O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength B-Wavelength O B-Wavelength I-Wavelength O O B-Wavelength O B-Wavelength I-Wavelength O O B-Wavelength B-Wavelength B-Wavelength B-Wavelength O B-Wavelength I-Wavelength O O O B-Wavelength O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Database I-Database I-Database I-Database O B-Database O B-Citation I-Citation I-Citation I-Citation O O O B-Dataset I-Dataset O B-Dataset O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O B-Person O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation 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 I-Citation 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 B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O B-Citation I-Citation I-Citation I-Citation 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 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 B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O B-Database O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject 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 B-CelestialRegion I-CelestialRegion O B-Citation I-Citation I-Citation I-Citation 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 B-CelestialObject I-CelestialObject O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O B-CelestialObject

during the first step and varied the abundances of the individual elements using the same masks. For a few elements, we extracted the lines of the particular element from the common masks and ran SME with these individual masks. The abundances of O, Sr, La, and Eu were derived from the spectral synthesis of individual lines not falling into the chosen SME spectral regions: the O i IR triplet λλ7771.94, 7774.16 and 7775.39 Å; Sr i λλ4607.33 and 7070.07 Å; La ii λλ5114.56, 5301.97, 5303.55, 5805.78 and 5808.32 Å; and Eu ii λλ6437.64 and 6645.11 Å. The carbon and nitrogen abundances were estimated by simultaneous fitting of the C 2 and CN molecular lines distributed in all regions covered by the SME analysis. The atomic parameters of the lines were extracted from the Vienna Atomic Line Database ( vald ; Kupka et al. 1999 ) using its 3rd release ( vald3 ; Ryabchikova et al. 2015 ). The atomic parameters for the C 2 and CN molecular lines were taken from Brooke et al. ( 2013 ) and the Kurucz's website (see below), respectively. The isotopic structure (IS) of Cu ii , Ba ii , and Eu ii was taken into account. For elements with odd isotopes the synthetic calculations included hyperfine splitting (hfs). Most of the data for isotopic and hyperfine splitting were obtained from the website of R. L. Kurucz, 2 who collected data and a bibliography for individual atomic species. In particular, the hyperfine structure constants for Na i were taken from Griffith et al. ( 1977 ), Tsekeris, Liao Gupta ( 1976 ), and Yei, Sieradzan Havey ( 1993 ); for Sc i and ii from Ertmer Hofer ( 1976 ) and Mansour et al. ( 1989 ); for V i from Childs et al. ( 1979 ), Palmeri et al. ( 1995 ), and Unkel et al. ( 1989 ); for Mn i, ii from Blackwell-Whitehead et al. ( 2005 ) and Holt, Scholl Rosner ( 1999 ); for Co i from Pickering ( 1996 ); for Cu i from Fischer, Hühnermann Kollath ( 1967 ) and Ney ( 1966 ); for Y i from Dinneen et al. ( 1991 ) and Villemoes et al. ( 1992 ); and for Ba i from Villemoes et al. ( 1993 ). All hfs data were collected in a new data base (Pakhomov et al. in preparation) and used by the internal vald programs for the hfs calculations. The average abundances for the final atmospheric model of TYC 8606-2025-1 are given in log (X/H) + 12 units in the second column of Table 3 . The third column of this table presents the current solar photospheric abundances (Asplund et al. 2009 ; Scott et al. 2015a , b ; Grevesse et al. 2015 ), while the fourth columns lists the elemental abundances derived for TYC 8606-2025-1 relative to the Sun. The last column of Table 3 provides information about different effects taken into account in the SME or spectral synthesis analyses. For clarity, the elemental abundances of TYC 8606-2025-1 relative to the Sun are shown in Fig. 2 , highlighting the overabundance of s-process elements, with the Ba abundance increased by a factor of ≈3 with respect to solar. Figure 2. Elemental abundances of TYC 8606-2025-1 relative to the Sun.


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

velocity. A transient current system is generated during a time corresponding to at least the travel time at the Alfvén velocity between the interaction site (e.g., the equator in the case of a satellite–magnetosphere interaction) and the planetary ionosphere. Because of the large size of the current system (several planetary radii in this example), this transient phase can last for a long time and may even be longer than the interaction time itself (see e.g. Neubauer 1980 ; Gurnett Goertz 1981 ; Saur et al. 2004 , for the Io-Jupiter case). In this case, electron acceleration is due to the parallel electric field associated to kinetic Alfvén waves above the ionosphere of the planet. This electric field is modulated at the Alfvén wave frequency and does not form electric potential drops, and hence does not directly form auroral cavities either (although cavities may slowly build up due to the excitation of ion acoustic waves, Hess et al. 2010a ; Matsuda et al. 2012 ). Thus, the electron density in the current system is the same as outside of it, with the cold component of the plasma remaining present, and the electron distribution is either a ring or a Kappa-like distribution ( Swift 2007 ; Hess et al. 2007b , 2010b ). 3.3. Unstable electron distributions Wave-particle resonance is reached when the Doppler-shifted angular frequency of the wave ω = 2 πf in the frame of the electron ( ω − k ∥ v r ∥ ) is equal to that of the gyration motion of resonant electrons (). Components k ∥ and v r ∥ are the parallel components (to the magnetic field lines) of the wave vector and of the velocity of the resonant particle, respectively. The electron cyclotron angular frequency is ω c = 2 πf c = eB / m e , with B being the magnetic field amplitude and e and m e the charge and mass of the electron. Finally, Γ r is the Lorentz factor associated with the resonant electron motion. The resonance condition therefore writes with In the weakly relativistic case ( v r c ), the resonance equation can be rewritten as: The resonance equation therefore forms a circle in the [ v ∥ , v ⊥ ] velocity space, whose centre v 0 , located on the v ∥ axis, is given by: which can be rewritten as where θ is the direction of the emission ( k cos θ = k ⋅ b = k ∥ ) and N = ck / ω is the refractive index value (which must be taken into account to reproduce the observations, as shown by Ray Hess 2008 ). The resonance condition can therefore be rewritten as Therefore, the resonance condition does not only define the angular frequency of the amplified wave ω = 2 πf , but also the direction of the emission θ . The resonance equation is under-constrained as there are two variables ( ω and θ ) to determine for a single equation. To solve it, one must consider another constraint brought by the CMI amplification equation, which states that the amplification occurs for positive gradients of the electron perpendicular velocity distribution around the resonant velocities v r ( Wu 1985 ). Given an


