in the NIR images and represents the red, old stellar population of the disc. The K s band isophotes trace the stellar density. In most of the cases, the LSB galaxy discs are found to host big, bright bulges; these have been discussed in earlier studies of bulges in LSB galaxies (Galaz et al. 2002 ). The diffuse stellar disc is barely visible in NIR for most of the sample. This can be due to two reasons: (i) they have a predominantly younger population of stars in the disc which cannot be traced very well in the NIR bands. However, most LSB discs show very little star formation. (ii) Instead, it is more likely that the surface mass density of the stellar discs (Σ * ) are very low and hence show very little structure in either NIR or optical images. Isophotal contours in K s do not show any significant twisting in the bar region for the sample galaxies. This suggests that the stellar orbits are aligned along the bar major axes (x 1 orbits) (Das, Anantharamaiah Yun 2001 ; Sormani, Binney Magorrian 2015 ). If there are stellar orbits perpendicular to the bar length (x 2 orbits), they will be apparent in the K s contours, but most of our sample show simple, nested, contours aligned along the bar major axis. Just from visual inspection, about half the sample of 29 galaxies in Fig. 1 have bright, classical bulges. The remaining have either boxy bulges or are bulgeless. Several galaxies have short oval bars and boxy bulges as well. These systems may represent bars that are undergoing secular evolution and may finally evolve into large, boxy bulges. (Kormendy Kennicutt 2004 ). The galaxies are individually described below. CGCG 381−048: it has a long thin bar which is clearly visible in all J , H , and K s bands. Bulge is small but brighter. Disc is very diffuse and hardly visible for short exposures. UGC 1920: it has an oval bar with a bright, classical bulge. Disc features are very faint. UGC 1455: the galaxy has a roundish, disky bar. Classical bulge. Very bright and covers a large fraction of the bar. The disc is faint. NGC 5905: long thin bar and a bright, classical bulge. Traces of spiral arms and a corotation ring are visible in the NIR images. UM 163: long thin bar and a large, classical bulge. But the disc is very faint. UGC 11754: it has an oval shaped, short bar. No clear bulge. Disc features are visible. PGC 68495: disky, oval bar. Small bulge. Galactic disc is diffuse and faint. UGC 2936: highly inclined galaxy that has a short, oval bar, and distinct spiral arms. The disc spiral arms are surprisingly clear. UGC 10405: very short bar with a bright bulge. Disc is poorly seen. 0223−0033: bright bulge with a small, oval bar followed by the spiral arms. The galactic disc is clearly visible in all the three bands. UGC 5035: small, oval bar and a large, classical bulge. UGC 9087: long bar with bright classical bulge. Disc is very faint. LSBC F568−08: short, oval bar. No clear bulge. Maybe a bar evolving into a bulge. LSBC F568−09: short bar with

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


an effective exit channel for molecules to desorb to the surface, in line with the conclusion from Yuan Yates ( 2014 ). In contrast, this study demonstrates that the photodesorption yield of CO 2 is not ice-structure dependent, which is incompatible with the preceding works based on IR spectroscopy for quantification (Öberg et al. 2009 ; Yuan Yates 2014 ). As mentioned in Muñoz Caro et al. ( 2016 ), the photodesorption yield of CO ice is independent of ice structure, and the linearly decreasing photodesorption yield for increasing deposition temperature might be due to orientational disorder. Therefore, whether they are polar CO or non-polar CO 2 , their structures are not directly related to the photodesorption yield. This work has implications for the interpretation of gas-phase observations toward cold interstellar and circumstellar environments where ice mantles were submitted to UV irradiation. The ice analog component studied in this paper, pure CO 2 ice, is believed to form in ice mantles by two processes. One is the CO 2 segregation out of the CO 2 –H 2 O mixture, leading to CO 2 inclusions in water ice. The other is a distillation process, in which CO evaporates from a CO 2 –CO ice mixture, leaving pure CO 2 behind (Pontoppidan et al. 2008 ; Kim et al. 2012 ). In the former process, UV irradiation of CO 2 inclusions in water ice produces CO, O 2 and CO 3 molecules that will be mainly retained in the ice with a negligible desorption. The latter evolutionary phase of the ice is favorable for the photodesorption of CO 2 , because CO 2 ice is exposed to the surface of ice mantles, and our experimental results are more directly applicable to this scenario. Only CO 3 is not expected to photodesorb in this case, according to the experiments. In particular, the photodesorption yields of CO 2 , the CO and O 2 photoproducts, in molecules photon −1 , should be valid to estimate the density of these species in the gas of cold environments. In dense clouds, the secondary UV field originated by excitation of molecular hydrogen is about 10 3 –10 4 photons cm −2 s −1 , and should be dominated by the molecular emission lines with a smaller contribution of the more energetic Ly α photons produced by atomic hydrogen. This UV emission spectrum, along with the total value of the UV flux, dictates the values of the photodesorption yields in our experiments. In Section 3.3 of this paper, we report the linear dependence of the photodesorption yields with the UV lamp emission and ice absorption spectra in the UV. Pure CO 2 ice is expected to be in the crystalline form in ice mantles, since the band around 4.30 μ m (2328 cm −1 ) of amorphous CO 2 ice is absent in the observed spectra toward dense clouds and protostars; this suggests that CO 2 ice was formed on the dust at temperatures above 25 K or was submitted later onto these temperatures (Escribano et al. 2013 ). We confirmed that this ice structure reflects the temperature of ice deposition in the

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


Red velocity vectors are km s −1 and white ones are km s −1 . The filament is forming just left of center where the two bubbles are merging. Figure 12. Same as Figure 11 , for model M5_27T1. Velocity vectors are color-coded, ranging from 20 to 1500 km s −1 . The strength of the GW determines how filaments evolve. We note two interesting cases outlined below. 5.2. Mass Anchors Model M5_34T (Figure 11 ) has sufficient energy to form a GW, but the wind does not entirely disrupt all filaments. As shown in Figure 11 two distinct bubbles emerge from the central starburst. Their boundaries merge to form a dense filament that stretches pc back to anchor on the starburst reservoir. The 540 km s −1 wind ablates mass off the reservoir, pushes it into the filament, and by 1.5 Myr has extended the filament pc above the disk plane where it is drifting along at only 50−100 km s −1 . Due to continual mass loading at the base of the filament it stays anchored, allowing it to persist and grow. At some point the filament should disrupt entirely due to either Kelvin–Helmholtz instabilities or heating and evaporation. But our resolution is insufficient to maximize filament survival time (see Cooper et al. 2009 ). 5.3. Filament Lift Off In model M5_27T1 (Figure 12 ) the filament again forms along the bubble contact. But now, after 1 Myr it detaches from the disk reservoir and lofts into the free-flowing wind of the now merged bubbles. This filament differs from its slow counterpart model M5_34T1; it has a larger cross section to the impinging wind, so it fragments more due to Kelvin–Helmholtz instabilities. The surrounding wind flows at 1420 km s −1 while the filament moves at 0−50 km s −1 before lift off but attains 200−500 km s −1 thereafter. This filament would be analogous to the disrupted clouds studied by Cooper et al. ( 2009 ). 6. SYNTHETIC ABSORPTION LINES We showed in Section 4 that cold gas emission entrained in the GW is 4–5 dex fainter than the galactic disk. A more sensitive probe of this gas may be its absorption of background starburst continuum. We synthesize absorption lines for three temperature regimes, denoted “molecular,” “warm,” and “soft X-ray,” with temperature ranges given in Table 1 . A trivial line source function suffices for kinematical signatures of the three temperature regimes. Absorption spectra are derived by integrating optical depth in N cells along the column viewed perpendicular to the diskThe velocity channels have a resolution of 10 km s −1 and range from −1800 to 200 km s −1 . Absorption profiles are shown in Figure 13 for models M5_27T1 (top panel) and M5_34T1 (bottom). The “soft X-ray” line shows the structure of the hot free-wind inside the expanding bubble. The velocity at maximum absorption is the average speed of the free wind. The long tail of the profile back toward Galaxy systemic velocity, especially prominent in model M5_27T1, reveals gas flowing radially at the average speed of the free wind but not entirely

