α and are the polar and azimuth angles of the wave vector of a transverse electromagnetic wave. In this case, the angle α is the observation angle. The spectral power of radiation at the emission frequency Q ω can be obtained in accordance with the expression for the total radiation power: Comparing expressions ( 4 ) and ( 5 ) we obtain: In our work, we will not apply head-on approximations, which, as noted in the work of Willes et al. ( 1996 ), can be violated at small wavenumbers of Langmuir waves and their narrow spectra. We will also not use the narrow-spectrum approximation proposed in Willes et al. ( 1996 ). The cited work also contains a scheme with the spatial orientation of the wave vectors of the merger of Langmuir waves and the generated transverse wave. In order not to limit ourselves to particular cases, we present the results of calculations according to direct expressions ( 2 ), ( 3 ), without using the simplifications usually inherent in these models, which are described in detail in Willes et al. ( 1996 ). Let us now consider radio emission at different spectra of Langmuir waves. Taking into account the work of Willes et al. ( 1996 ), we consider the case of axial symmetry of the radiating region and the spectrum of Langmuir waves in the form: where B is the normalizing coefficient in accordance with the normalization condition: W is the total energy density of Langmuir waves; and φ are the polar and azimuth angles of the Langmuir wave, where the angle is calculated relative to the axis of symmetry of the radiating region, δ is an even positive number. Let us first consider the case when , i.e. when does not depend on the Langmuir wave vector. Fig. 1(a) shows the distribution of radiation ( Q k ) over the wavenumber for different viewing angles α at δ = 2, k max = ω pe /(3 V T e ), k min = ω pe /(15 V T e ), and T e = 3 × 10 6 K, n = 10 16 m −3 . These values of k max and k min are chosen for the following reasons: Langmuir waves with a value greater than k max are effectively absorbed by thermal electrons as a result of Landau damping, and therefore we will not consider them. Langmuir waves in plasma are usually generated by beams of superthermal electrons, so we consider the region of phase velocities up to 15 V T e and assume that there are no Langmuir waves with large phase velocities (smaller wavenumbers). The observation angle α is the angle between the symmetry axis of the radiating region and the vector k . In this case, we assume that k 0 = ( k min + k max )/2, and σ is less than the value of k 0. Fig. 1(b) shows the distribution of radiation ( Q ω ) as a function of the frequency of the transverse electromagnetic wave. The calculation results for this case are shown in Figs 1 and 2 for different σ. At a small standard deviation (e.g. σ = 0.1 k 0 , Figs 1a , b ) the radiation is concentrated in a narrow frequency range. A similar type of Langmuir spectra can be generated, for example, by a fast electron beam. With


and the fraction of mass of formed stars that are NSs iswith being the IMF, Ψ( t ⋆ ) is our best-fit SFH, and Θ NS ( M ⋆ ) is 1 for star mass ranges of 8 M ⊙ M 20 M ⊙ , and zero otherwise. We drop the metallicity dependence in Θ NS because we only consider a solar metallicity for the galaxy, as a result of our spectroscopic fit. t ⋆ is the time when the progenitor of the NS was formed, therefore satisfying t ′ = t ⋆ + t life , with t life being the lifetime of the progenitor before becoming an NS. We assume a t life = 0.02 Gyr, but our calculation is insensitive to this choice as the typical lifetime of these massive stars (∼0.01–0.03 Gyr) is much shorter than the timescale over which the SFH found for NGC 4993 is changing at late times. We assume a Chabrier IMF, but this choice is not relevant, as we are only exploring the high-mass end of the IMF. Assuming α = 0.002 and the distribution of Δ t NSM from Vangioni et al. ( 2016 , their Figure 3 for solar metallicity), and our best-fit SFH from Equation ( 1 ) with t 0 = 3 Gyr and τ = 0.3, we get an NS formation rate of and a BNS merger rate of for the whole galaxy. Errors reflect the uncertainty on the SFH, which dominates our errors: they represent the two central quartiles of the rates distribution computed with the SFHs of the pixel SED fitting over the galaxy. Given the sensitivity of the BNS merger event rate to the recent SFR of a galaxy, it is somewhat surprising that GW170817 occurred in an old, early-type galaxy. We therefore ask what is the probability of observing such an event in any early-type galaxy within the LIGO-detectable volume. To make this estimate, we integrate the stellar mass function of early-type