O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion O B-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion 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 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 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 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 B-Model I-Model I-Model I-Model O O O O B-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula B-Formula I-Formula I-Formula O O O O 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 O O O O O O O B-Model 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 O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O B-Dataset I-Dataset I-Dataset I-Dataset O O O O O O O O O O O O O O O O O O O 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 B-Model I-Model I-Model 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

this value will be subject to a selection bias as it is easier to obtain unambiguous light curves for principal axis rotators, it is unlikely that a debiased value would reach the 40 per cent that our modelling suggests is required to explain our data. Therefore, we conclude that none of the above mechanisms can currently explain our observed trends with size. 5.2 Comparing results for the inner and outer main belt populations Figs 3 and 4 show that the rate at which the distribution of magnitude variation changes with diameter is greater for the inner belt than the outer belt. This may be due to either a difference in the reorientation of the objects between the two populations, or a difference in shape distribution. Unlike the difference in variability with diameter, the difference with semimajor axis is potentially more straightforward. Reorientation due to YORP will happen more slowly at greater heliocentric distances and thus objects in the outer belt should show systematically less variability, all other factors being equal. This agrees with what we see here. To test this, we assumed that the shape distribution of the outer belt was identical to that obtained for the inner belt. In order to assess the validity of this assumption, a best-fitting truncated Gaussian shape distribution was obtained for the outer main belt independently at 2 D 3 km using the previously outlined method. This gave an average axial ratio of 1 : 0.87 ± 0.09 : 0.74 ± 0.11 corresponding to a population with a shape distribution μ = 0.90, σ = 0.11. This is not significantly different from that found for the inner belt and therefore our assumption holds. The difference between the two populations must therefore be due to a difference in the degree of reorientation. Part of this may be due to the slower rate of YORP in the outer belt. At present our statistical model does not account for these effects and this may offer an avenue for future work. 5.3 Previous constraints on shape and spin A previous study by Szabó Kiss ( 2008 ) used a similar sparse light-curve sampling method, utilizing data from the SDSS Moving Object Catalogue. Assuming all objects to have spin axis parallel to the sky plane, they reported a shape distribution in good agreement with axial ratios from then-published light curves. We compared our findings to an updated distribution of axial ratios from current light curves (Kryszczyńska et al. 2007 ). The light curves given in this data base suggest an average asteroid shape with 1σ spread with axial ratio 1 : 0.76 ± 0.13 : 0.62 ± 0.11. This result is within 1σ of our own findings, albeit both 〈 b / a 〉 and 〈 c / b 〉 are smaller than our results. We then used the truncated Gaussian distribution for b / a and the approximated distribution for b / c obtained from the Kryszczyńska et al. ( 2007 ) data set, and varied the upper obliquity limit in an attempt to obtain a good fit from this large diameter shape distribution. It was possible to obtain


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

studied the typical outcomes of close encounters between planets and orbit-crossing planetesimals. Applying their results to the fifth planet shows that it would scatter most of the orbit-crossing material on to bound orbits, thus supporting the fifth planet as the cause of the scattered disc. However, this planet’s mass of is much lower than the mass of the scattered population (). It is impossible that a much less massive planet scattered the much more massive planetesimal population. Read et al. ( 2018 ) furthermore found that planets with a mass in the range from to corresponding to either a semimajor axis from 115 to 130 au or from 140 to 160 au, with the most massive planets being nearest to or farthest away from the star, similarly well explained the observations. Although any planet with a mass in excess of would eject orbit-crossing material, a fifth planet capable of scattering of planetesimals is still possible. As the fifth planet may or may not be real, we shift our focus on to the four confirmed planets. Referring again to the work by Wyatt et al. ( 2017 ), one sees that the gas giants of HR 8799, each for itself, would typically eject their orbit-crossing material in unbound orbits. This material would be on its way out of the system, but, unless this is a continuous process, it should only operate for a relatively short amount of time. For this process to be continuous, a constant flux of material would need to cross the giant planet’s path, which is unlikely. Therefore, we do not consider scattering through the giant planets to be responsible for the scattered disc either. Migration is considered to have occurred in the formation history of HR 8799, as neither core accretion nor gravitational instability could have produced all four planets at their current location (Currie et al. 2011 ). Although we focus in the discussion on outward migration, a similar case can be made for inward migration. Using the formula of Ida et al. ( 2000 ) to calculate the migration rate in our primordial disc, we find a rate of a few 10 s of . Such a fast migration would allow the planets to quickly reach their current location. Taking into account that migration stops when the mass within a few Hill’s radii becomes less than the planet’s mass (Kirsh et al. 2009 ), we find the fully formed planets in HR 8799 to be too massive to have undergone migration within the protoplanetary disc. However, if the planets accreted their gas envelope while migrating or even after the migration ceased, then the core masses rather than planet masses would have to be considered. Migration rate of these, less massive, cores would be lower, and they could easily create a scattered disc of planetesimals instead of ejecting them out of the system. Planet–planet scattering may have also occurred early on in the history of the HR 8799 system. If the planet cores formed closer to the star by core accretion, such a scattering event could have relocated the planets, bringing


O O O O B-Person I-Person B-Person I-Person B-Person I-Person I-Person O B-Person I-Person O O O O O O O O O B-Person I-Person O O O O O O O O O O O B-Wavelength O O O O O O O O O B-Person I-Person O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Database I-Database I-Database O B-Database I-Database I-Database I-Database O O O B-Organization B-Location I-Location O B-Archive I-Archive I-Archive I-Archive I-Archive I-Archive O O O O O O O O B-Grant O B-Grant O O B-Location B-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization O O O B-Organization I-Organization O O B-Grant O B-Person O O B-Grant I-Grant I-Grant O O B-Organization I-Organization I-Organization I-Organization O

We are grateful to M. Beasley, J. Beckman, F. La Barbera and R. Peletier for very useful discussions and valuable suggestions. We thank G. Bruzual for providing us with various versions of his models in the UV spectral range and for interesting suggestions. We also thank E. Toloba for providing us with fully reduced early-type galaxy spectra. We are grateful to the anonymous referee for valuable suggestions that helped us to improve the paper. This research has made an extensive use of the SIMBAD data base and VizieR catalogue access tool (both operated at CDS, Strasbourg, France), the NASA's Astrophysics Data System Article Service. This work has been supported by the grants AYA2013-48226-C3-1-P and AYA2013-48226-C3-2-P from the Spanish Ministry of Economy and Competitiveness ( MINECO ) and the Generalitat Valenciana under grant PROMETEOII/2014/069 . ER acknowledges a Marie Heim-Vögtlin grant from the Swiss National Science Foundation .


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ACKNOWLEDGEMENTS We wish to thank Michael Opitsch for useful discussion during the preliminary phase of this work. LC thanks the Department of Physics and Astronomy of the Padova University for hospitality while this paper was in progress. This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.


