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

density. Finally, a summary of our results is given in Section 5 . The transition HD( j 1 ) + X( j 2 ) → HD() + X( j 2 ) is denoted by hereafter. 2 CALCULATION DETAILS The PESs developed for the H 2 –H 2 system can also be applied to the HD + H 2 collisions. Under the Born–Oppenheimer approximation, the H 2 –HD interaction potential is identical to that of H 2 –H 2 . The main difference between H 2 –H 2 and HD–H 2 is that the centre-of-mass of one of the H 2 molecules is displayed from the middle of the interatomic distance to the centre-of-mass of the HD molecule. A coordinate rotation that shifts the centre-of-mass of H 2 to HD similar to that adopted by Sultanov et al. ( 2012 ) is utilized to obtain the H 2 –HD PES from the H 2 –H 2 Patkowski PES. We followed the corrected coordinate rotation approach as described in the appendix of Balakrishnan et al. ( 2018 ). Computations were carried out using the quantum CC method with a mixed-mode OpenMP/MPI version of the non-reactive scattering code molscat (Hutson Green 1994 ) modified by Valiron McBane ( 2008 ) and Walker ( 2013 ), referred to as vrrmm hereafter. Both the HD and H 2 molecules are treated as rigid rotors. The full quantum CC formulation is well documented in Green ( 1975 ). In the scattering calculations, the angular dependence of the interaction PES is expanded as where are radial expansion coefficients and are the bispherical harmonics. (14, 14, 8) quadrature points are used for integration along each of the angular coordinates (θ 1 , θ 2 , φ). As discussed in Balakrishnan et al. ( 2018 ), the leading anisotropic terms on the HD–H 2 potential, A 101 and A 022 , are nearly identical for both the Hinde PES and Patkowski PES. We excluded any terms beyond A 448 , because higher order terms do not make significant contributions and are not included in the PES of Patkowski et al. ( 2008 ). The modified log-derivative Airy propagator of Alexander Manolopoulos ( 1987 ) is applied to integrate the coupled channel equations and the log-derivative matrix propagated to sufficiently large intermolecular separations to yield converged results. The interval from R = 1 a 0 to the asymptotic matching radius R = 60 a 0 with a step size 0.05 a 0 is found to be adequate for the propagation. We also performed several convergence tests to verify the reliability of the computed collision data. Basis sets with [0 ∼ j 1 + 5; j 2 ∼ j 2 + 4] were found to be sufficiently large for collision energies smaller than 20 000 cm −1 . Basis sets [0 ∼ j 1 + 2; j 2 ∼ j 2 + 4] are sufficiently large for collision energies smaller than 1000 cm −1 . Since the full CC calculation is prohibitively expensive at high collision energies, the coupled-state (CS) decoupling approximation (Heil, Green Kouri 1978 ) is used for calculations for collision energies larger than 2000 cm −1 . The total wave function is expanded in the basis in the CC formulation, while in the CS formulation, is chosen to be the basis sets, where


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

is produced by the planet. We then Fourier transform the masked data back into phase versus velocity and display that in Fig. 6 . This shows an apparent retrograde trace, which we attribute to the shadow of a planet. This is again similar to what is seen in WASP-33 (Johnson et al. 2015 ). Figure 6. The spectral profiles through transit after removing the stellar pulsations via Fourier filtering. The planet trace is then readily seen moving in a retrograde direction. The left-hand panel shows the simultaneous TRAPPIST photometry of the transit. The planet's Doppler shadow seems to disappear towards the end of the transit (see Fig. 6 ). It is likely that it has been reduced during the filtering process, as a result of imperfect separation of the planetary and stellar-pulsation signals. This might have some effect on fitting the alignment angle λ, which depends on the slope of the Doppler shadow, but should have less effect on the other fitted quantities. In order to parametrize the planet's orbit, we then fitted the CCFs through transit, in a manner similar to the methods in Brown et al. ( 2017 ). Since we had subtracted the ‘minimum CCF’ above, we first add that back in to the filtered CCFs in order to reintroduce the stellar line profile, which is a key feature for constraining the value of v sin i ⋆ . The parameters that define the shape of the CCF line profile are the projected spin–orbit misalignment angle λ, the stellar line-profile full width at half-maximum (FWHM), the FWHM of the line perturbation due to the planet v FWHM , the stellar γ-velocity and v sin i ⋆ . These parameters were fitted using an MCMC fitting algorithm which assumes a Gaussian shape for the line perturbation caused by the planet. Both v sin i ⋆ and v FWHM have two data constraints, one from the shape of the line-broadening profile, and one from the slope of the trajectory of the bump across the line profile (given knowledge of λ). The value of v sin i ⋆ obtained in the spectral analysis was used as a prior in the fit. Initial values for the stellar line FWHM and the γ-velocity were obtained by fitting a Gaussian profile to the CCFs. The λ angle and v FWHM were given no prior. Details of the fitting algorithm are given in Collier Cameron et al. ( 2010a ), and the resulting system parameters are listed in Table 3 . Lastly, in Fig. 7 we show the pulsations without the planet trace, obtained by filtering to leave only the prograde quadrants, and then transforming back into velocity space. Figure 7. The spectral profiles through transit after removing the planet shadow via Fourier filtering. The stellar pulsations are seen moving in a prograde direction. 6 EVOLUTIONARY STATUS We then used MINES weeper , a newly developed Bayesian approach to determining stellar parameters using the MIST stellar evolution models (Choi et al. 2016 ). Examples of the use of MINES weeper in determining stellar parameters are shown in Rodriguez et al. ( 2017a , b ). We model the available B


The authors are grateful to the anonymous referee for improving the original manuscript.


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

The Canadian Galactic Plane Survey is a Canadian project with international partners, supported by the Natural Sciences and Engineering Research Council. We thank Blakesley Burkhart and Mordecai-Mark Mac Low for useful conversations, Sean Dougherty for his encouragement through the process of completing this paper, and the referee for insightful comments that have improved this paper. C.A.H. acknowledges financial support received via an Australian Postgraduate Award, and a Vice Chancellor's Research Scholarship awarded by the University of Sydney. B.M.G. acknowledges the support of the Natural Sciences and Engineering Research Council of Canada (NSERC) through grant RGPIN-2015-05948. N.M.M.G. acknowledges the support of the Australian Research Council through grant FT150100024. E.P. acknowledges the support from the European Research Council under the European Union's Seventh Framework Programme (FP/2007–2013)/ERC Grant Agreement n. 617199. The Dunlap Institute for Astronomy and Astrophysics is funded through an endowment established by the David Dunlap family and the University of Toronto. This research made use of APLpy, an open-source plotting package for Python hosted at http://aplpy.github.com .


