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within the time span of 21–39 days after the latest outburst onset (in the absence of intense bursts), Younes et al. ( 2020b ) precisely measured a much higher spin-down rate of 3.9 × 10 −11 s s −1 . This might suggest a hysteresis in the dynamical response in these highly magnetized systems that is accompanied by changes in burst activation. The polar magnetic field strength inferred for a vacuum dipole approximation (i.e., ) of SGR J1935+2154 is about 4.4 × 10 14 G. However, our X-ray spectral modeling of the persistent emission with the STEMS3D model, which includes radiative propagation in extremely magnetized settings, yielded a local surface magnetic field strength of 9.6 × 10 14 G. This difference is not surprising since the spin-down estimate applies to the global field configuration, and can be modified by plasma loading of the magnetosphere (Harding et al. 1999 ). Nevertheless, the surface magnetic field strength being considerably larger than the inferred value suggests that there may be multipolar magnetic topology, where local field strengths are much larger than the dipolar ones. Such a circumstance was observed in SGR 0418+5729, the first “low-dipole field” magnetar. Its magnetic field strength inferred from its spin parameters is 6 × 10 12 G (Rea et al. 2010 ). Güver et al. ( 2011 ) modeled the XMM-Newton spectrum of SGR 0418−5729 with the STEMS atmospheric emission model and obtained ∼ 10 14 G for the surface magnetic field strength. They proposed a dominant nondipolar magnetic field structure for SGR 0418−5729, a picture that is consistent with the discovery of a variable proton cyclotron absorption feature in later XMM-Newton observations (Tiengo et al. 2013 ). A significant multipolar magnetic configuration for SGR J1935+2154 is also supported by the complexity of its energy-dependent pulse profiles. Its low-energy X-ray pulse profile is dominated by a broad structure with a phase width of around 0.7–0.8. However, minor structures become pronounced above ∼3 keV, in the absence of bright persistent X-ray emission ( kT = 0.5 keV) from the surface of the neutron star. The BB+BB spectral fits indicate that this putatively hotter portion emanates from smaller regions, less than ∼0.2 km in size, and perhaps analogous to multipolar field components that are observed from small regions on the Sun. These structured pulse profiles contrast the comparatively simple two-peaked forms observed for active outburst phases in another magnetar, 1RXS J170849.0−400910, which can be attributed to antipodal polar hot zones in a dipole field configuration (Younes et al. 2020a ). Extension of the pulse profile analysis of Younes et al. ( 2020a ) to treat broader surface temperature profiles in magnetic colatitude is unlikely to generate the abrupt rises and falls in consecutive phase bins evident above ∼3 keV in Figure 1 . We suggest that strong temperature gradients in magnetic longitude are also required to reproduce the observed


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We thank the referee, Hiroyuki Hirashita, for his insightful comments, Laura Pentericci and Daniel Schaerer for their kind clarifications. The research leading to these results has received funding from the European Research Council under the European Union (FP/2007-2013)/ERC Grant Agreement no. 306476. PD acknowledges the support of the Addison Wheeler Fellowship awarded by the Institute of Advanced Study at Durham University. UM has been funded through a Marie Curie fellowship by the European Union (FP/2007-2013), grant agreement no. 267251.


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We thank the HET resident astronomers and telescope operators for continuous support. A.N., M.o.A., B.D.-S., M.i.A. and K.K. are currently supported by NCN grant 2012/07/B/ST9/04415. M.o.A. also acknowledges the “Mobility + III” fellowship from the Polish Ministry of Science and Higher Education. A.W. was supported by the NASA grant NNX09AB36G. G.M. acknowledges the financial support from the Polish Ministry of Science and Higher Education through the Iuventus Plus grant IP2011 031971. The HET is a joint project of the University of Texas at Austin, the Pennsylvania State University, Stanford University, Ludwig-Maximilians-Universität München, and Georg-August-Universität Göttingen. The HET is named in honor of its principal benefactors, William P. Hobby and Robert E. Eberly. The Center for Exoplanets and Habitable Worlds is supported by the Pennsylvania State University and the Eberly College of Science. This research has made extensive use of the SIMBAD database, operated at CDS (Strasbourg, France) and NASA’s Astrophysics Data System Bibliographic Services.


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This work has made use of the C2PAP cluster at the Leibniz-Rechenzentrum. NP is supported by the DFG cluster of excellence “Origin and Structure of the Universe”. GL acknowledges financial support from the ILP LABEX (under reference ANR-10-LABX-63) and from “Programme National de Cosmologie et Galaxies” (PNCG) of CNRS/INSU, France, and the ANR BIG4, under reference ANR-16-CE23-0002. This work was carried out within the Aquila Consortium.


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

pCO 2 case for a single multi-epoch case. 1 σ and 2 σ contours are included. 5. Atmospheric Retrievals To perform our retrievals we use the open-source radiative transfer and retrieval framework CHIMERA (Line Yung 2013 ; Line et al. 2013 ). It previously has been used to study the atmosphere of TRAPPIST-1e to determine the resolution that a future instrument needs to have in order to detect and constrain the abundances of molecules in the atmospheres of temperate terrestrial planets to high precision (Tremblay et al. 2020 ). Our retrieval setup is similar to that presented in Tremblay et al. ( 2020 ). For each of the combined spectra we fit for six parameters: an isothermal temperature profile ( T iso ), a radius scaling factor (x R p ), the cloud top pressure (), the mean molecular weight of the atmosphere, and the volume mixing ratio of H 2 O and CO 2 . We use the mean molecular weight (MMW) as a proxy to effectively fill the rest of the atmosphere with N 2 as this molecule is inert. 6. Results Each spectra that we retrieved had a different underlying cloud configuration, hence we wanted to determine if these physical processes impact the retrieved CO 2 abundance. The histograms presented in Figure 5 show that the retrieved abundances are consistent for each of the combined spectra, suggesting that the impact of cloud variability is not detectable with the resolution provided by JWST NIRSpec PRISM. This is further verified by the third panel, which shows consistent retrieved cloud top pressure for each spectra. While the cloud top pressure can be seen to vary in our models, this consistency in the retrieved cloud top pressures demonstrates that the precision of JWST NIRSpec PRISM will not be able to differentiate variable cloud spectra at any level of confidence. It can be seen from Figure 5 that for the CO 2 partial pressure greater than 10 −1 bars the posterior tends toward the upper prior, which is set by the physical limit of the volume mixing ratio, with the true value lying outside 1 σ . The lower partial pressures are not prior dominated and we are able to retrieve the correct volume mixing ratios within 1 σ . Further, the 10 cases for each partial pressure are consistent, suggesting that the variable clouds are not affecting the retrieved values. We are unable to constrain a water abundance due to its lack of strong spectral features in our models. Figure 5. Retrieved posterior distributions for four of the key parameters explored in this study. From top to bottom the four panels are: CO 2 abundance, H 2 O abundance, cloud top pressure, and temperature. Each colored histogram represents the retrieved parameter for one of the combined spectra (representing 10 different “observed” epochs), for a total 10 different combined spectra, each with different underlying cloud assumption. The thick solid vertical lines show the terminator-average abundance of CO 2 and H 2 O from the input models, while the dotted vertical lines represent


