBR for support (grant 15-02-01407) and Eberhard Karls Universität, Tübingen for its hospitality. Criticisms from the referee led to significant improvement of the paper.


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Acknowledgements ESW acknowledges generous support from the Swedish National Space Board. SBC was supported by NASA’s Origins of Solar Systems and Emerging Worlds Programs.


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

the Milky Way GRB scenario, we take Band parameter values: E 0 = 187.5 keV, α = −0.8, β = −2.3, spread over 1 keV–10 MeV range (Thomas et al. 2005 ). We obtain 3.96 × 10 18 eV cm −2 deposited in the top 1 g cm −2 of the atmosphere. The spectral information for the interstellar cloud scenario was obtained from Cummings, Stone Steenberg ( 2002 ) following the method in Pavlov et al. ( 2005 , 2011 ) giving the total fluence of 8.8 × 10 11 eV cm −2 s −1 . For modelling extreme solar events, estimating the spectrum is difficult because most of the events occurred before the satellite age. We selected the spectrum of the 2005 January 20 event here, because even though the event was not large by any standards, it was very well studied by a number of groups using both satellite and ground-based measurements. We rescaled its total energy to the Carrington event (2 × 10 33 erg) and took the Martian distance into account. The energy deposition rate was found to be 3 × 10 11 eV cm −2 s −1 assuming the event was spread over 24 h. The ion pair generation energy w of CO 2 is 33 eV ion pair −1 . The primary mechanism at play is photochemical escape, for example: CO 2 → CO + e − CO + O → O + CO O + + CO 2 → O + CO etc. A complete description of all the reactions and associated energetics can be found in standard textbooks such as Schunk Nagy ( 2009 ). We divide the deposited energy obtained from simulations by the ion pair generation energy to calculate ion pairs for each scenario. Our results are spread over a wide range of ion production rates, 1.2 × 10 16 ion pairs cm −2 s −1 from a Galactic GRB to 2.8 × 10 7 ion pairs cm −2 s −1 from gamma rays of an SN at 100 pc. Fig. 3 shows the ion production rates of different events along with their durations. Particles can escape the Martian atmosphere with just 0.125 eV amu −1 energy. With charge exchange, the fast ion becomes neutral and escapes, and the slower ion gets trapped in the magnetic field. Fast ions can directly knock the atoms out of the atmosphere, this process is known as sputtering. Ions also escape by gaining energy from ambipolar diffusion and by thermal escape according to Jeans equation. A Galactic GRB would directly deposit energy, produce ions (1.2 × 10 16 ion pairs cm −2 s −1 ) and transfer energy to kinetic energy of ions. The event is short lived but the magnitude of ionization and energy transfer is large. Thermal expansion due to a large energy deposition is possible in this scenario. In the nearby SN case, the gamma-ray and cosmic ray enhancements are ∼1 and ∼100 yr long, respectively. In addition to ion escape by large energy transfer, a fraction of the ions will also be picked up by solar wind and ICMEs during the period. Encounter with dense interstellar clouds would result in a ∼1-Myr-long enhancement in ionization rates (∼10 10 ion pairs cm −2 s −1 ). Extreme solar events are short-lived but as seen in Fig. 3 , can do significant damage and are relatively more frequent. Figure 1.


