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

But note that, as discussed above in Section 4.1 , a direct comparison of our results with the models of Madau Haardt ( 2015 ), Khaire Srianand ( 2015 ), and Puchwein et al. ( 2019 ) is difficult because of the inhomogenous redshift-dependent integration limits adopted by these authors. Before considering the deficit in the photoionization rate obtained from AGN at low redshifts relative to measurements from the Ly α forest as a photon underproduction crisis, it is worthwhile to recall various assumptions entering our derivation. With a spectral index of −1.7, our ionization rate estimate falls short of the Ly α forest measurements by a factor of ∼2 with an integration limit of M 1450 = −18 on the luminosity function. Madau Haardt ( 2015 ) implicitly assume an integration limit of M 1450 = −14 at ∼ 0 (see also Khaire Srianand 2015 ; Puchwein et al. 2019 ) as this limit corresponds to M * + 5 for the Schulze et al. ( 2009 ) luminosity function measurement. It is unclear if the assumption of unit LyC escape fraction is valid for such faint AGN, but we find that even with this extremely faint integration limit, the photoionization rate deficit is reduced by only about 25 per cent for a spectral index of −1.7. While this result does not change significantly if we assume a spectral index of −1.4 as suggested by Stevans et al. ( 2014 ), assuming a much harder spectrum with a spectral index of −0.56 (Scott et al. 2004 ) for faint ( M 1450 > −23) AGN completely alleviates the deficit for an integration limit of M 1450 = −18. One should also note that our ionization rate model ignores the large uncertainties in the H i column density distribution at the Lyman limit (Ribaudo, Lehner Howk 2011 ; Gaikwad et al. 2017a ; Shull et al. 2017 ). Alternatively, it may be possible to balance the ionization rate deficit by the contribution from low-redshift LyC-leaking galaxies (Izotov et al. 2016 , 2018a , b ). 4.5 Helium reionization We now consider the implications of our AGN luminosity function models for He ii reionization. The time evolution of the volume-averaged He iii fraction is given by (e.g. Haardt Madau 2012 ) where is the emission rate of ≥4 Ry photons per unit proper volume, 〈 n He 〉 is the average proper helium number density, and 〈 t rec,He 〉 is the average recombination time-scale for He iii . With our quasar emissivity model from Section 4.1 , the emission rate can be written as with the quasar spectral index α ν = −1.7 and the comoving 912 Å emissivity ε 912 () is obtained from the fits shown in Fig. 8 . The recombination time-scale in equation ( 29 ) is given by where 〈 n H 〉 = 1.881 × 10 −7 (1 + ) 3 cm −3 is the average proper hydrogen number density, α B is the Case B He iii recombination coefficient (Hui Gnedin 1997 ), and χ = 0.079 is the cosmic number fraction of helium for a cosmic helium mass fraction of Y He = 0.24. We assume that the clumping factor C for helium is the same as for hydrogen, for which Shull et al. ( 2012a ) obtained


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

A typical peculiar velocity of 300 km s −1 equates to a proper motion of 6.3 μ as yr −1 at 10 Mpc. A sample of objects with proper motion uncertainty σ μ = 100 μ as yr −1 would require roughly 250 independent measurements to reach this proper motion value and roughly 2300 measurements to achieve 3 σ significance. Such averaging to reduce statistical errors would only be possible if one knew a priori the orientation of each proper motion vector in the sample. Since this is not known, it is appropriate to examine the correlation of extragalactic pairs. Since the number of galaxies in a volume scales as N ∝ D 3 , and the number of possible pairs scales as , then the number of pairs scales as N p ∝ D 6 . The uncertainty in the transverse velocity correlation scales as . Using Equation ( 60 ), and assuming that the fractional proper motion uncertainty is much larger than the distance uncertainty, . The uncertainty in the correlation therefore scales roughly as . This relationship assumes that x / D ≲ 1, that pairs represent independent measurements of the peculiar velocity field (not strictly true), that the proper motion measurements in value and uncertainty are uniform among the sample, and it neglects the random orientations of pairs. Including these effects will impact the constant of proportionality and may diminish the favorable impact of distance on the uncertainty in the measured correlation statistic. The optimal strategy for measuring the transverse peculiar velocity created by large-scale structure will depend on the data in hand: the redshift distribution, pair separations, sample size, and proper motion precision. VLBI proper motions will likely have redshifts of z ∼ 1, proper motion uncertainties per object of σ μ ∼ 10 μ as yr −1 , and sample sizes of 500–1000 objects (e.g., Darling 2013 ; Truebenbach Darling 2017 ). Gaia AGN proper motions will have lower redshifts, smaller pair separations, and sample size ∼10 5 , but larger per-object proper motion uncertainties of ∼200 μ as yr −1 (e.g., Paine et al. 2018 ; Truebenbach Darling 2018 ). 6. Conclusions and Future Work We have developed two-point transverse peculiar velocity correlation statistics that connect the matter power spectrum to extragalactic proper motions. We have explored the impact of pair separation, distance, and angular separation on these correlations and suggested some strategies for future extragalactic proper motion surveys. Except for very nearby pairs of objects that subtend large angles, close pairs are more sensitive to large-scale structure than widely separated pairs, as one might expect. We develop correlation statistics for randomly oriented pairs of objects with various separation-to-distance ratios. Finally, we suggest that the sensitivity to the transverse velocity correlation improves with distance in volume-limited surveys, but the optimal detection strategy will depend on the nature of the proper motion data in hand. The work presented here has


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We thank the anonymous referee for useful comments that helped us to improve the content of the paper. Based on observations made with the GTC, installed in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias, in the island of La Palma. We acknowledge support from Mexican CONACYT grants CB-2010-01-155142-G3 (PI: YDM), CB-2011-01-167281-F3 (PI: DRG) and CB-2014-240562 (PI: MR). K.Z.A.-C. acknowledges support from CONACYT grant 351585.


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The authors thank the anonymous referee for the valuable comments. This work is partially supported by the National Basic Research Program (973 Program) of China under grant No. 2014CB845800.