galaxies from Weigel et al. ( 2016 ) and scale the per-solar-mass rate from Equation ( 2 ) to the mass contained within the LIGO-detectable volume (radius 80 Mpc). We find resulting in expected events. This calculation assumes that the SFH of NGC 4993 is representative of local early-type galaxies. In fact, much of the mass will be contained in more massive, and on average older and less star-forming, galaxies. We contrast this with a similar calculation for all galaxy types, using the cosmic SFR density from Gladders et al. ( 2013 ), finding and ∼0.5 expected events. This result shows that it is unlikely that we observed one such BNS merger with LIGO over the combined nine months of operations in an early-type galaxy. The assumptions in the calculation include the fraction of NS that form in binaries ( α = 0.002) and the delay time distribution, both coming from binary star models (where the progenitors of the BNS were already a bound system) and satisfying Milky Way constraints. If the BNS formation mechanism is via dynamical interaction, our result could point to a higher value of α or a shorter Δ t NSM for systems that recently underwent a galaxy merger, more so for those that have high stellar density (such as early-type galaxies). It is therefore of interest to know the


(e.g. Narayan et al. 2012 ; Yuan, Wu Bu 2012b ; Yuan et al. 2015 ). In the hydrodynamic (HD) simulation, there is no magnetic field, wind is found to be driven by the combination of gas pressure gradient and centrifugal forces. In the magneto-hydrodynamic (MHD) simulation, it is found that wind is driven by the combination of gas pressure gradient, magnetic pressure gradient and centrifugal forces (Yuan et al. 2015 , see also Moller Sadowski 2015 ). Recently, observations of both LLAGNs (e.g. Tombesi et al. 2010 , 2014 ; Crenshaw Kramemer 2012 ; Wang et al. 2013 ; Cheung et al. 2016 ) and the hard state of black hole X-ray binaries (Homan et al. 2016 ) show that winds are present in hot accretion flows. The reason for the existence of wind is also investigated by analytical works (e.g. Begelman 2012 ; Gu 2015 ; Mosallanezhad, Bu Yuan 2016 ). Bu et al. ( 2016a , b ) study whether wind can be produced beyond the Bondi radius. In these studies, the gravity of nuclear star cluster is taken into account. It is found that the radial profile of the gravity becomes flatter when stars gravity is taken into account. Also, it is found that wind cannot be produced in the presence of star gravity. Wind production can occur only within the Bondi radius of hot accretion flows. The simulations introduced above neglect radiative cooling. Non-radiative simulations of hot accretion flows can only be applied when the black hole accretes at very low rate, , where is the Eddington accretion rate (Sadowski et al. 2017 ). With the increase of mass accretion rate, radiative cooling effects will become important. Strong radiative cooling can decrease the gas pressure. As mentioned above, gas pressure gradient is an important force for driving wind. We can expect that when radiation becomes strong, wind should become weak. In this paper, we study how the wind strength changes with mass accretion rate. We are interested in wind due to the following two reasons. First, wind can take away mass, which can change the density profile of accretion flows. The change of density profile can affect the emitted spectrum of an accretion flow (e.g. Quataert Narayan 1999 ; Yuan, Quataert Narayan 2003 ). Secondly, it is now widely believed that AGN feedback plays an important role in the evolution of their host galaxies (e.g. Ciotti Ostriker 1997 , 2001 , 2007 ; Proga, Stone Kallman 2000 ; Proga 2007 ; Kurosawa Proga 2009 ; Novak, Ostriker Ciotti 2011 ; Gan et al. 2014 , 2017 ; King Pounds 2015 ; Ciotti et al. 2017 ). Wind can push away the gas outside an AGN. This can reduce the feeding rate of the central black hole. Also, the star formation rate may also be changed (e.g. Ciotti et al. 2017 ). In order to study wind feedback, we first need to study the strength of wind. The effects of radiative cooling on hot accretion flow have been taken into account recently (e.g. Wu et al. 2016 ; Ryan et al. 2017 ). In these papers, the effects of radiative cooling on wind strength have not