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

shock front with high velocity, overtakes the older bullets and decelerates. In the last panel, the newly ejected bullet E is in a comparable position as former bullet D in the first frame. The protostar launches outflow bullets labelled A through E corresponding to the left and right outflow lobe. In the remainder of the paper, we will only refer to the left lobe and therefore we drop the subscript L henceforth. The outflow bullets form an S-shaped chain of Herbig–Haro objects. The S-shape is due to the varying orientation of the angular momentum, , caused by anisotropic accretion onto the IAD from core (Ybarra et al. 2006 ; Wu, Takakuwa Lim 2009 ; Zhang et al. 2013 ; Frank et al. 2014 ). The first two bullets interact with the collapsing dense core material and are thus not visible in Fig. 8 . The timespan from 115 kyr to 122 kyr is chosen to capture the end of a cycle of an outflow bullet, here bullet D, when it hits the leading shock front. This cycle happens in a similar fashion for all other bullets, except the first bullet A. This is the first bullet that breaks out of the core and survives as a coherent structure. Bullets B and C have higher velocity and have overtaken A. Bullet D starts off faster still, and by the final frame it has overtaken all the others and hit the leading shock, where it is slowed down. Bullet E is even faster, but by the final frame it has not yet caught up with D and is in a similar position as former bullet D in the first frame. A sixth bullet has been launched, but is still inside the core, and therefore can not be seen on Fig. 8 . Fig. 9 shows the accretion rates onto the sink, and onto the protostar, , between (when the protostar forms) and . is relatively constant, between ∼2 × 10 −5 and . The accretion rate tends to decrease over time. It drops briefly, following an outburst, because the outburst heats the accretion disc (cf. Lomax et al. 2014 , 2015 ). The accretion rate of the protostar is low in the quiescent phase, , but approaches during an outburst. Note that the time resolution in Fig. 9 is too coarse to resolve the very short outbursts. The downtime between outbursts is and the duration of an outburst is (Stamatellos et al. 2007 , 2011b ). Figure 9. Evolution of the accretion rates onto the sink particle, (green), and the protostar, (blue). The labels, A–F, correspond to the outflow bullets formed in the individual outbursts (see Figs. 8 and 10 ). Note that the time resolution in this figure is too coarse to fully resolve the very short outbursts. 4.1 Position–velocity diagrams In order to determine whether the simulated outflow reproduces the ‘Hubble-Law’ relation, and individual ‘Hubble Wedges’, as observed, for example, by Bachiller et al. ( 1990 ); Arce Goodman ( 2001 ); Tafalla et al. ( 2004 ); Santiago-García et al. ( 2009 ); Wang et al. ( 2014 ), we construct PV-diagrams, i.e. false-colour plots of on the plane. Here, r is radial distance, and is radial velocity, both measured from the


O O O O O O B-Observatory I-Observatory O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O O O O B-Organization O O O O B-Observatory O O B-Organization I-Organization I-Organization B-Location I-Location O B-Organization I-Organization I-Organization B-Location B-Organization B-Location O B-Organization I-Organization I-Organization B-Location B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Location O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Location O O O O O O O O O B-Instrument O O O B-Organization I-Organization I-Organization I-Organization O B-Observatory I-Observatory O O O O O O O O O O O O B-Person I-Person I-Person B-Person I-Person B-Person I-Person O B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person O B-Person I-Person O O O O O B-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 O O B-Organization I-Organization O O O O B-Event I-Event I-Event I-Event I-Event I-Event I-Event I-Event O O O O O O O O O O O O O O O O B-Organization I-Organization I-Organization O B-Grant I-Grant I-Grant I-Grant B-Person I-Person

Based on observations obtained at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the National Research Council (Canada), CONICYT (Chile), the Australian Research Council (Australia), Ministério da Ciência, Tecnologia e Inovação (Brazil) and Ministerio de Ciencia, Tecnología e Innovación Productiva (Argentina). We are extremely grateful for the support of the NIFS teams at the Australian National University, Auspace, and Gemini Observatory for their tireless efforts during the instrument integration, commissioning and system verification: Jan Van Harmleen, Peter Young, Mark Jarnyk (deceased), Nick Porecki, Richard Gronke, Robert Boss, Brian Walls, Gelys Trancho, Inseok Song, Chris Carter, Peter Groskowski, Tatiana Paz, John White, and James Patao. Thanks must also go to Tracy Beck for her support during the commissioning and observations. We thank the anonymous referee for their valuable comments on the manuscript. MW acknowledges the generous travel support from Academia Sinica to attend the conference Star Formation Through Spectroimaging at High Angular Resolution in July 2011, which provided useful information for this study. This work was supported by the Australian Research Council through Discovery Project Grant DP120101792 (R. Salmeron).