O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument B-Citation I-Citation I-Citation I-Citation 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 B-Instrument 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 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 B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O B-Organization I-Organization I-Organization I-Organization O O O B-ObservationalTechniques O O O B-Instrument O O O O O O O O O O O O O B-Instrument O O O O O O O O O B-Organization 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 B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O B-Organization I-Organization O O O O O O O O O O O B-Organization O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O B-Identifier I-Identifier O O B-Identifier O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

sensitivity of COSIMA to D and H, as described in the next section. 2.2 Instrument mass fractionation The effect of instrument mass fractionation (hereafter IMF) varies from element to element. For sulphur isotopes, the effect was too small to be measured with COSIMA. For oxygen isotopes, the effect was a few per cent. Because D and H have the largest relative mass difference of any isotopes of any element, the effect of IMF is expected to be quite strong. This effect must be measured, using a suitable analogue for the cometary dust. The measurement was undertaken with the COSIMA reference model (RM) using samples of insoluble organic matter (IOM) from carbonaceous chondrites. Because no evidence for hydrated minerals has been seen in the cometary dust particles analysed by COSIMA (Bardyn et al. 2017 ) and because water is unlikely to remain in dust particles collected by COSIMA grains (as discussed above), it is expected that the H measured with COSIMA will be coming primarily from the high molecular weight organic matter of the sort discussed in Fray et al. ( 2016 ). Meteorite IOM is also macromolecular, with a complex structure. There is a similarity in SIMS response between the two substances, although the H/C ratio in the cometary matter tends to be higher than that in IOM (Fray et al. 2016 ; Isnard et al. 2019 ). Such organic matter has been estimated to constitute 45 per cent of the cometary dust particles by weight (Bardyn et al. 2017 ). Because of this, IOM seems to be the best available choice as an analogue material to measure IMF. IOM samples provided by the Carnegie Institution of Washington were subjected to TOF-SIMS analyses in the COSIMA RM. The D − /H − ratios measured for the various samples in COSIMA are plotted versus the D/H isotopic ratio measured at Carnegie by elemental analysis (Alexander et al. 2010 ) in Fig. 1(a) , while Fig. 1(b) shows the same data with a line that is forced to pass through the origin fitted to it. The inverse of the slope of that line gives the IMF for D/H in COSIMA – a factor of 3.19 ± 0.86. The uncertainty in this result – which is the dominant source of systematic error in the D/H isotopic ratio – is considered in the next section. Figure 1. Panel (a) shows the D − /H − ionic ratio measured in the COSIMA reference model for samples of insoluble organic matter (IOM) from a selection of chondrites provided by the Carnegie Institution plotted versus the D/H isotopic ratio measured in the lab at Carnegie. The difference between the two measurements is due to the COSIMA instrument mass fractionation (IMF). Panel (b) shows the same data, fit with a line forced to pass through the origin. The inverse of the slope of the line gives the IMF for the D/H ratio in COSIMA: a factor of 3.19. 2.3 The particle Jessica Lummene.2 The particle Jessica is different from the other particles in that a very long measurement was done upon it – over 12 h at each location for four locations, when for other particles


O O O B-Person I-Person O B-Person I-Person 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 O O O O O O O O O O O B-Person O B-Person I-Person O O O O B-Person O B-Person I-Person O O O O O O O O O O O B-Person I-Person O O O O B-Instrument O B-Person O B-Person O O O O B-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization O O O B-Organization O B-Grant O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Location B-Person O O O O B-Organization I-Organization I-Organization B-Fellowship I-Fellowship I-Fellowship I-Fellowship O O O B-Fellowship O O 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 B-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization I-Organization B-Person O B-Person O O O O O B-Organization I-Organization I-Organization O B-Organization O O B-Grant B-Person O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O O O O O O O B-Person O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O O O B-Software B-Citation I-Citation O B-Software B-Citation I-Citation O B-Software O B-Software B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Software B-Citation I-Citation I-Citation I-Citation O B-Software B-Citation I-Citation I-Citation O

The authors thank F. Halzen and A. Kheirandish for inspiring discussions that led to the section on neutrinos and G. Sigl for comments and feedback on the anisotropy of the arrival direction. Furthermore, the authors would like to thank the referee for their comments, which helped to clarify certain parts of this work. In addition, E.G.Z. thanks C. Pfrommer for interesting discussions, and L.M. thanks B. Eichmann for reading early parts of this work. The authors also thank C. Kopper for information on the IceCube data. L.M. and J.B.T. acknowledge support from the RAPP Center (Ruhr Astroparticle and Plasmaphysics Center sponsored by the MERCUR project St-2014-0040) and from the Research Department of Plasmas with Complex Interactions (Bochum). C.B. is supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-1256259. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. Support was also provided by the Graduate School and the Office of the Vice Chancellor for Research and Graduate Education at the University of Wisconsin–Madison with funding from the Wisconsin Alumni Research Foundation. C.B. and E.G.Z. also acknowledge support from the University of Wisconsin–Madison and NSF Grant No. AST-1616037. L.M. thanks the Astronomy Department of the University of Wisconsin, where part of this work was carried out, and E.G.Z. thanks the Department of Astronomy and Astrophysics at the University of Chicago, where it was completed. Software: matplotlib (Hunter 2007 ), pandas (McKinney 2012 ), numpy , scipy (van der Walt et al. 2011 ), healpy (Górski et al. 2005 ), ipython (Pèrez E 2007 )


O O O O O O O B-Telescope O B-Mission O O O O O O O O O O O O B-Person I-Person O B-Person I-Person O O O O O O O O O O B-Person O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Grant B-Person O O O O O B-Organization I-Organization B-Grant I-Grant I-Grant B-Grant O O O O B-Grant B-Grant O O O O O O O B-Organization I-Organization I-Organization B-Organization O O O O B-Organization I-Organization I-Organization I-Organization O B-Grant O O O O O O B-Grant O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O O O O B-Organization I-Organization I-Organization O O O B-Grant B-Person B-Person O B-Person O O O O O B-Location B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization B-Person O O O O B-Organization O B-Grant O B-Organization O B-Grant B-Person O O O O O B-Grant O B-Grant B-Organization B-Person O O O B-Organization I-Organization B-Grant I-Grant I-Grant B-Person O O O O O B-Organization B-Grant I-Grant B-Grant I-Grant O O B-Organization B-Person O O O O O B-Telescope O O B-Grant I-Grant I-Grant O O B-Observatory I-Observatory I-Observatory O O O O O O O B-Dataset I-Dataset I-Dataset I-Dataset O O O B-Observatory I-Observatory I-Observatory O B-Database I-Database I-Database O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O B-Database I-Database I-Database O O B-Organization B-Location I-Location

We acknowledge the dedicated team behind the Kepler and K2 missions, without whom this work would not have been possible. We thank Daniel Huber and Benoit Mosser for useful comments on an earlier version of the paper. MNL acknowledges the support of The Danish Council for Independent Research | Natural Science (Grant DFF-4181-00415). MNL was partly supported by the European Community's Seventh Framework Programme (FP7/2007-2013) under grant agreement no. 312844 (SPACEINN), which is gratefully acknowledged. Funding for the Stellar Astrophysics Centre (SAC) is provided by The Danish National Research Foundation (Grant DNRF106). The research was supported by the ASTERISK project (ASTERoseismic Investigations with SONG and Kepler ) funded by the European Research Council (Grant agreement no.: 267864). WJC, GRD, and AM acknowledge the support of the UK Science and Technology Facilities Council (STFC). SB acknowledges partial support from NASA grant NNX13AE70G and NSF grant AST-1514676. AMS is partially supported by grants ESP2014-56003-R and ESP2015-66134-R (MINECO). VSA acknowledges support from VILLUM FONDEN (research grant 10118). RAG acknowledges the support from the ANR program IDEE (n. ANR-12-BS05-0008) and the CNES. DWL acknowledges partial support from the Kepler mission under Cooperative Agreement NNX13AB58B with the Smithsonian Astrophysical Observatory. This research has made use of the Washington Double Star Catalog maintained at the U.S. Naval Observatory; the WEBDA data base, operated at the Department of Theoretical Physics and Astrophysics of the Masaryk University; and the SIMBAD data base, operated at CDS, Strasbourg, France.


