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

We thank the referee for her/his useful comments. T.D.-S. would like to thank M. Wolfire, J. Pineda, C. Ferkinhoff, D. Brisbin, and N. Scoville for stimulating discussions about PDR physics and models. T.D.-S. acknowledges support from ALMA-CONICYT project 31130005 and FONDECYT regular project 1151239. G.C.P. was supported by a FONDECYT Postdoctoral Fellowship (no. 3150361). N.L. acknowledges support from NSFC grant no. 11673028. K.I. acknowledges support by the Spanish MINECO under grant AYA2016-76012-C3-1-P and MDM-2014-0369 of ICCUB (Unidad de Excelencia “María de Maeztu”). This work was carried out in part at the Jet Propulsion Laboratory, which is operated for NASA by the California Institute of Technology. This work is based on observations made with the Herschel Space Observatory , a European Space Agency Cornerstone Mission with science instruments provided by European-led Principal Investigator consortia and significant participation from NASA. The Spitzer Space Telescope is operated by the Jet Propulsion Laboratory, California Institute of Technology, under NASA contract 1407. 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 NASA’s Astrophysics Data System (ADS) abstract service. T.D.-S. wants to thank the NASA Herschel Science Center (NHSC), and in particular D. Shupe, for providing access to their computer cluster, with which most of the Herschel /PACS data sets were processed. Part of this work was carried out at the Aspen Center for Physics, which is supported by the National Science Foundation grant PHY-1066293.


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

), equation ( 37 ) becomes At far from the centre, the flow speed is almost constant, and this equation is solved to yield a solution and the flux roughly varies as . Similarly, at far from the centre, where B 0 is dominated and the flow speed is constant, equation ( 38 ) with equation ( 39 ) is also solved to yield an approximate solution: and the mean intensity roughly varies as at least on the main dependence. In Fig. 8 , the emergent intensities I + ( p, z out ) at the outer boundary R out normalized by I * are plotted as a function of the impact coordinate p normalized by R * . The normalized luminosity is Γ * = 5, the typical optical depth τ * = 3, the blackbody intensity B 0 / I * = 1, and the values of β out are 0.1, 0.3, 0.5 from top to bottom. In contrast to the scattering case (Fig. 4 ), the emergent intensity in the outer envelope is quite large. This is also because the source emissivity is uniformly distributed in the entire space in the isothermal wind. Similar to the relations obtained in the scattering case (Fig. 5 ), in this isothermal wind we can also the relations on the parameters, although we do not discuss them for simplicity. Finally, we should mention the opacity effect. In this isothermal wind, we assume that the absorption opacity κ 0 is constant. In the realistic case, the absorption opacity depends on the physical quantities, e.g. the free–free opacity is proportional to . Hence, it is in the isothermal case. In this case, the results are quite similar to the scattering case. The reason is because the density is concentrated in the centre and quickly decreases towards the outer envelope, and therefore, the emissivity is also concentrated in the central core. 5 CONCLUDING REMARKS In this paper, we have examined the radiatively driven relativistic spherical winds from the central object with mass M and luminosity L * under Newtonian gravity and special relativity, by numerically solving the relativistic radiative transfer equation and relativistic hydrodynamical ones for spherical geometry, simultaneously and consistently. Namely, using the initial trial velocity profile, we iteratively solved the relativistic formal solution of the transfer equation to obtain specific intensities and moment quantities in the inertial and comoving frames. Using the comoving flux obtained, we then solved the relativistic hydrodynamical equations to obtain the refined velocity profile, and the mass-loss rate as an eigenvalue. We repeat these double-iteration procedures until both the intensity and velocity converge. We found that the momentum-driven winds with scattering are quickly accelerated near the central luminous core to reach the terminal speed (Fig. 2 ), similar to the radiative outflows without gravity (Fukue 2017b ). The behaviour of moment quantities and emergent intensity is quite similar to the previous results (figs 3 and 4 in Fukue 2017b ). The results of numerical solutions are roughly fitted by a relation of , which


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

Rope System The evolution of a flux rope in a partially open bipolar background field as discussed in Sections 3.1 and 3.2 is summarized in Figure 3 , where h stands for the geometric parameter and λ the control parameter. There are two branches of equilibrium states for the flux rope: the lower branch ( D ∼ A in Figure 3 ) and the upper branch ( C ∼ B in Figure 3 ). The two branches are separated by the upward (from lower to upper branch) and downward (from upper to lower branch) catastrophes. The upward (downward) catastrophe is an irreversible but reproducible process, and it takes place when the solution jumps from the lower (upper) branch to the upper (lower) branch with increasing (decreasing) control parameter. Therefore, the two branches and the two catastrophes form a circulation, as shown by in Figure 3 (a). Figure 3. Schematic representations of the equilibrium solutions of the magnetic flux rope system: the profile of (a) a certain geometric parameter of the rope ( h ) and (b) the magnetic energy in the computational domain ( E ) vs. a certain control parameter of the system ( λ ). An upper catastrophe occurs at λ = λ u , whereas a downward catastrophe occurs at λ = λ d . The subscripts 1, 2, 3, and 4 label the state of the system immediately before and after the upward catastrophic point, and immediately before and after the downward catastrophic point, respectively. Although the jump of h is opposite in sign, the jump of E is always negative, implying a magnetic energy release for both of the two catastrophes. The evolution of magnetic energy (Figure 3 (b)) is also a circulation consisting of the two branches and two catastrophes, but it is quite different from that of the geometric parameter (Figure 3 (a)). At the lower branch (), magnetic energy is stored with increasing control parameter, whereas it is reduced during both upward and downward catastrophes, and during the shift of the solution along the upper branch from B to C as well. The constraint exerted by the background field on the flux rope is larger for solutions at the lower branch than that at the upper branch, so that the growth rate of the magnetic energy with λ , dE / dλ , is larger for lower-branch solutions than upper-branch solutions. Consequently, at the upward catastrophic point ( λ = λ u ), the magnetic energy of the upper-branch solution is smaller than that of the lower-branch solution ( E 2 E 1 ), whereas at the downward catastrophic point ( λ = λ d ), the opposite is true ( E 3 > E 4 ). This provides the essential energy condition under which the downward catastrophe could occur. 3.4. Mechanism of Magnetic Energy Release During the Catastrophe It is widely accepted that magnetic energy is released by magnetic reconnection in solar eruptive activities (Benz 2008 ; Shibata Magara 2011 ). However, magnetic reconnections are prohibited during our simulation (see Section 2 ). There should be other mechanisms of magnetic energy release in addition to magnetic