O O O O O O O O O O O O O O B-Observatory O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Observatory O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-ObservationalTechniques I-ObservationalTechniques O 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 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 B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O B-Telescope O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O

variability, although this is also consistent with the calibration error. The future simultaneous, multi-frequency ALMA observations at the 300 GHz bands, are still required to provide better constraints on the instantaneous spectral energy distributions. The detailed analysis the Stokes flux variability, and the analytical modeling of the spectral energy distribution, are beyond the scope of this paper. They will be elaborated in forthcoming papers. 3.2. Polarization fitting, intrinsic polarization angle, and rotation measure During the observations, the target source is rotated with respected to the receiver frame, owing to the alt-azimuth mount of the ALMA antennae. If the polarization position angle and the polarization percentage do not vary significantly in a shorter timescale than the durations of our observing tracks (1–2 h, typically), then the polarization percentage and the polarization position angle can be fitted according to the following formula by definition: where denotes the observed Stokes flux, ( offset, hereafter) is an assumed constant normalized offset of observed Stokes as a result of the amplitude calibration errors or polarization leakage; is the polarization percentage; , , and are the polarization position angle in the sky (e.g. right ascension/declination) frame, the parallactic angle, and the Evector (Sect. 2 , Table 2 ), respectively (see also Hildebrand et al. 2000 ; Li et al. 2005 ). The application to the interferometric observations of point sources is straightforward since the visibility amplitude does not vary with uv distance. A generalized formulation for extended sources is given in Martí-Vidal et al. ( 2016 ). In practice, we determine our fitting results and errors using an iterative process. First, for each epoch of observations at each frequency, we perform a prior fitting of , and , based on XX and YY observed at various . From all data points, we then derive the standard deviation () of the difference between the observed and the priori fit. Finally, we disturb each data point of with a Gaussian random number of which the standard deviation is , and then re-fit , , and . In the end, , , and and their errors are determined by mean and standard deviations of fittings to 1000 independent realizations of the perturbed . We checked that those means converged to the values close to a priori fittings. We reject records which present poor signal-to-noise ratios with the measurements of Stokes fluxes, which could be observations at low elevation, or with poor weather conditions, or are observations of mosaic fields of which the pointing centers are far away from Sgr A* (e.g. outside of the central seven fields, see Figs. 1 , 2 ). Table 4 Polarization properties of Sgr A*. Notes. (1) Polarization position angle. (2) Measurements made from combining all ACA observations of B9-a and B9-b setups. We note that the extended emission surrounding Sgr A* is dominated by the unpolarized, free-free emission of the


O O O O O O O O O O O O O O O O O O B-Person O O O B-Organization O O O B-Grant O O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization O B-Organization O B-Grant O O B-Organization O O B-Grant O O B-Person I-Person B-Organization O O O B-Instrument O O B-Person I-Person B-Organization O O O B-Telescope O O O O B-Person I-Person B-Organization I-Organization 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 B-Telescope I-Telescope O O B-Observatory I-Observatory I-Observatory B-Location O O O B-Organization I-Organization I-Organization I-Organization O O O O O O O O O O B-Collaboration I-Collaboration O O O O O O O O O O B-Location B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization O O O B-Grant O B-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization O O O B-Grant O O B-Observatory I-Observatory O B-Observatory I-Observatory I-Observatory O O O B-Organization I-Organization I-Organization O O O O O O B-Database O O O B-Organization B-Location I-Location O O O O O O O O B-Telescope O B-Mission O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-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 O O O B-Archive I-Archive O B-Organization B-Organization O O B-Organization O B-Survey I-Survey O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O O B-Grant O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Survey O O O O O B-Location B-Organization I-Organization I-Organization O O B-Grant O O O O O B-Telescope O B-Observatory O O O B-Proposal

We thank the anonymous referee for a very thorough report, which led to numerous improvements in this manuscript. GCS was supported by NASA through Contract Number 1257184 issued by the Jet Propulsion Laboratory, California Institute of Technology under NASA contract 1407 and the NSF through Award 1108645. We thank Jean-Baptiste Marquette (IAP) for providing some EROS2 photometric data, Alistair Glasse (UKATC) for providing the JWST/MIRI filter response curves, and Sara Bladh (Padova University) for providing the results for her M-star models, including the gas-to-dust ratios. This publication is partly based on the OGLE observations obtained with the Warsaw Telescope at the Las Campanas Observatory, Chile, operated by the Carnegie Institution of Washington. This paper utilizes public domain data originally obtained by the MACHO Project, whose work was performed under the joint auspices of the U.S. Department of Energy, National Nuclear Security Administration by the University of California, Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48, the National Science Foundation through the Center for Particle Astrophysics of the University of California under cooperative agreement AST-8809616, and the Mount Stromlo and Siding Spring Observatory, part of the Australian National University. This research made use of the SIMBAD database, operated at CDS, Strasbourg, France. This publication makes use of data products from WISE and NEOWISE, which a joint projects of the University of California, Los Angeles, and the Jet Propulsion Laboratory/California Institute of Technology, funded by the National Aeronautics and Space Administration. Based on data from the OMC Archive at CAB (INTA-CSIC), pre-processed by ISDC. The CSS survey is funded by the National Aeronautics and Space Administration under Grant No. NNG05GF22G issued through the Science Mission Directorate Near-Earth Objects Observations Program. The CRTS survey is supported by the U.S. National Science Foundation under grants AST-0909182. Based on observations made with VISTA at ESO under programme ID 179.B-2003.


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

We thank Magnus V. Persson, Thanja Lamberts, Vianney Taquet, Catherine Walsh, and Maria N. Drozdovskaya for interesting discussions. We also thank the referee for his/her comments. Astrochemistry in Leiden is supported by the Netherlands Research School for Astronomy (NOVA), by a Royal Netherlands Academy of Arts and Sciences (KNAW) professor prize, and by the European Union A-ERC grant 291141 CHEMPLAN. K.F. is supported by the Research Fellowship from the Japan Society for the Promotion of Science (JSPS). Numerical computations were, in part, carried out on PC cluster at Center for Computational Astrophysics, National Astronomical Observatory of Japan.


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

The authors acknowledge the helpful comments and ideas of B. Ruiz Cobo and H. Socas Navarro provided during the development of the manuscript. We also want to thank Professor M. Carlsson for his helpful comments and corrections after reviewing the manuscript. JdlCR is supported by grants from the Swedish Research Council (VR) and the Swedish National Space Board (SNSB).