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

was derived as the distance between the two radii, where the normalized intensity profile becomes lower than (1 − 0.66 × (1 − Ī min )) ( Rosotti et al. 2016 ), where the outer of these two radii is defined as the CO wall ( R CO ). We defined the gap radius ( R gap ) as the midpoint between these two radii. Finally, the radius of the sub-mm ring ( R mm ) was defined as the radius of maximum intensity in the radial continuum intensity profile outside the gap radius. The distance of this ring from the gap is R mm − R gap . A visualization of these three radial parameters can be found in Fig. 6 . 4.2.1 Distance of the sub-mm ring from the gap radius The distance of the sub-mm ring from the gap radius (normalized to the gap radius itself) as a function of planet mass is presented in Fig. 11 . The plot shows a clear trend in which the distance of the ring increases with planet mass. The plot contains quantities derived for all eight simulations, and where the analyzed images were produced with three different beam sizes, specifically 0.03 ′′ , 0.08 ′′ , and 0.15 ′′ . The plot shows planet radii as derived from 13 CO. The same result holds for planet radii obtained from 12 CO or C 18 O, since for these three CO isotopologs, and for the beam sizes considered here (up to 0.15 ′′ ), the gap radius is always recovered with an accuracy 1.5 AU. The very small scatter of the ring distance for a given planet mass shows that this diagnostic does not depend on the disk viscosity, at least for the range of viscosities and planet masses analyzed here. Moreover, this diagnostic does not require the gap to be radially resolved; the only requirement is that for a given gap width and depth, the angular resolution is high enough to pick the presence of a gap. This is enforced by the rather small scatter with beam sizes. A linear fitting formula in log-log space can easily be retrieved, using all the points shown in Fig. 11 , leading to the simple relation Fig. 11 Distance of the sub-mm ring R mm from the gapradius R gap as a function of planet mass for all the simulations. The gap radius is estimated from the 13 CO J = 3-2 emission, whereas the ring radius is obtained from the maximum in sub-mm (850 μ m) continuum emission outside the gap radius. The ring distance is defined as the ring radius minus the gap radius. Circles, squares, and diamonds indicate quantities retrieved from images convolved with a 0.03 ′′ , 0.08 ′′ , and 0.15 ′′ beam, respectively, for sources located at a distance of 150 pc. The dashed green line shows a linear fit obtained for this relation in log–log space. The blue dashed-dotted line and brown dashed line indicate the fitting formula by Rosotti et al. (2016) obtained from hydro-simulations with 400 and 3000 planet orbits, respectively, where the gap location was inferred from synthetic scattered light maps. where A = −0.324 and B = 0.428. Interestingly, the relation between ring distance and planet mass is also well resembled by 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 B-Telescope 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 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 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 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 B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O 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 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

(blue) are different, but the deviations are smaller than the uncertainty, and therefore they are consistent enough to reveal the expansion rate of the ejecta. Fig. 8. Dimensionless expansion rate ( ζ ) vs. heliocentric distance ( D ) for the northern part (−5° λ 5°), middle part (−20° λ −5°), and southern part (−35° λ −20°) of the CME ejecta, respectively, between 18:09 UT and 22:49 UT on 3 April 2010, where λ is the latitude in the HEE coordinates. The red and blue crosses with the horizontal and vertical error bars correspond to STEREO-A/B, while the thick solid black line is the linear fitting of the data points. The dashed line shows the value of ζ equal to 1. For the northern and middle part of the CME, ζ keeps a high value of 0.87 ± 0.11 and 0.81 ± 0.09, respectively, at a distance between 25 R ⊙ and 55 R ⊙ (see Figs. 8 a and b). This suggests that the northern and middle parts of this CME maintained a nearly self-similar expansion but were still slowly pancaked. For the southern part of the CME, ζ is in the range of 0.39 ± 0.09 (see Fig. 8 c), which means a higher degree of flattening than in other parts. This is because the ambient solar wind was much slower than the CME, as shown in Fig. 6 b, which acted as an obstacle and prevented the CME from expanding. A similarly low expansion rate (0.48 ± 0.79) was reported by Gulisano et al. (2010) , but the difference is that the low expansion rate in their work is due to the compression by the faster background solar wind from the back. The question now is why the CME different latitudinal parts show different dimensionless expansion rates, or in broad terms, different dynamics. The CME on 3 April 2010 is not the only one with such diverse properties. Savani et al. (2010) have previously found a similar differentiated radial distortion event on 2007 November 14 in which an initially circular CME was observed to be distorted into an increasingly concave structure in STEREO-HI1 images due to the latitudinally varied solar wind velocity ahead. In many magnetohydrodynamic simulations, the fast and slow solar wind ahead of a fast CME could also lead to a similar highly distorted concave shape of the CME at a heliocentric distance larger than 20 R ⊙ (e.g., Manchester et al. 2004 ; Lugaz et al. 2005 ). Owens et al. (2017) further pointed out that CMEs with constant angular width cease to be coherent magnetohydrodynamic structures within 0.3 AU from the Sun because beyond a certain heliocentric distance, the information spreading speed (i.e., the Alfvén wave speed V A ) in magnetized plasma decreases less than the geometric separation speed of two points on the ejecta leading edge. Owens et al. (2017) suggested that different parts of a CME may be isolated from each other and the CME interacting with the background solar wind may be similar to dust cloud rather than a billiard ball as a whole. In their work, B , the magnetic field intensity within the CME, A , the CME cross-sectional area, and n


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The authors thank the European Research Council (ERC CoG No. 682275) for support of their work. D.G. thanks J.R. and J.J. for the hospitality and the outstanding cooperation.


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Support for this work was provided to R.B. by NASA through Hubble Fellowship grant #51354. The COS-Halos and COS-Dwarfs data sets were collected under program IDs 11598 and 12248, respectively (PI Tumlinson). The fellowship and observing programs were all awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS 5-26555.


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

our representations to this time span. Test calculations showed that our algorithm can lead to compact and precise representations for both degrees of freedom. With different procedure parameters, the resulting representations contain very different terms. This confirms the flexibility of our algorithm. In order to give representations as physical as possible, we resorted to the knowledge we have for the solution. Following Laskar et al. (2004) , we computed the fundamental frequencies of the secular solar system by applying the NAFF algorithm over time intervals of length 20 Myr for the proper modes , and 50 Myr for the proper modes 4 . From −35 Myr to 5 Myr with a step 0.1 Myr, we generated the samples of the fundamental frequencies ( g 1 , ..., g 8 , s 1 , ..., s 8 ) corresponding to these proper modes. The resulting nominal value of s 5 is about 0.00000015 arcsec yr −1 . The other frequency samples are shown in the panels of Fig. 9 , where the errors are estimated as the difference between the values of a frequency computed from the associated ephemeris and its quasi-periodic approximation. We also show in this figure the Chebyshev approximations of these fundamental frequencies. All of these Chebyshev approximations, the coefficients of which are listed in Table A.2 , were obtained by truncating those of degree 15. The truncation criterion was roughly that the discrepancy in a fundamental frequency should not induce an error in phase larger than 2 π /10 4 over several tens of million years. Fig. 9. Variations of major fundamental frequencies of the solar system over the time interval from −35 Myr to 5 Myr with origin at J2000. These frequencies (in arcsec yr −1 ) are computed by applying the NAFF algorithm to the proper modes of the secular solar system associated with major planets. The errors in the resulting frequency samples are estimated as the difference between the frequencies computed respectively from the original ephemeris and its quasi-periodic approximation. Also shown in this figure are the Chebyshev approximations of these varing fundamental frequencies (red curves), which are specified in Table A.2 . There are two important libration frequencies, r 1 = 0.251085 arcsec yr −1 of the resonance argument and r 2 = 0.117222 arcsec yr −1 of . To include them as additional fundamental frequencies, we expressed the main frequency as The d’Alembert characteristic, , was used to exclude non-physical frequency index vectors. To show to which degree our algorithm is practically useful, we discuss here the following two 100-term representations (R 100 for short), where with f = ( g 1 , ..., g 8 , s 1 , ..., s 8 , r 1 , r 2 ) and k = ( m 1 , ..., m 8 , n 1 , ..., n 8 , k 1 , k 2 ), the phase increment is associated with the main frequency ⟨ k , f ⟩. The way the residuals decrease with increasing number of representation terms in the two representation procedures of R 100 is shown in Fig. 10 . Fig. 10. Convergence property of the