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

ones are for the same voids after cleaning. The vertical dotted lines mark the void radius in both cases. We also show the background density level (solid horizontal black line) and the underdensity threshold of equation ( 12 ) computed for the different redshifts (dashed horizontal black line) as a reference. It can be noticed that, while vide void limits reside close to the compensation wall and embed a density that approaches the background, our voids are, by construction, defined in much deeper regions of the density field. These observations have to be kept in mind to understand how the algorithm we apply to clean the cosmic void catalogues affects the void structure. Thanks to this modification, we can be confident that the voids we are using to measure the size function are as close as possible to the objects for which we are able to construct the theoretical model. Fig. 2 compares the measured and modelled void size functions, defined as the comoving number density of voids in logarithmic bins of effective radii, divided by the logarithmic extent of the bins. The four panels show the results at different redshifts. The different symbols in the upper part of each panel show the void size distributions measured in the simulation snapshots at different resolutions, while the gray shaded regions represent the model predictions. The model depends on two thresholds, the one of the shell-crossing, which is fixed at the value , corresponding to our choice of threshold in the void catalogue cleaning, and the overdensity one, δ c , used to account for the void-in-cloud effect. There is a persisting uncertainty on the definition of the latter, since it is not clear if this effect becomes relevant at turn-around (corresponding to a density contrast of δ c ≈ 1.06) or when the overdensity collapses (at a density contrast δ c ≈ 1.69). Since in realistic occurrences we do not expect the spatial resolution of tracers to be high enough to inspect the radii range in which the void size function becomes sensitive to the void-in-cloud effect, we leave the overdensity threshold free to vary in the range 1.06 ≤ δ c ≤ 1.69, thus the shaded region of Fig. 2 . Figure 2. Upper part of each panel: Void size function prediction (gray shaded region) at four different redshifts (different panels) compared to the distribution of cosmic voids after applying the cleaning method described in Section 2.2 (different markers correspond to different simulations, the values of L box in legend corresponding to those of Table 2 ). Lower part of each panel: Logarithmic differences between the measured distribution and the Vdn model prediction. For the largest simulation () we only have snapshots at z = 0 and z = 1, thus the corresponding abundances are missing from the z = 0.5 and z = 1.5 panels. We cut the distribution measured in each of the simulations at twice the m.i.s. of the given simulation box (see Table 2 ). To highlight the difference between the theoretical model


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attention paid to the cryogenic solids of astrochemical relevance, it should be possible to verify additivity given a sufficiently large and varied number of measurements on ices. For our initial study with amorphous ices, we have adopted the method of bond contributions and the values of Denbigh ( 1940 ) to calculate R M values. Bonds used (and contributions to R M in cm 3 mole −1 ) were as follows: C–H (1.69), C–C (1.25), O–H (1.73), C–O (1.51), C=O (3.38), C=C (4.16), and C≡C (6.4). For example, from the five bonds of CH 3 OH, one finds R M = 3 (1.69) + 1.73 + 1.51 = 8.31 cm 3 mole −1 . Figure 7 compares calculated R M values for our compounds to our measured values for amorphous ices. The correlation between the observed and computed values is obvious. Admittedly, the agreement largely reflects the fact that the bond contributions used are from liquids, for which Figure 4 (c) already shows reasonable agreement with our work, but nevertheless the linearity of Figure 7 for ices is gratifying. Figure 7. Molar refractions measured for amorphous ices compared to values computed with a bond-additivity approach. All values are taken from Table 3 . 4.3. Isomers and Molar Refractions Isomeric pairs of molecules in which the number of each type of bond is the same provide another check on our results. For example, since the isomers propionaldehyde (propanal) and acetone each have six C–H bonds, two C–C bonds, and one C=O bond then on the basis of additivity the two compounds should have about the same R M value. Table 4 shows that for this pair of compounds and five others, the R M values are within about 1 cm 3 mole −1 for our 15 K measurements on amorphous ices. A propagation-of-error analysis using Equation ( 6 ) leads to uncertainties in R M of about 0.1 cm 3 mole −1 for the smaller molecules we studied up to about 0.4 cm 3 mole −1 for the larger ones. This implies that the values in Table 4 for isomers are within or almost within experimental error for our ices. Table 4 Molar Refractions of Six Isomeric Pairs Note. a The units of R M are cm 3 mole −1 . Values of R M are from Table 3 . 4.4. Comparisons to Earlier Work The lack of published laboratory data corresponding to that in our Tables 2 and 3 makes it difficult to compare our results directly to those in the literature. To two decimal places, our n for amorphous methyl formate at 15 K is 1.32, near the 1.30 at 20 K reported by Modica Palumbo ( 2010 ). Our n for amorphous CH 3 OH at 15 K is 1.296, roughly the average of the 1.257 and 1.33 at 20 and 25 K, respectively, already published (Luna et al. 2018 ; Sciré et al. 2019 ). In an earlier paper we combined room-temperature data for methyl propionate and n for the corresponding amorphous ice to estimate ρ for amorphous methyl propionate at 16 K (Hudson Mullikin 2019 ). The estimated density value was 0.702 g cm −3 , in contrast to the measured value of 0.764 g cm −3 reported here. The densities we determined for amorphous (15 K) and


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We thank Wenfei Yu for helpful discussions. This work was supported by the National Basic Research Program of China (973 Program) under grants 2014CB845800 and 2015CB857004 , the National Natural Science Foundation of China under grants 11573023 , 11573009 , 11473022 , 11403074 , 11333004 , 11222328 , 11133005 and U1331101 , the Knowledge Innovation Program of the Chinese Academy of Sciences , the CAS Open Research Program of Key Laboratory for the Structure and Evolution of Celestial Objects under grant OP201503 , and the Fundamental Research Funds for the Central Universities under grants 20720140532 and 20720160024 .


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Hinode is a Japanese mission developed and launched by ISAS/JAXA, with NAOJ as domestic partner and NASA and STFC (United Kingdom) as international partners. It is operated by these agencies in cooperation with ESA and NSC (Norway). We extend our gratitude to Hirohisa Hara and Toshifumi Shimizu who made a large number of insightful comments with their expertise in spectroscopy. We are also thankful to the GCOE program for proofreading/editing assistance. Facility: Hinode


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( 2003 ), the polarization degree of the dust emission 6 is expected to be a few to 10 percent for a typical line of sight at an angle 45 o with respect to the magnetic field (Lee Draine 1985 ). Similar to the polarimetry of IR emission from AGN torus (e.g. Packham et al. 2007 ; Lopez-Rodriguez et al. 2013 ), future IR polarimetry of TDEs could potentially play an important role in studying the dust properties and magnetic field around non-AGN. 4.2 Possible refinements of the model A few other complexities, which are ignored in our simple model, can be taken into account in future works. (1) The heating by the scattered UV-optical photons and dust IR radiation could be included by considering the time delay and related absorption coefficient. In this way, a spectrum of dust IR emission can be calculated and compared with future observations. (2) The clumpiness of dusty clouds will affect the radiative transfer. Since every clump will have a bright (hot) side and a dark (cold) side, dust temperature distributions are different in clumpy and smooth environments (Nenkova et al. 2008 ). (3) In the radiative transfer model in Section 3 , a single dust radius of a = 0.1 μm is used, but the true interstellar grain population has a broad size distribution, extending from a few Å (PAH molecules) to about 0.2 μm (or even larger). Most mass is in the larger grains, with half-mass grain radius typically ∼ 0.1 μm (half of mass is in grains with radius above this value), and the smaller grains contribute most surface area and hence most UV extinction (e.g. Laor Draine 1993 ; Weingartner Draine 2001 ). However, at the same distance from the central source, smaller grains sublime faster than larger ones (mostly due to higher grain temperatures), so it is unclear which grain size contributes most IR emission. Also, the properties of graphite and silicate grains are sufficiently different that their sublimation radii could be separated. A systematic study of grain size distribution and chemical composition could be done in the future with dust continuum radiative transfer codes such as DUSTY 7 and HYPERION, 8 although the dynamical propagation of radiation coupled with dust sublimation requires some modification of the codes. 5 SUMMARY We consider the impact of the UV-optical radiation ( E rad ∼ 10 51 –10 52 erg) from TDEs on the circum-nuclear medium. If the medium is dusty, the UV-optical radiation energy will be absorbed by dust within ∼1 pc from the BH and re-radiated in the IR. We calculate the bolometric light-curve from a 1D radiative transfer model, taking into account the time-dependent heating, cooling and sublimation of dust grains. We show that the dust emission peaks at 3-10 μm and has typical luminosities between 10 42 and 10 43 erg s −1 (with sky covering factor f Ω ranging from 0.1 to 1). This is detectable by current generation of ground-based and space telescopes. In the near future, JWST will be able to perform photometric and