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


calculated using Equation ( 30 ) in the Appendix , which are given bywhere represents a horizontal average. Figure 8. Measurements of horizontally averaged density gradients in layers for two low-Ta* simulations. Also shown are predicted density gradients for systems with given rotation rates and layer heights. Both simulations have Pr = τ = 0.1 and . We indeed find that the density gradients in layers are largest for the simulation with the higher rotation rate (Ta* = 0.1), and that the results from this simulation also fit well with prediction. The case with Ta* = 0.01, on the other hand, shows much greater variability in density gradient, particularly at larger layer heights, making it difficult to determine whether or not the theoretical predictions are valid. From Figure 8 we also see that in both cases the steepening of the density gradient is somewhat greater for smaller layers. However, this dependence of density gradient on layer height is weaker than the theory suggests. In Figure 4 we see that the simulation with Ta* = 0.1 spends a greater amount of time in the three- and two-layered phases than either of the other two simulations, and it consequently takes about twice as long as the nonrotating run (Ta* = 0) to reach the one-layered phase. The root cause is related to the lower supercriticality of convection within the layers combined with the increased stability of the interfaces. Through inspection of the density profiles of our layered simulations, we see that the positions and shapes of the interfaces in rotating simulations have less variability with time compared with nonrotating simulations. We also see in Figure 4 that the fluxes in the rotating layered systems oscillate less than they do in the nonrotating ones. Wood et al. ( 2013 ) already discussed these large-amplitude oscillations in nonrotating simulations and attributed them to the presence of large plumes of fluid punching through interfaces, periodically causing spikes in transport. In our layered rotating simulations (particularly the Ta* = 0.1 case), the absence of large-amplitude oscillations in the layered phase suggests that the motion of these plumes is inhibited, possibly because convection is weaker and the interfacial gradients are stronger. Since the plumes could be key players in the layer merger events, their suppression in the rotating simulations could also explain why the merger timescale is longer. All of these effects also contribute to the reduction of mean fluxes of temperature and chemical composition through density staircases in rotating ODDC compared with the nonrotating case. To show this quantitatively, Table 1 presents measurements of and (with standard deviations) for each value of Ta*. For low Ta* simulations, which clearly form convective layers, the fluxes are measured in the one-layered phase. The simulation with Ta* = 0.01 shows 2% and 7% decreases in thermal and compositional fluxes, respectively, compared to the nonrotating

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


giants, as can be seen in Fig. A1 (d). These stars are all flagged with suspect broad lines by the ASPCAP pipeline. 5.4 Carbon rich stars Carbon rich stars (discussed in Section 3.4 ) are also detected as outliers. In Fig. A1 (e), we can see the strong CN compared to OH lines for a few carbon enriched stars. The weirdness score increases with the strength of the CN features. 5.5 Young stellar objects Stars in this group show both H-Br emission lines as well as regular metallic absorption lines. They are mostly young stars included in the INfrared Survey of Young Nebulous Clusters (IN-SYNC, Cottaar et al. 2014 ). We detect stars with both broad and narrow emission, and with absorption that can be broad or narrow as well as double lined (SB2s). SIMBAD classification for stars in this group include ‘Variable star of Orion type’, ‘T Tau-type Star’, ‘Pre-main sequence Star’, and ‘Young stellar object’. 5.6 M dwarfs M dwarf stars are also detected as outliers. This is due to the small number of M dwarf stars in the APOGEE sample. Example spectra are in Fig. A1(g). 5.7 Other outliers Some of the objects detected as outliers did not fall into any of the above classes. These include a brown dwarf, a Wolf–Rayet star, a few AGB stars including an OH-IR star, and known variable stars, as well as three red supergiants observed in the massive stars ancillary program. Also detected as outliers are special non-stellar targets, such as the centre of M32, a few M31 globular clusters, and three planetary nebulae. Two outliers show double peaked H-Br emission lines, as well as absorption lines typical to the APOGEE data set. Both of these objects show RV modulations, suggesting they are multiple star systems. For the first, 2M04052624+5304494, the RV modulation of the absorption lines (determined from APOGEE visit spectra) could be modelled with a period of P = 11.152 ± 0.072 d, and amplitude of K = 78 ± 15 km s −1 . The emission lines in the APOGEE spectra show smaller RV modulation, if any. For the second, 2M06415063−0130177, the absorption lines RV changes by ∼160 km s −1 between two APOGEE visits. The visits are separated by 28 d. For the emission lines we could not get a good estimate on the RVs, as the emission line profiles change significantly between the visits. A CoRoT light-curve is available for this system, showing clear periodic modulation. A period of P = 29.04 d was derived for this light-curve by Affer et al. ( 2012 ). We note that this period does not agree with the RV modulation. For both of these systems, additional work is required to determine their nature. We also detect a group of objects with similar, very broad features. Most of these objects have SIMBAD classifications as contact binaries, mainly W Ursae Majoris. A few objects remain unexplained. We divide these objects into two groups. In the first group, we have objects with spectra that seems to have similar features to typical APOGEE red giants (by means of visual inspection). The