we do not consider the spherical reprocessor further. Figure 6. The spherical reprocessor of Brightman Nandra ( 2011 ), compared to the data. Colours as for Fig. 5 . 5 MYTORUS The toroidal X-ray reprocessor model, mytorus (Murphy Yaqoob 2009 ; Yaqoob et al. 2010 ), is illuminated by a central X-ray continuum source. The global covering factor of the reprocessor is 0.5, corresponding to a solid angle subtended by the structure at the central X-ray source of 2 (an opening half-angle of 60 o ). mytorus self-consistently calculates the Fe K α and Fe K β fluorescent line emission and includes the effects of absorption and Compton scattering on both the continuum and lines. mytorus offers the ability to leverage constraints on the Fe K line emission and spectral curvature together, to obtain both the global and line-of-sight column density. The model is therefore one of the most powerful available for fitting X-ray spectra. Although the nominal covering factor is fixed at 50 per cent of the sky as seen by the continuum source, one can model other physical possibilities using the ‘decoupled’ mode that allows for a different line-of-sight column to the gas responsible for reflection (the Fe line emission strength can still be linked self-consistently to the column of the reflector). Such a decoupling is often required in spectral analyses of high-quality broad-band X-ray spectra, because the column density in and out of the line-of-sight column density are not always the same (e.g. Risaliti et al. 2009 ; Marchese et al. 2012 ; Yaqoob et al. 2015 ). In our fits, a single power law was assumed to be seen in transmitted and scattered light, and this was implemented by linking the photon indices of these components in all fits. The general model form was where MYTZ designates the line-of-sight absorption, MYTS the scattered X-rays, and MYTL the line emission (both from material out of the line of sight, hereafter referred to as the ‘global’ gas), from mytorus . zg(10) represents 10 individual Gaussian lines (Table 2 ) present in the data that are not accounted for by the mytorus model. gs is a Gaussian smoothing component convolved with the torus neutral Fe line profile, using a kernel of σ = 30 eV at 6 keV. The power-law continuum is split over two sightlines, one is absorbed my MYTZ and the other is absorbed only by N H , a full-covering column of gas whose lower limit is set at the Galactic line-of-sight absorption, but whose upper limit is not constrained. 5.1 Coupled model fits Taking the ‘Coupled Model’ to mean one for which the line of sight and global column densities are tied together, we performed two variations on this fit. First, the angle of the global gas was fixed at θ = 90 o and the normalization of the global-scattered light and line emission were directly tied to the illuminating continuum. This model did not provide an acceptable fit to the data, yielding χ 2 = 709/438 dof with , while the full covering gas component gave , exceeding


light reflections. To further reduce the negative effects of the background filament radiation, its spectrum was recorded under high vacuum conditions (5 × 10 −8 mbar) and subtracted from measured molecular spectra. The electron energy was calibrated by measurement of the cross section of the (0, 0) band of (C 3 Π u –B 3 Π g ) at 337 nm (Zubek 1994 ; Országh et al. 2012 ) and the He i (1s2p 3 –1s4d 3 D 1,2,3 ) 447.14 nm emission line (NIST 2015 ). The (C 3 Π u –B 3 Π g )(0, 0) cross section exhibits a pronounced peak at 14.1 eV. The cross section for the He i (1s2p 3 –1s4d 3 D 1,2,3 ) transition exhibits a step at 23.736 eV. The electron energy calibration was performed in the mixture of C 2 H 2 :N 2 :He 1:1:1 (established by an absolute pressure gauge) to avoid problems with different charging effects of the electron monochromator electrodes in different gases. The difference between energy scales calibrated by nitrogen and helium was less than 0.015 eV. Two different measurement modes were used in the present study: (i) fluorescence spectra induced by monoenergetic electrons at fixed electron energy, and (ii) PECs—the intensity of photons of a specific wavelength detected as a function of the electron energy, sometimes referred to as the relative excitation function. PECs are proportional to a dissociative excitation-emission cross section (DEE CS) and can be calibrated to its absolute values. Additionally, PEC curves can be used for determination of the apparent thresholds in PEC, which are related to the thresholds for the dissociative excitation reactions (Stano et al. 2003 ). 