O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope B-Wavelength I-Wavelength O O O B-Instrument I-Instrument B-ObservationalTechniques I-ObservationalTechniques O O O O O O O O O O O O O O B-Instrument O O O B-Instrument O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 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 B-Telescope B-Wavelength I-Wavelength O O O O O O O O O B-Wavelength I-Wavelength O O O O B-Telescope I-Telescope I-Telescope I-Telescope I-Telescope I-Telescope I-Telescope I-Telescope I-Telescope I-Telescope I-Telescope B-Telescope B-Citation I-Citation I-Citation I-Citation O O O B-Mission 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 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-Telescope B-Wavelength I-Wavelength 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 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 B-Wavelength 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-CelestialRegion I-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

UT ( middle ), and 10:44:00 UT ( right ), denoted by dashed black lines in panel a . The radio contours are overlaid on AIA 211 Å running-difference images and LASCO C2 running-difference images that show the progression of the CME. Panel c : flux density spectra at NRH (red dots) and RSTN (orange triangles) frequencies at the same times as in panel b . The NRH flux densities were estimated over the northern source denoted Type IV in panel b . Flux density spectra were computed using the flux densities of the second component of the Type IV burst source at three times: 10:47, 10:55 and 11:03 UT, in Fig. 7 c. There is a clear power-law decrease at all times in Fig. 7 c, and this trend remains consistent from 10:47 UT until ∼11:05 UT (Fig. 6 ). After 11:05 UT, at 408–445 MHz, the Type IV radio source emission becomes faint and is comparable in brightness to active region and quiet-Sun emissions, as it drops below 10 sfu. At 10:47 UT, we estimate a negative spectral index of −1.6 that also includes contributions from a second source to the north in Fig. 7 b. After 10:49 UT (Fig. 4 c), the power-law decrease becomes clearer because only the Type IV source is present, and we estimate spectral indices of −3.3 at 10:49 UT and −2.3 at 11:03 UT. The second component of the Type IV burst shows an outward movement through time at all frequencies. The centroid locations of the second component of the Type IV burst are shown in Fig. 8 at 298 MHz. The centroids have been split into two periods: a stationary period at 10:44:20–10:49:20 (Fig. 8 a) and a moving period at 10:49:20–11:10:00 UT (Fig. 8 b). The centroids are superimposed on an AIA 171 Å running-difference image in Fig. 8 a and on a 174 Å running-difference image from the Sun Watcher using the Active Pixel System detector and Image Processing (SWAP; Berghmans et al. 2006 ) on board PROBA2 in Fig. 7 b. The SWAP image is used to show a larger field of view, and it has been limb-enhanced to show faint coronal loops beyond the solar limb. Fig. 8. Moving Type IV centroids at 298 MHz split into two phases: a stationary phase ( panel a ) and a moving phase ( panel b ). The centroids are overlaid on AIA 171 Å ( panel a ) and SWAP 174 Å ( panel b ) running-difference images that show the expansion of coronal loops in the negative x -direction behind the CME. The movement of the radio sources in panel b is coincident with the outward growth of the cusp-shaped loop system. The Type IV burst appears stationary for ∼5 min, but at this time, other sources are present. It is possible that various radio sources are superimposed, and we cannot accurately determine a centroid location. The moving period is characterised by the radio source moving away from the solar disc, and it starts after 10:49 UT, when the spectral index also shows a clear power-law decrease that remains consistent over time (Fig. 7 ). In both panels, the centroids are coincident with a cusp-shaped loop system that rises to increasing


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

for pairs of one-dimensional posteriors on the HL time of flight (Fig. 3 ). We see that with the HL network (solid lines), for 50percent of the skymaps the fidelity is above 0.8 for CBC-burst skymaps, and above 0.9 for LIB - cWB skymaps. The CBC-burst fidelity is a bit lower for the HLV network, while the LIB - cWB median fidelity stays close to 0.9. The two burst algorithms thus select the same sky ring very often. Strong correlation exists between the fidelity of the full skymap and that of the time of flight, implying that when slightly different rings are selected (low t HL fidelity) the overall fidelity is strongly reduced. Thus, the disagreement we found while comparing the full skymaps, Fig. 1 , is determined by both the placement of probability around the ring and the position of the ring itself, with the latter happening less frequently but having a large impact when present. Figure 3. The cumulative distribution of time-of-flight fidelity for pairs of algorithms in the HL (solid lines) and HLV (dashed lines) analyses. Fig. 4 shows the clear correlation between angular offsets and decreased fidelity using data from the HL network, as well as the corresponding values from GW150914 (stars), which fall within the scatter observed in simulations. We note that while there is quite a bit of scatter, the general trends seem to be independent of which algorithms are actually compared. This further suggests that low fidelity is driven by differences in the selected triangulation rings, because all algorithms produce triangulation rings. Figure 4. A scatter plot of the fidelity using the full skymap and the angular separation between triangulation rings. GW150914s values are shown as stars. We mentioned above that the GW150914 fidelity for LIB cWB was much lower than average. We can now understand why the LIB and cWB skymaps for GW150914 have support on different sky rings (see Abbott etal. 2016f ). They thus belong to this rarer class of reconstructed skymaps for which there is a significant drop of fidelity. Furthermore, one can compute the distribution of the angular distance between rings. We find that the distributions look unimodal, with mean smaller than 0.2 for all pairs of algorithms, and standard deviations in the range 2.54 (2.57) for the HL (HLV) network. 3.2 Searched area So far we have focused on the degree of similarity of skymaps, which was naturally prompted by the fact that burst and CBC skymaps were so different for GW150914. However, that is probably not the most relevant figure of merit to assess the chances of a successful EM follow-up. The fact that a skymap is larger or different might not lead to wasted telescope observation time as long as most of the probability is at the true position. In this section, we report the searched area found by the burst and CBC algorithms. We define the searched area as the amount of sky one needs to image, starting from the most likely skymap pixel and going down, until the true


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We would like to thank the referee for comments that have helped improve the paper. B.M., A.K., E.J.A., and F.B. acknowledge support from the Collaborative Research Centre 956, subproject A1, funded by the Deutsche Forschungsgemeinschaft (DFG). We would like to thank Carsten Kramer, Santiago Navarro, David John, Albrecht Sievers, and the entire IRAM Granada staff for their support during the instrument installation and observations. C.M.C. thanks the University of Texas at Austin College of Natural Sciences and NSF grants AST-1714528 and AST-1814034 for support. D.R. acknowledges support from the National Science Foundation under grant No. AST-1614213. Based on observations carried out under project Nos. 247-11, 227-12, 242-13, 117-14, and 232-15 with the IRAM 30 m telescope. IRAM is supported by INSU/CNRS (France), MPG (Germany), and IGN (Spain). This work was also supported through NSF ATI grants 1020981 and 1106284. Facility: IRAM: 30 m.