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C iii ] upper limit). Three similar systems from Berg et al. ( 2016 ) with COS detections of all four lines are plotted as blue squares. The ratios of O iii ]/He ii are inconsistent with any AGN models – all have more flux in O iii ] 1666 than in He ii 1640. The deep ESI spectra we obtained also provide constraints on the shape of the ionizing spectrum between 10 and 50 eV. The ratio of flux between the nebular He ii and H recombination lines is closely related to the ratio of He + -ionizing (228 Å) to H-ionizing photons (912 Å). The optical He ii λ4686 and H β lines are ideal for avoiding the uncertainties introduced by dust and aperture corrections. Our ESI spectra easily resolve the nebular and broad components of the He ii line (see Fig. 5 ) and thus allow a robust simultaneous fit to both, to which H β in the same spectrum can be compared (Section 3.4 and Table 10 ). The (dust-corrected) ratio of nebular He ii /H β is plotted as a function of gas-phase metallicity in Fig. 12 . In addition to the sample presented here, we plot the published measurements of this ratio for the local WR galaxies analysed by López-Sánchez Esteban ( 2010 ). The axis on the right displays the ratio Q(He + )/Q(H) assuming ideal Case B recombination proceeds for both H and He + (and 10 4 K, 10 2 cm −3 ; Hummer Storey 1987 ; Draine 2011 ). The Case B predictions should be treated with care as collisional excitation and low ionization parameters can result in deviations from this assumption (e.g. Stasińska Izotov 2001 ; Raiter, Schaerer Fosbury 2010 ), but demonstrate clearly the effect of changing the ionizing spectrum slope at the He + ionizing edge. Figure 12. Measured nebular He ii 4686/H β values (a proxy for the ratio of He + -ionizing to H-ionizing photons) versus gas-phase metallicity. Both our galaxies (blue circles, backed by red squares if nebular C iv was detected) and the WR galaxies presented by López-Sánchez Esteban ( 2010 ) are presented. The right axis indicates the corresponding Q(He + )/Q(H) assuming Case B recombination for both species. Both observational samples show a sharp transition with metallicity, with substantially larger ratios and harder spectra below 12 + log O/H ∼ 8. The nebular He ii /H β ratio reveals a sharp transition in the ionizing spectrum with decreasing metallicity. The maximum value of He ii /H β increases as the gas-phase metallicity decreases, with a marked upturn in this envelope around 12 + log O/H ∼ 8.0–8.2. Systems below 12 + log O/H 8.2 (Z ⊙ /3) reach relative nebular He ii fluxes nearly 10 times higher than those above this metallicity. This implies an order of magnitude increase in Q(He + )/Q(HI) as the metallicity of a young stellar population is decreased from Z ⊙ to Z ⊙ /10. A similar trend towards higher He ii /H β below 12 + log O/H 8.0 was found in the full sample of SDSS spectra analysed by Brinchmann et al. ( 2008b ) and Shirazi Brinchmann ( 2012 ), though we find a far more pronounced transition. This may

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


). These structures are lying mainly horizontally with respect to z = 0. This behavior is due to the fact that twist introduces local dips and mass tends to accumulate around these dips. However, at the center of the flux rope, even in the case with the strongest twist, the magnetic field lines are essentially horizontal, and therefore the dense material does not reorganize much along these lines, producing the horizontal structuring. Figure 16. Same as in Figure 14 but for N t = 4.3. Figure 17. Same as in Figure 14 but for N t = 8.5. 8. CONCLUSIONS AND DISCUSSION The time evolution of a cold prominence initially embedded in a magnetic flux rope has revealed interesting characteristics of the structure. We have concentrated on sustained prominences, i.e., detached from the photosphere. The different numerical simulations have shown how the magnetic field evolves in response to the dense prominence that is pulled downward by gravity. The various twisted flux ropes considered in this work, together with the embedded prominences, show a different evolution. We have shown that in some cases they are clearly evolving toward a stationary state. These quasi-stationary 3D solutions can be used in the future for other purposes such as the analysis of winking filaments produced by external perturbations like Moreton waves, EIT waves, or nearby flares and CMEs. During the relaxation to the quasi-stationary equilibrium, the system goes through several periodic vertical oscillations. In the linear regime, i.e., when the amplitude of oscillation is small in comparison with the local Alfvén speed, the process of continuum damping transfers the excess of energy in the system to the PCTR. It is in this highly inhomogeneous layer where the process of phase mixing takes place. This energy redistribution explains the attenuation of the position of the CM of the prominence body. Thus, at least in the linear regime the resonant absorption process is crucial in the relaxation of the structure. The energy in the PCTR is eventually dissipated by the numerical scheme used to perform the simulation, and this dissipation can be hardly avoided owing to the continuous generation of small spatial scales with time by the phase-mixing mechanism. Fortunately, although the numerical dissipation produces an energy loss, this does not necessarily mean that the attenuation of the CM is dominated by this artificial dissipation. In fact, it is known that a small dissipation does not change the damping time (Poedts Kerner 1991 ) of the quasi-mode (i.e., the resonantly damped global mode); it affects the dissipation in the layer but not the global attenuation (see Terradas et al. 2006a , for the linear time evolution with dissipation). The different convergence tests performed in the present study point in this direction. Wave leakage is not relevant in our model and does not contribute to the attenuation of the position of the CM. The problem studied here demonstrates the necessity

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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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


of periapsis ω , and time of periastron t peri ). These can be used to calculate the projected position of both components on the sky at any moment in time. In all previous cases of binary events with significant binary motion, Keplerian orbital motion provided only a small improvement relative to the linear approximation ( Skowron et al. 2011 ; Shin et al. 2012 ). This is not the case here, because, as we show below, the orbital period of the lens is similar to the duration of the event (e.g. Penny et al. 2011 ). Modelling of this event is an iterative process: for given microlensing parameters, we estimated the angular radius and distance to the source, we calculated best-fit microlensing parameters, and we repeated the procedure until all parameters converged. The best-fit microlensing parameters are presented in Table 5 . Uncertainties were calculated using the Markov chain Monte Carlo approach (MCMC; Foreman-Mackey et al. 2013 ) and represent 68% confidence intervals of marginalized posterior distributions. We note that another degenerate solution exists for the microlensing model that differs only by the signs of s z and γ z (( s z , γ z ) → − ( s z , γ z )). The second solution has the same physical parameters (except for Ω → π − Ω and ω → ω − π ) and differs by the sign of the radial velocity. Thus, the degeneracy can be broken with additional radial velocity measurements of the lens ( Skowron et al. 2011 ). Table 5. Best-fit microlensing model parameters of the Gaia16aye binary event. Notes. HJD′=HJD-2450000. We adopt t 0, par = t 0, kep = 7675. 4.3. Source star Spectroscopic observations of the event indicate that the source is a K5-type giant or a super-giant. If the effective temperature of the source were higher than 4250 K, TiO absorption features would be invisible. If the temperature were lower than 3800 K, these features would be stronger than those in the observed spectra. Spectral modelling indicates that the effective temperature of the source is 3933 ± 135 K. According to Houdashelt et al. (2000) , the intrinsic Johnson–Cousins colours of a star of this spectral type and solar metallicity should be , and (error bars correspond to the source of K4- and M0-type, respectively). We used a model-independent regression to calculate the observed colours of the source (we used observations collected in the Bialkow Observatory, which were calibrated to the standard system): V − R = 0.99 ± 0.01 and V − I = 1.91 ± 0.01. Thus, the colour excess is E ( V − I ) = 0.31 and E ( V − R ) = 0.16, consistent with the standard reddening law ( Cardelli et al. 1989 ) and A V = 0.62. According to the best-fitting microlensing model, the amount of light coming from the magnified source is V s = 16.61 ± 0.02 and I s = 14.70 ± 0.02. The V -band brightness of the source after correcting for extinction is therefore V 0 = 15.99 mag. Subsequently, we used the colour–surface brightness relations for giants from Adams et al. (2018) to estimate 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 B-Model I-Model I-Model 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 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 B-Model I-Model I-Model I-Model I-Model B-Model 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-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 B-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O 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 O O O B-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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Observatory I-Observatory O O O O O O O B-Wavelength O B-Wavelength O O O O O B-Wavelength O B-Wavelength O O O O O O O O O O O B-Wavelength O B-Wavelength O O O O O O B-Wavelength O B-Wavelength O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation 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 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 O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O


