O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject O B-Citation I-Citation O B-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 B-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion 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 B-Organization O O O O O O O O O O B-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-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 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 B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O B-CelestialObject O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O B-CelestialObject O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O B-CelestialObject I-CelestialObject O O O O O B-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject I-CelestialObject O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation 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 B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation 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 B-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 B-Citation I-Citation O O O O O B-CelestialObject O O O O

yielding mutually consistent rotation speeds seem to have all but invalidated those suggestions; comprehensive and up-to-date Galactic rotation curves no longer show any dip near the Sun’s Galactocentric distance, at least not those based on the main mass tracers (see, e.g., Bland-Hawthorn Gerhard 2016 ). It is still possible that the appearance of such a dip could be limited to the young(est) populations located in the Perseus spiral arm (e.g., Sofue 2013 ; Genovali et al. 2014 ). Genovali et al. ( 2014 ) also suggested that the clumpy distribution of classical Cepheids across the Galactic thin disk and their possible association with giant molecular clouds may hamper their use for Galactic rotation measurements. Note that the H i , CO, and field population tracers also imply larger values for both (at kpc) and the ratio than the canonical IAU recommendation, although the widths of their full distributions encompass the IAU values within their 1 σ ranges. In view of these distributions, and considering that both the field populations and the H i or CO gas kinematics reflect the underlying Galactic mass distribution most closely, we contend that the post-1985 combination of these measurements may indeed yield the most appropriate value for the Galactic rotation speed for . The 40 post-1985 measurements of based on field star samples, H i or CO observations, and Galactic mass modeling yield . Note that, while dominated by a statistical component, the uncertainty does include a contribution from a systematic component, given that the contributing values include such uncertainties. Similarly, the resulting ratio based on these values is Θ 0 / R 0 = 27.12 ± 0.39 km s −1 kpc −1 ( σ = 2.45 kms −1 kpc −1 ). At this point, it would be wise to perform a final check of the Galactic rotation speed at the solar circle by considering the Galaxy’s rotation curve with respect to the external reference frame provided by the Milky Way’s satellite galaxies and other Local Group members, as well as the Milky Way’s GD-1 giant stream. Fortunately, a number of studies have attempted to do just this. Lynden-Bell Lin’s ( 1977 ) and Einasto et al.'s ( 1979 ) original attempts yielded rotation speeds that bracketed the expected range. Lynden-Bell Lin ( 1977 ) determined km s −1 for kpc (with a reduced uncertainty of 13 km s −1 resulting from the application of more a priori constraints), while Einasto et al. ( 1979 ) found km s −1 , again for kpc. More recent derivations of in external reference frames, all recalibrated for , have resulted in (30) km s −1 (Kochanek et al. 1996 ) and (216 ± 18) km s −1 (Koposov et al. 2010 ). This thus implies that there is no compelling evidence suggesting that the IAU-recommended km s −1 is no longer valid, although it would be more appropriate to increase the recommendation to km s −1 , provided that the recommended Galactocentric distance is reduced from to kpc (Paper IV ). A comparison of the Galactic rotation speeds implied by


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

give rise to metal absorption in gaseous haloes. Simcoe et al. ( 2006 ) estimated absorbers sizes around z ∼ 2.3 galaxies ranging from the sub-parsec to the kiloparsec. This is consistent with the transverse scales of C iv absorbers derived in Rauch et al. ( 2001 ) from multisightline analysis of lensed QSOs at sub-kpc scales (see also Petitjean et al. 2000 , based on Mg II). Based on photoionization modelling of C iv absorbers at similar redshifts, Schaye, Carswell Kim ( 2007 ) derived typical densities of n H ∼ 10 −3.5 cm −3 with sizes of ∼100 pc. Similarly, Crighton et al. ( 2015 ) observe metal absorption lines arising near a z ≃ 2.5 galaxy and derive a (100–500) pc size constraint (see also Arrigoni Battaia et al. 2015 ), which they argue is a ubiquitous size-scale for all low-ion halo gas in the circumgalactic environments of both low and high redshift galaxies. Pieri et al. ( 2014 ) conclude that a typical low-ionization absorber associated with the CGM of strong Lyman α forest systems at z ∼ 2.5 is ∼30 pc in size. Furthermore, the gas giving rise to various absorption lines may also have unexpected geometries with little resemblance to spherical clouds (Churchill et al. 2015 ). Obtaining ∼100 pc hydrodynamic resolution at the virial radius by simply running higher resolution simulations of isolated haloes will be prohibitively expensive. Following the observed scaling of the gas resolution in the halo, we would obtain a mean r cell ≃ 0.1 kpc physical at z = 2 with a L14-class simulation. That is, gas mass resolution approaching 30 M ⊙ , requiring ≳ 10 10 gas cells in a 10 12 M ⊙ halo. This is not a realistic goal for the near future. Even given such a simulation, the minimum size of resolved clouds would be a few times larger than the size of individual resolution elements. On the other hand, numerical methods may enable novel ways to focus resolution within the halo regime. If we can avoid clustering the computational effort in the densest regions of space – within galaxies themselves – much higher spatial resolutions can be achieved in lower density media. In adaptive mesh refinement simulations, the refinement criterion can be chosen as desired, on the gradient of the neutral hydrogen fraction for instance (Rosdahl Blaizot 2012 ), or with a progressively refined uniform Eulerian grid which is volume filling (Miniati 2014 ). In our moving mesh simulations, we can enforce a target gas cell mass criterion of any type through adaptive refinement and de-refinement of Voronoi cells. In future work we will explore this possibility as a solution to the resolution issue, in addition to quantifying the rates and modes of accretion using the tracer particle information. 7 CONCLUSIONS In this first paper of the series, we present a suite of high-resolution cosmological hydrodynamic zoom-in simulations targeted at understanding the properties of halo gas and cosmological accretion in ∼10 12 M ⊙ haloes at z = 2. Using the moving-mesh code arepo


O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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

distances. We discuss the implications of this exception in Section 4.3.4 . Inserting equation ( 16 ) into equation ( 15 ) we use equations ( 3 ) and ( 9 ) to find the ram pressure for the Isothermal Sphere, and the NFW model, where . In the above expressions, f c is the cluster gas fraction, M v,clust and R c are the virial mass and radius of the cluster, respectively, and ε is a fudge factor, added to incorporate any uncertainties in the assumptions we made in our model, e.g. motion with velocities different than the virial velocity, and which also accounts for C ram . 4.3.2 Gravitational binding We wish to compare the ram pressure to the binding gravitational force per unit area acting on the satellite gas halo and determine the amount of mass stripped from the satellite. While expressing the ram pressure is relatively simple, as shown above, deter-mining the correct form of the gravitational binding force for the appropriate mass elements affected is not so straightforward. Ideally, one wishes to construct a simple spherical approximation for the binding force at a radius l in the satellite which will lead to a definition of a stripping radius l s . One option is to find the gravitational force which binds a spherical shell of width at a given radius l, divided by the cross-section of that shell where M (l) is the total mass profile and ρ(l) is the gas density profile of the satellite. This approximation suggests that the ram pressure ‘peels’ off spherical shells, like an onion, which is incongruous with the anisotropic nature of RPS. However, if the satellite halo is rotating with respect to its direction of motion, such that all parts of the outer shell experience the ram pressure, this approach may be justified. Another option is to examine a cylindrical shell of radius l and width (), oriented in the direction of motion of the satellite, and thus the direction of the ram-pressure force. McCarthy et al. ( 2008 ) employed this method by finding the maximal value of the restoring gravitational acceleration in the direction of the motion (and, by definition, the cylinder axis) as well as an upper limit of the projected surface density, resulting in an overestimation of the binding force which ensures that one finds an upper limit to the stripping radius. For a power-law spherically symmetric density profile ρ ∝ r −α , the maximal restoring acceleration is 2 and the surface density is The upper limit of the integral is formally but can be taken to L → ∞ when the integral converges (or to some set scale otherwise) to achieve an upper limit for the surface density. The gravitational binding force is then where ν is a factor of order unity For an Isothermal Sphere profile, we find ν = π/2. Yet another option is to assume that the gas halo is in hydrostatic equilibrium within the gravitational potential of the dark matter halo of the satellite, and use the gas pressure as a proxy for the binding force per unit area. For a power-law density


