the system cannot fulfil thermal and mechanical equilibrium conditions simultaneously unless some further assumptions are implemented. Since the initial state is in mechanical equilibrium and the upper and the lower layers have different densities, their temperatures cannot be the same. Thermal equilibrium, however, implies that both layers have the same temperature. In order to resolve this contradiction, JK proposed that one layer is optically thin and the second layer is optically thick. They also assumed that the system is adiabatic. In the optically thin regime, where opacity on one or both sides of the interface is negligible, continuity of E r holds on whereas T g is independent of E r . There are, however, further alternative ways to specify background state self-consistently. Jiang et al. ( 2013 ), for instance, argued that even when the background state is not strictly in thermal equilibrium, its evolution affects subsequent thermal evolution very slightly so long as the thermal time-scale is much longer than the instability time-scale. Under these circumstances, therefore, the initial configuration can be imagined to be in thermal equilibrium for exploring RT instability. Jiang et al. ( 2013 ) constructed an initial state with zero absorption opacity and effectively infinite thermal time-scale. As we mentioned earlier, JK assumed that one side of interface is in the adiabatic regime, and the other side is in the optically thin regime. Here, we follow JK assumptions for specifying the initial equilibrium state, which are applicable to some astrophysical systems. The momentum and the energy equations are written as where . Equation ( 34 ) is written based on the radiative equilibrium assumption. The parameter E represents the Eddington limit of the background state. We note that the introduced parameter E is then replaced by E 1 and E 2 for the lower and the upper layers, respectively. Also, we have Introducing the ratio of the radiation pressure to the gas pressure as r = p r / p g , we can then write and We note that the Eddington limit parameter E is a fixed input parameter; however, the parameter r is not a constant under our imposed conditions. 4.2 Linear perturbations After deriving the above equilibrium solutions, we can now linearly perturb RMHD equations. Following JK , we also apply adiabatic approximation by which we mean perturbed energy flux is neglected. It means that we require F ́ ≪ E t u ́. Using this approximation, we can assume that the opacity is a constant. Therefore, the parameter E becomes a constant, which is actually our implemented assumption. This parameter, however, may be different in the upper and lower layers. We thereby arrive at the following equations: As before, we assume that all the perturbed quantities are proportional to exp (ω t + i k x x ), and the above equations after lengthy but straightforward calculations reduce to the following equations: where parameters B and C depend on the input

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


with redshift in terms of the density parameters of both SF and AGN components of the RLF. In terms of luminosity evolution, parameters of both the SF and AGN components are consistent with being constant with redshift. We note that the normalization of the radio luminosity function of optically selected quasars by Kimball et al. (2011) and Condon et al. (2013) , shown in the first panel of Fig. 6 , is more than an order of magnitude lower than that constrained by fitting our data with the analytic RLF form of Eq. ( 8 ). The main cause of this difference is most likely different sample selection. While optically-selected quasar samples by Kimball et al. and Condon et al. contain only the unobscured quasars, sampling quasars with very high bolometric luminosities, our XQSO sample contains a combination of both obscured and unobscured quasars. By examining the hardness ratios (HRs) of XQSOs ( Civano et al. 2016 , Marchesi et al. 2016 , Pierre et al. 2016 ) and applying a threshold of HR = −0.2 to separate obscured from unobscured sources (e.g., Civano et al. 2012 ), we found that most of XQSOs (190/274) are obscured based on their X-ray emission and most likely would not be included in samples of optically-selected quasars. 5. Discussion In this section, we discuss the possible contributions to the detected radio emission: star-forming processes within the host galaxy in Sect. 5.1 and AGN activity in Sect. 5.2 . In Sect. 5.3 we define thresholds in 1.4 GHz radio luminosity below and above which more than 80% of the XQSOs are dominated by the star formation and AGN-related radio emission, respectively. This enables us to disclose the true composite nature of the XQSOs in which both star formation and AGN activity make a significant contribution to the radio luminosity. 5.1. Host galaxies of XQSOs The sample of XQSOs studied in this work was drawn from the moderate-to-high radiative luminosity AGN sample in COSMOS and high-excitation radio galaxy sample of AGN in XXL-S. Host galaxy properties of these AGN have been studied by Delvecchio et al. (2017 ; COSMOS) and in Paper XXXI (XXL-S). Both studies found that the host galaxies of these AGN have star formation rates (SFRs) and stellar masses consistent with typical main-sequence galaxies. The same conclusion was reached by Stanley et al. (2015) from an analysis of a sample of ∼2000 X-ray selected AGN (10 42 erg s −1 L 2−8 keV 10 45.5 erg s −1 ) detected in the Chandra Deep Field North and South and the COSMOS field. They studied the distribution of star formation-related IR luminosity and X-ray luminosity over 0.2 z 2.5, as proxies of SFRs and AGN activity, respectively. They found a strong evolution of their average L IR, SF with redshift, similar to that observed for the main-sequence galaxies. These results were confirmed by multiple other studies of quasar and AGN host galaxy properties (e.g., Rosario et al. 2012 , 2013 , Lanzuisi et al. 2017 , Stanley et al. 2017 , Suh et al. 2017 , 2019 ).

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 B-Wavelength O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O 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 B-Wavelength O O O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O B-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 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 I-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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-Survey O O B-Wavelength O O O O O B-Survey O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Survey O O B-Citation I-Citation B-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Wavelength O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O B-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion O B-CelestialRegion O O B-CelestialRegion I-CelestialRegion 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 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 B-Citation I-Citation I-Citation I-Citation O B-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 O


from isolated cold globules to rich clusters. There are two common observational measures of environment. First, there are the environmental conditions set by the properties of the natal molecular gas, particularly the dense gas. Second, there are environmental variations traced by the protostars, including the densities of young stars and the systematic changes in their properties. These protostars and their properties have been quantified with Spitzer data (Megeath et al. 2012 , 2016 ) and Herschel data from HOPS (Furlan et al. 2016 ). With Herschel observations at longer wavelengths and of wider fields than included in HOPS, Stutz Kainulainen ( 2015 ) measured the column density ( N H ) and mass distributions across Orion A, quantifying environmental differences. They found that the column density probability distribution functions vary with location. Furthermore, Stutz Gould ( 2016 ) and Stutz ( 2018 ) found that the mass per unit length ( M / L ) varies significantly across Orion A, with the Orion Nebula Cluster (ONC) having a higher M / L than the Integral-Shaped Filament (ISF), and the ISF having a higher M / L than LDN 1641. These column density and mass variations imply variations in the volume density and gravitational potential across the cloud. Environmental variations are also found in the radial velocities of the gas. González Lobos Stutz ( 2019 ) showed that gas radial velocities in both high- and low-density tracers show significant variations within the ISF. In particular, the northern portion has more centrally concentrated gas with stronger overall velocity gradients compared to the southern portion, which transitions to the LDN 1641 region. Systematic variations of the temperatures, line widths, and densities of cores across Orion A were also found by Wilson et al. ( 1999 ). Turning to the stellar content, the observed properties of the protostars vary with environment. Kryukova et al. ( 2012 ) found variations in the Orion clouds, where protostars are more luminous in dense regions. Stutz Kainulainen ( 2015 ) found that the fraction of protostars in the young Class 0 phase varies systematically with changes in environment as indicated by variations in the slope of the dust column density probability distribution function ( N -PDF) across the region. The variation in this fraction may result from differences in the star formation history between these regions, as also suggested by Fischer et al. ( 2017 ), the influence of feedback (Sadavoy et al. 2014 ), or variations in infall rates of the protostars due to variations in the densities of their birth environments (Kryukova et al. 2012 , 2014 ; Dunham et al. 2014 ). This paper is part of a series describing results from HOPS. These papers include evolutionary studies of protostars via modeling of their SEDs (Furlan et al. 2016 ; Fischer et al. 2017 ), the analysis of far-IR protostellar spectra (Manoj et al. 2013 , 2016 ), the discovery and characterization of the