scale height (Klahr Henning 1997; Pinilla et al. 2012; Testi et al. 2014; Johansen et al. 2014) . The regions in the disk midplane that correspond to the snowlines of major volatiles are particularly interesting. These may promote locally efficient grain growth through recondensation across the snowline or by changing the sticking properties of ice-coated grains and, in addition, the local release of volatiles from the ices may induce a local pressure bump that could trap large grains (e.g., Supulver Lin 2000; Wada et al. 2009; Ros Johansen 2013; Gundlach Blum 2015) . The dense regions of disk midplanes can be investigated at submillimeter and millimeter wavelengths, where the dust emission is more optically thin and can now be spatially resolved with present-day facilities, such as the Atacama Large Millimeter/submillimeter Array (ALMA) and the Karl G. Jansky Very Large Array (VLA). These facilities allow us to obtain sensitive and high angular resolution observations of the dust continuum and gas emission lines from protoplanetary disks and therefore study the radial variations of the physical parameters of the disk. Recent results include the study of the dust properties as a function of radius in disks (e.g., Guilloteau et al. 2011; Banzatti et al. 2011; Pérez et al. 2012, 2015; Menu et al. 2014; Tazzari et al. 2016) , and the clear identification of the CO snowline in nearby disks (Mathews et al. 2013; Qi et al. 2013, 2015) , through its effects on DCO and NH abundances. It is thus becoming possible to directly investigate the effect of the CO snowline on grain growth observationally. This snowline is thought to be one of the most important after that of water, because the CO abundance in protostellar ices is found to be about 3040% of HO (Öberg et al. 2011) . In this work we focus on the Herbig Ae star HD 163296, a bright and isolated object at a distance of parsec (van den Ancker et al. 1998) with a relatively massive disk (~0.1 M⊙: Qi et al. 2011; Isella et al. 2007) and an excellent prototype for gas- and dust-rich protoplanetary disks. An estimated age of 5 Myr was obtained from the comparison between H ipparcos astrometric measurements and pre-main sequence evolutionary models by van den Ancker et al. (1998) . The stellar parameters computed by Natta et al. (2004) are , , K. To study the dust properties in the protoplanetary disk around HD 163296, we re-analyse the ALMA science verification observations (de Gregorio-Monsalvo et al. 2013; Mathews et al. 2013; Rosenfeld et al. 2013) and for the first time discuss the continuum emission in Band 6, combined with new VLA observations from the Disks@EVLA collaboration. In Sect. 2 we describe the observational data, in Sect. 3 we report the main new results of our analysis, in Sect. 4 we present the result of our disk modeling, and in Sect. 5 we discuss the main implications for grain properties. Fig. 1 Continuum maps at different wavelengths, from the left : 850 m, 1.3 mm, and 9 mm, the

O O B-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation 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 B-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation B-Citation I-Citation I-Citation O O O O O O O O O O O B-Wavelength O B-Wavelength O O O O O O O O O O O O O O O O O O O O O B-Observatory I-Observatory I-Observatory I-Observatory B-Observatory O O B-Telescope I-Telescope I-Telescope I-Telescope I-Telescope I-Telescope B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation B-Citation B-Citation I-Citation I-Citation I-Citation 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 B-Citation I-Citation I-Citation I-Citation B-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O B-Citation I-Citation I-Citation I-Citation 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-Telescope I-Telescope O O O B-Model I-Model I-Model I-Model 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 O B-TextGarbage I-TextGarbage O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O B-Observatory O O O B-Citation I-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-Wavelength I-Wavelength O O O B-Telescope 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 B-Wavelength I-Wavelength B-Wavelength I-Wavelength O B-Wavelength I-Wavelength O


inferred from the shell modeling reported in Sect. 3.1 and Fig. 11 must be considered as strict lower limits. This is because the emerging spectrum is strongly weighted by sightlines with the lowest column densities, given that Ly α escapes through the paths of least resistance (e.g., Eide et al. 2018 ), generally orthogonal to the stream velocities in case of infall ( Gronke et al. 2017 ). Nevertheless, we note that an alternative scenario suggested by recent modeling is that radiation is emitted through the cooling of mixed gas occurring at the boundary between the phases ( Mandelker et al. 2019 ; Cornuault et al. 2018 ). In that case, Ly α radiation would originate from the combined dissipation of the kinetic energy of the stream and the thermal energy from the mixed gas that cools down ( Gronke Oh 2020a ). This scenario, and our calculations of gas mass flows in Sect. 3.1 , also imply a total cold gas mass present at each moment in the diffuse streams of the order of 10 11 M ⊙ (to be compared to the lower limit of ≈10 8 M ⊙ of neutral hydrogen). Is that a reasonable gas mass to be diffused into the intra-group gas? On the one hand, this is comparable to or smaller than the ISM mass of all group galaxies combined, and less than 10% of all baryons expected to be in the group given its DM estimate and assuming a universal baryon fraction. Assuming pressure equilibrium, the flowing gas would need to be confined in clouds with quite a small volume filling factor, of order 10 −3 to 10 −5 , which is qualitatively similar to what is discussed in theoretical works (e.g., Cornuault et al. 2018 ; McCourt et al. 2018 ; Gronke Oh 2020b ). This is required to reach a high-enough density to compensate for the much larger temperature of the hot medium. Such dense gas clouds would produce copious recombination Ly α photons following photoionization, if a source emitting enough ionizing photons towards this medium were to be present. This does not appear to be the case for RO-1001, at least given the evidence presented here. 5. Summary and conclusions The main findings of this work can be summarized as follows: RO-1001 is a group at z = 2.91 defined by four galaxies with stellar masses above 10 11 M ⊙ , originally selected as an overdensity of faint radio sources (12 σ excess) over a small, 10′′ region. The group contains an ongoing SFR of 1200 M ⊙ yr −1 mostly spread among three ALMA-detected, IR-luminous sources characterized by very compact IR sizes, for which we reported CO[3−2] detections with NOEMA. RO-1001 does not contain any detectable evidence of ongoing AGN activity, down to limits that are consistent with a cosmic average co-existence of an AGN and SFR at typical levels. The hosting DM halo mass is estimated to be typical for a group, with ∼4 × 10 13 M ⊙ consistently derived using three methods, including a blind X-ray measurement with significance of 3.1 σ . RO-1001 hosts a giant Ly α halo with a luminosity of 1.3 × 10 44 erg s −1 as