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

This work has been financially supported by the Programme National Hautes Énergies (PNHE). The research leading to these results has received funding from the European Union Seventh Framework Program (FP7/2007-2013) under grant agreement No. 312789. The XMM-Newton project is an ESA Science Mission with instruments and contributions directly funded by ESA Member States and the USA (NASA). This work is based on observations made with the NASA/ESA Hubble Space Telescope obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. These HST observations are associated with programs 13403 and 13316. This work is based on observations made with ESO Telescopes at the Paranal Observatory under programs 091.B-0183(H), 092.B-0920(A) and 093.B-0932(A). Karl G. Jansky Very Large Array (VLA) of the National Radio Astronomy Observatory is a facility of the National Science Foundation, operated under a cooperative agreement by Associated Universities, Inc. Support for CARMA construction was derived from the states of California, Illinois, and Maryland, the James S. McDonnell Foundation, the Gordon and Betty Moore Foundation, the Kenneth T. and Eileen L. Norris Foundation, the University of Chicago, the Associates of the California Institute of Technology, and the National Science Foundation. Ongoing CARMA development and operations are supported by the National Science Foundation under a cooperative agreement, and by the CARMA partner universities.


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

given the age determined by Burgasser Mamajek ( 2017 ), the activity index described in Section 3.2 , and the XUV fluxes that have been measured for the star (Bolmont et al. 2017 ; Bourrier et al. 2017 ; Wheatley et al. 2017 ). As noted earlier, the combination of these stellar attributes ensures that the TRAPPIST-1 planets will have been subjected to extended periods of activity-related atmospheric erosion. As such, the possible atmospheric erosion effects will need to be accounted for in consideration of the habitability potential of the planets. We calculated the incident flux and escape velocities for the TRAPPIST-1 planets based on the planetary and stellar properties provided by Gillon et al. ( 2017 ), where the bolometric luminosity is the result of spectral energy distribution analysis by Filippazzo et al. ( 2015 ). These calculated values are shown in Table 1 , and are depicted in Figure 5 along with the incident flux and escape velocities for various solar system objects. The cosmic shoreline based upon the estimates by Zahnle Catling ( 2017 ) is shown as a solid line, where the solar system objects to the left of the line tend to not have atmospheres and objects to the right tend to have (albeit sometimes tenuous) atmospheres. Note that the incident flux shown in the plot represents the total (bolometric) flux received at the distance of the planets from the host star. The derivation of the cosmic shoreline power law by Zahnle Catling ( 2017 ) utilized the scaling relationships of Lammer et al. ( 2009 ) that related extreme ultraviolet (EUV) and XUV excess to stellar age and spectral type. Thus, our adoption of the bolometric flux includes the atmospheric erosion effects of the intrinsic EUV and XUV radiation as a subset of the total flux. The XUV flux related to magnetic activity, as described in this paper, will add an additional component to the atmospheric eroding flux effects. Increasing the XUV component has the effect of down-weighting the influence of the escape velocity for retaining the atmosphere. This means that low-mass stars with a higher relative rate of XUV emission will have a substantially greater atmospheric erosion effect on their hosted planets. In Figure 5 , we include two additional lines for the cosmic shoreline that reduce the escape velocity effect by factors of 2 (dashed) and 4 (dotted). These lines thus represent stars for which the XUV flux is 16 and 256 times higher than the solar flux. In the case of the former, this indicates that only the g planet has a reasonable chance of retaining a planetary atmosphere, whereas in the case of the latter, all of the planets are likely to be barren. These shifts of the cosmic shoreline are consistent with the XUV flux measurements conducted by Wheatley et al. ( 2017 ) of TRAPPIST-1, which indicated that the incident flux received by the planets may be several orders of magnitude larger than that received by the Earth. Such incident flux would result in atmosphere


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We thank Anvar Shukurov and Andrew Fletcher for valuable discussions and for helpful comments on an early draft of the manuscript, and David Moss for useful feedback on a later version. We are also grateful to Romeel Davé Oliver Gressel, Marita Krause, Jonathan Zwart, Nathan Deg, Prasun Dutta, Pallavi Bhat, and especially Kandaswamy Subramanian for useful discussions. Finally, we thank the anonymous referee for insightful suggestions that helped to improve the paper.


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

flow direction forms with the grain’s velocity. The first part of Eq. ( 9 ) is the sum of radiation pressure force with the corpuscular pressure force split into its radial and transverse component. The latter part of Eq. ( 9 ) is the sum of the classical PR drag with the solar wind drag ( Marzari Vanzani 1994 ). The adopted numerical algorithm for solving the equations of motion is the RA15 version of the RADAU integrator ( Everhart 1985 ). 3. Initial conditions for asteroidal dust and cometary dust particles To compute the flux of dust particles released in the main belt through asteroidal collisions and reaching the Earth and Mercury, we adopted an initial distribution of orbital elements with the following characteristics ( Borin et al. 2009 ; Marzari et al. 1996 ; Dohnanyi 1969 ). The initial semimajor axis is randomly selected in between 2.1 and 3.3 AU, the initial eccentricity varies in the range 0.00.4 and the inclination is in the range . This choice reflects the typical orbital elements of the asteroid belt ( Gradie et al. 1989 ; Zappalá Cellino 1993 ; Zappalá et al. 1994 ; Milani Knezevic 1994 ). We assume a grain density of , which is a reasonable value for dust particles coming from the main belt asteroids ( Grün et al. 1985 ). Spherical particles are considered in the approximation of Mie’s theory for which , the dimensionless, radiation-pressure coefficient averaged over the solar spectrum, is 0.53 ( Marzari Vanzani 1994 ; Mukai et al. 1982 ). For the JFC dust particles we considered orbits with an initial semimajor axis in a range between 2.5 and 26.7 AU with the majority of dust grains in the range between 2.5 and 8 AU, eccentricity in a range interval between 0.3 and 0.9, and orbit inclination in the range between with a large concentration of particles in the range between . In this case, we assume a density of , the radiation pressure coefficient following the asteroids grain simulations ( Marzari Vanzani 1994 ; Mukai et al. 1982 ). The initial orbital elements of comets are taken from Nesvorny et al. (2010) and Levison Duncan (1997) , who followed the evolution of bodies originating in the Kuiper Belt as they are scattered by planets and evolve into the inner solar system. In their input list of source objects, Nesvorny et al. (2010) consider a JFC to become active at the time when the perihelion distance, q first drops below 2.5 AU in the Levison Duncan (1997) simulations. The orbital distribution of visible JFCs obtained with this model by Levison Duncan (1997) well approximates the observed distribution. Defining as the fading lifetime of JFCs, which is the time range between their first and last appearance ( Levison Duncan 1997 ; Nesvorny et al. 2010 ), we considered both the initial time and the final time () for each comet with perihelion distance . However, the outcome in terms of close encounters and impact speed was not significantly different, so we used the set with the final time. In Fig. 1 we illustrate the


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We thank the referee for his/her accurate revision of the paper. B.B. acknowledges support from grant PRIN-INAF 2011 “Black hole growth and AGN feedback through the cosmic time”. M.B. acknowledges support from the FP7 Career Integration Grant “eEASy”: “supermasssive black holes through cosmic time: from current surveys to eROSITA-Euclid Synergies” (CIG 321913). Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and the US Department of Energy Office of Science. The SDSS-III web site is http://www.sdss3.org/ . SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, Carnegie Mellon University, University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofisica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington, and Yale University.


