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

ACKNOWLEDGEMENTS JMDK is supported by the German Research Foundation (DFG; KR4801/1-1), the European Research Council (ERC; ERC-StG-714907), and SFB 881 (subproject B2) of the DFG. The participants of the Lorentz Center workshop ‘Formation of Stars and Massive Clusters in Dwarf Galaxies over Cosmic Time’ (2019 February 18–22) and particularly the SOC chair, Rychard Bouwens, are thanked for inspiring conversations that led to the development of this work. N. Bastian, I. Cabrera-Ziri, M. Chevance, N. Choksi, M. Gieles, O. Gnedin, S. Larsen, M. Maseda, J. Pfeffer, M. Reina-Campos, A. Sills, S. Trujillo-Gomez, C. Usher, E. Vanzella, and an anonymous referee are thanked for helpful feedback.


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Observatory B-Instrument O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O B-Citation 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 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-Citation I-Citation O B-Citation O B-Citation I-Citation I-Citation O B-Citation I-Citation 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 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 I-Citation 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

field strength in their study does not hold below 10 G, which is a typical mean field strength for CHs. In our study, the rates of change in mean FIP bias in the small flux regions during their late-decay phase are significantly faster than the rates of change observed in larger decaying ARs. Baker et al. ( 2015 ) and Ko et al. ( 2016 ) find remarkably similar rates of decreasing mean FIP bias in the range [0.004, 0.009] h −1 within the core of ARs over 2–5 days compared to a range of [0.1, 0.2] h −1 for R3, R4, and R7 during their late-decay phase. Once again, the rates of decrease exhibited in the large ARs are maintained over periods of days, whereas in the small regions within the CH, the rapid changes occurred in a matter of hours. 5.4. Spatial Distribution of FIP Bias The spatially resolved composition map in Figure 8 , as well as maps in previous studies (e.g., Baker et al. 2013 , 2015 ; Brooks et al. 2015 ), have revealed that FIP bias does vary over spatial scales of a few arcseconds. Patches of higher FIP bias (>2) were found in the core of the EFRs, which is consistent with the Hinode /EIS observations of large ARs in Baker et al. ( 2013 , 2015 ). There was enriched plasma in the vicinity of loops linking the positive polarity of R1 and the negative polarity of R2 (see patches of FIP bias in the range [2, 3] between the mask contours of Figure 8 (b), which spatially correspond to the loops connecting R1 and R2 in Figures 7 (a), (b) and Movie 2). The magnetic field alignment of R1 relative to R2 was favorable for reconnection between the external loops of each region. The reconnecting loops contain already enriched plasma but it is also possible that the Alfvén waves generated by reconnection may have stimulated the enrichment (e.g., Laming 2004 , 2015 ). Finally, the plasma composition within the two largest EFRs had non-Gaussian distributions ranging from photospheric to coronal FIP bias (Figure 9 ). The distributions were mildly skewed toward the higher end of the distributions, with 32%–36% of the pixels within the masked regions exceeding FIP bias = 2. The lower end of the range of FIP bias values was consistent with previous observations of FIP bias in newly emerged loops (Sheeley 1995 , 1996 ; Widing Feldman 2001 ; Laming 2015 ) and with studies of plasma composition in CHs (Feldman et al. 1998 ; Brooks Warren 2011 ; Laming 2015 ), whereas the upper end of the range, ∼3, was lower than the levels typically found in quiescent AR cores, ∼3–4 (e.g., Baker et al. 2015 ; Del Zanna et al. 2015 ). The fraction of pixels containing FIP bias >3 was small in these regions: ∼4% for R1 and ∼1% for R2. The extent to which plasma is enriched is likely to be affected by the CH environment. EFRs are partially or fully surrounded by CH field containing a large reservoir of unmodified photospheric-composition plasma. Interchange reconnection between the closed loops of the EFRs and the open field of the CHs creates pathways for mixing of


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A.M.B. was a Grote Reber Fellow for a portion of this project, and support for this work was provided by the NSF through the Grote Reber Fellowship Program administered by Associated Universities, Inc./National Radio Astronomy Observatory and the Virginia Space Grant Consortium. A.M.B. also acknowledges support from the Smithsonian Institution as a current Submillimeter Array (SMA) Fellow. A.M.B. would like to thank Karin Öberg for helpful discussions on ice chemistry. C.N.S. wishes to thank the Alexander von Humboldt Foundation for support. Support for B.A.M. was provided by NASA through Hubble Fellowship grant No. HST -HF2-51396 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS5-26555. E.H. thanks the National Science Foundation for support of his astrochemistry program.


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

We thank C. Steidel for providing a reduced HIRES/Keck quasar spectrum. This material is based upon work supported by the National Science Foundation under grant No. 1210200 (NSF East Asia and Pacific Summer Institutes). N.M.N. was also partially supported through an NMSGC Graduate Fellowship and a Graduate Research Enhancement Grant (GREG) sponsored by the Office of the Vice President for Research at New Mexico State University. G.G.K. acknowledges the support of the Australian Research Council through the award of a Future Fellowship (FT140100933). M.T.M. thanks the Australian Research Council for Discovery Project grant DP130100568, which supported this work.


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

resolution surrounding the selected minihalo. Each ‘parent’ particle within the most refined region is split into 64 ‘child’ particles, with a minimum mass of m gas = 1.85 M ⊙ and . These refined simulations are then run until the gas approaches the typical onset of runaway collapse at n = 10 4 cm −3 . 3.1.1 Halo 2 cut-out and refinement Once the simulation reaches 10 4 cm −3 all particles beyond 10 comoving kpc from the centre of the collapsing minihalo are removed to conserve computational resources. To achieve a maximum resolution comparable to Halo 1, all particles within the 10 comoving kpc volume are split into two child particles placed randomly within the smoothing kernel of the parent particle. This particle-splitting is repeated twice more; all particles within 8 comoving kpc are replaced by eight child particles; within 6 comoving kpc, each of these child particles is split into an additional 8 for a total of 128 child particles in the most refined region. At each step, the mass of the parent particle is evenly divided among the child particles and the smoothing length is set to , where h is the smoothing length of the parent and N new is the number of child particles created. All particles inherit the same entropy, velocity, and chemical abundances as their parent, ensuring conservation of mass, internal energy, and momentum. While our cut-out technique leads to a rarefaction wave propagating inward from the suddenly introduced vacuum boundary condition, the average sound speed at the edge of the most refined region is ∼1 km s −1 . As a result the wave only travels ∼0.5 pc over the remaining 400 000 yr of the simulation, a negligible fraction of the ∼350 pc physical box size. 3.2 Chemistry and thermodynamics We employ the chemistry network described in detail by Greif et al. ( 2009 ), which follows the abundance evolution of H, H + , H − , H 2 , , He, He + , He ++ , D, D + , HD and e − . All relevant cooling mechanisms are accounted for, including H and He collisional excitation and ionization, recombination, bremsstrahlung and inverse Compton scattering. In order to properly model the chemical evolution at high densities, H 2 cooling induced by collisions with H and He atoms and other H 2 molecules is also included. Three-body reactions involving H 2 become important above n ≳ 10 8 cm −3 ; we employ the intermediate rate from Palla, Salpeter Stahler ( 1983 ), but see Turk et al. ( 2011 ) for a discussion of the uncertainty of these rates. In addition, the efficiency of H 2 cooling is reduced above ∼10 9 cm −3 as the ro-vibrational lines of H 2 become optically thick above this density. To account for this we employ the Sobolev approximation together with an escape probability formalism (see Yoshida et al. 2006 ; Greif et al. 2011b for details). 3.3 Cosmic ray ionization and heating Each time a CR proton ionizes a hydrogen atom, an electron with average energy 〈 E 〉 = 35 eV is produced (Spitzer Tomasko 1968 ). Including the


