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

snapshots (see Table 3 ) – this is different from dark matter particles whose number count is constant across redshift and simulations. Figure 9. The MST constructed on halo catalogues derived from the HZ (blue), LZ (orange), and LN (green) N -body simulations. From left to right are the MST statistics: degree ( d ), edge length ( l ), branch length ( b ), and branch shape ( s ). They are plotted from top to bottom according to snapshots at redshift 1, 0.5, and 0. Corresponding shaded areas show the jackknife uncertainties in the measurements. The distribution of the MST statistics are indistinguishable from each other at all redshifts, demonstrating that we should expect to see similar lines of degeneracy as power spectrum. Note . To mitigate this issue, for each redshift we match the number of haloes to the lowest number found in the simulations (thus always matching the number of haloes found in the LZ simulations). For those with more haloes, we simply select the most massive haloes. In Fig. 9 , we find no real noticeable difference in the statistics suggesting the degeneracies of the MST may be similar to that found for P ( k ). 6 COMPARING THE SENSITIVITY TO COSMOLOGY OF POWER SPECTRUM, BISPECTRUM, AND THE MINIMUM SPANNING TREE In this section, we compare the sensitivities to cosmological parameters of power spectrum P ( k ), bispectrum B ( k 1 , k 2 , k 3 ), and MST, measured on the same halo catalogues, to establish whether the MST can improve parameter constraints. Specifically, we compare the constraints on A s , Ω m , and ∑ m ν for 10 sets of mock simulations. To obtain reliable posterior distributions for the three methods and their joint constraints, we would normally run a Markov Chain Monte Carlo (MCMC) using an analytic expression for the data vector. However, the MST statistics cannot be obtained analytically and hence have to be obtained from simulations. P ( k ), B ( k 1 , k 2 , k 3 ), and MST are therefore estimated from a grid of simulations in parameter space. To limit the noise in the estimates of the theory we take the mean of five simulations rather than just one at each point in parameter space. Additionally, since our simulation grid is rather sparse we use Gaussian process (GP) regression to interpolate the data vector. Finally, we use a corrected likelihood function (see Sellentin Heavens 2016 ; Jeffrey Abdalla 2018 ) which accounts for the use of an estimated covariance matrix. 6.1 COLA simulation suites A suite of COLA (Tassev, Zaldarriaga Eisenstein 2013 ) simulations were constructed using the mg-picola software (Winther et al. 2017 , an extension to l-picola by Howlett, Manera Percival 2015 ) which, among other things, can model the effects of massive neutrinos (Wright, Winther Koyama 2017 ). This allowed us to generate N -body-like simulations relatively cheaply (in terms of computation time), albeit by sacrificing accuracy at small scales. All simulations are run in boxes of lengths 250 , with 256 3


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O B-Wavelength O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O B-Wavelength O O O O O O O B-Model O O O O O O O O B-Wavelength O O O O O O O B-Wavelength O O O O B-Model O O O O O O O O O O O O O O O O O O O B-Telescope B-Dataset O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O O B-Wavelength O O O O O O O B-Model O O O O B-Model O O O O O O B-Wavelength O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O B-Model 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 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

there are some 1015 defining sources outside the central distribution that should be examined individually for possible contamination by the host galaxy or other anomalies. The lower left plot in Fig. 7 extending to mas shows more detail near the centre, but the distribution remains remarkably symmetric even at the highest resolution. The lower right plot in Fig. 7 is a close-up view of the very central region within mas in each coordinate and shows again the predominance of defining sources and the significant fraction of sources in the very inner zone at a few 0.1 mas from the centre. The very small bias in declination is now visible with more sources in the negative values of . The proportion of defining sources (blue squares) increases with resolution, but in all three plots the optical and radio positions are statistically in very good agreement for all three categories of sources despite the larger uncertainties in the radio data for the non-defining and especially the VCS-only sources. 4.1.2. Angular separations Table 1 gives the overall statistics of the angular separation () between the optical and radio positions, subdivided according to the type of ICRF source. The table shows that 94% of the optical positions are within 10 mas of the radio position of the associated ICRF2 source. This is quite remarkable given the limited time coverage and the numerous limitations of the astrometric solutions for Gaia DR1 as explained in Lindegren et al. (2016) . For the defining sources the percentage is even higher (98%). There is in fact a very consistent pattern in that the fraction of separations within a given limit () is always higher for the defining sources than for the non-VCS sources, which in turn have a higher fraction than the VCS-only sources. Since the distinction between the three categories is irrelevant for Gaia (cf. Fig. 4 ), this confirms the difference in the quality of the radio positions expressed by the quoted uncertainties in ICRF2. Table 1 Number of ICRF sources with angular separations between the optical and radio positions. Notes. In brackets are the percentages of sources in the group below the given limits. Fig. 8 Distribution of the angular distances between the Gaia solution and the ICRF2 positions. Left: the 2054 solutions closer than 10 mas to their radio position. Right: same for the 258 defining sources. Figure 8 shows the distribution of separations in graphical form. The difference between the whole set and the set of defining sources is even more conspicuous than for the coordinate differences. The median is 1.16 mas in one case and only 0.61 mas in the other. As mentioned earlier this is primarily due to the very different quality in the ICRF2 between the defining sources and the rest of the catalogue and confirms a well-known feature of the ICRF2 with fully independent observations. 4.2. Normalised differences In this section we discuss the positional differences scaled by their standard uncertainties. We


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Acknowledgements We would like to thank the referee for many thoughtful comments which helped to improve this paper. This work issupported by the Swiss National Science Foundation through the grant number 200020 - 162630. We acknowledge the financial support from the Programme National de Planétologie (PNP) of CNRS-INSU co-funded by the CNES, and by the Agence Nationale de la Recherche (ANR-14-CE33-0018). J.O. acknowledges financial support from the ICM (Iniciativa Científica Milenio) via the Núcleo Milenio de Formación Planetaria grant, from the Universidad de Valparaíso, and from Fondecyt (grant 1180395). J.M. acknowledges support from the NASA through the NASA Hubble Fellowship grant HST-HF2-51414.001 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS5-26555.


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Acknowledgments The majority of the work of MD was performed at Caltech and supported through a Jansky Fellowship of the National Radio Astronomy Observatory. MD also greatly appreciates earlier support from UCLA, and is indebted to Lech Walesa, the leader of Solidarnosc , for his key role in the fall of communism in Europe, which made it possible to conduct this study. DJ appreciates support from NASAs Origins programme. The data presented herein were obtained at the CSO, supported through NSF grant AST-0540882 at the time of the observations. The authors thank the telescope staff and I-Ting Ho for support, Nicolas Biver for comments and for providing published CO production rates of comet Hale-Bopp, and an anonymous referee for helpful suggestions.