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O B-Citation I-Citation I-Citation I-Citation O B-Citation O O B-Telescope O O B-Survey B-Citation I-Citation I-Citation I-Citation O O B-Telescope O O O O O O O O O O O B-Survey B-Citation I-Citation I-Citation I-Citation I-Citation 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 B-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O B-CelestialObject I-CelestialObject I-CelestialObject B-CelestialObject O O O O O O O O B-CelestialObject I-CelestialObject B-CelestialObject O O B-CelestialObject 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-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-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation 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 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 B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O B-Survey 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 O O B-Citation I-Citation I-Citation I-Citation O B-Citation O O O O O O O


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both the expansion history, due to the scalar field, and the evolution of the density perturbation amplitudes, due to the coupling. 3 SIMULATIONS For our study, we produced simulations of the following three cosmologies: a reference CDM, an uncoupled quintessence model and a CDEdark matter model with a coupling parameter 0 . Following Elahi etal. ( 2015 ), we choose ( h , m , b , 8 )(0.67, 0.3175, 0.049, 0.83), ensuring all cosmologies have parameters consistent with z 0 CDM Planck data (Planck Collaboration XVI 2014a ; Planck Collaboration XIII 2016a ). The coupling parameter, 0 0.05, in our simulation is chosen to test the boundaries of allowed coupling (see Pettorino etal. 2012 ; Xia 2013 ) in order to maximize any observational differences that may exist between this cosmology and the standard CDM model. The linear power spectrum and growth factor f dln D ( a )/dln a are calculated using first-order Newtonian perturbation equations and the publicly available Boltzmann code cmbeasy (Doran 2005 ). We note that although these simulations have neglected star formation and feedback physics, baryons do not appear to significantly change the void population. Large underdense regions remain underdense, regardless of whether the simulation includes dark matter only, or accounts for hydrodynamic or full baryonic physics (Paillas etal. 2016 ). Initial conditions are generated by perturbing particles placed on a Cartesian grid with the first-order ZelDovich approximation using a modified version of the publicly available n-genic code. The modified code uses the growth factors calculated by cmbeasy to correctly calculate the particle displacements in the non-standard cosmologies. All the simulations are started at z 100 with the same phases in the density perturbations. Choosing the same initial phases results in underdense regions forming in the same locations in all simulations. Each underdense region in a given simulation has a corresponding underdense region in other simulations (perhaps with different properties such as density or size, depending on cosmology). This is the case despite potentially different exact profiles of density perturbations between cosmologies with different power spectra, such as CDM and CDE. We use dark-gadget , a modified version of the p-gadget -2 N -body code (for more details, see Carlesi etal. 2014a ). The key modifications are the inclusion of a separate gravity tree to account for the additional long-range forces arising from the scalar field, and an evolving dark matter N -body particle mass that models the decay of the dark matter density. The code requires the full evolution of the scalar field , the mass of the dark matter N -body particle and the expansion history. Our simulations are 500 h 1 Mpc boxes containing 2512 3 particles (dark matter and gas) giving a mass resolution of m dm ( m gas )6.9(1.3)10 10 h 1 M . 1 Though the mass resolution is poor for identifying haloes, this resolution is more than enough to

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between the two models, though the BHWR model has a slightly higher duty cycle than the onyWind model that matches the correspondingly higher SMBH mass growth (compare Fig. 3 ). Figure 5. Time distribution of different accretion rates in units of the Eddington limit (so-called BH duty cycles) for the different models (see legend) compared to observations (square: Ho 2009 , circles: Greene Ho 2007 , upward-pointing triangles: Kauffmann Heckman 2009 , downward-pointing triangles: Heckman etal. 2004 , all taken from Novak etal. 2011 ). Both simulated models fall above all of the observed values at Eddington ratios of 1 and 10percent. 4 BH-GOVERNED ISM EVOLUTION IN THE GALACTIC CENTRE In the previous section, we have shown that feedback from the central SMBH is both necessary to, and capable of keeping an isolated ETG quiescent. The more physically complete feedback model, including both wind and radiative feedback, is more efficient at this than the pure wind-feedback model. In this section and the next, we will now examine how the feedback achieves the quiescence through its influence on the galactic gas, and how it creates metal-rich, large-scale outflows that enrich the CGM. We begin with Fig. 6 , which shows colour maps of the surface density (top row) and the density-weighted average temperature (central row) in a 10kpc thick, 10 10kpc wide region around the galactic centre (and therefore around the central SMBH), as well as the temperaturedensity phase diagrams of all the galactic gas (bottom row). In the maps, the line of sight is chosen to be parallel to the initial angular momentum of the hot halo. The solid vertical and horizontal lines in the phase diagrams mark the star formation thresholds in density and temperature, respectively, i.e. gas in the bottom-right corner of the diagrams is star forming. The individual temperaturedensity bins are colour-coded for gas particle number density, which is rising from blue to red colours. The dashed line marks the resolution of the simulation limit following the Jeans mass criterion. Above the dashed line, the Jeans mass of the gas is resolved, i.e. it is larger than the kernel mass M ker N ngb m gas 10 7 M , while it is unresolved below the line, meaning that gas in this region could collapse under self-gravity due to numerical noise. Almost all of the gas particles with unresolved Jeans mass are in the star-forming region of the phase space, and will be turned into star particles if they stay in this region. Hence, while this resolution does not allow us to make predictions about the substructure of the dense, cool gas, it is high enough to investigate the global and larger scale effects of AGN feedback that interest us in this paper. The three left columns show the state of the three models (from left to right: no-BH, BH-W, BH-WR) at the end of the simulation time, while the last column to the right shows the state of the BH-WR model about 30Myr before the end of the simulation. Figure 6. Maps