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

A.K.H.K. is supported by the Ministry of Science and Technology of the Republic of China (Taiwan) through grants 105-2112-M-007-033-MY2, 105-2119-M-007-028-MY3, and 106-2918-I-007-005. C.Y.H. is supported by the National Research Foundation of Korea through grants 2014R1A1A2058590 and 2016R1A5A1013277. J.T. is supported by NSFC grants of Chinese Government under 11573010 and U1631103. Facilities: NuSTAR , Swift .


O O O O O O O O O B-Survey O O O O O O B-Organization I-Organization I-Organization O B-Observatory I-Observatory I-Observatory B-Observatory O O B-Organization I-Organization I-Organization B-Person O O O O O B-Person I-Person O O O O O O O B-Location O B-Person I-Person O O O O O O B-Person O O O B-Organization B-Person O O O B-Observatory B-Organization I-Organization O B-Organization O O O O O B-Person I-Person B-Person I-Person O B-Person I-Person O O O O O O O B-Telescope O O B-Person O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O O O O O B-Organization O B-Location O B-Grant I-Grant I-Grant B-Organization O B-Grant I-Grant O B-Organization O B-Location O B-Grant I-Grant I-Grant I-Grant O O O O O O O O O O O B-Telescope I-Telescope I-Telescope O O O O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization O O O O B-Organization O O O O O O O O O B-Survey I-Survey I-Survey I-Survey I-Survey O O O O O O O B-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization O B-Telescope O O O O O B-Organization I-Organization I-Organization I-Organization B-Organization

We acknowledge the anonymous referee for their comments. The ATLASGAL project is a collaboration between the Max- Planck -Gesellschaft, the European Southern Observatory (ESO) and the Universidad de Chile. C.E.C. acknowledges the kind hospitality of M. Rubio and her family during her stay in Chile, and C. Kobulnicky for having suggested studying this object. L.C. acknowledges support from DIULS. V.F. acknowledges support from ESO-Chile Joint Committee and DIULS and would like to thank Ivan Valtchanov, Bruno Altieri, and Luca Conversi for their support and valuable assistance in Herschel data processing. V.F. also acknowledges support from the Faculty of the European Space Astronomy Centre (ESAC). This project was partially financed by CONICET of Argentina under project PIP 0356, UNLP under project 11/G120, and CONICyT of Chile through FONDECYT grant No. 1140839. This work is based [in part] on observations made with the Spitzer Space Telescope, which was operated by the Jet Propulsion Laboratory, California Institute of Technology under a contract with NASA. This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation. The MSX mission was sponsored by the Ballistic Missile Defense Organization (BMDO).


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

feedback on the cold neutral gas. For some sources we could only search for intervening H i absorption (e.g. gas intervening DLAs along the line of sight), which is an alternate cause for obscuration of the background radio quasar. Lastly, for some sources observed we had no prior redshift information. We report three H i absorption detections in our sample, one towards PKS 1829−718 that was previously unknown, another towards PKS 1740−517 (Allison et al. 2015 ), and the third a re-detection of one towards PKS 0500+019 (Carilli et al. 1998 ). All three detections are made towards sources selected by optical faintness, and we see no H i absorption towards sources selected by their WISE mid-infrared colours. However, the lack of detections in the WISE selected sub-sample is not yet statistically significant, and further analysis during the full FLASH project is required. Through optical spectroscopic follow-up and information within the literature for PKS 1829−718, PKS 1740−517, and PKS 0500+019, we find that the detected H i absorption is associated with the host galaxy of the AGN in each case. These three AGN are obscured by material in the host galaxy, e.g. a dusty torus formed following a galaxy merger event, or perhaps in a larger disc on the scale of ∼100 pc. We do not detect any H i absorption towards our higher redshift targets ( z > 1). This is not necessarily unexpected given the predicted number of DLAs along the line of sight for our redshift range of 0.4 z 1. One factor which negatively contributed to this include the occasional correlator block error resulting in corrupted segments of the spectrum. Another is that some targets had limited integration time resulting in higher optical depth limits, and corresponding higher H i column density upper limits (Table 3 ). This lowered our sensitivity to detecting H i gas in absorption. All detections are made towards GPS sources, and we find a 33 per cent H i associated absorption detection rate towards the GPS sources in our sample. These GPS sources are compact in linear extent and believed to be young or re-triggered in their AGN activity. We also find shallow and asymmetric H i absorption features in our survey, as seen in Carilli et al. ( 1998 ) and Ishwara-Chandra et al. ( 2003 ) towards red quasars, and low redshift studies towards young radio AGN. The full FLASH project, alongside other future all-sky H i absorption surveys (MALS and SHARP), will better increase our H i statistics. This in turn will improve our understanding of the impact of the radio AGN on its cold gas, and its evolution with redshift, during this crucial transitional stage in galaxy evolution. Intervening H i absorption studies alongside the other ASKAP survey science projects will increase our statistics of the obscured radio AGN population missed in optically selected samples, and understanding of the distribution of cold neutral gas with redshift for such sources. SUPPORTING INFORMATION Figure 9 . Averaged


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We are very grateful to an anonymous referee for a careful reading and constructive comments that helped us improve the clarity of the paper. We thank B-G Andersson for sending us a reference on graphene magnetism by hydrogen adsorption. We thank Bruce Draine, Alex Lazarian, Peter Martin, and Charles Telesco for insightful discussions at the initial stage of this work. Numerical calculations were conducted using a high-performance computing cluster at the Korea Astronomy and Space Science Institute (KASI).


O O O O O O O O O O O B-Organization I-Organization I-Organization O B-Grant I-Grant I-Grant O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O B-Organization I-Organization I-Organization O B-Grant I-Grant I-Grant O O B-Organization I-Organization I-Organization I-Organization O B-Telescope O O O O O O O O O O O O B-Organization O O O O O O O O B-Archive I-Archive I-Archive I-Archive I-Archive I-Archive O B-Telescope

This material is based on work supported in part by the National Science Foundation through Cooperative Agreement 1258333 managed by the Association of Universities for Research in Astronomy (AURA), and the Department of Energy under Contract No. DE-AC02-76SF00515 with the SLAC National Accelerator Laboratory. Additional LSST funding comes from private donations, grants to universities, and in-kind support from LSSTC Institutional Members. This research has made use of NASA’s Astrophysics Data System Bibliographic Services. Facility: LSST.