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

At = 0, cold accretion and cold wind recycling each contributes roughly half of the total stars formed, while hot mode accretion contributes of star formation. Cold accretion dominates the supply of star-forming gas in all three simulations until = 2.0, after which cold wind recycling and hot mode accretion start to be important. Compared to the other simulations, the haloes in Refσ3 form many more stars from both cold accretion and wind recycling, not because of more inflow but because they have less outflow as a result of the smaller mass-loading factors. The slower wind speed in the RefSlow model increases cold wind recycling by a large amount compared to the fiducial simulation. As a result, the galaxies at = 0 are slightly more massive as wind recycling gains importance after = 2, but their stellar masses are still consistent with the observations. Intermediate-mass haloes : The = 0 stellar mass from all three simulations is consistent with the observations within a small factor. The evolution of stellar content in these haloes is qualitatively similar to the small-mass haloes but with several major differences. First, stars from all accretion channels formed earlier in these more massive haloes, as is expected from the hierarchical assembly of galaxies. Secondly, both hot accretion and hot wind recycling, though still subdominant over most of the time, become more important at low redshifts, and together contribute of the total stars formed at = 0. Thirdly, cold accretion still dominates star formation at > 2 but nearly stops after = 2 when the shock-heated gas starts to develop a hot corona in these haloes. In the end, cold accretion only accounts for of the total stars formed. Cold wind recycling still plays a critical role in determining the final stellar mass of the galaxies, and largely accounts for the differences among the three simulations. Its contribution is more prominent in the RefSlow simulation. Massive haloes : At the massive end, galaxies from the Ref and Refσ3 simulations evolve very similarly and overproduce stars by a factor of 3 at = 0 (Fig. 11 ). The Ref simulation has larger η in small haloes, but the differences in η decrease with σ and become the same when . Therefore, the larger mass-loading factor in the Ref simulation only affects the progenitor galaxies during the earliest stages of their assembly when they were still small. Since these haloes assembled fast at high redshifts, the different scalings of η and σ in the low-mass haloes have little effect on the massive galaxies in our simulations. Compared to the intermediate-mass haloes, they have even earlier star formation and a higher fraction of hot accretion and hot wind recycling. Except for the RefSlow simulation, where cold wind recycling is clearly more important for stellar growth than the other channels, all four accretion channels contribute comparable amounts in the other simulations, with cold accretion + cold wind recycling and hot accretion + hot


O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion 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 B-Tag O O O O O O O B-Wavelength O O O O B-Wavelength I-Wavelength I-Wavelength 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 B-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject O O O B-Telescope B-Instrument B-Wavelength I-Wavelength I-Wavelength O O O O O B-Telescope O O O O O O O O O O O O O O B-Wavelength O O O O O O O O B-Wavelength I-Wavelength I-Wavelength O O B-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O B-Wavelength O O O O O O O O O O O O B-Tag O O O O

survive and maintain high levels of molecular gas fraction. To support this explanation, there is a noticeable difference in the number of YSOs detected in the Southern Pillars (>800) and in the western region where the Northern Cloud is (∼100), suggesting a lower level of triggered star formation toward the direction of the denser gas (Smith et al. 2010b ). 4.1.3. 8 <italic>μ</italic>m Figure 10 shows a comparison between the radio continuum emission and the 8 μ m image from Spitzer. In general, we detect some anticorrelation between the two tracers, with the radio continuum emission filling the cavities observed in the 8 μ m map. A Spearman’s rank correlation between the two images gives a value of 0.42, which indicates a poor level of correlation. As 8 μ m traces the polycyclic aromatic hydrocarbon (PAH) emission, it will be bright on the surfaces of the clouds being radiated by the nearby massive stars. Now, with the radio continuum map in hand, we are able to witness the complex distribution of the different gas phases in Carina, which deviates strongly from the classical view of a spherical region expanding symmetrically into the surrounding ISM. Because of the exquisite detail of our radio continuum image, we can see that the hot gas can indeed permeate through the molecular cloud and shape the material into features such as pillars, small shells, and arc-like structures. Figure 10. Color-composite image of the CNC-Gum 31 complex. Green shows the Spitzer IRAC 8 μ m map, while red shows the ATCA continuum image. A clear spatial anticorrelation between the two tracers is observed, with the radio continuum emission filling the cavities observed in the 8 μ m map. The 8 μ m map traces the PAH emission, so it will be bright on the cloud’s surfaces. Orange arrows show the apparent direction of the hot gas traced by the radio continuum map as it permeates through the denser gas, illuminating the cloud surfaces as traced by PAH emission. As the ionization fronts advance through the cloud, they can penetrate deep toward low-density regions and ultimately escape. Figure 4 shows structures resembling “plumes” at the edges of the H ii region. These features are likely to be tracing hot gas that had eroded the material in the nebula, extending to outside the molecular cloud, and now diffusing with the global component of the hot gas in the Galactic plane at distances >100 pc. There is clear alignment between the morphology of the illuminated gas traced by PAH emission and the plume-shaped structures traced by the radio continuum map. The direction of the elongated structures identified in the northeast section of the 8 μ m map (such as pillars and walls) is roughly the same as the direction of the plumes detected in the radio continuum (Figure 4 ). This correlation is more evident toward the Southern Pillars region, where the radio continuum emission is distributed along the cavities between the pillars. 4.1.4. 70 <italic>μ</italic>m In Figure 11 we


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The authors gratefully acknowledge financial support by CONICET through PIP 112-201501-00525. The authors are grateful to the anonymous referee for numerous suggestions and corrections on this paper.


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The authors would like to thank Nick Crump for assistance in the data processing, Harry Warren for comments on an early version of this paper, and the anonymous referee for many comments that have broadened and improved the scope of this work. This research was performed while J.W.R. held an NRC Research Associateship award at the U.S. Naval Research Laboratory with the support of NASA. This work was supported by JSPS KAKENHI Grant Numbers JP16K17671, JP15H05814. CHIANTI is a collaborative project involving George Mason University, the University of Michigan (USA), and the University of Cambridge (UK). This research has made use of NASA’s Astrophysics Data System.


