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

September 20, this was an 1833 (spatial) by 15 (slit width) box, 2019 October 1 had 15575 by 10, 2019 October 9 had 260 by 15, and 2019 October 10 had 18′′ by 24. The imaging data were extracted using circular aperture photometry with a radius of 250 and largely followed the reduction procedure outlined in Farnham et al. ( 2000 ) using the dust reflectance slope measured from our 2019 October 10 spectrum. The standard star used (HD 81809) is noted in that work to be less than ideal for blue/UV observations, so we have overestimated errors when possible. We note that for the 2019 September 20 and October 1 data sets, insufficient data were collected to allow a median combination of spectra, making the two data sets “look” even noisier than their later counterparts even though cosmic rays were cleaned from them. 3. Analysis, Modeling, and Results In order to search for molecular emission features, it is necessary to produce a flux-calibrated solar spectrum fit to subtract from the flux-calibrated data. This process creates a dust reflectance spectrum for the comet, which can be used to look for a spectral slope. The solar spectrum was taken from Chance Kurucz ( 2010 ) and binned to the resolution of each data set. The original flux-calibrated spectra, best-fit reflectance, and dust-subtracted comet spectra are shown in Figure 1 . The noisiness of the Bok data prevents a high-quality solar reflectance subtraction, while the later data become very linear after subtraction indicating a relatively good fit of the solar spectrum to the continuum points. Figure 1. Spectral observations of 2I/Borisov. The flux-calibrated and dust-subtracted spectra of all three nights of spectroscopy from 2019 October. The heliocentric and geocentric distances are listed underneath the telescope names and dates on the figure. The same background and background-subtraction process was applied to all data sets. The CN B–X (0–0) band centered at 388.3 nm can be seen clearly in the MMT and LBT data. (The data used to create this figure are available .) We consider the spectral slope between the blue, green, and red continuum regions defined for the Hale–Bopp filter set (Farnham et al. 2000 ) to compare reflectance slopes with other workers. These filters are centered at 4450, 5260, and 7128 Å, respectively. If we normalize our highest-quality data from 2019 October 10 at the green continuum point, then we find the blue-to-green slope to be S ′ = 22+/−4%/micron, and the green-to-red slope to be S ′ = 11+/−3%/micron. Fitzsimmons et al. ( 2019 ) suggested that the dust might be “redder” at shorter wavelengths, and our best data support that conclusion. After the reflected sunlight from dust was subtracted, we searched for emission from molecules in the coma of 2I/Borisov (Table 2 ). For each possible feature we subtracted a linear estimate of the background as determined by a fit to data on either side of the feature and then integrated using a trapezoidal method all flux


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

ACKNOWLEDGEMENTS We acknowledge financial support by the Deutsche Forschungsgemeinschaft within project Ur 32/27-2. Simulations were performed at the High Performance Cluster Elwetritsch (Regionales Hochschulrechenzentrum, TU Kaiserslautern, Germany).


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope B-Wavelength B-Wavelength I-Wavelength O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O 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 B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope B-Wavelength O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope B-Wavelength B-Wavelength O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O B-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-Telescope B-Wavelength B-Wavelength B-Wavelength O B-Wavelength I-Wavelength O O O O O B-Observatory B-Wavelength B-Wavelength I-Wavelength O B-Wavelength I-Wavelength 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

rotated about 1.1 turns. Accompanied by the rotation, some fine dark threads moved as a whole from the southeast to the northwest to the coronal loops (Figures 2 (a)–(f)). At last, most of the threads interacted with the overlying field (see also Figure 4 (f)). In this process, a circular ribbon developed at the site of filament eruption as indicated in Figures 2 (b) and (e). By 09:04 UT, an interaction between the shifting filament and the coronal loops occurred and a brightening of the filament appeared at the reconnection sites (indicated by the white arrow in Figure 2 (f)). The brightened plasma around the reconnection region may be heated to higher temperature. Meanwhile, the reconnection resulted in the formation of some newly closed hot loops connecting “P” to “N1” (indicated in Figure 2 (i)). From AIA 304 Å observations at 09:06 UT, the filament was split and disintegrated completely. It is clear that the draining process is not freely falling but shaped by the magnetic field, and the bulk of filament mass flowed away along the nearby magnetic field, taking the shape of a jet (Figures 2 (g) and (h)). Figure 2. AIA 94, 304 Å, and H α images showing the eruptive process of the filament and subsequent interaction between the filament and coronal loops. (a–c) H α images showing the filament eruption. The solid arrow in panel (c) denotes the shift movement of the filament during filament rising. (d–g) 304 Å images showing the eruptive filament colliding with coronal loops. The blue and white contours have the same meaning as in Figure 1 . The coronal loops originating from “N1” are superposed with white lines, such as in panel (d) of Figure 1 . (h, i) Close-up views of the interacting region at AIA 304 and 94 Å, for which the FOV is indicated by the dashed line box in panel (f). Panel (i) is a 94 Å image showing newly formed hot loops. The white lines with an arrow (slice1 and slice2) mark the slit position of time slices as shown in Figure 3 (c) and (f), respectively. The white box of panel (g) indicates the FOV for Figure 4 . The animated version of this figure compares the AIA 94, 211, and 304 Å images from 08:40 to 09:10 UT compressed to a 5 s movie. (An animation of this figure is available.) Figure 3. (a–c) H α images showing an unwinding motion of filament (counterclockwise from above). A curved arrow indicates the direction. (d) Time slice taken from H α images at the position marked by slice3 in panel (b). A strand rotating around the filament is highlighted by the white dotted line. Figure 4. (a, b) Normalized light curves of AIA 94, 304, 335, and 1600 Å, and the positive magnetic flux. Fermi HXR 10–14 keV and 14–25 keV fluxes are also plotted. The AIA curves and magnetic flux are calculated from the eruptive region outlined by the white box in panel (f) of Figure 2 . (c) Time-slice plot for the shift motion of the eruptive filament along slice1 in Figure 2 (c), with the white lines marking the filament threads. The two


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

The authors are thankful for the anonymous referee for his/her comments. JS acknowledges the support from the Capital Fund Management's J.P. Aguilar PhD fellowship and the ETH Post-doctoral Fellowship from the Swiss Federal Institute of Technology (ETH Zurich). The Nice group is thankful to the Agence Nationale pour la Recherche under grant ANR-13-BS05-0003-01 (MOJO). JS and FM acknowledges the support from Universidad Nacional Autónoma de México grant PAPIIT IA101113, FM also from CONACyT's grant 178377. This work has been in part carried out within the frame of the National Centre for Competence in Research ‘PlanetS’ supported by the Swiss National Science Foundation. Computations have been done on the ‘Mesocentre SIGAMM’ machine, hosted by Observatoire de la Côte d'Azur. Part of this work was performed using HPC resources from GENCI [IDRIS] (Grant 2015, [100507]).