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We thank the anonymous referee for detailed comments and suggestions. We would like to thank the members of the ENIGMA 14 14 http://enigma.physics.ucsb.edu/ group at the Max Planck Institute for Astronomy (MPIA) and UCSB for useful discussions and support. G.W. has been supported by the Deutsches Zentrum für Luft- und Raumfahrt (DLR) under contracts 50 OR 1317 and 50 OR 1512.


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Acknowledgements This work was supported by grant GA ČR 13-10589S. Access to computing and storage facilities owned by parties and projects contributing to the National Grid Infrastructure MetaCentrum provided under the programme “Projects of Large Research, Development, and Innovations Infrastructures” (CESNET LM2015042) is greatly appreciated. The Astronomical Institute Ondřejov is supported by the project RVO:67985815. This research made use of the IUE data derived from the INES database and of the HST data derived from the MAST database using the SPLAT package.


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We thank the anonymous referee for his/her comments. T.A. is supported by an ESA Research Fellowship in Space Science.


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this, for the remainder of this paper we will treat the plasma density within the loops as approximately uniform in space and constant in time, with a value of n e ≈ 10 11 cm −3 . Figure 6. Histogram of plasma electron number densities (with bin size ) for reliable pixels located within the bullet. 4.5. Cooling Time As noted in Section 4.2 , the loop emission appears first in Fe xxi and subsequently appears ∼11 minutes later in Si iv and O iv . The similar spatial location and appearance of the intensity features discussed above in Figure 3 suggests that the Si iv emission originates from the same evaporated plasma as the Fe xxi emission, which has subsequently cooled into the cooler spectral lines. Further, the nearly constant density in the loops (noted above) suggests that the cooling process is approximately isovolumetric. To estimate the cooling time, we recall from Aschwanden ( 2005 ) that the radiative and conductive cooling times (in seconds) are given, respectively, byandwhere T is the plasma temperature (in K), n e is the electron number density (in cm −3 ), and L is temperature gradient length scale (in cm); we have also defined the proton mass m p , the heat capacity at constant volume c v , the conductive coefficient κ 0 = 1.1 × 10 −6 , and the radiative loss function (Aschwanden 2005 ). For our purposes, we will approximate the temperature gradient length scale as the loop half-length. From inspection of Figure 1 (c) (which best shows the coronal loops), we find that the footpoint separation for the loops that cross the slit is about 217. As this observation was relatively close to disk center at the time of the flare, for the purposes of this study we will adopt a conversion factor of 730 km arcsec −1 to obtain a footpoint separation of ∼15.8 Mm and a loop half-length (assuming a elliptical loop with eccentricity e = 0.8; see Section 5 for our explanation of this choice) of ∼10.1 Mm. From Equations ( 2 ) and ( 3 ) we note that, for a 10.1 Mm loop that begins at ∼11 MK at density ∼10 11 cm −3 , the conductive cooling time is significantly shorter than the radiative cooling time and will dominate the energy losses. As noted above, thermal conduction will quickly eliminate any initial temperature inhomogeneities that were present in the loop, resulting in the loop possessing a uniform temperature structure. Later, by the time the loop plasma has cooled sufficiently for significant Si iv and O iv emission to appear, it is the radiative energy losses that dominate. To estimate a timescale for the overall cooling from the ∼10 MK to ∼80,000 K, we equate these two timescales and solve for T . This yields an approximate crossover temperature, T *, at which the two energy-loss processes are approximately equal, given byFor a loop as described above, this yields a crossover temperature of T * ≈ 5.7 MK, and substituting back into Equations ( 2 ) or ( 3 ) above gives a timescale for the loop cooling from the Fe xxi temperatures to Si iv


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

less concentrated (i.e. low n ) again. Note that error bars correspond to 1σ confidence intervals of the posterior distributions. 5 DISCUSSION 5.1 Morphological trends: two modes of star formation In nearby naked red nuggets stellar populations with different ages show different radial distributions (Fig. 4 ). In particular, we have shown how the effective radius remains almost constant up until ∼8 Gyr ago, but then it increases for younger ages. Note that individual points in Fig. 4 are not integrated values; i.e. they do not show how the galaxy would look at that time, but how the stars born at that time are distributed. The observed trend in R e , increasing with decreasing age of the stars, is effectively equivalent to the larger sizes of galaxies observed through bluer photometric bands (e.g. Evans 1994 ; Cunow 2001 ; Möllenhoff, Popescu Tuffs 2006 ; Kelvin et al. 2012 ) as younger stars will dominate the flux at shorter wavelengths. The peak in the Sérsic index evolution reveals a more complex scenario. The bottom panel in Fig. 4 suggests that a compaction phase takes place during the early live of red nuggets. This initial compaction is a well-known theoretical expectation, where gas is efficiently channelled towards the centre of dark matter haloes, leading to massive, gas-rich, compact, and star-forming discs (e.g. Gammie 2001 ; Dekel, Sari Ceverino 2009 ; Krumholz Burkert 2010 ; Cacciato, Dekel Genel 2012 ; Dekel et al. 2013 ; Dekel Burkert 2014 ; Zolotov et al. 2015 ; Dekel, Lapiner Dubois 2019 ). Observations of massive, compact and star-forming galaxies at high- z support this scenario (e.g. Barro et al. 2013 , 2014 , 2017 ; Huertas-Company et al. 2015 ; van Dokkum et al. 2015 ), but linking this population of galaxies to their more extended progenitors is not trivial. Our approach, tracing back in time the structural evolution of individual objects, shows that for our sample of galaxies an initial compaction took place, reaching a maximum ∼8 Gyr ago ( z ∼ 1). In order to explore the connection between SFR and compaction, we show in Fig. 5 the average evolution of sSFR–log Σ 1 in our sample, colour coded by the Sérsic index at that time (from Fig. 4 ). A clear connection can be seen between star formation activity and galaxy structure. The initial compaction takes place during the star-forming phase, as expected in a gas rich environment. Later, the actual quenching takes place when the compaction is maximal. This could be naturally explained if the gas brought towards the centre or the galaxy efficiently feeds the central supermassive black hole. The black hole would become therefore energetic enough to shut down star formation, likely leading to an inner bulge-like component (e.g. Silk Rees 1998 ; King 2003 ; Di Matteo et al. 2005 ; Sijacki et al. 2007 ; Silk 2013 ). Note also that the buildup of the central component is likely associated with a strong stellar feedback even, which would also favour the quenching process. The