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

with 10% and 30% of binaries. In the latter ones, the peak density is around the (0,0) point. The binaries contribute to producing an elongated structure with a lower density (which increases with the binary fraction). In NGC 5272 3 , the P1 sequence is relatively homogeneously populated with barely a very small overdensity near the origin. The same trend is observed for NGC 6254 (not shown), from which we conclude that either the binary fractions in GCs are underestimated, or binaries contribute only part of the extension of P1, and another process is at play. Fig. 7. Hess diagrams based on chromosome maps of the synthetic clusters with 10% ( top left panel ) and 30% ( top right panel ) of binaries, together with that of of NGC 5272 ( bottom panel ). A further test of the effects of binaries on the chromosome map is shown in Fig. 8 . We selected the cluster NGC 6254 since; (1) it shows an extended P1 ( Milone et al. 2017 ), (2) its metallicity corresponds to that of our models, and (3) the binary fraction decreases from the core to the outer parts of the cluster ( Dalessandro et al. 2011 ; Milone et al. 2012 ). To investigate whether or not this variation of the binary fraction is reflected in the shape of P1, we selected two regions of the cluster: the core and an annulus around it, as displayed in the left panel of Fig. 8 . We subsequently selected the stars brighter than the bottom of the RGB in each region and constructed their chromosome map. The results, shown in the right panel of Fig. 8 , do not show any significant variation of the extent of the chromosome map. This result does not depend on the choice of the core and annulus regions. If binaries governed the elongation of P1, one would expect a smaller extension in the outer regions of the cluster, which is not observed. Fig. 8. Left panel : position of stars brighter than m 814 W = 18.5 in the cluster NGC 6254. The red and blue circles indicate the two regions used to produce the chromosome maps of the right panel . Right panel : chromosome map of the stars inside the blue circle in the left panel (blue squares) and of the stars in between the red and blue circles (open red circles). Only stars brighter than m 814 W = 16.5 (i.e., above the bottom of the RGB) are considered in the chromosome maps. If binarity were the main reason for the extension of P1, one would also find a correlation between binary fraction and P1 extension. A simple comparison of two GCs with similar properties, NGC 5272 (M 3) and NGC 6205 (M 13), shows some qualitative trends. Both clusters are of about the same age, metallicity and mass ( Harris 1996 ; Marín-Franch et al. 2009 ), but M 3 shows an extended P1, while M 13 does not – see Fig. 5 of Milone et al. (2017) . According to Milone et al. (2012) , the total binary fraction in M 3 (M 13) is between 3 and 6% (2 and 10%). Thus, M 3 does not have a higher binary fraction that would explain its more extended P1. 3.3. Effect of the binary mass ratio


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We are grateful to the staff of the IRAM facilities for the continuing excellent support of the large CO survey programs we have been analyzing in this paper. We also thank Albrecht Poglitsch and Matt Griffin, the PACS and SPIRE teams, and ESA for their excellent work on the Herschel instruments and mission. Finally, we thank the referee, whose suggestions have led to a clearer manuscript overall. This paper makes use of the following ALMA data: ADS/JAO.ALMA#2013.1.00092.S. ALMA is a partnership of ESO (representing its member states), NSF (USA), and NINS (Japan), together with NRC (Canada), MOST and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO, and NAOJ.


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unavoidable; that is, first-principles numerical simulations that address this plasma regime with adequate separation between the ion and the electron scales may inevitably satisfy the conditions for nonlinear reconnection in turbulent eddies at sub-ion scales. Indeed, the biggest such simulation that we are familiar with reports spectra steeper than in the sub-ion range (Told et al. 2015 ), which could be a manifestation of reconnection-driven energy depletion in the eddies. It is interesting to analyze this result in light of recent MMS observations of so-called electron-only reconnection in the Earth's magnetosheath (Phan et al. 2018 ; Stawarz et al. 2019 ). In Boldyrev Loureiro ( 2019 ) we have estimated that the decoupling of the ions in these events requires or depending on whether one assumes a or magnetic field profile for the reconnecting field in the eddy. These estimates range from ∼6 to ∼12; combined with Equation ( 12 ) or ( 13 ) they suggest a rather narrow range of scales where nonlinear “electron-only” reconnection in the eddies may be possible. Remarkably, Phan et al. ( 2018 ) report a current sheet thickness of , strikingly consistent with these numbers and with Equation ( 12 ). This is certainly very encouraging, but one must also bear in mind that all our analytical results are only order of magnitude estimates which ignore order unity numerical prefactors. Another observationally based result which we interpret to be consistent with our analysis is the recent claim by Chen et al. ( 2019 ) that energy dissipation at kinetic scales in the magnetosheath is dominated by linear electron Landau damping (the energy dissipation rate via that channel being comparable to the energy cascade rate). Indeed, Equation ( 12 ) demonstrates that full reconnection in sub-ion scale eddies is permitted for typical magnetosheath parameters; and previous investigations of heating in (strong guide-field) collisionless reconnection (Loureiro et al. 2013 ; Numata Loureiro 2015 ) show that when β e ≪ 1 linear electron Landau damping is by far the dominant energy dissipation channel. Furthermore, Chen et al. ( 2019 ) report a steepening of the spectrum at the scales where Landau damping is prominent, consistent with our expectations of the effects of active collisionless reconnection in the cascade. 4.3. Low-beta Pair Plasmas For completeness, we address here the case of low-beta pair plasmas, for which governing equations and turbulence scalings are given in Loureiro Boldyrev ( 2018 ). In the MHD regime the same equations as for an electron-ion plasma apply; the discussion is thus unchanged from that of Section 3 . In the case of a collisionless pair plasma, the criterion stated in Equation ( 3 ) yields (exactly as in Equation ( 12 ) since the scaling for γ t is the same). This needs to be reconciled with the requirements for the existence of a tearing range in the first place: for a Harris-type reconnecting profile, these are (Loureiro Boldyrev


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ACKNOWLEDGEMENTS We acknowledge support from the National Science Foundation through grant NSF-1108957. Support for Program numbers 12634 and 12575 was provided by NASA through a grant from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Incorporated, under NASA contract NAS5-26555. AIZ acknowledges support from NSF grant AST-0908280 and NASA grant ADP-NNX10AD47G. TC and MD acknowledge partial support of NASA grant HST- GO-12065.01-A. The archival and Guest Observer data are based on observations made with the NASA/ESA Hubble Space Telescope, which is operated by the Space Telescope Science Institute.