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

large sin . To check this we included provisional results for stars with initial masses higher than 15 that have evolved into O and B giants ( Ramírez-Agudelo 2017 ; Schneider et al., in prep.). A Kuiper test of the updated distributions for groups 2 and 3 found that the probability to be drawn from the same parent distribution is still 10%. This preliminary test indicates that this possible bias can probably not explain the lack of fast rotators below log g 3.9, although we remark that the parameters for some stars still have to be confirmed, and we will revisit this in a future study. 6.1.4. Helium abundances Helium abundances for our sample were also indicated in Fig. 11 . Most of our stars have Y(He) 0.12, i.e. normal abundances within the estimated uncertainties. There were 14 stars for which we could not obtain good determinations of Y(He), and where only upper limits of 0.08 could be estimated (with the best-fitting models being 0.06 or less). As explained in Paper XIII, these low abundances could be a consequence of undetected binarity, the effects of low signal-to-noise ratio, and/or nebular contamination in the spectra. We found five stars with enhanced helium abundances (Y(He) 0.12) and log g 3.9. Two, VFTS 724 and VFTS 285, are rapid rotators with sin 370 and 600 , respectively. The rapid rotation of these two stars could explain their high helium abundances (see e.g. Maeder 1987 ; Langer 1992 ; Denissenkov 1994 ; Herrero et al. 1999 ). The other three stars (VFTS 089, 123, and 761) have intermediate and low rotation rates. Rapid rotation might still explain the He excess of these stars given that their true rotational velocities might be higher because of projection effects. Equally, their He enhancements might indicate past mass transfer from an undetected binary (e.g. Hunter et al. 2008 ), and they could be magnetic stars (see e.g. Schneider et al. 2016 ). We note that stellar winds are unlikely to be the cause for the He enrichment, as such strong winds should generate a larger surface enhancement, with wind features also seen in the spectra. 6.2. Mass-discrepancy problem As noted earlier, evolutionary masses () are typically estimated by placing a star in the H–R diagram (using results from spectral analysis) and interpolating between evolutionary tracks. Ideally, should agree with the spectroscopic mass (), calculated from , log g , and from the spectral analysis, but this is not always the case and is known as the “mass-discrepancy problem”. This discrepancy has been a challenge in the determination of masses in O-type stars since it was identified by Herrero et al. (1992) . Possible explanations have included uncertain distance estimates to Galactic stars, problems with stellar atmosphere models (e.g. underestimated gravities or the treatment of mass-loss), and problems in the evolutionary models (treatment of overshooting, rotation, and/or binary evolution). However, given a diversity of results across a range of


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

panel) shows these “anomalous radial velocities” based on all three transit observations. Before making this plot, long-term trends in the PFS radial velocities were removed by subtracting the best-fitting quadratic function of time to the out-of-transit data. This trend need not be astrophysical; because the observations were obtained without the use of an iodine gas absorption cell, the radial velocities are susceptible to intra-night drift of the instrumental profile and wavelength solution. We computed a model for the anomalous radial velocity based on the system parameters in Table 1 , using code provided by Boué et al. ( 2013 ). The model agrees well with the data, even without any further tuning of the model parameters. With this way of displaying and analyzing the data, the effects of spots are not as obvious. This is because the spots migrate smoothly across a significant part of the stellar surface over the timescale of the transit. We note, though, that not accounting for the influence of spots can cause a systematic bias in the resulting derived obliquities from the Rossiter–McLaughlin effect. If one part of the star is dimmer due to the presence of a group of spots, then the overall weighted velocity variation induced by a planet will be affected by the specific part of the star the planet transits through. This bias is irrespective of any possible spot-crossing events. Systematic uncertainties arising from such issues will need to be accounted in the error budget in Rossiter–McLaughlin observations (e.g., Oshagh et al. 2018 ). A light curve motivated spot-modeling exercise, in conjunction with an Rossiter–McLaughlin observation, can encompass such systematic uncertainties (Montet et al. 2020 ). 4. Discussion The finding of a well-aligned star and planetary orbit would not have been surprising a decade ago. Since then, though, we have learned that stellar obliquities are sometimes very large (e.g., Winn et al. 2010a ; Albrecht et al. 2012 ), and no longer take spin–orbit alignment for granted. High-obliquity orbits have been interpreted as evidence for dynamical processes that tilt the orbit of a giant planet after its formation within the gaseous protoplanetary disk. The large majority of previous obliquity measurements have been made for close-in giant planets around mature-age stars (Figure 4 ). Figure 4. Age-obliquity distribution for planets with obliquity measurements. DS Tuc Ab is the youngest system with its orbital obliquity measured by nearly an order of magnitude. Other systems with ages are labeled. The vast majority of planetary systems have ages estimated from isochrone modeling. Note that Kepler-63 (labeled) has an age estimated from gyro-chronology and spectroscopic activity indicators (Sanchis-Ojeda et al. 2013 ). Kozai and secular dynamical interactions can form a portion of the close-in Neptune and Jovian population. Their representative timescales and resulting orbital obliquities are noted in the figure. DS


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

This paper is based on Atacama Large Millimeter/submillimiter Array (ALMA) observations, program number 2013.1.00710.S. It makes use of the following ALMA data: ADS/JAO.ALMA#2013.1.00710.S. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), NSC and ASIAA (Taiwan) and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. AZ and LAC acknowledge support from the Millennium Science Initiative (Chilean Ministry of Economy) through grant ‘Nucleus RC130007’. LAC also acknowledges support from FONDECYT-CONICYT grant #1140109. HC acknowledges support from the Spanish Ministerio de Economa y Competitividad under grant AYA2014-55840P. SP acknowledges financial support by FONDECYT grant #3140601. DAP acknowledges FONDECYT grant #3150550.


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ACKNOWLEDGEMENTS The authors are grateful for the valuable machine learning discussion with S. Wiechecki Vergara. Inspiration provided by C. Role. Research was partially supported by Perspecta, Inc. This material is based upon work supported by the NASA Florida Space Grant under 2018 Dissertation And Thesis Improvement Fellowship (No. 202379). The LINEAR program is sponsored by the National Aeronautics and Space Administration (NRA Nos. NNH09ZDA001N, 09-NEOO09-0010) and the United States Air Force under Air Force Contract FA8721-05-C-0002. This material is based upon work supported by the National Science Foundation under Grant No. CNS 09-23050.