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MVdV acknowledges CNPq / Twas for financial support. EMdGDP acknowledges partial support from the Brazilian agencies FAPESP (grant no. 2013/10559-5 ) and CNPq (grant no. 300083/94-7 ). GK acknowledges support from FAPESP (grants no. 2013/04073-2 and 2013/18815-0 ) and PNPD/CAPES (grant no. 1475088 ). MVdV thanks Reinaldo Santos-Lima for fruitful discussions on different topics addressed in this paper. The authors also acknowledge the anonymous referee for a careful review. This work has made use of the computing facilities of the Laboratory of Astroinformatics (IAG/USP, NAT/Unicsul), whose purchase was made possible by the Brazilian agency FAPESP (grant 2009/54006-4 ) and the INCT-A. MVdV is grateful for the great hospitality of the Instituto de Astronomia, Geofísica e Ciências Atmosféricas (São Paulo University), where part of this work was developed.


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ACKNOWLEDGEMENTS Part of this work is based on archival data, software, or online services provided by the Space Science Data Center – ASI. We would like to thank the Instituto de Astrofísica de Canarias for the excellent working conditions at the Observatorio del Roque de los Muchachos in La Palma. The financial support of the German BMBF and MPG, the Italian INFN and INAF, the Swiss National Fund SNF, the ERDF under the Spanish MINECO (FPA2015-69818-P, FPA2012-36668, FPA2015-68378-P, FPA2015-69210-C6-2-R, FPA2015-69210-C6-4-R, FPA2015-69210-C6-6-R, AYA2015-71042-P, AYA2016-76012-C3-1-P, ESP2015-71662-C2-2-P, and CSD2009-00064), and the Japanese JSPS and MEXT is gratefully acknowledged. This work was also supported by the Spanish Centro de Excelencia ‘Severo Ochoa’ SEV-2012-0234 and SEV-2015-0548, and Unidad de Excelencia ‘María de Maeztu’ MDM-2014-0369, by the Croatian Science Foundation (HrZZ) Project IP-2016-06-9782 and the University of Rijeka Project 13.12.1.3.02, by the DFG Collaborative Research Centers SFB823/C4 and SFB876/C3, the Polish National Research Centre grant UMO-2016/22/M/ST9/00382, and by the Brazilian MCTIC, CNPq, and FAPERJ. The Fermi -LAT Collaboration acknowledges generous ongoing support from a number of agencies and institutes that have supported both the development and the operation of the LAT and scientific data analysis. These include the National Aeronautics and Space Administration and the Department of Energy in the United States, the Commissariat à l’Energie Atomique and the Centre National de la Recherche Scientifique/Institut National de Physique Nucléaire et de Physique des Particules in France, the Agenzia Spaziale Italiana and the Istituto Nazionale di Fisica Nucleare in Italy, the Ministry of Education, Culture, Sports, Science and Technology (MEXT), High Energy Accelerator Research Organization (KEK), and Japan Aerospace Exploration Agency (JAXA) in Japan, and the K. A. Wallenberg Foundation, the Swedish Research Council, and the Swedish National Space Board in Sweden. Additional support for science analysis during the operations phase is gratefully acknowledged from the Istituto Nazionale di Astrofisica in Italy and the Centre National d’Études Spatiales in France. This work performed in part under DOE Contract DEAC02-76SF00515. The OVRO 40-m monitoring program is supported in part by NASA grants NNX08AW31G, NNX11A043G, and NNX14AQ89G, and NSF grants AST-0808050 and AST-1109911.


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

the component CO lines in a merger model, measured in km s 1 . The HST images (Rix etal. 2004 ) show various clumps that indicate ALESS 122.1 and ALESS 67.1 could be mergers (Fig. 3 ). Taking the merger model and R to be 0.5arcsec (4.2kpc at z 2), which is the approximate separation of the clumps in HST optical counterparts (Fig. 3 ), the dynamical mass, M dyn sin 2 i , is 510 11 M for both ALESS 122.1 and ALESS 67.1. Figure 3. The CO(10) velocity structure of ALESS 122.1 (left) and ALESS 67.1 (right), overlaid on HST z band ( F 850 LP ) images from Rix etal. ( 2004 ) 3 . Both optical counterparts are clumpy or complex in the rest-frame UV, indicating either structured dust or a possible merging system. Blue contours indicate the CO(10) emission integrated from 300 to 0kms 1 at 3, 5, 7.... Red contours indicate the CO(10) emission integrated from 0 to 300kms 1 at 3, 5, 7.... Red and blue crosses mark the centroid of the blueshifted and redshifted emission, respectively. The images are 2020arcsec. However, the HST image does not reveal whether or not the systems contain a gaseous disc. In the presence of a gas disc, the dynamical mass can be estimated from the CO line kinematics, by comparing the spatial offset between the redshifted and blueshifted components of the CO line. This was determined by making 300kms 1 wide channel maps centred at 300 to 0kms 1 and 0 to 300kms 1 (Fig. 3 ). The centroid of the CO emission was determined for the maps, and we derive a spatial offset between the redshifted and blueshifted emissions of 1.20.6arcsec (10.25.1kpc) and 1.8 0.5arcsec (15.24.2kpc) for ALESS 122.1 and ALESS 67.1, respectively. This is comparable to CO(10) sizes observed in other SMGs by Ivison etal. ( 2011 ). Assuming this spatial offset represents rotating gas, then the dynamical mass M dyn sin 2 i = (2.11.1)10 11 M and (3.20.9)10 11 M for ALESS 122.1 and ALESS 67.1, respectively. These estimates are consistent with the dynamical masses derived from using the CO line FWHM and optical size from HST imaging. For a rotating model, Bothwell etal. ( 2013 ) found their sample of SMGs to have a median dynamical mass of (1.60.3)10 10 R M , where radius R is in kpc. Using the measured spatial offsets of 10 and 15kpc for R , the dynamical masses of ALESS 122.1 and ALESS 67.1 are consistent with the median dynamical mass of their SMG sample. The total baryonic mass can be calculated by combining the gas and stellar mass estimates for the SMGs. The stellar masses of ALESS 122.1 and ALESS 67.1 have been estimated by Simpson etal. ( 2014 ), who used absolute rest-frame H -band magnitudes from best-fitting SEDs to multiband photometry and a model mass-to-light ratio. They estimate ALESS 122.1 has a stellar mass of 5.210 10 M and ALESS 67.1 has a stellar mass of 4.410 10 M . These estimates are uncertain by a factor of at least a few, due to the difficulty in distinguishing between different model SF histories to predict an accurate mass-to-light ratio