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


relative to the forcing from m p is Even with the uncertainties of various parameters, the inner two planets are weakly coupled to the stellar spin. The stellar obliquity (relative to ) therefore varies between |θ ⋆ p − θ 12, p | and θ ⋆ p + θ 12, p (see equations 12 – 13 ; note that since L p ≫ L 12 = L 1 + L 2 for this system, is aligned with ). The observed stellar obliquity (λ ≥ 37°) then implies θ ⋆ p + θ 12, p ≥ 37° (see Li et al. 2014 , for a previous analysis). 5 DISCUSSION The main goal of this paper is to inform the readers that there is a simple way to assess the dynamical role of external perturbers on the spin–orbit misalignments of planetary systems. The key is to evaluate the star–planet spin–orbit coupling parameter (equation 9 ) in response to the differential precession induced by the external companion. We have presented analytic results in various limiting regimes, and discussed how the general results (see Fig. 1 ) scale with different physical parameters (Section 2). Similar analysis can be done for multiplanet systems (Section 4), with the generalised spin–orbit coupling parameter given by equation ( 31 ). As alluded to in Section 1 , continuing observations on spin–orbit misalignments and external companions in HJ and other compact planetary systems may shed light on the formation mechanism of close-in planets. Several recent works of such systems have either neglected some key physical ingredients (spin–orbit coupling) or made such a relatively simple problem unnecessarily complex or obscure. We hope that the results of this paper (see also Lai 2016 ) will make future analysis simpler and more transparent. A recent analysis on spin–orbit alignments of HJs around cool stars concluded that the exterior companions are coplanar (Becker et al. 2017 ). While this may be the case of a few systems with gas giant companion at ∼1 au, similar conclusions cannot be drawn for systems with a slightly more distant companion (see Section 3 , especially Fig. 2 ) since the spin–orbit coupling parameter ε ⋆1 depends sensitively on the perturber’s semimajor axis (; see equation 24 ). Certain HJ formation mechanisms (e.g. LK migration) require an external companion with a high inclination (>40°). As a result, constraints placed on the mutual inclination via the method discussed in this paper may in principle lead to a constraint on the migration mechanism. However, we emphasize that the inclination of giant planet companion may only be constrained when it is relatively close (at ∼1 au, so that ε ⋆1 ≳ 1, see equation 24 ), such as for WASP-41 and HAT-P-13. These systems clearly could not have formed in the classic LK migration picture (with the HJ originating at ∼1 au or beyond), because the initial configuration would be unstable. LK migration requires a much more distant companion (at, say ∼5 − 10 au, so that the initial configuration is stable). Such a companion will satisfy ε ⋆1 ≪ 1, so that it is unable to affect the star-HJ

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


Chandraobserved 4C +74.26for 70 ks in total using the HETGS in combination with the ACIS detector. The total exposure time was split into two observations that were taken two days apart. For both Obs-ID 4000 and 5195 we retrieved the Medium (MEG) and High Energy Grating (HEG) spectra and their respective response matrices from the tgcat 1 archive. We further treated these spectral products with the CIAO tools (version 4.6). For each observation and for both HEG and MEG, we combined the first positive and negative spectral order using the CIAO script add_spectral_orders. Hence, we fitted jointly HEG and MEG (allowing a free intercalibration factor) with a simple phenomenological power law to check for variability between the two observations. The fitted slopes (, ) and normalizations (Norm, Norm) were very consistent with each other (see below for a physically motivated fit). Therefore, we were able to sum the spectra of individual observations into a single spectrum to improve the signal-to-noise ratio. We did this using the CIAO script add_grating_spectra. We reduced the raw XMM-NewtonObservation Data Files (ODF), available at the ESA archive 2 , using the Science Analysis Software (SAS, version 13) and the HEASARC FTOOLS. We created calibrated EPIC-pn event files selecting only the unflagged single events. To check the time stability of the background we used the light curve in the hard 10–12 keV band, which is background dominated. A high level of background light due to soft proton contamination is evident towards the end of the observation. Thus, we cleaned the event file using a time filter, following the same procedure explained in Di Gesu et al. (2013) . For RGS-1 and RGS-2 we created calibrated event files and background light curves taking the background from CCD 9. The RGS background light curve was quiescent. Next, for all the instruments, we extracted the source and background spectra and we created the spectral response matrices. Finally, we extracted the source count rate in all the available OM filters, namely ( Å), ( Å) and ( Å). Using the interactive SAS tool omsource, we computed the source count in a circular region centered on the source coordinates and with a radius of 6 pixels. For the background we used another circular region of 12 pixels, free from other sources and instrumental contamination. We converted the count rates to fluxes using the standard conversion factors provided in the SAS watchout web page 3 . Hence, assuming , we corrected all the fluxes for the Galactic reddening ( =0.39, Schlafly Finkbeiner 2011 ). For the correction, we used the IDL routine ccm_unred, which dereddens a user-defined vector of fluxes using the Galactic extinction curve of Cardelli et al. (1989) . Fig. 1 Spectral energy distributions for 4C +74.26. Filled circles: OM fluxes corrected for the Galactic extinction. Open squares: X-ray intrinsic continuum obtained from a phenomenological fit of the EPIC-pn spectrum. Fig. 2

B-Telescope O O O O O O O O B-Instrument O O O O B-Instrument O O O O O O O O O O O O O O O O O O B-Identifier I-Identifier O B-Identifier O O O B-Instrument B-Instrument O B-Instrument I-Instrument I-Instrument B-Instrument O O O O O O O O O O O O O O O O O O O B-Software O O O O O O O O O B-Instrument O B-Instrument O O O O O O O O O O O B-Software O B-Software O O O O B-Instrument 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 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-Software O B-Software O O O O B-Telescope O O O O O O B-Archive I-Archive O O O O B-Software I-Software I-Software B-Software B-Identifier I-Identifier O O B-Software I-Software 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 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 B-Citation I-Citation I-Citation I-Citation I-Citation O O B-Instrument O B-Instrument O O O O O O O O O O O O O B-Instrument I-Instrument O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O O O O O O O O O O O O O O B-CelestialObject O O O B-Citation I-Citation I-Citation O O O O O O O B-Software O B-Software O O O O O O O O O B-CelestialObject O O O B-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 B-CelestialObject O O O B-Wavelength O O O O O O O O O B-Instrument O O O