3. Results and Discussion 3.1. Spectrum We have recorded the electron-induced UV–VIS spectrum of acetylene in the spectral range from 190 to 700 nm. The spectral range 190–257 nm was recorded at an electron energy of 70 eV and low resolution of the optical monochromator (2 nm FWHM), and the rest was recorded at 50 eV and higher resolution of the optical monochromator (0.4 nm FWHM). The spectral range 305–530 nm is presented in Figures 2 (a) and (b). All the spectra presented in this paper were corrected for the spectral response of the apparatus. The intensities in the spectra were calibrated to absolute values according to the known emission cross sections for the dissociative excitation-emission channel, which we will give more details on later. The spectra exhibit lines and bands corresponding to dissociative excitation of acetylene by electron impact (Beenaker et al. 1975 ; Tsuji et al. 1975 ). Figure 2. Acetylene spectrum in the wavelength region of (a) 310–420 nm and (b) 420–660 nm at electron energy 50 eV with slits set to 100 μ m (optical resolution ∼0.4 nm). Due to the lower sensitivity of the optical system in the region 190–257 nm, it was necessary to decrease the resolution of the optical monochromator (using 500 μ m for both slits). We were able to identify two C i lines at 193.1 nm (C i (2s 2 2p3s 1 P 0 –2s 2 2p 2 1 D)) and 248.4 nm (C i (2s 2


the spectrum, particularly below 4400 Å; in the data of WR102, a broad peak in the degree of polarization (∼1 per cent deviation) and polarization angle (∼8° deviation) is seen between 7100 and 7600 Å. The latter feature cannot be a line effect as it is located in a region of the spectrum that is devoid of strong lines, and although its origin remains unknown (the details of our investigations are given in Section 3.2 ), we are confident it is of spurious nature. Given these considerations, the analysis presented in the rest of this study was performed without the spectral region below 4400 Å in WR93b, and the range 7100–7600 Å in WR102. Figure 1. Spectropolarimetric data of WR93b (left) and WR102 (right). The panels, from top to bottom, respectively, the degree of polarization (red) and best Serkowski law fit (black); the residuals after Serkowski fit removal (orange); the polarization angle (blue); Stokes I (grey) and line identification. The grey areas represent the discrepant regions of the spectrum described in Section 3.1 . Excluding these wavelength ranges, the polarization in the direction of WR93b and WR102 rises up to ∼4.5 per cent and ∼10 per cent, respectively. Their polarization angles have distinct behaviours: WR93b exhibits a constant polarization angle of θ = 28.2°, whereas the polarization angle of WR102 shows a downward trend that can be fit with a line of the form θ = −1.08 × 10 −3 λ + 18.4 deg. A non-zero Δθ/Δλ can be explained either by the superposition of intrinsic and interstellar polarization (Coyne 1974 ) or by the presence in the line of sight of dust clouds with different particle sizes and alignments (Coyne Gehrels 1966 ). The merit of these interpretations is discussed in Section 3.5 . 3.2 7300 Å feature in WR102 In Section 3.1 , we highlighted a prominent feature in WR102 spanning the wavelength range 7100–7600 Å. This peak was labelled as spurious and disregarded in our analysis. Here, we detail the steps taken in investigating the nature of this feature. First, we explored whether the spike in polarization is intrinsic to the data. The fact that the feature is not associated with any strong line (as would be expected for a line effect present in the WR star) is, however, inconsistent with this idea. Additionally, plotting the polarization, calculated for each of the 12 sets of observations at four half-wave retarder plate angles (see Fig. 2 ), reveals that the shape and orientation (peak or trough) are highly variable from set to set, and no one set is consistent with another. To formally check whether the data are spurious, we look at the difference in instrumental polarization corrections (Δε, see Maund 2008 ) in this region of the spectrum. This property is expected to be 0 for polarization signals ≤20 per cent, and deviations indicate that the polarization does not reflect a real signal (Maund 2008 ). In Fig. 2 , it is clearly visible that Δε is consistent with 0 across the spectrum but deviates


photometry listed in Table 1 alone, the range of quoted spectral types translates to a reddening of E ( B V ) 0.09mag. Combining this estimate along with the two previous independent reddening estimates from Section 2 , we adopt a mean reddening estimate of E ( B V ) 0.070.02 and V band extinction of A V 0.240.07mag. Adopting the mean distance to the Ori OB1a from Hernndez etal. ( 2005 ) as representative for PDS110, we can now calculate stellar parameters like absolute magnitude ( M V = 2.540.11), apparent bolometric magnitude ( m bol = 10.140.08), absolute bolometric magnitude ( M bol = 2.520.11), luminosity (log(L/L ) = 0.890.05 dex) and radius ( R = 2.230.18R ). Interpolating between the pre-MS isochrones from Siess, Dufour Forestini ( 2000 ), the stellar mass is 1.6M and its age of 11Myr, consistent with