O O O O O B-Software O O O B-Software O O O O O O O O O O O O O B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O O O O O O O O O B-Software O O O O O O O O O O O O O O O O O O O B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O O O O O O O B-Software O O O O O O O O O B-Software O O O O O O B-Wavelength O O O O O O O B-Software O B-Software O O O O B-URL O O O O O 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 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 B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O O O O O O O O O O O O O O

times of the suboperations in chi2Image (left-hand panel) and chi2Profile (right-hand panel). Each vertical bar represents the smallest time across 20 calls of chi2* for a 4096 2 image. The CPU version is run with the optimal configuration of threads for this image size. CPU to GPU (Host to Device) copy operations are coloured in tones of blue. On the GPU, chi2Profile dramatically reduces the time spent in copying with respect to chi2Image and, even accounting for the extra-time needed to create the image, it manages to be 1.5 times faster than chi2Image . The important point of Fig. 7 is that all compute-intensive operations are faster on the GPU compared to the CPU, in particular the Fourier transform and the creation of the image. But the data transfers partly reduce this advantage, either because they are not needed at all on the CPU (for example the copy of read-only data like observations) or because the PCI express bus has a much reduced bandwidth and higher latency compared to accesses to the main CPU memory. For a large image, copying to the device actually takes longer than the FFT, that is why chi2Image is nearly 20 ms, or 50 per cent, slower than chi2Profile on the GPU, and that does not even account for the time needed to create the image on the CPU, which in this example takes another 20 ms. On the CPU, chi2Profile is only about 15 per cent faster than chi2Image . 7 CONCLUSIONS In this paper we have presented GALARIO, a GPU accelerated library for analysing radio interferometer observations. Distributed under the open source GNU LGPLv3, GALARIO is actively developed at http://github.com/mtazzari/galario and can be easily installed on machines with different configurations. Unlike single dishes, which directly measure the brightness of a source over a continuous region of the sky, radio interferometers measure its Fourier transform, sampling it at discrete locations and producing a collection of complex visibilities. The computational effort required to compare a model prediction to an observational data set of complex visibilities has increased dramatically in the last years due to the improved angular resolution and data rate of modern radio interferometers, which require larger matrix sizes and involve hundreds of thousands of visibility points. The process of computing synthetic visibilities from a model brightness involves several time-consuming matrix operations such as Fourier transforms, quadrant swaps, and interpolations. These operations have to be performed once for every likelihood evaluation, and the likelihood is called thousands or even a million times in the normal workflow required to fit a model to the data. In this context, GALARIO leverages the computing power of modern GPUs to accelerate the computation of the synthetic visibilities, thus reducing the overall execution time of the likelihood. For ease of use, GALARIO offers dedicated functions that produce directly the weighted χ 2 of the model for 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-CelestialObjectRegion B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O 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 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

are used in the heat transfer model (the simulation domain is shown in Fig. 4 ). At the surface, which is exposed to free space, radiation interaction with the external (solar) irradiation as well as the mutual radiative interaction of the various surface elements is taken into account. For the case that water ice resides on the whole or on parts of the free surface, sublimation causes a cooling effect, which has a feedback on the temperature evolution both on the surface and in the subsurface layers. The surface boundary condition is expressed as where A is the surface albedo (which is assumed negligible on the diffuse surface: A = 0), and F is the local irradiation intensity in [Wm −2 ]. The second term on the right-hand side describes the cooling effect caused by sublimation of water ice (if it is present at a particular position) and the third term is the heat flow towards the interior. The sublimation term is the product of the latent heat of sublimation ( L s = 2.778 × 10 6 J kg −1 ) and the mass-loss term caused by ice sublimation, where α is the accommodation coefficient, assumed to be α = 1 at icy spots where free sublimation prevails. For water ice, the vapour pressure constants have the values a = 3.56 × 10 12 Pa and b = 6141.7 K (Fanale and Salvail 1984 ). For the interior bottom and side boundaries of the computational domain (Fig. 4 ), adiabatic boundary conditions (vanishing heat flux) have been used. Figure 4. Illustration of the Abydos LAMsmall geometry (computation domain). The three surface points ( Ref , Top and Wall ) are indicated together with the vertical lines starting at these positions and directed towards the interior of the comet. The ‘active spot’ where water ice is exposed to the surface in some of our model computations is indicated in blue. In addition to the boundary conditions described above an initial temperature distribution over the whole domain of interest has to be defined, which can serve as a starting point for the time-dependent calculation. To obtain a reasonable estimate for such an initial temperature in the case of Comet 67P, we have consulted old papers published by Squyres, McKay Reynolds ( 1985 ) and by McKay, Squyres Reynolds ( 1986 ). These authors have calculated typical interior temperatures of cometary nuclei, in particular for short period Jupiter family comets. For such objects, they obtained with various spin axis orientations, comet core temperatures between 115 and 129 K (see table 1 of McKay et al. 1986 ). Therefore, in the absence of more detailed information and for reasons of simplicity we have assumed for the calculations presented in this paper, a constant initial temperature of 120 K throughout the domain of interest. 4 NUMERICAL IMPLEMENTATION 4.1 Model geometries and grids For the numerical implementation, we have developed the following procedure that turned out to be realistic w.r.t. the limitations in computer memory and computation time. It uses a combination of


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 O O B-CelestialObject O O O O O O O O O O O O O O B-CelestialObject 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 B-Citation I-Citation I-Citation I-Citation 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-Wavelength I-Wavelength I-Wavelength B-Telescope B-Instrument O O O O O O O B-Wavelength O B-Wavelength I-Wavelength I-Wavelength O O O O O O O O B-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O 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-Citation I-Citation I-Citation I-Citation O O O O O O O O O B-CelestialObject O O O O O O B-Software 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 B-CelestialObject O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation O O O O O O B-Citation I-Citation I-Citation I-Citation O O O B-Citation I-Citation I-Citation I-Citation O O B-Citation I-Citation I-Citation I-Citation O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O B-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O B-CelestialObjectRegion 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 B-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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

to calculate both the planetary and stellar spectra from 10 to 10 6 Å. The planetary, stellar, and orbital parameters used for the computation irradiated model of WASP-19b are summarised in Table 1 . 3 Results and discussion A thermal spectrum of WASP-19b from Anderson et al. (2010) , Anderson et al. (2013) , Gibson et al. (2010) , Burton et al. (2012) , Bean et al. (2013) , and Lendl et al. (2013) , is shown in Fig 1 . The planet-to-star flux ratio at 4.5 μ m is higher than the one at the 3.6 μ m Spitzer /IRAC channel. Moreover, at higher wavelengths, namely at 5.8 and 8.0 μ m, the planet-to-star flux ratio is even higher than 4.5 μ m. This clearly indicates the presence of excess emission in some photometric bands over others. Table 1 Planetary, stellar, and orbital parameters used in the model are from Butler et al. (2006) , Southworth et al. (2007) , Hebb et al. (2010) , and Hellier et al. (2011) . Fig. 1 Comparison of observed thermal spectra of WASP-19b with the modelled spectra calculated using PHOENIX (solid line) at different metallicities with an average dayside heat redistribution ( f = 0.5). The corresponding temperature-pressure profile is shown in the inset image (the grey shaded region corresponds to the structure inversion). The observed thermal spectrum of WASP-19b presented in this paper is adopted from Anderson et al. (2010 , 2013 ) (filled square and filled circles), Gibson et al. (2010) (filled upward triangle), Bean et al. (2013) (open circles), Burton et al. (2012) (open diamond), and Lendl et al. (2013) (filled downward triangles). The emission features at 4.5 μ m are due to CO in the presence of thermal inversion. The atmosphere of WASP-19b has been modelled with the parameters given in Table 1 using PHOENIX . It shows the presence of thermal inversion (see inset diagram, Fig. 1 ) and the equilibrium temperature is found to be ~ 2700 K. The comparison between observational data and our theoretical modelling (see Fig. 1 ) indicates that the excess planet-to-star flux ratio at 4.5 μ m is due to the presence of CO, which in turn is caused by thermal inversion that exists in the atmosphere. The corresponding pressure range, as probed by the secondary eclipse, is 10 −2 to 10 −3 bar. Previous studies of WASP-19b did not show any evidence of thermal inversion in its atmosphere ( Anderson et al. 2013 ; Bean et al. 2013 ). However, these studies were mainly based on retrieval techniques where abundances and thermal structure were fitted to the data. We investigate the effect of metallicity on the atmosphere of WASP-19b by changing all the heavy-elemental abundances by a factor of two. As shown by the inset image of Fig. 1 , the thermal inversion becomes stronger as the metallicity increases. This is mainly due to the temperature dependence of the thermal dissociation of various molecules, which changes the photospheric abundances ratio of TiO and H 2 O at different metallicities ( Parmentier et al. 2018 ). At higher