suppression of gas inflow into a massive core (Ikoma Hori 2012 ). For example, high opacities of dust grains in a disk reduce accumulation of a disk gas by a massive core (Lee et al. 2014 ; Lambrechts Lega 2017 ). Gas dynamics around a planet embedded in a disk would be another adjustment knob for the gas flow. Ormel et al. ( 2015 ) found that an isothermal gas flow from high altitude might escape from the gravitational sphere of a planet before accreting onto it. A rapid recycling of a disk gas regulates gas accretion onto a massive core, whereas in a non-isothermal case this recycling process would be limited by an entropy gradient between the ambient disk gas and the atmosphere (Cimerman et al. 2017 ; Kurokawa Tanigawa 2018 ). According to recent magnetohydrodynamic (MHD) simulations, the gas flow structure in a disk has two layers, which is similar to the layered accretion model (e.g., Gammie 1996 ). There can be a rapid gas flow driven by a disk wind near the disk surface due to the effect of magnetic braking (e.g., Bai Stone 2013 ; Suzuki et al. 2016 ), while the accretion flow would be weaker at the midplane of the disk. In fact, global ideal MHD simulations observed a supersonic accretion flow in the upper layer of a disk (Zhu Stone 2018 ). A rapid gas flow near the disk surface may put a brake on runaway gas accretion onto a planetary core. In this paper, we have investigated how a time-dependent layered accretion in a disk affects formation of super-Earths having H 2 /He atmospheres. We have performed N -body simulations for formation of close-in super-Earths, coupled with disk evolution based on MHD simulations and gas accretion onto a planetary core. Note that hydrogen can be generated from secondary processes such as degassing via oxidation of metallic iron by water (Abe et al. 2000 ) and H 2 O photolysis and escape from a planet via stellar X-ray and extreme ultraviolet (XUV) irradiations (e.g., Lammer et al. 2013 ) and interactions between the stellar plasma and a hydrogen atmosphere (e.g., Kislyakova et al. 2013 ). However, a long-term evolution of a super-Earth’s atmosphere after the formation stage (≳10 Myr) is beyond the scope of this paper. The paper is structured as follows: We present detailed descriptions of models in Section 2 . Results of gas accretion rates onto planetary cores and their orbital evolution are shown in Section 3 . The radial dependence of the occurrence rate of gas giants and the validity of our model are discussed in Section 4 . We summarize this study in the last section. 2. Model 2.1. Disk Evolution For the evolution of a protoplanetary disk including effects of magnetically driven disk winds, we adopt the model of Suzuki et al. ( 2016 ), in which the diffusion equation is given bywhere Σ g , Ω, c s , and H are the gas surface density, the Keplerian angular velocity, the sound speed, and the disk scale height, respectively. The first two terms on the right-hand side induce radial mass accretion

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


atmospheres with the classical 1D approach we can calculate abundance corrections and abundance errors. Given a measured LTE abundance, we define the abundance correction as the abundance difference compared to LTE, such that the non-LTE equivalent width matches the LTE equivalent width. 3 Results 3.1 Departure coefficients In order to understand the behaviour of the abundance corrections and , we can look at the variation of the departure coefficients, b ( τ R ) = n NLTE ∕ n LTE , for the 1D hydrostatic models and 2D models. For the first, b 1D values were calculated for the lower 3s 5 S and upper 3p 5 P levels of the O I 777 nm triplet in the 4D parameter space τ R , T eff , log g eff , ξ t . For each combination a cubic interpolation that splits the multi-dimensional case into a sequence of 1D interpolations was performed on the grid of 1D models to obtain departures from LTE as functions of the Rosseland optical depth. In the 2D models – due to the horizontal inhomogeneities produced by convection – departures from LTE b ( τ R ) are different for in- and outflows (e.g. Amarsi et al. 2016 ). In order to compare departures from LTE for 2D models with the 1D case, b 2D values for each individual 2D snapshot were horizontally averaged over surfaces of constant optical depth. Both 2D models predict a similar dependence of the abundance corrections on effective temperature. Since they are similar we focused on the nine-day model, and calculated median 2D departures from LTE. We plot the departure coefficients in Fig. 3 . Namely, the median 2D departures from LTE as a function of τ R and photometricphase for the lower and upper levels are shown by solid blue and red lines, respectively. One-dimensional interpolated b 1D departures from LTE are shown by dashed lines using the same colours for the levels. Qualitatively, the departures from LTE of 1D and 2D models show a similar dependence on the photometric phase. The lower and upper levels of the O I 777 nm triplet, namely 3s 5 S and 3p 5 P, are almost always overpopulated during the pulsating cycle. At photometric phases φ ph ≈ 0.3...0.8 the lower and upper levels are less underpopulated compared to the rest of the phases, due to the minimum on the light curve and effective temperature. Quantitatively, for this range of phases 1D and 2D models predict very similar optical depth dependences of the departures from LTE. As a result, the abundance correction is small. Moreover, the 2D non-LTE versus 1D LTE abundance correction turns out to be smallest, as shown in Sect. 3.5 . 3.2 O I 777 nm triplet profiles We illustrate the temporal evolution (over a pulsation cycle) of the normalised emergent LTE and non-LTE O I 777 nm triplet flux profiles in Fig. 4 for M3 and M9. The line profiles are shown without adding instrumental broadening or noise. This allows us to identify the occasional multi-component structure of the line profiles, for example at photometric phases φ ph = 0.299 and 0.318 for M3 and

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


8 of Savino et al. 2019 ) is about 0.5–0.6 × 10 −4 M ⊙ yr −1 , in good agreement with the SFR of about 0.4 × 10 −4 M ⊙ yr −1 measured in our work. The both measurements show the comparable total stellar mass 3.13 × 10 6 M ⊙ (4.2 × 10 6 M ⊙ ). The bottom panel of Fig. 4 shows the stellar mass formed in the last 2 Gyr versus the galaxy absolute magnitudes. The percentage of the mass formed is small for all the objects. This plot could demonstrate how intensive is the residual SF in dSph galaxies depending on the degree of isolation of the object. Highly isolated galaxies clearly show recent residual SF (>10 per cent of the total stellar mass), while within the virial radius it is practically zero. And XVIII and Tucana are situated beyond the virial radius (but within the LG zero-velocity sphere). Following the logic of the above plot, they should be located between those two extreme cases. None the less, Tucana is again out of the trend, located among the galaxies inside the virial radius. It also could be an argument in favour that in the past this dwarf was among the closer satellites of M 31. Simpson et al. ( 2018 ) predicted quenching of SF in satellite galaxies of the LG from a suite of 30 cosmological zoom simulations of MW-like host galaxies. The authors found that systems within host galaxy R 200 are comprised of two populations: first infall and ‘backsplash’ galaxies that have had a much more extended interaction with the host. Backsplash galaxies that do not returned to the host by z = 0, exhibit quenching properties similar to galaxies within R 200 and are distinct from other external systems. The last scenario are well match with the SF properties of Tucana dSph. It should be noted that the results are affected by the well-known problem of age–metallicity degeneration in the process of SFH measurement, and some dependence of the results on the isochrone set used (Williams et al. 2017 ). Besides, the obtained CMDs are somewhat not deep enough, in the sense that the photometric limit is brighter than MSTO. At the same time, uniform data set and its homogeneous processing should reduce the influence of these factors on the results of our comparative analysis to a minimum. When analysing SFHs of dwarf satellite galaxies in the nearby galaxy groups (first of all, the LG), one should take into account, that even in a particular mass range and fixed environment, there is a large degree of scatter in the SFHs, frequently noted in various researches (see e.g. Garrison-Kimmel et al. 2019 ). The mentioned study has used a set of about 500 dwarf galaxies taken from FIRE-2 (The Feedback In Realistic Environments 2) simulations to explore how their SFHs vary with environment. They conclude, that the satellites ( d ≤ 300 kpc) tend to form their stars earlier than equivalent 300 d 1000 kpc dwarfs, consistent with the picture, where interactions with MW-mass hosts inhibit SF. A galaxy could loss its gas due to ram pressure effects and tidal