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

reality, some of them may change during a stellar lifetime. Inner processes in stellar evolution such diffusion ( Dotter et al. 2017 ) or planet formation or engulfment ( Meléndez et al. 2009 ; Tucci Maia et al. 2019 ) alter the chemical composition in stars. Other inner mixing processes produced during dredge-up or induced by rotation can alter abundances such as [C/N] or Li ( Masseron et al. 2017 ; Aguilera-Gómez et al. 2018 ). We have to assume today that a selection of chemical abundances remains approximately intact in FGK main-sequence stars and can be used to trace chemical evolution. A few years ago, da Silva et al. (2012) studied several traits for chemical evolution studies of solar-type stars. In particular, [Y/Mg], [Sr/Mg], [Y/Zn], and [Sr/Zn] showed a significant trend as a function of age for their entire sample. When they performed a linear fit of [Y/Mg] as a function of stellar age for a sample of nearby solar twins, Nissen (2015) obtained slope of ∼0.04 dex Gyr −1 and interpreted this relation using nucleosynthesis arguments: massive stars produced Mg and expelled it into the interstellar medium on a different timescale than intermediate-mass stars reaching the AGB and producing Y. This has motivated discussions about whether abundance ratios can be used as “chemical clocks”, in particular if ages are difficult to measure. The exact dependence of [Y/Mg] or [Ba/Mg] on age is still debated, because it seems to further depend on stellar properties such as metallicity ( Feltzing et al. 2017 ; Skúladóttir et al. 2019 ; Delgado Mena et al. 2019 ), but not evolutionary state, at least before the AGB phase ( Slumstrup et al. 2017 ). In addition to [Y/Mg] and [Ba/Mg], [Al/Y] has also shown similar dependences with age ( Nissen 2016 ; Spina et al. 2016 ), at least for solar twins. Several other works that benefit from accurate age estimates have studied trends of abundance ratios as a function of age ( Bedell et al. 2018 ; Spina et al. 2018 ; Delgado Mena et al. 2019 ; Feuillet et al. 2018 , to mention recent works). Most of these analyses have been restricted to using abundance ratios in their classical form, as a function of iron (see Delgado Mena et al. 2019 for exception). Motivated by the fact that the chemical clocks discussed above do not include iron, we searched for other combinations in a sample of 30 elemental abundances. We found 55 relations that are as significant as those mentioned above. This new set of ratios can be used for the same applications as [Y/Mg]. In addition, the ratios can be applied to models of Galaxy evolution and to build stellar phylogenies ( Jofré et al. 2017 ; Jackson et al., in prep.). We report these findings in this Letter. 2. Data and methods We considered the sample of 80 solar twins (including the Sun) that was analysed by Bedell et al. (2018 , and references therein) and Spina et al. (2018) . This is the largest sample of solar twins that has been analysed using the differential technique for


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

We are grateful to Todd Hoeksema and Thierry Appourchaux for constructive discussion and Eric Fossat for providing the 80 s data he used. We also thank the SOHO GOLF and VIRGO/LOI teams for making their data available as per the SOHO data access policy, and the Birmingham Solar Oscillations Network group for access to the BiSON data. This work utilizes data obtained by the Global Oscillation Network Group (GONG) program, managed by the National Solar Observatory, which is operated by AURA Inc. under a cooperative agreement with the National Science Foundation. The data were acquired by instruments operated by the Big Bear Solar Observatory, High Altitude Observatory, Learmonth Solar Observatory, Udaipur Solar Observatory, Instituto de Astrofísica de Canarias, and Cerro Tololo Inter-American Observatory. We acknowledge support by HMI NASA contract NAS5-02139.


O O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O B-Telescope O O O O O O O O O B-Model I-Model O O O O B-Telescope 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 B-Telescope O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O B-CelestialObject I-CelestialObject O B-CelestialObject 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 B-Telescope O O O O B-Model I-Model I-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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-CelestialObject I-CelestialObject O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion O B-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion O O O O B-CelestialObject O O O O O