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

are often referred to as pebbles . Pebbles interact with the gas disc through gas drag and drift inwards ( Weidenschilling 1977 ; Brauer et al. 2008 ). Pebbles can become concentrated in pressure bumps and through the streaming instability (see Johansen et al. 2014 for a review), leading to planetesimal formation by gravitational collapse of the filaments. Planetesimals formed by the streaming instability have characteristic sizes of 100 km ( Johansen et al. 2015 ; Simon et al. 2015 ). In classical planet formation models, the cores of the giant planets form through mutual collisions between these planetesimals ( Pollack et al. 1996 ). However, to achieve a core mass high enough (≈10 M E ) to attract a gaseous envelope, a surface density of planetesimals of a few times the Minimum Mass Solar Nebula (MMSN) is needed. Additionally, the growth timescale increases steeply with orbital distance, making the formation of the ice giants in the solar system basically impossible to achieve with planetesimal accretion alone. Gravitational stirring of the planetesimals by a set of growing protoplanets decreases the growth rates even more ( Levison et al. 2010 ). In recent years, a new paradigm of solid accretion has emerged: pebble accretion ( Johansen Lacerda 2010 ; Ormel Klahr 2010 ; Lambrechts Johansen 2012 ; Morbidelli Nesvorny 2012 ). When a pebble enters the planetary Hill sphere, it is subject to gas drag, which robs the pebble of angular momentum, resulting in an inward drift of the pebble onto the planet. When the largest planetesimals have grown to a few hundred kilometers in size by accreting other planetesimals, rapid pebble accretion allows further growth to cores of ten Earth masses well within the lifetime of the protoplanetary disc ( Ida et al. 2016 ; Visser Ormel 2016 ; Johansen Lambrechts 2017 ). A growing planet opens a partial gap in the protoplanetary gas disc, which influences the motion of solids in the disc ( Paardekooper Mellema 2006 ; Rice et al. 2006 ). Pebble accretion stops when the gap carved by the planet generates a pressure maximum outside of its orbit, which stops the inward flux of pebbles ( Morbidelli Nesvorny 2012 ; Lambrechts et al. 2014 ). This is referred to as the pebble-isolation mass. As the influx of pebbles is stopped, the planet’s gas envelope loses its hydrostatic support, and the envelope can then contract to form a planet with an extensive gaseous atmosphere ( Lambrechts et al. 2014 ). In the solar system, pebble isolation is a potential mechanism to explain the dichotomy between the ice and gas giants, with ice giants never reaching the pebble-isolation mass and hence not able to undergo gas accretion within the lifetime of the protoplanetary disc ( Lambrechts et al. 2014 ; Venturini Helled 2017 ; Frehlik Murray-Clay 2017 ). Lambrechts et al. (2014) used hydrodynamical simulations to infer a pebble-isolation mass given by where H ∕ r is the discs aspect ratio. Lambrechts et al. (2014) found a weak


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

O.M. and P.V.D. would like to thank the Fermilab Theoretical Physics Department for hospitality. O.M. and P.V.D. are supported by PROMETEO II/2014/050, by the Spanish Grants SEV-2014-0398 and FPA2014–57816-P of MINECO and by the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreements No. 690575 and 674896. This manuscript has been authored in part by Fermi Research Alliance, LLC under contract No. DE-AC02-07CH11359 with the U.S. Department of Energy, Office of Science, Office of High Energy Physics. The United States Government retains and the publisher, by accepting the article for publication, acknowledges that the United States Government retains a non-exclusive, paid-up, irrevocable, world-wide license to publish or reproduce the published form of this manuscript, or allow others to do so, for United States Government purposes. This research used resources of the Argonne Leadership Computing Facility, which is a DOE Office of Science User Facility supported under Contract DE-AC02-06CH11357. An award of computer time was provided by the Innovative and Novel Computational Impact on Theory and Experiment (INCITE) program. This research is also part of the Blue Waters sustained-petascale computing project, which is supported by the National Science Foundation (awards OCI-0725070 and ACI-1238993) and the state of Illinois. Blue Waters is a joint effort of the University of Illinois at Urbana-Champaign and its National Center for Supercomputing Applications. This work made extensive use of the NASA Astrophysics Data System and arXiv.org preprint server.


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17 yr, Feng et al. ( 2015 ) found strong evidence for a second planet with orbiting with a period of 15.1 ± 1.1 yr. Like GJ 628 and GJ 649, GJ 849 has nearly solar [Ti/Fe] and kinematics that skew the age posterior to younger ages. Based on this, we estimate the age of GJ 849 to be . 5.2.11. GJ 876 The planetary system around GJ 876 is a benchmark system for studying the formation and migration of planets in compact systems. GJ 876 hosts a total of four known planets, three of which are in a Laplace 1:2:4 mean-motion resonance (Rivera et al. 2010 ). The resonance is chaotic but expected to be stable on timescales of at least 1 Gyr (Rivera et al. 2010 ; Martí et al. 2013 ). The old age we infer for GJ 876 ( Gyr) suggests that such chaotic resonances can be stable for several Gyr, assuming the planets migrated into this configuration soon after their formation (Batygin et al. 2015 ). Even though the innermost planet, GJ 876 d, is not in the resonant chain with the other three planets, our old age for GJ 876 has some interesting implications for its past migration. Originally, Rivera et al. ( 2010 ) estimated that planet d orbited with an unusually high eccentricity ( e = 0.207 ± 0.055) for a planet that orbits at only 0.02 au with a period of about 2 days. Recently, Millholland et al. ( 2018 ) and Trifonov et al. ( 2018 ) reanalyzed the system by fitting dynamical N -body models to existing and new RV data. Both analyses revised the eccentricity of planet d down to values more consistent with a circular orbit. Trifonov et al. ( 2018 ) reported a best-fit eccentricity of , while Millholland et al. ( 2018 ) reported a best-fit eccentricity of e = 0.057 ± 0.039. Using the Trifonov et al. ( 2018 ) estimate for the eccentricity, we constrain the minimum Q p of GJ 876 d to be >5 × 10 5 . Such a high Q p is surprising for an ∼7 M ⊕ planet. Our minimum Q p for GJ 876 d is an order of magnitude higher than the Q p of Uranus and Neptune and three orders of magnitude greater than the Q p of terrestrial bodies. A few scenarios could explain the nonzero eccentricity of GJ 876 d. One explanation is that the planet has a peculiar structure that is very inefficient at dissipating tidal energy. Another explanation is that GJ 876 d originally orbited with a larger semimajor axis where it gravitationally interacted with the outer three planets and, at some point in its history, fell out of a chaotic resonance with the outer planets and migrated in. A third scenario is that there is another, unseen planet in the system that is gravitationally interacting with GJ 876 d. We note that the eccentricity of GJ 876 d has undergone downward revision recently. If additional observations in future studies lead to further downward revision and the conclusion that the orbit is essentially circular, it may not be necessary to invoke one of the above scenarios to explain the orbit of GJ 876 d. In that case, our minimum Q p will be overestimated. However, given its proximity


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

and our purity of is calculated for real clusters with . However, our completeness decreases (80%) in this mass range (), as shown in Licitra et al. ( 2016a ). When fixing the slope at unity, we obtain () and a scatter of ( dex) for the complete (published) catalogs. In this case, the difference in a for the two samples is negligible, . The small shift in normalization (∼0.2 dex) compared to the diagonal is expected, because lensing mass estimates are generally higher than X-ray masses (Zhang et al. 2008 ; Rasia et al. 2012 ; Simet et al. 2017a ). When leaving the slope as a free parameter, we find and , with a scatter of ( and , with a scatter of ) for the complete (published) catalogs. The incompleteness when using the published catalogs appears to bias our fit slope, which becomes much shallower than the diagonal. In Figure 10 , we show the mass–luminosity and mass–temperature relations. We apply a logarithmic linear fit, in the form: where , for the , for the , , and . For the mass–luminosity relation, we find and , with a scatter ( and , with a scatter ) for the complete ( published ) catalogs. For the mass–temperature relation, we find and , with a scatter ( and , with a scatter ), for the complete ( published catalogs). The relations obtained with the published catalogs show again shallower slopes. Our results are consistent with the expected deviations from self-similarity (Böhringer et al. 2011 ). We summarize our results in Table 4 . Table 4 Results of the Fit of the Weak Lensing Mass vs. X-Ray Mass and Mass Proxy Relations: Note. “CC” refers to the complete catalogs and “PC” to the published catalogs (see text for the catalog definitions and values of the pivot mass, luminosity, and temperature used in the fit of the scaling relations). 6. Discussion 6.1. Comparison to Previously Derived Mass–Richness Relations In this section, we discuss our results in the context of similar current studies. As stated before and shown in Licitra et al. ( 2016a , 2016b ), our richness estimator λ is defined in a similar way as the richness from redMaPPer (Rykoff et al. 2014 ). The redMaPPer richness is defined as , where is the probability that each galaxy in the vicinity of the cluster is a red-sequence member and are weights that depend on luminosity and radius. In this calculation, only galaxies brighter than and within a scale radius are considered. The radius is richness-dependent and scales as . The RedGOLD richness is a simplified version of . We constrained the radial distribution of the red-sequence galaxies with an NFW profile and applied the same luminosity cut and radius scaling as in Rykoff et al. ( 2014 ), but did not apply a luminosity filter. Unlike the redMaPPer definition, our richness is not a sum of probabilities. Those choices were made to minimize the scatter in the mass–richness relation. For redshifts , the difference is only of 5–15%, while it increases to 40–60% at , where the redMaPPer richness is systematically higher