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


of SNe Iax, which are in the range 12+log(O/H)=∼8.16–8.87 (Magee et al. 2017 ; Lyman et al. 2018 ), somehow lower than the solar abundance (Caffau et al. 2008 ). This indicates that the site of SNe Iax may have relatively lower metallicity compared with other subtypes of SNe Ia, but comparable to that of SNe II or SNe Ibc. Note that Lyman et al. ( 2018 ) recently carried out an analysis of metallicity for the host galaxies and explosion sites of a large sample of SNe Iax through both integral-field and long-slit spectroscopy and they also found that the SN Iax explosion site metallicity distribution is similar to that of core-collapse SNe. We also measure the fractional flux of the SN site, which is the fraction for which the total host light in a pixel is fainter than or equal to the light in the pixel at the location of the SN. This parameter can be used to trace the difference/similarity between luminosity at SN locations and the light of the hosts (Fruchter et al. 2006 ). As the fractional flux is independent of galaxy morphology and size, it is thus a better parameter to quantify the correlation between SN progenitor environments and the light of their hosts (i.e. Wang et al. 2013 ). Such an analysis can be performed for 21 SNe Iax of our sample by using the host-galaxy images from SDSS DR12 (Alam et al. 2015 ) and Panstarrs (Chambers et al. 2017 ); the results are also tabulated in columns (9)–(11) of Table 5 . The distribution of the fractional fluxes of our SN Iax sample in the ugr bands is shown in Fig. 14 . The fractional flux distributions of SNe Ia, SNe Ibc and SNe II are overplotted for comparison and the measurements of these samples are taken from Wang et al. ( 2013 ). One can see that the progenitor populations of SNe Iax belong to the brighter regions of the host galaxies, similar to the case for SNe Ibc (especially in the g and r bands), suggesting that SNe Iax may arise in larger star-forming regions that produce more massive stars. This is also evidenced by the Kolmogorov–Smirnov (KS) test results, as tabulated in Table 6 . One can see that SNe Iax and SNe Ia trace the host-galaxy light differently, with a very low probability (i.e. P = 0.04 in r ) that they come from the same stellar populations. SNe Iax also show some differences from SNe II in the light distribution of progenitor populations, with KS test results of P = 0.13 in g and P = 0.17 in r , respectively. In the u band, however, we notice that SNe Iax seem to show large differences from all kinds of SNe in the fractional flux distribution. This is likely related to the relatively larger uncertainty in the SDSS u -band photometry. As for the comparison between SNe Iax and SNe Ibc, P values of 0.33 obtained in the g band and 0.37 in the r band indicate that the hypothesis that they share a similar fractional flux (and hence environment) distribution cannot be rejected. Figure 14. Histogram distribution of the fractional flux of the host-galaxy light at the location

O O O O O O O O B-Formula B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest 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 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-ObservationalTechniques O B-ObservationalTechniques I-ObservationalTechniques O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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-Dataset I-Dataset B-Citation I-Citation I-Citation I-Citation O O B-Survey 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 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-Wavelength O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O B-Formula I-Formula I-Formula O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey 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 O O O O O O O O O O O O O O O O O O O O O O O O O


× 5 pixel 2 raster pixd (after neighbour subtraction) centred on the target stars, and PSF( i, j ) is the value of the local PSF-model expected in the pixel ( i, j ). Introduced by Bedin et al. ( 2008 , see also Bedin et al. 2009 , 2010 ; Simioni et al. 2018 ), the parameter RADXS is a shape parameter that allows us to distinguish sources that deviate from a PSF shape. It is a comparison between the measured flux of the source outside the core (in an annulus 1.0 r 2.5 pixels) and the flux expected from the PSF-model. For RADXS >0, the source is broader than that expected from the model (i.e. galaxies), while for negative values of RADXS the source is sharper than the PSF (i.e. cosmic rays and artefacts). Finally, the KS2 routine gives the number of images in which a star is found ( N ) and the number of consistent measurements of the star used to compute its average position and flux ( N ). 3 COLOUR–MAGNITUDE DIAGRAMS In Fig. 2 , we show an example of selection of well-measured stars for the case of NGC 6752 and the photometric method 1. Similar plots can be made for the methods 2 and 3. The top and middle panels of Fig. 2 show the selection of the stars based on the distribution of the photometric errors ( RMS , left-hand panels), the quality of fit ( QFIT , centre panels), and the shape of the sources ( RADXS , right-hand panels), in the case of F275W (top panels) and F336W (middle panels) filters. The selection based on RMS and QFIT are performed as done by Milone et al. ( 2012 ): we divided the distributions in 12 magnitude bins and, in each bin, we calculated the 3.5σ-clipped average of the magnitude and of the parameter, where σ is the standard deviation associated with the average value in the given bin. We added to the mean parameter of each bin 3.5 × σ, and we linearly interpolated these points (green line). We excluded all the points above (in the case of the RMS ) or below (in the case of the QFIT ) the green line (azure points). For the sharp parameter, we selected all the stars that satisfy the condition: −0.15 RADXS +0.15. Bottom panels show the m F275W versus ( m F275W − m F336W ) colour-magnitude diagram (CMD) for the stars that pass the selection criteria in both filters (left-hand panel) and for the stars that were rejected in at least one filter (right-hand panel). In red, the stars that are saturated in at least one filter and that have been recovered from the ‘first-pass’ photometry. From the CMDs, it is clear that many stars with poor photometric quality are rejected. Figure 2. Procedure adopted for selecting well-measured stars in the cluster NGC 6752. Top and middle panels show the selection of the stars based on RMS (left-hand panels), QFIT (central panels), and RADXS (right-hand panels) parameters: in azure the stars that are rejected. Bottom panels show the m F275W versus ( m F275W − m F336W ) CMD cleaned by rejected stars in both filters (left-hand panel) and the CMD of the stars rejected in at least one filter. Red