on all rows as vertical dotted lines. Variation in GBT spectra among rows two, three, and four demonstrates some of the variations in OH content and distribution over the region that increases the uncertainty in T ex determined with the expected profile method. Also worth noting is the unusual case in the fourth row in which the 1665 MHz line appears to be brighter than the 1667 MHz line and the secondary component appears to dominate. This deviation is within the uncertainty so it could be attributed to noise, or perhaps it is evidence of a localized anomaly in the secondary component. Figure 5. VLA absorption spectra from Source 2 and GBT emission spectra from its vicinity for the expected profile. Gaussian fits are performed on the VLA spectra and shown superimposed with a dashed line, and the centroid velocity of the Gaussian fit is displayed as a vertical dotted line on each spectrum. VLA observations of Source 1 as well as three of the four nearby GBT observations for the expected emission profile are shown in Figure 4 . The fourth GBT observation was not used because T C at that position was too high. The VLA observations at Source 1 reveal the presence of two OH components: a primary component centered near −39 km s −1 (called Component A), and a secondary component centered near −37.5 km s −1 (called component B). The expected profiles made by averaging the GBT spectra from observations surrounding Sources 1 and 2, respectively, also display these two components, but in the case of the individual GBT spectra averaged, both components are not always detected together. As a result, it makes sense to treat the two components as separate OH features, fit the VLA absorption data as a sum of two Gaussian components, and compare the optical depth and line temperature values for the corresponding components when using Equation ( 2 ) to estimate the excitation temperatures. These T ex values can then be averaged together after their separate determinations, but if the components of the OH features are not treated separately, the analysis will be faulty. The results of this exercise are given in Table 1 . The uncertainties reported in this Table are calculated only from the error in the profile integral and the absorption optical depth measurements. Table 1 Excitation Temperatures for the Components of Source 1 Note. Errors from profile integrals and optical depth measurements. In order to estimate the error resulting from variation in OH, we look at some of the variation in OH profile integrals between adjacent pointings within our survey. We choose an example with background T C = 4.0 K in order to best approximate the regions surrounding Sources 1 and 2, which have similar background T C values, because we wish to avoid making assumptions about T ex and how that would affect emission profile integral strengths. Between coordinates l = 138625, b = 15, and l = 13875, b = 15, the profile integral at W5 radial velocities varies between a


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

of observing a region as empty as the Local Void (Section 4.2.2). The simulated Local Volumes have lower number density by up to a factor of 2 at the faint end of the luminosity function in the WDM model (Fig. 8 ). The probability of a region as empty as the observed Local Void is as high as 34 per cent in the WDM model, five times higher than that in the CDM model (Fig. 9 ). A more complete Local Volume galaxy census (e.g. the Dark Energy Spectroscopic Instruments Bright Galaxy Survey; DESI Collaboration 2016 ) should therefore provide a way to constrain the nature of dark matter. APPENDIX A: HALO MASS FUNCTIONS IN SIMULATIONS Fig. A1 shows the FOF halo mass functions at different redshifts in the COLOR and COLOR-WARM simulations as described in Section 2.1 . WDM halo mass functions flatten towards the low-mass end compared to those in CDM. As first indicated by Wang White ( 2007 ), spurious haloes form due to a numerical discreetness effect in warm and hot dark matter simulations. The mass limit of dark matter haloes below which spurious haloes form depends on the N -body particle mass of the simulation and the WDM particle mass assumed. In COLOR-WARM, the N -body mass resolution is m dm 6.2010 6 h 1 M , and the WDM particle mass is m x 1.5keV. This corresponds to a mass limit of M lim 2.4210 9 h 1 M and M min 0.5 M lim given by equations derived by Wang White ( 2007 ) and Lovell etal. ( 2014 ), respectively. These limits are indicated by dashed and dotted vertical lines in Fig. A1 . Below these mass limits, the halo mass functions steepen significantly due to the emergence of spurious haloes. Figure A1. FOF group mass (total particle mass) function at three redshifts in the simulations. Solid lines denote the COLOR simulation and dashed lines COLOR-WARM. The vertical dashed and dotted lines are the limiting masses below which spurious haloes form in COLOR-WARM, given by Wang White ( 2007 ) and Lovell etal. ( 2014 ). APPENDIX B: BOX AND RESOLUTION EFFECTS In this study, the simulation boxes we use are much smaller than the MS-W7 simulation that the GP14 model was calibrated with. In addition, the mass resolution of our simulations is about 100times higher than that of MS-W7. Fig. B1 shows the galaxy SMFs at z 0 of six COLOR-sized regions extracted from the MR-W7 simulation. We find that variations of up to 0.3 dex in galaxy abundance are expected due to cosmic variance. Figure B1. Left-hand panel: six random COLOR-sized regions (small coloured boxes) are extracted from MR-W7 (black dots denote the whole box). Right-hand panel: the galaxy stellar mass functions of the selected COLOR-sized regions (line colour corresponds to the box colour in the left-hand panel) combined with GP14 model. The black line is the stellar mass function of MR-W7 combined with the GP14 model. Fig. B2 shows the SMFs of the GP14 model combined with MR-W7 and COLOR, while the dotted line is the SMF when COLOR trees have all the branches below the resolution of