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only by extending supernovae observations to high redshifts ( z ∼ 1) can a measurement of both Ω m, 0 and Ω Λ, 0 be obtained ( Goobar Perlmutter 1995 ). By contrast, through Eq. ( 10 ) we can estimate Ω Λ, 0 today, with no reference to Ω m, 0 , using the effect of Λ on galaxy-cluster scales rather than on the Universe as a whole, and based on low-redshift observations alone. We note that the independence of Eq. ( 10 ) from Ω m, 0 holds only at z = 0. Producing an estimate of Ω Λ, 0 using Eq. ( 10 ) requires measuring the present-day slope and intercept of Ω ta ( z ), ideally within a redshift range where Ω ta grows linearly with z . When data from higher redshifts are used, nonlinear terms will introduce some dependence between the Ω Λ, 0 and Ω m, 0 estimates, which, however, can be quantified based on Eq. ( 8 ). In practice, once measurements of Ω ta are obtained, a nonlinear fit will be performed on the predicted Ω ta ( z ) parameterized by Ω m, 0 and Ω Λ, 0 (see lower panel of Fig. 1 ), which will yield a measurement of both cosmological parameters (similar to the contours of Fig. 3 ). For the range z ≤ 0.3 considered in Sect. 3 , the deviation of Ω ta ( z ) from its linear approximation around z = 0 is 10% for any value of Ω Λ, 0 : small, but not subdominant compared to the statistical uncertainties that can be achieved using the large number of available clusters out to this distance. For this reason, the predicted shapes of the constraints from Ω ta ( z ) in Fig. 2 should be viewed as approximations. The technique discussed here depends on independent measurements of Ω ta in different structures and it does not require completeness of the sample of clusters used. For this reason, the same result can be obtained with measurements in only a fraction of the z ≤ 0.3 SDSS clusters, if the sample is optimized in terms of its redshift distribution. There is also margin for improvement in the accuracy of the measurement of Ω ta in individual clusters, for example, by applying quality cuts based on the absence of massive neighbors ( Korkidis et al. 2020 ), mass cuts ( Köhlinger et al. 2015 ), or galaxy-number cuts ( Karachentsev Nasonova 2010 ; Lee 2018 ). About 500 well-selected z 0.3 clusters, uniformly distributed over redshift, with Ω ta measured with 25% accuracy in each, would be enough to establish Ω Λ, 0 > 0 at the 5 σ level. In estimating the potential accuracy of constraints on Ω m, 0 and Ω Λ, 0 , we assumed all uncertainties to be statistical. However, before any statement on cosmology can be made based on measurements of Ω ta ( z ), systematic errors have to be carefully considered as well. For the proof-of-principle calculation of Sect. 2 we used the model of spherical collapse of a single structure in an otherwise uniform and isotropic background universe. Although Korkidis et al. (2020) have shown that the predictions of spherical collapse for Ω ta persist in N -body simulations, they have also reported a small systematic shift


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EC would like to thank the Lady Davis foundation for financial support and Julio Navarro for the fruitful comments and interesting discussions. JS acknowledges support from the Alexander von Humboldt foundation. YH has been partially supported by the Israel Science Foundation (1013/12). SG and YH acknowledge support from DFG under the grant GO563/21-1. GY thanks MINECO (Spain) for financial support under project grants AYA2012-31101 and FPA 2012-34694. SP is supported by the Russian Academy of Sciences programme P-41. AK is supported by the Ministerio de Economía y Competitividad (MINECO) in Spain through grant AYA2012-31101 as well as the Consolider-Ingenio 2010 Programme of the Spanish Ministerio de Ciencia e Innovación (MICINN) under grant MultiDark CSD2009-00064. He also acknowledges support from the Australian Research Council (ARC) grants DP130100117 and DP140100198. He further thanks Isaac Hayes for shaft. We thank the anonymous referee for the useful comments and remarks. We also thank the Red Española de Supercomputación for granting us computing time in the Marenostrum Supercomputer at the BSC-CNS where part of the analyses presented in this paper have been performed.


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We thank Andrew Hearin and Peter Behroozi for useful discussions and the referee for detailed comments. Funding for PRIMUS has been provided by NSF grants AST-0607701, 0908246, 0908442, and 0908354 and NASA grant 08-ADP08-0019. A.L.C. acknowledges support from NSF CAREER award AST-1055081. We use data from the DEEP2 survey, which was supported by NSF AST grants AST00-71048, AST00-71198, AST05-07428, AST05-07483, AST08-07630, and AST08-08133. This study makes use of data from the AEGIS Survey and in particular uses data from GALEX , Spitzer , CFHT, and the Keck and Magellan telescopes.


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

1, 2, and 3 are A10 , M12 , P17 , respectively; for M 2500 , the relations come from C11 , M12 , P17 , respectively. The agreement or disagreement of M HE with the other mass estimates also highlights a key procedural/mathematical difference between the methods of estimation: we calculate M HE at individual radii, which does not make use of knowledge of the pressure profile across all radii. However, the Y – M mass makes use of Y , a cumulative sum of spherically integrated pressure within R 500 (or R 2500 ). Similarly, M VT is fit across all pressure bins at radii larger than 100 kpc. Physically, we may expect M HE , M VT , and ( Y – M ) A10 (or ( Y – M ) C11 for M 2500 ) to be similar, as they directly or indirectly rely on the assumption of HE. The other Y – M relations, being calibrated to weak lensing or simulations, should encapsulate the total mass without regard to dynamical state. We expect mass estimates that assume HE underestimate the total mass due to the so-called hydrostatic mass bias, which itself encompasses several biases. The primary bias is not actually the HE assumption, but rather that the pressure gradient used only accounts for thermal pressure. Thus the lack of account for non-thermal pressure underestimates the mass by 10%–30% (see also Lau et al. 2013 ; Nelson et al. 2014a ; Biffi et al. 2016 ; Khatri Gaspari 2016 ; Hurier Angulo 2018 ; Ettori et al. 2019 ). 5.3. Residuals An underlying quadrupole is observed in our residual map (Figure 5 ). Modeling the ICM with the same centroid and an ellipsoidal ICM distribution results in very similar residual decrements and removes this quadrupole. Beyond ellipticity in the core of the cluster, the only observed SZ substructure is also in the core of the cluster. The corresponding integrated Y ( Y cyl ) due to the substructure (decrement −25 μ K) is 3.0 × 10 −7 h 70 2/3 Mpc 2 , whereas we find Y cyl ( R 500 ) = 7.3 × 10 −5 h 70 2/3 Mpc 2 for our NP fit; thus substructure accounts for only 0.5% of the SZ signal within θ 500 and is not a significant source of scatter in the mass estimates from Y – M relations for this cluster. Figure 5. Residual map (in μ K) of the Minkasi map with the SZ centroid marked by a red cross, the radio sources marked by tri_up (purple on white), and the Herschel 500 micron centroid by a blue cross; the beam is shown in the bottom left. The black contours are every 2 σ , excluding 0 ( σ = 12.8 μ K). As noted before, the central pressure profile and the central point-source amplitude are degenerate. In addition to the central radio source, a second, nearby radio point source is observed at 4.9 and 8.5 GHz (Giacintucci et al. 2014 ). We find that these two sources contribute to a mild increase in the uncertainties in the inner two pressure profile bins. The spatial coincidence of our residual SZ decrement and the radio minihalo (Figure 6 ) may be suggestive of an underlying link. It would be equally interesting if there is a link between the SZ