O O O O O O O O O O O O O O O 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-Instrument 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 B-Model I-Model 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 B-CelestialObject O B-CelestialObject O B-Instrument O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O B-CelestialObject O B-CelestialObject 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 B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-CelestialObject O O O O O O O O O O O B-CelestialObject O B-CelestialObject O O O O O O O O O O O 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

are compatible with the literature data and achieve an accuracy similar or better with respect to the published measurements, which is a good test for this new instrument. The orbital fit is a minimum fitting, as described in Esposito et al. (2013) , where all the four orbits are simultaneously taken into consideration, using the assumption that the planet periods are commensurate. The IFS measurement is used for the closest planet e, as it provides smaller error bars. We assumed circular and non-coplanar orbits and tested three different configurations for the orbital period ratios between the planets. The fitted orbits are shown in Fig. 5 . The parameters of the orbital solutions are summarized in Table 7 . The uncertainties on the parameters were estimated using a quadratic combination of statistical and systematic errors. The statistical errors stem from the sensitivity of the fit to the errors bars on the astrometric measurements and are derived from 1000 random trials of the astrometric measurements assuming normal distributions ( Maire et al. 2015 ). The systematic errors are related to the uncertainties on the stellar mass and distance (Table 7 ), which propagate into the derivation of the semimajor axis. To assess them, we performed two sets of orbital fits. The first set assumes the nominal values for the stellar mass and distance, and the second set assumes a combination of values at the edge of the derived ranges, which provides the largest offset in orbital periods. Two orbital solutions are favored with similar reduced , with the orbital period ratios 2d:1e and 3d:1e. The IFS data point for planet e is out of the orbital solution with the orbital period ratio 5d:2e at 2.5 significance level. Further astrometric monitoring is required to distinguish between the orbital period ratios 2d:1e and 3d:1e. Fig. 5 Relative astrometry for the planets around HR 8799. The points available from the literature are represented with black filled circles, while new SPHERE measurements are represented with purple filled squares. The solid blue lines represent the orbital solution labeled A in Table 7 . Red lines connect the predicted and observed positions for all the data points. The dotted and dashed lines in the panel for HR 8799 e indicate the orbital solutions labeled B and C in Table 5, respectively. Table 7 Orbital elements fitted on the astrometric data in Fig. 5 . Notes. Case A: orbital solution setting circular orbits and 8b:4c:2d:1e mean motion resonance. Case B: orbital solution setting circular orbits and 4b:2c:1d and 5d:2e mean motion resonances. Case C: orbital solution setting circular orbits and 4b:2c:1d and 3d:2e mean motion resonances. For each planet, the notations refer to the orbital period, inclination, longitude of the ascending node, eccentricity, argument of periapsis, time of periapsis passage, and semimajor axis. The error bars on the orbital parameters are at 1 (see text). We also indicate the reduced for the nominal


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

can also be seen for physisorption at very low temperature (≤6 K), when the grain can be full of immobile atoms (Katz et al. 1999 ). A corollary of this behavior is that in case the accretion is very efficient, the dust grain could have a large abundance (∼10 −6 ) of a particular species depending upon its desorption energy. For most species, this effect can lead to a change in the gas abundance phase profile. 6. Conclusions We have studied the chemistry of simple molecules on interstellar dust grains bound strongly by chemisorption on graphite. Chemical simulations involving chemisorbed and gas-phase species have been run for both isothermal and warm-up conditions using simplified assumptions. The isothermal models were run between 150 and 400 K at an interval of 25 K, and the warm-up models have a temperature range between 10 and 400 K. For each case, we have run models with different values of adsorption barriers and binding energies to explore the sensitivity of our results to these uncertain chemisorption parameters. Our major conclusions are as follows. 1. The efficiency of chemisorption hinges strongly on the efficiency of adsorption. Models having the lowest adsorption barrier for all species (0.1 eV) were found to produce reasonably abundant chemisorbed species, although the abundance of a chemisorbed species depends both on the adsorption rate and also other processes such as its chemistry. The reduction by a factor of 2 of individual desorption energies calculated by us does not increase the abundances markedly. 2. For species such as CO, which are very efficiently formed in the gas phase at almost all temperatures (10–400 K), the existence of chemisorbed molecules will not have a significant impact on their gas-phase abundances. However, some chemisorbed CO can be locked on grains, leading to a reasonably high abundance of ∼10 −6 , so that it could be detectable using upcoming observational facilities. Species such as C 2 H 2 and NH 3 , which are less efficiently formed in the gas phase compared with CO, may show a change in their gas-phase abundances due to chemisorption. The chemisorbed species can also approach peak abundances near ∼10 −6 and may be detectable. 3. A reasonably large number of chemisorbed species show fractional abundances above 10 −8 under certain conditions. An attempt to detect them using JWST might be worthwhile if chemisorbed species with higher abundances can be detected with reasonable signal to noise. 4. For warm-up models, if the efficiency of adsorption is high, a steplike abundance profile versus time is calculated using the assumption that chemisorption is possible only in the first monolayer, which rules out the formation of more than one layer. 5. Our calculations are based on the scant existing literature and simplified assumptions. In the future, detailed quantum mechanical calculations and experiments will be required to extract essential parameters such as diffusion barriers, sticking


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

strengths where Proca stresses can be significant. As emphasized above, the model considered in this report is not that of dark matter; it may, however, account for the conjectured dark-matter effects in astrophysical settings even beyond galactic rotation curves. It may also be tempting to explore the influence of the negative pressure typical for the Proca electrodynamics on the cosmological-scale phenomena with a possible impact on the dark-energy scenarios. To have a significant effect, one would need the presence of a tangled magnetic field, with a correlation length exceeding the photon Compton length, filling the entire space. The field would have to be nearly force-free to survive on the cosmological timescales. Appendix A Quasi-steady-state Maxwell–Proca Equations A set of Maxwell–Proca equations reads as (see Jackson 1975 ; Goldhaber Nieto 1971 ) Here, and φ are the vector and scalar potentials, ρ and and j are the space charge and the current density satisfying the standard continuity equationNote that here we use the same notation for charge density as we do in the main text for the mass density. This, however, should not cause confusion because the charge density does not appear in any equations in the main text. The electric field is related to and φ byThe potentials satisfy the Lorentz gaugeThis (Lorentz) gauge now becomes the only possible one: Equation ( 54 ) is a direct consequence of Equations ( 50 )–( 52 ). The scalar and vector potentials become measurable quantities. Consider a system where the temporal variation of the “sources” (currents and charges) is slow in the sense that the characteristic time of this variation, , is long compared to the light-propagation time over the spatial scale of the system, L ,(we use the hat overscript to distinguish the characteristic time from temperature). Then, according to Equation ( 48 ), one has the following order-of-magnitude relation:If one associates with L and some velocity that characterizes the motions in the system, then one can say that E is first order in v/ c . Substituting the estimate ( 56 ) into Equation ( 50 ), one sees that the last term on the right is small compared to the first term on the left by a factor of and constitutes a correction of the second order. Neglecting this second-order term, one obtains the quasistatic version of Equation ( 50 ):Likewise, estimating A from Equation ( 49 ) as B × L and using Equation ( 56 ), we find from Equation ( 53 ) an order-of-magnitude estimate . Then, comparing the first and the second terms in Equation ( 54 ), we find that the second term is second-order small and can be dropped, so that Equation ( 54 ) is reduced toTaking the divergence of Equation ( 57 ), one finds that, to the same (first) order, the charge-continuity equation is reduced toThereby we obtain a set of equations describing quasi-steady-state processes in the Maxwell–Proca electrodynamics. The set consists of Equations ( 48 ) and ( 49 ) and Equations ( 58