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dex, log ( g ⋆ ) = 4.25 ± 0.14 (cgs), and V sin i ⋆ = 11.9 ± 0.3 km s −1 . We found no evidence of a double-lined binary or any blends of spectral components. Fig. 2 Transit light curves of EPIC 212036875 b obtained with MuSCAT2 (TCS) in g ′ ( upper left ), r ′ ( upper right ), i ′ ( lower left ), and z ′ ( lower right ) filters. The black solid line is the best-fit model accounting for the de-trending and transit components. The residuals are plotted in the lower portion of each plot. 3.3 Radial velocity follow-up with FIES The RV follow-up was performed with the FIbre-fed Échelle Spectrograph (FIES; Telting et al. 2014 ; Frandsen Lindberg 1999 ) mounted on the 2.56 m Nordic Optical Telescope (NOT) at the Roque de los Muchachos Observatory. We observed nine high-resolution ( R ≈ 67 000) spectra between 9 April and 22 May 2018 as part of our CAT and TAC programmes 57-015, 57-206, and 57-210, and OPTICON programme 2018A-044. To account for the RV offset caused by a major instrument refurbishment that occurred on 30 April 2018, we treated the RV taken between 9 and 26 April, and between 6 and 8 May as two independent data sets. In addition, 14 intermediate-resolution ( R ≈47 000) FIES spectra were also acquired between 12 May 2018 and 26 Feb. 2019, as part of the OPTICON programme 2018B-052 and the Spanish-Nordic programme 58-301. Depending on the sky conditions and scheduling constraints, we set the exposure times to 1800 – 3600 s for both resolutions. To trace the RV drift of the instrument we followed the strategy outlined in Gandolfi et al. (2015) and Buchhave et al. (2010) and bracketed the science exposures with long-exposed (60 – 90 s) ThAr spectra. We used the standard IRAF and IDL routines to reduce the data. The S/N of the extracted spectra ranges between ~35 and 75 per pixel at 5500 Å. Radial velocities were extracted via multi-order cross-correlations with the spectrum of the RV standard star HD 168009, for which we adopted an absolute RV of −64.650 km s −1 ( Udry et al. 1999 ). The FIES RVs are listed in Table A.1 . Figure A.2 shows the generalised Lomb-Scargle periodogram of the offset-corrected Doppler measurements (combined by subtracting the systemic velocities listed in Table 5 ). We found a very significant peak at the orbital frequency of the transiting BD with a false alarm probability FAP ≪ 10 −6 , proving that the Doppler reflex motion of the star induced by the orbiting companion is clearly detected in our data. 3.4 Subaru/IRCS AO imaging In order to obtain high-contrast, high-resolution images of EPIC 212036875, we performed AO imaging with the InfraRed Camera and Spectrograph (IRCS, Kobayashi et al. 2000 ) mounted on the Subaru 8.2 m telescope on 14 June 2018. The target star was used as a natural guide and AO correction was applied to obtain high-contrast K ′ -band images of the target. We used the fine-sampling mode (1 pix ≈ 21 mas), and implemented a five-point dithering to minimise the impacts of bad pixels and