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

) multi-redshift sample used Spitzer -IRS data to constrain the torus SED. This sample was discussed in great detail by Lusso et al. ( 2013 ), who showed a very good agreement with their results. Thus the data we present here represent well the results of Maiolino et al. ( 2007 ). Figure 9 shows all the NIR–MIR-based compilations of C f , including ours, for the case of complete isotropic dust emission ( b = 1) on the left, and maximum anisotropy ( b = 0) on the right. For the present sample, we only show the case of Bol 1350 = 2. The uncertainty on represents the range in this property that is used to derive the median values. The uncertainty on / is taken from the original papers (Lusso et al. 2013 ; Roseboom et al. 2013 ) or from the present calculations. Given the uncertainties on and , we estimate a combined uncertainty on C f of at least ±0.2 dex at all . We also show, as blue open squares, the median values obtained from Shen et al. ( 2011 ) and shown in Figure 8 left panel (). Figure 9. Covering factor as a function of in large AGN samples. Open black squares: the Mor Netzer ( 2012 ) sample. Full black circles: the Lusso et al. ( 2013 ) sample. Open red circles: the Roseboom et al. ( 2013 ) sample. Open blue circles: the the present z = 2–3.5 sample without the weak-NIR sources. Open blue squares: SDSS sources from the Shen et al. ( 2011 ) catalog with the same redshift and luminosity as the present sample and measured as explained in the text. The left panel shows the covering factors under the assumption of isotropic dust emission. As explained in the text, the Roseboom et al. ( 2013 ) values are scaled up by factors of 1.5–1.8 to allow for the different assumed bolometric correction factors. The parallel dotted lines show the range of ±0.15 dex around the mean value of 0.68. The right panel shows the same data for the case of complete anisotropy ( b = 0 in Equation ( 3 )). The dotted lines indicate a range of ±0.15 dex around 0.4. Figure 10. Median (top) and mean stacks. In each part, the high luminosity group is shown in the upper row and the low luminosity group in the lower row. From left to right: 250, 350, and 500 μ m. The crosses mark the centers of the stacks. The diagrams presented here show that all medians of all the samples used here, at all , are confined to a band of width ±0.15 dex in / around 0.68 for the isotropic case, and 0.4 for the case of complete anisotropy. Because much of the uncertainty in C f is systematic and depends on the poorly known bolometric correction factor, the inclusion of a large number of individual measurements cannot improve the situation by much. Thus, the torus covering factors that are based on NIR–MIR measurements show no indication for a decrease of C f with increasing source luminosity. This finding seems to contradict earlier findings, such as those presented by Lusso et al. ( 2013 ) and Roseboom et al. ( 2013 ). An independent way of estimating the covering factor is to compare 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O B-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

translation error of one pitch implies a 20% error in the 7 λ / D × 7 λ / D region around the center, whereas it reaches 60% in the largest DH (28 λ / D × 28 λ / D ). The more uncertainties there are on the positions of the actuators, the narrower the region of correction. We now consider that the modeled DM is not translated relative to the true one but is rotated around the pupil center. We calculate the estimated field and the RMSE for each rotation error. Results are plotted in blue on the right of Fig. 5 . As for the translation error, the larger the DH the more sensitive the PW is to the rotation error. For example, the RMSE is 10% for the largest DH (28 λ / D × 28 λ / D ) and 5% for the smallest one. Actuator 498 is at about two actuators from the pupil center such that a rotation of 10° corresponds to a translation of 0.35 pitch. From the translation error plot (center plot of Fig. 5 ), a 0.35 pitch translation error gives a RMSE of ∼10% for the largest DH and ∼5% for the smallest one. We therefore expect the PW estimation to be more sensitive to an error on the angular position of the DM if the actuator-probes are further away from the center of the pupil. We confirm this statement by executing the same study for a pair of actuator-probes closer to the edge of the pupil: actuators 283 and 251. The results plotted in red on the right of Fig. 5 confirm the following statement: the closer the pair of actuator-probes is to the center of the pupil, the more robust is the PW with respect to a rotational error. 4. Wavefront control Once the electric field E S 0 is estimated, DMs are controlled to minimize the stellar speckle intensity inside a DH. In this section, we present two wavefront control techniques (SCC and EFC) assuming small aberrations ( α and β ) and a single DM placed in the pupil plane. Both techniques use an iterative process and a control matrix. 4.1. SCC and EFC common strategy Classical AO systems measure and minimize the phase aberrations β in the pupil plane. In the context of HCI, this strategy is not optimal because the amplitude aberrations α also induce stellar speckles in the science image. Moreover, DMs cannot control all the high spatial frequencies because of the limited number of actuators. Therefore, even if there are no amplitude aberrations, one DM cannot completely null the phase β . That is why Malbet et al. (1995) proposed to minimize the stellar speckle intensity inside a DH in the science image instead of the phase in a pupil plane. This has two main advantages. The field induced by both amplitude and phase aberrations can be minimized. And a stronger attenuation can be reached using the frequency-folding phenomenon and by decreasing the size of the DH ( Bordé Traub 2006 ; Give’On et al. 2006 ). We assume a single DM placed in the pupil plane and we consider that the focal plane field E DM = iC [ Aφ ] induced on the science detector is a linear combination of the DM actuator voltages : where G is the