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

the estimates of physical parameters based on the spectral energy distribution (SED) fitting tool. The final results of this work are summarized in Sect. 6 . 2. Observations, data reduction, and photometric and astrometric calibrations The observations were carried out using the 0.81 m (32′′) Tenagra telescope, which uses a science camera with 2048 × 2048 pixels having an effective plate scale of ∼0.98′′ per pixel and a field of view of 16.8 × 16.8 arcmin 2 . The images in the V R I filters were acquired between May 2012 and June 2013 over 90 nights, often three times each night but within one hour, while the B -band images were taken only over two nights. There are only 5 frames in B and around 250 frames in V R I , taken with exposures varying from 420s in B to 90s in I . Calibration images (bias and flats) were obtained nightly and the pre-processing of images (bias subtraction, flat-fielding, etc.) was done in IRAF 1 . Finally, 760 scientifically useful images were used to perform photometry. Figure 1 shows the color-composite image of the selected star-forming region towards IC 5070 obtained using the V R I images taken on the first night. Fig. 1. Color composite image of the young star-forming region towards Pelican Nebula obtained using the V R I -band images. The cyan circles represent the location of the variable stars. The time-series photometry of the processed images was performed using DAOPHOT/ALLSTAR ( Stetson 1987 ) and DAOMATCH/DAOMASTER ( Stetson 1993 ) routines. In this process all sources above the 4 σ threshold in each image are selected and the aperture photometry is obtained with a radius of 4 pixels. The point spread function (PSF) is determined from 20 bright and isolated stars in each image, which is used to perform the PSF photometry using ALLSTAR on all images. The frames taken on the first night are selected as the master image in each filter and the PSF photometry are used as input to DAOMATCH to derive accurate frame-to-frame coordinate transformations. These transformations are used to obtain the corrected magnitudes of the stars relative to their magnitudes in the master image for all frames using DAOMASTER. The photometry includes 1307 sources with more than 50 observations in the target field, and over 1000 stars with both V - and I -band measurements. Within our target region, optical counterparts of 77 of the ∼135 YSOs from Rebull et al. (2011) were found within 3′′ matching radius in our photometry. The photometric calibration to Landolt filters ( Landolt 2009 ) was performed using the standard star photometry carried out on the same night as the master frame. The standard transformation equations are: where, b , v , r , i are instrumental magnitudes; B , V , R , I are standard magnitudes; and X b , X v , X r , X i are the airmass in the B V R I filters. The maximum uncertainty of these coefficients and the dispersion in these relations are on the order of 0.02 magnitude. If the star is observed in one


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We would like to acknowledge insightful discussion with Ofer Cohen as we were getting this project underway. This work was supported by an INSPIRE grant from the NASA Science Foundation (AST-1461918). Ms. Mei Maruo’s participation was supported by the Tomodachi STEM @ Rice University Program funded by the US–Japan Council.


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

(Makarov 2012 ). This result holds for a wider range of realistic models, such as the Newtonian creep model developed by Ferraz-Mello ( 2015 ). The orbital eccentricity and average viscosity are the two crucial parameters defining these probabilities. The issue of dynamical stability and long-term survival of a tightly packed close-in system such as TRAPPIST-1 has already been discussed in the discovery paper by Gillon et al. ( 2017 ). A system with the observed set of parameters breaks up within a relatively short time in numerical N -body integrations. Fine-tuning of initial orbital parameters is required to find a long-term stable configuration within the observational uncertainties. This indicates that the multidimensional parameter space is shredded, with small islands of stable solutions separated by areas of instability. How can a real physical system of high complexity converge on a small island of stability among an infinite number of possible unstable configurations? The stability islands should be attractors, i.e., there should exist a regulatory force driving the system to one of such islands and damping small perturbations. Gillon et al. ( 2017 ) suggested that considerable tidal effects can provide the required stabilization. However, tidal forces act much too slowly even for such close planets, while the break-up of an unstable system happens well within 1 Myr. Even though tidal effects are important on the lifetime scale, we still have to explain how the system originally found a stable configuration. Tamayo et al. ( 2017 ) proposed that a convergent migration in a protoplanetary disk can be such a regulatory mechanism. Subject to dynamic friction in the disk, young planets migrate generally inward and toward smaller eccentricities. Still, something would halt this process when a planet reaches a stability niche, even before the disk dispersal. This may be possible when the stability niche is also associated with a certain mean-motion resonance (MMR), or better still, a system of MMRs with other planets, because an MMR is known to be an attractor. The surviving protoplanets end up in intricate patterns of near-commensurability (Terquem Papaloizou 2007 ), a class of N -body systems radically different from the solar system. Luger et al. ( 2017 ) find that the TRAPPIST-1 system represents a chain of MMRs, where each triplet of adjacent planets is locked in a three-body resonance. In this paper, we begin with testing a long-term stable configuration suggested by Quarles et al. ( 2017 ). We also test the system for chaos, using the siblings method in numerical integrations. The resulting orbital eccentricities for the seven planets, termed for brevity as TR1-1, TR1-2, ..., TR1-7 (instead of the traditional notation TRAPPIST-1 b , c , ..., h ), are used to estimate the likely spin–orbit end states of the planets, assuming an Earth-like rheology described by the Maxwell model. We show that not all of the planets are expected to


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

the quick knowledge of effectiveness and the computational methods (like extrapolations and flux-rope fitting) for further determining the magnitude of the CME impact. Bothmer Schwenn ( 1998 ) compared the helicity of a set of quiescent filaments using the hemispheric helicity preference (Rust Kumar 1994 ) with their ICME counterparts. They found a significant agreement in quiescent filaments to the rule (89%; a total of 9 filaments). Savani et al. ( 2015 ) also used the hemispheric helicity rule for obtaining the axis orientation for eight events but they warn that extra care must be taken while determining axis orientation of filaments that are between multiple active regions. Several statistical surveys on the hemispheric preference of helicity show varying degrees of compliance (for example, see HaiQing et al. 2009 ). In some of these studies (e.g., Martin et al. 1994 ), quiet regions show a higher degree of preference compared to the active regions. However, none of the studies show a 100% compliance with the hemispheric helicity rule indicating that independently obtaining the field direction at each source region is important. In order to avoid errors arising from exceptions in the hemispheric helicity rule and/or issues in disambiguation techniques, we have relied solely on filament observations and LOS magnetograms for obtaining the required parameters. We believe our method has performed well and has given reliable results. The human eye performs well in obtaining the chirality with images of reasonable resolution, but it is impractical to have human eyes analyze each and every filament. The advent of computer vision in solar physics is promising: automating filament chirality determination using machine-learning techniques (Martens et al. 2012 ; Aggarwal et al. 2018 ) will help in preparing computationally efficient and effective measures against severe space weather effects. Knowing whether there will be a geomagnetic effect or not is of primary importance to start taking precautionary measures. However, precautionary measures during a false alarm and the resulting expenditures can be avoided with the method used in this paper. Furthermore, our method of determining the axial field direction is more quick and straightforward than computationally expensive methods such as force free extrapolations and determining helicity (Bothmer Schwenn 1998 ; Yurchyshyn et al. 2001 etc.). In the current study we consider only the north–south component of the axial magnetic field of the filament. This is deemed useful as a first step in omitting ICMEs that will not be geoeffective. However, it is necessary to know the exact, quantitative direction and strength to determine where an ICME might reconnect with the magnetosphere and its severity. Utilizing vector magnetograms to determine the exact orientation and further study the field in the corresponding flux ropes at L1 will be useful in determining their orientations. Active region filaments