O O O O O O O O O O O O O O O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Person I-Person O O O O B-Person O O O B-Organization O O B-Grant O B-Grant O O O O O B-Software O O B-Organization B-Location O B-Organization B-Location B-Software O O B-Organization B-Software I-Software B-Software O O B-Organization B-Observatory O B-Organization O B-URL O O O B-Instrument O O O B-Organization B-Organization O O B-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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O B-Telescope O O O O O O B-Wavelength O B-Wavelength O O B-Wavelength I-Wavelength O O O O O O O O O O O O O B-Wavelength I-Wavelength B-Wavelength I-Wavelength O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-CelestialObject I-CelestialObject 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

good λ 2 fits for the other RMs measured at different locations as well (some of them are shown in Figure 3 ) and also in the other five data sets not presented in Figure 2 . We omitted the jet and RMs at ≈900 mas from the core at 2 GHz for better visualization; those data are presented in Figure 3 . At lower frequencies, Faraday rotation is observable in more outward regions of the jet due to longer cooling times of the jet plasma. At higher frequencies, Faraday rotation is observable closer to the compact upstream emission thanks to better angular resolution and less depolarization. We note that the RM distributions are patchy at all frequencies because significant linear polarization is detected only in some parts of the jet, possibly due to substantial depolarization in the other parts. We also note that it is unlikely that those patchy RMs are artifacts because we found that the RMs in different epochs at the same observing frequency are detected in similar locations of the jet (see Appendix C ). Figure 2. Color map of the RM distribution, overlaid on contours of the total intensity of the M87 jet in three VLBA data sets (out of eight) at 2 (a), 5 (b), and 8 GHz (c). Contours start at 0.79, 0.54, and 0.53 mJy per beam for the 2 GHz, 5 GHz, and 8 GHz maps, respectively, and increase by factors of 2. The RM colorscale in units of rad m −2 is shown at the top-right corner. Beam sizes are illustrated by the gray shaded ellipses. All maps are rotated clockwise by 23° relative to astronomical R.A.–decl. coordinates for better visualization. EVPA as function of λ 2 , along with the best-fit λ 2 laws at the locations indicated by the black dashed arrows, is shown in (d)–(f). We note that all RMs measured at different locations show good λ 2 fits (see Figure 3 ). We omitted the jet and RMs at ≈900 mas from the core at 2 GHz for better visualization (see Figure 3 ). Figure 3. Same as Figure 2 but including HST -1 at ≈900 mas from the core at 2 GHz and showing EVPA– λ 2 diagrams for various jet locations where significant Faraday rotation is detected. 3.2. Radial RM Profile To obtain a radial RM profile along the jet, we calculated spatially binned RM by taking the weighted mean of all values in each separated region of the map with similar RM values. A priori, taking a weighted mean over a part of a map assumes that all individual pixels are independent from each other, which is not the case here. Pixels values are correlated across the extension of a resolution element (here, the synthesized beam). Thus, we first calculated a mean value, then its formal error (which assumes all pixels to be uncorrelated), and then multiplied this formal error by , where n is the number of the pixels used for taking the mean, Σ RM the size of the map region with RM values, and Σ FWHM the area within the FWHM of the synthesized beam. We present the mean distance from the black hole, the binned RM values, and corresponding RM errors in Table 2 . This data is used


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 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 B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 the shortening of the flux tube or slingshot effect of the collapsing field (i.e., the Fermi acceleration of type A or B; Northrop 1963 ), causing an increase in the parallel energy. However, Figure 5 (a) demonstrates that this is only the case for small pitch angles. However, these orbits are reflected at the bottom boundary ( z = 0). This assumption is presumably unrealistic, as discussed in Section 9 . It is also noteworthy that none of the orbits illustrated in Figure 4 have come close enough to the generalized x -line or the separator to have crossed the presumed region of the parallel electric field (within the estimated ion inertial length or resistive scale). Thus, pre-acceleration by the direct electric field is probably not an important factor unless this region were greatly extended, for instance, through turbulent effects. The stepwise energy gain, as illustrated in Figure 5 , can be interpreted in two ways. This becomes obvious from the energy equations (see Giuliani et al. 2005 ; Grady et al. 2012 ), which, for simplicity, we write in its nonrelativistic form, which is derived from Equations ( 7 ) and ( 8 ) with neglect of the inertia term The parallel electric field term is included in Equation ( 28 ) for completeness; although, it is disregarded in our orbit calculations, as discussed in Section 3.4 . The first and last terms on the rhs of Equation ( 27 ) describe the betatron effect from the increasing (or decreasing) magnetic field strength or the drift motion into the spatially increasing (or decreasing) magnetic field. Similarly, the last term in Equation ( 28 ) describes the gain (or loss) from the motion in a curved field, which is the first-order Fermi acceleration (type B; Northrop 1963 ). However, these last terms can also be re-written as where and are the gradient and curvature drifts, as defined in Equation ( 7 ). Thus, the betatron and Fermi acceleration of the electrons in the collapsing field are equivalent to the gradient B and curvature drift components, respectively, antiparallel to the electric field (see, Northrop 1963 ; Birn et al. 2013 ). These terms dominate the acceleration. It occurs at the loop tops because both the drift and the field gradients are largest there. 6. Parameter Effects Choosing the high-shear, initially force-free case as an example, we have explored the influence of various parameters on the amount and location of particle acceleration. Figure 6 provides a comparison of the flux enhancements for t = 110 at z = 1, which is slightly above the photospheric boundary, for different energies, pitch angles, and relativistic parameters ξ (representing the ratio of the characteristic energy to the electron rest energy). Panels (a)–(d) of Figure 6 show the relative energy gains, as a proxy of the flux enhancement, for different parameters indicated in the margin, while panels (e)–(g) show MHD quantities that might be related to the energetic particle fluxes: downward Poynting flux S z ,


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

more evident the lower is the observed stellar mass of the galaxy, because of the low chemical enrichment predicted by the more truncated IGIMF. Therefore, the IGIMF does not seem to work in the regions of very low SFR and metallicity typical of UFDs. In the case of CVn I, which is considered more as a dSph galaxy, a short infall time-scale, typical of UFDs, does not allow us to reproduce the cumulative SFH derived by observations, since it predicts a too step rise of the cumulative SFH. However, if a longer infall time-scale is assumed, the MDF and the [α/Fe] abundances are not well reproduced, for both the two IMFs. Therefore we are not able to determine which IMF better reproduces the four observational constraints of this galaxy. More data on this galaxy are necessary before drawing firm conclusions. We are forced to conclude that the models with the Salpeter IMF are able to better reproduce the data than the IGIMF, at least for the version adopted here ( R14 ). Perhaps an IGIMF with a weaker dependence on the SFR and a stronger dependence on metallicity would better fit the properties of these extremely small galaxies. Recently, a new IGIMF has been proposed by Yan, Jerabkova Kroupa ( 2017 ) and Jeřábková et al. ( 2018 ) which enhances the dependence of the slopes of IMF on metallicity, extending it to the low mass range. Such IMF has been applied to the chemical evolution of elliptical galaxies by Yan et al. ( 2019 ). Nevertheless, the models assuming the Salpeter IMF that we have selected as the ones best reproducing the present-day stellar mass match well the [α/Fe] trends but, for a large number of galaxies, they predict too many metal-poor stars than what have been derived by observations. This is similar to the G -dwarf problem but, with the exception of CVnI which has a longer SF episode, it persists even for longer infall time-scales than the one adopted here (τ inf > 0.005 Gyr). The explanation of such a discrepancy could be an observational bias: the samples we have used to build-up the MDFs could be influenced by the instrumentation capability to detect extremely low-metallicity stars because of the weak spectral lines characterizing these stars. Comparing the abundances of UFD stars with the Galactic ones, we suggest that at least a fraction of UFDs could not be the building blocks of the halo given the different [α/Fe] trends observed for UFDs and the Galactic halo. To draw firmer conclusions more data about UFDs are necessary and more elements should be studied such as barium (Spitoni et al. 2016 ). For future projects, it will be interesting to put more stringent constraints on the stellar mass and IMF of UFDs by using photo-chemical evolution models that reproduce at the same time the observed chemical abundances and photometric properties (including the CMD) of UFD stars, taking into account the intrinsic incompleteness of observations (see also Vincenzo et al. 2016 ). Finally, another promising follow-up will be to study