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

with elastic collision with the surface, reproduces the observations well. Although it is an empirical approach, it allows sorting among the products that should undergo the chemical desorption. The basic idea underlying our proposition is inspired by dynamic calculations in specific systems such as H+H on graphite ( Morisset et al. 2004 ; Bachellerie et al. 2007 ) or O+H on graphite ( Bergeron et al. 2008 ). We have illustrated the mechanism of this scenario in Fig. 4 . The first step consists of a collinear approach parallel to the surface. When the molecule is formed, the trajectories of both atoms adopt a more disordered motion symptomatic of the high internal energy in vibration and rotation of the newly formed molecules, up to a point where the molecule interacts with the surface and that a part of the motion is transferred perpendicularly to the surface that causes the desorption. Fig. 4 Illustration of the chemical desorption process. After an initial meeting (1), the molecule is highly excited; (2) and converts a fraction of its energy into vertical motion through interaction with the surface (3). We point out that the chemical desorption process seems to favor small molecules with low binding energies. Therefore, this process may be part of the reason COMS are present in dark clouds. We note that our prediction of about one percent of chemical desorption for methanol would be sufficient to sustain the observed value, as modeled by Vasyunin Herbst (2013) . The second part of our paper will examine the effect of the deriving our formulae in an astrophysical context. That the chemical desorption efficiency on water ice substrates is reduced is somehow to be expected. A similar behavior has been observed in photodesorption of CO. Pure CO ices exhibit an efficient wavelength-dependent photodesorption of up to one percent per incident photon ( Bertin et al. 2013 ) or possibly lower by a factor 3–11 ( van Hemert et al. 2015 ). Some authors have estimated the CO photodesorption on water substrate to be about 10 ( Öberg et al. 2009 ) or one order of magnitude lower ( DeSimone et al. 2013 ). However, even if the CO photodesorption process is poorly constrained, the water substrate clearly prevents or dramatically reduces its efficiency. This probably is due to the very fast transportation of energy in the water network and to the reduction of the indirect photodesorption. For chemical desorption on water substrate, the weakness of our coarse model probably lies in the assumption of elastic collisions, which are not adapted to the case of water. Many more experimental investigations and detailed computations would help to solve this problem. Finally, we note that even if water ice substrate seems to be a good trapping environment and can dramatically reduce the chemical desorption efficiency, CO layers in the central part of dark clouds are expected to cover an inner water layer around the solid seeds of dust. Therefore, another set of


O O O O B-Person I-Person O O O O O O O O O O O O O O O B-Person O O O B-Person I-Person O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O O O O B-Software O O O O O O O B-URL O O O O O O O O O B-Survey I-Survey I-Survey I-Survey O O B-Organization B-Telescope O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization O B-Grant O O O O O O B-Location B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O B-Grant O O O B-Organization I-Organization O O B-Grant I-Grant I-Grant I-Grant O O B-Grant B-Person O O O B-Grant I-Grant I-Grant O O O O O O B-Location I-Location O O B-Organization I-Organization O O O O O O B-Grant I-Grant I-Grant I-Grant B-Person O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O B-Grant

We thank the referee, J. Braine, for his comments and suggestions that improved the readability, clarity, and correctness of this paper. C.S. wants to thank F. Galliano for his input on the dust grain composition and for making his dust model available. Most of the numerical analysis conducted in this work have been performed using phy++, a free and open source C++ library for fast and robust numerical astrophysics (cschreib.github.io/phypp/). This work is based on observations taken by the CANDELS Multi-Cycle Treasury Program with the NASA/ESA HST, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. This research was supported by the French Agence Nationale de la Recherche (ANR) project ANR-09-BLAN-0224 and by the European Commission through the FP7 SPACE project ASTRODEEP (Ref. No: 312725). LC benefited from the thales project 383549 that is jointly funded by the European Union and the Greek Government in the framework of the program “Education and lifelong learning”. T.W. acknowledges support for this work from the National Natural Science Foundation of China under grants No. 11303014.


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

the shock to larger radii. This means that for a significant fraction of time between the passages through the primary and the secondary shocks, the electrons have lower Lorentz factors than just behind the primary shock, and the magnetic field is also lower. The radiative losses are therefore relatively small (except for the period right after the passage of the primary shock). The electrons then spend a long time in a “freezer,” until the gas passes through the secondary shock (mini-accretion shock), when its density increases back to the initial state (at least approximately). The electrons’ Lorentz factor and the strength of the magnetic field increase accordingly. As a result, the synchrotron emissivity is boosted by a factor (e.g., Markevitch et al. 2005 ), where p is the slope of the relativistic electrons energy spectrum and C is the volume compression factor. In terms of the spectral index α = ( p − 1)∕2 in the radio band, the boost factor is . This expression is based on the assumption that the magnetic field is enhanced by a factor C 2∕3 . For the shock with M ~ 1.5, the compression is C ≈ 1.7. For α = 2, the corresponding boost of the radio flux purely due to adiabatic compression is F ≈ 10. Unlike the “runway” merger shock, the mini-accretion shock does not feature a rarefaction region downstream and, therefore, the radio emission is controlled by radiative losses. Once again the question arises of whether the short radiative times pose a problem. The distance over which the secondary shock front can travel during t max is l max ~ c s t max ≲ 180 kpc (for ν = 1.4 GHz), assuming that the shock moves with the sound speed 5 . At ν = 150 MHz, this distance will be ~500 kpc. This is smaller than the size (radius) of the radio halo of some 700 kpc (not by a huge factor, though), which used to be an argument against the single shock acceleration scenario. However, in the scenario, where secondary shocks are responsible for the compression and, possibly, reacceleration of electrons, this problem can be alleviated. The electron reacceleration scenario implies that there is a pool of nonthermal relativistic electrons produced by MHD shocks and turbulence due to the cluster merging history and fast moving galaxies in the cluster. Then the diffusive shock acceleration (DSA) mechanism would reproduce the slope of the pool electron spectrum in a shock downstream if the pool distribution had a power-law spectrum of index . Otherwise, the spectrum in the shock downstream would have the standard test particle DSA index if the slope of the pool distribution has a steeper spectrum (see e.g., Blandford et al. 1987 ). Therefore, the shock with M ~ 1.5, and the compression ratio C ≈ 1.7 propagatingin the cluster plasma regions without the prominent preexisting nonthermal population have p = 5.2 and the synchrotron radio emission index α = 2.1. On the other hand, energetic particle acceleration by intensive MHD turbulence and multiple shocks may