O O B-Person I-Person O O O B-Person I-Person 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 O B-Person I-Person O O O B-Person B-Person O B-Person O O O O B-Organization B-Grant I-Grant I-Grant B-Grant O B-Grant B-Person O O O O O O B-Organization B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O B-Location B-Organization O O O B-Grant O O O O B-ComputingFacility I-ComputingFacility I-ComputingFacility O O O O B-ComputingFacility I-ComputingFacility I-ComputingFacility O O O B-Organization I-Organization I-Organization I-Organization O O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization O O O O O O B-Organization I-Organization I-Organization O O O O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O B-Grant O B-Software B-Identifier B-Citation I-Citation I-Citation I-Citation O B-Citation O B-Citation O B-Software B-Identifier B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Software B-Citation I-Citation I-Citation I-Citation O

We thank Tony Piro for his encouragement, Stefan Taubenberger for providing access to data, and Carles Badenes, Stéphane Blondin, Hector Martínez-Rodríguez, Alison Miller, Rüdiger Pakmor, Stuart Sim, and Frank Timmes for helpful discussions. K.J.S., D.M.T., and B.J.M. received support from the NASA Astrophysics Theory Program (NNX15AB16G and NNX17AG28G). D.K. is supported in part by a DOE Office of Nuclear Physics Early Career Award, and by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Divisions of Nuclear Physics, of the US DOE under Contract No. DE-AC02-05CH11231. This research used the Savio computational cluster resource provided by the Berkeley Research Computing program at the University of California, Berkeley (supported by the UC Berkeley Chancellor, Vice Chancellor of Research, and Office of the CIO), high-performance computing resources provided by the University of Alabama, and resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the US DOE under Contract No. DE-AC02-05CH11231. Software: MESA (v8845; Paxton et al. 2011 , 2013 , 2015 ), FLASH (v4.2.2; Fryxell et al. 2000 ; Dubey et al. 2009 ), SEDONA (Kasen et al. 2006 ).


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

giant component fractions imply the fundamental difference in the pathway topology between Snap100 and Lévy fractals; Snap100 has more efficient pathways to connect all galaxies at a shorter linking length than Lévy fractals. Very likely, this is due to the filamentary structures in Snap100, lacking in Lévy fractals. The middle panel of Fig. 2 shows the diameters. We can again see clear separations of Snap100 from the Lévy walk models. Snap100 reaches the maximum diameter, 300, at the linking length, 1.1 h −1 Mpc, while Lévy walk models reach the maximum diameters around 200 for linking lengths near 2.0 h −1 Mpc. Even for 100 Lévy walk realizations, none of the Lévy walk models can match the diameter measurements of Snap100. Hence, both the size of the giant component and diameter are network measures that discriminate the Lévy walk topologies from the Illustris simulation, despite the data sets being constructed to have matching abundance and two-point correlation statistics. The linking length for maximum diameter is related to the inflection point of the growth curve of giant component fractions; the rate of growth of the giant component decreases after reaching the maximum diameter. This transitioning feature occurs due to the ‘saturation’ of connecting edges. At first (i.e. small linking length values), increasing the linking length results in adding new vertices and increasing the size of the connected network components. However, once the largest diameter is reached, increasing the linking length tends to form new pathways within the existing structure between more far-flung members and only slowly increases the overall size of the connected structure. Therefore, the diameter is maximized at this critical scale, transitioning from ‘growing phase’ to ‘saturating phase’. The previous percolation studies are closely related to this maximum diameter scale, though they have not measured these specific diameters. If the system size is infinite, the diameter measurements transit from finite values to an infinity near this scale. The bottom panel of Fig. 2 shows transitivity results. Again, none of Lévy walk models mimics the transitivity curve of Snap100. We note that the statistical variances of transitivity measurements are much smaller than the other measurements as shown in Fig. 2 , since a single realization of the network is statistically large enough for counting triangles. Hence, the difference of transitivities between Snap100 and Lévy fractals also suggests that Snap100 is topologically very different from Lévy fractals. An interesting feature is the difference of convexities between Snap100 (concave or ‘cup’) and Lévy fractals (convex or ‘hat’). The transitivities of Snap100 are high for small linking lengths, then decrease to a minimum transitivity at 0.4 h −1 Mpc as the linking length increases. After this, the transitivities slowly increase to 0.8. This transitivity trend of Snap100 is related to the transition between the


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

0.02, respectively. These values are also within the typical range obtained in the study of GRB afterglows (Medvedev 2006 ). We note that different values of ε e and ε B will only change the normalization, but not the slope, of the η jet – relationship (cf. equation 3 below). We then calculate the synchrotron emission from these accelerated electrons. Like any other jet models in literature, our jet model is phenomenological. Besides, we assume that all the jet parameters remain unchanged for different sources and accretion rates, which is certainly a strong assumption. This is partly because we still do not have good constraint on them. To conclude, the only free parameter in our jet model is its mass-loss rate . We note that the L R is found to be a power-law function of (see also Heinz Sunyaev 2003 ). 2.2 Hot accretion flow model Depending on the accretion rate, two types of hot accretion flow exist. They are the advection-dominated accretion flow (ADAF; Narayan Yi 1994 , 1995 ; Abramowicz et al. 1995 ) below certain critical accretion rate and the luminous hot accretion flow (LHAF; Yuan 2001 ) above it (see review by Yuan Narayan 2014 ). LHAF is thermally unstable (Yuan 2003 ). But if accretion rate is relatively low, , the growth time-scale of the thermal instability is larger than the accretion time-scale, so the gas can remain hot throughout the flow. We call it type-I LHAF. Above , the growth time-scale of the thermal instability is shorter than the accretion time-scale thus some cold dense clumps should be formed, embedded in the hot phase medium. We call it type-II LHAF or two-phase accretion flow. We follow the standard approach to calculate the dynamical structure and the emitted spectrum of ADAFs and type-I LHAF (e.g. YCN05 ). The L X at 3–9 keV band is then derived from the spectrum. For the two-phase accretion flow, optical/UV radiation from cold clumps will provide additional (likely dominant) seed photons for the inverse Compton scattering process, to generate the X-ray emission. The whole process is obviously complicated, depending on the detailed dynamics of the two-phases accretion flow such as the filling factor and temperature of clumps and so on. Following Yuan Zdziarski ( 2004 ), we simplify the problem by replacing the electron energy equation with the Compton y -parameter. With the assumption that the electron advection term is zero in the two-phase flow, we can calculate the radiative cooling rate. The bolometric luminosity can then be derived (Xie Yuan 2012 ). In order to derive 3–9 keV L X , we assume the spectrum to be a simple power law with exponential cutoffs at both the high and low ends, i.e. F E ∼ E 1−Γ exp (− E min / E )exp (− E / E max ), where the photon index Γ is constrained by the Compton y -parameter. E min is set arbitrarily to be 0.02 keV. E max is numerically determined by the electron temperature, i.e. E max = kT e , at the location where most of the radiation comes out (Yuan Zdziarski 2004 ).


