O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Model I-Model I-Model I-Model 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-CelestialObjectRegion I-CelestialObjectRegion 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 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 B-CelestialObjectRegion I-CelestialObjectRegion 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 B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Tag O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O

2009 ). 3 Test model A simple 1-D test model is now defined. This allows numerous simulated data sets to be created so that the p -values computed according to Sects. 2.1 and 2.2 can be compared and any differeces established with high statistical confidence. 3.1 Hubble expansion The null hypothesis is that the local Universe is undergoing an isotropic, cold Hubble expansion with Hubble parameter h 0 = 70 km s −1 Mpc −1 . Moreover throughout the local Universe there exists a population of perfect standard candles of absolute bolometric magnitude M = −19.0. Finally, we suppose that the redshifts z of these standard candles are measured exactly, but that their apparent bolometric magnitudes m have normally-distributed measurement errors with σ m = 0.3 mag. 3.2 Ideal samples In order to test p -values when the null hypothesis is correct, we need data sets consistent with the above description of the Hubble flow. We define the local Universe as extending to z max = 0.2, so that to a good approximation the geometry is Euclidean. If we suppose the standard candles to be uniformly distributed in space, a sample { z i } is created with the formula where the x i are independent random numbers ∈ (0, 1). The distances of these n standard candles are and their measured apparent bolometric magnitudes are where the z G are independent gaussian variates from . The n pairs comprise a data set D from which the posterior probability density Λ( h | D ) of the Hubble parameter h can be inferred. Moreover, the global GOF between Λ( h | D ) and D can be tested with the p -values of Sects. 2.1 and 2.2 . 3.3 Imperfect samples In order to test p -values when the null hypothesis is false, we need to modify either the model or the data. If we continue to make inferences based on the Hubble flow defined in Sect. 3.1 , we can introduce a violation of the null hypothesis by contaminating the data sample with an unrecognized second class of standard candles with a different absolute bolometric magnitude. Thus the data set D now comprises n 1 pairs with given by Eq. ( 15 ) and n 2 pairs with given by and where n = n 1 + n 2 . Thus, the sample is now contaminated with a second population of standard candles that are brighter by Δ M magnitudes. The investigator is unaware of this, and so carries out a Bayesian analysis assuming an ideal sample. 4 Comparison of <italic>p</italic>-values The Bayesian p -values defined in Sect. 2 are now computed for simulated data samples derived as described in Sect. 3 . Fig. 1 Comparison of p -values. For J = 200 ideal samples D j , is plotted against log p B . 4.1 Null hypothesis correct In order to compare p -values in this case, J independent ideal samples D j are created as described in Sect. 3.2 , and then p -values for each D j computed as described in Sects. 2.1 and 2.2 . With a constant prior π ( h ) in the interval ( h 1 , h 2 ) with h 1 = 64 and h 2 = 76 km s −1 Mpc −1 , the posterior density Λ( h | D j ) is obtained from Eq. ( 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 B-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 O O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-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 B-Citation I-Citation I-Citation I-Citation O O O O B-Citation I-Citation I-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 B-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 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 B-Citation I-Citation I-Citation O O B-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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

The saturation of the MRI and the outcome of a disc subject to these non-ideal effects is still the subject of intense debate. Stratified models including Ohmic and ambipolar diffusion only have shown that the disc could become essentially laminar (i.e. not turbulent) in the midplane, with a strong magnetically driven jet at the disc surface ( Bai Stone 2013 ; Simon et al. 2013 ; Gressel et al. 2015 ). For radii 1 between 1 and 10 au (where Hall effect dominates diffusive processes) a large-scale midplane stress is found by adding the Hall effect, with a strong field polarity dependence and no turbulence ( Lesur et al. 2014 ; Bai 2014 ), whereas the outer disc is found to be essentially insensitive to the Hall effect ( Bai 2015 ), though some polarity dependence could persist ( Simon et al. 2015 ). The results of Lesur et al. (2014) and Bai (2014) and, in particular, the presence of a large-scale “laminar” stress are both important and potentially problematic results. In effect, these simulations were done in the stratified shearing box framework ( Hawley et al. 1995 ) with a very limited radial extension (typically a few scale heights), so the Lesur et al. (2014) and Bai (2014) results indicate that the MRI is indeed active in these simulations, but it tends to produce structures that are larger than the simulation box. As a matter of fact, unstratified shearing box models have already indicated that the Hall-dominated MRI is prone to produce large-scale structures, such as zonal fields and flows ( Kunz Lesur 2013 , hereafter KL13) in wide enough boxes. All of these elements tend to point toward the fact that the Hall effect could be an efficient mechanism for triggering self-organisation in protoplanetary discs. In this paper, we explore this hypothesis using full 3D cylindrical models of accretion discs dominated by the Hall effect. Our aim is not to reproduce the exact structure of a disc with its detailed ionisation equilibrium but to test the hypothesis of self-organisation in a global model, free of the artefacts found in local, i.e. shearing-box simulations. We start by describing the physical framework in detail and giving and some remarkable facts concerning Hall dynamics. We then depict our numerical model and present the tests performed to validate it along with a reproduction and discussion of the multifluid models of O’Keeffe Downes (2014) . Next, we move to the core of the paper with the presentation and characterisation of several Hall-dominated models, putting emphasis on the physical mechanisms driving self-organisation. We then explore some potential treats to these mechanisms such as diffusive effects and more complex field configurations. We conclude by discussing the link between these results and recent observations along with extensions of this work to more realistic numerical setups. 2. Framework 2.1. Physical model We want to model a thin disc of partially ionised gas orbiting a central mass and threaded by a


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

Acknowledgements We thank Andrew Baker, Laure Ciesla, Annalisa De Cia, Loretta Dunne, Haley Gomez, Leslie Hunt, Suzanne Madden, Joshua Peek, Molly Peeples, Paola Santini, Raffaella Schneider, Jason Spyromilio, Phil Wiseman and Svitlana Zhukovska for stimulating discussions and/or providing data. We thank the referee for useful suggestions. We further acknowledge the Kavli Institute for Theoretical Physics ‘Cold Universe’ workshop where some of this work was completed. This research was supported in part by the National Science Foundation under Grant No. NSF PHY11-25915. RSS thanks the Downsbrough family for their generous support, and acknowledges support from the Simons Foundation through a Simons Investigator award.