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

channels, thus the results are extremely sensitive to the cross-section of the 27 Al( p , γ) 28 Si reaction: the comparison with the Al measured in E stars seems to require slightly lower rates, but the differences are not sufficiently significant to require a supplementary analysis on this argument. Sodium is the most delicate species entering this discussion, because the surface abundance reflects the equilibria between the production and the destruction mechanisms (see Section 4.3 ), both very sensitive to the temperature, thus exposed to significant variation during the TP phase. This explains the TP evolution of the surface sodium, shown in the right-hand panel of Fig. 3 . As reported in Table 1 , the average sodium of the ejecta, [ Na/Fe ] ∼ 0.5, is similar to the quantity observed in E stars. Despite the vigorous destruction of sodium in the advanced TP phases, the ejecta are enriched in sodium (by a factor ∼3), because during the initial part of the evolution the sodium in the envelope reaches abundances 10–20 times higher than in the matter from which the star formed; this can be clearly seen in the right-hand panel of Fig. 3 . Such a large increase in the surface sodium is partly due to the accumulation of 22 Ne during the SDU (see discussion in Section 4.2 ); an additional motivation is that the sodium enrichment of the envelope takes place during the initial TP phases, when dust production is at the maximum efficiency (region labelled as Mg in the right-hand panel of Fig. 3 ): this favours the release of large quantities of sodium-rich gas into the interstellar medium. 5.3 Can we obtain oxygen-free ejecta? Oxygen deserves a separate discussion. The SAGB yields reported in Table 1 have [ O/Fe ] ∼ −0.2, ∼4 times smaller than FG stars. On the other hand, Fig. 1 above and fig. 3 in Carretta et al. ( 2018 ) show that some stars belonging to group E have extremely low surface oxygen, up to 20 times lower than observed in FG stars; furthermore, some of these measurements are upper limits. We did several tests, by varying the HBB modelling and the description of mass-loss: our conclusion is the impossibility of producing SAGB ejecta with such low oxygen contents. The only possibility is that the stars suffer extremely low mass-loss during the initial TP phases, until most of the oxygen in the envelope is consumed, via p-capture. The rate of mass-loss required to accomplish this task should be below yr −1 , far too small for this high luminosity, expanded stars. In this case, the overall agreement between the yields of SAGB stars and the chemistry of E stars would be substantially worse, because the gas ejected would be practically sodium free and would show magnesium depletion and silicon enrichment far in excess of the quantities observed. On the other hand, it is not possible to reproduce all the oxygen abundances of E stars at the same time, given the large spread observed, amounting to almost 1 dex. Oxygen is very peculiar on


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

ii regions are sensitive to time since the onset of the most recent burst, driving scatter from the average relationships. Henry et al. ( 2000 ) found that chemical evolution models differing only by their assumed star formation efficiencies (SFEs) produced a range of primary N/O plateaus. We illustrate the effect of varying the SFE by over-plotting the Henry et al. ( 2000 ) constant SFR models, where efficiency has been varied by a factor of 25, on our N/O versus O/H data in Figure 14 . For low SFRs, the buildup of oxygen is slow and on the order of the lag time before intermediate-mass stars begin ejecting nitrogen. This allows a high N/O plateau to be established at low oxygen abundances (darkest purple curve). On the other hand, high SFRs early in the SFH form a large number of massive stars that produce greater levels of oxygen ahead of N enrichment, establishing a lower plateau (lightest purple curve) and shifting the entire N/O–O/H trend in Figure 14 to the right toward greater O/H. In between these scenarios, continuous star formation with roughly 250 Myr between bursts will result in N and O increasing in lockstep, dependent on the elemental yields. The coupling of the N/O plateau with galaxy SFH is also reported by cosmological hydrodynamical simulations of individual regions within spatially resolved galaxies (Vincenzo Kobayashi 2018 ). In these simulations, asymptotic giant branch (AGB) stars contribute significant N at low O/H, but the exact value of the primary N/O plateau will vary from galaxy to galaxy according to the relative contributions from SNe and AGB stars, as determined by their galaxy formation time and SFH. On the left-hand side of Figure 14 , we extend the highest N/O plateau from NGC 5194 (green) and the lowest N/O plateau from NGC 5457 (yellow). Based on the above discussion, for the low N/O plateau of NGC 5457, we can put forth an SFH scenario in which the SFE was high early in the galaxy’s evolution, allowing oxygen to build up from many bursts of star formation before nitrogen was returned from longer-lived intermediate-mass stars. Due to the higher level of nucleosynthetic products from massive stars, contributions from secondary nitrogen production may dominate over primary nitrogen production at relatively low O/H and S/H values. On the other hand, the high N/O plateau of NGC 5194 could be due to an SFH in which low SFE at early times allows nitrogen production, although delayed, to keep pace with oxygen and sulfur production and enrich the ISM. Here, we assume low SFE to mean either constant, low SFRs or long quiescent periods between bursts. In this scenario, primary nitrogen production is the dominant mechanism until the galaxy reaches relatively high O/H. Note, however, that this is a very simplistic model where N/O is changing monotonically, in a hierarchical galaxy-building scenario that may not be true. In summary, the primary N/O plateau sensitively probes the SFH of a galaxy, rather than being set by