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


solves the MHD process of an isolated, twisted magnetic flux tube, initially placed in the convection zone, buoyantly rising into the atmosphere. The full set of basic resistive, adiabatic MHD equations in conservative form are solved by a finite difference scheme with the spatial derivatives by the fourth-order central differences and the temporal derivatives by the four-step Runge–Kutta scheme. Periodic boundary conditions are applied for the x -direction and symmetric boundaries for both the y - and z -directions. The initial background atmosphere of the simulation is gravitationally stratified, which consists of an adiabatically temperature-gradient convection zone (, where km is the length unit of the FES model), the cool isothermal photosphere/chromosphere (), and the hot isothermal corona (). The flux tube is initially placed at with the form of and , where r is the radial distance from the tube’s axis, the radius, kG the axial field strength, and the twist intensity (the negative sign indicates a left-handed twist). The middle of the tube is made buoyant by a small density deficiency and the tube started to emerge due to its own buoyancy. As the time-dependent bottom boundary data for the data-driven model, we extracted the time sequence of 2D data at fixed heights from the FES model. To test the behavior of the data-driven model with different inputs, data sets at three different slices from the FES model are used, including (referred to Z00 , representing the photosphere), ( Z10 , i.e., the chromospheric layer), and ( Z20 , i.e., the coronal base). The slices were sampled at every (where s is the time unit of the FES model) from 0 to 500. The slices spanned over , resolved by the uniform grid spacing of 200 × 200, thus the resolution is . The data sets include three components of magnetic and velocity field, i.e., , and v z . As we have mentioned in Section 1 , the Lorentz force in the boundary data is an important factor affecting the output of the data-driven model. Thus we quantitatively assess the Lorentz force as well as torque in the data of different layers. The sum of Lorentz force (and torque ) in a volume can be expressed by surface integral (Aly 1989 ; Sakurai 1989 ), and by neglecting contribution from the side and top boundaries, they can be written as integrals of the 2D data sets:andFollowing Duan et al. ( 2020 ), to assess the data with respect to the force-free condition, the forces can be normalized by the integrated magnetic pressure force F p that is given byand the normalized forces are ratios defined as , , and , respectively. Similarly, the normalized torques are defined as , , and , where T p is magnitude of the net torque induced by only the magnetic pressure force, whereFor a field being close to force-free, it must have ratios much less than unity, i.e., and . Metcalf et al. ( 1995 ) suggested that the magnetic field can be considered as force-free if the normalized forces are all less than or equal to

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


consistent with previous studies that show an anticorrelated relationship between the magnetic field strength and the ionopause altitude (Elphic et al. 1980 ; Russell Vaisberg 1983 ; Phillips et al. 1985 ; Angsmann et al. 2011 ). The ionospheric thermal pressure balances the magnetic pressure difference at the ionopause. To sustain stronger magnetic pressure, it needs higher thermal pressure, and thus higher plasma density in the ionosphere. Therefore, the ionopause would be pushed down to a lower altitude with higher plasma density. However, it is important to point out that this process is based on an assumption that the ionization of the ionosphere is not significantly changed. Figure 4. Left to right: the magnetic field strength near the periapsis prior to, during, and after the passage of the ICME on November 4, November 5, and November 6, respectively. The IMA measurements of heavy ion density are overplotted (red dots). The heavy ion density on November 6 is not available. Nevertheless, the altitude of the ionopause during the strong ICME (Figure 4 (b)) did not decrease at all considering that the magnetic field strength increased a lot. The magnetic pressure differences () across the ionopause on November 4 and 6 are 0.7, and 1.1 × 10 −8 dyn cm −2 , respectively. But on November 5, the magnetic pressure difference reaches 2 × 10 −7 dyn cm −2 ( from 250 to 116 nT) or 9.0 × 10 −8 dyn cm −2 even if we use 200 nT as the magnetic strength in the ionosphere. To balance such atypically higher magnetic pressure, the plasma density of the ionosphere must be correspondingly much greater. The heavy ion densities measured by the IMA instrument are also shown in Figure 4 . Although the resolution of IMA data is low, we can still easily see that the ionospheric plasma density was over 1000 cm −3 during the strong ICME with respect to that less than 400 cm −3 during quiet solar wind. The much higher ionospheric plasma shows that the ionosphere had been greatly excited and perhaps entirely expanded under the impact of the strong ICME. The strengthened ionosphere during the passage of ICME has been evidenced by the fact that the magnetized ionosphere can be demagnetized by some ICMEs during solar minimum (Zhang et al. 2008a ). Due to the limitation of measurements, we have no ideas about the reason why the ionosphere was greatly enhanced by the ICME. However, previous study of the Venus and Mars ionosphere has determined that the solar energetic particles (SEPs) could cause extra ionization of the neutral particles in exosphere through impact ionization and charge-exchange reactions (Futaana et al. 2008 ). Simulations also show that the SEPs can effectively increase the ionization rate of the Venusian atmosphere (Plainaki et al. 2016 ). 4. Discussions and Conclusions We have presented very detailed observations of the induced magnetosphere and ionosphere during the passage of the extremely strong ICME on 2011 November 5. From our observations, a clear

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must come from combinations of the harmonics contained in . Recall that we defined containing both synodic terms with harmonics λ 1 − λ 2 and λ 2 − λ 3 , which we wrote in equation ( 16 ) in terms of the new variables . Therefore, the harmonics that are included in are combinations of these synodic harmonics; more specifically, they come from the products of their cosines. 6 Using the standard trigonometric identity , the resulting harmonics are so the harmonic with the lowest fraction of is . Specializing now to the case of a chain with the same resonance index k (1) = k (2) = k , this simply gives With the aid of an algebraic manipulator, one can compute the full expression of and select the desired harmonic term (we used the software package wolfram mathematica ), thus obtaining its coefficient (actually, one can see that this term emerges solely from the term ). We avoid writing here the full expression, which is rather cumbersome; moreover, as in ( 35 ), we evaluate it at the reference values of the actions so the term multiplying the cosine becomes a numerical coefficient, and we write this term as Since we want to compare the frequency of to that of , we need to consider the resonant Hamiltonian in the variables, expand the ‘barred’ variables around the equilibrium point characterized by the equilibrium actions and the equilibrium angles (equation 20 ) as in Section 4.3 , and then introduce the transformation to the action-angle variables , which transforms into the sum of decoupled harmonic oscillators plus higher order terms (equation 22 ). It is also useful to translate the value of around its initial reference value introducing . Therefore, we write in terms of the variables . The Hamiltonian will now contain harmonic terms of type where is an integer combination with coefficients of the angles φ 1 , ..., φ 4 , which we can calculate explicitly. Therefore, whenever , a secondary resonance is crossed. We can rewrite this expression as . Since the Hamiltonian has d’Alembert characteristics in each pair ( I l , φ l ), and the values of the actions are initially (that is, before their excitation) small, the strongest secondary resonances will come from lowest integer combinations , that is, where most h l are zero. We also note that since and the frequencies ω l are all negative, a secondary resonance term can only appear when , which, together with the requirement that be small, is tantamount to requiring that all non-zero integers h l are positive. Since we calculated ω ( m pl ) in Section 4.3 , we can calculate for each the relative frequency as a function of m pl , and check if any of these vanish for some value of m pl , which corresponds to crossing a secondary resonance. We carried out the calculation with the aid of the mathematica software in the reference case k = 3 and a 1 ≃ 0.1, which corresponds to the evolution shown in Fig. 1(b) (and also Figs 2 and 3 ). We found that contains, among many others, the following

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Software I-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O