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M.T. and L.T. acknowledge support by the DFG cluster of excellence Origin and Structure of the Universe ( www.universe-cluster.de ). This work has been supported by the DISCSIM project, grant agreement 341137 funded by the European Research Council under ERC-2013-ADG. M.T. and L.T. thank Eva Wirström, the Gothenburg Centre for Advanced Studies in Science and Technology and the participants of the workshop Origins of Habitable Planets hosted at Chalmers (Gothenburg) in June 2016 where considerable part of this work was fruitfully discussed. M.T. is grateful to Cathie Clarke for insightful discussions. The fits have been carried out on the computing facilities of the Computational Center for Particle and Astrophysics (C2PAP) as part of the approved project “Dust evolution in protoplanetary disks”. M.T. acknowledges usage of the Max Planck Gesellschaft Hydra computing cluster for code testing, for which is grateful to Paola Caselli. Figures have been generated using the Python-based matplotlib package ( Hunter 2007 ). Staircase plots of PDFs have been generated with a user-modified version of the Python-based triangle package ( Foreman-Mackey et al. 2014 ). This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France. This work was partly supported by the Italian Ministero dell’ Istruzione, Università e Ricerca through the grant Progetti Premiali 2012 – iALMA (CUP C52I13000140001). A.N. acknowledges funding from Science Foundation Ireland (Grant 13/ERC/I2907). C.F.M. acknowledges an ESA Research Fellowship. This paper makes use of the following ALMA data: ADS/JAO.ALMA#2013.1.00220.S, ADS/JAO.ALMA#2013.1.00226.S. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), NSC and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ


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

wave. Thus, there is a continuous flux of particles crossing R c from below. These particles get accelerated to high LF and advected with the Alfvén wave as a result of the strong electric field 2 in the charge starvation zone. The continuous loss of particles from the interior of R c causes the e ± density to decrease with time, and the region that was not charge starved before becomes charge starved. We estimate the speed at which R c moves inward. The current amplitude ( I aw ) associated with the Alfvén wave packet along is roughly independent of R; I aw is the integral of current density over the cross-section of the wave packet. Thus, the number of particles that cross R c per unit time and are subsequently advected by the Alfvén wave is ∼ I aw /2 q . The cross-sectional area of the wave packet, A aw , increases as R 3 as the wave follows the dipole field lines. Therefore, d R c /d t ∼ − I aw /(2 qnA aw ). This result can be recast in a slightly more convenient form as d R c /d t ∼ − n c /2 n; I aw / A aw ∼ j , and j can be written in terms of n c and n using equations ( 4 ) and ( 6 ). A corollary of this result is that e ± present in the NS magnetosphere are depleted (advected by the wave) on a time of the order of 〈 n / n c 〉 R c / c , which is a few ms. Thus far, we have discussed how the Alfvén current below R c supplies a flux of particles into the charge starvation region where they are quickly accelerated and advected by the wave. We now describe how particles the Alfvén wave packet encounters at the head of the wave at R > R c also get trapped and advected by the wave. Charge particles of one sign – those that experience the force of the field in the forward direction – are swept up by the wavefront and compressed into a thin sheet of width much smaller than λ aw and forced to move with the wave. Particles of the opposite charge move in the reverse direction, along , at a speed of ≈ c for about half a wavelength and there they start accumulating in a thin sheet; these results follow from equation ( 16 ) for γ. The Coulomb field in the thin sheet increases with time as more charges are swept up by the wave and accumulate in the sheet: where R is the location of the wavefront at time t . The Coulomb field strength exceeds the wave-field E d for , and at that point the sheet starts spreading in the longitudinal direction at close to the speed of light. Since the Coulomb fields at the front and the back sides of the sheet do not decrease as the width of the sheet increases, the spreading continues until the sheet thickness becomes ∼λ aw /2. Particles in the sheet now overlap with particles of opposite charge in the adjoining half-wavelength of the Alfvén packet, thereby partially shielding E cou . The physics of the system is that charge particles of one sign swept up at the front of the Alfvén wave packet, within λ aw of R c , accumulate in a thin sheet near the leading front. The sheet starts to spread longitudinally, after about


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

the surface, which naturally underestimates the extinction. The curves are shown in Figure 3 (top) for both the truncated and full disks. At a given location, the optical depth of the outer disk is generally lower for the truncated disk with radial drift, as we would expect. Note that it does not move all the way inward to the truncation radius since there are still small grains out to the gas disk radius. Figure 3. Top row: effective opacity () to external FUV radiation for the different small/large dust mass distributions over steradians. The left and right columns show the full model and drift-dominated model, respectively. The dashed and solid lines indicate and . The line color corresponds to the different small grain dust fractions, gray (10%) and black (1%). Bottom row: for the case, the ratio of desorbed molecule flux from photodesorption vs. thermal desorption (). The solid line indicates where the processes are equal. We compute the local flux, , and adopt a value for the yield of photodesorbed CO of molecules photon −1 , which is appropriate for the FUV photodesorption experiments of Fayolle et al. ( 2011 ). Figure 3 (bottom) compares the relative desorption fluxes from the ISRF to thermal processes () for the case. Large values correspond to efficiency in each process, i.e., regions of the disk where is large implies photodesorption dominates thermal desorption and vice versa. In all models, thermal desorption dominates the inner disk and transitions to photodesorption in the outer disk. We find that the transition is substantially further out for the drift-dominated model and that the transition occurs rapidly. In the case with drift, thermal desorption dominates ISRF photodesorption inside of , and for the full disk the transition occurs at ∼80 AU. These results are non-obvious, as radial drift increases outer disk heating but also decreases the opacity to external FUV. We find similar results for 1% small grain mass case, with values of 400 AU (drift) and 70 AU (full), respectively. 4. DISCUSSION Based on these results, we expect radial drift to alter the disk temperature profile and enhance thermal desorption of CO in the outer disk. To approximately estimate the enhancement in CO column density, we take the temperature profile and assign a CO abundance of 10 −4 per H 2 for dust temperatures between 17 and 200 K. We calculate the vertically integrated column density of CO versus radius and then compare the models with and without drift and find the maximum enhancement in CO column is ∼2–2.5 times higher outside of the large grain radius. Recently, observations of IM Lup have shown multiple rings of DCO + , a direct product of CO-driven chemistry (Öberg et al. 2015 ). Furthermore, Tang et al. ( 2015 ) report multiple CO ring structures in both 12 CO and 13 CO in GG Tau. Radial temperature variations increasing CO sublimation in the outer disk may be contributing to these structures, though they should be modeled in detail to


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

The authors thank the anonymous referee for constructive comments and suggestions that greatly improved the paper. We would like to thank the telescope operators and supporting astronomers at the Palomar Observatory and the Keck Observatory. Some of the data presented herein were obtained at the W.M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W.M. Keck Foundation. The research is made possible by the data from the Kepler Community Follow-up Observing Program (CFOP). The authors acknowledge all the CFOP users who uploaded the AO and RV data used in the paper. This research has made use of the NASA Exoplanet Archive, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program. J.W.X. acknowledges support from the National Natural Science Foundation of China (grant No. 11333002 and 11403012), the Key Development Program of Basic Research of China (973 program, Grant No. 2013CB834900) and the Foundation for the Author of National Excellent Doctoral Dissertation (FANEDD) of PR China. J.W. acknowledges the travel fund from the Key Laboratory of Modern Astronomy and Astrophysics (Nanjing University).