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Ia cluster rates with redshift has been used to explain the distribution of Fe in the ICM, as well as the SN Ia delay time distribution and respective predictions for single- versus double-degenerate progenitors (Sharon et al. 2010 ; Barbary et al. 2012 ; Friedmann Maoz 2018 ). Looking forward, assuming that the majority of short GRBs are linked to BNS merger progenitors, the true fraction of short GRBs that occur in galaxy clusters may similarly play a role in r -process element enrichment of the ICM and intracluster light (ICL). In addition, the large physical offsets of cluster short GRBs from their most probable hosts, relative to those associated with field galaxies, is of interest in understanding their origins. A natural explanation for the occurrence of short GRBs at tens of kiloparsecs away from their host galaxies, but within galaxy clusters, are the large systemic velocities that BNS systems may experience (Zevin et al. 2019 ), coupled with the older stellar population in clusters that contribute to longer delay times. Galaxy cluster studies have also shown that the ICL and BCGs compose ≈30%–50% of the cluster stellar mass (Zhang et al. 2019 ). In particular, the origins of the ICL and ICM have been linked to the disruption of dwarf galaxies (Gregg West 1998 ) or the tidal stripping of outer material from more typical galaxy cluster members (Gallagher et al. 1972 ; DeMaio et al. 2015 , 2018 ). Since 30% of short GRBs occur in the halos of their host galaxies (Fong Berger 2013 ; Zevin et al. 2019 ), beyond a few effective radii, the locations of these short GRBs are situated amid prime material for stripping to contribute to the ICL and ICM. 6. Conclusions We have presented identification of the early-type, quiescent host galaxy of GRB 161104A and a detailed investigation of the large-scale galaxy cluster environment surrounding GRB 161104A. We have also presented new modeling of 20 additional short GRB host galaxies, as well as the identification of the large-scale environment of GRB 090515 as a galaxy cluster. We summarize with the following conclusions: 1. The putative host of GRB 161104A is an early-type, quiescent galaxy at z = 0.793 ± 0.003. By jointly fitting the host photometry and spectroscopy from Magellan with Prospector , we determine a stellar mass of M ≈ 1.6 × 10 10 M ⊙ , mass-weighted age of t m ≈ 2.12 Gyr, metallicity of , dust extinction A V ≈ 0.08, and ongoing SFR ≈ 0.099 M ⊙ yr −1 . 2. Using deep optical and NIR observations, we determine that the host of GRB 161104A and most of the galaxies surrounding the XRT position are at similar redshifts of z ∼ 0.8. We confirm their membership in a cluster at a median redshift of z = 0.79 using DES cluster catalogs. We also show that GRB 090515 resides in a cluster at z ∼ 0.4. This makes GRB 161104A the fifth short GRB associated with a cluster and the highest-redshift short GRB known to be associated with a galaxy cluster. 3. We model the broadband SEDs of 20 additional


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This research has made use of the NASA Astronomical Data System (ADS), the NASA Extragalactic Database (NED) and is based on observations obtained with XMM–Newton , an ESA science mission with instruments and contributions directly funded by ESA Member States and NASA. This research is also based on observations with the NASA/UKSA/ASI mission Swift . AL, SV and JR acknowledge support from the UK STFC.


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Acknowledgements We thank the anonymous referee for useful comments on the manuscript. We thank Jeffrey Chan for useful advice on the determination of the survey depth. We acknowledge financial support from “Programme National de Cosmologie and Galaxies” (PNCG) funded by CNRS/INSU-IN2P3-INP, CEA and CNES, France, and from “Projet International de Coopération Scientifique” (PICS) with Canada funded by the CNRS, France. 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 and of the GOLDMine database ( http://goldmine.mib.infn.it/ ) ( Gavazzi et al. 2003b ). M. B. was supported by MINEDUC-UA projects, code ANT 1655 and ANT 1656. A. L. work was supported by the Sino-French LIA-Origin joint program. M. S. acknowledges support from the NSF grant 1714764 and the Chandra Award GO6-17111X. M. F. acknowledges support by the science and technology facilities council (grant number ST/P000541/1). E. W. P. acknowledges support from the National Natural Science Foundation of China through Grant No. 11573002. K. S. acknowledges support from the Natural Sciences and Engineering Research Council of Canada (NSERC).


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We would like to thank Genavie Spence for her work on data analysis, and Samar Safi-Harb for insightful discussions. We would also like to thank the referee for helpful comments. Support for this work was provided by the National Aeronautics and Space Administration through Chandra Award Number GO3-14072, issued by the Chandra X-ray Observatory Center, which is operated by the Smithsonian Astrophysical Observatory for and on behalf of the National Aeronautics Space Administration under contract NAS8-03060. Facilities: CXO , HESS .


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

and electron and ion heating, respectively. In the left-hand panels each individual histogram (denoted by line style and color) corresponds to a different type of heating function. This means, for example, that the solid blue histogram includes emission measure ratios for all values of t N , but for only those cases where heating events are evenly spaced (i.e., β = 0) and chosen from a power-law distribution of α = −1.5. The right panels show these same emission measure ratios, but now categorized by t N . For example, the solid red histogram includes emission measure ratios for every type of heating function (i.e., uniform, all α and all β ), but for only those runs where t N = 3000 s. Note that we choose to only show results for five values of t N for aesthetic purposes. Figure 8. Histograms of emission measure ratios EM( T hot )/EM( T cool ), where T hot = 10 6.942 K and T cool = 10 6.187 K, for all heating function types and heating frequencies for the single-fluid case. In both panels each histogram is normalized such that for each distribution P ( x ), and the bin widths are calculated using the Bayesian blocks method of Scargle et al. ( 2013 ). Left: emission measure ratios separated by heating function type for all heating frequencies, 250 ≤ t N ≤ 5000 s. Because there are too few (20) EM ratio measurements for the uniform case to construct a meaningful histogram, we denote the median of the uniform results with a vertical line, shown here in purple. Right: emission measure ratios separated by waiting time, t N . For aesthetic purposes, only five values of t N are shown, t N = 1000, 2000, 3000, 4000, 5000 s. Figure 9. Same as Figure 8 , but for the case where only the electrons are heated. Figure 10. Same as Figure 8 , but for the case where only the ions are heated. Considering first the left-hand panels, in the single-fluid model (Figure 8 ) the ratio is largely insensitive to α and is peaked sharply at ∼1–1.25 although the distribution peaks at slightly higher values for the β = 1 case (∼1.5). Note that the uniform heating results (whose median is denoted by the vertical purple line near ∼0.6) show emission measure ratios significantly less than those in the power-law cases, consistent with the reduced hot emission shown in Figure 3 . For electron heating (Figure 9 ) the ratio is again insensitive to α , but is narrower and falls off more quickly toward higher emission measure ratios. The β = 0 cases (for all α ) peak just above 0.5, with the β = 1 cases all peaking at slightly higher values just at or below 1. For ion heating (Figure 10 ), the β = 0 distributions peak at lower values compared to those with β = 1. Again the results are relatively insensitive to α . However, compared to the electron heating case, all of the distributions are much wider and peak at higher values, ∼1.75 for β = 0 and ∼2–2.5 for β = 1. Furthermore, in the β = 1 case, the α = −2.5 distribution peaks at lower values compared α = −1.5, −2.0. Turning to