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

starbursts that have inclination-corrected central brightness ( = 22.6 mag arcsec −2 for a kinematic inclination = 452) comparable to VCC 848 (Lelli et al. 2014 ). Because the rotation velocity gradient slope is proportional to the square root of local matter density for a solid-body rotation curve, we can infer that the merging event of VCC 848 has not built up an exceptionally compact core. 4.3. Dynamical and Baryonic Mass Profiles We use the rotation curve of the approaching half to determine the cumulative dynamical mass profiles (=/G), which are shown in Figure 5 . We also overplot mass profiles of the baryonic components, including stars and atomic and molecular gas, in Figure 5 . All of the profiles are extracted using the same geometric parameters as determined from the 2 dbat kinematic fitting. The stellar mass is estimated by using the ( g − i )–mass-to-light relation calibrated for Local Group dwarf galaxies (Zhang et al. 2017 ). Details about the procedure of stellar mass estimation are given in Paper I . We adopt a logarithmic stellar mass uncertainty of 0.2 dex, which is applicable to color-based mass estimation for low-dust-extinction cases (Zhang et al. 2017 ). The atomic gas mass is equal to the H i gas mass multiplied by a factor of 1.36 to account for helium. The molecular gas mass is indirectly inferred from the SFR estimated with H α luminosities (Catalan-Torrecilla et al. 2015 , Equation (10)) by adopting a constant molecular gas consumption timescale of (5.25 ± 2.5) × 10 −10 yr −1 found for nearby disk galaxies at (sub)kiloparsec scales (Bigiel et al. 2008 ; Leroy et al. 2008 ). 18 18 Another method of estimating the molecular gas mass is based on a metallicity-dependent gas-to-dust ratio (G/D). According to the G/D−metallicity relation from Rémy-Ruyer et al. ( 2014 ), VCC 848 is expected to have a of 3.00 ± 0.37 for (O/H) = 8.03 (Table 1 ). In addition, Grossi et al. ( 2015 ) determined a total dust mass of 10 5.01 M ⊙ (the value has been adjusted to reflect our adopted distance) within the central ∼30′′ of VCC 848. Therefore, the total gas mass (atomic plus molecular) within the central 30′′ is estimated to be , and hence the most likely molecular gas mass is ∼10 7.5 M ⊙ , found by subtracting the atomic gas contribution (Figure 5 ). This molecular gas mass is in reasonable agreement with that (10 7.6 M ⊙ ) inferred from the SFR-based method shown in Figure 5 . We choose to use the SFR-based method in this paper. This is because, besides their low spatial resolution, the Herschel images of VCC 848 generally have signal-to-noise ratios that are too low (except for the brightest star-forming sites) to allow for constructing a robust radial profile of dust mass densities. Figure 5. Accumulated radial profiles of the dynamical mass as well as the stellar, atomic, and molecular gas masses within the central 30′′. The same geometric parameters derived from the 2 dbat fitting of the H i velocity field (Figure 3 ) are used to


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2.2 GTC spectroscopy Candidates have been followed up with optical spectroscopy using the Optical System for Imaging and low-Resolution Integrated Spectroscopy (OSIRIS; Cepa et al. 2000 ) instrument on the Gran Telescopio Canarias (GTC) since 2012. Table 2 shows a summary of our GTC spectroscopic observations. The spectra were mostly obtained using the R500R grism, with three making use of the R300R grism. These provide resolving power of around 500 and 300, respectively. The spectra were reduced using standard procedures with IRAF 1 . The HgAr, Ne, and Xe arcs were used on the wavelength calibration of our spectra. Spectral flux calibrations were achieved with standard stars (Oke 1974 , 1990 ; Hamuy et al. 1994 ; Bohlin, Colina Finley 1995 ). Spectral features caused by telluric absorptions in these spectra were not corrected. Five objects were observed twice to gain additional exposure time, and for the purposes of this paper we combined the spectra of these objects from both epochs. Table 2. Summary of the characteristics of the spectroscopic observations made with the OSIRIS on the GTC. R500R and R300R grisms cover a wavelength range of 480–1020nm. A 0.8 arcsec slit used for all observations. Note . References for flux calibration standard stars are 1. Bohlin et al. ( 1995 ); 2. Hamuy et al. ( 1994 ); 3. Oke ( 1974 ); 4. Oke ( 1990 ). 2.3 VLT spectroscopy We have also obtained optical-NIR spectroscopy of five of our candidates, a known sdL8 subdwarf and three radial velocity standard L dwarfs using the X-shooter spectrograph (Vernet et al. 2011 ) on the Very Large Telescope (VLT) since 2014. Table 3 shows a summary of our VLT spectroscopic observations. These X-shooter spectra were observed in an ABBA nodding mode with a 1.2 arcsec slit providing a resolving power of 6700 in the VIS arm and 4000 in the NIR arm. These spectra were reduced with ESO Reflex in a lazy mode (Freudling et al. 2013 ). The flat field used for the science data was also used for flat-fielding the flux standard star spectrum (by set flat strategy to false). Telluric corrections were achieved for both VIS and NIR arms using telluric standards that were observed right after or before our targets at a very close airmass. To extract telluric spectra for correction, we fitted and normalized spectra of telluric standards stars to their continuum and removed non-telluric features (e.g. hydrogen absorption lines) with iraf splot . These X-shooter spectra were smoothed by 101 and 51 pixels in the VIS and NIR arms, respectively, for display in figures, which reduced the resolving power to about 600 and increased their signal-to-noise ratio (SNR per pixel) by 10 and 7 times. Table 3. Summary of the characteristics of the spectroscopic observations made with X-shooter. Wavelength ranges for the VIS and NIR arms are 530–1020 and 990–2480 nm. 1.2 arcsec slits are used for both VIS and NIR arms. DENIS-P J025503.3−470049, 2MASS J08354256−0819237, and DENIS-P


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fraction of the kinetic energy transferred to CRs by a single SN and SNR is the comoving SN rate. In principle, one should account also for helium nuclei. For simplicity, we assume here that particles can be treated as four protons, and hence be absorbed in the proton spectrum efficiency. In addition to the SFR, to derive SNR we need to know the number of SNe explosions per solar mass of forming stars, which is given by where ( m ) is the initial mass function of Population II/I stars, for which we assume the following form: with x 1.35 and m c 0.35 M ; m lies in the range [0.1, 100] M (Larson 1998 ). We neglect the contribution from Population III stars. Their SF history is very debated and still highly uncertain. In fact, detailed studies, exploiting cosmological hydrodynamical simulations implementing chemical feedback effects, have shown that Population II/I stars dominate the global SFR at any redshift (Tornatore etal. 2007 ; Maio etal. 2010 ). Moreover, the recent surveys hunting for Population III stars in the Milky Way have found no metal-free stars so far, implying that they are rare in the Milky Way even if they exist (Beers Christlieb 2005 ). Combining the above formulae, equation ( 19 ) becomes Particle acceleration in SN explosions is believed to occur through diffusive shock acceleration, which leads to momentum power-law spectra of accelerated particles. With this in mind, we assume that the source function of volume-averaged CR protons injected by SNe (defined as a rate per unit energy and volume) is where E is the proton kinetic energy, E 0 1GeV, m p is the proton mass, v / c is the dimensionless velocity of the particle, 2 is the slope of the differential spectrum of accelerated particles and C ( z ) is a redshift-dependent normalization obtained by imposing that the total kinetic energy rate equals , i.e. In equation ( 24 ), we fix E max 10 6 GeV (Lagage Cesarsky 1983 ), and we verify a posteriori that our conclusions are not strongly dependent on our choice of E min 10keV. From equation ( 23 ), one can easily realize that is the key parameter determining the fraction of the total kinetic energy released that goes into protons with E 1GeV. We keep as the only free parameter of the model. In Fig. 3 , we plot the source function as a function of the kinetic energy for three different values of . We found that protons with kinetic energies below 10MeV represent 0.5percent, 2.7percent and 13percent of the total kinetic energy released for 2,2.2 and 2.5, respectively. Figure 3. Source function of CR protons with respect to their kinetic energy at z 10 for a spectrum slope 2 (blue line), 2.2 (green) and 2.5 (red). 3.2 Energy losses in the IGM CRs can be an efficient heat source especially for a low-density gas. When the CR proton ionizes an atom, it transfers a certain fraction of its kinetic energy to the electron, which is either used for further atomic excitation and ionization or distributed via elastic collisions to other