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ACKNOWLEDGEMENTS GAMA is a joint European-Australasian project based around a spectroscopic campaign using the AngloAustralian Telescope. The GAMA input catalogue is based on the data taken from the Sloan Digital Sky Survey and the UKIRT Infrared Deep Sky Survey. Complementary imaging of the GAMA regions is being obtained by a number of independent survey programs including GALEX MIS, VST KiDS, VISTA VIKING, WISE, Herschel -ATLAS, GMRT, and ASKAP providing UV to radio coverage. The VISTA VIKING data used in this paper are based on observations made with ESO Telescopes at the La Silla Paranal Observatory under programme ID 179.A-2004. GAMA is funded by the STFC (UK), the ARC (Australia), the AAO, and the participating institutions. The GAMA website is http://www.gama-survey.org/ . This work made the extensive use of topcat Taylor ( 2005 ) and stilts Taylor ( 2006 ) software packages, which are supported by an STFC grant to the University of Bristol.


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

such amplification is two-fold: partly due to a contribution from vortical flow and partly associated with the enhanced Rayleigh–Taylor instability. The spatial location of the maximum magnetic field is quite near the immediate downstream, indicating that amplified magnetic field could occur in the immediate vicinity of an SNR shock. It is not surprising to see the discrepancy between our results and the results given by Guo et al. ( 2012 ), which could be attributed to the time-dependent effective adiabatic index adopted here. Reproducing such a feature is pivotal, as X-ray thin rims seen in some SNRs, and their coincidence with the inferred shock locations have suggested an amplified magnetic field occurring at or within a short distance to forward shock. The maximum values of density and magnetic field are also obtained under this circumstance. Besides, we also trace the relative positions of contact discontinuity and the derived profiles are consistent with the observational results for two typical Ia SNRs: SN 1006 and Tycho. It is noteworthy that the lowest value of our derived profile in both cases is about 1.02 which seems at odds with suggested value ∼1.0 from X-ray observations (Warren et al. 2005 ; Cassam-Chenaï et al. 2007 , 2008 ; Miceli et al. 2009 ). Meanwhile, we also find no obvious ejecta protrusions which have been identified by several authors both in Tycho and SN 1006 irrespective of their elusive origin (Velázquez et al. 1998 ; Rakowski et al. 2011 ). The foregoing inconsistency indicates us that there may exist alternative scenarios which can further enhance Rayleigh–Taylor instability or even modify the initial ejecta profile, thus reducing the relative positions of contact discontinuity to match observations. As a recent attempt, Ferrand et al. ( 2019 ) have investigated the imprint of an asymmetrical SN Ia explosion on the resulting SNR morphology with a state-of-the-art scheme. The clumpy patterns are clearly seen in their synthetic thermal emission maps and the entire SNR morphology seems very realistic-looking (resembling the X-ray observational results of Tycho). Some Rayleigh–Taylor fingers are even protruding beyond the main forward shock, which is in accord with the findings in Orlando et al. ( 2012 ) where the ejecta clumping serves as an underlying assumption. Moreover, by postprocessing our data, a compared inspection with the case of no acceleration is given. The shock positions, radially averaged magnetic fields, time evolutions of the maximum magnetic field strength, and its relative locations in different circumstances have been depicted. The closer analysis reveals that when consider the turbulent background solely, the forward shock extends but the ripples seem to be less obvious. The maximum radially averaged magnetic field is smaller than the case with efficient acceleration by a factor of about 1.9. Similar conclusion can be drawn for the evolution of the maximum magnetic field strength. As for the


O O O O O O O O O O O O O O O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O B-Grant O O B-Organization I-Organization I-Organization I-Organization O O O B-Grant O O O B-Survey I-Survey I-Survey I-Survey I-Survey O O O O B-Organization I-Organization I-Organization I-Organization O B-Location B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O O B-Survey O O O O O O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility O O B-Organization I-Organization I-Organization O B-Survey O O B-URL O B-Survey O O O O B-Collaboration I-Collaboration I-Collaboration O O O O O O B-Collaboration I-Collaboration O O B-Collaboration I-Collaboration I-Collaboration O B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O B-Collaboration I-Collaboration I-Collaboration O B-Collaboration I-Collaboration I-Collaboration B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization B-Organization I-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization B-Organization I-Organization I-Organization B-Organization B-Location B-Organization I-Organization I-Organization B-Organization B-Location B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization B-Observatory I-Observatory I-Observatory I-Observatory I-Observatory B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization B-Observatory I-Observatory B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Observatory I-Observatory I-Observatory B-Collaboration I-Collaboration I-Collaboration I-Collaboration B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization O B-Organization I-Organization

We thank the referee for comments that helped to improve the presentation of this paper. This research was supported by the National Natural Science Foundation of China under grant No. 11903002 and the Guangxi Natural Science Foundation under grant No. 2017GXNSFAA198348. Funding for the Sloan Digital Sky Survey IV was provided by the Alfred P. Sloan Foundation, the U.S. Department of Energy Office of Science, and the Participating Institutions. SDSS-IV acknowledges support and resources from the Center for High-Performance Computing at the University of Utah. The SDSS website is http://www.sdss.org/ . SDSS-IV is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS Collaboration including the Brazilian Participation Group, the Carnegie Institution for Science, Carnegie Mellon University, the Chilean Participation Group, the French Participation Group, Harvard-Smithsonian Center for Astrophysics, Instituto de Astrofísica de Canarias, The Johns Hopkins University, Kavli Institute for the Physics and Mathematics of the Universe (IPMU)/University of Tokyo, Lawrence Berkeley National Laboratory, Leibniz Institut für Astrophysik Potsdam (AIP), Max-Planck-Institut für Astronomie (MPIA Heidelberg), Max-Planck-Institut für Astrophysik (MPA Garching), Max Planck-Institut für Extraterrestrische Physik (MPE), National Astronomical Observatories of China, New Mexico State University, New York University, University of Notre Dame, Observatário Nacional/MCTI, The Ohio State University, Pennsylvania State University, Shanghai Astronomical Observatory, United Kingdom Participation Group, Universidad Nacional Autónoma de México, University of Arizona, University of Colorado Boulder, University of Oxford, University of Portsmouth, University of Utah, University of Virginia, University of Washington, University of Wisconsin, Vanderbilt University, and Yale University.