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concentration and asymmetry derived with pyca ; and (11) [O iii ] luminosity in units of 10 40 erg s −1 . Table 2. Control sample parameters. (1) identification of the AGN host associated with the control galaxy; (2)–(12) same as (1)–(11) of Table 1 . Twelve control sample objects have been paired to more than one AGN hosts and appear more than once in the table. In order to assess quantitatively the morphological variety of the AGN and control samples, we have derived the concentration index C and asymmetry index A of the sample galaxies using the publicly available code pyca (Menanteau et al. 2005 ). This calculation was made using the r -band images in order to maximize the galaxy signal-to-noise ratio. We have also obtained for all galaxies of the sample the morphological classifications from GZ1 (Lintott et al. 2011 ). From the GZ1 classification probabilities, we have separated the galaxies in four large classes: ellipticals (E), spirals (S), merging (M) and intermediate elliptical/spiral (E/S); this last class corresponds to galaxies whose GZ1 elliptical and spiral probabilities are rigorously the same and exceed 50 per cent when combined. Most of the 62 AGN in our sample have luminosities erg s −1 , with only 17 having larger luminosities. We use this threshold – postulated by Kauffmann et al. ( 2003 ) – to characterize these 17 AGNs as ‘strong AGN’. SDSS-III ugriz negative images (Fukugita et al. 1996 ) of the four most luminous of these strong AGNs are shown in Fig. 1 ; the remainder are available online. Figure 1. SDSS-III ugriz negative images of the four strongest AGN from our sample (left-hand columns) and their control sample equivalents (centre and right-hand columns). The mangaID of each host is indicated above its respective panel. Each chart is 51 arcsec on a side; north is up, east to the left. Inspection of the SDSS-III spectra showed that most of the strong AGN in our sample present coronal lines: at least one of the lines [NeV] λ3425 Å, [FeV ii ] λ3760 Å or [FeX] λ6374 Å are detectable above 3σ. A small number of objects among the most [O iii ]-luminous ‘weak AGN’ also present some of these lines. Coronal lines are thought to be produced by photoionization from the AGN (Mazzalay, Rodríguez-Ardila Komossa 2010 ; Rodríguez-Ardila et al. 2011 ) and to be associated with outflows (Müller-Sánchez et al. 2011 ). Being insensitive to star formation as opposed to the [O iii ] λ5007 Å, the presence of coronal lines reinforces the AGN nature of the 17 most [O iii ]-luminous objects in our sample, and suggests a transition between high- and low-ionization AGN at erg s −1 , in concordance with Kauffmann et al. ( 2003 ). We note that our AGN selection is based on single-fibre SDSS-III observations, which limits us to sources with AGN-photoionization signatures within 3 arcsec of the galactic centre. Wylezalek et al. (in preparation) has recently developed an AGN selection algorithm taking full advantage of the spatial dimension of


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

is comparable to our results. There are many possible drivers for high excitation conditions. Daddi et al. ( 2015 ) found that the ratio of CO(5–4) to lower J CO emission is well correlated with the average intensity of the radiation field and with Σ SFR among local spirals, local ULIRGs, and z ∼ 1.5 MS galaxies. This is consistent with the model of Narayanan Krumholz ( 2014 ). They combined hydrodynamic simulations of disk galaxies and galaxy mergers with molecular line radiative transfer calculations, motivated to examine the origin of a broad range of observed CO SLEDs in local and high-redshift galaxies. They found that CO SLEDs are well correlated with the galaxy-wide SFR surface density, which is attributed to the increase of gas density and temperature. As shown in Figure 8 , we find that their model for galaxies with Σ SFR ∼ 5 M ⊙ yr −1 kpc −2 agrees with our results. Figure 8. CO SLEDs normalized to the CO(1–0) line for the GRB 080207 host galaxy and other types of galaxies. The values for the Milky Way, M82, SMGs, and QSOs/radio galaxies (RGs) are taken from the compiled data in Carilli Walter ( 2013 ), (U)LIRGs are from Papadopoulos et al. ( 2012 ), and z ∼ 1.5 MS galaxies are from Daddi et al. ( 2015 ) and Bolatto et al. ( 2015 ). We plot the (U)LIRGs, SMGs, and QSOs/RGs with CO detection up to J ≥ 4. The average values are shown in bold dashed lines. The gray solid line represents the constant brightness temperature ( J 2 ). The gray dotted–dashed line represents the model of Narayanan Krumholz ( 2014 ) with Σ SFR = 5 M ⊙ yr −1 kpc −2 . Table 4 CO Brightness Temperature Line Ratio Note. The error is 1 σ . It might also be possible that the high CO excitation condition is attributed to a strong radiation from an active galactic nucleus (AGN). While no strong evidence for an AGN has been reported, the optical emission-line diagnostic with the Baldwin–Phillips–Terlevich (BPT) diagram (Baldwin et al. 1981 ) studied in Krühler et al. ( 2015 ) shows that the host galaxy is located in a starburst–AGN composite region. The significantly high radio-derived SFR (850 M ⊙ yr −1 ) derived in Perley Perley ( 2013 ) compared to other methods could be explained by the contribution of an AGN to the observed radio flux. Since peaks in CO SLED for AGNs are J ≳ 8–10 (e.g., Meijerink et al. 2006 ), where high interstellar medium (ISM) excitation occurs in X-ray dissociation regions, observations of higher J CO lines are important in diagnosing the presence of an AGN. 4.6. Implication for GRBs as a Tracer of SFR History There is ongoing debate as to whether GRBs occur in normal star-forming galaxies or occur under particular circumstances, and whether they can be used as an unbiased tool to trace star formation in the universe. It is suggested that GRBs prefer low-metallicity environments with a threshold of 0.3–0.7 Z ⊙ (e.g., Woosley Heger 2006 ; Graham Fruchter 2013 ; Vergani et al. 2015 , 2017 ; Perley et al. 2016b ). The metallicity effect on the


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The authors would like to thank D. Aubert for making his SPL code available to us. We acknowledge fruitful discussions with K. Benabed, S. Colombi, M. Kilbinger, and S. Prunet in early phases of the project. We also thank G. Lavaux, Y. Rasera, and M-A Breton for stimulating interactions around this project. We are also grateful to A. Leauthaud for constructive comments about the comparison with her GGL lensing results. CL is supported by a Beecroft Fellowship. This work was supported by the Agence Nationale de la Recherche (ANR) as part of the SPIN(E) ANR-13-BS05-0005 ( http://cosmicorigin.org ) ERC grant 670193, and AMALGAM ANR-12-JS05-0006 projects, and by the Centre National des Etudes Spatiales (CNES). NEC is supported by a RAS research fellowship. This research is also funded by the European Research Council (ERC) under the Horizon 2020 research and innovation programme grant agreement of the European Union: ERC-2015-AdG 695561 (ByoPiC, https://byopic.eu ). This work has made use of the Horizon Cluster hosted by the Institut d’Astrophysique de Paris. We thank S. Rouberol for running the cluster smoothly for us.