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

targets since the spectroscopic target selection was mostly done in a colour–colour space. The well-established morphology–density relation (Dressler 1980 ; Postman et al. 2005 ) can be translated to a morphology–clustercentric radius relation (e.g. Whitmore, Gilmore Jones 1993 ; Goto et al. 2003 ). That is, early-type galaxies are more frequent in the cluster core while late-type galaxies are more frequent in the outer regions of clusters. Moreover, the morphology of galaxies is related with other physical properties such as their stellar masses, colours and SF rates. In this sense, the morphology of galaxies can also be inferred from their colours, for example: early-type galaxies tend to be red, whereas late-type galaxies tend to be blue. In this context, the relation between the morphology of galaxies and the environment can be explained by a colour–environment relation (Blanton et al. 2005 ; Skibba et al. 2009 ; Grützbauch et al. 2011a ). In the case of MACS0416 and MACS1206, the spectroscopic colour fractions as a function of projected distance from the cluster centre obtained in Section 4.6.1 (see left-hand panel of Fig. 5 ) show that galaxies in clusters and substructures follow a colour–clustercentric radius relation. Galaxies within , independent of whether they are part of a cluster or substructure, tend to be redder than galaxies beyond . This suggests that this result is likely a consequence of the effect of the cluster environment over the properties of galaxies traced by their colours (e.g. Miller 1986 ; Byrd Valtonen 1990 ; Boselli et al. 2014 ). Moreover, studying the colour fraction of galaxies as a function of the distance from the cluster or substructure centre (see right-hand panel of Fig. 5 ), we note that the total colour–clustercentric radius relation in substructures follows similar trends observed in the main clusters. According to this, substructures may be considered as down-scaled versions of clusters in which galaxy properties, traced by their colours, have been sculpted by the gravitational potential and physical processes within the substructures (e.g. ram-pressure stripping and galaxy–galaxy interactions), which can stop SF and turn galaxiesred. Fig. 6 shows the spectroscopic colour fractions as a function of projected distance by separating galaxies in all environments according to their stellar masses in massive () and less massive (). We note that fraction of green galaxies is constant in all environments, independent of the stellar mass of the galaxies and that massive galaxies tend to be red independent of the environment in which they are located. Besides, the fraction of red galaxies ( f r ) in clusters and substructures at is higher than the f r in the field, independent of the stellar mass. This result is in agreement with the result presented in the left-hand panel of Fig. 5 , in which the cluster environment models galaxy properties traced by their colours at least within . Beyond f r in


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

evolution is computed by solving the rate equations with one Jacobi iteration with implicit Eulerian time discretization, with a coupling between thermal and chemical states at subcylces in the hydrodynamical time-step (see Bryan et al. 2014 , and references therein for more details). Table 1. Main parameters of the three runs in the Chronos++suite used in the present work. From the left- to right-hand columns define the presence of radiative cooling or star-forming particles, the critical gas number density n * to trigger star formation in the Kravtsov ( 2003 ) model, the time-scale for star formation t * , the thermal feedback efficiency, and the magnetic feedback efficiency ( ε SF and ε SF, b ) from star-forming regions; the efficiency of Bondi accretion α Bondi in the Kim et al. ( 2011 ) model for SMBH; the thermal feedback efficiency and the magnetic feedback efficiency ( ε BH and ε BH, b ) from SMBH; the intensity of the initial magnetic field, B 0 ; the presence of sub-grid dynamo amplification at run time; the ID of the run and some additional descriptive notes. All simulations evolved a volume using 1024 3 cells and DM particles, starting at redshift z = 38. The name convention of all runs is consistent with Vazza et al. ( 2017 ). Table 2. List of observable properties and adopted detection threshold. Note : We associate to each observable a reference instrument, which loosely corresponds to the adopted observational cut. All the runs adopted the Lambda cold dark matter (ΛCDM) cosmology, with density parameters Ω BM = 0.0478 (BM representing the Baryonic Matter), Ω DM = 0.2602 (DM being the dark matter), Ω Λ = 0.692 (Λ, being the cosmological constant), and a Hubble constant H 0 = 67.8 km s −1 Mpc −1 and σ 8 = 0.815 (Planck Collaboration XIII 2016 ). The initial redshift is z = 38, the spatial resolution is (comoving) and the constant mass resolution of for DM particles. Additional details on our sample of simulations can be found in Vazza et al. ( 2017 ) and Gheller Vazza ( 2019 ). An RGB rendering of the projected distribution of different mass components (DM, ionised gas, and neutral Hydrogen) in our CSFBH2 model at z = 0.045 is shown in Fig. 1 . This example shows, at least in a qualitative way, the general difficulty of detecting the diffuse gas in the cosmic via cross-correlation: although on large scales all tracers are well correlated and part of the same web pattern, on scales smaller than a few they present different level of clustering and concentration, making their cross-correlation signal challenging to detect. Figure 1. RGB rendering of the matter distribution in our simulated volume for the CSFBH2 model at z = 0.045: DM density (blue), ionized gas (pink), and neutral hydrogen (green). 2.2 Multiwavelength synthetic observations and halo catalogues We generated emission maps of our simulated volume at different wavelengths, including a number of emission/absorption channels: X-ray emission: we assume for simplicity a


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

the uncertainties of the PFI-PE peak energies. We find that the PFI-PE energy resolution achieved in the present PFI-PE measurement is within the FWHM range of 1.5–2.0 cm −1 for the PFI-PE bands, indicating that these PFI-PE bands have minor perturbations by near resonance autoionizing Rydberg states. Table 1 Comparison of Ionization Energies (IEs) in cm −1 Obtained from the Present VUV–PFI–PE and VUV–PIE Rydberg Series Measurements and Those Calculated Using Known Spectroscopic and IE Data Notes. a Obtained from the present PFI-PE measurement. b Obtained from Page Gudeman ( 1990 ). c Calculated using known spectroscopic data and the IE value from the literature (see the text). d Obtained based on the present PIE Rydberg series measurement. The observed PFI-PE bands are also depicted in Figure 1 as the lower stick spectra. However, since the relative intensities of these PFI-PE peaks have not been measured carefully, we have arbitrarily set all four PFI-PE bands of the Co atom to have the same intensity. The ionization energy (IE) of the Co atom was previously determined to be 7.8810 eV (63,564.5 cm −1 ) by Page Gudeman ( 1990 ) by employing the double-resonance fluorescence-dip technique. The latter IE value is found to be in excellent agreement with the lowest PFI-PE peak at 63,564.0 ± 1.5 cm −1 observed in the present study. According to the NIST atomic database (Kramida et al. 2016 ), the four lowest spin–orbit levels of neutral Co are 4 F 9/2 , 4 F 7/2 , 4 F 5/2 , and 4 F 3/2 (in ascending order), and the four lowest spin–orbit levels of the Co + ion are 3 F 4 , 3 F 3 , 3 F 2 , and 5 F 5 (in ascending order). The energies of the 4 F 7/2 , 4 F 5/2 , and 4 F 3/2 excited levels of neutral Co measured with respect to the ground 4 F 9/2 state of Co have been reported to be 816.00, 1406.84, and 1809.33 cm −1 , respectively. The energies of the 3 F 3 , 3 F 2 , and 5 F 5 excited spin–orbit levels of Co + measured with respect to the ground 3 F 4 state of Co + have also been determined to be 950.51, 1597.32, and 3350.58 cm −1 , respectively. Thus, the IE of Co observed at 63,564.5 cm −1 can be assigned as the photoionization transition Co(3d 7 4s 2 4 F 9/2 ) Co + (3d 8 3 F 4 ). This IE[Co( 4 F 9/2 ) Co + ( 3 F 4 )] value, along with the known spacings of the spin–orbit states for Co and Co + , allows the calculation of the photoionization transition energies from the 4 F 9/2 , 4 F 7/2 , 4 F 5/2 , and 4 F 3/2 states of the Co atom to excited spin–orbit levels 3 F 3 , 3 F 2 , and 5 F 5 of the Co + ion. We found that such IE calculations predict IE[Co( 4 F 9/2 ) Co + ( 3 F 3 )] = 64,515 cm −1 for Co(3d 7 4s 2 4 F 9/2 ) Co + (3d 8 3 F 3 ), IE[Co( 4 F 9/2 ) Co + ( 5 F 5 )] = 66,915.1 cm −1 for Co(3d 7 4s 2 4 F 9/2 ) Co + (3d 7 4s 1 5 F 5 ), and IE[Co( 4 F 7/2 ) Co + ( 3 F 3 )] =63,699.0 cm −1 for Co(3d 7 4s 2 4 F 7/2 ) Co + (3d 8 3 F 3 ). These calculated IE values for the photoionization transitions are included in Table 1 to compare with the


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Acknowledgements MR and CD acknowledge funding from the European Research Council Starting Consolidator Grant (no. 307209). CD acknowledges support from an STFC Consolidated Grant (ST/L000768/1). We thank Anthony Challinor for helpful discussions and comments on a draft of the paper. We also thank Martin Bucher for useful discussions in the early stages of this work. We acknowledge the use of the psm package (Delabrouille et al. 2013 ), developed by the Planck working group on component separation, for making the simulations used in this work. Some of the results in this paper have been derived using the healpix package (Górski et al. 2005 ).