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

The initial sample contains 777 spectroscopically unobserved SuperWASP/ ROSAT objects, with rotation periods ≲ 5 d, declinations >−20°, 8 V 15 and spectral-types FGK, corresponding to 0.7 V − K s 3.8. Targets in the first list are selected from the parent sample. A second list comprised of a subset of 160 targets whose proper motions and positions are compatible with membership of the Pisces MG. B and V photometry for all targets was sourced from the catalogue that provides the smallest errors: APASS DR9 (Henden et al. 2016 ), UCAC4 (Zacharias et al. 2013 ) or NOMAD (Zacharias et al. 2005 ). All K s photometry is from 2-Micron All-Sky Survey (2MASS; Cutri et al. 2003 ). 2.1 Selecting potentially young stars in superWASP We learned from BJM15 that the majority of the raw light curves of young stars exhibited irregular features as well as sinusoidal behaviour, indicative of star-spot modulation and/or chromospheric plages – both prognostic of stellar youth. We not only assigned priority to any objects whose light curves displayed any of these features but also demanded clean light curves and consistent rotation period measurements over several seasons of observations. We also tried to screen out, through manual inspection of the light curves, targets that looked like eclipsing binaries. The reader is referred to section 2 of BJM15 for a description of the SuperWASP project and post-processing techniques used to measure rotation periods, which are identical to those carried out in this work. Table 1 shows the details of the period measurements for the sample of likely-young and single objects in our sample, which are defined in Section 5.7 . Fig. 1 displays rotation periods as a function of V − K s colour for our entire observed sample. Details for the other observed targets are provided online. We obtained spectroscopy for 122 stars, 103 selected from the criteria described here, and a further 19 satisfy these criteria, but have proper motions consistent with membership of the Pisces MG (see the next section). Figure 1. Rotation periods and V − K s colour for the entire sample observed in this paper. Red squares represent 17 objects that were identified to be likely-young stars and were considered likely-single (referred to as the ‘likely-young sample’, see Section 5.7 ). These objects are labelled from 1 to 17 and their corresponding SuperWASP names are provided in Table 1 . Any objects that had two or more separate radial velocity measurements whose mean values varied by more than 2 error bars from each other were assumed to be short-period binaries (see Section 4.2 ) and are denoted here by open green circles. All other objects are shown with filled green diamonds. This symbol scheme is used throughout this work, unless otherwise stated. The various lines represent the I- and C-sequence gyrochrones proposed by Barnes ( 2003 ) and calibrated by Mamajek Hillenbrand ( 2008 ), plotted at a range of ages. Table 1. Measured periods for the


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

kinematics study of Clarkson et al. ( 2008 ). Awiphan et al. ( 2016 ) presented a more recent version of the model (variant BGM1307) and compared it with a large ensemble of 470 events from the MOA-2 survey (Sumi et al. 2013 ). Awiphan et al. ( 2016 ) concluded that there was a reasonable level of agreement once allowance was made for brown dwarfs that are missing from the BGM. However, the model appeared to underpredict the observed rate from the Galactic bulge significantly. Sumi Penny ( 2016 ) subsequently showed that at least part of the cause of this discrepancy was undercounting of source stars within the MOA-2 analysis and correcting for this resulted in much better agreement with the model. After investigation of a number of different BGM variants, we have decided to use BGM1307 as the basis for MaBμlS-2. The BGM separates the Galaxy into four components; the thin disc, thick disc, bar and halo, each with their own stellar initial mass functions (IMFs), star formation rates (SFRs), kinematics and ages. Interstellar extinction is included for UBVRIJHK photometric bands using a 3D extinction model from Marshall et al. ( 2006 ). The solar position relative to the Galactic Centre and plane in the BGM is taken to be R 0 = 8 kpc and z 0 = 15 pc, respectively. The following description of the Galactic components quotes lower limits on their respective stellar mass functions, but an upper limit is not included. While interesting lens candidates such as intermediate-mass black holes and other compact objects are represented in the high-mass regime, the BGM does not include them. Due to the steepness of the mass functions at high mass, these objects also do not contribute significantly to the overall microlensing parameters outlined in Section 3.1 . 2.1 The thin disc The thin-disc component is subdivided into seven age groups, each with their own luminosity and effective temperature distributions. The mass density is modelled by the difference of two exponentials in cylindrical polar coordinates (r, z) ; one representing the body of the disc with scalelength R d = 2170 pc and the other representing a central hole with scalelength R h = 1330 pc (Robin et al. 2012b ). It is given by where ρ 0 is the component normalization density, and ε is the axial ratio of the ellipsoid. The SFR is taken to be constant across the whole disc. The IMF is given by a broken power law, which is the same across all age groups : Each age group of the thin disc has its own velocity dispersion, to mimic the secular evolution, and follows the relation from Gomez et al. ( 1997 ); these average to km s −1 , with a maximum of km s −1 for the oldest component. The rotational velocity of the local standard of rest (LSR) is 240 km s −1 , with the rotation curve taken from Caldwell Ostriker ( 1981 ). The LSR is defined as the mean velocity of material in the solar neighbourhood, centred on the Sun within 100 pc. The peculiar motion of the Sun relative to the LSR is assumed to


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

ACKNOWLEDGEMENTS DFT and FCZ acknowledge support from the Spanish Ministry of Economy, Industry and Competitiveness grants PGC2018-095512-B-I00, SGR2017-1383, and AYA2017- 92402-EXP. DV acknowledges support from the Spanish Ministry of Economy, Industry and Competitiveness grants AYA2016-80289-P and AYA2017-82089-ERC (AEI/FEDER, UE). FCZ is supported by a Juan de la Cierva fellowship. DFT acknowledges the participants of the Workshop on Magnetospheres of Neutron Stars and Black Holes (June 2019, Goddard Space Flight Center) for comments.


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

S.M.H. acknowledges support from Ramanujan Fellowship SB/S2/RJN-73 and the Max-Planck Partner group program. S.M.H. is grateful to Martin Woodard, with whom many useful conversations were had, for helping resolve several technical issues. This research was supported in part by the International Centre for Theoretical Sciences (ICTS) during a visit for participating in the program—Turbulence from Angstroms to Light Years (ICTS/Prog-taly2018/01).


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This paper is based on data collected at the Subaru Telescope, which is operated by the National Astronomical Observatory of Japan. We thank the anonymous referee for helpful suggestions and Takashi Hattori for taking the data for us. This research was supported in part by the National Natural Science Foundation of China (11373055) and the Strategic Priority Research Program “The Emergence of Cosmological Structures” of the Chinese Academy of Sciences (Grant No. XDB09000000). C.W. acknowledeges the support from the National Natural Science Foundation of China (11273029). Facility : Subaru (FOCAS)


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

efficiency of sublimation in this context, compared with the incidence of “dry rain” in the Earth’s atmosphere, can be ascribed to a combination of two factors: the relatively high silicate vapor mass fraction (typically X sil ∼ (0.3–1) X H when refluxing of pebble debris from the envelope begins to balance pebble accretion) and an infall time that is a factor ∼10 3 times longer than for raindrops. Of course, much larger planetesimals that survive transport through the envelope may still inject solid/liquid silicates into the core. 3. Envelope Expansion in Response to Planetesimal Heating and Dust Loading: Semianalytic Treatment As a prelude to the numerical investigation described in Sections 4 and 5 , we now present a semianalytic model of an envelope with a low dust density and outer radiative structure. This model connects smoothly to a uniform medium of a fixed temperature T disk and gas density ρ g ,disk . As the dust abundance rises, the inner convective layer grows in size, and eventually overwhelms the Bondi radius. Assuming that the dust abundance in the outer radiative layer is tied directly to the solid accretion rate, we can work out the critical value of above which convection extends beyond the Bondi radius, some refluxing of solids will occur, and the self-consistency of the model breaks down. We next quantify the reduction in dust size due to convective stirring, and demonstrate how a convective layer that traps accreted solids may expand in response to deep heating by large planetesimals. 3.1. Two-layer Convective-radiative Envelope Even a small amount of embedded dust acts as a powerful coolant, in the sense that any excess of gas temperature over ambient radiation temperature is rapidly converted into thermal radiation via collisions between gas molecules and grains (e.g., Chiang Goldreich 1997 ). The presence of an ambient blackbody radiation field of temperature T disk is therefore assumed, with an internal energy amounting to a small fraction of the ambient gas energy density. The temperature is buffered near T disk in the outer bound envelope, around the Bondi radius, and grows in the inner, optically thick envelope. In a state of spherical hydrostatic and radiative equilibrium at local temperature T g and uniform luminosity ,The opacity is per unit mass of dust. We first consider the case of uniform dust-mass fraction X d (although the equations presented here do not depend on this assumption). We rescale radius to R B , temperature to T disk , and gas density to ρ g ,disk . Then the preceding equations can be writtenwhereand the luminosity is expressed in terms of a core-accretion time,Taking cm 2 g −1 (see Appendix A ), the characteristic optical depth at the Bondi radius isand The solution to Equation ( 25 ) is shown in Figure 2 for β = 0 and a range of values of the parameter ε rad (10 −4 , 10 −3.5 , 10 −3 , ... 10 0.5 , 10). When ε rad ≪ 1, the temperature remains flat some distance inside R B , whereas the