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

variations in the inferred and for highly reddened SNe if the dust distance is in the right range (Bulla et al. 2018 ). 2. For nonuniform ISM dust, the later phases will have values more consistent with each other while earlier phases will show larger and random (but correlated) variations. (For example, see Figure 8 for F13 : while the variations in F13 are over-stated, as discussed here, the trends are qualitatively correct). This effect is independent of the distance between the SN and foreground dust, and we find that typically it will be small even for highly reddened SNe. 4. Conclusions Even though there is clear evidence for ISM density fluctuations on scales of 10 au or even below, we show that due to the steep spectral index of the ISM column density power spectrum and because the SN photodisk is much smaller ( in diameter) than the typical ISM structure (), substantial variations on pc scales translate to much smaller fluctuations on the scale of SN photodisk. We provide a way to set the normalization for ISM density fluctuations on length scales relevant to SNe Ia based on MW dust emission observations (Miville-Deschênes et al. 2007 ). We have found that the expected time variations of EW(Na i ) and for SNe Ia due to nonuniform ISM would be typically much smaller than the predictions in Patat et al. ( 2010 ) and Förster et al. ( 2013 ), respectively. The observations of two SNe Ia highly reddened by at least mostly interstellar dust, SN 2012cu and SN 2014J, are consistent with the results of our analysis. The observed color variations for SN 2006X have been attributed to a light echo (Bulla et al. 2018 ) rather than nonuniform ISM, and so are also consistent with our analysis. We therefore conclude the following, if nonuniform ISM density in the SN host galaxy follows a scale-free power-law power spectrum. (1) The expected variation of extinction for SNe Ia with mag is negligible and is certainly smaller than what is currently scientifically relevant for SN cosmology. This, combined with mounting evidence that interstellar dust is likely the dominant source of reddening for SNe Ia, significantly reduces the concern about time variation of extinction for SNe Ia due to nonuniform dust density in cosmological studies. (2) For the study of extragalactic ISM density nonuniformity, it may be possible to detect small variations in extinction across phases for a highly reddened SN. The rms can be as large as ∼0.1 mag over a phase range of, say, from −10 to +50 days, with the shallowest spectral index (). A larger phase coverage would be better for this purpose (earlier observations would especially help, as they allow the observation to sample closer to the full extent of the photodisk at the last observed phase). Huang et al. ( 2017 ) demonstrated that in order for such a detection to be feasible, it is important to not only have an unreddened SN that is well-twinned with the dust-obscured SN, but the observed phases of these two SNe


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 O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O 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 B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation O B-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 our purpose. The electron screening effect is negligibly small in the region of ρ = 10 6 –10 7 g cm −3 and T > 2 × 10 9 K, where carbon detonation would occur, so we do not include this effect. Figure 7 shows the comparison between simulations with and without carbon burning for the case of . The red lines indicate the case with carbon burning, while the black ones indicate the case without. Although the orbital evolution (Figure 7 (a)) is almost the same, the maximum temperature (Figure 7 (c)) realized in the case with carbon burning is higher than the case without during the merger phase. This difference comes from the nuclear energy release (Figure 7 (b)). We confirmed that the inclusion of carbon burning increases the maximum temperature. Figure 8 summarizes the density and temperature of a particle which has the smallest τ CC / τ dyn ratio for all the cases we recalculated, including nuclear burning. The symbols surrounded by black frames are the results of the cases with carbon burning. Figure 7. Merger of WDs. The red lines indicate the case with carbon burning, while the black lines indicate the case without. (a) The orbital evolution, (b) the energy release rate of carbon burning, and (c) the time evolution of maximum temperature. Figure 8. Same as Figure 3 , but for the case with carbon burning. The symbols surrounded by black frames are the case with carbon burning while those without black franes are the case without. The black dashed line is the demarcation of the detonation condition by Seitenzahl et al. ( 2009 ). Since our simulations include only carbon burning, the effect of nuclear reactions would be underestimated. To check this effect, we perform post-processing calculations using an α -chain reaction network containing 13 species from 4 He to 56 Ni (Timmes 1999 ). Figure 9 shows the results for a particle which has the highest temperature in the case of . This calculation was done for a period in which carbon burning continued. The red lines indicate the case with the α -chain reaction network, while green lines indicate the case with only carbon burning. Because we find essentially no difference between them, our simulations including only carbon burning are appropriated to estimate the effect of nuclear burning, and being consistent with the previous studies using α -chain networks (Pakmor et al. 2010 , 2011 , 2012b ; Raskin et al. 2012 ), at least until the initiation of detonation. Figure 9. Post-processing analysis in the case of . We have calculated nuclear energy generation using the 13 species α -chain reaction network (Timmes 1999 ). Green lines denote the case of only carbon burning while the red lines indicate those of post-processing results. (a) Density, (b) temperature, (c) specific internal energy, and (d) pressure. Thus, the inclusion of carbon burning lowers q cr to realize violent merger-induced explosions if we use the same criterion as in Section 3.2 . In Figure 10 (a), the green triangles are the


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We acknowledge many useful conversations on the algorithms presented in this paper with Marijn Franx. We greatly appreciate Pratika Dayal, Kristian Finlator, Nicholas Gnedin, Chuanwu Liu, Brian O’Shea, Pierre Ocvirk, and Bin Yue for sending us the predictions they derive for the LF results at high redshift. We thank Kristian Finlator for discussing with us at length different turn-over mechanisms that would impact the UV LF at low luminosities. Austin Hoag kindly sent us the v2 Bradac models for HFF cluster MACS 0416. R.S.E. acknowledges financial support from the European Research Council under Advanced Grant FP7/669253. In addition, we acknowledge the support of NASA grant HST-AR-13252, NASA grant HST-GO-13872, NASA grant HST-GO-13792, NWO vrij competitie grant 600.065.140.11N211, and NWO TOP grant TOP1.16.057.


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

We thank Todd Thompson for helpful discussions, and the anonymous referee for helpful suggestions. Support for PFH was provided by the Gordon and Betty Moore Foundation through Grant #776 to the Caltech Moore Center for Theoretical Cosmology and Physics, an Alfred P. Sloan Research Fellowship, NASA ATP Grant NNX14AH35G, and NSF Collaborative Research Grant #1411920. Numerical calculations were run on the Caltech compute cluster ‘Zwicky’ (NSF MRI award #PHY-0960291) and allocation TG-AST130039 granted by the Extreme Science and Engineering Discovery Environment (XSEDE) supported by the NSF. EQ is supported in part by NASA ATP Grant 12-ATP12-0183, the David and Lucile Packard Foundation, and a Simons Investigator Award from the Simons Foundation. CAFG was supported by a fellowship from the Miller Institute for Basic Research in Science, by NASA through Einstein Postdoctoral Fellowship Award PF3-140106 and grant 10-ATP10-0187, by NSF through grant AST-1412836, and by Northwestern University funds.