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We thank our anonymous referee for helpful comments. This study was financed by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior – Brasil (CAPES) – Finance Code 001. Part of this research is suported by INCT do e-Universo, Brazil (CNPQ grants 465376/2014-2). Based in part on observations made at the Laboratório Nacional de Astrofísica (LNA), Itajubá-MG, Brazil. BM thanks the CAPES/Cofecub-394/2016-05 grant. G.B.R. acknowledges the support of the CAPES and FAPERJ/PAPDRJ (E26/203.173/2016) grants. ARGJ thanks FAPESP proc. 2018/11239-8. MA thanks CNPq (Grants 427700/2018-3, 310683/2017-3 and 473002/2013-2) and FAPERJ (Grant E-26/111.488/2013). VL’s research was supported by an appointment to the NASA Postdoctoral Program at the NASA Jet Propulsion Laboratory, California Institute of Technology, administered by Universities Space Research Association under contract with NASA. RVM acknowledges the grants CNPq-306885/2013, CAPES/Cofecub-2506/2015, FAPERJ/PAPDRJ-45/2013 and FAPERJ/CNE/05-2015. JIBC acknowledges CNPq grant 308150/2016-3. FBR acknowledges CNPq support, proc. 309578/2017-5. RS and OCW acknowledge Fapesp proc. 2016/24561-0, CNPq proc. 312813/2013-9 and 305737/2015-5.


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O B-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 B-Tag O O O O O O B-Wavelength I-Wavelength O O B-Wavelength I-Wavelength O O O O O O O O O B-Wavelength I-Wavelength 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-CelestialObject 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 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 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 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 B-Formula I-Formula I-Formula I-Formula O O O B-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 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 B-Wavelength I-Wavelength I-Wavelength I-Wavelength O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength 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 B-Wavelength I-Wavelength I-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

modelled continuum. Star formation history was modelled by a short burst of star-forming galaxies with age less than 10 Myr, which represents the young stellar population in addition to continuous star formation responsible for older stars with ages t 1 and t 2 ( t 1 t 2 ) randomly varied in the range between 10 Myr and 15 Gyr. The derived age t 2 of the oldest stars is 10 Gyr in most of galaxies. The relation between [Mg/Ne] and stellar mass is shown in Fig. 4 . The linear regression to all Mg II galaxies is shown by a solid blue line and average values in bins of stellar masses by solid green lines. A slight slope is seen, meaning that more massive galaxies have higher magnesium depletion. In particular, [Mg/Ne] ≃ –0.15 for low-mass galaxies with M ⋆ ≃ 3 × 10 7 M ⊙ and ≃–0.35 for high-mass galaxies with M ⋆ ≃ 3 × 10 10 M ⊙ . A similar behaviour is seen for the magnesium depletion, which increases with metallicity (Figs. 1 c and d). Fig. 4. [Mg/Ne] – mass of stellar population log( M ⋆ / M ⊙ ) relation. Symbols are as in Fig. 1 . A linear regression to all Mg II galaxies is shown by the solid blue line, and the average values in bins of stellar masses are represented by solid green lines. 4.2. Dependence of [Mg/Ne] on O32 O 32 = [O III ] λ 5007/[O II ] λ 3727 is an important parameter to search for galaxies with Lyman continuum (LyC) escaping radiation. The parameter O 32 is usually used for the selection of galaxy candidates able to ionise the intergalactic medium, which is interesting in connection with the problem of the reionisation of the Universe at redshifts z ∼ 5–10. The dependence of [Mg/Ne] on O 32 is shown in Fig. 5 . There is very large scatter of [Mg/Ne] for Mg II galaxies with O 32 ∼ 0–3 (Fig. 5 a). Nevertheless, in galaxies with O 32 below 3–4 [Mg/Ne] is constant, but at higher O 32 [Mg/Ne] increases with increasing O 32 . Linear regression to all the galaxies (purple line) and average values in bins of O 32 (blue lines) demonstrate an increase in [Mg/Ne] with increasing O 32 , which depends on the ionisation parameter. Moreover, the galaxies with O 32 > 5 are above the average value of [Mg/Ne] (long solid red and dashed black lines). We note that almost all galaxies with O 32 > 5 have low masses (log( M ⋆ / M ⊙ ) 9.0), low metallicities (12 + log O/H 8) and high EW(H β ) > 150 Å (dots inside green circles). In Fig. 5 b we only show galaxies with abundances derived by the direct T e method and accuracies better than 40% (more than 2.5 σ ) for the weak but important Mg II λ 2797Å and [O III ] λ 4363Å emission lines. Galaxies with flux ratios I [O III ] λ 4959/ I (H β ) less than 0.7 were also excluded to ensure that we use only high-excitation galaxies whose [O III ] λ 4363Å emission lines are reliably detected. The trend of increasing [Mg/Ne] with increasing O 32 becomes even more evident (purple line in Fig. 5 b). Fig. 5. Panel a : [Mg/Ne] – O 32 relations for all Mg II emitters depicted as in Fig. 1 . The dots


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

4 Power distributions for phase fractions in different H I phases at v LSR = 0 km s −1 . Top left : WNM; top right : LNM; bottom left : CNM. Black lines show all-sky data, red lines are for | b | > 20°. Spectral indices are derived at 10 l 100 as indicated by the vertical lines. Bottom right : uncertainties from the Gaussian decomposition (black) and ringing caused by apodization (red). Fig. 5 Velocity distribution of average H I phase fractions for CNM, LNM, and WNM using unpublished data from Kalberla Haud (2018) . Next we consider the power spectra derived from the Gaussian components of different H I phases. Figures 8 and 9 show still local minima for the CNM spectral indices, however the spectral indices for the other phases are now mostly anti-correlated; the WNM has a particularly smooth distribution. Spectral indices derived from power spectra of the total observed H I also show smooth changes. For high latitudes ( Fig. 9 , red) we find a steepening in anti-correlation to the WNM, but with local minima that are affected by the CNM and LNM. In the all-sky case ( Fig. 8 , black) we observe a smooth trend, but influences from the CNM and LNM are weak. Velocity dependences for the spectral indices have been observed before ( Kalberla Kerp 2016 ; Kalberla et al. 2017 ). Recently, Choudhuri Roy (2019) have presented data that show a steepening of the spectral indices at velocities that are considered to be representative for the CNM. Spectral indices for 13 CO (2–1) and 12 CO (3–2) channel maps in the Perseus cloud were observed by Sun et al. (2006) with a steepening of the indices that can be described asan average structure of the index spectrum similar to the line profile. Numerical studies of the condensation of WNM into CNM structures caused by turbulence and thermal instabilities were conducted by Saury et al. (2014) . They found that turbulence plays a key role in the structure of the cold medium; it can induce the formation of CNM when the WNM is pressurized and put it in a thermally unstable state. They found evidence for subsonic turbulence with a shallow power index γ ~ −2.4. Recent high resolution simulations by Wareing et al. (2019) have shown that the thermal instability dynamically can form sheets and filaments on typical scales of 0.1–0.3 pc, explaining that as the structure grows in the simulation, the density power spectrum rapidly rises and steepens. Wareing et al. (2019 ; Fig. 10) derive γ ~ −3, but the steepening is most prominent on scales below 1 pc. Fig. 6 All-sky velocity dependences of spectral indices for H I phase fractions. The thin lines represent the scatter for one-sigma uncertainties. Fig. 7 High latitude velocity dependences of spectral indices for H I phase fractions. The thin lines represent the scatter for one-sigma uncertainties. The preferred width of the filaments in the range 0.1–0.3 pc is consistent with unresolved cold small-scale structures observed by Clark et al. (2014) and Kalberla et al.