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deficit due to a gap (or hole) opened by the secondary black hole migrating within the circumbinary disk. Given the morphological evidence that Mrk 231 is indeed a recent merger (e.g., Hamilton Keel 1987 ; Hutchings Neff 1987 ; Surace et al. 1998 ; Veilleux et al. 2002 , 2006 ), and the dearth so far of black hole binaries in the cores of quasars (e.g., Eracleous et al. 2012 ; Popović 2012 ; Shen et al. 2013 ; Liu et al. 2014 ; Runnoe et al. 2015 ), contrary to theoretical expectations (Begelman et al. 1980 ; Yu 2002 ; Merritt Milosavljević 2005 ), the binary black hole explanation for the peculiar SED of Mrk 231 is potentially a very exciting new explanation of the Cycle 19 data, so it deserves to be examined in detail taking into account the new constraints from the Cycle 21 data. As pointed out by Yan et al. ( 2015 ), numerical simulations of black hole binaries (e.g., Miller Krolik 2013 ; Farris et al. 2014a , 2014b ; Roedig et al. 2014 ) show that the accretion onto the secondary black hole is expected to vary on a timescale of the order of the black hole binary orbital period, t orb ∼ 1.2 years, or less. However, as described here and in Paper I , the UV continuum emission in Mrk 231 has been surprisingly constant over the last several years. There is no evidence for any flux variations in the FUV continuum emission between 2011 (Paper I ) and 2014 (this paper), or ∼3 × t orb , and in the NUV continuum emission between 1992 (Smith et al. 1995 ) and 2014 (this paper), or ∼18 × t orb . This is not to say that the UV continuum of Mrk 231 does not vary at all. In fact, there is some evidence that the continuum level near 1300 Å in the 1978 archival International Ultraviolet Explorer ( IUE ) spectra of Mrk 231 (published in Hutchings Neff 1987 ) was ∼1.5× higher than the continuum level measured in our recent COS FUV data. But, the binary black hole model has difficulties explaining the stability of the UV emission in recent years. It would imply a (unrealistically) steady accretion stream of gas from the inner edge of the circumnuclear binary to the mini-disk of the secondary black hole over timescales of ∼3–18 t orb . A potentially fatal hurdle of the binary black hole model is the stability of the Ly α profile over a period of ∼3 year (∼3 × t orb ). In this model, the mini-disk of the secondary black hole is expected to dominate the line emission in the FUV, and the large blueshift of Ly α , C iii ], and C iv would therefore be due to the expected large line of sight velocity of the secondary black hole as it orbits the primary black hole. However, if this were the case, one would expect the centroid of the Ly α profile to shift in velocity from –3000 to at least +3000 km s −1 over half an orbital period. This is firmly ruled out by the new Cycle 21 data. Another difficulty with the binary black hole model is the fact that the absorption lines are only observed in the NUV and optical, but not in the FUV. This means that the BALR must be


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all slices. This signature clearly indicates the existence of an antinode near the footpoints of the fan loop. 3.3. Estimation of Loop Length and Velocity of the Oscillations The footpoint of the fan loop that was away from the active region was distributed, and therefore not seen clearly in normal-intensity images of 171 or 193 Å. Thus, it was not straightforward to measure the length of the fan loops. Moreover, the shape and appearance of fan loops also changed with time (see animations a and b). To estimate the length, we chose the frames where the fan loops were best seen in normal-intensity images. We chose several points along the visible segment of the fan loops and interpolated a cubic spline between them. The length of the interpolated curve should be approximately equal to the projected length of the fan loops. The orange curves in Figure 2 are the fitted spline curves that represent the projected length of fan loops at the location of three artificial slices. We found the length of the fan loops at the locations of S1, S2, and S3 to be 62, 74, and 54 Mm, respectively (see Table 1 ). Note that the estimated length is the projected length in the plane of sky. Assuming the length of the fan loop is the same in 171 and 193 Å, we estimated the phase velocity of oscillations in 171 (193) Å to be 75 (85), 83 (101), and 65 (91) km s −1 at the locations of S1, S2, and S3, respectively. The phase velocity of oscillations, v , are comparable to the speed of sound in 171 and 193 Å. 3.4. Temperature and Density of the Fan Loop We estimated the temperature and density of the fan loop using the automated differential emission measure technique as developed by Aschwanden et al. ( 2013 ). The temperature of the fan loops was found to be ∼0.7 MK, which is much cooler than the hot loops as observed by hot SUMER lines (Wang et al. 2002 ) and in the AIA 94 Å channel (Wang et al. 2015 ). We also observed that the electron density decreased along the loop. Since the temperature of fan loops is low, they appear brighter in the 171 Å channel and diffuse in hotter channels like 193 Å. We should point out that a fan loop may consist of several finer strands and we have not considered that scenario here. 4. Discussion and Conclusions We observe intensity oscillations in a non-flaring fan loop system as seen in AIA 171 and 193 Å images. The intensity variations were out of phase close to two footpoints of fan loops, and the amplitude of the intensity oscillations varied along fan loops at the location of artificial slices. The amplitude of intensity oscillations first decreased and then increased while moving from one footpoint to another along the fan loop. It should be noted that it is difficult to identify the differences between standing and propagating waves without spectroscopic signatures. Recently, Yuan et al. ( 2015 ) have performed forward modeling of standing slow magnetoacoustic waves in flaring loops. They have reported that the variation of


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We would like to thank the anonymous referee for thoroughly reading the manuscript and providing useful feedback. We acknowledge funding from NSF ACI-1036211, NSF AST- 1517593, NSF AST-1009781, and the BlueWaters PAID program. The B lue T ides simulation was run on facilities on BlueWaters at the National Center for Supercomputing Applications. SMW acknowledges support from the UK Science and Technology Facilities Council (STFC) consolidated grant ST/L000652/1. ERS acknowledges support from the UK Science and Technology Facilities Council (STFC) consolidated grant ST/L000733/1. CL acknowledges support from a UK Science and Technology Facilities Council (STFC) PhD studentship.