B-Model I-Model O O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation O O O O O O O O O O O O O O O O O O O O B-Model I-Model 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 B-Model I-Model O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O B-Model I-Model 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 B-Model I-Model O O O O O O B-Model I-Model I-Model B-Software O O O O O O O O O O B-Model B-Citation I-Citation I-Citation I-Citation O O B-Model I-Model I-Model I-Model I-Model I-Model B-Model O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Model B-Software 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 O B-Citation I-Citation I-Citation I-Citation O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O B-Software O O O O O O O O B-Software O O B-Model I-Model I-Model I-Model O O O O O O B-Model I-Model O O O O B-Citation I-Citation I-Citation I-Citation O B-Software 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 B-EntityOfFutureInterest O O O 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 B-CelestialObject I-CelestialObject O O O O O O O B-Software O O O O O O O B-Model O O B-Formula I-Formula I-Formula I-Formula I-Formula B-Formula I-Formula I-Formula I-Formula B-Formula I-Formula I-Formula B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

Snowball bifurcation less likely (Joshi Haberle 2012 ; Shields et al. 2013 , 2014 ). Planetary heat transport, if efficient enough, could destabilize partially glaciated states on a tidally locked planet and reintroduce a Snowball bifurcation as was discussed by Checlair et al. ( 2017 ). However, the authors did not explicitly model ocean heat transport, motivating further investigation into its role in possibly retrieving the Snowball bifurcation. Considering dynamic oceanic processes could increase the overall planetary heat transport, potentially making a bifurcation possible. Hu Yang ( 2014 ) previously modeled a tidally locked planet orbiting an M-star using an atmospheric GCM (CAM3) coupled to a dynamic ocean. They did not directly look for bifurcations or hysteresis, but found a smooth transition from a partially glaciated to a fully ice-covered planet, suggesting the potential lack of a bifurcation. In this Letter, we investigate the effects of including a dynamic ocean on the Snowball bifurcation for tidally locked planets in a coupled ocean–atmosphere GCM (ROCKE-3D). 2. Methods 2.1. Model Description We performed our calculations using ROCKE-3D (Way et al. 2017 ), a fully coupled ocean–atmosphere general circulation model (GCM) that is derived from NASA Goddard Institute for Space Studies ModelE2. ROCKE-3D has previously been used to examine the climate states of slowly rotating and tidally locked exoplanets, including Warm and Snowball climates (Del Genio et al. 2017 ; Way et al. 2018 ; Jansen et al. 2019 ). The reader is referred to Way et al. ( 2017 ) and references therein for details regarding ROCKE-3D and its parent model, but we note that ROCKE-3D includes a thermodynamic–advective sea ice model. In contrast with previous studies of Snowball bifurcations on tidally locked planets (Checlair et al. 2017 ), ROCKE-3D considers ice advection, allows for partial ice coverage within cells, and includes dynamical ocean heat transport. Our present investigation using ROCKE-3D thus represents a significant advance over prior work. 2.2. Model Configurations Our experiments consider an Earth-like planet with regard to mass, radius, surface gravity, and atmospheric mass and composition (although we exclude O 3 ). Our simulated planet nonetheless differs from the Earth in several ways. We simulate a tidally locked planet in a circular orbit with a 50 day period around an M-star (Kepler 1649, M5V). We chose the stellar spectrum from ROCKE-3D’s default spectra. It is based on the BT-Settl spectrum with T eff = 3200 K, log g = 5, Fe/H = 0 (Allard et al. 2012 ). The surface of the planet is covered exclusively by ocean. The ocean in our model consists of five layers and is considerably shallower than Earth’s, reaching a maximum depth of 189 m. In this configuration, running the model on 44 CPU cores requires on average 180 hr of wall time. A deeper ocean would increase the computational cost considerably. Our model configuration is summarized in


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ACKNOWLEDGEMENTS The authors thanks an anonymous referee for comments that improved the contents of this Letter. TS thanks T. H. Saitoh and R. Maiolino for useful discussion. TS and the other authors thank the ALMA staff for their kind support. NL acknowledges support by National Key RD Program of China #2017YFA0402704 and NSFC #11673028. This Letter makes use of the following ALMA data: ADS/JAO.ALMA#2015.1.00003.S. ALMA is a partnership of ESO (representing its member states), NSF (USA), and NINS (Japan), together with NRC (Canada), NSC and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO, and NAOJ.


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

years. This is due in large part to deep, wide-field imaging surveys such as the Two Micron All Sky Survey (2MASS; Skrutskie et al. 2006 ) and the Sloan Digital Sky Survey (SDSS; York et al. 2000 ), which have enabled large-scale studies of the Milky Way to its outermost radii, and have resulted in the discovery of a variety of new and interesting substructures that lie within the Milky Way’s halo (Ivezić et al. 2012 ). Our understanding of the formation of the Galactic halo has therefore evolved from a simple Eggen, Lynden-Bell, Sandage (ELS; Eggen et al. 1962 ) monolithic collapse model to a much more complex and dynamic structure that is still being shaped by the merging of neighboring smaller galaxies (Searle Zinn 1978 ). This merger process is predicted by hierarchical ΛCDM models of galaxy formation (Steinmetz Navarro 2002 ; Bullock Johnston 2005 ; Font et al. 2011 ). In addition to classical globular clusters (Harris 1996 , 2010 ) and classical dwarf galaxies (Mateo 1998 ), these modern surveys have also discovered many low-luminosity globular clusters (Koposov et al. 2007 ; Balbinot et al. 2013 ), a large number of ultra-faint dwarf galaxies (Willman et al. 2005a , 2005b ; Belokurov et al. 2006a , 2007 ; Zucker et al. 2006 ; Walsh et al. 2007 ), and stellar streams, which are thought to have originated from the tidal disruption of either dwarf galaxies (see, e.g., the Sagittarius stream; Majewski et al. 2003 ; Belokurov et al. 2006b ) or globular clusters (see, e.g., the Palomar 5 tidal tails; Odenkirchen et al. 2001 ). However, there are other structures that cannot be classified by one of these familiar designations. Modern wide-field deep imaging surveys have enabled for the first time the discovery of large-scale, highly diffuse halo structures that can cover up to several hundred square degrees on the sky. Examples of these recently identified extended stellar distributions include the Virgo overdensity (VOD; Jurić et al. 2008 ) and the Hercules–Aquila (HerAq) cloud (Belokurov et al. 2007 ), both located about 20 kpc from the Sun, and the Pisces overdensity (Sesar et al. 2007 ) at a distance of about 85 kpc. These overdensities have generally been identified by noting excesses of a particular stellar tracer in a restricted area of the sky. For example, excess halo stars were first found in the Virgo constellation (Vivas et al. 2001 ), , by using RR Lyrae stars as tracers. This structure is known as the Virgo stellar stream (VSS) and lies about 20 kpc from the Sun (Duffau et al. 2006 ). In a similar location in the sky, Jurić et al. ( 2008 ), working with a large sample of Milky Way disk and halo stars from SDSS, identified a very extended overdensity that stood out from smooth models of the Galaxy’s thin/thick disks and halo at a heliocentric distance of ∼6–20 kpc. This structure is dubbed the VOD and appears to encompass an area as large as 1000 deg 2 . Bonaca et al. ( 2012 ) used a later data release from SDSS and estimated


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This work was supported by the German Deutsche Forschungsgemeinschaft, DFG project number DFG STR645/7-1. This work is based on data obtained with the STELLA robotic telescopes in Tenerife, an AIP facility jointly operated by AIP and IAC. Detailed comments from an anonymous referee are also appreciated.