the rest of Ori OB1a. 4.2 SED disc model To model the SED of PDS 110, we used the self-consistent irradiated, accretion disc models of DAlessio etal. ( 2006 ) to create a model grid using the stellar parameters of PDS 110 in Table 2 . We adopted a dust sublimation temperature of 1400K to set the inner radius of the disc. We included outer disc radii of 50, 150 and 300au, viscosity parameters () of 0.01, 0.001 and 0.0001 and dust settling parameters (; i.e. the dust-to-gas mass ratio in the upper disc layers relative to the standard dust-to-gas mass ratio) of 1.0, 0.5, 0.1, 0.01, 0.001 and 0.0001. The minimum grain size in the disc atmosphere was held fixed at 0.005 m while we varied the maximum grain size between 0.25, 1.0 and 2.0m to reproduce the 10 m silicate emission feature. The inclination angle was fixed at 60. Table 2. Determined Stellar Parameters for PDS 110. Based on the -squared values, the best-fitting model has a max = 0.25 m , = 0.5, = 0.01 and an outer radius of 300au. Uncertainties are beyond the scope of this analysis. This disc model has a mass of 0.006 using equation (38) in DAlessio etal. ( 1999 ). While there are no millimeter data available to provide spatial constraints, a large outer radius of 300au is consistent with the significant MIR and FIR excess of this object given that the strength of the disc emission is related to the disc mass, which, in turn, depends on radius (DAlessio etal. 1999 ). We also note that = 0.5 corresponds to a relatively flared disc. Here, we measure a disc height at 2 of 0.3au. 4.3 Photometry Some out-of-eclipse variability is seen with peak-to-peak amplitudes on the order of 3percent. From the measured v sin( i ) (64kms 1 ), we would naively estimate a P rot of 1.7d. However, searches with lomb-scargle periodograms (Press Rybicki 1989 ) on both the entire data set and shorter segments do not detect any coherent period of variation attributable to rotation, with the signals dominated by day- and month-aliases from the ground-based surveys. This suggests that variations are stochastic or quasi-periodic, as has been seen for T-Tauri stars before (Rucinski etal. 2008 ; Siwak etal. 2011 ).


model component, given as with the electron and hydrogen densities n e and n H , respectively, and the filling factor f . We used the ratio of n e ≈ 1.21 n H for the LMC abundance of 0.5 solar ( Sasaki et al. 2011 ). With this, we can estimate the hydrogen density from the normalization with Assuming an ideal gas, the pressure can then be estimated from the temperature of the plasma, which we obtained from the spectral fits: with the X-ray temperature T x and the Boltzmann constant k B . And with the pressure P we can estimate the thermal energy E stored in the plasma with Additionally, the mass of the plasma can be calculated using with the m H and μ being the hydrogen mass and molecular weight of the ionized gas, respectively. We used the spectral fit results of the tessellates for the calculations, as those results cover most of the X-ray spur and the surroundings. The derived values are given in Table 4 . We derived the results for each region individually and then took the average of the resulting map over regions which correspond to the large scale structures in the vicinity. The upper and lower limits were calculated by taking the average of the upper and lower limit map of the respective derived parameter. The volume V was estimated by calculating the area of each tessellate polygon region using the Shapely 7 python package. Multiplied with the depth of the X-ray emitting plasma, we obtain the volume of each region. We varied the depth for the volumes, depending on the region the tessellates are located in, to account for the complex geometry of the ISM. We took the values given by Points et al. (2001) and additionally, we estimated the depth of the 30 Dor region with z = 300 pc based on the extent of the structure. The assumed depth is by far the largest factor of uncertainty in the calculations, however, the order of magnitude should be approximately correct. The thermal energy E and mass M of the plasma was also normalized to the volume in cm 3 . Otherwise we would obtain the total numbers for each tessellate region, which would not be comparable between different regions. We give the results without assuming any specific filling factor, as this parameter is largely unknown to us. Based on the true value of the factor the results could change slightly. If we compare, for example, a filling factor of f = 1 versus f = 0.3, the pressure, hydrogen density and mass would increase by a factor ~ 3 while the thermal energy would decrease by that factor for f = 0.3. To gain further insight into the geometry of the hot plasma, we compared the absorption column from the spectral fits with the column density N H of the H I data. This ratio is a measure how deeply the plasma is embedded inside the X-ray absorbing material ( Maggi et al. 2016 ). A value smaller or close to unity suggests that the plasma is located more to the front and consequently a value larger then unity that the plasma is located to the back. We obtain the column density N H