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

in magnetospheric size for the Earth, both with solar rotation and age. We calculate the magnetospheric size considering the Earth's magnetic field to be constant with time (blue solid line) and varying with time according to the model by Zuluaga et al. ( 2013 ; purple dotted line). This model is constrained by magnetic field measurements showing a 50 per cent field strength for a 1 Gyr system estimated by Tarduno et al. ( 2010 ). We can see that both models differ only slightly, with the most significant differences occurring around 1–2 Gyr, showing a spread of just under 1 R M . In particular, we find at early ages, both models predict magnetospheric sizes of ≈ 3 R E . This is understandable, considering the weak dependence on the planetary magnetic field of 1/6, shown in equation ( 23 ). We find a small magnetospheric standoff distance of 3.0 R E for a young Earth 100 Myr old, with the same planetary magnetic field as today ( B p = 0.3 G). These standoff distances would be similar to extreme modern day events, such as the 2003 Halloween storm (Rosenqvist et al. 2005 ), caused by coronal mass ejections (CMEs). However, these transient CME events last only on the scale of hours, but at 100 Myr these magnetosphere sizes would have been typical. Increased solar activity at younger ages (e.g. CMEs) would further compress the young magnetosphere, resulting in even smaller standoff distances. Younger stars are expected to be more active and would be more likely to produce large and more frequent transient events such as CMEs. Figure 4. We observe trends in magnetospheric size with respect to rotation (left-hand panel) and age (right-hand panel). Blue x's: calculated standoff distances with a constant planetary magnetic field of 0.3G. The solar-Earth scenario as it is currently, given as ⊕ . Purple dashed line: This depicts the standoff distances of the magnetosphere if the planetary magnetic field varied according to models described in Zuluaga et al. ( 2013 ). 5 DISCUSSION 5.1 Global properties Since direct observations of mass-loss rate and radio emission from stellar winds are difficult to obtain, we can use models to help understand the physical processes behind these winds. These models can provide information on the strength and location of the wind emission, therefore aiding in observing these winds directly. Recently, there has been research into the mass-loss rates of solar-analogue winds and how they would effect an orbiting planet, including a young Earth. Although some work focuses directly on the Sun–Earth interaction (Sterenborg et al. 2011 ), others focus more on the stellar evolution of these types of stars (Wood et al. 2002 , 2005 , 2014 ; Cranmer Saar 2011 ; Matt et al. 2012 ; Fichtinger et al. 2017 ) and their effects on exoplanets (Vidotto et al. 2012 , 2013 , 2015 ; See et al. 2014 ; Zuluaga, Mason Cuartas-Restrepo 2016 ; See et al. 2017 ). The main basis of our models is the temperature–rotation relation we presented in Fig.


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

of the solver in regions with steep gradients, can be used to mitigate this problem at the expense of making the method more diffusive. There are many different possible limiters, each trading stability and diffusion in a different way (e.g. Toro 2009 ). High-order slope estimation would be particularly challenging in our galaxy formation simulations. We model stellar feedback by directly modifying gas properties in cells surrounding young star particles, often resulting in sharp discontinuities within the density, velocity, and energy fields. We have chosen the MinMod slope limiter (e.g. Toro 2009 ) which is the safest choice in terms of suppressing instabilities, but consequently also the most diffusive. We find that, if we adopt a less diffusive slope limiter, the solution becomes unphysical; with the current implementation of feedback, we are hence required to adopt the MinMod slope limiter in order to maintain stability. In contrast, galaxy simulations accounting for strong stellar feedback via source terms in the Riemann solver, e.g. using a non-thermal pressure (Agertz et al. 2013 ; Kretschmer, Agertz Teyssier 2020 ), have successfully been carried out using slope limiters such as MonCen (Agertz Kravtsov 2015 ). We leave a more systematic investigation of this topic for future work, and instead focus here on a completely new solution to the diffusion problem. If neither the solver nor the cell size can easily be changed, the final alternative is to ensure the rate of flow relative to the grid is small. However, haloes with a naturally small net velocity are exceptionally rare. For example, in the region used by the EDGE project, of all haloes move at velocities greater than at the time of early star formation, z = 16. As we will see, this is unavoidable in cosmological volumes, and already enough to cause substantive numerical errors. Further, adding a spatially uniform velocity offset to the initial conditions cannot usefully reduce even a single halo’s net speed: the cosmological expansion ‘redshifts’ the momentum of particles. Any uniform velocity offset that is not associated with a potential gradient therefore decays proportionally to 1 + z ; in contrast, the physical velocities grow (during matter domination in the linear regime) as (1 + z ) −1 . Therefore, uniform velocity offsets rapidly become insignificant compared to the growing physical velocities. Our solution is to use the genetic modification approach (Roth, Pontzen Peiris 2016 ; Rey Pontzen 2018 ; Stopyra et al. 2020 ) to post hoc modify the initial conditions such that the velocity of a chosen halo is minimized, while its environment, accretion history and other properties are minimally affected. In fact, we have already adopted this approach as a matter of course for published EDGE results (Rey et al. 2019 , 2020 ). In this paper, we examine the effects of disabling the modification in one of our galaxies in order to compare the AMR solution with and without rapid


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

is the proton/electron mass ratio, Θ = is the electron/proton parallel temperature ratio, and is the parallel electron beta parameter in the Maxwellian limit κ → ∞. The dispersion relation for bi-Maxwellian-distributed electrons is obtained from equation ( 14 ) by changing Z κ with the Maxwellian plasma dispersion function from equation ( 12 ). 3 EFHI SOLUTIONS We have solved the dispersion relation (equation 14 ) numerically, and analysed the unstable firehose solutions for a wide variety of plasma regimes susceptible to this instability. In this section, we present the main features of the EFHI, namely, growth rates, wave-frequencies, and wavenumbers, as well as the anisotropy thresholds, and restrict our discussions only to a number of representative cases. However, the anisotropy thresholds displayed and analysed in the second part of this section cover extended conditions encountered in space plasmas, for instance, in the solar wind and planetary magnetospheres. Since only the electrons are anisotropic, in the next analysis we omit the labelling subscript ‘e’, for the anisotropy, A , and the plasma beta parameter, β ∥ . The effects of Kappa-distributed electrons are triggered by their temperature anisotropy and the abundance of suprathermal populations, which is quantified by the finite (low) values of the power-index κ. 3.1 Unstable solutions First, we examine the growth rates and the wave-frequency of the EFHI for different plasma regimes conditioned in principal by the parallel plasma beta parameter β ∥ , the electron anisotropy A , and the power-index κ. The regimes identified in Figs 1 and 2 are specific to the firehose instability, when a magnetized plasma becomes penetrable by the LH EM fluctuations propagating parallel to the magnetic field with frequencies higher than the proton cyclotron frequency. All the unstable modes, i.e. with γ > 0 in Fig. 1 , exhibit this property that becomes evident in Fig. 2 , where their wavenumber dispersion extends to high frequencies exceeding Ω p . Increasing the presence of suprathermals, i.e. lowering the power-index κ, the range of unstable wavenumbers is restrained, but the wave-frequencies and the instability growth rates are enhanced. These effects are in general stimulated by increasing the plasma beta parameter β ∥ , the temperature anisotropy and the electron–proton temperature contrast Θ. Plots evidencing the influence of Θ are not shown here, being less relevant for the scope of this paper. The unstable solutions displayed in Figs 1 – 4 are obtained for the same value of this parameter, namely, for Θ = 4 in accordance to the observations in the slow solar wind (Newbury et al. 1998 ). Figure 1. Effects of the suprathermal electrons quantified by the power-index κ =2, 2.2, 3, 6, ∞, on the growth rates of EFHI for different plasma beta explicitly given in each panel. Here is the one used in equation ( 14 ). Figure 2. Effects of the suprathermal electrons (κ =2, 2.2, 3, 6, ∞) on the