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

GHz were respectively, obtained based on the integrated profile of 2.25/8.60 GHz with typical SNRs >10.28 in the middle of each segment. Then, the time-of-arrivals (ToAs) of pulses were obtained by cross-correlating integrated profiles with the standard template of corresponding frequencies with pat command. Next, we combined the ToA sets from 2.25/8.60 GHz after removing the delay of the receiver system, and carried out timing analysis with TEMPO2 software package (Hobbs, Edwards Manchester 2006 ) to measure the spin properties of the magnetar. The length of each segment lasted until there were obvious changes in the integrated profiles or the error of fitted exceeded 2.70 × 10 −12 which was about 10 per cent of mean (Champion et al. 2020a ). In Table 1 , two adjacent segments are distinguished with different background colours. The top three panels of Fig. 1 show the fitted ν, , and DM changing with the time along with some previous published results (Borghese et al. 2020 ; Champion et al. 2020a , b ; Enoto et al. 2020 ; Hu et al. 2020b ; Joshi Bagchi 2020 ; Lower et al. 2020b , c ; Lower Shannon 2020 ; Rajwade et al. 2020 ; Ridolfi et al. 2020 ). The data points from Champion et al. ( 2020a )’s work were captured from the published plots with the open-source software engauge digitizer . 2 Figure 1. The plots about ν, , DM, W 50 , S 2.25 , S 8.60 , and α of Swift J1818.0–1607 changing with the time. The best fit long-term ν for our observation data and all observation data are shown with solid and dot line, respectively, in top panel. Table 1. Parameters of Swift J1818.0–1607 observations. a Start time. b Mean flux density at 2.25/8.60 GHz. c Spectral index. d Integrated profile morphology: single (S), double (D), and triple (T) peaks. It is clear that the long-term decline trend of ν previously reported by Champion et al. ( 2020a ) and Hu et al. ( 2020a ) went on in our observations, though still changes erratically on short time-scale. We did a linear fit to the ν measurements with the least-square method base on only ours and all observation results shown in the top panel of Fig. 1 . The best-fitted was about and , respectively. Champion et al. ( 2020a ) also reported a similar fitted of using the data spanning nearly 100 d. Combined with all observations, the showed continuous oscillations instead of random variations after the discovery burst. It also was noticed that the amplitude of the oscillation seems to decrease in time. The DM values obtained with TMRT are consistent with previous values. The DM range is between 699 and 705 except for three observations before MJD 59040 (Joshi Bagchi 2020 ; Karuppusamy et al. 2020 ; Lower et al. 2020b ). 3.2 Integrated profiles Integrated profiles of pulsars provide important information of the structure of the radiation beam. With updated ephemeris, the integrated profiles for each epoch of 2.25/8.60 GHz observations were obtained and showed chronologically in Fig. 2 . For easier comparison,


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

y -axis, and time is given on the x -axis in days. 2.1. Perturbation in an Accretion Disk One purpose of our model is to simulate the long-term variability in SMBHBs. The variability can be caused by the dynamical parameters of the system, as is shown in Figure 1 , but also by the intrinsic variability of one of the components. As often observed in the light curves of single active galactic nuclei (AGNs), under long-term monitoring, the flux perturbations are present in the form of outbursts (Shapovalova et al. 2010 ; Graham et al. 2017 ), in the form of long-lasting flares as in the case of binary black hole candidates NGC 4151 (see Figure 2 in Shapovalova et al. 2008 ) and E1821+643 (Shapovalova et al. 2017 ), or as remarkably low states or minimum states characterized by an exceptionally weak continuum and line fluxes, also seen in the case of binary black hole candidates NGC 4151 (Shapovalova et al. 2008 ) and NGC 5548 (Bentz et al. 2007 ). The long-term variability of some objects has been successfully modeled by the variety of disk perturbations ranging from the precession of an elliptical disk, or a disk with a spiral arm, to bright spots, highly ionized fast accretion disk outflows, and rotated, sheared, and decayed bright spots (see Jovanović et al. 2010 ; Popović et al. 2012 , and references therein) and cold spots (Kasliwal et al. 2017 ). The perturbations are well localized in the light curve, which possibly reflects the sharp edges of the emission region, and usually resemble a Gaussian-like form. If the angular dimension of the emission region is much smaller than the viewing angle, a distant observer could not detect the anisotropy of its radiation. Based on the above reasons, the perturbations in the light curves have been modeled with Gaussian, exponential, and various other functional forms (e.g., Valtaoja et al. 1999 ; Kudryavtseva et al. 2011 ; Angelakis et al. 2015 ). Kaulakys Alaburda ( 2009 ) and Kelly et al. ( 2011 ) proposed models of light curves based on superpositions of exponentially decaying perturbations occurring at random times and with random amplitudes (the latter is also recognized as Gaussian process regression). Gaussian-like perturbations could arise from the intrinsic quasar variability, for example, the convergence of the Poissonian process once applied to the AGN light curve as reported by Pecháček et al. ( 2008 , 2013 ) can be understood in the general statistical sense as convergence to the Gaussian random process (Fageot et al. 2017 ). Based on previous discussion, there is some evidence that the Gaussian-shaped perturbations are seen in AGNs and even in magnetohydrodynamical simulations, though it is not the only type that can emerge. Usually considered perturbation is in the form of an outburst, which is obtained directly from the magnetohydrodynamic simulation with a hot spot in the disk (Balbus Hawley 1991 ; Abramowicz et al. 1992 ; Poutanen Fabian 1999 ; Życki 2002 ; Armitage Reynolds 2003 ;