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

γ-ray telescopes, and, possibly, by some of the currently operating ones. To our knowledge, these results have never been reported before. We have discussed how different choice of parameters (such as source redshift, primary proton energy and angular distribution, extragalactic magnetic field, and extragalactic background light models) would change the observable spectra. We have also provided a qualitative discussion of the main stages of cascade development and the effects of additional processes. This study could significantly facilitate future axion-like particle searches in the optically thick region of blazar spectra. In addition, our work might be useful in extreme TeV blazar studies as well as in several related branches of γ-ray astronomy, including extragalactic background light and extragalactic magnetic field measurements. APPENDIX A: THE IMPACT OF FLUCTUATIONS ON THE OBSERVABLE SPECTRA The observable spectrum in the framework of the MHCM depends on the EGMF structure, in particular, on the number of proton trajectories used in our study. In Fig. A1 , we show the observable SEDs averaged over various numbers of proton trajectories. We conclude that the statistics of 10 2 trajectories is sufficient to obtain a stable enough average observable spectrum for E 10 TeV, and the use of 10 3 trajectories already allows one to robustly determine the shape of the spectrum for E 30 TeV. Figure A1. Average observable SEDs for the KD10 EBL model option and the following numbers of trajectories: 10 (black curve), 100 (red curve), 10 3 (green curve), and 10 4 (blue curve). In addition, we have calculated the observable SEDs for 10 2 individual proton trajectories to demonstrate the impact of fluctuations on the shape of the observable spectrum (see Fig. A2 ). The blue-to-red gradient of colours gives a visual representation to the values of the ratios of different individual SEDs at two benchmark energies: 10 TeV and 100 GeV. Blue colours represent lower ratios, while red colours – higher ones. We note that at E = 5 TeV, the maximal difference between the flux corresponding to 95 per cent of the trajectories is limited to the factor of 2.5. Figure A2. Observable SEDs for the KD10 EBL model option and 10 2 individual trajectories; colours represent the ratios of individual SEDs at 10 TeV and 100 GeV. APPENDIX B: DISTRIBUTION OF THE CRITICAL DISTANCE In Fig. B1 , we present a histogram of a distribution on ‘the critical distance’ L cr (see Section 4.1 for definition of this parameter). The normalization of this histogram corresponds to the case of discrete probability density function, i.e. with summation over the bins of the histogram, with the N th bin containing the largest value of L cr . Figure B1. Histogram of the critical distance L cr distribution (red curve). APPENDIX C: SPECTRA WITH AND WITHOUT TPP, URB, and DPP In Fig. C1 , we present histograms of the observable spectra of γ-rays and electrons calculated with the CRPropa3 code for


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We are grateful to the anonymous referee for a number of helpful suggestions. Support for this work was provided by the National Research Foundation of Korea to the Center for Galaxy Evolution Research, and by KASI under the RD program (Project No. 2014-1-600-05) supervised by the Ministry of Science, ICT and future Planning. M.P. acknowledges support from Mid-career Researcher Program (No. 2015-008049) through the National Research Foundation (NRF) of Korea. Software: IRAF, DAOPHOT II/ALLFRAME (Stetson 1987 , 1994 ).


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The authors thank the anonymous referee for the useful comments and suggestions, which helped to improve the paper. We are grateful to Emanuele Daddi for useful discussion, Maria Cebrián for providing the effective radii from the NYU-VAGC catalogue and Helena Domínguez-Sánchez, Kenneth Duncan, Andrea Grazian, Chiara Mancini and Adam Muzzin for providing their mass functions. A.C. is also gratetful to Alfonso Veropalumbo for helpful discussion. We also acknowledge the support of the grant PRIN MIUR 2010 The dark Universe and the cosmic evolution of baryons: from current surveys to Euclid. Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the US Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England. The SDSS Web Site is http://www.sdss.org/ . The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions. The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington.


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Hinode is a Japanese mission developed and launched by ISAS/JAXA, with NAOJ as domestic partner and NASA and STFC (UK) as international partners. It is operated by these agencies in cooperation with ESA and the NSC (Norway). CHIANTI is a collaborative project involving the following Universities: Cambridge (UK), George Mason, and Michigan (USA). This work was partially supported by the JSPS Core-to-Core Program 22001. The work of D.H.B. was performed under contract with the Naval Research Laboratory and was funded by the NASA Hinode program.


B-Person B-Person B-Person O B-Person O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O O O O B-Organization O B-Grant O O O O B-Grant I-Grant B-Grant I-Grant O B-Grant I-Grant B-Person O O O O O O B-Fellowship O O B-Organization B-Location O O O B-Grant I-Grant O B-Grant B-Person B-Person O B-Person O O O O O B-Organization O B-Organization I-Organization O B-Grant B-Grant I-Grant O B-Grant O O B-Organization B-Location O B-Organization B-Location B-Person O O O O O B-Location B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O O B-Location O O B-Organization B-Grant O O B-Person I-Person O B-Person I-Person O O O O B-Model O O O O O O O O B-Database O O O B-Organization B-Location B-Location O B-Software O O O B-Database O O O O O O O O O O O O O O O O O O

E.D.M., V.Zh.A., N.C.S., and S.G.S. acknowledge the support from Fundação para a Ciência e a Tecnologia (FCT) through national funds and from FEDER through COMPETE2020 by the following grants UID/FIS/04434/2013 POCI–01–0145-FEDER–007672, PTDC/FIS-AST/7073/2014 POCI–01–0145-FEDER–016880, and PTDC/FIS-AST/1526/2014 POCI–01–0145-FEDER–016886. E.D.M. acknowledges the support from the fellowship SFRH/BPD/76606/2011 funded by FCT (Portugal) and from the Investigador FCT contract IF/00849/2015/CP1273/CT0003. V.Zh.A., N.C.S., and S.G.S. also acknowledge the support from FCT through Investigador FCT contracts IF/00650/2015/CP1273/CT0001, IF/00169/2012/ CP0150/CT0002, and IF/00028/2014/CP1215/CT0002 funded by FCT (Portugal) and POPH/FSE (EC). J.I.G.H. acknowledges financial support from the Spanish Ministry of Economy and Competitiveness (MINECO) under the 2013 Ramón y Cajal program MINECO RYC–2013–14875, and the Spanish ministry project MINECO AYA2014–56359-P. We thank Sara Bisterzo and Donatella Romano for kindly providing their GCE models. This research has made use of the SIMBAD database operated at CDS, Strasbourg (France), the IRAF facility, and the VALD3 database. Finally, we are sincerely grateful to the anonymous referee, whose careful review helped to improve this paper.