O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialRegion I-CelestialRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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-Instrument I-Instrument O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O

have half-light radii of 60pc, would be barely resolved with NIRCam. 3.2.2 The main epoch of GC formation Each individual GCP will be totally dark (in UV) before experiencing its main (1G) burst of star formation, quickly reaching its peak SFR and brightness, then followed by rapid decline, possibly punctuated by a series of secondary (2G) bursts. Then rapidly turning passive and fading well below observability. A uniform GC formation rate between z 8 and 3 has been assumed above, but it may well be that the GC formation rate is initially very low, then peaks at a specific redshift and then declines, with few clusters still forming at lower redshifts. Having explored this redshift range, observations should then be able to identify such a golden age of GC formation, therefore establishing the relative timing of GC and galaxy formation, and providing, incidentally, a straight check for local GC ages as inferred from isochrones. 3.2.3 Clustering GC are not uniformly distributed in the local Universe, but clusters around their parent galaxies. This must be the case also at high redshift, while they are forming, though the parent galaxy may not be in place yet. Thus, one expects candidate GCPs to be highly clustered, lying within groups of 100kpc, or 20arcsec size (see Table 1 ). With sufficient statistics, it should be possible to directly establish the connection between the peak of GC formation and the stage of development of the host galaxy: clusters of GCPs as signposts of incipient massive galaxy formation. 4 DISCUSSION AND SUMMARY GCPs identified via BB photometry will need a spectroscopic confirmation, and the most obvious and timely follow up will be with JWST itself, either with the NIRCam grizm capability or with NIRSpec. In the longer run, 3040m class telescopes with their adaptive optics capabilities will offer unparalleled resolution. However, even before spectroscopic observations, some confirmation may come for those GCP candidates detected in more than one band, with SED fits providing age, mass and redshift constraints. Of course, more information could be gathered for those objects detected with NB filters, but they could be at most just a few. Designing a specific observing plan is far beyond the scope of this Letter. From the estimates given here it is relatively easy to infer what kind of information could be obtained for given invested observing time. On the other hand, deep multiband imaging over many fields, either primary or parallel, will certainly be done with JWST . This exercise has demonstrated that GCPs can be detected, with the number of detections critically depending on the mass of the progenitors, i.e. on the mass budget factor f MB . If GCPs were just marginally more massive than their present-day progeny then only the most massive ones could be detected, i.e. would have BB fluxes at formation above the thresholds given in Table 2 , scaled to the actual integration time. If this were the case, than the massive


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Identifier I-Identifier 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 B-Wavelength I-Wavelength O O O O O O O O B-Wavelength I-Wavelength O O O O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Identifier I-Identifier O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Identifier I-Identifier O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength 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 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-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

features may be seen within a “mossy” region that is oriented roughly along the axis of the supergranular network elements. In this case, the presence of small loops is hardly surprising, given that the underlying network is interspersed with minority-polarity flux elements. Figure 12. Moss-like region associated with supergranular magnetic network located just north of NOAA 12321, 2015 April 18. The circled area has radius 30′′ and is centered at (265′′, 391′′). Top panel: sharpened 17.1 nm image recorded at 14:29:47 UTC. Second panel: sharpened 19.3 nm image recorded at 14:29:42 UTC. Third panel: sharpened 21.1 nm image taken at 14:29:47 UTC. Bottom panel: HMI magnetogram recorded at 14:29:49 UTC and saturated at ±100 G. In this case, the looplike fine structure seen inside the moss is consistent with the presence of positive-polarity flux elements scattered in and around the negative-polarity network. Finally, Figure 13 shows an inverted-Y structure embedded in an area of moss inside NOAA 12335, as observed at 06:14 UTC on 2015 May 5. The base of the structure is rooted in strong negative-polarity plage, but the bright moss occupies a much wider area, extending through the weaker-field region to the south. The dark areas in the 17.1 nm image in the top panel represent fibrilar and filament material located near large- and small-scale polarity inversion lines. Figure 13. Moss region inside NOAA 12335, 2015 May 5. The circled area has radius 12′′ and is centered at (−376′′, −152′′). Top panel: 17.1 nm image taken at 06:14:35 UTC. Second panel: sharpened version of the same image. Third panel: sharpened 19.3 nm image taken at 06:14:30 UTC. Bottom panel: HMI magnetogram recorded at 06:14:51 and saturated at ±100 G. The inverted-Y structure is located in strong negative-polarity plage, but the underlying moss extends southward into areas of weaker photospheric field. These examples suggest that a strong underlying photospheric field is neither a necessary nor a sufficient condition for the presence of bright moss. 5. Summary and Discussion We have presented illustrative examples of inverted-Y structures embedded inside Fe ix 17.1 nm moss, where the underlying photospheric field was purely unipolar according to simultaneous HMI magnetograms. (Additional examples may be seen in Figures 2, 4, and 5 of Wang 2016 .) The triangular or dome-shaped bases of these structures had horizontal dimensions of ∼3′′–6′′ or ∼2–4 Mm. In the standard topological interpretation, the base contains minority-polarity flux, with a null point located at its apex. The lifetimes of the looplike footpoint features ranged from less than a minute to the order of an hour, with the smaller features generally being shorter-lived than the larger ones. As an alternative possibility that does not require the presence of minority-polarity flux, the triangular structures might represent canopies overlying individual granular cells, with thermal pressure dominating above the


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

We thank Benjamin Bromley, Eric Charles, Scott Kenyon, Christopher Kochanek, Sebastien Muller, and Dan Schwartz for valuable comments and discussions. We thank the referee for providing comments that have led to a tighter discussion. A. B. is supported by the Department of Energy Office of Science, NASA the Smithsonian Astrophysical Observatory with financial support from the NCN grant DEC-2011/01/M/ST9/01891. M.J.G. is supported by the Smithsonian Institution.


O O O O B-Person I-Person O O O O O O O O O O O O O O O O O B-Person I-Person O B-Person I-Person O O O O B-Collaboration O O O O O O O O O O O O B-Telescope I-Telescope I-Telescope O O O O O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization O O O O B-Organization O O O O O O O B-Organization O O O O O B-Organization O O O O O O O O O O B-Organization B-Grant I-Grant I-Grant O O O O O O O B-Database I-Database I-Database B-Database O O O O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization I-Organization I-Organization

We thank the referee, Dennis Zaritsky, for a thoughtful review that led us to broaden the scope of this paper. We also thank Matt Bershady and Rob Swaters for conversations about the DiskMass project. This work is based in part on observations made with the Spitzer Space Telescope , which is operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA. Support for this work was provided by NASA through an award issued by JPL/Caltech. Other aspects of this work were supported in part by NASA ADAP grant NNX11AF89G. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.


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

signatures, it will also be important to better explore problems such as disk formation, the formation of disk outflows, and the termination of accretion by means of multidimensional simulations in the future. We note that the fallback accretion energy is more likely to be activated in hydrogen-rich progenitors from the perspective of stellar evolution. It is hard to achieve the conditions required to form magnetars in hydrogen-rich progenitors (e.g., Heger et al. 2005 ) because of efficient angular momentum transport from the core to the hydrogen-rich envelope, in particular if dynamo action is considered. For fallback-powered SNe, one needs to form an accretion disk near the compact remnant to have the accretion disk wind powering the SNe. Such an accretion disk can be formed even if the initial rotational period of the core is small because shells farther out in the envelope have higher specific angular momentum and can easily reach Keplerian velocities before being accreted onto the central compact object. Even if the angular momentum in the envelope is not sufficiently large, asymmetric explosions may impart sufficient angular momentum to the outer envelope by imparting some tangential velocity onto the fallback material, as found in a more energetic fallback supernova model (C. Chan et al. 2019, in preparation), which is enough to make an accretion disk as it falls back. Fallback-powered SNe may also be affected by the interaction between SN ejecta and a dense circumstellar medium (CSM) surrounding them. Although the 40 progenitor we studied does not experience much mass loss during its evolution, more massive progenitors are expected to undergo significant mass loss before the explosions due to the pulsational pair instability (Woosley 2017 ). After forming a dense CSM due to the pulsational pair instability, the progenitors are expected to collapse by forming BHs and may result in the fallback-powered SNe. Therefore, the existence of a dense CSM could be common in the fallback-powered SNe. The possibility of CSM interaction in fallback SNe needs to be studied further in the future. Difference in CSM configurations with the same central engine can result in a variety of LCs (e.g., Fischer et al. 2018 ). Finally, fallback-powered SNe may be common among the explosions of the first stars. It has been predicted that the first stars have a top-heavy initial mass function (e.g., Hirano et al. 2015 ), and many of them are likely to be massive enough to form a BH during their explosions. Pair-instability SNe from the first stars (Heger Woosley 2002 ) are generally considered as potential SNe that could become bright enough to be observed even from this early epoch of cosmic evolution in the future transient surveys, especially in near-infrared (e.g., Scannapieco et al. 2005 ). We have shown that the fallback-powered SN from the 40 first star can be as luminous as pair-instability SNe. The mass range of pair-instability SNe that can be as