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

offering a realistic quantification of the effect, we resort to a simulation of an isolated halo of mass . The simulation is similar to those used by Nusser ( 2018 ) to study the effect of dynamical friction of the population of the star clusters in NGC 1052-DF2 . The simulation contains 2.4 × 10 5 particles of equal mass distributed according to the Einasto mass profile. The particles were advanced forward for 10 Gyr using the publicly available treecode by Barnes Hut ( 1986 ). Further details can be found in Nusser ( 2018 ). We select those particles found at distances of less than a trimming radius r tr = 10 kpc from the halo centre in all 50 snapshots covering the last 5 Gyr of the simulation. We assume that those particles were never at a farther distance and we identify them as composing the halo surviving a tidal stripping process. We then project the particle velocities along a single axis (the l.o.s) and compute the corresponding velocity dispersion, σ u , at a 3D distance r from the centre. We compare this with the velocity dispersion computed from all original particles (i.e. including pre-trimming particles passing by from distances beyond 10 kpc). The red and blue solid curves in the top panel of Fig. 2 plot square velocity dispersions versus r for the trimmed (tidally stripped) and the untrimmed haloes. The l.o.s velocity variance is represented by the solid curves. As r approaches the trimming radius of 10 kpc, of the trimmed halo (red solid curve) falls substantially below the untrimmed halo (blue solid). The ratio of between the two curves approaches unity only at r 2 kpc. The dotted curves represent the variance, , of the radial (from the halo centre) velocity component. The red dotted curve actually drops to zero at 10 kpc, since there are no particles moving beyond that radius. The dashed curves are the tangential velocity variance divided by 2, . Trimming also reduces the tangential dispersion but the reduction in the is mainly due to the lowered dispersion in the radial direction. Note that the velocity dispersion ellipsoid in the original halo is skewed to the tangential direction with an anisotropy parameter for 2 ≲ r ≲ 10 kpc. The reduction in σ u clearly depends on the parameter β of the original halo. We emphasize that the numerical experiment presented here is simply for illustration purposes. In fact, haloes in simulations with generic initial conditions based on the ΛCDM model have a marked tendency at large radii towards a positive β (e.g. Colín, Klypin Kravtsov 2000 ; Mamon Łokas 2005 ; Ascasibar Gottlöber 2008 ; Mamon, Biviano Murante 2010 ; Lemze et al. 2012 ; Sparre Hansen 2012 ). This implies both a more significant reduction in σ u and also a more isotropic velocity ellipsoid in the trimmed halo at r r tr . Figure 2. Top: The variance of velocity, versus the 3D radius, of particles inside a radius of r tr = 10 kpc in a simulated halo of . The blue curve is the variance from particles in the pre-trimmed


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Model I-Model I-Model 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 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 B-Person I-Person O O O O O B-Telescope B-Dataset O B-Telescope B-Dataset O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O B-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 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

of position and velocity or momentum, and that are conserved throughout the orbit. There are three action coordinates: radial action ( J R ), vertical action ( J Z ), and angular momentum ( L z ). By providing all three action coordinates, one can perfectly describe an entire orbit at any point in time or space. Traditionally, actions were incredibly difficult to calculate. In fact, they can only be analytically solved for a small subset of convenient galactic potentials. As computers became more advanced, astronomers developed ways to numerically approximate action coordinates. Sanders Das ( 2018 ) used the Stäckel Fudge method for approximating actions (Binney 2012 ), which interpolates on a distribution of phase-space coordinates generated from an axisymmetric potential. Resulting errors on the actions are propagated through from errors on parallax, proper motion, and radial velocity. We use the vertical actions calculated by Sanders Das ( 2018 ) to determine whether stars in our sample are members of the thick or thin disc (see Section 3.2 ). 2.4 Cross-matching and quality cuts In order to compare the motions of our planet host and stellar samples, we used Megan Bedell’s catalogue of data cross-matched between Gaia DR2 and Kepler DR25 with a 1 arcsecond search radius, downloaded on 2019 January 9. The two catalogues were matched using the RA and Dec coordinates of every star. The final cross-matched catalogue contains 197 090 stars, 1647 of which are confirmed planet hosts. We make the following quality cuts on both our planet host and field star samples: We removed stars with negative parallax values. This left our planet host sample with 1637 members and our field star sample with 195 545. We removed giants as well as massive and very-low mass dwarfs from our data by discarding stars with logg 4 and effective temperatures 4000 or >8000. We did this because Kepler was optimized for finding planets around FGK stars and therefore has a lower completeness for giants (Sliski Kipping 2014 ). This left our planet host sample with 1477 stars and our field star sample with 148 860 stars. We removed stars with relative errors in the total velocity (see Section 3 ) >10 per cent to minimize the error propagated through our analysis. Much of the error in the velocity calculation comes from uncertainties in the parallax, so making this 10 per cent cut ensures that we are only using stars with small parallax uncertainties and therefore reliable distances consistent with those in Bailer–Jones et al. ( 2018 ). This left us with two final samples of Kepler FGK dwarfs with reliable galactocentric velocities: a planet host sample with 1437 members and a field star sample with 140 918 members. Fig. 1 shows the galactocentric X-Y positions of the stars in the cross matched catalog, color-coded by how far they got in the sample selection process. Our field star sample is shown in black points and our planet host sample is shown in blue. Figure 1. Face-on view


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

The authors thank the anonymous reviewer for a very prompt and helpful set of comments. HNL is partially funded by STFC grant ST/L000636/1. SF acknowledges funding from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013)/ERC Grant agreement n258729.


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

Acknowledgements The authors wish to thank Richard Booth, Antonella Natta, Karin Öberg, and Jennifer Bergner for insightful comments and interesting discussions. A.M. and S.F. acknowledge an ESO Fellowship. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 823823, (RISE DUSTBUSTERS). This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Ref no. FOR 2634/1 ER685/11-1. This paper makes use of the following ALMA data: ADS/JAO.ALMA#2016.1.00459.S. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), MOST and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ.


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

for the independent frequencies are also quoted. Formal errors on the amplitudes are ± 0.3 mmag in u and ± 0.2 mmag in v , y , B , and R . These formal errors are known to underestimate the real errors by about a factor of 2 (Handler et al. 2000 ; JHS ). The S/N quoted is for the data set used to create Fig. 3 . The detected signals are separated in groups of independent pressure and mixed modes (numerical subscripts), gravity modes (letter subscripts), as well as first-, second-, and third-order combination frequencies, respectively. The residuals from this solution were searched for other signals that may be intrinsic to the star. We analysed the amplitude-scaled residuals in the different filters (whereby the u data were divided by 1.5, the v and B data are divided by 1.05, and the R data are multiplied by 1.05 to scale them to amplitudes similar to that in the y filter), and using different combinations of data sets. Even though some interesting possibilities for further intrinsic pulsation frequencies offered themselves, we prefer to err on the side of caution and stop the frequency search at this point. Nevertheless, it is interesting to note that the residual scatter in the light curves (6.4 mmag per point in u , 5.2 mmag per point in v , 4.5 mmag per point in y , 5.5 mmag per orbit in B , and 4.2 mmag per orbit in R ) is larger than the precision of the observations. This may be partly explicable by data reduction imperfections, but residual intrinsic stellar variability is also likely involved. 4 MODE IDENTIFICATION BRITE-Constellation was designed to obtain multicolour time series photometry specifically to provide identifications of the spherical degree l of the modes of pulsating stars (Weiss et al. 2014 ). Daszyńska-Daszkiewicz ( 2008 ) provided diagnostic diagrams to perform such mode identifications from a comparison of the amplitude ratios and phase shifts between the two BRITE passbands. The four strongest modes of ν Eri are, both spectroscopically and photometrically, uniquely identified (De Ridder et al. 2004 ; Handler et al. 2004 ; Daszyńska-Daszkiewicz Walczak 2010 ): the strongest mode is radial (spherical degree l = 0) and the high-amplitude triplet consists of dipole modes ( l = 1). In Fig. 4 , the observed uvyBR amplitude ratios are compared to theoretical predictions for the used Strömgren and BRITE passbands for these four modes. Figure 4. Identification of the spherical degree of the four strongest pulsation modes of ν Eri. The filled circles with error bars are the observed amplitude ratios, in order of increasing wavelength u / u , v / u , B / u , y / u , and R / u . The full lines are theoretical predictions for radial modes, the dashed lines for dipole modes, the dashed–dotted lines for quadrupole modes, the dotted lines for l = 3 modes, and the dashed–dot–dot–dotted lines are for l = 4. The thin error bars delineate the uncertainties in the theoretical amplitude ratios. The theoretical amplitude ratios were