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

be given elsewhere (D. Radice et al. 2017, in preparation). A summary of the simulations is given in Table 1 . Table 1 Gravitational and Baryonic Masses, Compactnesses, Tidal Deformability Parameters, BH Formation Time, and Disk and Ejecta Masses Notes. Disk and ejecta masses are given at the final simulation time. a NS gravitational mass. b NS baryonic mass. c NS compactness, . d Dimensionless quadrupolar tidal parameters, Equation ( 2 ). e Dimensionless tidal parameter, Equation ( 1 ). f Gravitationally bound material with outside of the apparent horizon. g Dynamic ejecta mass, computed as from the flux of unbound matter through the coordinate-sphere . h BH formation time, in milliseconds after merger. i Final simulation time, in milliseconds after merger. We compute the mass of the dynamic ejecta and of the remnant accretion disk for each model. Our results are shown in Table 1 and Figure 1 . The typical dynamic ejecta masses in our simulations are of the order of , in good qualitative agreement with previous numerical-relativity results. We do not find any clear indication of a trend in the dynamic ejecta masses as a function of the binary parameters or EOS. However, we find a clear correlation between the disk masses and the tidal parameter . According to our simulations, binaries with inevitably produce BHs with small accretion disks. These cases are incompatible with the infrared data for AT2017gfo, even under the assumption that all of the matter left outside of the event horizon will be ejected. Figure 1. Remnant disk plus dynamic ejecta masses (upper panel) and BH formation time (lower panel) plotted against the tidal parameter (Equation ( 1 )). For models that do not collapse during our simulation time, we give a lower limit. The horizontal dashed line shows a conservative lower limit for AT2017gfo, , obtained assuming that the entire disk is unbound. The vertical dotted line is . Errors on and are estimated following Equation ( 3 ) and are added in quadrature. The reason for this trend is easily understood from the lower panel of Figure 1 . The NS dimensionless quadrupolar tidal parameters depend on the negative-fifth power of the NS compactness ( Equation ( 2 )). Consequently, small values of are associated with binary systems having compact NSs that result in rapid or prompt BH formation. In these cases, the collapse happens on a shorter timescale than the hydrodynamic processes responsible for the formation of the disk. Consequently, only a small amount of mass is left outside of the event horizon at the end of the simulations. Binaries with larger values of produce more massive disks, up to , and longer lived remnants. In these cases, neutrino driven winds and viscous and magnetic processes in the disk are expected to unbind sufficient material to explain the optical and infrared observations for AT2017gfo (Perego et al. 2014 ; Wu et al. 2016 ; Siegel Metzger 2017 ). 4. Discussion On the basis of our simulations and 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 B-CelestialObject I-CelestialObject O O B-Model O O O O B-Model I-Model O B-CelestialObject O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject 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 B-Model I-Model I-Model O O O O O O O O O O O B-Wavelength O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O B-Model O O O O O B-Model O O O O O O B-Model I-Model I-Model O O O O O O O B-ObservationalTechniques I-ObservationalTechniques O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O B-Wavelength 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 O O O B-CelestialObject O B-CelestialObject 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 B-Model O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O B-CelestialObject I-CelestialObject B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O B-CelestialObject 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 B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O B-Wavelength O O

of mag, with mag. The power law removes any degeneracy in the slope of the dust extinction law, and thus excludes the possibility of significant grey dust. Another example is GRB 120815A , whose SED is fit by a power law and SMC-like extinction to give an value of 0.08 mag, which is significantly smaller than the of 0.44 mag. We find that GRB 121024A is also best fit with a power law. Indeed, Fig. 9 shows that only one object that has an overpredicted was fit with a broken power law. Although there is strong evidence for dust destruction caused by the GRB itself ( Morgan et al. 2014 ), this would not cause a discrepancy between and . Any dust that extinguishes the GRB would also be visible in depletion, so if that dust is destroyed it is no longer visible in depletion or extinction. Fig. 9 as measured directly from the SED against that calculated from the DTM. The green line indicates a 1:1 conversion between the two. Blue circles represent SEDs best fit with a simple power-law, whereas red triangles are used for broken power-law fits. Empty points refer to depletion measured from low-resolution spectra. Large error bars are due to significant errors in several measured parameters being combined in quadrature. Intervening systems such as absorbers are known to contain similar quantities of dust as galaxies (e.g. Ménard Fukugita 2012 ), although QSO-DLAs tend to show very little reddening ( Krogager et al. 2016 ; De Cia et al. 2016 ). For the group (2) objects, we notice that 050820A , 100219A , 111008A , and 130408A all have intervening absorbing systems. Should these objects have a high dust content, they could significantly affect the SED of the GRB afterglow, such that the reddening caused by dust in the host galaxy itself is indeed smaller, and thus pushes these objects towards the 1:1 line. However, for these intervening systems to be the reason for a much higher than from DTM, they would need to contribute around 80% of the extinction along the line of sight, whereas the systems in our sample are much weaker in metal line absorption than the host DLA (e.g. in GRB 100219A, Thöne et al. 2013 ). We therefore find it unlikely that a significant amount of the extra extinction is caused by intervening systems. 6.5. Equivalent dust column density Having established that depletion is a good tracer of the dust, and with being accurate and reliable, we look to the relation used to calculate , Eq. ( 10 ). This is based upon the relation between hydrogen and dust in the Galaxy, where a column of cm results in an of 0.45. We note that the value of the Galactic gas-to-dust ratio varies depending on the sample and technique used to measure it. We use the result of Watson (2011) . Measurements of this value have been consistent over the past few decades, and include those by Bohlin et al. (1978) , Predehl Schmitt (1995) , and Güver Özel (2009) . The value used does not alter the fact that a significant discrepancy is observed. In DLAs, the hydrogen


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This work was performed using HPC resources from GENCI-IDRIS (grant 2017-040219). It has been supported by Programme National Soleil-Terre (PNST/INSU/CNRS).


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E.Z. and J.H. acknowledge support from NASA grant NNX16AG83G. R.K. was partially supported by the Max-Planck/Princeton Center for Plasma Physics and NSF grant AST-1517638. This work was also carried out as part of the IBEX mission, which is part of NASA’s Explorer program. The work reported in this paper was performed at the TIGRESS High Performance Computing Center at Princeton University, which is jointly supported by the Princeton Institute for Computational Science and Engineering and the Princeton University Office of Information Technology’s Research Computing department.