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


on the low branch. Mass is being fed into the annulus at a greater rate than it is able to process it and so mass accumulates and Σ increases. Eventually, the annulus reaches the low-temperature bifurcation point and leaps to the high hot state. The annulus, now above the Σ-nullcline, begins losing mass because its accretion rate exceeds the supply rate. Once the high-temperature bifurcation point is reached, the annulus drops to the low-temperature state and the process is repeated. The red curve in Fig. 4 (a) corresponds to a numerical simulation of equations ( 15 ) and ( 17 ) and illustrates this basic behaviour quite clearly. In Fig. 4 (b), we plot the evolution of Σ and T c as a function of time. Here, one can observe the two time-scales at work, especially in the (blue) T c curve. In between outbursts there is little change in temperature, but a build up in mass (seen in the red curve) occurring on the slow viscous time-scale t Σ . Interleaving these phases are the abrupt bursts occurring on the short thermal time-scale t th . 3.2.2 Z Cam type simulations Z Cam variables intermittently behave in a similar manner to U Gem variables but occasionally remain on the high-temperature branch in a quasi-steady state for months to years before dropping to quiescence and undergoing a fresh batch of outbursts. This is attributed to a shift in the Σ-nullcline upwards (due to a change in mass transfer, δ ≠ 0), so that the intersection is beyond the saddle node. Of course, the system must be close to criticality if this is to be possible. To demonstrate this in our model, and δ are chosen such that the fixed point oscillates between the stable high-temperature branch and the unstable branch. When the fixed point is on the upper branch the system is stable and will remain in a standstill. A decrease in pushes the fixed point on to the unstable branch and the system undergoes periodic orbits resulting in trains of outbursts. In Fig. 5 , we show an example of standstill–outburst-train cycles. Figure 5. Time evolution of the surface density and central temperature with and b 0 = 0 with mass transfer variation. The variation amplitude is δ = 0.1 and t I = 5 × 10 6 s. The system clearly switches between outburst trains and standstills. 3.3 Results: stochastic With the basics established, we include a fluctuating viscosity (β ≠ 0). The fluctuation time-scale is taken to be 10 t orb , which is motivated by MRI shearing box simulations (Hawley et al. 1995 ). The amplitude is set at b 0 = 0.1. First, we consider the case where there is no mass transfer variability (δ = 0). To obtain a fixed point on the high-temperature branch close to the bifurcation point we choose . A deterministic system with this configuration would remain in the high-temperature state indefinitely. A stochastic system however will see the fixed point jostle about as the two nullclines fluctuate with α, sometimes sitting on the upper branch, sometimes dropping to the middle branch

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


χ 2 ), constrained by all of the photometric detections and upper limits from NIR to radio wavelengths (Figure 4 ). Parameters are analyzed under a Bayesian approach generating a posterior probability distribution function. The SED fitting failed to tightly constrain fracAGN given the lack of mid-IR photometric points (which differentiate between AGN and star-forming galaxies) and the loose constraint from the NIR. The posterior probability distribution suggests that the AGN component contributes at most ∼20% to the total IR luminosity, with the highest probability being assigned to a contribution of 0%–5%. This is consistent with the estimation from the L X / L FIR ratio in Section 3.1 . The model SED with the maximum 20% AGN fraction is also plotted in Figure 4 , which is inconsistent with the 100 μ m Herschel /PACS upper limit. Figure 4. Best-fit SED (black) from CIGALE PYTHON. Different components are color-coded. The data points from left to right are HST /WFC3 F110W+F160W, Spitzer /IRAC 3.6 μ m + 4.5 μ m, Herschel /PACS 100 μ m + 160 μ m, Herschel /SPIRE 250 μ m + 350 μ m + 500 μ m, APEX/LABOCA 870 μ m, SPT 1.4 mm + 2.0 mm, and ATCA 5.5 GHz + 2.1 GHz. We do not include the ATCA 9.0 GHz upper limit, which is less constraining, because the source may be resolved at this frequency. The inset plot shows the normalized probability distribution function of the AGN fraction in the total IR luminosity. The AGN most probably contributes less than 5%. The dash–dotted line is the model curve with the maximum 20% AGN contribution to the IR. In this model, the AGN contribution does not extend to the radio part of the SED. The ATCA radio continuum upper limits at 2.1 and 5.5 GHz are consistent with the FIR-to-radio correlation for star-forming galaxies. The radio part of the SED for radio-loud AGN would be at least a factor of ∼2 higher (e.g., Rush et al. 1996a , 1996b ; Morić et al. 2010 ). 3.3. Theoretical Expectations We have provided evidence that SPT0346-52 is star formation dominated in the IR. Since our SFR is mainly constrained by the FIR photometric data, L IR being almost all from star formation suggests that the inferred SFR reflects the true SFR. We examine whether this observed high SFR can be physically explained in the framework of “maximum” starbursts (Elmegreen 1999 ) where a substantial fraction of available gas is consumed to make stars. Following Tacconi et al. ( 2006 ), the maximum (“Schmidt-law”) SFR can be written aswhere Elmegreen ( 1999 ) defines as the star formation efficiency, f g is the gas fraction, M tot is the total (dynamical) mass of the system, t dyn is the dynamical time, and v c is the circular velocity in km s −1 . We use the definition in Tacconi et al. ( 2006 ), v c = 0.67 × v FWHM = 410 km s −1 ( v FWHM = 613 ± 30 km s −1 measured from the low- J CO(2-1) line; Aravena et al. 2016 ). Assuming a gas fraction of 0.3–0.8, we utilize the observed SFR of 3600 ± 300 M yr −1 to 19 19 Here we adopt the SFR

O O O O O O O O O O O O O O B-Wavelength O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength B-Telescope B-Instrument O O O O O O O O B-Software B-Software O O O O O O O O O O O O B-Telescope B-Instrument B-Wavelength B-Telescope B-Instrument B-Wavelength I-Wavelength I-Wavelength O B-Wavelength I-Wavelength I-Wavelength B-Telescope B-Instrument B-Wavelength I-Wavelength I-Wavelength O B-Wavelength I-Wavelength I-Wavelength B-Telescope B-Instrument B-Wavelength I-Wavelength I-Wavelength O B-Wavelength I-Wavelength I-Wavelength O B-Wavelength I-Wavelength I-Wavelength B-Telescope B-Wavelength I-Wavelength I-Wavelength B-Telescope B-Wavelength I-Wavelength O B-Wavelength I-Wavelength O B-Telescope B-Wavelength I-Wavelength O 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 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 B-Wavelength O O O O O O O O O O O O O O O O O B-Telescope B-Wavelength O O O O B-Wavelength O B-Wavelength I-Wavelength O O O O B-Wavelength O O O O O B-Wavelength O O O O O B-Wavelength O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O B-CelestialObject O O O O O O B-Wavelength 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 B-Citation I-Citation 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-Model 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 B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O B-Wavelength I-Wavelength 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


( 2010 ). They have also shown that when these are combined with lower limits required to avoid the compactness problem, values of Γ 0 are in the range 10 2 –10 3 . Concerning direct estimates (rather than limits) of Γ 0 , a spectral break in the prompt component has been observed only in a few cases (Ackermann et al. 2011 ; Tang et al. 2015 ). Most of the available estimates of the value of Γ 0 have been inferred from the detection of an early peak in the afterglow lightcurve. Ghirlanda et al. ( 2012 ) collected all GRBs with known redshift and with an early peak in the optical lightcurve, and inferred Γ 0 under the assumption that the peak corresponds to the blast wave deceleration time. The Γ 0 values have been derived both for a constant and wind-like medium, and are shown in Fig. 4 as star symbols (the green colour refers to optical lightcurves, while the yellow colour refers to a similar analysis applied to GeV lightcurves of LAT GRBs with temporally extended GeV emission). The most stringent limits derived in this work lie above most of the values inferred from GRBs with an optical peak. This implies that the non-detection of synchrotron afterglow radiation is consistent with the simplest model, and there is no evidence that mechanisms producing a suppression of the GeV flux (see Section 2.2 ) are at work. The possibility of testing the relevance of these processes is however limited by the instrument sensitivity. We can conclude that present instrument capabilities are not pointing to the need for a relevant suppression of the high-energy afterglow synchrotron flux. On the other hand, the upper limits lie not far from (and sometimes below) the estimated values of Γ 0 . This suggests that the LAT should be able to detect the synchrotron afterglow component for those GRBs with the largest bulk Lorentz factors and largest energetics. A fraction of the LAT-detected GRBs are indeed characterized by the presence of an emission above 100 MeV lasting much longer than the prompt radiation, whose flux decays in time as a PL (Ackermann et al. 2013 ). These are the brightest GBM GRBs, and a large Lorentz factor Γ 0 > 500 has been inferred for them. An association with synchrotron afterglow radiation has been claimed to be consistent also with their spectral and temporal properties (Kumar Barniol Duran 2009 , 2010 ; De Pasquale et al. 2010 ; Ghirlanda, Ghisellini Nava 2010 ; Ghisellini et al. 2010 ; Lemoine, Li Wang 2013 ; Nava et al. 2014 ; Beniamini et al. 2015 ), although photons with particularly large energies (>10 GeV) detected at late times (>10 2 s) are in excess of the synchrotron limit and require a different explanation (Piran Nakar 2010 ; Wang, Liu Lemoine 2013 ; Ackermann et al. 2014 ). Finally, we comment on the dependence of these results on the unknown parameters ε e and η γ , with reference to a homogeneous density medium (similar considerations hold also for a wind-shaped density medium). In the first regime, where observations