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

is σ = 0 km s −1 (so any apparent velocity dispersion would be due entirely to binaries and measurement error); in scenario 2, we assume an intrinsic dispersion of σ = 2.7 km s −1 , which is close to our best-fitting dispersion of Ret II for the mean period assumed here. For each realization, we first calculate the uncorrected dispersion using 3σ-clipping: we find the maximum likelihood values of μ, σ, then remove stars that lie beyond 3σ, and repeat as needed until no such outliers are present. In order to find cases that roughly resemble Ret II, we repeat many random realizations and keep three cases for which the uncorrected dispersion σ clip lies between 2.5–3.5 km s −1 . This required several realizations before three such cases were found for either scenario. In scenario 2 (σ = 2.7 km s −1 ), we did choose one realization with σ clip = 2.3 km s −1 to see if a non-zero intrinsic dispersion can be recovered even for a lower σ clip value. After applying our analysis to these mock data, the resulting posteriors in the intrinsic dispersion are plotted in Fig. 5(a) for the scenario where σ = 0 km s −1 . In all three cases we infer that σ 1.5 km s −1 at greater than 90 per cent confidence; the most probable intrinsic dispersion is well below 1 km s −1 in all cases. Thus, our method appears unlikely to find a peak at σ > 2 km s −1 if the apparent velocity dispersion is dominated by binaries. In Fig. 5(b) we plot the resulting posteriors for the cases where the true σ = 2.7 km s −1 . Here we see that σ = 0 km s −1 is ruled out in all cases; in none of these cases do we find a most probable intrinsic dispersion lower than 2 km s −1 . This builds confidence that, despite the relatively small sample size, our binary-corrected velocity dispersions can be trusted. Figure 5. Posteriors in velocity dispersion for simulated data sets, where the velocity measurements are randomly resampled for each star in Ret II. In (a) we simulate a ‘galaxy’ with intrinsic dispersion σ = 0 km s −1 , while in (b) the simulated galaxy has intrinsic dispersion σ = 2.7 km s −1 . Although each case has a high uncorrected dispersion σ clip determined from sigma-clipping, our method can clearly differentiate between these two scenarios despite the relatively small sample sizes. As we mentioned above, despite Ret II having a most probable intrinsic dispersion of 3 km s −1 in our analysis, there is still a non-zero probability of σ = 0 km s −1 . What are we to make of this? First keep in mind that if the K15 measurements are not systematically offset from the higher resolution J15 measurements by ≈1–3 km s −1 , the probability of Ret II having σ = 0 km s −1 essentially vanishes. If we retain the possibility of a large offset between the K15 and J15 data sets, then there are three possible explanations: either (i) Ret II’s true intrinsic dispersion is in fact somewhere between 0–3 km s −1 , and the peak appearing at 3 km s −1 is merely due to the small sample size; (ii) Ret


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Sky Survey (RASS). For A478 and Ophiuchus, we corrected the MCXC luminosities by factors of 1.34 and 1.25, respectively, to account for the different N H derived from our Chandra fits, which were factors of 2.0 and 1.8 higher than the database values adopted for the RASS catalogs. This makes the luminosities internally consistent with those for the central regions that were derived directly from Chandra observations. For Perseus, even the 0.15 R 500 radius is not fully covered by one Chandra ACIS-I observation, so we used the Chandra mosaic from Aharonian et al. ( 2017 ) to derive the luminosity within 0.15 R 500 . To convert the 0.1–2.4 keV luminosities to the more physically meaningful bolometric ones, we need gas temperatures, which we have derived from Chandra spectral fits in the same regions for most clusters. The temperature fits are summarized in Table 6 ; their errors include the statistical uncertainty and a 10% uncertainty on the value of N H . For Perseus, Ophiuchus, and 2A 0335+096, Chandra coverage is too small to probe an average temperature within R 500 , so we used average cluster temperatures from the literature instead, which come from instruments with a larger field of view (see Table 6 ). For Perseus and Ophiuchus, whose total mass is estimated from the M 500 − T X relation (the 2A 0335+096 mass comes from Planck ), this should result in slightly underestimated masses and R 500 , because the cool core biases the average temperature low. This will not affect our conclusions in any significant way. For a further eight clusters, marked with a in Table 6 , the Chandra field of view is smaller than R 500 but covers enough of it to derive a reliable temperature for the region, considering the steeply declining radial brightness profiles and the relatively small contribution of the missing emission to the spectrum. For these clusters, we use Chandra temperatures fitted in smaller regions given in the notes for Table 6 . For Perseus, for simplicity, we used one ACIS-I pointing (Table 5 ) out of many available to derive a temperature for r 0.15 R 500 , as it almost covers the whole region. The statistics of that data subset are more than sufficient. The above simplifications are adequate because we are using the temperatures only for the luminosity conversion. For each cluster region, we converted the 0.1–2.4 keV luminosities to the bolometric luminosities (Table 6 ) using a conversion factor appropriate for the corresponding temperature (Böhringer et al. 2004 ). The luminosity errors in Table 6 include the uncertainty on the temperature and a 10% ROSAT – Chandra flux cross-calibration uncertainty, added in quadrature. The latter was evaluated by comparing the R 500 0.1–2.4 keV luminosities derived from Chandra and those determined from ROSAT for the 10 clusters in our sample with both the Chandra and the MCXC measurements. We found that our Chandra luminosities are, on average, 6% higher than the RASS ones, with a scatter of ∼10%.