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

We would like to thank the staff of the East Asian Observatory for their invaluable support in the completion of the BISTRO survey. We also wish to thank the people of Hawai’i for granting us access to the unique geographical site of the Maunakea observatory. Furthermore, we are grateful to the GAS Consortium for generously granting us access to their spectroscopic data. We also thank the anonymous reviewer for their helpful and detailed comments. Finally, we thank B.-G. Andersson, Kelvin Au, Jordan Guerra Aguilera, James Lane, Anna Ordog, Amélie Simon, Ian Stephens, and Julien Vandeportal for helpful discussions. This research was conducted in part at the SOFIA Science Center, which is operated by the Universities Space Research Association under contract NNA17BF53C with the National Aeronautics and Space Administration. The James Clerk Maxwell Telescope is operated by the East Asian Observatory on behalf of the National Astronomical Observatory of Japan, Academia Sinica Institute of Astronomy and Astrophysics, the Korea Astronomy and Space Science Institute, and the Center for Astronomical Mega-Science (as well as the National Key RD Program of China with No. 2017YFA0402700). Additional funding support is provided by the Science and Technology Facilities Council of the United Kingdom and participating universities in the United Kingdom and Canada. SCUBA-2 and POL-2 were built through grants from the Canada Foundation for Innovation. This research used the facilities of the Canadian Astronomy Data Centre operated by the National Research Council of Canada with the support of the Canadian Space Agency. This research has also made use of the simbad database and of NASA’s Astrophysics Data System Bibliographic Services. The Starlink software (Currie et al. 2014 ) is currently supported by the East Asian Observatory. M.K. was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT Future Planning (NRF-2015R1C1A1A01052160). W.K. was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF-2016R1C1B2013642). C.W.L. was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (NRF-2016R1A2B4012593). D.L and K.Q. are supported by National Key RD Program of China No. 2017YFA0402600 and acknowledge the support from the National Natural Science Foundation of China (NSFC) through grants U1731237, 11473011, 11590781, 11629302, and 11725313. Software: S tarlink (Currie et al. 2014 ; Parsons et al. 2017 ; Chapin et al. 2013 ), The IDL Astronomy User’s Library (Landsman 1993 ).


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A.R.G.S. acknowledges the support from FCT (Portugal) through the grant reference SFRH/BD/88032/2012. M.S.C. and P.P.A. are supported by FCT through the Investigador FCT contracts of reference IF/00894/2012 and IF/00863/2012 and POPH/FSE (EC) by FEDER funding through the program COMPETE. Funds for this work were provided also by the EC, under FP7, through the projects FP7-SPACE-2012-31284 and PIRSES-GA-2010-269194. T.L.C. acknowledges the support of the UK Science and Technology Facilities Council (STFC).


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

n s is the number density of the s th species of the fluid. The mass density is given by Chattopadhyay ( 2008 ) and Chattopadhyay Ryu ( 2009 ), where , is the composition parameter and . The electron and proton masses are and , respectively. For single-temperature flow, the isotropic pressure is given by The EoS for multi-species flow is (Chattopadhyay 2008 ; Chattopadhyay Ryu 2009 ) The non-dimensional temperature is defined with respect to the electron rest mass energy, . Using equations ( 19 ) and ( 20 ), the expression of the energy density in equation ( 21 ) simplifies to where The expressions of the polytropic index, the adiabatic index and the sound speed are given as Integration of first law of thermodynamics (equation 13 ) by assuming adiabatic flow ( Q + = 0) and using the EoS (equation 22 ) gives us the adiabatic relation of multi-species relativistic flow (Chattopadhyay Kumar 2013 ; Kumar et al. 2013 ), where k 1 = 3(2 − ξ)/4, k 2 = 3ξ/4 and and is the constant of entropy. Equation ( 24 ) is the generalized version of . Combining equations ( 24 ) and ( 14 ), we get the expression of entropy accretion rate, Re-arranging equations ( 10 )–( 14 ) with the help of equations ( 9 ), ( 7 ), ( 19 ), ( 20 ) and ( 22 ) in geometric units, we present the spatial derivative of flow variables v , l and Θ, where Here, contains an extra term l 2 v /( r 2 γ 2 ) compared to the inviscid case (Chattopadhyay Chakrabarti 2011 ). There is γ φ term in the expression of disc height (equation 12 ). The radial derivative of equation ( 14 ) implies that the radial derivative of the specific angular momentum will be non-zero, which causes the extra term to appear. There are many height prescriptions (Lasota 1994 ; Riffert Herold 1995 ; Peitz Appl 1997 ), and choice of any one of them apart from the one used will not affect the result qualitatively. Then, Moreover, These differential equations are integrated by using fourth-order Runge–Kutta numerical method with the help of using critical point conditions and l′Hospital rule at critical point. 2.2.1 Sonic point equations Mathematical form of critical point equation is , which gives two equations as and Here, the subscript ‘c’ denotes the same physical quantities described in equations ( 26 )–( 28 ), but evaluated at the location of the critical point. The velocity gradient on the sonic point, i.e. (d v /d r ) c , is obtained by employing l′Hospital rule. 2.2.2 Relativistic shocks for viscous flow The relativistic shock conditions were first obtained by Taub ( 1948 ), which for viscous flow in the presence of mass-loss are where . We have solved four shock conditions ( 31 )–( 34 ) simultaneously, where viscous shear tensor () is continuous across the shock and we obtained the relation between pre-shock (suffix ‘−’) and post-shock (suffix ‘+’) flow variables, where . Here, , . From equation ( 11 ), viscous shear tensor can be written as . 2.3 Outflow equations The jet being tenuous, we idealize it to be


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

of protons that decay into pions, f sec 0.7 is the ratio of secondary and total cosmic ray e , m p and m e are the masses of protons and electrons, and c is the speed of light. The normalization of the proton injection spectrum Q p, 0 can be directly related to the supernova rate via where 0.1 is the fraction of the supernova energy E SN 10 51 erg that is converted into kinetic energy of cosmic rays (Dorfi 2000 ). The Lorentz factor p, 0 10 9 eV/( m p c 2 ) 1 marks the low-energy end of the cosmic ray proton spectrum. When travelling through the interstellar medium, cosmic rays lose energy continuously. The total number N e () of e can be described as where the energy losses are determined by the cooling time-scale e . At steady state, we find The different energy loss channels are: ionization (ion), bremsstrahlung (brems), inverse Compton scattering (IC), synchrotron emission (synch), and galactic outflows (wind). The individual time-scales can be summarized as and result in the total cooling time-scale Here, T 6.6510 25 cm 2 is the Thomson cross-section, u B B 2 /(8) is the energy density of the magnetic field B , u ISRF is the energy density of the interstellar radiation field (ISRF), n is a gas density, H is the galactic scaleheight, v wind the velocity of the galactic wind, and is the e Lorentz factor. 2.2 Synchrotron emission in a galactic magnetic field In the presence of a magnetic field, cosmic rays perform spiral motions and hence are constantly accelerated. A single electron with a Lorentz factor results in the spectral power where K 5/3 ( x ) is the modified Bessel function of second kind and (see e.g. the review by Blumenthal Gould 1970 ). To find the synchrotron emission L , synch produced from the full population of cosmic rays, one has to integrate over the cosmic ray distribution, i.e. The last integral over the pitch angle is roughly 8.9 for a cosmic ray spectrum with a slope of 2.2 and the lower limit of the integration is e, 0 10 7 eV/( m e c 2 ) 20. We note that the synchrotron luminosity L synch, is directly proportional to the supernova rate , which determines the total number of cosmic rays (see equation 3 ). As the supernova rate is correlated with the SFR, synchrotron emission can be used to estimate a galaxys SFR. 2.3 Freefree emission and absorption At low frequencies and high gas densities, the interstellar medium is optically thick and synchrotron emission, holding the information about the SFR, is absorbed. The optically thick regime is characterized by an optical depth ff larger than 1. The value of ff depends on the electron temperature T e , the emission measure EM , and the frequency : with The number density of the free electrons n e can be related to the gas density via the ionization degree f ion : n e f ion n . The filling factor f fill describes the clumping of the medium (Ehle Beck 1993 ; Berkhuijsen, Mitra Mueller 2006 ; Beck 2007 ). Hence, the critical frequency crit at which ff 1, determining