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

in a scattering process the frequencies of the incoming and outgoing photons are completely uncorrelated. Therefore, it is very important to clarify when this limit can be safely applied. As mentioned before, the hypothesis of CRD is generally suitable for treating weak spectral lines, and it is a good approximation for modeling the core region of strong lines of the intensity spectrum. On the other hand, it turns out to be completely unsuitable for modeling the extended wings of strong resonance lines. In light of this, we provide a detailed comparison between the results obtained through the full PRD calculation and in the limit of CRD. In Figure 3 , the emergent intensity and Q / I profiles calculated in the absence of a magnetic field are shown, for the Sr ii 4078 Å line and for the Sr i 4607 Å line, comparing the full PRD calculation (solid line) to the calculation in the CRD limit (dashed–dotted line). This limit has been obtained by setting the elastic collision rate , while keeping all other parameters, including the depolarizing collision rates, as they were. In other words, we artificially modify the branching ratios so that all scattering processes occur through the redistribution matrix. For both lines considered, the intensity is greater at line center when using the CRD approximation than when PRD is considered. This can be qualitatively understood as follows. In the limit of CRD, the scattered radiation at a given frequency depends on a weighted average of the incoming radiation over the whole line profile, and it thus takes into account that, for an absorption line, the intensity increases going from the core to the wings. On the other hand, in the limit of CS the scattered radiation is related only to the incoming radiation at that same frequency. PRD phenomena relax such coherency, relating the scattering radiation to the incoming one, but over an interval that is generally smaller than the one considered in the CRD case. This same reasoning explains why, in PRD, the intensity is instead larger in the wings. Figure 3. Intensity (top row) and Stokes Q / I (bottom row) profiles of the emergent radiation calculated for an LOS with in the absence of a magnetic field, for the Sr ii line at 4078 Å (left column) and for the Sr i line at 4607 Å (right column), considering the FAL-C atmospheric model. In each figure, the results for the full PRD calculation (solid line) and the results obtained in the CRD limit (dashed–dotted line) are plotted. The reference direction of positive Q / I is taken perpendicular to the vertical direction. Figure 3 clearly shows that the difference between CRD and PRD calculations is, as expected, rather small in the Sr i 4607 Å line. In particular, we expect that, once the Stokes profiles are smeared to properly account for the effects of the atmosphere’s macroturbulent velocity and of the finite spectral resolution of a typical instrument, the differences between both calculations will be negligible. The


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 B-Wavelength O O B-Wavelength I-Wavelength O B-Formula I-Formula I-Formula O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O B-Survey O O O O O O O O O O O O O O O O B-Wavelength 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 O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength 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 O O O O O O O O O O O O O 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 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 B-Wavelength O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O B-ObservationalTechniques I-ObservationalTechniques O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-CelestialObject O O O O O B-Organization 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 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

3 shows the measured fractional linear polarization as a function of wavelength for the six stars measured in the B , V , R , and I bands. Fixing K = 1.15 ( Serkowski et al. 1975 ) and leaving λ max and p max as free parameters, we fit the six polarization profiles to Eq. ( 1 ) using weighted least-squares. Fig. 3. Wavelength dependence of polarization for six of the stars in the R -band sample (USNO-B1 identifiers shown in the legend). Debiased fractional linear polarization ( p̂ ) measured in the Johnsons-Cousins B , V , R , and I bands (horizontal axis shows effective wavelength). For each star, a line shows the best-fit Serkowski law (Eq. ( 1 ), with K set to 1.15). The fit λ max are in the range 580 ± 46 nm–643 ± 34 nm, while the fit p max are in the range 0.9%−1.7%. Although limited by the uncertainties of the measurements, we find no evidence for substantial differences between the best-fit value of λ max in this sample compared to canonical values ( Serkowski et al. 1975 ). If grain alignment were unusually efficient in this region with smaller grains able to be aligned, we might have expected a shift of λ max toward shorter wavelengths than the typical 550 nm ( Martin et al. 1999 ). This is not observed. 3.3. Magnetic field morphology If the magnetic field morphology is responsible for the high submillimeter polarization fractions, then any region with high p 353 should have a magnetic field that lies mostly in the plane of the sky with no substantial change in orientation either along the line of sight or within the beam. The orientation of the magnetic field as projected on the plane of the sky is probed by the optical polarization angle θ R as well as the submillimeter polarization angle rotated by 90°. Within an 80′ beam centered on this region we find χ 353 + 90° =112.8 ± 0.6°. The polarization angles inferred from stellar polarimery do not vary significantly across the region (Fig. 4 , left). The standard deviation of the distribution of θ R is consistent with it arising from measurement uncertainties, suggesting little beam depolarization. Fig. 4. Left : distribution of stellar polarization angles, θ R for stars farther than 250 pc (solid line). The dashed vertical line shows the χ 353 +90° from Planck at 80′ resolution. Right : probability density functions of the orientation of linear HI structures ( θ RHT ) for different velocity ranges (shown on the right). We only consider velocity ranges within the peak of the HI intensity spectrum. The filled circles in the bottom mark the mean value, ⟨ θ RHT ⟩ for each velocity range. All angles are measured in the Galactic reference frame, according to the IAU convention. Linear structures seen in HI have also been shown to trace the interstellar magnetic field ( Clark et al. 2014 ). Recently, Clark (2018) proposed that changes in the orientation of these structures in velocity space can be used to probe variations of the magnetic field orientation along the line of sight. By


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The authors thank the anonymous referee for constructive comments that helped improve this paper. This work is supported by National Science Foundation of China through grants NSFC-11303015 and NSFC-11133004, the National Key Research and Development Program of China (2016YFA0400803), NSFC-11773015 and NSFC-11133001. Facility: CXO (ACIS) .


O O O O O B-Organization I-Organization B-Grant O O O O O O O B-Dataset I-Dataset I-Dataset I-Dataset O O O B-Observatory I-Observatory I-Observatory O O O O O O O O O O O O O O O O O O O O O O O

This research was supported by GA ČR 13-10589S. This research has made use of the Washington Double Star Catalog maintained at the US Naval Observatory. The authors would like to thank the anonymous referee for his/her comments on the manuscript, which led to significant improvement of the paper.