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

Matthaeus et al. 2007 ), but which for the purposes of comparison has the benefit of having been used in previous electron modulation studies, as well as providing results not vastly different from those derived using a more realistic spectral form (Engelbrecht Burger 2013a ). Expressions for derived using different energy-containing range spectral indices can be found in Shalchi et al. ( 2010 ) as well as Engelbrecht Burger ( 2015 ). The results of this calculation are shown in the right panel of Figure 2 . The solutions where PUI effects have been neglected are considerably smaller than the corresponding values, with a less steep rigidity dependence, in contrast with what is usually assumed in cosmic-ray modulation studies. A decrease in dynamical effects leads to larger perpendicular MFPs due to their dependence on . When , the PUI-affected solutions are very small relative to when PUI effects are ignored, as expected, but now assume values larger than the corresponding parallel MFPs. This is a consequence of the dependence in Equation ( 10 ). Choosing leads to perpendicular MFPs smaller than the corresponding at 50 and 100 au, and larger at 10 au. Figure 1. Wavelike energies (top panel) and parallel correlation scales (middle panel) yielded by the Oughton et al. ( 2011 ) TTM model both with (blue lines) and without (red lines) PUI driving. Bottom panel shows (Equation ( 9 )) at 1 MeV as function of μ at 10 au using inputs from the abovementioned TTM. Figure 2. Parallel mean free paths at various radial distances taking into account PUI effects (red lines) and neglecting them (blue lines; Equation ( 6 )), as a function of rigidity for full dynamical effects (; top panels) and reduced dynamical effects (; bottom panels). To study the effects of PUI-driven waves on the electron drift coefficients, an expression for the turbulence-reduced drift coefficient proposed by Engelbrecht et al. ( 2017 ) is employed, where the lengthscale corresponding to the drift coefficient is given bywhere denotes the total transverse variance. This expression reduces to the weak scattering, full drift lengthscale in the absence of turbulence. Figure 3 shows this drift lengthscale as function of rigidity for and at various radial distances, including the PUI-affected perpendicular MFPs from Figure 2 for the purposes of comparison. Note that this figure is plotted on a different scale to that of Figure 2 , for the purpose of clarity. Solutions computed without PUI effects (blue lines) decrease sharply from the weak scattering values (black lines) at the lowest rigidities, due to the larger values of at these rigidities, and remain well below the calculated assuming no PUI effects for both values of α . When PUI effects are included, though, the drift lengthscale at 10 au also drops below the weak scattering value for both values of α , and remains below the corresponding . At 50 and 100 au, however, the PUI-influenced drift coefficient becomes very similar to the


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

DZ's work is supported by a Research Excellence Scholarship from the University of Nottingham and the China Scholarship Council. AAS and CJC acknowledge financial support from the UK Science and Technology Facilities Council. This paper is partially based on SDSS data. Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and the US 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, 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.


O O O O O O O B-Citation O O O O O O O O O O O B-Dataset I-Dataset B-Dataset I-Dataset O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-ObservationalTechniques I-ObservationalTechniques O O O O O O O O O O O O O O O O B-Survey I-Survey O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey O O O O O B-CelestialObject I-CelestialObject I-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject I-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject O B-CelestialObject I-CelestialObject I-CelestialObject O O O O O O O O O B-Survey O O B-CelestialObject I-CelestialObject I-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject I-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject I-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject I-CelestialObject O B-CelestialObject I-CelestialObject I-CelestialObject O O O O O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject O O O O O O O O O O O O O B-Survey I-Survey O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O B-Instrument O O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject I-CelestialObject O B-CelestialObject I-CelestialObject I-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject I-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 I-CelestialObject B-CelestialObject I-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject O B-CelestialObject I-CelestialObject I-CelestialObject O O O B-CelestialObject I-CelestialObject I-CelestialObject O O O O O O O O O B-Dataset O O O O O O O O O O O O B-Dataset O O O O O O O O O O O O B-CelestialObject O O O O O O B-CelestialObject O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

6′′ of the central source detected by M98 and compare it with the current number (including objects from the WDS catalog, Gaia DR2, and companions detected in this paper, see below) the number has grown from 12 to 28, an equally impressive advancement. As we will show in future papers, there is still room for significant improvements in the case of new spectroscopic orbits. The same should be true for the discovery of new astrometric companions, not only using lucky imaging but also more sophisticated techniques such as the ones used in the southern hemisphere by the SMaSH+ survey ( Sana et al. 2014 ). The value of our results lies mostly in the updated detailed information, such as the homogeneous revision of the spectral classification of the sample applying the criteria we have developed for GOSSS, that can be used for future global analyses of the multiplicity in O stars. We indeed plan to do such analyses in future papers ourselves but it is also worthy to point out some results for individual systems in this work. We present first-time O-type GOSSS spectral classifications for 17 objects: HD 170 097 A, QR Ser, BD − 13 4923, HD 190 967, HD 193 611, HDE 228 989, HDE 229 234, Cyg OB2-3 A, ALS 15 133, ALS 15 148, Cyg OB2-1, ALS 15 131, Cyg OB2-20, Cyg OB2-15, ALS 12 502, DN Cas, and IU Aur AB. For another six objects we present their first-time B-type GOSSS spectral classifications: HD 193 322 B, Cyg OB2-3 B, HD 15 558 B, HD 16 429 C, MY Cam B, and LY Aur B. We have identified one eclipsing system as SB2 for the first time, HD 170 097 A, and derived its separate spectral classifications. To that one we can add a second eclipsing system in the sample, ALS 12 688, that was identified as having double absorption lines for the first time in GOSSS III. For another eclipsing binary, V747 Cep, we detect moving lines (SB1) for the first time using our LiLiMaRlin spectra. For two systems that have published SB1 orbits, BD − 16 4826 and θ 2 Ori A, we publish the first spectrograms with double lines (SB2) and derive their first true separate spectral classifications. For HD 168 112 AB we also publish the first SB2 spectrograms and separate spectral classification. We have also detected nine new astrometric components, one each around HD 190 967, ALS 15 133, Cyg OB2-A11, Cyg OB2-1, ALS 12 502, DN Cas, and MY Cam A and two around IU Aur AB. The results of this paper will be added to GOSC at the time of publication, which will reach version 4.2. With them, GOSC will contain a total of 655 objects: 611 in the main catalog (Galactic O stars), 32 in supplement 2 (Galactic early-type stars), and 12 in supplement 3 (Galactic late-type stars). It is not possible to do a full multiplicity analysis based on our 92 stars for two reasons: the sample is too small and is biased. The most obvious bias is that we selected our stars from systems that had spectroscopic orbits previously published, so no single targets are included. Note, however, that several SB1?