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ACKNOWLEDGEMENTS AKM would like to thank Council of Scientific and Industrial Research (CSIR) for financial support through research fellowship No. 524007. This research has made use of NASA’s Astrophysics Data System Bibliographic Services. We acknowledge the HPC@IISERM, used for some of the computations presented here. Authors thank Professor D Narasimha for useful discussions and comments. JSB thanks Professor Varun Sahni and Professor Sergei Shandarin for insightful discussions on singularities and caustics, and also for useful comments on the manuscript. Authors thank Richard Ellis, Prasenjit Saha and Liliya Williams for detailed comments on the manuscript. Authors also thank Ms Soniya Sharma who worked on some aspects of this problem for her MS thesis.


O O O O O O O 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 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 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 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 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 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 B-Survey I-Survey 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 B-Survey I-Survey O O O O O O O O O O O O O O O B-Survey I-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey I-Survey O O O O O O O O O O O O O O O O B-Survey I-Survey O O O O O O O O O O O O O

of individual absorption lines such as their width and asymmetries, but with a heightened signal to noise. The CCF is binned in 0.5 km s −1 increments, owing to the R = 55 000 resolving power of the spectrograph. Two different spectral type masks were used: G2 and K5. These were chosen based on the spectral type of the primary star, which in our sample ranges between K2 and F0. Dumusque et al. (2012) demonstrated that the closeness of the spectral type mask largely affects only the absolute radial velocity and not the radial velocity variations. Only having two spectral type masks therefore does not hinder our analysis. The CCF of each measurement was compared with a Thorium-Argon spectrum, which was used as a wavelength-calibration reference ( Lovis Pepe 2007 ). This accounted for variations in the instrument which would otherwise impose a drift on the measured radial velocity of the star. The main source of variation was the pressure of the spectrograph, which followed the ambient atmospheric pressure because CORALIE, unlike HARPS and HARPS-North, is not pressurised. In 2014 a Fabry-Pérot unit was added to provide even more precise calibrations. 5.2 Outlier removal For each CCF, which is approximately Gaussian, we measure the span of the bisector slope. The bisector is calculated by tracing vertically the midpoint of the CCF at each value of flux intensity. The span of the bisector slope is the difference between the bisector at the top and bottom of the CCF ( Queloz et al. 2001b ). The bisector therefore reflects any asymmetries in the absorption lines. We remove any observations with bisector positions more than three interquartile ranges below the first quartile or above the third quartile. Such outliers may be from the wrong star being observed accidentally, or an abnormally low signal to noise observation. A visual inspection was also done of the data to outliers in the CCF’s Full Width Half Maximum (FWHM). 5.3 Calculation of radial velocity uncertainties In Table A.1 three different σ radial velocity uncertainties are listed. The first value, σ 1800s , is mean the photon noise uncertainty for all observations of 1800 s, which was the typical observation length during the BEBOP programme. The value σ median is the median photon noise precision for all observations, that is both the 1800 s observations taken for BEBOP and earlier, shorter observations taken in the EBLM programme. Fig. 4 Time-series of 1519 radial velocity observations of the 47 eclipsing binaries in the BEBOP programme. Red diamonds are observations for 1700 s or longer. Blue squares are for shorter observations. It is seen that all binaries typically receive two long observations initially before a series of short observations as part of the EBLM programme. A series of long observations typically commenced near the end of 2013 as part of the BEBOP survey. After removing observations with significant outlier bisector values there may still remain some


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

in 1997 during which it also stayed in the LHS during the entire outburst (Revnivtsev et al. 2000 ; Brocksopp et al. 2001 ). During the 1997 outburst, a similar photon index was observed (Γ = 1.4–1.5; Revnivtsev et al. 2000 ). There are three even earlier detections of X-ray activity of transient sources that can be spatially related to GS 1354–64. During two of these detections the source was in the HSS, while the remaining one caught a source in the LHS (see Tanaka Lewin 1995 , and references therein). In case all observations are related to the same source, this source shows ‘normal’ outbursts with LHS and HSS and so-called ‘failed’ outbursts where it stays in the LHS during the entire outburst. A BHB that is known to show both types of outbursts is H1743−322 (Stiele Yu 2016 , and references therein). Unlike GS 1354–64, H1743−322 shows outbursts quite frequently. Another possibility is that only the ‘failed’ outbursts are related with GS 1354–64 and that the HSS are from a nearby transient source. About 10 X-ray binaries (including neutron stars and black holes) are known that have only been observed during outbursts where they stayed in the LHS (Capitanio et al. 2009 , and references therein). To be certain that GS 1354–64 belongs to the type of BHBs that show ‘normal’ outbursts, we would need to observe an HSS with a modern X-ray satellite that allows us to confirm that the thermal X-ray emission is spatially consistent with the position of GS 1354–64 obtained during the observation of the Comptonized emission during the 2015 outburst. The covariance ratio obtained from the XMM–Newton observation decreases with decreasing energy below 1 keV, while the one obtained for LHS observations of GX 339–4 and Swift J1753.5−0127 increases with decreasing energy (Wilkinson Uttley 2009 ; Stiele Yu 2015 ). The increase of the covariance ratio towards lower energies has been interpreted as a sign of additional disc variability on longer time-scales. Thus, the decrease observed in GS 1354–64 can be either regarded as a sign of missing disc variability on longer time-scales or as a sign of additional variability on short time-scales. For two observations of H1743−322 taken during the 2008 and 2014 ‘failed’ outbursts, we also found covariance ratios that do not show an increase at lower energies. In case of H1743−322, the covariance ratios remained rather flat (Stiele Yu 2016 ). In Stiele Yu ( 2015 ), we investigated the energy dependence of the characteristic frequency of the BLN in PDS and found that for a noise component with a characteristic frequency above 1 Hz the characteristic frequency in the 1–2 keV band is lower than in the 4–8 keV. From the XMM–Newton data of GS 1354–64, we obtain a characteristic frequency of Hz in the 1–2 keV band which is lower than the characteristic frequency of Hz in the 4–8 keV band, although this result is not significant as the errors are big. The sources investigated in Stiele Yu ( 2015 ) showed either an increase of


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We are grateful to Georges Meynet, who refereed this paper, for many constructive comments that helped us improve the paper. This work was supported by the Basic Science Research program (NRF-2016R1D1A1A09918398) through the National Research Foundation of Korea (NRF) and by the Korea Astronomy and Space Science Institute under the RD program (Project No. 3348-20160002) supervised by the Ministry of Science and ICT. S.C.Y. acknowledges the support by the Monash Center for Astrophysics via the distinguished visitor program.