O O O B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person O B-Person I-Person O O O O O O O O O O O O O O B-Observatory I-Observatory I-Observatory O O O B-Organization I-Organization I-Organization O B-Grant O B-Grant B-Person O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O B-Fellowship I-Fellowship O O B-Organization I-Organization I-Organization I-Organization O B-Organization O O O O O B-Software I-Software I-Software I-Software B-Citation I-Citation I-Citation I-Citation O

The authors thank Adam Riess, Daniel Eisenstein, Eric Linder, Kaisey Mandel, Andrew Friedman, and Raul Jimenez for very useful discussions and suggestions to improve this work. Supernova cosmology at the Harvard College Observatory is supported by National Science Foundation grants AST-156854 and AST-1211196. A.A. acknowledges, also, the Instituto Avanzado de Cosmología of Mexico, and the Mexico-Harvard Fellowship sponsored by Fundación México en Harvard and CONACyT. We acknowledge the use of emcee: The MCMC Hammer (Foreman-Mackey et al. 2013 ).


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

and using 16 Gigabytes of RAM takes between 5 to 10 s. Including the pixel-error map calculation increases the computing time to approximately 10 min. For comparison, the Super-Pixel method typically requires several minutes to extract the binary field, where the actual time depends on the image pixel resolution and the number of Super-Pixels employed. The computational speed of our network thus makes it particularly useful as a component in a Bayesian statistical inference framework to perform EoR parameter estimation using tomographic statistics (e.g. Gazagnes et al. 2021 ). We compare the accuracy of our approach with a feature finding method from the field of image processing, the so-called Super-Pixel method, which Giri et al. ( 2018 ) showed to be superior over simple thresholding methods. The results show that our neural network can identify neutral regions in the mock observations at least as well and often much better than the Super-Pixel method. We show a visual comparison and the resulting pixel-per-pixel error map tested on our ‘fiducial’ model. This error map gives valuable insight into the parts of the image that are hard to recover and helps us check for overfitting. We studied the accuracy of a range of derived quantities from the recovered binary fields, comparing the performance of SegU-Net with the Super-Pixel method. These quantities are the volume-averaged ionization fraction – the evolution of which provides the reionization history, the size distribution of the ionized (BSD) and neutral (ISD) regions, the dimensionless power spectra of the recovered binary fields, and the three Betti numbers, which quantify the topology of the segmented data sets. For all quantities, we find that the SegU-Net results are more accurate than the Super-Pixel results, especially for the early and late stages of reionization, where the Super-Pixel method often struggles to produce accurate results. Machine learning methods generally are sensitive to the properties of the training set. Therefore, we tested SegU-Net on input data with different properties than the training set. First, we analysed the performance on data sets with different noise levels than the network was trained. We found that SegU-Net yields accurate results for data sets in which the noise level is characterized by an observing time of , which approximately corresponds to an SNR ≳3. Secondly, we applied the network to mock observations calculated from the results of a fully numerical reionization simulation, rather than the seminumerical simulations used to train the network. We find that SegU-Net achieves the same level of accuracy when applied to this data set and therefore is not sensitive to the type of simulation employed during the training process. We want to point out that similar efforts are being made by Gagnon-Hartman et al. ( 2021 ). They focus on reconstructing the segmented maps of ionized and neutral regions in the context of foreground mitigation using the


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

were a ≈ 1730 au and e ≈ 0.99999, corresponding to separation at pericentre d per ≈ 3.8 R ⊙ and the companion filling its Roche lobe 89 per cent (radius-wise), which is sufficient for circularization in all our models. Fig. 3 shows the detailed evolution of the binary orbital parameters a and e , as well as the pericentre separation d per . Even though the binary was affected by more than 5000 encounters, the vast majority of interactions had very little effect on its orbit, with only a few inducing significant changes of orbital parameters. The average mass of fly-by stars in the only 10 encounters during which the orbital energy was changed by more than 10 per cent was ∼13.5 M ⊙ , whereas the average mass of all stars encountered by the binary was ∼0.62 M ⊙ . In fact, it is very typical for the majority of dynamically formed LMXBs in our simulations that the dynamic evolution of a binary is mainly dependent on a few key encounters with, on average, exceptionally massive fly-bys. This is connected to the fact that, on average, the amplitude of a velocity kick induced by a fly-by to one binary component with respect to the other can be analytically estimated as proportional to the fly-by's mass (e.g. Hills 1981 ), i.e. Here, a is the semimajor axis of the binary, M fly-by is the mass of the fly-by, b is the impact parameter and v rel is the fly-by's velocity, relative to the mass centre of the binary. This suggests that the local stellar mass distribution has influence on the time-scale of evolution through dynamical interactions and therefore the effectiveness of the LMXB's dynamical formation channel. We discuss this further in Section 5.2 . Figure 3. Detailed evolution of orbital parameters a and e , as well as distance at pericentre d per = a (1 − e ) for an exemplary, typical binary that has undergone tidal circularization (noticeable as a rapid decrease of both semimajor axis and eccentricity at the very end of evolution). This particular system was subject to over 5000 stellar encounters, most of them occurring during the second half of its evolution. The binary was subject to several major changes of orbital parameters as a result of encounters with exceptionally massive fly-bys. For instance, the most significant change of eccentricity from 0.71 to 0.09 at around 3.7 Gyr (coupled with an increase of the semimajor axis from 345 to 530 au) was caused by an interaction with a ∼4.5-M ⊙ star, whereas the mean mass of fly-bys in our simulations is ∼0.62 M ⊙ . Additionally, the encountered star was passing by with a relatively low speed of ∼45 km s −1 with respect to the binary (the mean relative speed of all fly-bys is ∼125 km s −1 ), which granted an exceptionally long time of gravitational interaction. 4.2 Evolution of orbital parameters The evolution of orbital parameters in Fig. 3 also illustrates a general trend of steadily increasing semimajor axis. This is an average regularity for all of our evolutionary paths leading towards


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ACKNOWLEDGEMENTS We thank Hiranya Peiris, Benjamin Joachimi, Fergus Simpson, and the referee for helpful comments on the pre-print version of this paper. We thank Frankie Nobis-Efstathiou for help with the early stages of this project. We also thank Anthony Challinor, Steven Gratton, and members of the KiDS team for comments on aspects of this analysis. We also thank members of the Planck Parameters team. PL acknowledges support from an Isaac Newton Studentship at the University of Cambridge and from the Science and Technologies Facilities Council.