O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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-Mission O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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

3 (d), and can be compared with the MHD results in panel (a). There are several similarities between the two solutions, although also some important distinctions. First, both solutions produce two equatorial coronal holes at roughly the same Carrington longitudes. Additionally, both solutions map to the same positive-polarity equatorial coronal hole for roughly the same intervals, spanning the first encounter. However, the size and shape of the equatorial holes are substantially different, with the PFSS solution producing much smaller areas, in spite of the fact that we set the source surface radius to 2.0 R S , which is typically lower than is usually used, and chosen to open coronal holes as much as possible. Moreover, prior to first encounter, the PFSS solution mapped to the negative-polarity southern polar coronal hole, and, thus, this transition would not be associated with a current sheet crossing. By flying PSP ’s trajectory through the heliospheric solution, we are able to recover the predicted plasma and magnetic field variables in situ. These are summarized in Figure 4 . The panels show, from top to bottom, radial speed, radial component of the magnetic field ( B r ), scaled B r , plasma number density ( N p ), scaled N p , and the heliocentric position of the spacecraft, as summarized by distance ( R ) and Carrington longitude. Focusing first on panels (a), (b), and (d), we note the following points. First, the speed remained approximately constant during the interval from first encounter to second encounter (∼525 km s −1 ). Second, the magnetic field switched from positive polarity to negative polarity (day of year: 302), and remained so for approximately three weeks. It also increased to a maximum negative value of −80 nT. Third, plasma density rose to almost 80 cm −3 ; however, the peak in density lagged the magnetic field peak by approximately one day. Figure 4. Time series of predicted (a) radial velocity ( v r ), (b) radial magnetic field ( B r ), (c) scaled B r , (d) plasma number density ( N p ), (e) scaled N p , and (f) location of spacecraft in terms of heliocentric distance (aqua) and Carrington longitude (magenta). In (c) and (e), the radial magnetic field and number density have been scaled by r 2 to account for the radial fall-off expected from flow into a spherical geometry. These variations, however, are misleading, in the sense that both the density and radial magnetic field fluctuations lie on top of the geometric expansion of the solar wind, which naturally produces a 1/ r 2 fall off with heliocentric distance, or, because the spacecraft is moving toward perihelion, an increase of r 2 . To address this, in panels (c) and (e) of Figure 4 , we have removed the 1/ r 2 variation and scaled the measurements to 1 au values. Both the values and variations are markedly different (compare panels (b) and (c) and panels (d) and (e)). Now, B r remains virtually flat (∼8 nT) for the entire duration of the encounter. Number


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

available for the recombination, resulting in the observed slight isotopic gradient with depth. Fig. 9 Left : D/H ratio measured in the labelled residue from a hot region (red), the bulk (green), and a cold region (blue). Black point indicates the D/H estimated from the IR ice mixture spectra prior to irradiation. Right : D/H histogram with dots corresponding to the hot (red), bulk (green), and cold (blue) D/H values. As a result, the total residue appears as a mixture between a poly-HCN component formed in the N 2 -CH 4 layers with some D due to migration and another layer formed within or at the vicinity of the D-rich ice layer. The use of a CD 4 layer was chosen to maximize the range of D/H variation in the residue. Formation of precursors at the direct vicinity of this layer induces the very high D/H ratios observed in this laboratory simulation, which are much larger than the values observed in UCAMMs or interplanetary organic matter in general. Strikingly, the spatial scale of the isotopic anomalies found in the residue is comparable to that observed in UCAMMs or IDPs ( Duprat et al. 2010 ; Messenger 2002 ). This suggests that the micro-scale isotopic heterogeneities observed in these organics may result from irradiation/condensation of thin ices layers with isotopic heterogeneities. In addition, these experiments show that energetic particle irradiation of D-rich ices preserves the bulk isotopic composition of initial ices and produces a residue which is an excellent candidate precursor compatible with the organic matter observed in UCAMMs. 5.1.2 Timescale The interaction of high energy ions from the GCR with the surface of objects orbiting at far heliocentric distances (in the Kuiper Belt or in the Oort cloud region) have been studied for more than a decade (e.g. Cooper et al. 1998 , 2003 ). These swift ions penetrate icy surfaces and deposit energy along their tracks. Ultraviolet photons may also contribute to the deposited energy, but they affect a much lower ice volume, as their penetration depth does not exceed a few to hundreds of nanometers. The dose deposited by cosmic rays at large heliocentric distances can be modelled using a functional form for the ions differential flux ( Shen et al. 2004 ). Including the respective Galactic abundance of elements and integrated over a wide energy range, Shen et al. (2004) give a mean deposited energy of about 6 × 10 −15 eV molecule −1 s −1 in ices, corresponding to an ionization rate of about 3 × 10 −17 s −1 . We irradiated our samples up to a total dose of 19 eV molecule −1 (≈4.0 × 10 23 eV cm −3 ), corresponding to about 100 million years of exposition to the GCR. This time is small compared to the solar system age and thus fully compatible with the astrophysical timescale of irradiation of small bodies after their formation. The irradiation period is therefore not time-constrained. It contrasts with the scenarios restricted to a hypothetical high irradiation episode occurring during


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

those in A2, but there are too few points in A3. Statistically, the difference in the slope between A2 and A3 is not significant, although, neither is that between A1 and A3. 5. DISCUSSION The galactic conformity is very marginal in the central area of the Virgo Cluster (A1), which seems to be similar to the result in WHL J085910.0+294957 from Lee et al. ( 2014 ). Since the analysis in Lee et al. ( 2014 ) was limited to the central area within 500 kpc radius, the two clusters (Virgo and WHL J085910.0+294957) commonly show only weak signals of small-scale conformity in their central areas (∼2 σ significance). On the other hand, the signal of small-scale conformity in A2 appears to be more obvious, showing significance close to 3 σ . In the case of the outermost area A3, as mentioned in the previous section, the signal is very weak due to the insufficient size of the sample. It is noted that the correlation coefficient in A3 is as large as 0.44, which is similar to the value in A2, while that in A1 is only 0.27. This is not a decisive evidence of small-scale conformity in A3, but it shows a possibility that a clearer signal of conformity may be detected if a larger sample is available. In this paper, however, because the uncertainty for the result in A3 is too large, we will focus on the results in A1 and A2. These results show that small-scale conformity is weak or somewhat ambiguous in the inner region (roughly within the virial radius), while it seems to be more obvious in the outer region of the Virgo Cluster. Note that, in Section 3.1 , the average standard deviation of color indices in faint companions around a given bright galaxy is 0.116. This value is only approximately one fourth of the distribution over the entire sample, which ranges from 0.25 to 0.70. This small value of the average standard deviation of color indices implies that the faint companion galaxies in a possible group tend to have similar properties rather than have randomly mixed properties, which is consistent with the expected small-scale conformity. Lee et al. ( 2014 ) suggested three scenarios regarding the origin of the small-scale galactic conformity in a cluster. The first is the “tidal dwarfs” scenario, in which the massive galaxies are partially torn out by tidal interactions with many other galaxies (harassment) or the cluster potential itself, forming many low-mass galaxies that may be the faint companions we observe. The properties of these low-mass galaxies must be similar to their host massive galaxy because they have been a single galaxy. If this scenario is correct, the conformity may be detected better in the inner region than in the outer region of a cluster, because the tidal force by a cluster is stronger in the inner region and more numerous massive galaxies exist in the inner region of a typical cluster, which may cause stronger harassment. However, this does not agree with our results that show an exactly opposite trend. Furthermore, the