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f from the MCMC analyses at z = 0.5 and z = 1. We utilize the monopole and quadrupole up to the k max given in Table 1 , and the hexadecapole up to for TNS and for EFTofLSS at z = 0.5, while for TNS and for EFTofLSS at z = 1. In contrast to the exploratory, full P ( k , μ) Fisher matrix analysis performed in Section 4 , at z = 0.5 we find that the EFTofLSS model does significantly better than the TNS model and the gain from the inclusion of the hexadecapole in the EFTofLSS model is also larger with respect to the TNS case. At z = 1, where the models have the same range of validity, the improvement is less dramatic. An important point we wish to reemphasize is that taking the hexadecapole up to too high a k max (the ones found in Table 1 ) produces biased estimates of the growth rate f for both models, with the exception of the EFTofLSS case at z = 0.5 where indeed we can take k max = k max,4 . This is what has been done in the Fisher analysis in Section 4 , which uses the full P ( k , μ) up to the same k max from Table 1 . As we have already stated, the MCMC analysis resembles what is done in a real data analysis procedure, and is therefore more robust and reliable. To reiterate the point above, we have also performed checks to see what happens if we set the same k max = k max, 4 for TNS at z = 0.5. We found that including the hexadecapole at the same k max results in for TNS giving a (barely) unbiased result for f . This results to a larger error of , compared to our default case with error. We have also checked that increasing k max = k max,4 beyond results in a biased recovery of f . A similar test can be found in fig. 4 of Paper I . Further, we note that in earlier work by Taruya, Saito Nishimichi ( 2011 ), Fisher matrix forecasts using the multipole expansion were performed for the TNS model equipped with a linear bias prescription, taking the same k max for monopole, quadrupole, and hexadecapole. The authors showed that the monopole and quadrupole contain most of the constraining power, but the hexadecapole can somewhat help to further decrease the errors. While the model considered in Taruya et al. ( 2011 ) is not the same as the one we consider in this work, the main result is general: it is preferable to include the monopole and quadrupole at a derived common k max and then add the hexadecapole for as long as the constraints are not biased. 5.1 The effect of positivity priors on the EFTofLSS constraints It is important to comment on the effect of the positivity priors imposed on the EFTofLSS parameters ; these can have a non-negligible effect on the EFTofLSS f constraints. More specifically, we have found that if the fiducial values for these parameters are sufficiently away from zero so that no positivity priors are needed, the f constraints can increase substantially. This explains the apparent inconsistency between our MCMC results and some of the MCMC results in Paper III . In this paper a different set of simulations, cosmology,


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The Astronomical Validation activities were made possible thanks to the invaluable support of the local technical staff and the technical commissioning team. The authors thank Cees Bassa and Ramesh Karuppusamy for their important help in setting up the ROACH backend for pulsar observations. D. Perrodin thanks Gemma Janssen for providing WSRT timing residuals shown in Fig. 15 . F. Loi gratefully acknowledges the Sardinia Regional Government for financial support of her PhD scholarship (P.O.R. Sardegna F.S.E. Operational Programme of the Autonomous Region of Sardinia, European Social Fund 2007–2013 – Axis IV Human Resources, Objective l.3, Line of Activity l.3.1.). From 2012 to 2014, D. Perrodin was supported by the ERC Advanced Grant “LEAP”, Grant Agreement Number 227947 (PI M. Kramer), which also provided a 10-gigabit-ethernet switch and a storage cluster for SRT LEAP observations. M. Pilia was supported by the Sardinia Regional Government through the project “Development of a Software Tool for the Study of Pulsars from Radio to Gamma-rays using Multi-mission Data” (CRP-25476). A. Ridolfi and C. Tiburzi gratefully acknowledge support from the Max-Planck-Institut für Radioastronomie. C.Tiburzi also acknowledges support from the Universitaet Bielefeld. V. Vacca was supported by the DFG Forschengruppe 1254 “Magnetisation of Interstellar and Intergalactic Media: The Prospects of Low-Frequency Radio Observations”. The development of the SARDARA backend was funded by the Autonomous Region of Sardinia (RAS) using resources from the Regional Law 7/2007 “Promotion of the scientific research and technological innovation in Sardinia” in the context of the research project CRP-49231 (year 2011): “High resolution sampling of the Universe in the radio band: an unprecedented instrument to understand the fundamental laws of the nature”. The Sardinia Radio Telescope is funded by the Department of University and Research (MIUR), the Italian Space Agency (ASI), and the Autonomous Region of Sardinia (RAS). It is operated as national facility by the National Institute for Astrophysics (INAF).


O O O B-Dataset O O O O O O O O O O O O B-Dataset O O O O O O O O O O B-Dataset O O O O O O B-Dataset O O O O O O O O O O O O O O O O O O B-Dataset O O O O B-Dataset B-Dataset B-Dataset B-Dataset B-Dataset B-Dataset B-Dataset B-Dataset O O B-Dataset B-Dataset B-Dataset O O O B-Dataset B-Dataset B-Dataset O O O B-Dataset O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Dataset O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Dataset O O O O O O O O O O O O O O O O O O O O O O O O B-Dataset B-Dataset B-Dataset B-Dataset B-Dataset B-Dataset B-Dataset B-Dataset B-Dataset B-Dataset O O B-Dataset O O O O O O O O O O O O O O O O O O O O B-Dataset O O O O O O O O O O O O O O O O O O O O O O O B-Dataset O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Dataset B-Dataset B-Dataset O O O O O O O O O O O O O O O O B-Dataset B-Dataset B-Dataset O O O O O O B-Dataset O B-Dataset O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Dataset O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength 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 B-Citation O O O O O O O O O O O O O O O O O O O O B-Dataset O B-Dataset O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O