O O O O O O O O O O O O O O O O O O O O O O O O B-Organization I-Organization I-Organization I-Organization B-Organization B-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship O O O O O O B-Event I-Event I-Event O O B-Organization I-Organization I-Organization B-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization O O O O O B-Organization I-Organization B-Person O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O B-Grant O B-Grant O O O O O O O O O B-Organization I-Organization I-Organization B-Organization O B-Telescope O B-URL O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization B-URL O O O O O O O O O O B-Observatory I-Observatory O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O O O O B-Organization O O O O B-Collaboration I-Collaboration O B-Organization I-Organization I-Organization B-Location I-Location B-Organization I-Organization I-Organization B-Location B-Organization B-Location B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Location B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Location O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Location I-Location I-Location O O O O O O O O O B-Observatory I-Observatory I-Observatory O B-Observatory O B-Grant O O O O O O O O O O O B-Instrument I-Instrument I-Instrument I-Instrument I-Instrument I-Instrument B-Instrument B-Instrument O O O O B-Instrument I-Instrument I-Instrument I-Instrument O O B-Organization I-Organization I-Organization I-Organization B-Instrument O O O O B-Organization I-Organization I-Organization O B-Person I-Person I-Person B-Person I-Person B-Person I-Person I-Person O B-Person I-Person O O O O O O O B-Archive I-Archive I-Archive O O O O O B-Organization I-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Grant I-Grant I-Grant O O O O O O O B-Database I-Database I-Database O O B-Database I-Database I-Database O B-URL O O O O O B-Database I-Database I-Database O B-URL O O O O O O O O O B-Survey I-Survey I-Survey I-Survey I-Survey O O O O O O O B-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization O O O O O O O B-Database O O O B-Organization B-Location I-Location


O O O O O O O O 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 B-Wavelength O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O B-Wavelength O O O O O O O B-Instrument 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-Instrument O O O O O O O O B-Dataset O O O O O O O O O O O O O O O O O B-Wavelength O O O B-Instrument O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Tag B-Dataset O O O O O O O O O B-Dataset B-CelestialRegion I-CelestialRegion I-CelestialRegion O O B-Instrument O O O O O B-Wavelength I-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-CelestialRegion I-CelestialRegion I-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 B-Wavelength O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength 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 B-Wavelength I-Wavelength O O O O O O

needed, the sampling has been done over 10 6 randomized maps. To determine the random cases, we explored three different procedures: (1) randomization of the γ-ray sample coordinates by drawing an equal number of positions homogeneously distributed over the sky, making sure that only random sources with b II values in the same range as the original γ-ray catalogue are considered. This leaves untouched the IceCube positions, which are known to be not uniformly distributed, but might lose any large-scale structure present in the γ-ray sample; (2) to at least partially obviate this, we have also randomized only the γ-ray sample right ascensions; (3) randomization of the IceCube right ascensions, making sure that only random sources that can be associated with the γ-ray catalogue within the relevant error circles are considered (for example, a | b II | 10° IceCube random source can still be associated with a 2WHSP object provided it has a large enough error radius). This preserves any large-scale structure present in the γ-ray sample plus the IceCube declinations. However, the requirement above does not conserve the total area sampled by the IceCube error circles, resulting in a biased test statistics. As a result, we used procedures (1) and (2), conservatively taking as our best estimate of the probability of random association the largest of the two probabilities. Since our three catalogues are somewhat overlapping, in particular at large fluxes and FoM (see Section 2.2.2 ), the number of bins per scan is 10, and the points are not independent, we do not correct the probabilities for the ‘look elsewhere effect’ (which would take into account the artificial p-value reduction due to the application of multiple tests). We have also fixed the catalogues studied at the beginning of this work as well as the bins in flux and FoM used for the scans. 4 RESULTS 4.1 <italic>Fermi</italic> 2FHL Fig. 1 shows the chance probability of association of 2FHL high Galactic latitude sources with IceCube events for objects having F (>50 GeV) larger than the value on the x -axis and a randomization of the γ-ray sample on right ascension, which gives the most conservative result. Red squares indicate the whole high Galactic latitude sample, black circles denote HBL only, and blue triangles represent non-HBL sources. The numbers give the observed (above the points) and average random value (below the points) of N ν for HBL. Fig. 1 shows the following: for the whole sample and for HBL the chance probability is strongly dependent on γ-ray flux, with an anti-correlation between probability and flux up to F (>50 GeV) ∼ 1.8 × 10 −11 photon cm −2 s −1 with a p-value 10 −4 according to a Spearman test. We attribute the turn-over in p-value at very large γ-ray fluxes to small number statistics; p-values ∼1.8 per cent are reached for F ( > 50 GeV) ≳ 1.8 × 10 − 11 photon cm −2 s −1 for the whole sample; p-values ∼0.4 per cent are reached for F ( > 50 GeV) ≳ 1.8 × 10 − 11


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This work is based on research supported in part by the National Research Foundation (NRF) of South Africa (grant no. 106049). Opinions expressed and conclusions arrived at are those of the authors and are not necessarily to be attributed to the NRF. N.D. was supported under grant no. 50OC1302 by the Federal Ministry of Economics and Technology on the basis of a decision by the German Bundestag. This work was carried out within the framework of the bilateral BMBF-NRF-project “Astrohel” (01DG15009) funded by the Bundesministerium für Bildung und Forschung and the NRF. The responsibility of the contents of this work is with the authors.


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

scenario is that the gas and ice chemically evolve while accreting onto the disk ( Visser et al. 2009 , 2011 ; Drozdovskaya et al. 2014 , 2016 ). A final scenario is known as reset; this is when all of the molecules are dissociated into their base elements ( Visser et al. 2009 ; Pontoppidan et al. 2014 ; Eistrup et al. 2016 ). The distinction between any of the scenarios is not important to the discussion of C/O, after all, the number of carbon and oxygen atoms in the gas and ice does not change. Nonetheless, which scenario initializes the chemical state of the gas disk can have a drastic impact on the chemical evolution of its volatiles ( Eistrup et al. 2016 ). In this work we follow the initial volatile elemental abundance of Eistrup et al. (2016) , where C/O = 0.34, and assume thatthe volatile molecules are inherited from the pre-stellar core. For now, we similarly assume that the initial chemical state of the refractories follows the ISM, meaning that there was no chemical interaction between the gas and refractory dust during the collapse of the cloud. If the chemical composition of the dust is representative of the ISM then it has an atomic carbon-to-silicon ratio C/Si ISM = 6 ( Bergin et al. 2015 ). Based on chemical equilibrium simulations of condensing refractories in protoplanetary disks, Alessi et al. (2017) found that the most abundant silicates have silicon-to-oxygen ratios no lower than ~ 1∕4, i.e., mostly enstatite (MgSiO 3 ) or forsterite (MgSiO 4 ). While they produce oxygen-bearing iron species (fayalite – Fe 2 SiO 4 , ferrosilite – FeSiO 3 ) within 5 AU, the majority of iron-bearing materials are troilite (FeS) and pure iron. When iron-oxides become more abundant, it is at the expense of enstatite, meaning that C/O remains unchanged, implying that refractories are generally carbon rich relative to oxygen (C/O > 1). If we assume that the dust is composed of only enstatite (Si/O = 1∕3, C/O = 2) and the Sun accretes gas and dustwith the characteristic gas-to-dust ratio (100) then we can estimate the photospheric C/O. The mean molecular weight of the gas is 2.4 g mol −1 , while the molecular weight of the dust is 172.4 g mol −1 (6 carbon atoms per enstatite molecule − m mol,enstatite = 100.4 g mol −1 ). Hence, Table 1 Carbon-to-hydrogen (C/H) and carbon-to-oxygen (C/O) ratios for the volatiles (gas), refractories (gr), and combined (tot) given the simple model (mdl) where dust mass is dominated by enstatite and solid carbon (with C/Si = 6). Notes. We note that C/O tot = (C gas + C ref )/(O gas + O ref ). where n dust is the number of groupings of six carbon atoms and one enstatite molecule. Therefore (see a summary in Table 1 ), and hence The volatile carbon and oxygen abundances of Eistrup et al. (2016) are n C,gas = 1.8 × 10 −4 n H , and n O,gas = 5.2 × 10 −4 n H . Combining these values with our computed elemental abundances from our simple refractory model, we predict a solar photosphere with C/O = 0.52, and C/Si = 15,