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

the IC file, which sets two haloes + star system simultaneously. The NGC 1052 system and the NGC 1052-DF2 system are always initially placed 400 kpc apart, with a fixed relative velocity of 250 km s –1 towards each other, which is consistent with the gravitational acceleration of free-falling from infinity and checked later to satisfy the velocity projection requirement. In order to control the NGC 1052 stellar distribution precisely to match the deprojection of the cored n = 3.4 Sérsic profile, we use a static baryonic potential kept at the centre of NGC 1052 instead of living particles. The NGC 1052 halo and NGC 1052-DF2 halo are simulated by 5.54 million and 0.06 million halo particles, respectively, and 0.1 million star particles simulate the luminous NGC 1052-DF2 profile. [Such initial configuration and simulation set-up is shared by the simulation for an alternative dark matter model; see the last paragraph. The physics for the pure CDM model is later tested by higher resolution simulation (Yang, Yu An 2020 ).] The gravitational softening length is 114 pc for halo particle and 14.4 pc for star particle. The bulk of the parameter scan is 2D, namely on the impact parameter b and the stellar Plummer radius r P (equivalent to its central density ρ c ). 3 RESULTS AND DISCUSSION In Fig. 3 , we plot the information extracted from the snapshots, which can be consistent with the observation after the encounter; here and later, d is the true 3D distance between the centres of the two galaxies. First, in the left-hand panel, we can see that with a scan of impact parameter at a spacing of 0.2 kpc, all simulations within this b range give small enclosed DM mass within the 7.6 kpc, which can be consistent with the observation, at the level of M / L 8. This is a consequence of the initial radial distribution, since before encounter the enclosed mass at the corresponding radius has a similar ratio. We can see that generally the smaller the impact parameter, the larger the stretch, and the smaller the enclosed mass in the 7.6 kpc. In the lower subpanel, we check the visual velocity relative to the central NGC 1052, and in a region, it can be consistent with the observed value. Figure 3. The combination of the two effects explains the observed lack of DM in NGC 1052-DF2. Left-hand panel: DM enclosed within the 7.6 kpc from several simulation snapshots after the encounter, in which we scan the impact parameter from 3.0 to 4.0 kpc. In the bottom subpanel, we also check the radial velocity relative to NGC 1052 and confirm that the observed 293 km s –1 can be reproduced within several snapshots. The two groups of curves are for NGC 1052-DF2 passing visually in front of or behind the central NGC 1052, respectively. They correspond to the two extremes in their final velocity angles with the line of sight, when considering the non-zero impact parameter and the bending of trajectory. Right-hand panel: The probability histogram by randomly selecting 10 star


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

ACKNOWLEDGEMENTS KEKC and MPK acknowledge support from the UK’s Science and Technology Facilities Council (grant agreement No. ST/M001008/1). JEG is supported by the Royal Society. MJM acknowledges the support of the National Science Centre, Poland through the POLONEZ grant agreement No. 2015/19/P/ST9/04010; this project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 665778. KK acknowledges support from the Swedish Research Council and the Knut and Alice Wallenberg Foundation. NB acknowledges support from the European Research Council Advanced Investigator Program, COSMICISM (ERC-2012-ADG-20120216, PI R.J.Ivison).


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We thank the anonymous referee for valuable comments. We also thank Bertram Bitsch, Hidekazu Tanaka and Takanori Sasaki for useful comments and suggestions. Numerical computations were conducted on the general-purpose PC farm at the Center for Computational Astrophysics, CfCA, of the National Astronomical Observatory of Japan. This work was supported by JSPS KAKENHI Grant Number 16H07415.


O O O O O O O O B-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship O O O O O B-Organization I-Organization I-Organization O O B-Fellowship O B-Person O O O B-Organization O B-Grant O O B-Person O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Grant I-Grant I-Grant O O B-Grant O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O O O O O O O O O B-Telescope I-Telescope I-Telescope B-Telescope O O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O B-Location I-Location I-Location I-Location O B-Location B-Observatory I-Observatory I-Observatory I-Observatory B-Observatory O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O B-Organization I-Organization I-Organization B-Organization O O O O O O O O B-Observatory I-Observatory I-Observatory I-Observatory B-Observatory I-Observatory I-Observatory I-Observatory O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O O O O O B-Organization I-Organization I-Organization O O B-Survey O O O O O B-Organization I-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization O O B-Location B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Survey O O B-URL O B-Survey O O O O B-Collaboration I-Collaboration I-Collaboration O O O O O O B-Collaboration I-Collaboration O O B-Organization I-Organization I-Organization O B-Collaboration I-Collaboration I-Collaboration B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O B-Collaboration I-Collaboration I-Collaboration O B-Collaboration I-Collaboration I-Collaboration B-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Collaboration I-Collaboration I-Collaboration I-Collaboration I-Collaboration B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization O B-Collaboration I-Collaboration I-Collaboration B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O B-Organization I-Organization O O O O O O O O O B-Telescope B-Instrument O B-Telescope O O B-Software B-Software

This research was conducted as part of the Cerro Tololo Inter-American Observatory REU Program, which is supported by the National Science Foundation under grant AST-1062976 respectively. R.Z. acknowledges support from NSF grant AST-1108948. Support for S.D. is provided by the Ministry of Economy, Development, and Tourism’s Millennium Science Initiative through grant IC120009, awarded to The Millennium Institute of Astrophysics, MAS. This research is based in part on observations obtained at the Southern Astrophysical Research (SOAR) telescope, which is a joint project of the Ministrio da Cincia, Tecnologia, e Inovao (MCTI) da Republica Federativa do Brasil, the US National Optical Astronomy Observatory (NOAO), the University of North Carolina at Chapel Hill (UNC), and Michigan State University (MSU). It is also partly based on observations at Kitt Peak National Observatory, National Optical Astronomy Observatory, which is operated by the Association of Universities for Research in Astronomy (AURA) under a cooperative agreement with the National Science Foundation. Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the participating institutions, the National Science Foundation, and the U.S. Department of Energy Office of Science. The SDSS-III website is http://www.sdss3.org/ . SDSS-III is managed by the Astrophysical Research Consortium for the participating institutions of the SDSS-III Collaboration, including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, Carnegie Mellon University, the University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofisica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, the Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington, and Yale University. We thank the anonymous referee for useful comments. Facilities: WIYN (Hydra) , SOAR . Software: IRAF, Topcat.