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We thank the anonymous referee for their various helpful comments and suggestions. IDR and LCP thank the National Science and Engineering Research Council of Canada for funding. We thank X. Yang et al. for making their SDSS DR7 group catalogue public, L. Simard et al. for the publication of their SDSS DR7 morphology catalogue, and the NYU-VAGC team for the publication of their SDSS DR7 catalogue. This research would not have been possible without these public catalogues. Funding for the SDSS has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the US Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England. The SDSS website is http://www.sdss.org/ .


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The authors would like to thank the referee, John Landstreet, for useful comments that improved the manuscript. L.F. acknowledges financial support from the Alexander von Humboldt Foundation. T.M. acknowledges financial support from Belspo for contract PRODEX GAIA-DPAC. N.L. and A.R. acknowledge financial support from the DFG-CONICYT International Collaboration Project (DFG-06). S.S.-D. acknowledges funding by the Spanish Ministry of Economy and Competitiviness under the grants AYA2010-21697-C05-05, AYA2012-39364-C02-01, and Severo Ochoa SEV-2011-0187, and by the Canary Islands Governments under grant PID2010119. L.F. is greatly in debt to Oleg Kochukhov for providing most of the tools used here for reducing and analysing the HARPSpol data. L.F. also thanks Gregg Wade, John Landstreet, and Coralie Neiner for fruitful discussions. The authors thank Andreas Irrgang, Ignacio Negueruela, Henk Spruit, Gautier Mathys, and Alexander Kholtygin for useful comments. S.H. and M.S. thank Thomas Szeifert for providing the pipeline for the FORS spectra extraction.


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A. Strugarek is a National Postdoctoral Fellow at the Canadian Institute of Theoretical Astrophysics, and acknowledges support from Canada’s Natural Sciences and Engineering Research Council. This work was supported by the ANR 2011 Blanc Toupies and the ERC project STARS2. We acknowledge access to supercomputers through GENCI (project 1623), Prace (8th call), and ComputeCanada infrastructures.


O B-Collaboration I-Collaboration I-Collaboration 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 B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization O O B-Location I-Location O B-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Location O B-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Location O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O B-Organization I-Organization I-Organization I-Organization B-Organization O B-Location 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 O B-Location O O O O O O O O O O O O O O B-Organization I-Organization I-Organization I-Organization O B-Location O O B-Organization I-Organization I-Organization I-Organization O B-Location O O O O O O O O O O O B-Telescope O B-URL O O B-Organization O O O O O O O O O B-Collaboration I-Collaboration I-Collaboration B-Organization O B-Location O O O O O O B-Organization O B-Grant O B-Grant O B-Observatory O B-Telescope O O B-Software O B-URL O B-Citation I-Citation I-Citation I-Citation I-Citation O B-Software O B-URL O B-Software O B-URL O B-Citation I-Citation I-Citation I-Citation O B-Software O B-URL O B-Citation I-Citation I-Citation I-Citation O B-Software O B-URL O B-Citation I-Citation I-Citation O B-Software B-Citation I-Citation O

The Fermi LAT Collaboration acknowledges generous ongoing support from a number of agencies and institutes that have supported both the development and the operation of the LAT, as well as scientific data analysis. These include the National Aeronautics and Space Administration and the Department of Energy in the United States; the Commissariat à l’Energie Atomique and the Centre National de la Recherche Scientifique/Institut National de Physique Nucléaire et de Physique des Particules in France; the Agenzia Spaziale Italiana and the Istituto Nazionale di Fisica Nucleare in Italy; the Ministry of Education, Culture, Sports, Science and Technology (MEXT), the High Energy Accelerator Research Organization (KEK), and the Japan Aerospace Exploration Agency (JAXA) in Japan; and the K. A. Wallenberg Foundation, the Swedish Research Council, and the Swedish National Space Board in Sweden. Additional support for science analysis during the operations phase is gratefully acknowledged from the Istituto Nazionale di Astrofisica in Italy and the Centre National d’Études Spatiales in France. We made use of data products based on observations obtained with Planck ( http://www.esa.int/Planck ), an ESA science mission with instruments and contributions directly funded by ESA Member States, NASA, and Canada. This work was partially funded by NASA grants NNX14AQ37G and NNH13ZDA001N. Facilities: Fermi , Planck . Software: Astropy ( http://www.astropy.org , Astropy Collaboration et al. 2013 ), Fermipy ( http://fermipy.readthedocs.io/ ), GALPROP ( http://galprop.stanford.edu/ , Vladimirov et al. 2011 ), HEALPix ( http://healpix.jpl.nasa.gov/ , Górski et al. 2005 ), ROOT ( http://root.cern.ch/ , Brun Rademakers 1997 ), matplotlib (Hunter 2007 ).


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This work is supported by the national science foundation of China (grant nos. 11025316 and 11121062), National Basic Research Program of China (973 Program) under grant no. 2009CB24901, the CAS/SAFEA International Partnership Program for Creative Research Teams (KJCX2-YW-T23) and China Postdoctoral Science Foundation (2013M531231).