O O O O B-Citation I-Citation I-Citation I-Citation O O O O B-Dataset I-Dataset I-Dataset I-Dataset O O B-URL O O O B-Person I-Person 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Model I-Model I-Model B-Citation I-Citation I-Citation 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 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 B-Formula I-Formula I-Formula O O O O O O O O O O O O O O B-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Survey 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 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 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-TextGarbage I-TextGarbage O


which could make the analyses more complicated. We analyzed the PILS data for lines of CH3SD similarly to what Drozdovskaya et al. (2018) did for CH3SH. We adopted an excitation temperature T ex = 125 K, a source size of 0.5′′, and a full line width at half maximum (FWHM) of 1 km s −1 . We did not detect CH3SD, but we derived an upper limit on its column density of 8.8 × 10 14 cm −2 (±0.88). The 12 most constraining lines are shown in Fig. 3 . Drozdovskaya et al. (2018) determined a column density of 4.8 × 10 15 cm −2 (±0.48) for CH3SH 2 . Our upper limit corresponds thus to a D/H ratio of less than 0.18 ± 0.025; the uncertainty was estimated as previously ( Drozdovskaya et al. 2018 ). This value is probably not particularly constraining compared with the deuteration of H2CS per H atom of ∼0.05 ± 0.007 ( Drozdovskaya et al. 2018 ). Deeper interferometric observations are required in order to conclusively verify whether the level of deuteration of H2CS is lower, higher, or preserved at the next level of chemical complexity into CH3SH. Fig. 3. Sections of the Protostellar Interferometric Line Survey (PILS) toward a position slightly off-set from source B displaying the 12 most constraining lines of CH3SD. 5. Conclusion and outlook In the present work, the rotational spectrum of CH3SD has been investigated in the frequency range 150−510 GHz in order to provide accurate predictions for astronomical searches. Extensive assignments have been made for the ground, first, and second excited torsional states up to high J and K a quantum numbers (see Table 1 ). The detailed modeling of the absorption spectra of the CH3SD has been performed in a global fit of a dataset of 4905 rotational transitions to the RAM Hamiltonian containing 78 parameters. The overall weighted standard deviation of the global fit is 0.9 in the range 150–510 GHz, indicating that our set of parameters reproduces the assigned lines within experimental uncertainties. Transition frequencies calculated from these parameters should be reliable for astronomical observations. A first attempt to search for CH3SD in the PILS data turned out to be negative. The upper limit, though not unreasonable, is not very constraining either. Future, even more sensitive observations may provide insight into the deuteration of CH3SH. A search for the potentially more abundant CH2DSH was hampered by insufficient laboratory data reported for this isotopolog. Calculations of the rotational spectrum of CH3SD will be available in the catalog section of the Cologne Database for Molecular Spectroscopy, CDMS, ( Endres et al. 2016 ). The input and output files of the fit as well as auxiliary files are available in the data section of the CDMS 3 . Appendix A: Additional tables Table A.1. Spectroscopic parameters of CH3SD (cm −1 ). Notes. (a) n = t + r , where n is the total order of the operator, t is the order of the torsional part and r is the order of the rotational part, respectively. The ordering scheme of

O O O O O O O O O O B-Survey 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-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 B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation 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-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 B-Survey I-Survey I-Survey I-Survey B-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Database I-Database I-Database I-Database I-Database B-Database O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-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


not trivial, the main obstacle being the lack of robust estimates for key parameters (e.g., distance, Doppler factor), as well as the lack of contemporaneous multi-wavelength radio observations. In most cases, the range of available frequencies was confined in the lower frequency range (43 GHz). The observed flux density at higher frequencies was the result of extrapolation by assuming that the spectral index derived from the highest available frequencies of each microquasar remains constant up to 142.33 GHz (which is the highest available frequency for the supermassive BH sample). To estimate the relativistic boosting and revert to the rest frame, we gathered for each source all available estimates in the literature for the velocity of the jet, distance, and viewing angle (Table 1 ). For each source, we created a parameter space set by the extrema of the aforementioned quantities. We then uniformly drew a random value for each of these parameters and calculated . We repeated this process 10 4 times and calculated the mean and spread (minimum, maximum) of for each source. The y -values for the microquasars in Figure 3 are the mean, and the y -axis errorbars the spread for each of the sources that resulted from the random sampling. We follow a similar procedure for the , by gathering all the available estimates in the literature and calculating the mean and spread. The x -values for the microquasars in Figure 3 are the mean, and the x -axis errorbars are the spread for each of the sources. The microquasars, parameter ranges, and the references to them are the following. For SS 433. we used radio data from Trushkin et al. ( 2003 ), and parameter values from Seward et al. ( 1980 ), Fender ( 2001 ), Trushkin et al. ( 2003 ), Bowler ( 2010 ), Panferov ( 2010 ), Cherepashchuk et al. ( 2013 ), and references therein. For GRS 1915+105, we used radio data from Rodriguez et al. ( 1995 ), and parameter values from Mirabel Rodríguez ( 1994 ), Fender ( 2001 , 2003 ), Fender Belloni ( 2004 ), Miller-Jones et al. ( 2005 ), Punsly ( 2011 ), Reid et al. ( 2014 ), Zdziarski ( 2014 ), Punsly Rodriguez ( 2016 ), and references therein. For Cyg X-3, we used radio data from Koljonen et al. ( 2010 ), and parameter values from Fender et al. ( 1997 ), Ling et al. ( 2009 ), Hjalmarsdotter et al. ( 2009 ), Vilhu et al. ( 2009 ), Dubus et al. ( 2010 ), Vilhu Hannikainen ( 2013 ), Zdziarski et al. ( 2012 , 2013 , 2016 ), and references therein. For GRO J1655-40, we used radio data from Hannikainen et al. ( 2000 ), and parameter values from Hannikainen et al. ( 2000 ), Trushkin ( 2000 ), Mirabel et al. ( 2002 ), Fender ( 2003 ), Fender et al. ( 2004 , 2010 ), Narayan McClintock ( 2005 ), Motta et al. ( 2014 ), Stuchlík Kološ ( 2016 ), and references therein. For V* V404 Cyg, we used radio data from Gallo et al. ( 2005 ), and parameter values from Cherepashchuk et al. 2004 , Heinz Merloni ( 2004 ), Miller-Jones et al. ( 2009 ), Khargharia et al. ( 2010 ), Xie et al. ( 2014