along with the RP1 backbone composite series used in our plage area composite (dashed blue) and RP1 backbone composite series keeping only the days common with the RP1 individual series (dashed red). Bottom : RP1 backbone composite series when varying the included individual datasets based on their bandwidth. The different curves show the RP1 backbone composite by keeping Ba, Co, Kh, RP2, SF1, SF2, Te, Up (dashed green), Br, ML, BB (dashed blue) and Ka, PM, VM (dashed red). The RP1 backbone series used for our composite is shown in solid black. Depicted are annual median values (solid lines) along with the 1 σ asymmetric intervals (shaded surfaces). The SC numbers are given below the curves. Finally, we also test the effect of including data taken with different bandwidths in the backbone series. For this purpose, we use the RP1 backbone and produce three different versions of it: (i) keeping only datasets with either bandwidths narrower than 2 Å or broader than 3 Å (Ba, CL, Co, Kh, PS, RP2, SF1, SF2, Te, Up). Since the RP1 bandwidth is 2.5 Å, these limits imply that the chosen bandwidths differ by at least ±0.5 Å from that of RP1. (ii) including only datasets with the nominal bandwidth between 2 Å and 3 Å, that is, within ±0.5 Å of the bandwidth of RP1. In this case, we further subdivide the datasets according to whether the bandwidths that have been assigned to them; ii (a) appear to be consistent with their actual behaviour (BB, Br, ML) ii (b) or their assigned bandwidth does not appear to be consistent with their actual behaviour (Ka, PM, VM). For this test, we considered the BB and ML datasets only over the periods when the final instrumentation was used (see Appendix B ), in order to avoid inconsistencies due to instrumental changes. Figure 15 b displays the three test backbone series in comparison to the one used in our composite. All three reconstructions of the RP1 backbone series lie within the uncertainties. There are generally small differences, which are greater in 2011, before 2000, and after 2018, reaching up to 0.01 in disc fraction. 5. Summary and conclusions We processed 43 datasets of full-disc Ca II K observations spanning the period 1892–2019 to derive the evolution of plage areas over the last 12 solar cycles. We processed the data consistently with the method developed by Chatzistergos et al. (2018b , 2019b) . An extra step in the processing was added to ensure accurate results from the analysis of images from the Ky and YR datasets, which suffer from specific artefacts along arcs on the solar disc. We adapted our processing such that these artefacts can be precisely accounted for and showed that we can obtain accurate results for those datasets as well. We used our results for the 38 datasets with observations centred at the Ca II K line to create a plage area composite by applying the backbone approach employed by Chatzistergos et al. (2017) to create a sunspot group number composite. We created two backbones, one


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

show that after ∼5 kyr the combined wind of the stars leaves the cluster itself, forming a collective cluster shell. We calculate the shell radius as the density-weighted average distance from the origin following Equation (23) in Rosen et al. ( 2017 ). We obtain at corresponding to an approximate expansion rate of the shell to be 18.7 . For comparison, we also calculate a density-weighted average velocity expansion of 9.05 , which is a factor of ∼2 lower than the value derived previously. Typically, observations infer the bubble age from the dynamical timescale, where both and are observationally inferred values of the shell radius and shell expansion rate, respectively (e.g., Li et al. 2015 ). Our measured values stated above for the shell velocity imply that inferring the bubble age from these quantities will underestimate the dynamical age of the bubble because the shell velocity is decreasing in time. In the top panel of Figure 5 we compare the time for the bubble material to cool, , to the characteristic bubble expansion time using from above. In each cell we calculate the cooling time given byHere is the thermal energy of the gas parcel, is the energy loss rate via cooling, and is the cooling function taken from Gnat Sternberg ( 2007 ). Here we have used for a fully ionized plasma of solar composition, where and are the electron and ion number density, respectively. To calculate in each cell we use , where assumes all helium is ionized at solar metallicity. Figure 5. Top panel: ratio of the cooling time for the bubble material to the characteristic bubble expansion time at t = 10.5 kyr. For these calculations we remove the cells that are dominated by numerical effects. Bottom panel: Mach number weighted by cell-mass within the cluster wind as a function of temperature and density at t = 10.5 kyr. We show only gas with K so that we do not include contributions from the background ISM. In the top panel of Figure 5 we show using the characteristic bubble expansion time kyr in all cells. As the cooling timescale has a strong dependence, density enhancements due to clumping will lead to faster cooling times. To take this into account we calculate on a cell-by-cell basis. We find a cell-mass−weighted average of kyr and a cell-mass weighted average of for the hot stellar winds inside the bubble shell. Figure 5 also shows that the majority of the gas within the shell, especially at the center where the density is lowest, has . At larger radii closer to the shell boundary we find . This is likely due to the turbulent mixing between the low-density, high-temperature shock-heated gas and high-density, low-temperature shell. Because the energy loss via cooling is negligible within the bubble, and instead the thermalized wind energy is transferred via adiabatic expansion, thereby driving the dense bubble shell. We note that we find that the regions around the most massive stars at the center of the simulation are dominated by numerical effects and


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model O O O O O O O O O O O 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 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 B-Tag I-Tag 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 B-Observatory B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 B-Observatory O O O B-Model I-Model I-Model O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

Fig. A.1 Transitions of CHCN, covered by our ALMA survey. The best-fit LTE synthetic spectrum of CHCN is displayed in red and overlaid on the observed spectrum of Sgr B2(N2) shown in black. The green synthetic spectrum contains the contributions of all molecules identified in our survey so far, including the species shown in red. The central frequency and width are indicated in MHz below each panel. The angular resolution (HPBW) is also indicated. The -axis is labeled in brightness temperature units (K). The dotted line indicates the 3 noise level. Fig. A.1 continued. Fig. A.1 continued. Fig. A.1 continued. Fig. A.1 continued. Fig. A.2 Same as Fig. A.1 for CHCHCN, . Fig. A.2 continued. Fig. A.2 continued. Fig. A.3 Same as Fig. A.1 for CHCHCN, . Fig. A.3 continued. Fig. A.3 continued. Fig. A.4 Same as Fig. A.1 for CHCHCN, . Fig. A.4 continued. Fig. A.4 continued. Fig. A.5 Same as Fig. A.1 for CHCN, . Fig. A.6 Population diagram of CHCN, toward Sgr B2(N2). Only the lines that are clearly detected, do not suffer too much from contamination from other species, and have an opacity below 2.5 are displayed. The observed datapoints are shown in black while the synthetic populations are shown in red. No correction is applied in panel a) . In panel b) , the optical depth correction has been applied to both the observed and synthetic populations and the contamination from all other species included in the full model has been removed from the observed datapoints. The purple line is a linear fit to the observed populations (in linear-logarithmic space). Fig. A.7 Same as Fig. A.6 for CHCHCN, . Fig. A.8 Same as Fig. A.6 for CHCHCN, . Fig. A.9 Same as Fig. A.6 for CHCHCN, . Fig. A.10 Same as Fig. A.1 for CHCHDCN. Fig. A.11 Same as Fig. A.1 for CHDCHCN in its out-of-plane conformation. Fig. A.12 Same as Fig. A.1 for CHDCHCN in its in-plane conformation. The full synthetic model (in green) does not contain any contribution of CHDCHCN in its in-plane conformation (in red). Fig. A.13 Same as Fig. A.1 for CHCN, . Fig. A.14 Same as Fig. A.1 for CHCN, . Fig. A.15 Same as Fig. A.1 for CHCN, . Fig. A.16 Same as Fig. A.1 for CHCN, . Fig. A.17 Same as Fig. A.1 for CHCN, . Fig. A.18 Same as Fig. A.1 for CHCN, . Fig. A.19 Same as Fig. A.1 for CHCN, . Fig. A.20 Same as Fig. A.1 for CHCN, . Fig. A.21 Same as Fig. A.6 for CHCN, and . Fig. A.22 Same as Fig. A.6 for CHCN, and . Fig. A.23 Same as Fig. A.6 for CHCN, , , and . Fig. A.24 Same as Fig. A.1 for CHCN, . Fig. A.25 Same as Fig. A.1 for CHCN, . Fig. A.26 Same as Fig. A.1 for CHDCN, . Fig. A.27 Same as Fig. A.6 for CHDCN. Fig. A.28 Same as Fig. A.1 for HCN, . Fig. A.29 Same as Fig. A.1 for HCN, . Fig. A.30 Same as Fig. A.1 for HCN, . Fig. A.31 Same as Fig. A.1 for HCN, . Fig. A.32 Same as Fig. A.1 for HCN, and . Fig. A.33 Same as Fig. A.1 for HCN, . Fig. A.34 Same as Fig. A.1 for HCN, . Fig. A.35 Same as Fig. A.1 for HCN, and . Fig. A.36 Same as Fig. A.1 for HCN, . Fig. A.37 Same as Fig. A.1 for HCCCN, . Fig. A.38