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


pulsars. Timing noise manifests as a red-noise (time-correlated) process in the TOAs, and is typically described by a wide-sense stationary stochastic process (Groth 1975 ), modelled as either random walks in the pulsar spin parameters, or with a more general power spectrum. The origin of this noise is unclear. While some of it may be caused by variable torques associated with changes in the pulsar magnetosphere state (Lyne et al. 2010 ), a significant fraction is likely associated with rotational irregularities interior to the star (Melatos Link 2014 ). The properties of timing noise vary markedly across the pulsar population, with its strength depending on the pulsar spin frequency ν and frequency derivative (Shannon Cordes 2010 ), and likely other factors because of the large dispersion levels of timing noise between pulsars. For example, the most stable MSP, PSR J1909−3744 shows no evidence for instabilities with phase variations limited ≲100 ns (≈0.3 per cent of pulse phase) over 11 yr (Shannon et al. 2015 ). In contrast, the timing noise in young pulsars and magnetars can contribute many cycles of pulse phase on week to month time-scales (Livingstone et al. 2011 ), both making it difficult to find a phase-coherent solutions in poorly sampled data and presenting challenges to TOA-modelling algorithms. While finding the origin of timing noise is important for understanding neutron stars, it is also necessary to account for timing noise as part of a general timing model for the pulsar. This is necessary to eliminate, or at least mitigate, bias in the estimation of other parameters in the model (Coles et al. 2011 ; van Haasteren Levin 2013 ; Lentati et al. 2014 ; Kerr et al. 2015 ). In addition to exhibiting timing noise, pulsars can experience glitch events (e.g. Espinoza et al. 2011 ; Yu et al. 2013 ), in which they are observed to suddenly change spin state, with the most significant component being increases in spin frequency that can exceed 1: 10 5 (Manchester Hobbs 2011 ). Glitches have been modelled with permanent changes in ν and , as well as transient components, in which changes in ν are modelled to decay (typically exponentially) on time-scales τ. Occasionally multiple glitch-decay components (with different time-scales) are invoked, particularly when high cadence (daily or higher) observations (e.g. Dodson, McCulloch Lewis 2002 ). Glitch components are often identified and characterized by searching for variation of spin frequency and frequency derivative in subsets of the data (Lyne et al. 2015 ). This method is suboptimal because it does not utilize the phase coherence of the pulse arrival times. The study of glitches is further complicated by the presence of timing noise. There are two prevailing theoretical models for glitches. In the first, glitches are associated with the transfer of angular momentum between the superfluid interior and solid crust of the neutron star (Anderson Itoh 1975 ; Alpar et al. 1984 ). A

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power. In AGN and LI(N)ER galaxies, the molecular component is more dominant than in star-forming galaxies. There is, however, significant variation from galaxy to galaxy. Studying the relative contribution of different phases to the outflow rate and the kinetic power as a function of SFR or α bol revealed no clear trends (see e.g. Section B1 ). Figure 6. Relative contribution of the molecular (blue), ionized (green), and neutral atomic (red) phases to the total kinetic power of the outflow. The galaxies whose names are in red are star-forming galaxies. Next we investigate the mass outflow rate of the three different phases, ionized, neutral atomic, and molecular for galaxies which have measurements (or upper limits) for at least two phases. This comparison can be seen in Fig. 7 , where we plot the different mass outflow rates against each other. The samples in the three plots are slightly different. To increase the statistics, in each plot we show the galaxies with measurements in both of the phases plotted. We distinguish between high-redshift sources ( z > 1, green) and low-redshift sources ( z 0.2, black). The data points with a red edge have no reliable extinction correction for the ionized phase and thus should be treated as lower limits. These figures clearly show that the ionized mass outflow rate is much smaller (up to 2–3 orders of magnitude smaller) than the neutral atomic or molecular mass outflow rate. A major caveat is that some ionized outflow rates might be underestimated because of an uncertain extinction correction. But even if these points are ignored, the ionized outflow rates are significantly lower (cf. Fig. 5 , which only includes galaxies with proper extinction correction). This confirms previous findings which estimate the ionized phase to contribute only minimally (Rupke Veilleux 2013 ; Carniani et al. 2015 ; Ramos Almeida et al. 2019 ). The figure on the top right highlights that outflow rates in the molecular and neutral atomic phase are similar (usually within 1 dex). This picture might be slightly skewed, however, as we include upper limits in the molecular and ionized, but not in the atomic neutral outflow phase. However, the relative contribution of the ionized outflow rate to the total outflow rate varies from galaxy to galaxy (from ≤ 1 to 10’s of ) and a simple prescription as in Fluetsch et al. ( 2019 ) might not be fully appropriate to determine the total outflow budget. If electron densities from auroral or trans-auroral lines are a better estimate than the densities based on the [S ii ] doublet (as suggested by Davies et al. 2020 , see Section 3.2.1 ), then the contribution of the ionized phase would drop even further by additional 1–2 orders of magnitude and hence it would become negligible also in star-forming galaxies. Figure 7. Comparison between the outflow rates in the ionized, molecular, and neutral gas phases. The black symbols represent the low-redshift ( z 0.2) sources while the green symbols