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

section’s findings suggest that turbulence is essential for bringing about condensation in a medium with a non-negligible entropy gradient. More sophisticated numerical simulations that solve complete sets of hydrodynamical and magnetohydrodynamical equations will be needed to quantify with greater precision the relationship between turbulence and the critical t cool / t ff ratio for condensation within media with and without dynamically important magnetic fields. Concurrently, simulations of self-regulating mechanical AGN feedback should be analyzed for correlations between the rate at which ambient gas condenses into cold clouds and the values of t cool / t ff and σ t / σ v in the ambient medium. This paper will leave those investigations for the future and instead turn to the question of global self-regulation. 4. Coupling between Precipitation, Feedback, and Turbulence Previous work on precipitation-regulated feedback has assumed that the condensation threshold depends on either the t cool / t ff ratio alone (e.g., McCourt et al. 2012 ; Sharma et al. 2012b ) or the parameter combination , which accounts for the failure of buoyancy damping to suppress condensation when α K is sufficiently small (Voit et al. 2017 ). 3 3 Gaspari et al. ( 2017 , 2018 ) have recently proposed a different criterion for condensation in a turbulent medium that compares t cool with the timescale for eddy turnover. See the Appendix for a discussion of how that criterion relates to the results of Section 3 . However, an additional dependence on σ t / σ v , such as that shown in Figure 7 , can transform the feedback loop into a converging cycle that settles into a particular equilibrium state. This section explores global convergence to thermal balance in a precipitating medium by dropping the thermal balance requirement and developing a toy model that illustrates how turbulence can couple with precipitation. The model illuminates the conditions under which coupling produces a long-lasting equilibrium state in agreement with observations of both the precipitation threshold and the turbulent velocity dispersion in galaxy cluster cores. 4.1. A Toy Model for Coupling In order to keep the overall model as simple as possible, the dynamical timescales of the feedback system are assumed to be much shorter than its thermal and cosmological timescales, so that the ambient gas remains close to hydrostatic equilibrium. The model further assumes that heat input does not change the slope of the ambient entropy profile, which is constrained to be K ( r ) ∝ r 2/3 in a gravitational potential with t ff ∝ r . As a result, the gas temperature remains constant at , with a specific thermal energy that remains invariant while the gas gains and loses heat energy. Instead of causing the temperature to rise and fall, heat input causes the gas to expand and radiative losses cause the gas to contract, while gravitational work keeps kT steady. In such a constrained system, the t cool / t ff


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We thank the anonymous referee for helpful comments that greatly improved this manuscript. We thank Professor Jennifer Patience for kindly providing the SINFONI spectra of CT Cha B. We thank the whole Magellan Staff for making this wonderful telescope possible. We would especially like to thank Povilas Palunas (for help over the entire MagAO commissioning run). Juan Gallardo, Patricio Jones, Emilio Cerda, Felipe Sanchez, Gabriel Martin, Maurico Navarrete, Jorge Bravo and the whole team of technical experts helped do many exacting tasks in a very professional manner. Glenn Eychaner, David Osip and Frank Perez all gave expert support which was fantastic. It is a privilege to be able to commission an AO system on such a fine telescope and site. The MagAO system was developed with support from the NSF MRI and TSIP programs. The VisAO camera was developed with help from the NSF ATI program. Y.L.W.'s and L.M.C.'s research was supported by NSF AAG and NASA Origins of Solar Systems grants. J.R.M. is grateful for the generous support of the Phoenix ARCS Foundation. J.R.M. and K.M. were supported under contract with the California Institute of Technology funded by NASA through the Sagan Fellowship Program.


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XS thanks Eiichiro Komatsu for carefully reading the manuscript and giving helpful suggestions, as well as Erwin Lau and Surhud More for discussions and comments, and Susmita Adhikari for explaining the details of their method.


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

catalogue, in units of (100 km s −1 ) 2 . The bin width is 500 km s −1 (redshift). The black dashed line shows the original simulation catalogue; the red solid line with error bars is the average of the perturbed catalogues. The error bars show the standard deviation of the perturbed results, which is regarded as the measurement error. The background contours indicate the cosmic variance from Fig. 2 . Figure 5. The dashed line shows the standard deviation of the cosmic variance of the correlation statistic ψ 1 at the redshift separation bin 0–500 km s −1 of the simulation catalogues as a function of sample size. The solid line indicates measurement error of the perturbed sample averaged over all the bins as a function of sample size, in units of 1000 km 2 s −2 . The contours show the 68 per cent and 95 per cent ranges of the results, whereas the error bars are the standard deviations of the measurement errors. 4.3 Measurement error and sample size Once we have a large enough sample size to adequately probe a volume, we do not expect cosmic variance to change with sample size, since in this case it is due to the variations between volumes of a similar size. To decrease the cosmic variance we would need to increase the depth of our sample; larger volumes should vary less as we approach the scale of homogeneity for the Universe. In contrast, we can reduce the effect of measurement errors by increasing our sample size, even if the volume being probed stays the same. To characterize the effect of sample size on measurement errors, we select new mock surveys with up to 20 000 galaxies by changing in equation ( 1 ) while leaving the other selection function parameters unchanged. We then perturb them using the same method described in Section 4.2 . In Fig. 5 , we show how the cosmic variance and measurement errors of the correlation statistic ψ 1 changes with sample size. Increasing the sample size reduces the statistical errors significantly, while, as expected, the cosmic variance doesn’t show significant difference. 5 CORRELATION RESULTS Fig. 5 shows the relationship between sample size and statistical error. Using this relation, we can calculate the statistical error of CF3 surveys, which have many more data points than the CF2 surveys. Fig. 6 shows the correlation function of CF3-galaxy survey with Hubble constant H 0 = 75 km s −1 Mpc −1 ; this is the value given by Tully et al. ( 2016 ) as the best fit to the data. We see that the correlation function of CF3 is larger than the mean value of correlations of mock catalogues. Hellwing et al. ( 2017 ) show that cosmic variance of local group (LG) observer mocks with a Virgo-like cluster is larger than the Copernican observer mocks without Virgo, which explains the smaller mean correlation value from mocks in Fig. 6 . Figure 6. Velocity correlation functions of CF3-galaxy survey with H = 75 km s −1 Mpc −1 . ψ 1 , ψ 2 , ψ ∥ , and ψ ⊥ are in units of (100 km s −1 ) 2 . The solid line shows the