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength B-Wavelength O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O B-Model I-Model O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-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 B-Model O O O O O O O O O O B-Telescope 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 B-Telescope O O B-Wavelength O B-Wavelength O O O B-Telescope O O O O O O O B-Formula I-Formula I-Formula O O O O B-Wavelength O O O O O O B-Wavelength O O O O O B-Wavelength O O O O O O O B-Wavelength B-Wavelength O O O B-Wavelength B-Wavelength O O O O O O O O O

larger than the PSF FWHM (orange dashed line). The 3D half-light radii agree with the two observational methods for the bright galaxies. The sizes of faint galaxies show a steeper decline than the observational data, indicating potential systematic errors in observations below the instrumental resolution limits. We examine how well the measured sizes using the three different methods recover the true 3D half-stellar mass radii. Fig. 10 illustrates the ratio of the F115W (rest-UV) sizes to the 3D half-stellar mass radii as a function of stellar mass, with the F115W sizes obtained by the three methods. We have combined sampled from simba -25 and simba -50. Solid green lines represent the median of the ratios, and the shaded regions show 1σ spread in the size ratios. For the growth curve method and 3D half-light radii, we also show results using the no-dust sizes with magenta lines. Figure 10. Similar to Fig. 9 , but showing comparisons of the measured F115W sizes (rest-UV) to the galaxy 3D half-stellar mass radii as a function of stellar mass. Shaded regions represent 1σ spread in the size ratios. The 3D half-light radii traces the half-mass radii very well at z = 6. Due to the finite pixel size and smoothing by the PSF, size measurements in real observations bias the ‘true’ sizes, which we find to be a mass-dependent effect. Focusing first on the right-hand panel of Fig. 10 , the no-dust 3D half-light sizes are smaller than the 3D half-stellar mass radii, but the ratios are roughly constant. This indicates that although more concentrated than mass, light traces mass well in these simulated z = 6 galaxies, so these galaxies can only have weak age gradients. When including dust extinction, the sizes could be a factor of 1.5–3 larger than sizes without dust for galaxies with M * ≳ 10 9 M ⊙ , and also overestimate the half-mass radii by up to a factor of ∼1.5. This suggests that the centres of the galaxies are more dust-attenuated. Indeed, we will show in Section 3.4.3 that the centres of these galaxies are younger but with more dust extinction. Results obtained with the two observational methods are generally similar, as shown in the left-hand and middle panels. The sizes of galaxies with M * 10 8 M ⊙ are overestimated by factors of 1.5–2, owing to the finite resolution of the mock images and smoothing of the PSF. Overall, simba produces galaxy sizes that are in good agreement with current HST observations at z = 6. We also find that the observed sizes are a biased tracer of the true half-stellar mass radii. Moving forward, we will explore predictions for JWST observations. 3.4.2 Rest-optical versus rest-UV sizes Since future JWST observations will be able to explore the z ∼ 6 galaxies in the rest-frame optical wavelengths, we explore how the rest-frame optical sizes compare with the rest-frame UV ones. Fig. 11 shows comparisons between the F444W (rest-optical) sizes and the F115W (rest-UV) sizes, measured using the growth curve method, the Sérsic


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

a systemic velocity for the SNR. The broad range of ejecta space velocities and expansion indices (see Table 1 ) that we measure in our sample may be characteristic for an SNR transitioning from the free-expansion phase to the Sedov–Taylor phase. Measurements of the proper motion at various locations along Kepler’s forward shock by Katsuda et al. ( 2008 ) and Vink ( 2008 ) found expansion indices of 0.47–0.82 and 0.3–0.7, respectively. For remnants nearing the Sedov–Taylor phase, Chevalier ( 1982 ) estimated η = 0.4 for s = 0 and η = 0.67 for s = 2 ambient density power-law solutions. Hence, our ejecta velocity measurements and previous forward shock analyses apparently suggest that the kinematics for some regions in Kepler may be dominated by nearly free expansion, while others are better described by Sedov–Taylor dynamics. New 3D hydrodynamical simulations that focus on Kepler and these high η knots may give some insight into their origin. The knots N2, N5, N1, and N3 have the highest measured space velocities (6100–8700 d 6 km s −1 ), and are all located in the “steep arc” (DeLaney et al. 2002 ) of Kepler’s SNR, a “bar” of bright X-ray emission that runs from east to west, located about halfway between the center of the remnant and the outer edge of the main shell. They are projected close to each other within a small (50′′ × 20′′) area. This proximity, and similarities in their measured Si abundances, space velocity vectors, and expansion indices, suggest that these knots might have originated generally from a “common” layer of the exploding white dwarf. Sato Hughes ( 2017b ) measured properties of another knot (they label “N4”) projected within the steep arc, which exhibited similar properties to N2, N5, N1, and N3. This suggests that ejecta within the steep arc have generally homogeneous kinematic and spectroscopic properties. In the western Ear, we measure high space velocity in region Ear2, v s ∼ 5800 d 6 km s −1 . Such a high velocity may be expected considering the knot’s projected location in the western Ear feature, which protrudes out about 30% beyond the main shell. Interestingly, knot Ear1 has a significantly smaller space velocity, v s ∼ 3300 d 6 km s −1 , even though it is projected very close to the position of Ear2. Knot Ear1 may be interacting with a CSM-dominated feature identified by Burkey et al. ( 2013 ) projected adjacent to it, which could have caused it to significantly decelerate recently. Such an interaction between ejecta and CSM may produce H α emission. We searched for H α emission at the location of Ear1 in the archival Hubble Space Telescope images (with the F656N filter) of Kepler (Sankrit et al. 2016 ). We found a faint wisp centered at Ear1's position, possibly indicating the presence of shocked CSM gas, which would support our conclusion of an ejecta-CSM interaction there. Considering their spatial proximity and similarly high Si abundance, it seems likely that Ear1 and Ear2 were produced very near each