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We thanks R. Angulo, C. Hernández-Monteagudo, and O. Hahn for useful discussions. G.H. and R.A, acknowledge support from Spanish Ministerio de Economía and Competitividad (MINECO) through grant number AYA2015-66211-C2-2. U.K. acknowledges support by the Israel Science Foundation (ISF grant No. 1769/15). We acknowledge the use of HEALPix ( Górski et al. 2005 ).


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

modes are combined. Had that study examined the case of ω = 90°, it would have found smaller widths showing that the dynamics is more complex than just summing up single mode widths. This fact was later recognized in a more recent article (Gallardo 2020 ). Secondly, our analytical disturbing function as well as our multiple-argument pendulum models not only give precise resonance widths for each mode, their combinations, and their variations as functions of ω, they also agree with the chaos indicator. So our approach is not just to compare the analytical widths to the integration of the full equations of motion like it is done in the ‘dynamical map’. Instead, we seek the numerical separatrices obtained from measuring precisely how two nearby orbits diverge. In this sense, it is worth reminding the reader that the megno chaos indicator is one of the most precise diagnostic tools in resonance dynamics. In conclusion, the fact that the disturbing function is an expansion with respect to eccentricity (as in this work we used the second interpretation of the disturbing function without expanding with respect to inclination like in section 5.3 of Paper I) does not mean that it cannot probe the dynamics accurately. For instance, we could even explain for the first time the width of the chaotic separatrix layer of the inner 2:1 resonance as well as predict accurately the extent of the asymmetric libration domains for outer resonances. Therefore, the conclusion of Gallardo ( 2019 ) regarding the importance of the disturbing function at arbitrary inclinations and the analytical pendulum models is unjustified. While in the process of developing our multi-argument two-harmonic pendulum model to derive resonance widths for outer as well as inner resonances, we learned of the work of Lei ( 2019 ). The author tested the conclusion of Gallardo ( 2019 ) that the expansion of the disturbing function cannot model the 3:1 resonance accurately and developed what they termed a ‘multi-harmonic pendulum model’ and applied it to the disturbing function of Paper I. The author says that the disturbing function they use is somewhat different but it is not as they choose from the outset not to expand the perturbing potential with respect to inclination. That possibility is already present in Paper I and was termed the second interpretation of the disturbing function in section 4.3 of Paper I. It was already used to estimate resonance widths in section 5.3 of Paper I and was reprised in this paper. What Lei ( 2019 ) does differently is to rewrite the fully derived disturbing function (3) by trigonometrically splitting the resonant argument with respect to as follows: The details of the indices in the above sums are found in Lei’s paper and are not essential to our discussion. The author then selects from this new expression the ‘harmonics’ of in order to model the 3:1 resonance with the disturbing terms: We use the quotes to refer to harmonics in Lei’s formulation in


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

The authors thank Prof Subir Sarkar (University of Oxford) for stimulating discussions related to this work. This research was supported in part by the Engineering and Physical Sciences Research Council, UK (EP/M022331/1, EP/N014472/1, EP/N002644/1, EP/P010059/1). All data that support the findings of this study are available from the authors upon request.


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-CelestialObject O O O O O O O O O O B-Citation 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-Instrument I-Instrument I-Instrument I-Instrument I-Instrument O O O B-Location I-Location B-Location I-Location I-Location I-Location O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O B-CelestialObject 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 B-Citation O O O B-Instrument I-Instrument I-Instrument 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-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 B-CelestialObject 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 B-Instrument B-Citation I-Citation I-Citation I-Citation O O O O O O B-Location I-Location 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 B-Wavelength I-Wavelength O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument I-Instrument O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O

19:03 to 19:39 UT. We plot in panels (e) and (f) of Figure 11 the maps of Alfvénic Mach number (with and without accounting for magnetic mirroring) covering the interval from 19:03 to 19:43 UT. During this time interval, the magnetic connections from the shock are on open field lines connected to the AR and to polar coronal holes. Significant magnetic turbulence must prevail in the AR in order for the modeled location to agree with the observations. 5. Connecting the Shock Evolution with the Time History of the Relativistic Protons at Earth In this section, we investigate whether particles accelerated by shocks crossing field lines reaching Earth can explain the time history of relativistic protons observed in GLE72. Kurt et al. ( 2019 ) detail observations made by several neutron monitors. They show that the proton angular distribution was strongly anisotropic early in the event and only became isotropic at about 18:00 UT. The Fort Smith (FSMT) neutron monitor located in the Northwest Territories (60 north, 112 west) was relatively closely aligned with solar magnetic field lines at 16:00 UT. Therefore, it provides an excellent monitor of early particle acceleration at the Sun. We plot the pressure-corrected FSMT 1 and 5 minute count rates from 15:30 to 17:00 UT in Figure 12 . The rates rise in response to the event at about 16:08:30 UT. Figure 12. Comparison between the evolution of the and the time history of the GLE72 count rates from FSMT neutron monitor (see text for details). In determining the evolution of the shock wave parameters at regions well connected to Earth, we use the methods presented in Kouloumvakos et al. ( 2019 ) and also in our discussions in Sections 3 and 4 . The shock wave intersected magnetic field lines that were well connected to Earth at 15:57 UT, and it became supercritical around 15:59 UTl. 7 7 This assumes that the shock accelerating the particles was quasi-perpendicular requiring a critical Mach number of ∼2.7, which was reached at 15:59 UT. The mean M A and M fm parameters continued to increase, reaching a maxima near 18:00. The mini-neutron monitor DOMC (Usoskin et al. 2015 ) NM station situated at the South Pole recorded the most intense flux with a peak at 18:50 UT (see Mishev et al. 2018 ). The density compression ratio saturated within 15 minutes and reached an asymptotic value of 4. Using a similar model to the one used in Section 4.3 to predict the time profile of the γ -ray emission, we examine the shock origin of the particles that access field lines reaching Earth. We consider an function that includes only the term sh discussed in Section 4.3 , which approximates the effectiveness of shock acceleration. In order to directly compare estimated proton flux with the FSMT NM count rate, we need to shift to account for the time it took the protons to reach Earth. A common approach is to assume that the particles propagate along IP magnetic field lines following a Parker spiral whose shape is defined by