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

Drake et al. 2009 ), retrieved from the Catalina Surveys Data Release 2. Between the WISE and NEOWISE-R epochs, the source dimmed by approximately 1 mag in both W1 and W2 , with further, lower amplitude variability observed between the epochs of each survey independently. In contrast, there is no strong optical variability observed by CRTS. This is consistent with both spectroscopic classifications, as in both an intermediate-type and a type 2 AGN, the optical emission is dominated by the host galaxy. The large drop in mid-IR fluxes suggests that the change in spectroscopic classification is most likely due to a decrease in accretion rate rather than a change in obscuration. Figure 10. Light curve of WISEA J142846.71+172353.1 in the optical from CRTS (green points) and in the WISE bands W1 (purple points) and W2 (red points). All magnitudes are shown in the AB system to limit the dynamic range of the vertical axis. For W1 and W2 , the small circles show the individual frame photometry in the AllWISE and NEOWISE-R surveys. The large circles show the median of each epoch. 5. Comparisons with Other Surveys As mentioned earlier, a number of AGN catalogs already exist in the literature that are similarly as large as ours. In this section, we compare with a number of them in order to characterize how they differ from our R90 and C75 catalogs as well as to assess what the relative completeness and biases are. We consider both mid-IR selected catalogs as well as catalogs selected in different wavelength ranges and, hence, affected by very different systematics. 5.1. Secrest et al. (<xref ref-type="bibr" rid="apjsaaa00abib79">2015</xref>) WISE AGN Catalog Recently, Secrest et al. ( 2015 ) presented an all-sky AGN catalog selected purely on their WISE colors, based on the selection criteria of Mateos et al. ( 2012 ). These criteria require a detection in the W3 band. A13 showed these criteria to be less reliable than the R90 criterion at faint W2 magnitudes, though they are equally reliable at brighter magnitudes. The trade-off is that the Mateos et al. ( 2012 ) selection criteria are more complete at faint W2 magnitudes than the R90 selection. As noted by Jarrett et al. ( 2011 ), requiring a detection in W3 can be particularly useful near the high survey coverage areas at the EPs, where W1 and W2 are confusion limited, and the lower source density W3 band provides robust photometry. However, the lower sensitivity of the W3 band restricts the AGN sample size created using the selection criteria of Mateos et al. ( 2012 ). Additionally, Secrest et al. ( 2015 ) required a 5 σ detection in all three WISE bands, creating a robust catalog at the cost of decreasing the number of sources selected. Indeed, the full catalog presented by Secrest et al. ( 2015 ) consists of 1,354,775 sources, and once we apply the same spatial filters as described in Section 3.1 , the catalog is reduced by 15% to 1,140,022 sources. This is roughly 25% of the sources in our R90


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the result of different masers flaring as the shock passes through the cluster, then we can estimate the distance between the flaring masers. If we assume the shock front is travelling at v ≈ 100 km s −1 = 10 7 cm s −1 and the time between flares is Δ T ≈ 1.5 × 10 7 s, we estimate the distance between the masers is Δ r ≈ 1.5 × 10 14 cm ≈ 11 AU. As already mentioned, the velocity extent of the water masers associated with W49N is ±200 km s −1 . Heckman Sullivan ( 1976 ) suggest that less than 10 per cent of the total integrated flux density across the entire spectrum is from these extreme-velocity masers. Also Goss et al. ( 1976 ) reported that the extreme-velocity maser features associated with W49N are weak relative to the low-velocity features. From the results of Very-long-baseline interferometry (VLBI) observations it has been inferred that the emission regions, where these extreme-velocity maser features exist, are more compact than those with intermediate (±20 km s −1 ) and velocities nearer to the local standard of rest velocity. The size of these maser clusters is less than 10 4 AU and they are located on the periphery of the intermediate-velocity maser features (Knowles et al. 1974 ). However, here we find that most of the water-maser flux density appears concentrated in the blue-shifted features and, in particular, the water maser at v = −81 km s −1 (Figs 2 and 3 ) is much stronger than the intermediate- and low-velocity masers. The extreme-velocity water masers associated with W49N have velocities that are more than 10 times faster than the isothermal speed of sound, ∼10 km s −1 , and concentrated in a region of only 0.1 pc in size. Larson ( 1973 ) showed that the accretion of matter onto a protostar has a velocity limited to a few times the speed of sound. Ergo, accretion cannot explain the appearance of extreme-velocity masers in W49N. Objects travelling at such extreme velocities would be dynamically unstable (Strel’nitskii Syunyaev 1972 ). Strel’nitskii Syunyaev ( 1972 ) proposed three possible acceleration mechanisms that may explain the extreme-velocity masers: acceleration by radiation pressure, stellar wind activity from hot massive stars, and by shock waves propagating through the maser space. Silk Burke ( 1974 ) suggested another acceleration mechanism: shock waves from supernova explosions. There is a supernova remnant near W49B; however, there is no non-thermal source in the vicinity of W49N. This may not eliminate it as a possible explanation, since supernovae less than 100 years old do not produce distinguishable radio emission (Spencer Burke 1973 ). Low-mass protostars in the T Tauri phase (Strom, Grasdalen Strom 1974 ) have extreme-velocity optical spectral features (∼100 km s −1 ) known as Herbig–Haro objects (Kuhi 1964 ). However, this model (Herbig 1974 ) cannot explain the asymmetrical nature of extreme-velocity water-maser features associated with W49N. Asymmetric models associated with the scattering of light


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along their main branch progenitor history (according to a given radius definition). In practice, applying this definition to merger trees created by almost any halo finder leads to erratic results due to spurious, temporary subhalo periods. In major mergers, for example, the host–subhalo relation can be ambiguous and switch between two halos, after which point the eventual host halo would be classified as a flyby halo. We follow the strategy of Mansfield Kravtsov ( 2020 ) to eliminate such cases: we do not count a halo as a flyby if its former host is no longer alive, if the former host is a subhalo of the halo in question, or if the former host’s mass is now smaller than that of the halo in question (all defined given the same radius and mass definition). In some cases, particularly for subhalo epochs at high redshift, the host may not be part of the merger trees because it never exceeded the necessary mass threshold. We also discard such events because the peak host mass was clearly smaller than the current mass of the halo in question. We emphasize that this definition of what constitutes a flyby halo is not unique. For example, we could consider future epochs to establish whether a flyby halo will eventually fall into its former host. Similarly, omitting any one of our exclusion criteria causes noticeable changes in the flyby fraction, raising the suspicion that f flyby is not a particularly well-defined quantity. Nevertheless, the relative differences in flyby fractions according to different radius definitions do remain similar, which is the focus of our work. Figure 4 shows the flyby fraction in the WMAP7 cosmology at z ≈ 0 and z = 2; the meaning of the lines is very similar to Figure 3 (see the Appendix for details). Regardless of the radius definition, mass variable, or redshift, f flyby asymptotes to zero at the highest masses and increases toward low masses. At the smallest masses we can probe, f flyby is still increasing so that we cannot put an upper bound on it. At fixed M 200m,bnd , f flyby varies between about 7% and 12% at the low-mass end. While this range sounds relatively modest, the relative fractions differ substantially between mass definitions, especially at intermediate masses. For instance, at M ≈ 10 12 h −1 M ⊙ , using R sp,90% leads to only 15% of the flyby halos found when using R 500c . When plotted as a function of peak mass, the fractions are shifted to higher values (middle column of Figure 4 ). In reverse, the shift means that flyby halos are more likely to have a high ratio of peak to current mass, meaning that they have lost mass at some point along their trajectory, which makes sense given that they had an encounter with a larger halo. Finally, the right column of Figure 4 shows the same results as a function of . In all cases, the relative differences between the radius definitions are similar. At higher redshift (bottom row), all curves are shifted to lower masses. Figure 4. Same as Figure 3 but for