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

from this indicator (Kewley Ellison 2008 ). At the time that Tüllmann et al. derived their metallicities, the tools for assessing which branch to adopt for this double-valued indicator were less robust. Extraplanar H ii regions in the two massive spirals NGC 3628 and NGC 4522 show modest or no abundance offsets relative to their disks. Our results for these galaxies are consistent with the conclusions reached by Stein et al. ( 2017 ). In particular, the nebula at z ≈ 1.4 from the midplane of NGC 4522 is projected onto extraplanar H i identified as matter being stripped from the disk via the ram pressure interaction with the intracluster medium of the Virgo cluster in the maps of Kenney et al. ( 2004 ). Stein et al. ( 2017 ) noted that the extraplanar H ii regions in NGC 3628 are projected onto an H i filament seen in the maps of Wilding et al. ( 1993 ) that has been identified as a tidal feature due to the interaction of this galaxy with its neighbor NGC 3627. Thus, the extraplanar H ii regions may plausibly arise in gas stripped from both of the galaxies, and they represent fundamentally different phenomena than the extraplanar H ii regions in NGC 55 and NGC 4013. The spiral galaxy NGC 4522 resides in the Virgo cluster; direct imaging shows spectacular evidence for ram-pressure-stripping of gas from the disk (Abramson Kenney 2014 ). The extraplanar H ii region measured in this galaxy is associated with this material that seems to clearly have an origin in the disk of that galaxy (Stein et al. 2017 ). We derive a joint abundance offset between the two disk H ii regions observed and the single extraplanar H ii region of = −0.03 ± 0.07 (68% confidence), consistent with no offset. This is as expected for material recently stripped from the disk. In the case of NGC 3628 (part of the Leo Triplet of galaxies), two extraplanar H ii regions are seen at z ≈ 3 kpc in close proximity to one another. Stein et al. note that these H ii regions are likely associated with a filament of H i at similar velocities that likely represents tidal material due to an interaction of NGC 3628 with its neighbor NGC 3627 (Wilding et al. 1993 ). There are hints that the filament may have arisen in the outer parts of NGC 3628 (Stein et al. 2017 ), but they seem inconclusive. Compared with the single disk H ii region measured in that galaxy, we find offsets of = −0.17 ± 0.10 and −0.05 ± 0.11 (68% confidence). If one assumes a single abundance offset is appropriate, the joint distribution implies = −0.12 ± 0.07. There is a hint that the abundances of these H ii regions may have a slightly lower abundance than the disk, but the hint is not robust at the 95% level. While the extraplanar regions tracing stripped material have abundances consistent with the disks of those galaxies, the extraplanar nebulae in the dwarf galaxy NGC 55 have higher abundances than the disk. The extraplanar H ii regions in NGC 55 seem to be connected with supershells produced by vigorous star


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

This work is funded by IBM, ASTRON, the Dutch Ministry of Economic Affairs and the Province of Drenthe. It is also part of the SKA-TSM project and supported by the Northern Netherlands Provinces Alliance (SNN), Koers Noord and the Province of Drenthe, and the European Community FP7 programme MIDPREP, Grant Agreement PIRSES-GA-2013-612599. This work is based upon research supported by the South African Research Chairs Initiative of the Department of Science and Technology and National Research Foundation. The authors would like to thank Jonathan Kenyon, Julien N. Girard and Gianni Bernardi for their valuable suggestions. The authors would also like to thank the anonymous reviewer for his constructive feedback.


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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 B-CelestialObject O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

anti-correlation between the expansion factor and the wind speed, which is in agreement with observations (see Wang Sheeley 1990 ; Wang 2016 ). At the source surface, the global anti-correlation is shown with a brownish line, and no correlation can be extracted for the point near minimum alone. Figure 9. Correlation between the wind speed and the expansion factor at three different heights in the corona: at the optimal source surface radius (on the left panel), at the sonic point (middle panel) and at (where the wind speed is computed for all panels). The colors indicate the parameter , so that orange colors indicate a very weak dipolar component (near maximum) and black colors indicate a strong dipolar component (near minimum). We see that the correlation changes with the cycle phase. The positive correlation between and the wind speed is the strongest at large heights, due to expansion beyond the sonic point. Nevertheless, higher in the corona, we can obtain two different regressions, for simulations whose parameter is over or below 50% of the maximum value () for the period considered. For near minimum cases, we get a positive correlation (shown by a black line) between the wind speed and the expansion factor starting at the sonic point. This correlation gets better as we go up in height at . Hence, for a simple, near-dipolar configuration of the solar magnetic field, where most of the open field lines come from the large polar coronal holes, the expansion around and beyond the sonic point operates a significant reorganization. Of course, beyond the source surface, the total area is conserved and both super and under radial expansion must compensate. As such, super (under) radial expansion increases (decreases) the wind speed, and the correlation between the terminal speed and the total expansion factor is reversed (see also Pinto Rouillard 2017 ). The additional acceleration provided only by the super radial expansion is maximum on field lines that cross local maxima of . This process must influence the acceleration of the fast solar wind, which is thought to occur at large distances from the Sun, where Alfvén waves dissipate. The correlation (shown by the orange line) stays globally negative for points near maximum of activity everywhere in the corona. In Figure 10 , we show the mass flux as a function of the expansion factor at the source surface ) at different heights in the corona. As shown by the blue dots, a large expansion below the source surface (associated with slow streams) increases the mass flux at the coronal base, through the velocity that is left free in the boundary. The mass flux at the surface spans over an order of magnitude, and the mass loading diminishes the energy per particle and the terminal speed. This explains the good correlation between the wind speed and the expansion factor at the source surface. However, near the source surface, the mass flux/expansion correlation is reversed with faster wind (low )


O O O O O O O O O O O O O O O O O O O O O O O O B-Organization I-Organization I-Organization B-Organization O B-Grant O B-Grant O B-Person B-Person O O O B-Organization O B-Grant O B-Grant I-Grant I-Grant I-Grant O B-Grant O O O O O O B-Software I-Software O O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility B-Organization I-Organization I-Organization I-Organization I-Organization O O O B-Grant I-Grant I-Grant O B-Person O O O O O O B-Archive I-Archive I-Archive I-Archive I-Archive I-Archive O O O O O O O O O O B-Software B-Citation I-Citation I-Citation I-Citation O B-Software O B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O

We wish to acknowledge the anonymous referee whose questions and comments improved the content and quality of the manuscript. This research was supported by National Science Foundation (NSF) grants AST-1109243 and AST-1615848 to M.L.N. J.H.W. acknowledges support from NSF grant AST-1333360 and Hubble Theory grants HST-AR-13895 and HST-AR-14326. The simulations were performed using the ENZO code on the Comet system at the San Diego Supercomputer Center, University of California, San Diego, with support from XRAC allocation MCA-TG98020N to M.L.N. This research has made use of NASA’s Astrophysics Data System Bibliographic Services. The majority of the analysis and plots were done with yt (Turk et al. 2011 ). ENZO and yt are developed by a large number of independent researchers from numerous institutions around the world. Their commitment to open science has helped make this work possible.