O O O O O O O O B-Observatory O O O B-Observatory I-Observatory I-Observatory I-Observatory O O B-Grant I-Grant O O O O O O O O B-Organization I-Organization I-Organization I-Organization B-Organization O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O O O B-Organization I-Organization I-Organization O B-Organization B-Observatory I-Observatory I-Observatory O O O O O O O B-Archive I-Archive I-Archive I-Archive I-Archive O O O O O B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O O O O O B-Location B-Organization I-Organization I-Organization I-Organization I-Organization O O O O O O O B-Location I-Location B-Grant I-Grant O B-Organization O O B-Grant O O O B-Organization I-Organization O O B-Grant O O O O O B-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O O O O O B-Grant I-Grant I-Grant O O O O O O O O O O B-Event I-Event I-Event I-Event I-Event O O O B-Organization B-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization O O O O O O O O B-Person B-Person O B-Person O O O O O B-Location B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O B-Grant B-Person O O O B-Organization B-Fellowship B-Person O O O B-Observatory O B-Grant I-Grant B-Person O O O O O O B-Organization O B-Grant I-Grant O O O O O B-Person O O B-Location I-Location B-Grant I-Grant O O O B-Grant O O O O O B-Person B-Person B-Person O O O O O B-Organization I-Organization I-Organization I-Organization B-Grant B-Person O O O O B-Organization O B-Grant I-Grant O O O B-Grant O O O O B-Organization O O O B-Grant B-Person O O O O O O B-Organization I-Organization I-Organization B-Grant I-Grant O B-Person I-Person B-Person O O O O O B-Organization B-Location O O O O O O B-Grant O O O B-Organization O O O O B-Grant O B-Grant O O B-Organization O B-Grant O B-Grant O B-Grant

Based on data products from observations made with ESO Telescopes at the La Silla Paranal Observatory under programme ID 188.B-3002. These data products have been processed by the Cambridge Astronomy Survey Unit (CASU) at the Institute of Astronomy, University of Cambridge, and by the FLAMES/UVES reduction team at INAF/Osservatorio Astrofisico di Arcetri. These data have been obtained from the Gaia -ESO Survey Data Archive, prepared and hosted by the Wide Field Astronomy Unit, Institute for Astronomy, University of Edinburgh, which is funded by the UK Science and Technology Facilities Council. This work was partly supported by the European Union FP7 programme through ERC grant number 320360 and by the Leverhulme Trust through grant RPG-2012-541. We acknowledge the support from INAF and Ministero dell’ Istruzione, dell’ Università e della Ricerca (MIUR) in the form of the grant “Premiale VLT 2012”. The results presented here benefit from discussions held during the Gaia -ESO workshops and conferences supported by the ESF (European Science Foundation) through the GREAT Research Network Programme. We thank the anonymous referee for insightful comments. D.G., S.V., and B.T. gratefully acknowledges support from the Chilean BASAL Centro de Excelencia en Astrofísica y Tecnologías Afines (CATA) grant PFB-06/2007. C.M. acknowledges support from CONICYT-PCHA/Doctorado Nacional/2014-21141057. R.E.C. acknowledges funding from Gemini-CONICYT for Project 32140007. F.M. gratefully acknowledges the support provided by Fondecyt for project 314017. This work was partly supported (A.R.C.) by the European Union FP7 programme through grant number 320360. This work was partly supported (A.D., G.T., R.Ž.) by the grant from the Research Council of Lithuania (MIP-082/2015). S.G.S. acknowledges the support from FCT through Investigador FCT contract of reference IF/00028/2014 and the support from FCT through the project PTDC/FIS-AST/7073/2014. C.L. gratefully acknowledges financial support from the European Research Council (ERC-CoG-646928, Multi-Pop, PI: N. Bastian). V.A. acknowledges the support from the FCT (Portugal) in the form of the grant SFRH/BPD/70574/2010, the support by FCT through national funds (Refs. PTDC/FIS-AST/7073/2014 and PTDC/FIS-AST/1526/2014) and by FEDER through COMPETE2020 (Refs. POCI-01-0145-FEDER-016880 and POCI-01-0145-FEDER-016886).


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

and magnetic fields, and has been shown to produce realistic galaxy populations in large-scale cosmological boxes (Vogelsberger etal. 2013 ; Genel etal. 2014 ). The most novel aspects of the simulations, with respect to previous studies, are the large simulation sample, high resolution, the inclusion of magnetic fields that are seeded, grown and evolved in a fully cosmological context, and the BH model that has been used in only one simulation set previous to this study (Marinacci etal. 2014a ). The suite comprises 30 simulations with typical baryonic mass resolution of around 510 4 M , three of which have higher resolution counterparts with eight times better mass resolution. The sample size, resolution and galaxy formation model make these simulations some of the most advanced and comprehensive found in the literature. We analysed the properties of the stellar components of these simulations, and found that they lie on the expected stellar masshalo mass relation, and are consistent with other key observables such as flat rotation curves, the massmetallicity relation and present-day SFRs. The simulated galaxies are, on average, slightly too massive in the stellar component, particularly at earlier times such as z 3. This may indicate the need for early stellar feedback (see e.g. Aumer etal. 2013 ; Stinson etal. 2013a ). Such feedback may bring down the stellar masses of our simulations and reduce the number of compact galaxies (see Fig. 5 ), which we will investigate in future work. The mass distributions of our simulated galaxies are realistic and produce rotationally supported discs: most of our simulations have flat rotation curves, with velocities that match the TullyFisher relation for Milky Way-mass galaxies. We note that in the past, it has proven to be difficult to reproduce flat circular velocity curves for galaxy discs in haloes in the virial mass range 1210 12 M (see for example, Stinson etal. 2010 ; Mollitor, Nezri Teyssier 2015 ; Wang etal. 2015 ), although a variety of recent models have achieved some success (Aumer etal. 2013 ; Stinson etal. 2013a ; Marinacci etal. 2014a ; Schaller etal. 2015a ; Colin etal. 2016 ). The circularity distributions indicate that at least two-thirds of the simulations have well-defined, rotationally supported disc components, with disc-total mass ratios of up to 0.60.7 for the most disc-dominated simulations. These are among the highest disc-total mass ratios in the literature, along with Aumer etal. ( 2013 ). The vertical structure of our simulated discs appears to be somewhat thicker than expected from observations in the Milky Way, which may be related to energy from stellar feedback that acts to puff up the gas disc (see Marinacci etal. 2016 ). Rokar etal. ( 2014 ) reported a similar conclusion, although their feedback recipe included radiation feedback that destroyed the morphology of their disc in addition to thickening it. However, the inner discs of our simulations show some consistency


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

We are grateful to the referee, Professor M.A. Dopita, for his constructive comments. LSP and EKG acknowledge support in the framework of Sonderforschungsbereich SFB 881 on ‘The Milky Way System’ (especially subproject A5), which is funded by the German Research Foundation (DFG). LSP thanks for the hospitality of the Astronomisches Rechen-Institut at Heidelberg University where part of this investigation was carried out. This work was partly funded by the subsidy allocated to Kazan Federal University for the state assignment in the sphere of scientific activities (LSP).


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

The authors would like to thank the anonymous referee who provided useful suggestions that improved this manuscript. RCS gratefully acknowledges support through a grant from the STScI JDF. This research has made use of the Fabry Perot data base, operated at CeSAM/LAM, Marseille, France. The authors also acknowledge NSF grants AST 95- 29098 and 00- 71198 to UC Santa Cruz. RCS would like to thank A. Dutton for helpful comments. We wish to extend thanks to those of Hawaiian ancestry on whose sacred mountain we are privileged guests.