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

G. The blue and red solid circles denote the current positions of two example binaries with initial parameters days and , and day and , respectively. Figure 4 shows the distribution of the binaries at end of the evolution with f = 0, 0.02, 0.1, and 0.3, corresponding to either the donor star having evolved to be a WD or the age of the binary exceeding Hubble time. The binaries with orbital periods at the beginning of the second RLOF above the so-called bifurcation period (Pylyser Savonije 1988 , 1989 ) evolve into low-mass binary pulsars (LMBPs), with a helium WD companion (depicted with circles), while those with orbital periods below the bifurcation period evolve into compact LMXBs with substellar companion stars (depicted with triangles). To see how the bifurcation period changes with mass transfer and evaporation, we present the orbital period evolution for five NS binaries with different f values in Figure 5 . It seems that the bifurcation periods are quite close to each other (∼1 day) and increase slightly with increasing f . Figure 4. Distribution of the final orbital period and donor mass under different values of f . The blue and red symbols have the same meanings as in Figure 2 . The solid line is the theoretical – relation of LMBPs given by Tauris Savonije ( 1999 ). Figure 5. Post-AIC evolution of the orbital period under different values of f for five NS binaries. Here denotes the time at AIC. From top to bottom, the initial parameters are: days and , days and , days and , days and , and days and . The solid line in the four panels in Figure 4 is the theoretical relation for LMBPs given by Tauris Savonije ( 1999 ). We can see that if there is no evaporation in the post-AIC evolution, the resulting distribution is well-consistent with the theoretical relation, which is the same as in the LMXB evolution. However, once evaporation is included, the distribution deviate from the theoretical prediction, especially in the case of f = 0.3: for a given , the orbital period is longer than expected. The reason is that in the late stage of the evolution, the orbital evolution and mass loss are mainly driven by evaporation rather than mass transfer via RLOF (see also Jia Li 2016 ). To demonstrate the detailed evolutionary processes, in Figures 6 and 7 , we present two representative examples for the post-AIC binaries, which are marked in Figures 3 and 4 . Figures 6 and 7 correspond to the blue circle with days and , and the red triangle with day and , respectively. Figure 8 compares the rates of AML caused by different mechanisms in the evolutionary paths presented in Figures 6 (left panel) and 7 (right panel). In Figures 6 and 7 , the left panel displays the evolution of the mass transfer rate (black solid line), the evaporative wind loss rate (red line), and the donor mass (blue line). The black dashed line represents the critical mass transfer rate for disk instability. The right panel depicts the evolution of the NS mass (solid line) and


B-Survey I-Survey I-Survey I-Survey B-Survey B-Citation I-Citation I-Citation O B-Dataset I-Dataset I-Dataset I-Dataset O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Dataset I-Dataset I-Dataset I-Dataset O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 B-CelestialObject O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Citation I-Citation I-Citation O O O O O O O O O

Evolution of 21-cm Structure (EOS; Mesinger etal. 2016 ) 9 2016 data release. These semi-numerical reionization simulations are 1.6Gpc on a side with a 1024 3 grid and include state-of-the-art subgrid prescriptions for inhomogeneous recombinations and photo-heating suppression of star formation. The 2016 EOS data release corresponds to two simulation runs, with the efficiency of supernovae feedback adjusted to approximately bracket the expected EoR contribution from faint galaxies. The two runs are: Faint galaxies the EoR is driven by galaxies residing in haloes with masses of 10 8 M h / M 10 9 , and is characterized by numerous small cosmic H ii regions. Hereafter we will refer to the EoR morphologies resulting from this simulation as S mall H ii . Bright galaxies the EoR is instead driven by galaxies residing in haloes with masses of M h 10 10 M , and is characterized by spatially more extended H ii structures. We refer to these simulated EoR morphologies as L arge H ii . We note that the L arge H ii ionization fields have a factor of few10times more power on large scales during the EoR, compared to the S mall H ii ionization fields. Although these are two opposite extremes in terms of H ii region sizes, the S mall H ii EoR morphology is likely more realistic (see the discussion in Mesinger etal. 2016 ), and so we use this simulation as our fiducial model. Nevertheless, we include both extremes to explore the dependence of our results on EoR morphology. We construct samples of sightlines through our simulations which are terminated on one end at a halo, and then extended in a random direction through the simulation volume for a distance of 200 comoving Mpc. Along each sightline, we sum the contributions from all encountered H i patches to construct a composite optical depth for the damping wing (e.g. Miralda-Escud 1998 ). We purposefully exclude the H i contribution from pixels 16 comoving Mpc (2 physical Mpc) from the QSO host halo.This corresponds to the minimum possible radius of the H ii region around ULAS1120 inferred from measurements of its near zone (Mortlock etal. 2011 ). We do not explicitly include the flux from the QSO in our reionization maps. Doing so would require assumptions about the QSO lifetime and ionizing luminosity. Neglecting the QSO ionizing contribution implies that the surrounding H ii region could be larger than predicted by our EoR models. For a given a larger surrounding H ii region implies a smaller integrated damping wing optical depth. Thus if the QSO contributes in growing the surrounding H ii region, our modelled optical depths should be associated with even higher values of , shifting the probability distribution functions (PDFs) we present below towards larger . At z 7.1, we select 10 4 identified haloes in the mass range 6 10 11 M h /M 3 10 12 , consistent with the inferred dynamical mass of the host halo of ULASJ1120 (Venemans etal. 2012 ). Importantly, these higher host halo masses, made possible


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Acknowledgements We thank the anonymous referee for her/his fruitful comments. The ASTE project is led by Nobeyama Radio Observatory (NRO), a branch of National Astronomical Observatory of Japan (NAOJ), in collaboration with University of Chile, and Japanese institutes including University of Tokyo, Nagoya University, Osaka Prefecture University, Ibaraki University, Hokkaido University, and the Joetsu University of Education. M.O. and S.P. are members of the Carrera del investigador científico of CONICET, Argentina. M.B.A. is a doctoral fellow of CONICET, Argentina. This work was partially supported by grants awarded by ANPCYT and UBA (UBACyT) from Argentina. M.R. wishes to acknowledge support from FONDECYT(CHILE) grant No 1140839. M.O. is grateful to Dr. Natsuko Izumi for the support received during the ASTE observations.


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

We are grateful for the extraordinary contributions of our CTIO colleagues and the DES Camera, Commissioning and Science Verification teams in achieving the excellent instrument and telescope conditions that have made this work possible. The success of this project also relies critically on the expertise and dedication of the DES Data Management organization. Funding for the DES Projects has been provided by the US Department of Energy, the US National Science Foundation, the Ministry of Science and Education of Spain, the Science and Technology Facilities Council of the United Kingdom, the Higher Education Funding Council for England, the National Center for Supercomputing Applications at the University of Illinois at Urbana-Champaign, the Kavli Institute of Cosmological Physics at the University of Chicago, Financiadora de Estudos e Projetos, Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro, Conselho Nacional de Desenvolvimento Científico e Tecnológico and the Ministério da Ciência e Tecnologia, the Deutsche Forschungsgemeinschaft, and the Collaborating Institutions in the Dark Energy Survey. The Collaborating Institutions are Argonne National Laboratories, the University of California at Santa Cruz, the University of Cambridge, Centro de Investigaciones Energeticas, Medioambientales y Tecnologicas-Madrid, the University of Chicago, University College London, the DES-Brazil Consortium, the Eidgenössische Technische Hochschule (ETH) Zürich, Fermi National Accelerator Laboratory, the University of Edinburgh, the University of Illinois at Urbana-Champaign, the Institut de Ciencies de l'Espai (IEEC/CSIC), the Institut de Fisica d'Altes Energies, the Lawrence Berkeley National Laboratory, the Ludwig-Maximilians Universität and the associated Excellence Cluster Universe, the University of Michigan, the National Optical Astronomy Observatory, the University of Nottingham, the Ohio State University, the University of Pennsylvania, the University of Portsmouth, SLAC National Accelerator Laboratory, Stanford University, the University of Sussex, and Texas AM University. PM, ES, EH, KP, KH are supported by the US Department of Energy under Contract No. DE- FG02-91ER40690. SB, TK, MH, JZ, BR acknowledge support from European Research Council in the form of a Starting Grant with number 240672. DG was supported by SFB-Transregio 33 ‘The Dark Universe’ by the Deutsche Forschungsgemeinschaft (DFG) and the DFG cluster of excellence ‘Origin and Structure of the Universe’. The DES participants from Spanish institutions are partially supported by MINECO under grants AYA2009-13936, AYA2012-39559, AYA2012-39620, and FPA2012-39684, which include FEDER funds from the European Union. This paper has gone through internal review by the DES 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 B-Telescope O O O B-Observatory O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Observatory O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Wavelength O O O O O O O O O O O O O O O O O B-Telescope O B-Wavelength I-Wavelength O O B-Observatory 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 B-Observatory 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 B-Observatory O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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