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 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 B-Citation I-Citation O O O B-Citation I-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 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-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-Instrument B-Citation I-Citation I-Citation I-Citation O B-Instrument B-Citation I-Citation I-Citation I-Citation O O B-Instrument 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 O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Database I-Database I-Database B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O

late times based on sophisticated simulations is presented in Mirizzi et al. ( 2016 ). In these studies the initial conditions have been prepared using other supernova models, thereby separating the PNS cooling from the explosion mechanism. In order to explore the connection between progenitors and compact objects using the neutrino signal, it is essential to study the long-term neutrino emission starting from the initial stellar model and include the thermal evolution of the PNS born in the resulting explosion. Evolution from the supernova explosion to the formation of a neutron star has been studied in 1D (Totani et al. 1998 ; Hüdepohl et al. 2010 ; Fischer et al. 2010 ) for selected progenitors and to a limited extent in 2D (Suwa 2014 ). 11 11 See Nakamura et al. ( 2015 ) and Horiuchi et al. ( 2018 ) for limitations of these models. Neutrino light curves in the 1D models by Totani et al. ( 1998 ) and Dalhed et al. ( 1999 ) have been routinely used to evaluate the total event number at neutrino detectors (see also Mirizzi et al. 2016 ). Due to limitations in the ability of these predictions and their focus on explosion dynamics, the expected number of neutrino events at underground neutrino detectors such as IceCube (Tamborra et al. 2013 ), Super-Kamiokande (Ikeda et al. 2007 ), and Hyper-Kamiokande (Abe et al. 2011 ; Hyper-Kamiokande Proto-Collaboration et al. 2018 ) has been estimated only for the dynamical phase using various models and numerical simulations to discuss these detectors’ ability to probe the physics of the supernova. As a result, the long-term behavior of the neutrino burst from the PNS has not been studied in detail with modern simulations covering a variety of progenitors. Our first aim in the current study is, therefore, to predict the basic features of the expected number of events at Super-Kamiokande for the full time sequence of supernova models. We utilize neutrino emission properties from a supernova neutrino database (Nakazato et al. 2013 ), which covers the complete dynamical evolution of the event from gravitational collapse to the cooling of the PNS. Through comparisons of event numbers for a set of progenitors systematically obtained from neutrino-radiation hydrodynamics (RHD) and PNS cooling simulations, we explore the differences in neutrino signals among models based on different progenitors. We discuss the time profile of the event rate for both early times around the bounce and the later phases of PNSs. We estimate the basic features of the event rate evolution for various models to assess whether one can extract information on the progenitor from future observations of a supernova neutrino burst. This is an important step in discussing the possibility of studying the progenitor’s mass, metallicity, and explosion timing, for instance, immediately after detection at Super-Kamiokande. Our second aim is to demonstrate the importance of the late phase of supernova neutrino emission. We study the long-term


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−1 . Observations of BG Ind were obtained simultaneously in two cameras on WASP-South over three observing seasons, from 2012 July 3 to 2014 December 6. Fluxes are measured in an aperture with a radius of 132 arcsec for the 85-mm data and instrumental trends are removed using the SYSRem algorithm (Tamuz, Mazeh Zucker 2005 ). Data points more than 5 standard deviations from a phase-binned version of the light curve were rejected and the entire night of data was rejected if more than one-fourth of the observations were identified as outliers based on this criterion. An 8-d section of the WASP measurements is shown in Fig. 2 . Note, we converted the original HJD(UTC) times of the WASP observations into BJD(TDT) for the forthcoming analyses. We also applied the same transformations for all the archival data that we describe below. Figure 2. An 8-d-long section of the WASP observations of BG Ind (blue circles). Red dots represent the best-fitting spectro-photodynamical model solution (see later, in Section 3 ) projected back to the epoch of each individual WASP measurement, while the black line shows the evenly phased model solution. The residuals curve is also shown below. 2.4 Other ground-based archive photometric data used for our analysis We downloaded publicly available Strömgren u, v, b, y photometric observations from the ESO archive (Manfroid et al. 1991 ; Sterken et al. 1993 ). These observations were carried out between JDs 2 446 581 and 2 447 069. The light curves in each bandpass contain 175 measurements. We used these data primarily to determine additional times of eclipses in binary A. Unfortunately, however, the majority of the nightly observations contain only a few measurements, and we were therefore able to determine the mid-times of only two primary eclipses (see below, in Section 2.6 ) from this data set. BG Ind was also observed by Jens Viggo Clausen and collaborators as part of their long-running observing programme to measure absolute dimensions for solar-type stars in eclipsing binaries, carried out since 1994 at the Strömgren Automatic Telescope at ESO, La Silla. Unpublished data and manuscripts that were in preparation from this observing programme have been made available to one of us (PM), from which we extracted five more eclipse times (see again, in Section 2.6 ). The observing procedures and data reduction for these observations are similar to those described in Clausen, Helt Olsen ( 2001 ). 2.5 Disentanglement of the light curves For the combined analysis of all the observational data, we used the original TESS time-series, i.e. the net light curve of the two binaries together. However, at the start of the analysis, we found it worthwhile to disentangle the light curves of the two binaries, so we could examine each one separately. We have described this process in substantial detail in Powell et al. ( 2021 ). Therefore, we review only the highlights here. First, we folded and binned the Sector 1 (i.e. Year 1) TESS SAP


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Laurent Chemin acknowledges the financial support from CNES. We are grateful to an anonymous referee whose suggestions led to clarify the discussion, content, and structure of the manuscript. This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration ( http://ned.ipac.caltech.edu ). We acknowledge the usage of the HyperLeda database ( leda.univ-lyon1.fr ). The SDSS image is from cosmo.nyu.edu/hogg/rc3 , prepared by David W. Hogg, Michael R. Blanton, and the Sloan Digital Sky Survey Collaboration.


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

observations for a sample of 14 luminous nearby QSO host galaxies that we interpret in conjunction with the available optical integral field observations. This data set significantly extends the sample of luminous unobscured QSOs with molecular gas mass estimates at low redshift. Our main results of this work can be summarized as follows: We detect the 12 CO(1–0) emission line in 8 of 14 targets (∼60 per cent) with a clear preference for disc-dominated and major merger systems with a detection rate of nearly 80 per cent. The integrated 12 CO(1–0) emission line matches the spatially integrated Hα line profile, indicating that both are tracing star formation regions when averaged over kpc scales. We also detect the 12 CO(2–1) emission line in 7 of 11 targets (∼60 per cent). The corresponding r 21 brightness temperature ratio is close to 1 and ranges between 0.5 and 1.3. Some of the lowest ratios may suggest that the CO emission is already sub-thermal at J = 2 in these systems. While the disc-dominated QSO host galaxies exhibit similar gas fractions and gas depletion time-scales compared to non-AGN host galaxies, we find that bulge-dominated QSO hosts have systematically smaller gas fractions but shorter gas depletion times, given their elevated SFRs. The two major mergers in our sample show high gas fractions and rather short gas depletion times as expected from simulations for strongly interacting systems. We report a positive correlation between BH accretion rate and total molecular gas mass for disc-dominated QSO host galaxies after combining our sample with literature data. We interpret this as an upper limit of BH accretion rate, given our initial selection for the most luminous QSO at the considered redshift. We can explain this trend using a simply toy model that links the circumnuclear gas surface density with the total gas mass through a simple scaling relation for discs. The BH accretion rate in bulge-dominated QSOs host galaxies is significantly higher given their molecular gas content compared to disc-dominated QSOs hosts. This may be explained either by a more compact or steeper gas surface density gradient, by removal of the outer envelope of gas through feedback or by a significantly higher gas temperature, leading to a different composition of the different phases of ISM. While we did not measure a higher CO line excitation based on the r 21 temperature brightness ratio, this needs to be investigated with more excitation-sensitive observations. Despite the relatively small sample size of this study, we can confirm that the molecular gas content and star formation efficiency, at least in disc-dominated QSO hosts and major mergers, are indistinguishable from the corresponding population of non-AGN galaxies. Negative AGN feedback that either reduces the star formation efficiency or significantly lowers the cold gas content through galactic outflows is an implausible scenario for the majority of QSO hosts studied in this work.