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We thank Noemie Globus for help. This research was supported by a grant from the Israel Science Foundation No. 1277/13.


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We thank Hugh Hudson for the comments and discussions on the paper. The authors were supported by the Czech Science Foundation under grants 18-06319S (J.J. and M.Š.) and 16-18495S (J.K.). J.J., J.K., and M.Š. acknowledge the support from RVO:67985815. 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 NSC (Norway).


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

We thank C. Leonard for the ab initio curves and P. Bernath for the experimental line list. This work was supported by the ERC under the Advanced Investigator Project 267219 and made use of the DiRAC@Darwin, DiRAC@COSMOS HPC cluster and Emerald CfI cluster. DiRAC is the UK HPC facility for particle physics, astrophysics and cosmology and is supported by STFC and BIS. The authors would like to acknowledge the work presented here made use of the EMERALD high performance computing facility provided via the Centre for Innovation (CfI). The CfI is formed from the universities of Bristol, Oxford, Southampton and UCL in partnership with STFC Rutherford Appleton Laboratory. We also acknowledge the networking support by the COST Action CM1405 MOLIM.


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GO-14161, with R. Peterson as PI. As described further by Peterson (in prep.), this spectrum was acquired with the E230H grating of the STIS echelle spectrograph and the slit for a resolving power . Adopting five of the six E230H “prime” wavelength settings, with central wavelengths 201.3 nm, 226.3 nm, 251.3 nm, 276.2 nm, and 301.3 nm, resulted in an analysis coverage of 188.0–314.0 nm. The total exposure time of 106.4 ks (29.5 h) yielded per two-pixel resolution element at all wavelengths, except for the bluest and reddest. To compare the abundances deduced from the HST spectra and the visible, we also used ground-based spectra from the ESO Very Large Telescope archives (spectrographs UVES and HARPS). For wavelengths shorter than 400 nm we used HARPS spectra. They have a resolving power and a signal-to-noise per pixel (S/N) better than 150 per pixel. At longer wavelengths, in the blue we combined the individual UVES spectra to a mean UVES spectrum with a resolving power and a S/N per pixel better than 500. In the red, in order to minimise the influence of the telluric lines, and taking advantage of the fact that following Carney Latham (1987) and de Bruijne Eilers (2012) , HD 84937 shows no detectable velocity variability, we used three different mean spectra each obtained by combining individual spectra with almost the same geocentric radial velocity. Therefore, the positions of the telluric lines relative to the stellar lines are almost the same. These three mean spectra were obtained consecutively on a single night every year between 2002 and 2004. The resulting mean red spectra reach a resolving power of about 45 000 and a S/N per pixel equal to 310, 510, and 350, respectively, in the region of the red C i lines. 3. Spectral analysis and abundance measurements In our analysis we used OSMARCS model atmospheres ( Gustafsson et al. 2008 ) together with the turbospectrum LTE synthesis code ( Alvarez Plez 1998 ; Plez 2012 ). In this code, the collisional broadening by neutral hydrogen is generally computed following the theory developed by Anstee O’Mara (1991) , Barklem et al. (2000) and Barklem O’Mara (2000) . For the computations we adopted the model parameters and [Fe/H] derived for HD 84937 in the same way as in Peterson Kurucz (2015) and Peterson (in prep.): = 6300 K, = 4.0, and = 1.3 , along with the iron abundance they derived with these parameters, . These values deduced only from the UV spectra are in excellent agreement with the values derived for this star by Lawler et al. (2013) and Sneden et al. (2016) based on photometry and accurate H ipparcos parallaxes. The parameters and deduced abundance for each atomic line considered for this analysis are listed in Table 1 . The mean abundances of the different elements are given in Table 2 . For the computations of [X/H] we adopted the solar abundances (C) = 8.5 4 , (Mg) = 7.54, (Si) = 7.52, (P) = 5.46, (S) = 7.16, (K) = 5.11, and (Ca) = 6.33, following Caffau et al. (2011b) or Lodders et


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Apart from the much higher signal-to-noise ratio, the real part of the visibilities show a behavior similar to that shown by Andrews et al. (2012) , with a drop off from 1.72 Jy at the shortest baselines to a minimum of 0.057 Jy near 190 k, followed by a second maximum of 0.123 Jy around 275 k and a subsequent decrease to 0.028 Jy at our longest baseline of 410 k. The data of Andrews et al. (2012) continue to longer baselines of 600 k with fluxes approaching 0 Jy. Fig. 2 Real (black points) and imaginary (red points) parts of the visibilities of project 340.S (previously presented in Qi et al. 2013 ) in Jy vs deprojected baseline length in k. The inset shows the region of 120–420 k in greater detail. The dashed black curve shows the recalculated single power-law model of Andrews et al. (2012, their model pC) , which fails to reproduce the data on baselines 290 k. A much better fit is found for a broken power-law model described in Sect. 3 (solid blue curve). Because both models are symmetric, the imaginary parts of their visibilities are all 0 (not shown). We overplot the data with the model presented by Andrews et al. (2012, their model pC) which they find to best fit the continuum data. We recalculate the model at the exact observing wavelengths of the ALMA data. Our model is geometrically thin and uses only the midplane temperatures as calculated by Andrews et al. (2012) (see Sect. 3 ). Our model curve therefore differs in detail from the one shown by Andrews et al. (2012) , but qualitatively shows the same behavior. In particular, it fits the data well out to baselines of 290 k but severely underpredicts the emission on baselines of 300 and 400 k, corresponding to angular scales of – (27–37 au). In the next section we attempt to find a model description that provides a better fit. 3. Model fitting To further investigate the disk structure that best describes the observed emission, we consider the deprojected and radially binned real visibilities of data set 340.S. We fit to the 41 data points plotted in Fig. 2 rather than the full set of complex visibilities to speed up calculations. Since the observed emission is symmetric (imaginary visibilities are all 0) and the 41 data points in Fig. 2 fully sample the curve and do not average out any detected asymmetric structure, this simplification is allowed. As a consequence of using only the binned visibilities, our fitting places relatively little weight on the shortest baselines, which represent the total flux. Because we are primarily interested in the spatial distribution of the emission, rather than the total amount, our results are not affected. However, even a small discrepancy in total flux would be accentuated if we would calculate a residual image. For this reason, we refrain from imaging the residuals and exclusively work with the visibilities. The real part of the visibilities, , are related to the intensity distribution of the source by where is the baseline length, is the