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

observed data. However, it is worth noting that the end frequency may be difficult to detect as LIGO is not currently very sensitive to frequencies above ∼1000 Hz. Figure 11. Example of GW quantities considered in the correlation matrix for a 15 M ⊙ progenitor with α Λ = 1.25, which does not explode successfully. The blue line is the early slope between 500 and 1000 Hz, and the orange line shows the slope just prior to collapse , between collapse to a BH and 500 Hz below the final frequency. These quantities will be used to compare between simulations and explore correlations with properties of the progenitor and explosion. Green line is the function fit of the peak GW frequency after 0.5 s postbounce. Although the parameters we consider seem rudimentary, we experimented with using various arbitrary functional fits to the frequency evolution with time, but found that as with the neutrino evolution, the fitting parameters were not well correlated with the progenitor and explosion process, especially in comparison with the parameters we have adopted. For example, Morozova et al. ( 2018 ) used a quadratic fit of the form to characterize the peak GW frequency between 0.5 and 1.5 s postbounce. However, we have found that although this functional fit captures well the shape of the peak frequency at early times, it fails to capture the behavior as the peak frequency levels out at late times ( t > 1.5 s postbounce). We propose instead a fit of the form , which better captures the behavior at later times. An example of such a fit is shown in Figure 11 . The coefficients of both functional fits are not well correlated with properties of the progenitor or explosion. Nonetheless, such fits may be useful for studies of detectability, as priors in LIGO data searches, etc., and thus the fit coefficients can be found online, 11 11 Publicly available at [doi: 10.5281/zenodo.3822555 ]. but we will not discuss them further in this work in our exploration of correlated quantities. It is easiest to see how these GW parameters change with the properties of the progenitor and explosion by looking at the correlation matrix. Figure 12 shows the correlation matrix between progenitor, explosion, and GW properties for simulations that explode successfully. Again, there are many additional parameters that could be included, but all showed weak correlations with the GW emission and thus we do not include them here. The GW eigenfrequencies are intimately related to the PNS mass and the core compactness ξ 2.5 , because they are sensitive to the structure of the core and its evolution. Figure 12. Correlation matrix for observable GW quantities and underlying progenitor and explosion properties for simulations that successfully explode. The quantities considered are core compactness ( ξ 2.5 ), PNS mass () at 1 s postbounce, explosion energy ( E expl ), and early peak GW frequency slope () between 500 and 1000 Hz. The lower-left half shows the correlation strength, ranging


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CP and VFC are funded by Italian Space Agency (ASI) through contract Euclid – IC (I/031/10/0) and acknowledge financial contribution from the agreement ASI/INAF/I/023/12/0. We acknowledge the support from the grant MIUR PRIN 2015 Cosmology and Fundamental Physics: illuminating the Dark Universe with Euclid .


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Acknowledgements The authors thank Jaime de la Cruz Rodríguez for his helpful comments on an early version of the manuscript. Financial support from the Spanish Ministry of Economy and Competitivity through projects AYA2014-55078-P, AYA2014-60476-P and AYA2014-60833-P is gratefully acknowledged. The authors wish to acknowledge the contribution of Teide High-Performance Computing facilities to the results of this research. TeideHPC facilities are provided by the Instituto Tecnológico y de Energías Renovables (ITER, SA). URL: http://teidehpc.iter.es . This work was also supported by computational resources provided by the Australian Governmentthrough the Pawsey Supercomputing Centre under the National Computational Merit Allocation Scheme.


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This work is partly supported by the DST-India grant no. Sr/S2/HEP-048/2012 and an India–Israel joint research grant (6-10/2014[IC]). We thank Matt Kunz for sharing the code that was used in Latter Kunz ( 2012 ). We also thank Ramesh Narayan for useful discussions on the global linear stability analysis.