O O O O O O O O O O O O O O O O O O O O O O B-ComputingFacility O O O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility O O O B-Grant O O B-Organization B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O B-ComputingFacility O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility O O B-Organization I-Organization O O O B-Organization O B-Grant O O B-ComputingFacility I-ComputingFacility I-ComputingFacility O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O O O O B-Organization B-ComputingFacility I-ComputingFacility I-ComputingFacility O B-URL O O O O O O B-Organization B-ComputingFacility I-ComputingFacility B-Grant I-Grant I-Grant O B-Organization B-Grant I-Grant I-Grant I-Grant B-ComputingFacility O O O O B-ComputingFacility I-ComputingFacility O O O O O O O O O B-Organization I-Organization I-Organization O O O B-Grant I-Grant

Acknowledgments The authors thank the referee for the comments and suggestions in their helpful report. Computer time for the simulations performed with GENESIS was provided by HPC resources of Cines under the allocation A0010406957 made by GENCI (Grand Equipement National de Calcul Intensif). Those performed with FARGO utilized: Queen Mary's MidPlus computational facilities, supported by QMUL Research-IT and funded by EPSRC grant EP/K000128/1; and the DiRAC Complexity system, operated by the University of Leicester IT Services, which forms part of the STFC DiRAC HPC Facility ( www.dirac.ac.uk ). This equipment is funded by BIS National E-Infrastructure capital grant ST/K000373/1 and STFC DiRAC Operations grant ST/K0003259/1. DiRAC is part of the National E-Infrastructure. This research was also supported in part by the National Science Foundation under Grant No. NSF PHY-1125915.


O O O O O O O O O O O O O O O B-Organization B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O O B-Organization O O O O O O O O O B-Survey O B-Collaboration I-Collaboration O B-Telescope I-Telescope I-Telescope O O O O B-Organization I-Organization I-Organization O O B-Grant O O O O O O O B-Organization B-Grant I-Grant I-Grant I-Grant I-Grant O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization O B-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Grant I-Grant O O O O O O O O O B-Observatory O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Organization I-Organization I-Organization I-Organization O O O B-Survey I-Survey O O O O O B-Location B-Organization I-Organization I-Organization O B-Location B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Location O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Location I-Location O B-Organization I-Organization I-Organization I-Organization O B-Location O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility O O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Location I-Location I-Location I-Location I-Location B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization O O B-Organization I-Organization O O B-Survey I-Survey I-Survey O B-Organization I-Organization O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O B-Organization I-Organization O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization B-Organization B-Location B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O O O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O B-Observatory I-Observatory I-Observatory I-Observatory O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O O B-Collaboration I-Collaboration I-Collaboration O B-Software I-Software I-Software I-Software O O O O B-Organization I-Organization I-Organization O O O B-Grant O B-Survey O O B-Location O O O O O B-Organization O O B-Grant B-Grant B-Grant O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O O O O O O O O O O B-Organization I-Organization I-Organization O O B-Location I-Location B-Grant I-Grant I-Grant B-Grant O B-Organization O O B-Grant B-Grant O B-Grant

Acknowledgments We thank the anonymous referee for useful comments. We acknowledge the support of the DFG Cluster of Excellence Origin and Structure of the Universe, the Transregio programme TR33 The Dark Universe and the Ludwig-Maximilians-Universitt. This paper has gone through internal review by the DES and SPT collaborations. The South Pole Telescope is supported by the National Science Foundation through grant PLR-1248097. Partial support is also provided by the NSF Physics Frontier Center grant PHY-1125897 to the Kavli Institute of Cosmological Physics at the University of Chicago, the Kavli Foundation and the Gordon and Betty Moore Foundation grant GBMF 947. We are grateful for the extraordinary contributions of our CTIO colleagues and the DECam Construction, Commissioning and Science Verification teams in achieving the excellent instrument and telescope conditions that have made this work possible. The success of this project also relies critically on the expertise and dedication of the DES Data Management group. Funding for the DES Projects has been provided by the US Department of Energy, the US National Science Foundation, the Ministry of Science and Education of Spain, the Science and Technology Facilities Council of the United Kingdom, the Higher Education Funding Council for England, the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign, the Kavli Institute of Cosmological Physics at the University of Chicago, the Center for Cosmology and Astro-Particle Physics at the Ohio State University, the Mitchell Institute for Fundamental Physics and Astronomy at Texas AM University, Financiadora de Estudos e Projetos, Fundao Carlos Chagas Filho de Amparo Pesquisa do Estado do Rio de Janeiro, Conselho Nacional de Desenvolvimento Cientfico e Tecnolgico and the Ministrio da Cincia, Tecnologia e Inovao, the Deutsche Forschungsgemeinschaft and the Collaborating Institutions in the Dark Energy Survey. The Collaborating Institutions are Argonne National Laboratory, the University of California at Santa Cruz, the University of Cambridge, Centro de Investigaciones Energticas, Medioambientales y Tecnolgicas-Madrid, the University of Chicago, University College London, the DES-Brazil Consortium, the University of Edinburgh, the Eidgenssische Technische Hochschule (ETH) Zrich, Fermi National Accelerator Laboratory, the University of Illinois at Urbana-Champaign, the Institut de Cincies de lEspai (IEEC/CSIC), the Institut de Fsica dAltes Energies, Lawrence Berkeley National Laboratory, the Ludwig-Maximilians Universitt Mnchen and the associated Excellence Cluster Universe, the University of Michigan, the National Optical Astronomy Observatory, the University of Nottingham, The Ohio State University, the University of Pennsylvania, the University of Portsmouth, SLAC National Accelerator Laboratory, Stanford University, the University of Sussex, Texas AM University and the OzDES Membership Consortium. The DES data management system is supported by the National Science Foundation under Grant Number AST-1138766. The DES participants from Spanish institutions are partially supported by MINECO under grants AYA2012-39559, ESP2013-48274, FPA2013-47986 and Centro de Excelencia Severo Ochoa SEV-2012-0234. Research leading to these results has received funding from the European Research Council under the European Unions Seventh Framework Programme (FP7/2007-2013) including ERC grant agreements 240672, 291329 and 306478.


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

Acknowledgements We are grateful to Dr. H. Shimabukuro for helpful comments on a draft version of this manuscript. This work is supported by Grant-in-Aid from the Ministry of Education, Culture, Sports, Science and Technology (MEXT) of Japan, Nos. 24340048, 26610048, 15H05896, 16H05999, 17H01110 (KT) and 16J01585 (SY), and Bilateral Joint Research Projects of JSPS (KT).


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

This work was supported in part through the Air Force Office for Scientific Research, FA9550-15-1-0213, by Ministerio de Economía y Competitividad of Spain, CTQ2014-58617-R, and by Xunta de Galicia through project GRC2014/032. The authors also thank “Centro de Supercomputación de Galicia (CESGA)” for the use of their computational facilities.


O O O O O O O O O O B-Organization I-Organization I-Organization B-Fellowship I-Fellowship I-Fellowship O O O B-Fellowship O O O O O O O O O O O O O B-Person I-Person B-Person I-Person O B-Person I-Person O O O O O O

ACKNOWLEDGEMENTS This material is based on work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1329626. The authors would also like to acknowledge the aid of both anonymous referees, Lars Hernquist, Brent Tully, and Larissa Nofi in preparing this document for publication.