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


for small values of the BH spin and θ v , those effects should have a minor weight on the results. For the fitting procedure, we used the sources NGC 5548 and MRK 509 (see Appendix C for details) also studied by KD 18. We found that, as for KERRBB, the modeling with AGNSED of the optical-UV-X SED is degenerate: by changing the model parameters (i.e., BH mass, spin, Eddington ratio, corona size) appropriately, it is possible to reproduce the same set of data (for some reference values, see Fig. C.1 ). For NGC 5548, results from both models are compatible while for MRK 509, KERRBB BH masses are larger than the AGNSED ones by a factor ≲0.2 dex (Fig. C.2 , right panel). We argue that for NGC 5548, the absence of relativistic effects in AGNSED is balanced out by modeling a large corona above the disk, leading to the same BH mass. Instead, for MRK 509, the smaller X-ray corona leads to different results because it does not compensate the differences between the two models. In general, KERRBB observed disk luminosity is dimmer than the intrinsic one because of a compact corona located in the inner region of the disk, the presence of which modifies the AD emission and leads to an overestimated BH mass. By correcting the KERRBB disk lumminosity by a factor ≲0.2 dex, results from the two models related to MRK 509 show better compatibility (see Appendix C for more details about this correction). The partial compatibility between KERRBB and AGNSED shows that BH masses estimated though the SED fitting procedure clearly depend on the adopted model and their physical background. Despite these findings, KERRBB results for both sources are still compatible with SE and RM ones within uncertainties (Fig. 4 ). Moreover, results presented by KD 18 are compatible with ours for what concerns the BH spin: taking their finding for the BH masses as reference values, both their results and ours favor low values of a . 6. Discussion and conclusions We used the relativistic thin AD model KERRBB ( Li et al. 2005 ) to infer the BH masses of 28 sources from the AGN Black Hole Mass Database ( Bentz Katz 2015 ). These sources have a BH mass estimate from the RM studies and show clear evidence in the UV band of the so-called Big Blue Bump produced by the radiation coming from an AD around a SMBH. Since we did not have information about the viewing angle for the majority of them, we assumed that the Type 1 QSOs were observed with θ v ≤ 45° in order to avoid the absorption from the dusty torus (assumed to have an average opening angle of ∼45°). Our results can be summarized as follows: The majority of the sources of our sample show a good match between data and the modeling with KERRBB. The modeling led to a relatively good estimate of the spectrum peak position (i.e., peak frequency and luminosity; see Appendix B ) with a small uncertainty (∼0.05 dex on average). The total uncertainty related to the AD BH mass estimates is ∼0.45 dex, which is connected to the unknown BH spin

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


9799, the total population of GCs out to (the limit of the ACS field of view, as well as the limit of the halo-light photometry) is brighter than I = 27.0 from integration of the radial profile. This limit is 0.12 mag fainter than the GCLF peak (Paper I) and thus should include 54% of the total over all luminosities assuming the GCLF is Gaussian in number per unit magnitude, and using the parameters from Paper I. We therefore obtain for (110 kpc). Integrating the light profile (Seigar et al. 2007 ) to the same radius gives a total integrated magnitude , which corresponds to assuming a mean color for giant early-type galaxies. The specific frequency of the GC system is then . If we were to choose to integrate the entire GC system profile all the way to the WFC3 field at R = 300 kpc, the result would be clusters, but this estimate is much more uncertain. For UGC 10143, if again we restrict the calculation conservatively to the ACS field of view (), the total number of GCs with is , which translates into over all magnitudes. Integration of the halo light (Donzelli et al. 2011 ) into the same radius gives , . Finally then, to that radius. The more risky extrapolation of the GC profile out to the WFC3 field limit at (270 kpc) would give . The UGC 9799 GC system is therefore relatively richer than for UGC 10143, but the specific frequencies of both are in the range observed for other BCGs (e.g., Harris et al. 2013 ). For NGC 4889, the profile integration gives clusters brighter than (); this limiting magnitude is very near the GCLF peak point. We therefore double that number to , which when combined with gives a specific frequency of . This galaxy is very luminous, but relative to its size, it does not have an exceptionally populous cluster system in the more typical BCG range. The story is somewhat different and more complex for the central Coma cD NGC 4874: Peng et al. ( 2011 ) estimate GCs excluding the more extended IGC population. When we use , as did Harris et al. ( 2009 ), we obtain . If instead N tot is normalized to the entire luminosity profile out to a much larger radius of 520 kpc, then S N decreases markedly to 3.7 ± 0.1 (Peng et al. 2011 ); but since the IGC clusters outnumber the “intrinsic” GCs that are more clearly associated with the galaxy itself, this lower specific frequency is perhaps more of a statement about S N (IGC). In this respect, it is worth noting that Durrell et al. ( 2014 ) find for the Virgo cluster GCs in their entirety, of which a large fraction are IGCs, and less than a quarter are from M87 itself. 8. DISCUSSION For extremely broad and nearly featureless MDFs such as we find in NGC 6166 (Paper II), UGC 9799, and UGC 10143, the imposition of a bimodal Gaussian numerical model, or any simplistic multimodal fitting process, begins to look increasingly arbitrary. Transformation of their CDFs back into the underlying metallicity distribution by way of Equation ( 1 ) yields a similarly broad unimodal MDF. We stress

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C.1 shows the losses at these three wavelengths, and for the weak sources with fluxes 400 mJy these losses clearly become more significant at the short wavelength range (closer to m), while the losses are moderate above the m. We used this information to correct the average correlated fluxes of the sources for this work. For the source with high correlation losses we took the average correlated flux obtained after the data reduction and multiplied it by the decorrelation correction factor obtained from our dilution experiment. Appendix D: Dust sublimation Fig. D.1 Temperatures for the three smallest grain sizes of each species in a shell with a radial optical thickness of ( top ) and ( bottom ). The colors indicate the different species of grains: blue – graphites , green – graphites , and red – silicates. Fig. D.2 Convergence of the temperature for the three smallest grains. Each line indicate the relative difference after each iteration. The darker the color, the higher the number of iterations. The radiative transfer code RADMC-3D does not include an internal computation to account for dust sublimation. To include dust sublimation in our models, we slightly modified the code. Each time a photon package enters a cell, it increases the energy of the cell and thus increases the temperature of the dust of this cell. When the dust in the cells exceeds the dust sublimation temperature, the dust inside the cell is completely removed. To accurately estimate the temperature of the system using dust sublimation, we performed an iterative process for which the code several times computed the temperatures and removed the corresponding cells. When the differences between different iterations were below a certain tolerance (we took a value of 5%), we performed a last computation without removing any dust in the cells to ensure the conservation of energy in the system. To show how our implementation of the dust sublimation works in different situations we show examples of an optically thick and optically thin case. In Fig. D.1 we show the temperature of the three smallest grains of each species for a spherical shell with and , respectively. Both shells have an initial inner radius of 0.3 pc and an outer radius of 5 pc. We can observe clearly that in the optically thick case, the temperature rises more quickly and the sublimation radius for the three species are closer than in the optically thin case. We made sure that we had enough cells close to the inner radius to obtain an accurate solution. In Fig. D.2 , we show for the optically thick case, the relative differences between each iteration and our final computation. After a few iterations, the temperature in every cell reaches a relative difference below our tolerance value. Appendix E: Acceptance levels For our method we used linear transformations computed for each model to remove the mean values, normalize the variance, and remove correlations. We expect that if our models agree with the

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