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 B-Telescope O O B-Observatory O O B-Citation I-Citation I-Citation I-Citation 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 B-Observatory I-Observatory I-Observatory I-Observatory 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 B-Collaboration I-Collaboration I-Collaboration I-Collaboration B-Collaboration 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 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-Telescope I-Telescope I-Telescope I-Telescope B-Telescope B-Citation I-Citation I-Citation I-Citation O O O O B-Observatory I-Observatory I-Observatory O B-Observatory 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 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-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 B-Telescope O O O B-Observatory O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O B-Observatory O O O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O B-Telescope O O O O O O B-CelestialObject O O O B-Wavelength I-Wavelength O

spectral line, which is used to derive the information of the magnetic fields. In addition, Qiu Gary ( 2003 ) discussed the possibility of change in line profiles during a transient polarity reversal observed in the photospheric magnetic field measurements obtained from the MDI instrument aboard SOHO space mission. Wang ( 1992 ) and Wang et al. ( 1994 , 2002 ) reported abrupt and permanent changes in the evolution of magnetic fields in the flaring region during the different class of solar flares using the data from Big Bear Solar Observatory. Later on, extensive analysis done by Sudol Harvey ( 2005 ) and Petrie Sudol ( 2010 ) of X- and M-class solar flares using the line-of-sight (i.e. longitudinal) magnetic fields obtained from Global Oscillation Network Group (GONG; Harvey et al. 1996 ) instruments, showed abrupt and permanent changes in the magnetic fields in the flaring locations within 10-min duration with a median magnitude of 100 G. In addition, Kumar et al. ( 2016 ) also found abrupt and persistent changes in line-of-sight magnetic fields at different locations in active region during an M6.5 class solar flare using the data from Helioseismic and Magnetic Imager (HMI; Schou et al. 2012 ) instrument aboard the Solar Dynamics Observatory ( SDO ; Pesnell, Thompson Chamberlin 2012 ) space mission. Hudson et al. ( 2008 ) and Fisher et al. ( 2012 ) proposed that abrupt changes in the magnetic fields can lead to an impulsive change in Lorentz force, which is also known as ‘magnetic-jerk’, and this can induce seismic emission in the sunspots. However, Raja Bayanna et al. ( 2014 ) observed distortions in the two circular polarization states of light, the left (LCP) and the right circular polarization (RCP) observations in the flaring locations which showed transient changes in Doppler velocity and line-of-sight magnetic fields during an X-class flare, using the line profile observations from HMI instrument aboard the SDO space mission. They showed that observed transient changes in Doppler velocity and line-of-sight magnetic fields in flaring locations are prone to artefacts in the measurements. Therefore, in this paper, we present a detailed analysis of seismic emission in the sunspots, which are away from the flare ribbons and hard X-ray footpoints accompanying large solar flares. Such acoustic enhancements are supposed to be free from any flare related problems in the observational data. In the following sections, we first describe the observational data and selection criteria for choosing the active regions aimed for our analysis. This is followed by methods of analysis and the results obtained. We finally conclude with discussions concerning our results. 2 THE OBSERVATIONAL DATA We have extensively used observations from the HMI instrument aboard the SDO spacecraft, which is a solar space mission of the National Aeronautics and Space Administration (NASA). The HMI instrument observes the photosphere of the Sun in Fe i 6173 Å absorption


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

GRAVITY was developed via a collaboration of the Max Planck Institute for Extraterrestrial Physics, LESIA of Paris Observatory and IPAG of Université Grenoble Alpes/CNRS, the Max Planck Institute for Astronomy, the University of Cologne, the Centro Multidisciplinar de Astrofisica Lisbon and Porto, and the European Southern Observatory. Part of this work was supported by the European Union under ERC grant 639248 LITHIUM. J.W. is supported by the Heising-Simons Foundation 51 Pegasi b postdoctoral fellowship. A.A., P.G., and N.A. acknowledge funding from Fundação para a Ciência e Tecnologia through grants PTDC/CTE-AST/116561/2010, SFRH/BD/52066/2012, COMPETE FCOMP-01-0124-FEDER-019965, UID/FIS/00099/2013, and SFRH/BSAB/142940/2018. R.G.L. acknowledges funding by H2020 Marie Curie fellowship 706320.


O O O O O O O O O O B-Person I-Person O O O O O O B-Person B-Person O B-Person O O O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Grant I-Grant B-Person O B-Person O B-Grant I-Grant I-Grant O O O O O O O O O O O O O O O B-Telescope I-Telescope I-Telescope B-Telescope O O O B-Observatory I-Observatory I-Observatory I-Observatory I-Observatory I-Observatory I-Observatory O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Location I-Location I-Location I-Location B-Software O O O O B-Observatory I-Observatory I-Observatory I-Observatory O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O O O O O B-Organization I-Organization I-Organization O O O O O O O O O B-Organization I-Organization I-Organization B-Organization O B-Telescope O B-URL O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization B-URL O O O O B-Organization O O O O O O O O O O O O O B-Collaboration I-Collaboration I-Collaboration B-Person O B-Organization I-Organization I-Organization I-Organization I-Organization 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 I-Person O O O O O O O O O O O O O B-Person O B-Person I-Person O O O O O O O O O B-Person I-Person B-Organization I-Organization I-Organization O O O O B-Software I-Software I-Software O O O O O O O O B-Organization I-Organization I-Organization I-Organization O O B-Grant

The authors thank Jacob Heerikhuisen for sharing the model of the heliosphere that allowed them to assess the distance to the heliospheric termination shock, and Charles Smith for encouraging them to publish the first ideas of the study developed here. J.M.S. thanks Marcin Szpanko for the help with preparation of Figure 17 and Duncan Pettengill (Wolfram Technology Group) for technical support with Wolfram Research Mathematica software. The presented study is supported by the Polish National Science Center grant No. 2015/19/B/ST9/01328.