B-Tag O B-Tag I-Tag I-Tag I-Tag I-Tag I-Tag I-Tag I-Tag I-Tag I-Tag I-Tag I-Tag I-Tag I-Tag I-Tag I-Tag I-Tag I-Tag I-Tag I-Tag I-Tag I-Tag I-Tag I-Tag I-Tag I-Tag I-Tag I-Tag I-Tag I-Tag B-Software I-Software 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 B-Software I-Software O O O O O O O O O O O O B-Software I-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 I-Software O O O O O B-Model 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 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 B-Model O O O O B-Model O O O O O O B-Model O O O O O O O O O


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3000 au × 3000 au region of the densest collapsed core in each simulation (projections for the entire simulation domain are shown in Figure 2 ). The mean field points in the horizontal ( x ) direction. The strong-field case () shows highly elongated structure (perpendicular to the mean-field direction) and a classical hourglass magnetic field morphology aligned with the mean-field direction. The weak-field simulations () show more chaotic magnetic field morphology dictated by turbulence, with pinches and clumps. Figure 3 shows the deviation in the mean magnetic field () from its large (parsec) scale direction as a function of scale: alignment becomes poorer with weaker mean-field strengths. The degree of alignment can remain tight to the smallest scales in the strong mean-field regime. Figure 3 also shows a related quantity: the (volume) fraction of gas within a sphere of radius r (the length scale) that has a magnetic field aligned within 30° of the large-scale mean-field value (). Figure 1. Density-averaged line-of-sight magnetic field and projected gas densities zoomed in on a core in each of the simulations. The arrow in the top left represents the initial magnetic field. Figure 2. Density-averaged line-of-sight magnetic field and projected gas densities of the entire simulation domain (5.2 pc) for the four simulations. Each box is centered on the corresponding prestellar cores shown in Figure 1 . Figure 3. Top: deviation of the mean magnetic field averaged over some length scale around the core from the large (parsec) scale field. Bottom: fraction of gas inside a sphere of radius the length scale with the magnetic field aligned within 30° of the large-scale mean-field value. 4. Density Scaling of the Magnetic Field The relationship between density and magnetic field is important for theoretical models and observations. B ∝ ρ 2/3 is predicted for collapsing clouds with weak magnetic fields (i.e., gravitational energy dominating magnetic energy). The same scaling is also predicted for flux-frozen, isotropic collapse in general. Lazarian et al. ( 2012 ) interpreted the observed B ∝ ρ 2/3 from Zeeman measurements as a signature of reconnection diffusion being most efficient at lower densities (i.e., before collapse proceeds) in the weak-field limit. In contrast, theoretical predictions for anisotropic contraction models, often expected in the strong-field limit, predict a weaker scaling: B ∝ ρ 1/2 (Tritsis et al. 2015 ). We test the density magnetic field scaling relationship using our high dynamic range Arepo simulations. We plot the occupation of the gas in the density/magnetic field phase diagram for our simulations in Figure 4 . The collapse occurs where the gas is compressed by turbulence above the critical density , which is defined as the density at which the background level of turbulent pressure is subdominant to the gas pressure (Krumholz McKee 2005 ; Li et al. 2015b ). That is, the critical pressure is obtained by equating with .


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We thank the anonymous referee for careful consideration of this manuscript and helpful comments. J.K.T. thanks G. Valori and F. Zuccarello for helpful discussions. This study was supported by the Austrian Science Fund (FWF): P25383-N27, P27292-N20, V195-N16; and by the Österreichischer Austauschdienst (OeAD), the Slovak Research and Development Agency (SRDA): SK 01/2016, SK-AT-2016-0002; the Scientific Grand Agency: VEGA 2/0004/16, the Thousand Young Talents Plan (a sub-program of the 1000 Talent Plan); and the Joint Research Fund in Astronomy (U1631242) under cooperative agreement between the National Natural Science Foundation of China (NSFC) and the Chinese Academy of Sciences (CAS). SDO is a mission for NASA’s Living With a Star (LWS) Program. SDO data are courtesy of the NASA/ SDO and HMI science team. RHESSI is a NASA Small Explorer Mission. GOES is a joint effort of NASA and the National Oceanic and Atmospheric Administration (NOAA).