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

of the sigmoid (Figure 6 ). Unfortunately, restricted by the projection effect, we cannot determine the real height of the erupting structure and its evolution with time, but can only derive its projection distance from the source region as shown in Figure 6 (b) and the velocity component in the plane of sky in Figure 6 (a). Assuming that the eruption is along the radial direction, the linear velocity is corrected to be around 60 km s −1 . Figure 5. Time-slice plots of HMI line-of-sight magnetograms showing the emergence phase (a) and cancellation phase (c) of the bipolar region. The directions used for making the time-slice plots are indicated by the blue lines in the two magnetograms at 19:35 UT on 2017 January 28 (b) and 06:36 UT on 2017 January 30 (d). The slopes of the oblique lines represent the moving velocities of the positive and negative polarities. Figure 6. (a) Time-slice plot of AIA 211 Å images showing the eruption process. (b) The slice is taken along the direction to the northwest (the line in blue) as indicated in the AIA 211 Å image at 14:05 UT on 2017 January 30. The slope of the oblique line in panel (a) represents the moving velocity of the erupting structure along the plane of sky. 2.3. Thermal Property of Mini-sigmoid The observed flux of passband i can be written as , where the R i ( T ) is the temperature response function and DEM( T ) is the plasma DEM in the corona. Knowing the observed flux F i and response function R i ( T ), we resolve the DEMs of each pixel in the mini-sigmoid source region following the method in Cheng et al. ( 2012 ), using the “xrt_dem_iterative2.pro” routine in SSW package. The emission measure maps at the four temperatures are shown in Figure 7 . One can see that the temperature of the sigmoidal structure is around 2.0 × 10 6 K (Figures 7 (b4) and (c4)). It is interesting that, before the appearance of the sigmoid, two J-shaped structures that constitute an apparent sigmoid have a higher temperature of 2.5 × 10 6 K (Figure 7 (d3)). Such a difference in temperature between the double J-shaped loops and the S-shaped structure is in agreement with the expectation that the sigmoidal field lines, are formed by the reconnection between two sheared arcades near the PIL. With the J-shaped arcades being closer to the reconnection site, they tend to be heated up to a higher temperature. Shortly afterwards, these J-shaped arcades transform into the sigmoidal structures, which then cool down probably due to the expansion. This is basically consistent with the observations by Tripathi et al. ( 2009 ). Figure 7. Temporal evolution of the EM distributions of the sigmoid source region at the four temperatures intervals ranging from 80 to 250 MK. 3. Nonlinear Force-free Field Structures of Mini-sigmoid 3.1. Flux-rope Insertion Method Through the flux-rope insertion method (van Ballegooijen 2004 ; Bobra et al. 2008 ; Su et al. 2009 ), we further reconstruct the nonlinear force-free field structures of


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

limit. The simple method above ignores that limits will be more stringent when considering larger volumes over which the detection probability of individual repeating FRBs is smaller. Furthermore, it cannot account for changing population densities with redshift, i.e. Φ → Φ( z ). The probability p ≥2 ( F th , z ) of detecting two or more bursts from a given FRB depends on both the distance z and the beam sensitivity B , which governs the detection threshold F th = F 0 / B as discussed in Section 2.3 . The expected number of observed repeating FRBs, Λ rep , in a given survey is then given by where ε( z ) weights the sensitive solid angle over beam sensitivity according to the detection probability. Unlike equation ( 14 ), the integral in equation ( 21 ) extends over all z , allowing for many repeating FRBs at large distances to contribute to the expected number of events. The factor p ≥2 ( B, z ) in the integrand gives different weights per unit volume – generally, this will be close to unity for z ≲ z lim , and fall more rapidly than increasing volume beyond this. To calculate p ≥2 ( B, z ), it is most useful to first calculate the expected number of bursts, λ( B, z ), so that p ≥2 ( B, z ) ≡ p ≥2 (λ( B, z )). λ( B, z ) can be found for the burst energy distribution of equation ( 1 ) by inverting equation ( 9 ), with z lim → z and λ lim → λ, i.e. In the case of a Poissonian distribution, p ≥2 (λ) is given simply by although the result will be different for different distributions (see e.g. Section 4 ). Evaluating p ≥2 allows equation ( 21 ) to be evaluated for any hypothesized Φ. It is useful to write Φ as the product of a z -dependent factor φ( z ) and its value in the current epoch, Φ 0 , i.e.: This allows limits on Φ 0 to be set for any given observed number of repeating FRBs by choosing appropriate Λ rep = Λ lim . The limit Φ lim on Φ 0 can be calculated as The implicit assumption here is that Φ lim will be an upper limit on the FRB density. However, this need not be the case, and both upper and lower limits could be calculated by choosing appropriate Λ lim should one or more repeating FRBs be detected, as is the case for the recent results from the Canadian Hydrogen Intensity Mapping Experiment (CHIME; CHIME/FRB Collaboration et al. 2019b ). 6.1 Volumetric limits from the ASKAP/CRAFT lat50 survey In order to limit Φ 0 , the z -dependence of the FRB population density φ( z ) is chosen to be an integer power n of the star formation rate (SFR). As per Macquart Ekers ( 2018b ), values of n = 0 (no dependence), n = 1 (stellar origin), and n = 2 (approximately tracing AGN activity) are considered. Evidently, this does not encompass models with significant delay-time, e.g. long-duration mergers, as tested by Cao, Yu Zhou ( 2018 ). The normalized SFR is taken from Madau Dickinson ( 2014 ), giving For the standard parameter set, n = 0, 1, 2, and using Φ 0 = 1 Mpc −3 , the integrand in equation ( 22 ) is shown in Fig. 11 . This is proportional to


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The authors thank the anonymous referee, whose comments improved this manuscript. We are grateful to Melanie Krips, Karl Schuster, and all the staff of the IRAM facilities for their excellent support.


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We sincerely appreciate the comments of our reviewer, Alexander James Mustill, and his work to improve this paper. Our gratitude to Dimitri Veras and Renu Malhotra for their insightful and encouraging comments on an early draft. RAS is supported by the National Science Foundation under Grant no. AST-1410174 and Grant no. DGE-1143953. KMK is supported by the National Science Foundation under Grant no. AST-1410174. AS is supported by the European Union through ERC Grant no. 279973. The numerical simulations presented herein were run on the El Gato supercomputer, which is supported by the National Science Foundation under Grant no. 1228509.