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

used in Barro etal. ( 2013 ) and van Dokkum etal. ( 2015 ) plotted for reference in addition to the van der Wel z 0.75 relation with its intrinsic scatter. Also plotted are the red nugget populations from Taylor etal. ( 2010 ), Damjanov etal. ( 2009 ) and van Dokkum etal. ( 2008 ), which suggest an evolution towards increasing size at lower redshifts. Our source galaxies are much more consistent with this trend within the red nugget populations, whereas the lens galaxies are consistent with the global population (though they span a very small range in stellar mass). Table 5. Inference on the sizemass relation for the source galaxy population, for 1C and 2C models. The parameters correspond to those defined in equations ( 3 ) and ( 4 ); we model the sources as following the linear relation log( R e /kpc) SM log( M /10 11 M ) SM with an intrinsic scatter SM in the log R e direction, and allowing the masses to be drawn from an underlying Gaussian distribution . It can be seen from Fig. 2 that the EELs sources are compact. We also plot the fits to the sizemass relation from van der Wel etal. ( 2014 ) both at z 0.25 and 0.75, which are chosen to bracket the redshifts of the EELs sources in the left-hand panel. Nearly all the sources lie distinctly below these lines. For comparison, the lens galaxy sample straddles the z 0.25 sizemass relation, as might be expected given their average redshift . In the right-hand panel, we show the EELs lenses and sources alongside the red nugget populations from van Dokkum etal. ( 2008 ), Damjanov etal. ( 2009 ) and Taylor etal. ( 2010 ), which span redshifts between z 2 and z 0, in addition to the compactness criteria for classifying high-redshift nuggets used by Barro etal. ( 2013 ) and van Dokkum etal. ( 2015 ) and the global z 0.75 sizemass relation of van der Wel etal. ( 2014 ), along with its intrinsic scatter. Seen in this context, the EELs source population appears to occupy a region closer to the red nuggets rather than normal ETGs. We note, however, that the relations shown on this plot are meant to define some sort of boundary between compact and non-compact objects, with the former all lying below it; our EELs sources are instead scattered above and below these lines. Specifically, 9 out of the 13 systems would be classed as compact according to Barro etal. ( 2013 )s criterion, whereas van Dokkum etal. ( 2015 )s slightly stricter definition reduces this to 7 though, due to differences in the two criteria at high and low masses, these two subsamples do not completely overlap. Given the distinct position in sizemass space of our sources, in addition to the diversity of conflicting compactness definitions that exist, we do not think it is valuable to classify our sources in this way. Rather, we simply note that they seem to be quite massive and significantly more compact than the majority of ETGs at similar redshifts, and may be better associated with the red nugget population. For instance, they may


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The authors thank Jamie Kennea and Phil Evans of the Swift team for their help with the analysis of the Swift /XRT follow-up observations; Kevin Hurley and the IPN team for their efforts to triangulate GRB 160530A, which helped plan the Swift /XRT observations; Varun Bhalerao and Dipankar Bhattacharya with the Astrosat team for helping cross-calibrate COSI’s timing performance with Astrosat; the NASA Columbia Scientific Ballooning Facility team for successfully flying (and landing) COSI and making this work possible. COSI is funded by NASA grant NNX14AC81G-APRA. The Swift Guest Observer analysis is supported through NASA grant NNH15ZDA001N-SWIFT. This work is also supported in part by CNES. Software: GEANT4 (Agostinelli et al. 2003 ), MINUIT (James Roos 1975 ), MEGAlib (Zoglauer et al. 2006 ), ROOT (Brun Rademakers 1997 ).


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

The author would like to thank René W. Goosmann for his comments on the text, Ariane Lançon for her advises on galaxy structures and physics, and Mari Kolehmainen for proof-reading this paper. This work was supported by the Centre national d’études spatiales (CNES) who funded this project through to the post-doctoral grant “Probing the geometry and physics of active galactic nuclei with ultraviolet and X-ray polarized radiative transfer”.


O O O O O O O O O B-Model I-Model I-Model I-Model B-Model O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-TextGarbage I-TextGarbage B-URL O O O O O O B-Model I-Model I-Model I-Model I-Model O O O O O O O B-Model I-Model 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 B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-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 I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


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


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

LIGO-Virgo network (1200 yr −1 detections at design sensitivity) under this model variation of Mandel de Mink ( 2016 ) and de Mink Mandel ( 2016 ). 6. Summary and Conclusion We have created and analyzed models of thermal winds from twin-star close binaries in circular orbits. Each of our models adopts q = 1, and we set the binary components surface based on a factor times the potential at the L 1 Lagrange point, f Φ . The wind initial sound speed is set based on a hydrodynamic escape parameter, λ . We examine the emergent wind distributions in each model, as well as the fluxes of mass and angular momentum carried away from the binary by the wind. Some key findings of our study are: 1. The acceleration of winds from about the binary components leads to a symmetric outflow traced by spiral density waves in the plane of the orbit (Figure 1 ). The subsonic acceleration region can surround either the individual binary components, or the entire binary, when f Φ ≲ λ /2 (Figure 2 ). The resulting outflow is largely similar to that of a spherical wind, with the addition of density and velocity waves in the equatorial plane due to the binary’s motion (Figure 1 ). 2. Eventual wind radial velocities are related to the surface sound speeds. At low sound speeds, radial velocities exceed that of a single-object wind model, implying that orbital motion imparts additional kinetic energy to the wind (Figures 3 and 4 ). 3. Mass loss rates from the binary are enhanced relative to the estimated superposition of two single-object winds. This effect is best modeled as a function of wind velocity, as shown in Figure 5 , and approximated by Equation ( 29 ). 4. The specific angular momentum carried by the wind depends primarily on the wind velocity as well (Figure 7 ). It is enhanced well beyond the binary’s specific angular momentum for the slower winds, which circulate around the binary before escaping near the outer Lagrange points (Figure 8 ), and we provide an approximating formula in Equation ( 32 ). The dependence of wind mass loss rate and specific angular momentum on wind velocity, as modeled by Equations ( 29 ) and ( 32 ) may have implications for models of massive, near-contact twin binaries undergoing chemically homogeneous evolution due to rotationally enhanced mixing. In particular, Mandel de Mink ( 2016 ) and de Mink Mandel ( 2016 ) argue that the model is sensitive to both the mass and angular momentum carried by winds. Our results suggest that for contact systems with low-velocity winds, mass loss rates and angular momentum loss rates will both be enhanced. Comparison to the model variations of Mandel de Mink ( 2016 ) and de Mink Mandel ( 2016 ) suggest that the high angular momentum loss rates may indicate an enhancement in the portion of binaries that undergo chemically homogeneous evolution that leave binary black hole remnants that can merge in a Hubble time. Productive avenues for future study include modeling twin-star winds that are radiatively,


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The authors acknowledge Malcolm Walmsley for critical reading of the manuscript and helpful comments. A.V. and P.C. acknowledge support from the European Research Council (ERC, project PALs 320620).