are for inclined (left) versus face-on (right) orientation. While both Figs 11 and 12 relate to the simulation without cooling, virtual infrared views on the run with cooling are shown in Figs 13 and 14 . Fig. 13 contrasts Keck (top row) with ALMA (bottom row) images at three times in the evolution ( t = 4.5, 5, 5.5). This demonstrates that resolution is once more key to clearly distinguish the very fragmented mixing zone where dust now gets concentrated in a more spherical (rather than clearly spiral) fashion, dominated by local dust clumps and filaments (as shown in Fig. 6 ). Fig. 13 shows in each panel how a linear colour scale (shown with contours) no longer yields a clearly detectable rotating spiral pattern, as outward moving large localized clumps may seem unaligned with the underlying orbital motion. The colour scale in Fig. 13 plots the same data in a logarithmic scale (as was also adopted for all previous figures), where only in the ALMA views, one can still find evidence for a rotating spiral pattern. Again, this longer wavelength view shows grain emission from both the large and small grains. Note that the possible failure to detect a clear spiral pattern in infrared views may have significant consequences for interpreting actual infrared evolutions, where binarity is easily linked with clear rotating spirals: our findings suggest that more erratically varying dusty WR environments could be binary systems where radiative cooling effects induce the variability. Disentangling episodic dust makers from binary configurations using only infrared variability is thus poorly constrained. Figure 13. Synthetic images for the run with cooling. Top row for Keck at 2.45 μm, bottom for ALMA at 400 μm, for time 4.5, 5 and 5.5. Convolution is done with 20 versus 2 pixels. We show linearly distributed contours, on top of a logarithmic colour image. Figure 14. Synthetic images for ALMA on the run with cooling. We compare images for two times t = 5.4 (left) and 5.9 (right), for face-on (top) versus inclined (bottom) orientation. Finally, Fig. 14 contrasts virtual ALMA views at times 5.4 (left column) and time 5.9 (right column) for the case with cooling (using the same representation as for the adiabatic case in Fig. 11 ). The difference between top and bottom row is purely in orientation, where the top view is for the face-on line of sight, while the bottom has an inclination of 35°. Unlike the adiabatic case from Fig. 12 , where the overall orientation with respect to the spiral obviously mattered, the case with cooling shows little variation with viewing angle. This is in line with the more volume-filling, spherical redistribution of the mixing zone, as well as with the fact that the views are always dominated by the densest clumps and filaments. This effect will return in virtual photometric observations, which we discuss in the next paragraph. 3.2.3 Virtual photometric observations The fact that we obtained virtual infrared views over areas


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considered at the highest density ( ρ max ), i.e., at t = t coll . From this stage onward, we have assumed that the temperature of the dust and the gas is the same. Thus, we have considered a negative slope for T gas for the collapsing phase. Throughout the first phase, the visual extinction parameter is considered to be constantly increasing from to finally at in t = t coll . Second phase: the second phase of the simulation corresponds to a warm-up phase. Since G10 is a high-mass star-forming region, we consider a moderate warm-up timescale ( t w ) 5 × 10 4 yr (Garrod 2013 ). Therefore, during this short period, the temperature of the cloud from T ice can reach the highest hot-core temperature T max . The density, temperature, and visual extinction parameter remain constant at ρ max , T max , and , respectively. Third phase: this phase belongs to the post-warm-up time. Here, we have considered a post-warm-up timescale ( t pw ) of 10 5 yr, so the total simulation time is . The parameters such as density and visual extinction are assumed to be the same as they were in the warm-up phase. The temperature of the cloud is kept at T max throughout the last phase. 4.2. Binding Energies and Reaction Pathways To study the desorption energy (BE) and reaction pathways of three peptide-bond-like species HNCO, NH 2 CHO, and CH 3 NCO and their isomers/precursors, we use the Gaussian 09 suite of programs (Frisch et al. 2013 ). Recently, Das et al. ( 2018 ) made an extensive effort to estimate the BE of 100 interstellar species on water-ice surfaces by applying a quantum chemical approach and compared their values with the available experimental results. They found that on average, the computed BE shows a larger deviation from experiments when they considered a single water molecule as a substrate. The deviation is minimal when they used pentamer or hexamer configurations of water clusters. They provided a scaling factor for the extrapolation as the computation was performed with smaller water structures. We carry out a quantum chemical study to find out the BEs of the three peptide-bond-related species considered in this work along with their potentially observable isomers. To estimate the BEs of these species, we have used a similar method and basis set (MP2/aug-cc-pVDZ) as mentioned in Sil et al. ( 2017 ) and Das et al. ( 2018 ). Our calculated BE values are given in Figure 7 . For some cases, we have found multiple probable sites for the adsorption and thus obtained multiple BE values. In that case, we take the average of the multiple BEs. Calculated BEs with a single water molecule are then scaled up by a factor of 1.416 (Das et al. 2018 ) to have a realistic estimation. Additionally, in Figure 7 we present the BE values for some of these species with a hexamer configuration of water clusters. Since the BEs with the pentamer/hexamer configurations show minimum deviation (Das et al. 2018 ), one can use these BE values in the model without scaling. We are