B-Survey I-Survey I-Survey I-Survey I-Survey B-Survey 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 B-CelestialObject O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O B-Survey O O B-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 I-Citation I-Citation O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O B-CelestialObject O O O B-CelestialRegion I-CelestialRegion O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O B-CelestialObject O B-Software O O O O O O O O O O O O O O O O O O O O O O O B-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 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 I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O B-CelestialObject O O O O B-Software O O O O O O O O O O O O O O B-Survey B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialRegion I-CelestialRegion O O O O O B-CelestialObject O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O B-Survey 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 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 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 B-CelestialObject O

UKIRT Infrared Deep Sky Survey (UKIDSS), Bochanski et al. ( 2014 ) were able to identify two stars with distances above 200 kpc, making them the most distant known MW stars. Figure 10 shows that these most distant stars appear consistent with the remote northern stream branch predicted in our simulation. Bochanski et al. ( 2014 ) already associated the M-giants in a distance range of 20–90 kpc in the UKIDSS data with Sgr. However, the more distant detections in their sample were not connected with the stream because the models of Law Majewski ( 2010 ) do not feature stars beyond ∼75 kpc. Our study shows that some of the most distant known MW stars could have originated in Sgr. 4. Discussion and Conclusions We have taken a two-pronged approach to building a new model of the Sgr orbit through the MW halo. Rather than integrate the present-day phase-space coordinates backward in time, we perform an exploration of parameter space with a semianalytic integration of the Sgr trajectory starting 7–8 Gyr ago. This method is chosen because it allows for the inclusion of non-time-reversible effects. In particular, dynamical friction and tidal stripping are expected to be important in the regime where the mass of the Sgr progenitor is ≳10 10 M ⊙ . We then build on these results to simulate the trajectory of Sgr with GADGET and compare the resulting tidal stream to observational data. Our main conclusions are as follows. 1. Comparing the simulated position and velocity of Sgr today to the measured quantities, we find that our analytic model favors a narrow range of the initial orbital angular momentum of Sgr, with large incidence angles ( θ init ≳ 60°) and initial velocities in the range 80 km s −1 ≲ v init ≲ 100 km s −1 . 2. The mock Sgr stream resulting from the GADGET simulation reproduces most of the sky positions, heliocentric distances, and line-of-sight velocities found by 2MASS (Majewski et al. 2004 ). Similarly to previous studies, the line-of-sight velocities of the leading arm are not replicated by the model, suggesting that further work on the triaxiality of the MW halo or the inclusion of the LMC influence is necessary. 3. The simulated debris stream projected on the plane of the Sgr orbit is in unprecedentedly good agreement with the SDSS stellar tracers from Belokurov et al. ( 2014 ). The apocentric distances and position angles of the stream are reproduced to within 20% of the measured values. In particular, the model of the Sgr orbit presented here is the first to naturally reproduce the recently detected distant trailing arm at ∼100 kpc, optimizing only for the remnant coordinates rather than fitting for the stream properties. We believe that this feature arises because of the larger initial separation (125 kpc) used in our simulation compared to other works in the literature (e.g., Law Majewski 2010 ; Purcell et al. 2011 ; Gómez et al. 2015 ). 4. Above all, this work predicts the existence of two novel and distant arms of the Sgr stream.


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It is a pleasure to thank Maosheng Xiang and Ted Mackereth for providing us insights on their results for our safety checks, and Gregory Green for practical help on using the Bayestar17 extinction map. We thank Diane Feuillet and Andy Gould for useful discussions on APOGEE selection function, and Alina Boecker and Ryan Leaman for advice on stellar populations. We are grateful to Sofia Feltzing and Paul McMillan for helping to improve the clarity of the writing. This project was developed in part at the 2018 NYC Gaia Sprint, hosted by the Center for Computational Astrophysics of the Flatiron Institute in New York City and at the 2018 Gaia –LAMOST hack-a-thon, held in Shanghai. N.F. acknowledges support from the International Max Planck Research School for Astronomy and Cosmic Physics at the University of Heidelberg (IMPRS-HD). H.-W.R. received support from the European Research Council under the European Union’s Seventh Framework Programme (FP 7) ERC Grant Agreement n. [321035]. Y.S.T. is grateful to be supported by the NASA Hubble Fellowship grant HST-HF2-51425 awarded by the Space Telescope Science Institute. The following software was used during this research: Astropy (Astropy Collaboration et al. 2013 ), Galpy (Bovy 2015 ) Matplotlib (Hunter 2007 ).


O O B-Instrument I-Instrument I-Instrument I-Instrument I-Instrument B-Instrument O O O O O O B-Telescope I-Telescope I-Telescope I-Telescope 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 B-Instrument I-Instrument I-Instrument O O O O O B-Telescope I-Telescope O O B-Observatory I-Observatory B-Location 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 B-CelestialObject I-CelestialObject 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 O O O O O O 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 O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O B-CelestialObject I-CelestialObject I-CelestialObject I-CelestialObject I-CelestialObject B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject 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 B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O

20092010 with Fibre-fed, Extended Range, chelle Spectrograph (FEROS), ( R 48000) installed on the La Silla 3.6-m telescope and are in the form of flux and wavelength calibrated spectra, all pre-processed using the FEROS standard data reduction pipeline. In addition, we present two spectra ( R 60000) recorded during 2013 August with the sandiford echelle spectrograph, which is mounted on the 2.1-m telescope at the McDonald Observatory, Texas. The raw data were extracted and reduced using the standard software packages of Horne Horne ( 1986 ). All absorption-line velocities quoted in this Letter are in the heliocentric frame of reference. Every HD 183324 spectra had narrow absorption lines positioned at the bottom of a rotationally broadened, but deep, stellar Ca ii -K absorption line at 3933.7. The stellar continua were each fit with a ninth-order polynomial over the same velocity ranges in order to determine a residual intensity absorption profile for the far weaker circumstellar/interstellar Ca ii K-lines. This process has been described in detail elsewhere (Welsh Montgomery 2015 ), and the resultant eight residual intensity profile plots are shown in Fig. 1 . All eight profiles consist of two complexes of absorption lines, with one set occurring at negative velocities spanning the 40 to 10kms 1 range, and the other set spanning mostly positive velocities in the 10 to 65kms 1 range. The EW of both absorption complexes were measured over these respective velocity ranges and are listed in Table 1 . The negative velocity absorption profiles are generally characterized by a two-component structure with velocities at V 22 and 33kms 1 , although an additional weak component at V 41kms 1 is detected in the 2010 August 31 data. The values of these two main absorption velocities are close to those of the projected velocities of the Mic and Eri local interstellar gas clouds (Redfield Linsky 2008 ). This two-component absorption component has a highly variable EW that varies from 4.0 to 10.0m. Previous observations of HD 183324 in 2011 also show a similar absorption variability of this two-component structure (Welsh Montgomery 2013 ). It is unlikely that this absorption variation is due to the passage of an interstellar cloud residing between us and HD 183324, and thus it is most probably due to the addition of circumstellar gas from evaporating exocomets. Figure 1. Observations of the Ca ii 3933.7 line showing variable circumstellar absorption over the 10 to 65kms 1 velocity range. The radial velocity of the star is at 12kms 1 . Table 1. HD 183324 Ca ii absorption data. The positive velocity profiles shown in Fig. 1 are characterized by absorption components whose strength and velocity change appreciably over time. The combined EW value of this absorption component varies from 1.8 to 9.5m and has a velocity structure with variable central velocities spanning 10 to 60kms 1 . Variability of this component was also observed at a lower level (EW = 0.8 to