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

the stability of the orbits in the sense of keeping them within a well-defined section of the available orbital parameter space, Fig. 1 indicates that the eccentricity may eventually reach values that lead the aphelion closer to the Earth–Moon system, perhaps triggering an impact or an ejection from NEA parameter space. Conversely, a larger value of the eccentricity may lead to a shorter perihelion and an eventual collision with the Sun or an ejection from the Solar system or into its outskirts. In our case, the value of the aphelion distance, that oscillates between those of the semimajor axes of Venus and the Earth, can become as high as 1.02 au (see Fig. 6 , right-hand panel), opening the door to eventual impacts on our planet if one of the nodes reaches aphelion (see also Ribeiro et al. 2016 ). Members of the Atira population can eventually become impactors as a result of the complex orbital evolution discussed here and in the event of an impact, they will most probably come from out of the Sun’s glare. 3.3.2 Vatira evolution The evolution of 2019 AQ 3 shown in Fig. 1 initially leads to brief periods (in thick red/grey) in which the aphelion distance of 2019 AQ 3 , Q 0.718 au i.e. 2019 AQ 3 , an Atira, becomes a transient Vatira. This opens the door to transitions between the two dynamical classes. In fact, the dynamical context that keeps 2019 AQ 3 in a chaotic but relatively stable state may be effective in enabling a dynamical pathway to go from the Atira orbital realm into the Vatira one as shown by the evolution after about 3.5 Myr into the future. The progressive reduction in the value of the semimajor axis eventually leads to a transition from the Atira population into the Vatiras that avoid encounters with Venus altogether. Fig. 6 shows that transitions to and from the Vatira orbital realm are also possible well away from the nominal orbit. Our calculations show that a combination of secular evolution and eventual close encounters with Venus triggers the transitions. Atiras do not cross the orbit of the Earth–Moon system and Vatiras do not cross the orbit of Venus; both Atiras and Vatiras define disjoint subsets. Atiras can impact on Venus, Vatiras cannot; therefore and although the members of both dynamical classes interact with Venus, they do it quite differently. We may now argue that the distinctive dynamical property of putative, long-term stable Vatiras is that they must be virtually and dynamically detached from Venus. This implies a robust difference between the dynamical behaviour of hypothetically stable Atiras, such as those discussed by Ribeiro et al. ( 2016 ), and stable Vatiras. In general, Atiras may still experience close encounters with Venus, Vatiras cannot. When the Lidov–Kozai resonance is at work, in addition to avoiding close encounters with Venus at aphelion, close encounters with Mercury at perihelion are also reduced, but the orbit of Mercury is far more eccentric (0.21) and inclined (70) than that of


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T.D.M. acknowledges support from the Kepler Participating Scientist Program (NNX14AE11G). We thank the anonymous referee, Daniel Huber, Jack Lissauer, Juna Kollmeier, and David Hogg for providing helpful suggestions that improved both the analysis and the presentation herein. This paper includes data collected by the Kepler mission. Funding for the Kepler mission is provided by the NASA Science Mission directorate. The authors acknowledge the efforts of the Kepler Mission team for obtaining the light curve products used in this publication, which were generated by the Kepler Mission science pipeline through the efforts of the Kepler Science Operations Center and Science Office. The Kepler Mission is led by the project office at NASA Ames Research Center. Ball Aerospace built the Kepler photometer and spacecraft, which is operated by the mission operations center at LASP. These data products are archived at the NASA Exoplanet Science Institute, which is operated by the California Institute of Technology, under contract with the National Aeronautics and Space Administration under the Exoplanet Exploration Program. This research has made use of NASA’s Astrophysics Data System.


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

fluid with a special cooling function (Lin Youdin 2017 ; Lovascio Paardekooper 2019 ). Dropping the subscript “c” for clarity, our one-fluid model equations in the local shearing box to O ( t s ) are (Laibe Price 2014 ; Lin Youdin 2017 ; Lovascio Paardekooper 2019 ; Chen Lin 2020 ; Paardekooper et al. 2020 ), where f d ≡ ρ d / ρ is the dust fraction. Note that for the isothermal gas we consider, so . The second term on the rhs of Equation ( B5 ) vanishes in a particle disk where ρ g → 0, because solids do not feel pressure gradients. Conversely, for a dust-free gas disk ( ρ g / ρ → 1), we recover the full pressure support from the global disk. The second term in the parentheses on the rhs of Equation ( B6 ) arises from the contribution to the terminal velocity approximation from the large-scale radial pressure gradient in Equation ( B3 ). B.1. Approximate Equilibria As in the two-fluid model, we seek steady, horizontally uniform solutions. The mass, energy, and vertical momentum equations are then where in Equation ( B8 ) we ignore the term a posteriori for consistency with the small t s approximation used to derive the one-fluid model. These equations may then be solved for constant τ s = t s / f g = St/Ω to yield From here, it is clear that v z = O (St), so it is self-consistent to ignore the term. Equations ( B10 )–( B12 ) are in fact the same solutions as in the full two-fluid model in the limit St ≪ 1 (see Equations ( 19 )–( 21 ); recall β → St for St → 0 and note v z = f d v d z ). The horizontal momentum equations are where we ignore the quadratic term in Equation ( B13 ) to obtainThis is expected on physical grounds for tightly coupled dust (St → 0). In this limit, the mixture behaves close to a single fluid with orbital velocity depending on the level of dust enrichment. For ε → 0, we have a pressure-supported gas disk at sub-Keplerian velocity (assuming η > 0), while ε → ∞ corresponds to a particle disk on exactly Keplerian orbits, because then v y → 0. Next, we use Equations ( B15 ), ( B14 ), and ( B11 ) to obtainNotice the radial velocity of the dust–gas mixture’s center of mass depends on height. It is only zero at the midplane and for ∣ z ∣ → ∞ where ε → 0. For η > 0, the specific angular momentum decreases with increasing ∣ z ∣: the mixture gains pressure support as it becomes more gas-rich away from the midplane. This means that as a parcel of the mixture settles, it finds itself having an angular-momentum deficit compared to its surrounding; it thus drifts inwards ( v x 0), as indicated by Equation ( B16 ). B.2. Linearized Equations We linearize the one-fluid equations about the above basic state, with nonuniform v x ( z ), v y ( z ), and v z ( z ). As in the main text, we assume axisymmetric perturbations in the form of and similarly for other variables. The linearized equations are whereand recall Q = δ ε / ε and W = δ ρ g / ρ g = δ P / P . B.3. Mode Energetics Following Ishitsu et al. ( 2009 ), we multiply the x , y , and