O O O O O O O O O O O O O O O O O O O O O O O O O O B-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization B-Organization O O O O O O B-Mission O O O B-Organization I-Organization I-Organization O O O O B-Collaboration I-Collaboration O O O O O O O O O B-Collaboration I-Collaboration O O O O O O O O O O O O O O O O O O O O B-ComputingFacility B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility O B-Organization B-Organization I-Organization I-Organization I-Organization O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

Acknowledgements We thank the referee for helpful comments and multiple suggestions that significantly improved this paper. This work is part of a thesis co-funded by the University Aix-Marseille and the Centre National d’Études Spatiales (CNES) in the context of the upcoming Euclid mission of the European Space Agency, as developed by the Euclid Consortium. The authorswould like to thank the members of the AMAZED team who provided helpful feedback and insightful discussions on this topic. This work benefitted from access to databases managed by the CESAM (Astrophysical Data Center of Marseille) in LAM (Laboratoire d’Astrophysique de Marseille). We would also like to express our thanks to all the contributors whose fruitful comments and revision of this manuscript helped us expand our understanding and improve the paper.


O O O O O O O O B-Observatory O O O B-Observatory I-Observatory I-Observatory I-Observatory O O B-Proposal B-Proposal O B-Proposal O O O O O O O O O O O B-Person I-Person O O O B-Instrument O O O O O B-Person I-Person O O B-Telescope O B-Person I-Person O O O O B-Instrument O O B-Person I-Person O O O O O O O O B-Organization I-Organization B-Organization O O B-Grant I-Grant O B-Grant I-Grant B-Person O O O B-Organization B-Fellowship I-Fellowship O B-Telescope I-Telescope O O O O O O B-Observatory I-Observatory I-Observatory O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O O O B-Organization I-Organization O O B-Organization I-Organization

This work is based on observations made with ESO telescopes at the La Silla Paranal Observatory under programs 74.C-0209(A), 75.C-0014(A) and 91.C-0768(A). We would like to thank the anonymous referee for their comments, Casey Deen for performing the CRIRES observations and reading the manuscript, Chris Koresko for providing Keck/NIRC photometry, Hongchi Wang for helpful analysis of NACO photometry, and Peter Abraham for helpful discussions. This research was funded under Deutsche Forschungsgemeinschaft (DFG) programme nos. WO 857/10-1 and WO 857/13-1. CFM gratefully acknowledges an ESA Research Fellowship. The Submillimeter Array is a joint project between the Smithsonian Astrophysical Observatory and the Academia Sinica Institute of Astronomy and Astrophysics and is funded by the Smithsonian Institution and the Academia Sinica.


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

by supergiant shells. Simulations of supernova-driven turbulence in a representative section of a stratified galactic disk by Joung Mac Low ( 2006 ) came to a similar conclusion. Neglecting the action of self-gravity on the gas, they found that only 10% as much gas was swept up into regions able to gravitationally collapse as would have been required to maintain the star formation rate implied by the input supernova rate. 3. Toomre Instability Therefore, we now turn to large-scale gravitational instability in disks (Safronov 1960 ; Toomre 1964 ; Goldreich Lynden-Bell 1965 ), which offers an alternative mechanism to assemble gas dense enough to form molecules. Galactic dynamics appears to be driven by such instabilities, which at the largest scales drive spiral arm formation (Agertz et al. 2009 ; Wada et al. 2011 ). When these instabilities grow strongly enough because of gas infall or galaxy mergers they lead to the formation of giant clumps (Li et al. 2005 ) in what is called violent disk instability (Agertz et al. 2009 ; Dekel et al. 2009 ). (Those clumps may well themselves collapse into clusters of small clumps as shown by Behrendt et al. 2016 .) That molecular clouds can form more quickly by gravitational instability than collisional agglomeration was shown by Elmegreen ( 1990 ), despite their apparently having the same dependences on density and velocity dispersion. The Toomre instability criterion for gaseous disks (Goldreich Lynden-Bell 1965 ) iswhere Σ g is the surface density of the gas, σ g is its velocity dispersion including both thermal and nonthermal components, G is the gravitational constant, and κ 2 = −4 ωB is the square of the epicyclic frequency, with Oort’s constantIn a galaxy with a flat rotation curve, the second term in B can be neglected. In this case, , so that . The timescale for growth of a perturbation in an isothermal gas disk can be expressed in terms of Q g as (Wang Silk 1994 )At the solar circle, with r = 8 kpc, the rotational velocity ωr = 220 km s −1 , dropping only slowly to 170 km s −1 at a Galactic radius of 60 kpc (Xue et al. 2008 ). Thus, the epicyclic frequency κ = 1.26 × 10 −15 s −1 , and the growth time τ g = f ( Q ) κ −1 , where κ −1 ≃ 25 Myr and f ( Q ) is a function of Q with a value of order unity. If the diffuse gas with mass M d ∼ 4 M m (Ferrière 2001 ) forms into molecular clouds on the Toomre timescale, then the molecular gas formation rate would beIf the molecular gas is being dispersed on a timescale of the order of 10 Myr, this formation rate can replenish it at more than the required rate given in Equation ( 3 ). 4. Variation with Redshift We now consider how the timescale for molecular gas formation by gravitational instability varies with redshift. The Toomre timescale τ g ∝ ω −1 . The disk angular velocity of a galaxy ω can be characterized by its value at the exponential scale length of the disk ω ( R d ) = V c / R d , where V c is the roughly constant circular velocity of the disk


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

Table 6 shows a comparison of the jet half-opening angles derived from the best fits in this work with hydrodynamical modelling performed by Ryan et al. ( 2015 ) for four GRBs common to both studies. Our model produces systematically narrower jets (most likely caused by the model attempts to fit the early-time luminosity) that are partially consistent with Ryan et al. ( 2015 ) in errors (e.g. GRBs 051016B and 060614), and where they are not (e.g. GRB 061006), they are broadly consistent to ∼2σ–2.5σ. Table 6. Table showing the half-opening angles (in radians) for four GRBs, calculated from f B = 1 − cos (θ j ). θ j values are from the global best fits of this work (uncertainties are 95 per cent confidence interval); θ 0 values are from Ryan et al. ( 2015 ). Comparing our results with that of Gompertz et al. ( 2014 ), we can see the inclusion of fallback accretion within the propeller model allows for an improvement in fitting the ‘tail’ of the fading afterglow. This can be seen in GRBs 051227, 060614 and 061006, where Gompertz et al. ( 2014 ) did not produce such good fits to the tail. Hence, fallback accretion is a necessary addition to the propeller model in order to fully explain the energetics and morphologies of SGRBEEs. Additionally, the extended model handles variability and flares within the data much more naturally than Gompertz et al. ( 2014 ) and copes with the early-time luminosity detected by BAT. The parameters derived from the fits in Fig. 6 are presented in Table 7 . We find that the magnetic fields derived from the fits are in the moderate to high end of the parameter space and that the sample generally has slow initial spins. The slow initial spins are most likely due to the additional fallback spinning the magnetar up and, therefore, the constraints on high initial spin rates is relaxed. This has an impact on the value of the magnetic field derived as the fit moves along the correlation between B and P i discussed in Gompertz et al. ( 2014 ). The sample fits also tend to favour massive discs and narrow jet opening angles. This is most likely due to the model extracting as much of the available energy as possible to fit the high luminosities at early times in the light curve, data which was not included in the fits of Gompertz et al. ( 2014 ). The values of ε, δ, η dip and η prop are widely distributed throughout the parameter space. The derived parameters are consistent with predictions for a magnetar (Giacomazzo Perna 2013 ; Mereghetti, Pons Melatos 2015 ; Rea et al. 2015 ) and are also consistent with the results in Gompertz et al. ( 2014 ). Table 7. Parameters derived from the best global fits to the SGRBEE sample (bold values in Table 5 ). Reported errors are 95 per cent. Values marked with an [L] have reached a parameter limit; those marked with [F] were fixed during fitting. The values are also presented to indicate goodness of fit. We will now examine how increasing the number of free parameters affects the fits