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

high SFRs of the present sample result in some of the X-ray luminosities being even greater than the erg s −1 value often used to identify sources as clear AGNs (e.g., Hornschemeier et al. 2001 ; Barger et al. 2002 ; Bauer et al. 2004 ; Szokoly et al. 2004 ) based on maximal local star-forming galaxy X-ray luminosities. Laird et al. ( 2010 ) similarly concluded that very high SFRs were responsible for the high X-ray luminosities of most of the sources in their submillimeter-selected sample in the same field. The AGN-classified sources in Figure 4 (b) show a much wider spread in , ranging from near quasar X-ray luminosities to nearly X-ray undetected sources. However, there are a number of sources with luminosities close to those of the star-forming galaxies, and there is clearly not a one-to-one correlation between our classifications and X-ray luminosity. 4. THE FIR-RADIO CORRELATION Radio power is often used along with the FIR-radio correlation as a measure of the SFR (e.g., Cram et al. 1998 ; Hopkins et al. 2003 ; Netzer et al. 2007 ; Mineo et al. 2014 ; Mushotzky et al. 2014 ). However, this could be risky when no other information is available on whether a source is AGN dominated or star-formation dominated. After all, it is well known that some local radio-quiet AGNs lie on the FIR-radio correlation (e.g., Condon 1992 ; Morić et al. 2010 ; Wong et al. 2016 ), even if it is not understood why. In Figure 5 , we plot (a) luminosity and (b) luminosity versus radio power for the radio sources with spectroscopic or photometric redshifts and erg s −1 Hz −1 . We use colors to denote the sources classified as star-forming galaxies (green circles), composites (blue circles), and AGNs (red circles). In (a), we also mark the sources that Chi et al. ( 2013 ) found to be AGNs using VLBI observations with surrounding black circles. All of these sources lie below the FIR-radio correlation. The star-forming galaxies in (a) have a mean , where we have computed the error with the jackknife resampling statistic; all lie within a multiplicative factor of three of the median value ( q = 2.35), which we denote by shading. Five AGNs and four composites also lie in the region. Figure 5. (a) luminosity and (b) luminosity vs. 20 cm power for the radio sources with spectroscopic or photometric redshifts and erg s −1 Hz −1 . Green circles denote star-forming galaxies, blue circles composites, and red circles AGNs. The central black line shows the median FIR-radio correlation of the star-forming galaxies, and the shading shows the region where we consider the sources to lie on the FIR-radio correlation (multiplicative factor of three of the central value). In (a), we mark the sources that Chi et al. ( 2013 ) found to be AGNs using VLBI observations with surrounding black circles. All of these sources lie below the FIR-radio correlation. In Figure 6 (a), we show the SEDs of 12 of the star-forming galaxies that lie on the FIR-radio correlation, as defined by the


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This research was supported by NASA under contracts JPL-1266313 at the University of Michigan, JPL-1345493 at the Southwest Research Institute, and JPL-1502225 at the University of Colorado. Rosetta is an ESA mission with contributions from its member states and NASA.


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that (except for initially small pitch angle cases) sin θ o ≫ 1/γ o or γ ∥ /γ o ≪ 1 and, from equation ( 17 ), we can write This implies that for τ = γ ∥ /η ≈ 1/(ηsin θ o ) we have γ ≈ 1.3/sin θ o . Thus, even if an electron had started with an almost infinite energy, it loses most of its kinetic energy in a time interval of the order of 1/η, reducing to perhaps a mildly relativistic status (for not too small an initial pitch angle). For instance, let us consider γ o = 10 3 and θ o = π/4; then γ ∥ ≈ 1/sin θ o = √2. Then from equation ( 17 ) or equation ( 19 ) we obtain, for τ = 1/η, γ = 2.3. In another example, taking γ o = 10 4 and θ o = π/3, for τ = 1/η we obtain γ ∥ ≈ 1/sin θ o = 2/√3 and γ = 1.7. Thus 1/η represents the characteristic decay time of synchrotron electrons over which they turn from ultrarelativistic into mildly relativistic ones. On a shorter time-scale, where γ is still highly relativistic, we can write Then we have Equation ( 21 ) is the same relation as in equation ( 3 ), which tells us that there is an upper energy cut-off for highly relativistic electrons in a synchrotron source, . Also, while τ 1/2 = 1/(ηsin 2 θ o γ o ) gives the half-lifetime of the synchrotron electrons (Kardashev 1962 ; Pacholczyk 1970 ; Rybicki Lightman 1979 ), τ ∼ 1/η gives the decay time over which radiating synchrotron electrons turn from ultrarelativistic into mildly relativistic ones. This follows from equation ( 17 ), which gives an exact formula true for all γ, including mildly relativistic electrons, and includes the effects of the pitch-angle changes implicitly. An explicit expression for the pitch-angle changes is derived in the next section. 4 PITCH ANGLE CHANGES Both β and θ in β ⊥ = β sin θ are functions of time. Therefore we can rewrite equation ( 13 ) as Also, since , we have Eliminating from equations ( 22 ) and ( 23 ), we obtain (also see Petrosian 1985 ) This is the relation for the rate of change of the pitch angle of a charge undergoing synchrotron radiative losses. The negative sign implies that the pitch angle decreases with time and aligns with the magnetic field. The rate of alignment is very slow for low pitch angles (θ ≈ 0) as well as for high pitch angles (θ ≈ π/2) and the highest rate of change of pitch angle is for θ = π/4. With the help of equation ( 16 ), we can integrate equation ( 24 ) to obtain In equation ( 25 ), θ θ o , because the pitch angle always reduces with time. There are many notable points. If θ o = π/2, then θ = π/2 also, because if the pitch angle is π/2 then the radiating electron always moves in a circular path in the plane perpendicular to the magnetic field. Also, if θ o = 0 then θ = 0 too, as there is no more reduction in pitch angle. For any 0 θ o π/2, θ → 0 as τ → ∞. For large γ o values, which can be used to estimate the change in pitch angle with time. For example, for, say, θ o = π/3 and θ = π/6, cosh (ητsin θ o ) = 3, which gives τ ≈ 2/η for this change in the pitch angle. Thus there are