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

M 87 is likely anchored close to the innermost stable circular orbit (ISCO). Performing such an analysis in other sources is clearly fundamental for testing the variety of possible scenarios. However, while future instruments with improved capabilities (e.g. phased ALMA) will certainly enrich the sample of suitable targets, this is currently quite limited. In this Letter we present, for the first time, a detailed imaging of the jet base in Cygnus A through global VLBI observations at 86 (GMVA). Among the powerful FR II radio galaxies, Cygnus A is one of the very few two-sided sources whose jet launching region can be probed with sufficient sensitivity at high radio frequencies. At the source redshift () 1 and assuming a black hole mass of ( Tadhunter et al. 2003 ), GMVA observations allow scales of the order of to be probed. The large jet viewing angle enables a prominent counter-jet to be detected in this source, which represents a fundamental advantage when investigating the nuclear regions of a jet. In fact, since the transverse width can be determined continuously along the two-sided flow, the assumption-dependent back-extrapolations of the properties of the jet apex can be replaced by actual measurements. The following analysis complements a previous VLBI study at 43 of the jet transverse profile and of the kinematic properties ( Boccardi et al. 2016 , hereafter B1). This revealed the presence of a pronounced transverse stratification, both in flux density (limb brightening) and bulk Lorentz factor (), typical of a flow with spine-sheath structure. Table 1 Log of observations at 86 GHz (3 mm) and characteristics of the clean maps shown in Fig. 1 . Notes. Column 1: Date of observation. Column 2: Array. VLBA_3mm indicates the part of the Very Long Baseline Array (all but the Hancock and St. Croix antennas) which is equipped with 86 GHz receivers; On – Onsala 20 m; Eb – Effelsberg 100-m; PdB – Plateau de Bure Interferometer; PV – IRAM 30-m atop Pico Veleta; Mh – Metsähovi. Column 3: Beam FWHM and position angle for untapered data with uniform weighting. 2. Observations and VLBI images The GMVA data set comprises three epochs from observations in 2009/2010 with a cadence between five and seven months (Table 1 ). The duration of the observations was 1516 h, 8 of which were spent on Cygnus A. This, together with the large number of antennas employed and with the favourable declination of the source, enabled good uv-coverage. Data were recorded in single polarization mode with a recording rate of 512 , which corresponds to an observing bandwidth of 128 . The correlation took place at the MPIfR in Bonn, Germany. The data reduction was carried out in AIPS ( Greisen 1990 ). Aside from the standard calibration procedures, special care was devoted during the fringe fitting. First, as described in Martí-Vidal et al. (2012) , the manual phase calibration was applied. Single sub-band phases and delays were calculated using one or more scans showing


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

We thank D. Gurnett for the Voyager wave spectrogram, N. Schwadron for the IBEX Ribbon spectrogram, and J. Harding for preparing Figures 1 , 2 , and 4 . I.H.C. thanks H. Elliott, V. Florinski, D. McComas, D. Melrose, N. Pogorelov, G. Zank, and E. Zirnstein for helpful advice and discussions. He also thanks the University of Sydney for support under its Special Studies Program (SSP), J. LaBelle and G. Zank for hosting his SSP visits to Dartmouth College and the University of Alabama at Huntsville (UAH), respectively, and the staff and colleagues at Dartmouth, UAH, and SwRI for their support and interest during his visits. S.A.F.’s research at SwRI was supported by NASA through the Explorer Program.


O O O O O O O O O O O O O O O O O O O O O O O B-Person I-Person O B-Person I-Person O O O O O O O O O O O O O O O O B-Person I-Person O O O O O O O O O O O O O O O O O B-Person I-Person I-Person O O O O O O O O O O O O O B-Observatory O B-Identifier O B-Identifier B-Observatory O O O O B-Observatory O O O O B-Organization B-Location O B-Organization B-Location O O B-Organization B-Location B-Organization O B-Organization B-Location O B-Organization B-Location I-Location I-Location O O O O B-Location I-Location I-Location O B-Observatory I-Observatory I-Observatory O O O B-Observatory B-Organization O B-Observatory O O O B-Person O O O O B-Grant B-Organization I-Organization I-Organization B-Organization O O O B-Grant O B-Grant I-Grant I-Grant I-Grant O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization I-Organization B-Person O O O O O O B-Fellowship I-Fellowship I-Fellowship I-Fellowship O O B-Fellowship B-Person O O O O B-Organization I-Organization I-Organization I-Organization B-Organization B-Grant I-Grant I-Grant O B-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship O O B-Fellowship I-Fellowship I-Fellowship I-Fellowship O O O O O O B-Archive I-Archive I-Archive I-Archive O B-Database O O O B-Organization B-Location I-Location O B-Citation I-Citation I-Citation I-Citation O O O O O O B-Software O O O O O O O B-Software O B-Citation I-Citation I-Citation O B-Software O B-Citation I-Citation I-Citation I-Citation O B-Software O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O B-Software O B-Citation I-Citation O

Acknowledgements The authors wish to thank the anonymous referee for the constructive comments that significantly improved the paper. The authors are grateful to Brett McGuire and Roman Motiyenko for providing the line strengths of CH 3 OCH 2 OH spectroscopic data. The authors acknowledge Gleb Fedoseev for the valuable discussion about the desorption temperatures from the TPD experiments of the O-bearing COMs and Troels C. Petersen for discussions of the statistical methods. This paper makes use of the following ALMA data: ADS/JAO.ALMA#2012.1.00712.S and ADS/JAO.ALMA#2013.1.00278.S. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada), NSC and ASIAA (Taiwan), and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ. The group of J.K.J. acknowledges support from the H2020 European Research Council (ERC) (grant agreement No 646908) through ERC Consolidator Grant “S4F”. Research at Centre for Star and Planet Formation is funded by the Danish National Research Foundation. A.C. postdoctoral grant is funded by the ERC Starting Grant 3DICE (grant agreement 336474). M.N.D. is supported by the Swiss National Science Foundation (SNSF) Ambizione grant 180079, the Center for Space and Habitability (CSH) Fellowship and the IAU Gruber Foundation Fellowship. This research has made use of NASA’s Astrophysics Data System and VizierR catalogue access tool, CDS, Strasbourg, France ( Ochsenbein et al. 2000 ), as well as community-developed core Python packages for astronomy and scientific computing including Astropy ( Astropy Collaboration 2013 ), Scipy ( Jones et al. 2001 ), Numpy ( van der Walt et al. 2011 ) and Matplotlib ( Hunter 2007 ).