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

, will produce a bow shock if their radius is larger than the mean free path of gas molecules (Landau Lifshitz 1959 ). The mean free path for molecular collisions is with being the H 2 cross-section. Thus, for objects larger than km, bow shocks are formed if the gas density . The post-shock gas has a high temperature and can be efficient in thermal sputtering. However, bow shocks are not expected to form for objects of and . 5. Numerical Results 5.1. Destruction in the ISM Assuming that H 2 objects of various sizes are produced in a nearby GMC, we estimate the minimum size of objects that could reach the Earth. The closest GMC, W51, is located at a distance of . Thus, at a speed of , it takes yr for objects to reach the solar system. Figure 1 compares the various destruction times with for different object radii at a typical speed. The sublimation time is obtained using the equilibrium temperature (see Section 2 ). We find that only very large objects of radius could survive thermal sublimation and reach the solar system. The minimum size of the objects that can survive is obtained by setting , yielding Figure 1. Comparison of various destruction timescales (slanted colored lines) as a function of the object radius (in meters) to the travel time from a GMC at a distance of 5.2 kpc, assuming a characteristic speed of 30 km s −1 (horizontal black line). 5.2. Destruction on the Way from the Center of GMCs to the ISM The total gas column density toward the densest GMC amounts to extinction of (see e.g., Mathis et al. 1983 ), which corresponds to a hydrogen column density of based on the scaling with (Draine 2011 ). Assuming a mean GMC density and a GMC radius , the travel time is . Equation ( 22 ) implies a destruction time by gas collisions of , which is longer than the travel time. As shown in Section 2 , collisional heating is important in GMCs because of their high density, . Assuming that a fraction η of the impinging proton’s energy is converted into surface heating to a temperature below , collisional heating raises the temperature of the surface towhich implies effective cooling by evaporation (see Equation ( 9 )). To find the actual equilibrium temperature, we solve Equation ( 12 ) and obtain for , assuming . Substituting this typical temperature into Equation ( 3 ) yields The minimum size of the objects that can survive is obtained by setting , yielding We conclude that H 2 objects cannot survive their journey from their GMC birthplace to the ISM if their radius is below . The actual value would be larger because the surface temperature is higher when objects are moving through the core of GMCs with higher gas density. 5.3. Destruction in the Solar System When ‘Oumuamua entered the solar system, solar radiation heated the frontal surface to an equilibrium. We numerically solve Equation ( 12 ) and obtain the equilibrium temperatures and at heliodistances D = 0.25 and . Substituting these temperatures into Equation ( 4 ), one obtains and


O O O O O O O O O O O O O B-Person I-Person O O O O O O O O O O O O O O O O O O O O O O O B-Person I-Person O O O B-Model I-Model O O O B-Person I-Person O B-Person I-Person O O O O O O O O O O O O O O O O O O B-Organization I-Organization I-Organization O O B-Organization I-Organization B-Grant I-Grant I-Grant B-Grant O B-Organization O O O B-Grant B-Grant O O O O O O B-Software I-Software B-Citation I-Citation I-Citation O O O O B-Software O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O B-Software O O B-Identifier B-Citation I-Citation O O O O O O O O B-Software B-Identifier O B-Software B-Identifier O B-Software B-Identifier B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Software B-Identifier B-Citation I-Citation I-Citation I-Citation O B-Software B-Identifier B-Citation I-Citation I-Citation I-Citation O B-Software B-Identifier B-Citation I-Citation I-Citation I-Citation O B-Software B-Citation I-Citation O B-Software B-Identifier B-Citation I-Citation O B-Software B-Identifier B-Citation I-Citation O O B-Software B-Citation I-Citation I-Citation O

ACKNOWLEDGEMENTS First and foremost, we would like to record our sincere gratitude to Achim Weiss for his guidance and input. His valuable insights and our fruitful discussions have greatly contributed to this paper. We would like to thank Zazralt Magic for providing the Stagger grid as well as James Kuszlewicz and Earl Bellinger for their useful discussions. Part of the research leading to the presented results has received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement no 338251 (StellarAges). Software: Calculations were performed using the hephaestus pipeline (Angelou, in prepreparation) making use of the garstec (Weiss Schlattl 2008 ; Jørgensen et al. 2018 ) stellar evolution code and the adipls pulsation package 0.3 (Christensen-Dalsgaard 2008 ). Analysis in this manuscript was performed with anaconda 3.6.8 and python 3.6.8 packages NumPy 1.15.0 (Van Der Walt, Colbert Varoquaux 2011 ), scipy 1.2.1 (Jones et al. 2001 ), pandas 0.23.3 (McKinney et al. 2010 ), emcee 2.2.1 (Foreman-Mackey et al. 2013 ), matplotlib (Hunter 2007 ), corner 2.0.1 (Foreman-Mackey 2016 ), wquantiles 0.5 (Sabater 2015 ), and sobol (Burkardt Chisari 2011 ).


O O O O B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person O B-Person I-Person O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Proposal O O O B-Observatory I-Observatory I-Observatory O O O B-Software I-Software O O O O O O O O O O O O O O O O O B-Observatory I-Observatory O O O O O O O O O B-Person I-Person B-Person I-Person B-Person I-Person O B-Person I-Person B-Observatory O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O O O O B-Organization O O O O B-Collaboration I-Collaboration O B-Organization I-Organization I-Organization B-Location I-Location O B-Organization I-Organization I-Organization B-Location B-Organization B-Location B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Location O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Location

We wish to thank Trevor Dorn-Wallenstein, David Kann, Locke Patton, Patricia Schady, and Paula Szkody for their valuable advice and feedback on this work. We also wish to thank the anonymous referee for invaluable feedback that has greatly improved the quality of this manuscript. This paper was based on observations (Program ID GS-2016B-FT-7) obtained at the Gemini South Observatory (processed using the Gemini IRAF package) as part of the Gemini Fast Turnaround program. We thank the entire support staff of the Gemini Observatory for their efforts and assistance, with particular thanks to Kristin Chiboucas, Mischa Schirmer, Rene Rutten, and Morten Anderson. Gemini is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the National Research Council (Canada), CONICYT (Chile), Ministerio de Ciencia, Tecnología e Innovación Productiva (Argentina), and Ministério da Ciência, Tecnologia e Inovação (Brazil).