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


normalized to unity at 1 keV, this is seen as a decrease of the reflection amplitude. Figure A2. An example illustration of the effect of the emission of the bottom lamp and of the emission of the top lamp circling around the BH (i.e. crossing twice the equatorial plane). The blue solid and red dashed curves show the observed reflection spectra computed with reflkerr_lp for δ = 0 and 1, respectively, for h = 2, a = 0.998, r in = 4.9, r out = 1000, Γ = 1.7, kT e = 200 keV, ξ = 1, kT bb = 50 eV, and θ o = 9° (thick curves) and 30° (thin curves). The black dotted curve shows the observed primary spectrum. We see the actual reflected spectra may be much weaker with respect to the observed primary emission than those in the approximate (δ = 0) case. In the shown case, this is due mostly to the primary emission of the bottom lamp gravitationally focused toward the observer, which enhances the observed primary flux by as much as a factor of 10 in the case of θ o = 9°. Since our plotted primary spectra are normalized to unity at 1 keV, this enhancement is seen here as a decrease of the amplitude of the reflection. We emphasize that properly assessed reflection amplitude gives an important constraint on the lamppost model, where both the fraction and the radial distribution of photons illuminating the disc surface are fully determined by the height of the primary X-ray source. Then, the radial emission profile is strictly related to assumed geometry, and treating the fraction of reflected photons as a free parameter leads to results which are not self-consistent. Still, our model allows the user to make it free. APPENDIX B: <monospace>hreflect</monospace> We describe here details of our hybrid reflection model. In particular, we apply rescaling of the xillver spectra to account for an angular distribution of reflection predicted by this model, which is different than that of ireflect (with the reflection strength in ireflect larger by a factor of ≃1.5 for edge-on directions). In some cases, we apply also a minor rescaling related with differences of the incident spectra. We explain the criteria which we use to establish the rescaling factor, denoted below by f . We follow an approach similar to that of Done Gierliński ( 2006 ). We use xillver , which applies a more accurate absorption model, as a reference for the spectral shape below ∼20 keV, and ireflect , which correctly describes the angular distribution of the reflected radiation using the exact Klein–Nishina cross-section, as a reference for the reflection amplitude. The absorption model applied in ireflect assumes that the absorption coefficient above 12 keV is ∝ E −3 , then, the depth of its absorption edge at these energies can be matched to that predicted by xillver by modifying any parameter (we choose ξ) affecting the absorption level at 12 keV. As can be seen below, the shapes of ireflect spectra with such an adjusted ξ typically agree very well with those of xillver in the ∼10–30

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


constrain the escape fraction of the ionizing radiation and/or the presence of faint satellite galaxies during the late stages of cosmic reionization. We have predicted radial surface brightness profiles that include the contribution from (i) fluorescent emission powered by ionizing radiation leaking from the central galaxy (as in Mas-Ribas Dijkstra 2016 , for two different CGM prescriptions), and (ii), nebular emission from faint satellite sources that possibly resided within the halo of the central galaxies (as in Mas-Ribas et al. 2017 ). We have compared our predictions with observations of Ly α halos at z = 5.7 and z = 6.6, and have also predicted H α and visible continuum surface brightness profiles may be detectable within future JWST observations. We present and discuss our findings below. 1. Our comparison of models to observations favors the model with a very low escape fraction of ionizing radiation, , from galaxies within the range of magnitudes . This scenario implies that these galaxies do not contribute significantly to the reionization process. Therefore, if galaxies are the major contributors to the reionization process, as recently restated by Parsa et al. ( 2017 ), a large population of faint sources with a high ionizing escape fraction is necessary. 2. The presence of faint satellite sources is unclear. Two out of four comparisons with current Ly α data indicate that satellite sources might contribute to the extended Ly α emission, but the effect of systematics and uncertainties in the observations do not allow for a clear conclusion. Given the required existence of faint sources driven by the low escape fraction results, if the presence of satellite sources around brighter galaxies is ruled out by the observations, this might imply that the population of faint objects is spread out within the IGM, making its detection more challenging. 3. JWST will be able to probe the ionizing escape fraction from one bright, galaxy up to distances of a few tens of pkpc from the center. Fainter galaxies and/or a high S/N for the continuum observations require the observation and stacking of several objects. We stress that we have adopted and extrapolated two CGM models that were derived to match observables at redshifts around . The validity of our results therefore depends on the ability of these two models to realistically describe the medium surrounding galaxies. While a more detailed parameterization of the CGM at high redshift (if currently feasible) is beyond the scope of our work, future observations of extended emission, together with absorption studies (e.g., Dijkstra Kramer 2012 ; Hennawi Prochaska 2013 ; Prochaska et al. 2013 , see also Steidel et al. 2010 , 2011 ), will clearly enable us to use our proposed method to further constrain the escape fraction. The prospects for doing this experiment at lower redshifts, , are interesting, as the surface brightness for emission lines depends on redshift as . However, the contribution

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


a low self-interaction cross section). However, it seems unlikely that this same model could then be responsible also for the much larger dark matter core reported in Fornax (e.g. Goerdt et al. 2006 ; Walker Peñarrubia 2011 ; Cole et al. 2012 ; Pascale et al. 2018 ) and the similarly large cores reported in nearby gas-rich isolated dwarf irregulars (e.g. Moore 1994 ; Flores Primack 1994 ; Read et al. 2017 ). By contrast, models in which dark matter is heated by bursty stellar feedback could naturally account for such a diversity of central dark matter densities, at least in principle. Recall that whether or not a dark matter core can form from such ‘heating’ depends on: (i) the pre-infall dark matter halo mass, M 200 ; (ii) the halo concentration parameter, c 200 ; (iii) the total stellar mass, M * ; and (iv) the size of the dark matter core (e.g. Di Cintio et al. 2014 ; Read et al. 2016a ; Contenta et al. 2018 ; Bermejo-Climent et al. 2018 ). (Smaller cores require less energy to form and form more rapidly.) Dark matter cores are also easier to form at high redshift when the star formation rates are high and the halo masses are smaller (Madau, Shen Governato 2014 ). This suggests that small (pc) dark matter cores may indeed form very early in the Universe even in ultra-faint dwarfs. This effect could be ubiquitous, or it could be stochastic, depending on the merger history, spin and/or concentration of any given dwarf (e.g. Laporte Peñarrubia 2015 ). We will return to this issue in more detail in a forthcoming paper where we present GravSphere models for all of the Milky Way classical dwarfs. 8 CONCLUSIONS We have used a new mass modelling method, GravSphere , to measure the central dark matter density profile of the Draco dwarf spheroidal galaxy. Our key findings are as follows: Using mock data with sampling, binary star population, and foreground contamination similar to that for the real Draco dwarf, we showed that GravSphere is able to successfully recover the dark matter density profile of a tidally stripped Draco-like dwarf within its 95 per cent confidence intervals (Fig. 4 ). However, while we were able to distinguish the amplitude of the central density, , of our cored and cusped mocks at 95 per cent confidence, the logarithmic slope of the density profile, , depended on our choice of priors. This sensitivity to the prior diminishes with improved spectroscopic sampling (Appendix B ). We then applied GravSphere to the real Draco data. We inferred a high central density of with logarithmic slope at 95 per cent confidence, consistent with expectations from pure-dark matter structure formation simulations in ΛCDM (Fig. 7 ). We tested the robustness of this result, showing that even using a rather extreme prior on γ DM that biases us towards cored models, our GravSphere models still favour a logarithmic slope of at 95 per cent confidence, steeper than that of a uniform-density core. Dark matter models with a high central density and a