O O O O O O O O O O O O O O B-Person O B-Person I-Person O B-Person I-Person O O O O O O O O O O B-Telescope O O O O O O O B-Organization I-Organization I-Organization I-Organization O B-Location O B-Grant O B-Grant I-Grant I-Grant B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization O O O O O B-Grant I-Grant I-Grant I-Grant I-Grant O O B-Grant B-Person O O O O B-Fellowship I-Fellowship O O O B-Fellowship O O O O O O O O O B-Database O O O O O O B-Database O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-Observatory I-Observatory I-Observatory I-Observatory I-Observatory I-Observatory O O O O O O B-Organization I-Organization I-Organization O O O O O O O O B-Organization I-Organization I-Organization O O B-Grant

We acknowledge the referee for valuable comments that have improved the paper a lot. M.L.G. thanks M. Lister and G.-Y Zhao for helpful comments on the model fitting method to the VLBA data. This work is supported by the National Natural Science Foundation of China (No. 11273050); the 973 Program 2015CB857100; Key Laboratory of Radio Astronomy, Chinese Academy of Sciences; and the program of the Light in China’s Western Region (Grant No. YBXM-2014-02). N.M. is funded by an ASI fellowship under contract number I/005/11/0. This research has made use of data from the MOJAVE database that is maintained by the MOJAVE team (Lister et al. 2009 ). This research has made use of data from the University of Michigan Radio Astronomy Observatory which has been supported by the University of Michigan and by a series of grants from the National Science Foundation, most recently AST-0607523.


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

Figure 2 reports the flux measurements in these bands, each split into three distinct bands, 3–7 keV, 7–30 keV, and 30–80 keV for 70 70 The upper edge of the NuSTAR energy range is actually 79 keV, but owing to the negligible impact on the flux values, in this paper, we will use 80 keV for simplicity. NuSTAR and 0.2–0.4 TeV, 0.4–0.8 TeV, and >0.8 TeV for MAGIC and VERITAS. The temporal coverage for the >0.8 TeV band is a about 2 hr longer than for the 0.2–0.4 TeV band because of the increasing analysis energy threshold with the increasing zenith angle of the observations. The exquisite characterization of the multiband flux variations in the X-ray and VHE gamma-ray bands reported in Figure 2 will be used in the sections that follow for the broadband variability and correlation studies. Figure 2. Light curves in various VHE and X-ray energy bands obtained with data from MAGIC, VERITAS, and NuSTAR (split in 15 minute time bins) and Swift-XRT (from several observations with an average duration of about 17 minutes). For the sake of clarity, the 0.3–3 keV fluxes have been scaled by a factor 0.5. The statistical uncertainties are, in most cases, smaller than the size of the marker used to depict the VHE and X-ray fluxes. (The data used to create this figure are available .) 4. Multiband and Multi-timescale Variability 4.1. Fractional Variability The flux variability reported in the multiband light curves can be quantified using the fractional variability parameter F var , as prescribed in Vaughan et al. ( 2003 ): denotes the average photon flux, S denotes the standard deviation of N flux measurements, and denotes the mean squared error, all determined for a given instrument and energy band. The uncertainty on F var is calculated using the prescription from Poutanen et al. ( 2008 ), as described in Aleksić et al. ( 2015a ). This formalism allows one to quantify the variability amplitude, with uncertainties dominated by the flux measurement errors and the number of measurements performed. The systematic uncertainties on the absolute flux measurements 71 71 The systematic uncertainties in the flux measurements at the radio, optical, X-ray, and GeV bands are of the order of 10%–15%, while those of the VHE bands are ∼20%–25%. do not directly add to the uncertainty in F var . The caveats in the usage of F var to quantify the variability in the flux measurements performed with different instruments are described in Aleksić et al. ( 2014 , 2015a , 2015b ). The most important caveat is that the ability to quantify the variability depends on the temporal coverage (observing sampling) and the sensitivity of the instruments used, which are somewhat different across the electromagnetic spectrum. A big advantage of the study presented here is that the temporal coverage of the three bands in X-rays (from NuSTAR) and the three bands in VHE gamma-rays (from MAGIC and VERITAS) is exactly the same, which allows us to make a more direct comparison of the variability


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This work was funded by the French ANR under the Contract No. ANR-13-BS05-0008-02 IMOLABS. This work was also supported by the French program “Physique et Chimie du Milieu Interstellaire” (PCMI) funded by the Conseil National de la Recherche Scientifique (CNRS) and Centre National d’Etudes Spatiales (CNES).


O O B-Person I-Person O O O O O B-Person I-Person O O O O O O B-Grant I-Grant O B-Grant O B-Telescope I-Telescope I-Telescope O O O O O O B-Location B-Location B-Location O B-Location I-Location B-Wavelength O O O O O O O O O O O O O B-Telescope O B-Proposal B-Proposal B-Proposal O B-Proposal O O 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 B-Telescope O O O B-Location O O O O B-Location I-Location B-Grant I-Grant I-Grant B-Grant O O O O B-Grant I-Grant O B-Telescope O O O B-Organization B-Organization I-Organization I-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O O O O O O B-Database I-Database I-Database B-Database O O O O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization I-Organization I-Organization

We thank Thomas Krichbarum for critically reading the manuscript. T. An thanks the grant support from the 973 programme (No. 2013CB837900). The European VLBI Network is a joint facility of independent European, African, Asian, and North American radio astronomy institutes. Scientific results presented in this publication are derived from the following EVN projects: RP017, EY018, EY019, and EY020. The study has received funding from the European Commission Seventh Framework Programme (FP/2007-2013) under grant agreement No. 283393 (RadioNet3). e-VLBI research infrastructure in Europe is supported by the European Union's Seventh Framework Programme (FP7/2007-2013) under grant agreement number RI-261525 NEXPReS. The WSRT is operated by ASTRON (Netherlands Institute for Radio Astronomy) with support from the Netherlands Organization for Scientific Research. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.


O O O B-Person I-Person O O O O O B-Observatory O O O B-CelestialObject I-CelestialObject B-Person I-Person O O O O O B-CelestialObject I-CelestialObject O O B-Person I-Person O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O B-Person O O O O B-Organization I-Organization I-Organization B-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship O O O B-Fellowship B-Person O O O B-Organization O B-Grant O O O O O O O B-Observatory O B-Identifier I-Identifier O B-Identifier B-Observatory O O O O B-Observatory O O O O B-Organization B-Location O B-Organization B-Location O O B-Organization B-Location O B-Organization O B-Organization B-Location O B-Organization B-Location I-Location I-Location O O O O B-Location I-Location I-Location O B-Observatory I-Observatory I-Observatory O O O B-Observatory B-Organization O B-Observatory O B-Observatory I-Observatory I-Observatory I-Observatory O O O O O B-Organization I-Organization I-Organization O O O O O B-Organization I-Organization I-Organization O O O O O O O O O O B-Organization I-Organization I-Organization B-Organization B-Mission I-Mission O B-URL O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization B-URL O O O O B-Organization O O O O O O O O O O O O O B-Collaboration I-Collaboration I-Collaboration