O O O B-Person I-Person O O O O O O O O O O O B-Organization I-Organization I-Organization O O B-Telescope O O O O O O O O O O O O O B-Telescope O B-Telescope O O O O O O O O B-Organization I-Organization I-Organization I-Organization B-Organization

The contributions by P. Bergman, including the interesting discussions, are highly appreciated. We also thank the Swedish APEX team and the APEX staff on site for their help with the observations. As part of our Odin and Herschel work, this research has been supported by the Swedish National Space Board (SNSB).


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 I-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 B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O B-Mission B-Instrument O B-Instrument O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Instrument O O O O O O O O O O O O O O O O O O O O O O B-Mission B-Instrument O O O B-Mission B-Instrument O O O O O O O O O O O O O O O O B-Mission B-Instrument O O O O O O O B-Mission B-Instrument O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O B-Instrument O O O O O O O B-Mission 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 B-Mission B-Instrument O O O O O O O O O O O O O O O O O O O O B-Mission B-Instrument O O O O O O O O O O O O O O O O B-Mission B-Instrument O B-Mission B-Instrument O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument 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

right edges of the distribution correspond to the points at which particles just enter and exit the E ′ detector, L1, and are caused by anticorrelated variations of Δ E and E ′, which can occur as a result of variations in the particle path lengths through the Δ E detector (e.g., caused by differences in incidence angle) or Bohr/Landau fluctuations in Δ E . Simulations of the instrument response can be used to take these effects into account. Particles with E / M values beyond the high-energy end of the distribution are detected and identified using detectors deeper in the telescope. The relatively small number of He nuclei reaching the L2 detector in this weak event were not used in this study. Figure 6 shows mass histograms that result from projecting the data shown in Figure 5 on the mass axis. The middle panel corresponds to the region of the IS⊙IS/EPI-Hi plot to the left of the vertical red line and the right panel to the region to the right of this line. The red curves show Gaussian fits to the central regions of the peaks, which result in similar standard deviations of σ M = 0.18 and 0.20 amu for the low- and high- E / M regions, respectively. However, the low-energy mass peak has more prominent non-Gaussian tails. Figure 6. Mass histograms for the time period 2019-109 12:00 to 2019-113 12:00 from ACE /ULEIS and IS⊙IS/EPI-Hi. The IS⊙IS/EPI-Hi histograms are shown for two subsets of the data selected based on whether the E / M value is less than or greater than 1.2 MeV nucleon –1 , where E / M is calculated from the total energy and the assumption that M = 4. Red curves show Gaussian fits to the central regions of the 4 He peaks in the two IS⊙IS/EPI-Hi panels. Figure 7 shows the derived masses of the detected He events as a function of the time of detection at both PSP /IS⊙IS/EPI-Hi (top panel) and ACE /ULEIS (bottom panel). In order to obtain good separation between and , only those He events from PSP /IS⊙IS/EPI-Hi that have MeV nucleon –1 were used. ACE /ULEIS measured the highest intensity of both He isotopes on 2019-110 before midday. This was during one of the intervals during which IS⊙IS/EPI-Hi was turned off (gray bands). After midday on 2019-111, when IS⊙IS/EPI-Hi observed the highest intensity of both isotopes, ACE /ULEIS was still observing , but intensities of both He isotopes were lower than they had been during the first half of the previous day. The event at PSP /IS⊙IS/EPI-Hi continued through much of 2019-112, being cut off when the instrument was again turned off around 18:30 on 2019-112. At ACE /ULEIS, no He was observed after midday on 2019-112. Figure 7. Calculated He mass vs. time from PSP /IS⊙IS/EPI-Hi and ACE /ULEIS. The IS⊙IS/EPI-Hi data are restricted to events from the >1.2 MeV nucleon –1 subset shown in the right panel of Figure 6 . Gray regions indicate times when IS⊙IS/EPI-Hi was turned off. To derive abundance ratios between and , we have used IS⊙IS/EPI-Hi data from the E / M interval 1.35–1.75 MeV nucleon


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

that for the initial core as a whole (β core = 1.9), is much smaller than what is typically adopted in MHD simulations of protoplanetary discs, as mentioned earlier. Interestingly, the magnetic energy is dominated by the poloidal component of the magnetic field rather than the toroidal component, as shown by the values of β t and β p in Fig. 15 for each disc, which are the ratios of the thermal to magnetic energy due to the toroidal and poloidal field component, respectively. The disc remains significantly magnetized at later epochs. The values of λ d and β are formally 9.2 and 2.5, respectively, at the epoch when , smaller than their counterparts at the earlier epoch of , but they are affected by a relatively low-density region that satisfies the disc criteria but is detached from the main body of the disc (see panel v of Fig. 15 ). By the last epoch shown (panel aa, ), the disc has λ d = 23 and β = 7.7, with the magnetic energy strongly dominated by the poloidal field component. As the AD coefficient increases, the disc starts to form earlier. For example, by the epoch when , a disc is already well-developed in the most magnetically diffusive model (M0.0AD10.0, panel l), clearly visible although underdeveloped in the second most diffusive model (M0.0AD3.0, panel k), but barely discernible in the standard AD case (panel j). Another trend is that, as the AD coefficient increases, the disc is somewhat bigger (compare the discs in the last three columns of Fig. 15 ) and more massive, with the disc mass increasing from for Model M0.0AD1.0 to for M0.0AD3.0 to for M0.0AD10.0. The disc remains significantly magnetized, with λ d ∼ 10−20 and β ∼ 10−20 typically, and the magnetic energy dominated by the poloidal field component in most cases. The main exception is the last epoch of the most diffusive model (M0.0AD10.0, ), when the disc is significantly less magnetized, with λ d = 32, β = 59, and the magnetic energy dominated by the toroidal field component instead. Turbulence changes the formation and properties of discs substantially, as illustrated by Fig. 16 , which is the same as Fig. 15 but for all models with sonic turbulence () and different levels of AD. The change is the most pronounced at the earliest epoch (), when the disc is well developed in all AD models and is clearly visible (although underdeveloped) even for the ideal MHD case (panel a). The ideal MHD disc is strongly magnetized, with λ d = 3.8 that is comparable to that of its parental core (especially the central part that is less magnetized compared to the core as a whole) and a plasma-β that is much less than unity (β d = 0.1). The strong magnetization, we believe, is the reason that the disc enabled by turbulence early in the ideal MHD case is transient; the magnetic braking is simply too efficient to allow the disc to persist for a long time. The same is broadly true for the early discs formed in the two weakest AD cases (Model M1.0AD0.1 and M1.0AD0.3), even though their masses


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

ACKNOWLEDGEMENTS The authors thank to an anonymous referee for his/her valuable comments that helped to improve the article. This project has been supported by the Hungarian NKFI Grant K-119517 and the GINOP 2.3.2-15-2016-00003 of the Hungarian National Research, Development and Innovation Office, and the Lendület LP2018-7/2019 grants of the Hungarian Academy of Sciences, and by the Slovak Research and Development Agency under the contract No. APVV-15-0458. AD was supported by the ÚNKP-19-4 New National Excellence Program of the Ministry of Human Capacities and the János Bolyai Research Scholarship of the Hungarian Academy of Sciences. AD and GyMS would like to thank the City of Szombathely for support under Agreement No. 67.177-21/2016. This paper includes data collected with the TESS and Kepler missions, obtained from the MAST data archive at the Space Telescope Science Institute (STScI). Funding for the TESS mission is provided by the NASA Explorer Program. Funding for the Kepler mission is provided by the NASA Science Mission Directorate. STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 526555.