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


sampling rate. 4. Discussion 4.1. Prominences From the H α tomogram, we can estimate the size and location of the satellite emission that we associate with prominences by assuming that they are corotating with the secondary star. The projected distance of these features from the center of mass (CM) of the binary is simply r = v /Ω, where v is the inclination-corrected velocity amplitude of the emission and Ω is the angular velocity of the secondary. The orbital inclination is expected to be ∼75° based on our assumed stellar masses and the mass function measured by Marsh et al. ( 2016 ). Therefore, the correction between the radial velocity and space velocity is less than 10%. For the orbital period from Marsh et al. ( 2016 ), the inverse angular velocity is 2043 s rad −1 . Assuming a mass for the WD of 0.8 M ⊙ , then the mass ratio of the system is q ≈ 0.3 for a secondary with a mass typical for an M5 dwarf. The radius of the secondary’s Roche lobe is (Eggleton 1983 ). Since the secondary is probably close to filling its Roche lobe, we use this as the stellar radius and compare it to the size of the prominences. The brightest emission from the prominences is seen around 500 km s −1 , corresponding to 4.4 Roche radii from the CM. The prominences precede and trail the secondary by ± 0.15 in phase, meaning that the prominences extend 3 stellar radii from the surface of the secondary. The faint emission behind the secondary at 1000 km s −1 corresponds to 8.7 stellar radii from the CM, or about 5 stellar radii from the backside of the red dwarf. In isolated magnetized stars, the corotation radius is where the gravitational pull of the star balances the centrifugal acceleration of plasma trapped in the field. Prominences found at or beyond the corotation radius are called “slingshot” prominences (Steeghs et al. 1996 ). In binary systems the balance between centrifugal and gravitational forces is found at the Lagrangian points. The L 4 and L 5 points are actually rather broad regions that make an equilateral triangle with the primary and secondary stars. For the assumed parameters of the AR Sco binary, the L 4 and L 5 points are 370 km s −1 from the CM. The prominences extend more than 30% farther than L 4 and L 5 points. The trailing prominence differs in phase from the L 5 point by 20°. The L 2 point is expected to be at 4.5 Roche radii from the CM, or a velocity of 500 km s −1 , while the faint prominence behind the secondary is seen at twice that distance. We conclude that the prominence emission extends well beyond the outer Lagrangian points. The stability of slingshot prominences has been modeled by Ferreira ( 2000 ). Such prominences can be stable out to ∼5 stellar radii if the dipole surface magnetic field is larger than ∼100 G, and out to 10 stellar radii for a 500 G field. A quadrupole field would require ∼500 G for prominence stability at 5 stellar radii. The WD field at the secondary is expected to have an average field strength of order

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


the evolution after 18.25 days but underpredicts the millimeter-band data and the observations above ≈10 GHz before 8.55 days. Figure 10. Same as Figure 8 , but now including energy injection between 0.15 and 0.26 days (Section 4.3 ), a standard RS contributing to the optical/NIR light curve before 2 × 10 −3 days and to the radio at 1.5 days (Section 5.1 ), and a refreshed RS contributing to the millimeter-band light curve (Section 5.3 ). Figure 11. Same as Figure 9 , but for the model (solid) shown in Figure 10 decomposed into FS (dashed) and RS (dotted) contributions. The two RS components are best distinguished at 1.5 days, where the lower-frequency component arises from an RS in the original shell producing the GRB, while the higher-frequency component arises from the collision of two shells at 0.15 days, which also produces the X-ray rebrightening. The red shaded regions represent the expected variability due to scintillation. To summarize, the continued high flux density of the X-ray detections after ≈1 day suggests that the X-ray excess at ≈0.26 days is not due to late-time central engine activity, but is caused by a rebrightening of the FS radiation. The multiband data are consistent with a wind-like circumburst medium, requiring a single episode of energy injection at ≈0.2 days. The resultant model fits the optical and X-ray evolution and matches the radio SED after 18 days. However, this model underpredicts the CARMA light curve, as well as the 5–83 GHz SED at 1.5 and 8.55 days. To account for these deficits, we next investigate the effect of including emission from additional components. We delineate the evidence for their presence and consider their possible physical origins. 5. Multicomponent Models 5.1. Reverse Shock In Section 3.2 , we discussed the apparent multicomponent structure of the radio SEDs between 1.5 and 18.2 days. In the previous section, we have shown that while a single FS model can reproduce the gross features of the radio light curves, such a model cannot explain the multiple peaks in the SED at 1.5 days, the ≈14 GHz peak at 4.5 days, and the SED at 8.55 days. Of these, the greatest discrepancy between data and model arises in the radio SEDs at 1.5 and 4.55 days. We now consider whether each spectral peak at 1.5 days can in turn be ascribed to radiation from an RS. An RS propagating into GRB ejecta is expected to produce synchrotron radiation with its own set of characteristic frequencies, ν a,r , , and ν c,r , and peak flux . These quantities are related to those of the FS at the deceleration time, ec , when the RS just crosses the ejecta, and the relation between the two sets of break frequencies and fluxes allows for a determination of the ejecta Lorentz factor and magnetization. After the RS crosses the ejecta, the flux above ν c,r declines rapidly, 16 16 The angular time delay effect prevents abrupt disappearance of flux above ν c,r ; instead, we expect (Kobayashi Zhang 2003 ). as no electron is

O O O O O O O O B-Wavelength 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 B-Wavelength O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O B-Wavelength O O O O B-Wavelength O O O O O O O O O B-Telescope O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Model I-Model 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 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 O O O O O O O O O O O O O B-TextGarbage I-TextGarbage O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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


metallicity than QGs-A. The median stacked spectra, corrected for dust extinction, of QGs-A and QGs-B have a blue stellar continuum, suggesting a young mean stellar population. The analysis confirms a weak [] emission and that also other high ionization emission lines (such as []) are weak in both QGs stacked spectra, and the [] /H α ratios are consistent with a low ionization level. On the contrary, [], H α and H β (i.e. low ionization lines) are still strong and with an Hα flux slightly weaker () than the one of SF galaxies. We find that QGs have D n 4000 and EW(H α) values intermediate between SF and already quenched galaxies, confirming that they have just stopped their star formation and have a young/intermediate mean stellar population. In the colour-mass diagram, the bulk of the QGs-A and QGs-B resides in the blue cloud region, and only few of them (∼3 per cent) lie in the green valley region. The QGs have masses log( M /M ⊙ ) > 9.5, comparable with those of the SF population, being the QGs-B, on average, more massive. This suggests that, as expected in a downsizing scenario, star formation quenching has not started yet for low-mass galaxies, consistently with a lack of low-mass red galaxies. Their H α emission is compatible with a just quenched SFR of the order of 0.6–10 M ⊙ yr −1 , similar to that of the SF main sequence population, suggesting the presence of residual ionized gas in our QGs. The emission from the median stacked spectra is, however, weaker than that in the SF population, suggesting that the depletion of the gas has started. The morphologyand concentration index (C=R90/R50) of QGs are similar to those of the SF population, suggesting that no morphological transformation has occurred yet, in the early phase after the quenching of the star formation. However, some of them have a concentration index higher than the threshold that divides the early-type from the other galaxy types (i.e. C > 2.6) and they could have experienced morphological transformation during the interruption of the star formation. Compared to the parent SF population, we find an excess of QGs in high-density environments (∼42 per cent), in particular for QGs-B. QGs in high-density environments are preferentially satellites (from ∼60 to 80 per cent). Approximatively 5 per cent of QGs are in groups/clusters which have more than 30 members, but no one of them is the brightest galaxy in its environments. From the fraction of QG candidates ( of the SF population) we estimate the quenching time-scales for these populations to be between 10 and 18 Myr. These values are compatible with the sharp quenching models by C17 . If we assume that at most 50 per cent the entire SF-[]undet population (∼7.5 per cent) is in a low ionization state, as witnessed by the low but not extreme [] /H α ratio in their stacked spectrum, we obtain an upper limit to the quenching time-scale of ≃ 0.76 Gyr. In this case, the quenching time-scale is compatible with galaxies which are

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