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smoothing scales. The error bars are given by the standard deviation from 200 realizations. The 5,10 h 1 Mpc smoothing scale gives similar rms and bias for linear redshift distortion parameter but slightly more bias for larger smoothing. Even though is a nuisance parameter in BAO analysis, it is interesting to observe the value fitted, as it indicates the level at which the redshift corrections are using the right value of the velocity field. The 2 /dof values are very similar between the different smoothing scales explored. Table 4. Best fits for and . Mean and rms from 200 reconstructed QPM mocks. Second block refers to the results using the covariance matrix from 1000 mocks with a fixed smoothing scale of 15 Mpc h 1 . The accuracy in the value is very similar between 5 and 15 h 1 Mpc, but visibly degrades when going to higher smoothing scales. The smaller dispersion for is for 1015 h 1 Mpc; however, the 15 h 1 Mpc is significantly biased (5.3), thus, 10 h 1 Mpc is the best option if we considered only . As we find a relative large bias in 15 h 1 Mpc h 1 Mpc compared to 5, 10, 40 h 1 Mpc, we perform a cross-check between the results using the four smoothing scales as a sanity check. We included in Fig. 5 the dispersions plots of the 15 fits from the mocks, and the R = 5,10, and 40 Mpc h 1 . The legend includes the values of the correlation coefficient in the three cases. The results show that effectively we are using the same set of mocks as they show very high correlation coefficient and that changing the smoothing scale of reconstruction affects slightly the correlation between the results. Figure 5. Dispersion plots of 15 versus 5, 10, 40 . The legend includes the values of the correlation coefficient in the three cases. The large values of the correlation coefficient just show that we are effectively using the same set of mocks for the test and that changing the smoothing scale of reconstruction affects the correlation between the results slightly, but remains large. For , the least significant bias ( b / lower) is for the 5 h 1 Mpc smoothing scale. Considering and simultaneously, the best option is 5 h 1 Mpc which gives the less significant bias with smaller dispersion (0.8 in and 0.9 in ). We find maximal variations in the mean value for best-fitting parameters, 0.5percent for and 0.3percent for , producing D A , H 0.5percent. In the case of , the precision seems to be very similar for the 5 and 15 h 1 Mpc smoothing scales and slightly lower for the 40 h 1 Mpc. The accuracy is also similar for 5 and 15 h 1 smoothing scales and clearly degrades when using a higher smoothing scale. The 2 /dof values are very similar between the different smoothing scales explored. 4 Fig. 6 presents the distributions of the uncertainties for and parameters for different smoothing scales and the quantitative fitting results for the uncertainties are summarized in Table 5 . We can see that the smoothing scale strongly affects the error distributions


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

(Bovy 2015 , dashed red). We also show recent measurements by Callingham et al. ( 2019 ), Eadie Jurić ( 2019 ), Erkal et al. ( 2019 ), and Vasiliev et al. ( 2021 ) with the filled black star, orange circles, purple triangle, and brown square, respectively. Our circular velocity profile shown in Fig. 6 is in excellent agreement with the Cautun et al. ( 2020 ) profile. This model uses MW rotation curve data derived from Gaia DR2 to fit an adiabatically contracted dark matter halo. Interestingly, Cautun et al. ( 2020 ) find a relatively ‘average’ halo concentration for the MW, of and a total (pre-LMC infall) mass of M ⊙ , in excellent agreement with our total mass estimate. Moreover, our total MW mass also agrees with recent measurement using the more distant satellite galaxies as tracers (e.g. Callingham et al. 2019 ; Li et al. 2020 ). It is reassuring that our results at intermediate radii are in such good agreement with independent measures from both the inner and outer halo. 6 CONCLUSIONS In this work, we have applied a distribution function method to a large sample of distant ( r > 50 kpc) halo stars to estimate the mass of the MW out to 100 kpc. We pay particular attention to the systematic effect of unrelaxed substructure, and the dynamical influence of the LMC. Our main conclusions are summarized as follows: We use a rigid MW–LMC model to constrain the systematic reflex motion effect of the massive LMC on our halo mass estimate. As shown by Erkal et al. ( 2020 ), the (pre-infall LMC) halo masses are overpredicted due to the velocity gradients caused by the recently infalling LMC. However, we find that a simple velocity offset correction in v los and v b can minimize the overestimate caused by the reflex motion induced by the LMC, and, assuming a rigid LMC mass of 1.5 × 10 11 M ⊙ , we can recover the true mass within 1 − σ. By applying our method to a sample of MW-mass haloes from the Auriga simulation, we find that the halo masses are typically underestimated by 10 per cent. However, this bias is reduced to if we only consider haloes with relatively quiescent recent accretion histories. The residual bias is due to the presence of long-lived shell-like structures in the outer halo. The halo-to-halo scatter is for the quiescent haloes, and represents the dominant source of error in the mass estimate of the MW. We apply our distribution function method to N = 483 halo stars when high-probability Sgr stars are excluded. The overall sample has a radial velocity anisotropy, β = 0.5, in good agreement with recent measures in this radial range (Bird et al. 2019 , 2020 ). Our estimated mass within 100 kpc is M (100 kpc) = 6.07 ± 0.29 (stat.) ± 1.21 (sys.) × 10 11 M ⊙ . A systematic bias correction (), and additional uncertainty (), are included based on our results from the Auriga simulations. The mass estimates are slightly higher when we do not include a velocity offset to correct for the reflex motion induced by the LMC, or slightly lower


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

emission produced by electrons spiralling on the magnetic field lines in a dipolar magnetic field. From the literature (e.g. Svestka 1981 ; Bastian et al. 1998 ), it is assumed that in the radio range the emission comes from the non-thermal electrons that are accelerated in the corona and then propagate down to the foot-points of the loops with a commonly accepted power-law distribution in energy. Nevertheless, when taking into account the comparison between radio and hard X-ray observations, our 3D magnetic loop radio modelling agrees reasonably well with the literature in relation to the location and sizes of the radio source. The ambient plasma is supposed to be a quiescent background with some temperature and density profiles. It is widely known that the radio emission emanates from the chromosphere to corona where the electrons are trapped due to magnetic mirroring. Thus, the number density of non-thermal electrons refers to different locations in the loop and different distribution of trapped or precipitating particles, from which it follows that a detailed determination of the emitting region parameters in microwaves and hard X-rays is important. We present an alternative approach to the time-consuming process to calculate a non-homogeneous model – each time one is needed for a flare analysis – by providing a data base of pre-calculated models constrained by some statistical properties of a large sample of Nobeyama observations. We know that this data base is still limited in terms of the wide range of parameter combinations needed to calculate the gyrosynchrotron emission to describe all possible scenarios of flares in the microwave. We statistically analysed 10 important parameters, that in general cannot be directly observed, to explain a flare as shown in Fig. 6 . We found that 8 out of 10 parameters in the simulations were recovered with a relative error ≤20 per cent on average. We consider this result an improvement for flare analysis in terms of the time consumed with the calculations. Although the data base was produced using equally distributed parameters from the lower to upper limits, the geometric bias discussed in Section 6.1 results in differences in the distributions of geometry, magnetic field, and energy parameters. In the energy parameters, the observed solar bursts show preferences for lower non-thermal electron density and a slight preference for higher densities for the limits used here. The magnetic field distribution shows some preference for higher values than the centre of the data base range we used. We also noted some shift in the distribution for loop-top events. In general, the geometric parameter distribution shows a tendency for bigger loops. Differences between individual solutions are mainly due to the degeneracy of results with quite similar χ 2 in the dominion of 10 parameters. This is the reason that we preferred the averaged solution weighted by the χ 2 . Table 3 shows the best parameters inferred