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ACKNOWLEDGEMENTS The authors are grateful to the anonymous referee for a thoughtful report that helped improve the clarity of this work. AM was partly supported by an ‘ERASMUS+ for traineeship’ grant and partly by the NewCompStar network, COST Action MP1304. AM thanks the hospitality of the Anton Pannekoek Institute for Astronomy in Amsterdam, where most of this research was carried out. ND is supported by a Vidi grant awarded by the Netherlands Organization for Scientific Research (NWO). RW is supported by Top-1 grant from NWO. The authors acknowledge financial contribution from the agreement ASI-INAF I/037/12/0, as well as fruitful discussion with the international team ‘The disc–magnetosphere interaction around transitional millisecond pulsars’ at the International Space Science Institute, Bern. This work is partially supported by the HERMES Project, financed by the Italian Space Agency(ASI) Agreement n. 2016/13 U.O


O O O O O O B-Organization I-Organization I-Organization O O O B-Grant B-Person O O O O O B-Fellowship I-Fellowship I-Fellowship I-Fellowship O O 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 O O O O O O O O O O O O B-Person I-Person O O O B-Dataset I-Dataset I-Dataset O O B-Survey O O O O O B-Organization I-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization O O B-Location I-Location B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Survey O O O B-URL O B-Survey O O O O B-Collaboration I-Collaboration I-Collaboration O O O O O O B-Collaboration I-Collaboration O O B-Organization I-Organization I-Organization O B-Collaboration I-Collaboration I-Collaboration B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O B-Collaboration I-Collaboration I-Collaboration O B-Collaboration I-Collaboration I-Collaboration B-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Collaboration I-Collaboration I-Collaboration I-Collaboration I-Collaboration B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization O B-Collaboration I-Collaboration I-Collaboration B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O B-Organization I-Organization

This work was supported by the National Science Foundation under grant no. AST-1313169. RM was also supported by an Alfred P. Sloan Fellowship. We thank Jonathan Blazek, Uroš Seljak, Robert Lupton, Elisa Chisari, and Shadab Alam for useful discussions about this work. We thank the anonymous referee for helpful suggestions, and we thank Ananth Tenneti for sharing the MB-II shape catalogue. Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and the U. S. Department of Energy Office of Science. The SDSS-III web site is http://www.sdss3.org/ . SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, Carnegie Mellon University, University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofisica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington, and Yale University.


B-Person O B-Person O O O O O B-Organization O O B-Organization I-Organization I-Organization I-Organization O O B-Person O O O B-Organization O O O B-Grant O O O B-Organization I-Organization I-Organization B-Organization B-Organization I-Organization I-Organization I-Organization O B-Organization O B-Grant B-Person O O O B-Organization O B-Grant O O O O O O B-Archive I-Archive I-Archive I-Archive I-Archive I-Archive O B-Database O B-Database O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O B-Archive I-Archive I-Archive O O B-Organization I-Organization I-Organization I-Organization I-Organization O O O O B-Organization O O O B-Telescope O O O B-Instrument O O O O B-Instrument O O O O O O O O O O O O O

K.E.K. and M.P.E. were supported in part by NASA via the Air Force Research Laboratory. Support for G.C.S. was provided by NASA through contract No. 1257184 issued by the Jet Propulsion Laboratory (JPL), California Institute of Technology under NASA contract 1407. O.C.J. acknowledges support from NASA grant NNX14AN06G. This research has made use of NASA’s Astrophysical Data System Bibliographic Services, the Simbad and VizieR databases operated at the Centre de Données astronomiques de Strasbourg, and the Infrared Science Archive at the Infrared Processing and Analysis Center, which is operated by JPL. We thank the JWST Helpdesk and the MIRI team for making the MIRI filter functions available and the referee for helpful suggestions to clarify the paper.


O O B-Mission I-Mission O B-Mission I-Mission I-Mission O O O O O B-Organization B-Database I-Database I-Database O B-URL O O O O O O O O B-Mission O O B-Organization B-Database O O O O O O O O O B-Database I-Database I-Database I-Database O B-URL O O O O O O O O O O O O O B-Grant I-Grant I-Grant I-Grant I-Grant O B-Organization I-Organization B-Grant O B-Grant O B-Organization I-Organization I-Organization I-Organization O B-Location B-Organization O O B-Grant O B-Grant

We acknowledge Venus Express and Pioneer Venus Orbiter teams as well as the NASA Planetary Data System ( http://ppi.pds.nasa.gov ) for providing the data. We also thank ACE team and NASA CDAWeb for providing magnetometer data at 1 au, and the World Data Center SILSO ( http://www.sidc.be/silso/ ) for using the sunspot number data. This work is supported by the Science and Technology Development Fund of Macao SAR (008/2016/A1 and 119/2017/A3) and National Natural Science Foundation of China (NSFC) under grants 41564007 and 41731067.


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

to a time-span of 3.7 yr). The magnitude difference is only 0.08 mag, which is within the combined photometric error (0.11 mag). We also find that the I -band magnitude at t = 586 d is consistent with the extrapolation of SN 2014C’s earlier MMT light curve. Thus, it is possible that SN 2014C has faded significantly in the I band by t = 586 d, after which the light from Cluster A dominates the I -band brightness. We also note that the emission lines in the I band are much weaker than those in the B, V , and R bands ( M15 ; Anderson et al. 2017 ). To be conservative, however, we do not exclude the possibility that the SN was still bright in the I band and we regard the measured F814W brightness as an upper limit for Cluster A . Similarly, the F336W -band magnitude also remains almost constant from t = 1003 to 1462 d (which corresponds to a time-span of 1.3 yr). The magnitude difference is only 0.06 mag, which is comparable to the combined photometric error (0.05 mag). Note that during the same period, the F555W -band magnitudes faded by 0.17 mag. Yet, SN 2014C, like many other interacting SNe, exhibits a blue pseudo-continuum, which may arise from blended iron lines produced by the ejecta–CSM interaction ( M15 ; see also, e.g. SN 2006jc, Pastorello et al. 2007 ; Bufano et al. 2009 ). As a result, we cannot rule out the possibility that the F336W band is contaminated by the pseudo-continuum emission from the SN. Thus, we regard the F336W -band brightness also as an upper limit for Cluster A . The F275W and F300X bands were only observed at a single epoch. Both bands cover the [Mg ii ] doublets at ∼2800 Å; the F300X band also covers the [Fe ii ] line at ∼2950 Å. These two lines are important coolants and often appear to be very strong in emission for interacting SNe (Fesen et al. 1999 ; Fransson et al. 2005 ; Bufano et al. 2009 ). Thus, F275W and F300X bands may be contaminated by the SN light, although it is difficult to estimate the amount of its contribution. Still, they place important upper limits for the brightness of Cluster A at UV wavelengths. In summary, SN 2014C’s light was still significant until at least 4 yr post-explosion (the last epoch of F555W observation). This is consistent with the conclusion of T19 that SN 2014C experiences ongoing interaction between its ejecta and CSM at large distances. Still, the HST observations provide very important constraints on Cluster A ’s SED from the UV to the F814W band, a much wider wavelength coverage than the pre-explosion observations in the B, V, R , and F658N bands. Thanks to the higher spatial resolution provided by the new data, the measured SED of Cluster A is now much cleaner, i.e. without significant contamination from its nearby sources. 4 PROPERTIES OF THE HOST STAR CLUSTER We further try to infer the properties of Cluster A by fitting model spectra to its observed SED. Note that Cluster A is still associated with a considerable amount of (ionized) gas, given its bright