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

scale them by the corresponding PFs estimated over the same energy ranges. However, also this procedure might not necessarily yield a realistic estimate of the total flux of the pulsar, as it implicitly assumes that no difference exists between the spectral shapes of the pulsed and pulsed plus unpulsed emission (which is not necessarily the case). 3.2 Estimating the spectrum of the total X-ray emission For all those cases where the spin signal is not detected in the X-ray band, or the photon counting statistics is too low to extract a meaningful pulsed spectrum, the closest approximation to the intrinsic pulsar spectrum and flux can only be derived by a spatial analysis of the total emission (pulsed plus unpulsed). This approach leads to estimate an upper limit to the real flux, owing to the possible residual contamination from the background. It is expected to give a very close approximation to the intrinsic pulsar emission especially in the Chandra data, where this contamination can be minimized. 3.3 Similarities and differences in the pulsed and total X-ray SEDs: a few examples In Fig. 1 , we show a comparison for a few X-ray SEDs extracted considering either the total (pulsed plus unpulsed) emission (in black; this work, with procedural details given below) or the pulsed-only emission (in red; from Kuiper Hermsen 2015 ). In most cases, these SEDs overlap in energy only partially, as the pulsed SEDs were typically extracted at higher energies with respect to the pulsed plus unpulsed SEDs that are extracted here over the soft X-ray energy range (below 10 keV). Figure 1. Total (pulsed plus unpulsed) and pulsed-only X-ray SEDs for a sample of pulsars. The former were derived in this work and are shown in black, the latter are taken from Kuiper Hermsen ( 2015 ) and are shown in red. Clearly, the total (pulsed plus unpulsed) spectrum of J0205+6449 and J1513−5908 cannot be reproduced just by scaling the pulsed spectrum for the (average) value of the PF (≳21 per cent and ∼88 per cent), indicating a strong contamination from diffuse emission in the pulsar spectral data, which can hardly be removed (this is clearly more evident for the case of J0205+6449, and it is consistent with the detection of the PWN also at GeV energies (Li et al. 2018a ). On the other hand, the total and pulsed SEDs of J1813−1246, J1846−0258, J2022+3842, and J2229+6114 are consistent with each other once the pulsed SED is rescaled by the value for the corresponding PF, implying a comparatively small contamination from the diffuse and/or background emission. In particular, the pulsed SEDs of J1813−1246, J2022+3842, and J2229+6114 are slightly below the corresponding total SEDs (note that in all these cases the PFs are >75 per cent; see Table 1 ). Although the pulsed SED of J1846−0258 appears considerably below the SED for the total emission, the two SEDs turn out to be consistent with each other once the rather small PF is taken into account (∼31 per cent; see again Table 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 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 B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O B-Citation I-Citation O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O B-Model I-Model I-Model 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 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Citation I-Citation 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

axial fluxes, and encircled by the same twist field present in the two original tubes. In this way, the helicity, in the form of twist, inverse-cascades to ever larger scales. The PIL forms a natural boundary of the flux system: when the twist reaches this boundary, it cannot proceed further, since all of the flux has already reconnected. The end result of the process is a mostly axial and untangled field throughout the interior of the region, and a highly sheared field concentrated near the boundary of the region, i.e., at the PIL. This is precisely what is observed as a filament channel. The smooth internal field corresponds to the laminar coronal loops observed routinely on the quiet Sun and shown in Figure 1 . In this way, the helicity condensation model provides a natural mechanism for the simultaneous formation of highly sheared filament channels and laminar, untangled coronal loops. These two, seemingly unrelated features of the solar atmosphere are actually created by a single process (Antiochos 2013 ). The helicity condensation model was initially simulated by Zhao et al. ( 2015 ), who injected magnetic helicity into a plane-parallel Parker corona (Parker 1972 ). In the plane-parallel representation, the boundaries of the region of imposed twisting flows serve as the boundaries of the flux system, in analogy with the PILs in coronal-field configurations. Those authors found that photospheric motions that inject the same helicity everywhere form filament channels at the flux-system boundaries. Furthermore, randomizing the photospheric motions while keeping the same helicity injection rate did not qualitatively affect the accumulation of twist flux. Zhao et al. ( 2015 ) also tested the effect of injecting helicity of opposite signs on adjacent flux tubes, and found that their fields could not reconnect due to the twist components being co-aligned. In subsequent work (Knizhnik et al. 2015 , hereafter KAD15 ), we rigorously tested the helicity condensation model. We found not only that it qualitatively produced results consistent with the properties of filament channels, but that the inverse cascade of magnetic helicity due to reconnection produces a twist flux at the boundary of the flux system that agrees quantitatively with the predictions of the helicity condensation model. Based on this result, we estimated that with the helicity preference observed on the Sun, filament channels will form in about a day or so, in agreement with observations of their formation (Martin 1998 ; Gaizauskas 2000 ). We showed that helicity condensation agreed both qualitatively and quantitatively with observed properties of filament channels, and that the process produced a much less twisted coronal-loop region away from the flux-system boundaries. Those results were obtained for a 100% helicity preference, however, meaning that all of the helicity injected into the corona was of the same sign. An obvious question to be raised is: what happens if a


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parameters. The AR with the largest area and longest time of occurrence during the time considered, labeled as NOAA AR 12192, is such an example. As shown in the synoptic maps in Figures 2 (a) and (b), AR 12192 is near a large unipolar region (in blue color), which originates from previous ARs in an AC. We will simulate the formation of this unipolar region in Section 4.2 . The standard set of control parameters is able to identify AR 12192 on CR 2156. On CR 2157, the recurring AR 12192, relabeled as ARs 12209, 12213, and 12214, is mixed with new flux emergence near and within it. We find that the standard set of control parameters is unable to identify AR 12192 on CR 2157. Consequently we have to choose a different set of control parameters: kernel threshold 100 G, erosion size 10 Mm, growth threshold 20 G, and dilation size 60 Mm, to identify the more diffusive AR 12192. We refer to this set of control parameters as the special set. As shown in Figures 2 (c) and (d), the two configurations of identified AR 12192 differ vastly. The two configurations of AR 12192 possess different parameters, presented in Table 2 . During CRs 2156–2157, AR 12192 shows an increase in area and a decrease in flux, and a notable change in tilt angle. Our SFT simulation tests show that the evolution of AR 12192 during CRs 2156–2157 cannot be achieved by SFT transport terms only. This implies new flux emergences, as flux emergence is important in changing the properties of AR 12192 (McMaken Petrie 2017 ). Such new emergence superposes with existing flux, and cancels with existing opposite polarities. Thus, it is expected that the observed evolution of the AR during CRs 2156–2157 is different from the evolution solely deduced from the previous occurrence of the AR on CR 2156. Therefore, we choose the special set of control parameters for processing AR 12192 on CR 2157 for the following simulations. Figure 2. Identified ARs on synoptic maps. The left column shows synoptic maps of CR 2156 (a) and CR 2157 (b), with the ARs (enclosed by black curves) identified by the automatic identification method using the standard set of control parameters. AR 12192 and the unipolar region in proximity are indicated with black arrows. The middle and right columns show AR 12192 identified using the standard set of control parameters on CR 2156 (c), and identified using the special set of control parameters on CR 2157 (d), as well as AR 12222 identified using the standard set of control parameters on CR 2157 (e), and identified using the special set of control parameters on CR 2157 (f). Table 2 Parameters of AR 12192 Identified on CR 2156 and CR 2157 The two sets of control parameters produce different results not only for AR 12192, but for other ARs as well. We show the difference for AR 12222 as an example, in the last row of Table 1 . As shown in Figures 2 (e) and (f), when the special set of control parameters is applied, AR 12222 shows a growth in size and flux, as well as a