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

and 0.4307keV, respectively. If that is indeed the origin of these features, it would be consistent with the presence of strong, highly ionized C and N emission lines in the UV (Cenko etal. 2016 ). Interestingly, Miller etal. ( 2015 ) also suggest several highly ionized emission features are present in their high-resolution spectra, particularly near the O K-edge. Figure 6. Merged X-ray spectra of ASASSN-14li seen at early times (first 200d, black crosses) and later times (after 200d, red crosses). Each spectrum is binned with a minimum of 20 counts per energy bin. The early-time spectrum is best fit with two Gaussian emission features superimposed on a blackbody (black solid line), while the late-time spectrum is consistent with a purely blackbody model (red solid line). The residuals from the fits are shown in the bottom panel. Irrespective of the origin of the emission features, the X-ray emission from ASASSN-14li is reasonably well described by a blackbody. The temperature of the X-ray emission shows only a moderate decrease with time, from 810 5 K down to 4.510 5 K. We also find that between the early- and late-time observations, the mean column density decreases by a factor of 2, becoming comparable to at later times. This could indicate that at early times the material surrounding the TDE was dense, not highly ionized, and obscured the lower energy X-rays, while at late times the material surrounding the event has been nearly completely ionized and thus transparent to the lower energy X-ray photons. We note that the amount of material required to produce this absorbing column is small relative to the overall mass budget, even in the contrived scenario where all of the absorbing material is spherically distributed at the H-emitting radius: M, where f is the covering fraction, r 17 is the characteristic radius of the absorbing material in units of 10 17 cm and N 20 is the hydrogen column density in units of 10 20 cm 2 . Furthermore, our modelling suggests there may be a factor of a few variability in the column density between the individual epochs. Unfortunately the spectra for the individual epochs do not reach the S/N required for a precise determination of the column density. We also note similar variability and overall decrease in the absorbing column in the eight temporally binned spectra. The moderately decreasing temperature and variability in the column density are similar to the findings from Miller etal. ( 2015 ), but we have increased the temporal baseline by a factor of 3. Finally, we note that the Swift XRT detector lacks the energy coverage to discriminate between a bremsstrahlung and blackbody spectrum. While we have assumed the X-ray emission to be well described as a blackbody, there is only marginal evidence that the X-ray spectrum turns over at lower energies. It is plausible that the X-ray emission arises from tidal debris shocking the ambient medium in the vicinity of the SMBH. For ionized gas in the strong shock


O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O B-Grant O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O B-Grant

This work was supported by the Spanish Ministry of Science and Innovation under project number FIS2009-09898 and by the Spanish Ministry of Economy and Competitiveness under project number FIS2013-40653-P.


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

can be noticed as a non-local equation of state as it describes the radial pressure as a function of the energy density at a specific point on the manifold (under the constraint f ( R, T, Q ) = R ). Now, we consider two subcases as follows. 4.1 The Gokhroo and Mehra Ansätz In order to continue the systematic analysis, we take the assumption introduced by Gokhroo and Mehra, as where K ∈ (0, 1), and μ o is a constant. Utilizing equation ( 59 ) in equations ( 10 ) and ( 17 ), we get and Further, from equations ( 11 ) and ( 12 ), we obtain It could be useful to introduce new structural variables as In this context, after substituting equation ( 63 ) in equation ( 62 ), we obtain which appears to be in form proposed by Ricatti. The integration of this expression produces the line element in terms of z and Π in the background of f ( R, T, Q ) theory as where C is integration constant. Thus, one may write the effective forms of physical variables as Such kind of solutions could be helpful to understand some hidden and very interesting features of the spherical systems. Di Prisco et al. ( 2011 ) calculated such results in the background of GR. These results were modified by Sharif and Yousaf for the cases of cylindrically Sharif Yousaf ( 2012b ) and shearfree spherical Sharif Yousaf ( 2012a ) structures. Yousaf ( 2017 ) and Bhatti ( 2016 ) further extended these results for Einstein-Λ gravity. To obtain non-singular characteristics of the obtained solutions, the obtained solutions ( 66 )–( 68 ) should satisfy equations ( 19 )–( 21 ) at the boundary. 4.2 The polytropic fluid with zero complexity factor In this subsection, we study polytropic relativistic fluid in the presence of f ( R, T, Q ) corrections. To deal with the system of equations, we require vanishing complexity factor condition to supplement with the polytropic equation of state. Here, we consider two cases of polytropes separately. The first one is with the polytropic constant K , polytropic exponent γ and polytropic index n . To make the dimensionless form of TOV equation and the mass function, we may define some new variables as where subscript c shows that the quantity is calculated at the centre. At the boundary r = r Σ (ξ = ξ Σ ), we have ψ(ξ Σ ) = 0. Putting these dimensionless variables in TOV equation, we get Differentiating ν(ξ) and substituting the value of m ( r ), we get In two ordinary differential equations ( 72 ) and ( 73 ), there are three unknown functions ν, ψ, and Π. For the unique solution of these equations, we need an extra condition. To obtain this, we assume the vanishing complexity factor condition in form of dimensionless variables. This gives These differential equations have a unique solution for arbitrary values of two parameters n and α. Any solution of these equations provide the mass, density, radius, and pressure of peculiar stellar object for the specified values of n and α. Now, we consider the second case of polytropic equation of state , where μ b


O O O O O O O O O O O O O O B-Person O O O O O O O B-Fellowship I-Fellowship I-Fellowship O B-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization O O O O B-Organization O O O O O O B-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization B-Survey O O O B-Location O O O O O O O O B-Telescope I-Telescope O B-Survey O O O O O O O O O B-Survey I-Survey I-Survey I-Survey O O B-Survey I-Survey I-Survey I-Survey I-Survey O O O O B-Survey O O O O O O O O O O O O B-Telescope B-Survey B-Telescope B-Survey B-Telescope B-Survey B-Telescope O B-Telescope B-Survey B-Telescope O B-Telescope O B-Wavelength O B-Wavelength O B-Survey O O O O B-Organization B-Location O B-Organization B-Location O B-Observatory O O O O O B-Survey O O B-URL O O B-Telescope B-Survey O O O O O O O O O O O B-Observatory O O O B-Observatory I-Observatory I-Observatory I-Observatory O O O B-Proposal

The authors acknowledge the reviewer for their detailed and thoughtful comments on this work. MA is funded by an appointment to the NASA Postdoctoral Program at Ames Research Centre, administered by Oak Ridge Associated Universities through a contract with NASA, and acknowledges past funding from the University of Western Australia and the University of St Andrews. GAMA is a joint European-Australasian project based around a spectroscopic campaign using the Anglo-Australian Telescope. The GAMA input catalogue is based on data taken from the Sloan Digital Sky Survey and the UKIRT Infrared Deep Sky Survey. Complementary imaging of the GAMA regions is being obtained by a number of independent survey programmes including GALEX MIS, VST KiDS, VISTA VIKING, WISE , Herschel -ATLAS, GMRT, and ASKAP providing UV to radio coverage. GAMA is funded by the STFC (UK), the ARC (Australia), the AAO, and the participating institutions. The GAMA website is http://www.gama-survey.org/ . The VISTA VIKING data used in this paper are based on observations made with ESO Telescopes at the La Silla Paranal Observatory under programme ID 179.A-2004.