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

of the solution operator is Note that the exponential in equation ( 6 ) is simply a formal way to write down an operator. It is acting on the function to its right, in the above case this is the identity Id. To see that this construct indeed provides a solution to the differential equation with initial conditions y 0 , note that the series expansion of the exponential results in a series of differential operators acting on Id( y 0 ). This series is simply the Taylor expansion of the solution φ around t = 0. Since it is not possible to write down an explicit solution for the N -body problem, we turn to operator splitting methods. One way to view an operator splitting method is to take a differential equation of the form and rewrite it as Note that due to the linearity of the Poisson bracket, we have . This implies that for Hamiltonian systems we can split the equations of motion by splitting the Hamiltonian H into two parts, i.e. H = A + B . Depending on the splitting, we get two new sets of differential equations that we can study independently: In practice, we will choose a splitting that allows us to easily solve these new differential equations independently. In other words, we want to be able to explicitly write down the solution operators and . Using the notation from above, we have but because these exponentials are operators, not scalars, we unfortunately cannot use standard rules for exponentials. Specifically, we typically have For illustration purposes, imagine the above equation were true. We could then solve the differential equation in equation ( 7 ) by first applying the solution operator φ [ B ] to our initial conditions for a time t (remember, operators act to the right), then take the result and apply the solution operator φ [ A ] on it, again for time t . The result of the last operation would then correspond to the solution φ [ H ] at time t . But because the equation above is not true, we need to rely on the Baker–Campbell–Hausdorff (BCH) identity, 2 to get a similar expression where is a commutator. So if we apply the splitting procedure described above (corresponding to the left-hand side of equation 12 ), we do not solve the differential equation , but some other differential equation (given by the argument in the exponential on the right-hand side of equation 12 ). Formally, we can write down the Hamiltonian corresponding to the differential equation that we are actually solving as where we have used which follows from the Jacobi identity. Although we do not end up solving the Hamiltonian system we were trying to solve, the fact that we can write down a different Hamiltonian system that we seem to solve exactly is often quoted as why symplectic integrators have superior properties. 3 We can study the properties of this ‘nearby’ Hamiltonian to see how far our approximation is from the true solution. As we can see from the equation above, for small t , the Hamiltonian is close to the original Hamiltonian and only


O O O 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 B-Software I-Software O O O O B-Person I-Person B-Citation B-Citation O O O O O O O B-Instrument I-Instrument O O O O B-Organization O B-Grant O O B-Organization B-Grant I-Grant I-Grant I-Grant B-Grant O O O O O B-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O O O O B-Grant I-Grant B-Grant I-Grant O O B-Location I-Location O B-Grant O O O B-Survey O B-Survey O O O O O B-Organization I-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization O B-Location B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Location B-Organization O B-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization O B-Location O B-Survey O O O B-URL O O B-Survey O O O O B-Collaboration I-Collaboration I-Collaboration O O O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization B-Organization O B-Organization I-Organization I-Organization I-Organization O B-Collaboration I-Collaboration I-Collaboration B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Collaboration I-Collaboration I-Collaboration O B-Organization I-Organization I-Organization I-Organization B-Telescope B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization B-Organization O B-Organization I-Organization I-Organization B-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization O B-Observatory I-Observatory I-Observatory I-Observatory O O B-Organization I-Organization I-Organization O O O O O B-Telescope O O B-Organization O O O O O O O O O B-Organization O O O B-Organization O O O O O O O O O O B-Dataset I-Dataset I-Dataset I-Dataset I-Dataset O O O O O O O B-Organization I-Organization I-Organization I-Organization O O B-Organization

We thank the anonymous referee for the constructive report that helped us to improve the readability of the paper. The author acknowledges the use of the TOPCAT 3 and STILTS 4 software packages written by Mark Taylor (2005, 2006). This paper uses data taken with the MODS spectrographs built with funding from NFS grant AST-9987045 and the NSF Telescope System Instrumentation Program (TSIP), with additional funds from the Ohio Board of Regents and the Ohio State University Office of Research. We acknowledge financial support from the ARCHES project (7th Framework of the European Union, No. 313146). Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the US Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England. The SDSS Web Site is http://www.sdss.org/ . The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions. The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington. Based on observations obtained with XMM-Newton , an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA. This research has made use of data obtained from the 3XMM XMM-Newton serendipitous source catalogue compiled by the 10 institutes of the XMM-Newton Survey Science Centre selected by ESA.


O O O O O O O O O O O O O O O O O O O O O B-Person I-Person O O O O B-Telescope O O B-CelestialObject O B-Person I-Person O B-Person I-Person O O O O O O O O O B-Software O B-Software O O O B-Person B-Person B-Person B-Person O B-Person O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O O O B-Organization I-Organization I-Organization I-Organization B-Organization O B-Grant I-Grant I-Grant O O B-Grant I-Grant I-Grant I-Grant B-Person B-Person O B-Person O O O B-Organization O O B-Grant B-Grant O B-Grant O B-Person O O O O B-Grant I-Grant O O O O B-Grant O O O O O O O O B-ComputingFacility I-ComputingFacility O O B-Organization I-Organization I-Organization I-Organization O O O B-Grant I-Grant I-Grant O O O O O B-Grant I-Grant O B-Grant I-Grant O O O O O O O O O O O B-Organization B-Grant I-Grant I-Grant I-Grant I-Grant

We thank the anonymous referee for the comments that have greatly helped improve the presentation of our results. We also thank Emanuele Dalessandro for sending us his HST photometry for M3, and Luca Sbordone and Fiorella Castelli for their expert advice in the use of the ATLAS9 and SYNTHE packages. Support for A.A.R.V., M.C., J.A.-G., R.C.R., and S.A. is provided by the Ministry for the Economy, Development, and Tourism’s Programa Iniciativa Científica Milenio through grant IC 120009, awarded to the Millennium Institute of Astrophysics (MAS); by Proyecto Basal PFB-06/2007; and by Proyecto FONDECYT Regular #1141141. A.A.R.V., J.A.-G., and R.C.R. acknowledge support through FONDECYT postdoctoral grants #3140575, 3130552, and 3130320, respectively. J.A.-G. acknowledge support by the FIC-R Fund, allocated to the project 30321072. This work was done (in part) using the Geryon computer at the Center for Astro-Engineering UC, part of the Basal PFB-06 project, which received additional funding from QUIMAL 130008 and Fondequip AIC-57 grants for upgrades. Additional support for this project is provided by CONICYT’s PCI program through grant DPI20140066.


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