width of the horseshoe region in front and at the rear of the planet in order to minimize the effect of an asymmetry, we prefer not to introduce a source of asymmetry of the horseshoe region. 4 The planet mass is introduced progressively over two orbital periods, and the width of the horseshoe region is measured 20 orbits after the introduction of the planet. We perform a systematic study for three values of the aspect ratio: h = 0.03, h = 0.04 and h = 0.05. For each of these values, we perform 30 calculations with a planetary mass varying in a geometric sequence from 0.05 h 3 to 4 h 3 . The width of the horseshoe region is determined automatically by dichotomy, averaging the results in φ = 1 rad and φ = −1 rad. We find that more accurate results are obtained if the disc is inviscid when q 0.4 h 3 , and viscous for larger masses. For lower mass indeed, a viscous drift of the disc can distort severely the horseshoe region (Masset 2002 ), whereas for high masses, the planet can trigger vortices on the edges of its horseshoe region if the disc is inviscid, which precludes an accurate determination of the width of the horseshoe region. For low masses, we have the scaling (Lega et al. 2015 ; Masset Benítez-Llambay 2016 ): whereas for large masses we recover the scaling found in 2D simulation with softened potential (Masset et al. 2006 ): Using the width normalized to the pressure length scale X s = x s /( hr p ) and denoting with Q the planetary mass normalized to the thermal mass : we can rewrite equations ( 24 ) and ( 25 ) as and The lack of an explicit reference to h in these expressions suggests that the normalized width of the horseshoe region has a universal dependence on the mass expressed in thermal masses. Fig. 6 confirms this expectation. We find that a function that gives the asymptotic behaviours of equation ( 27 ) and ( 28 ) and that matches satisfactorily the width behaviour for intermediate masses is a blend of the asymptotic values at low- and large mass with weights respectively ε and 1 − ε, where ε = 1/(1 + 2 Q 2 ). This yields or Figure 6. Normalized half width of the horseshoe region as a function of the mass in thermal masses. The data from the three different aspect ratios coincide nearly exactly. The solid curve corresponds to equation ( 29 ), the dotted curve to equation ( 27 ) and the dashed curve to equation ( 28 ). This figure should be compared to fig. 7 of Lega et al. ( 2015 ). From now on we will use equation ( 30 ) to evaluate the width of the horseshoe region. As a side result, this leads us to a reasonable definition of an intermediate mass protoplanet as a protoplanet that has a horseshoe width intermediate between the widths given by the low-mass and high-mass scaling (equations 24 and 25 ). Examination of Fig. 6 shows that this broadly corresponds to 0.2 h 3 ≲ q ≲ 2 h 3 . We assume that the corotation torque tends towards its linear value when dissipation (either viscous or thermal) is large, regardless of the


in two galaxies (A and C), while velocity dispersion (third row) is unusually low in C for an elliptical galaxy. We present the rotation parameter as a function of radial distance from the galaxy center (bottom) defined as Equation ( 1 ). Galaxies A and C have a fast rotator profile, whereas B shows a typical profile of a slow rotator. Figure 1. Three examples of model galaxies at z = 0. First row: projected stellar density within 4 R eff in log scale. Second row: mass-weighted radial velocity map of the stellar component with projected stellar density contour. Third row: mass-weighted radial velocity dispersion of the stellar component with projected stellar density contour. Last row: radial profile of rotation parameter. Most of the model galaxies in our clusters are early type in morphology, yet their kinematic properties vary significantly, as found in recent IFU spectroscopic observations. Figure 2 shows the model galaxies in comparison with the ATLAS observational data in the rotation parameter versus ellipticity plane. In a simplistic case of circular symmetry, 0.1 if and if , while (dashed curve) has been suggested as a demarcation line between slow and fast rotators. The observational data and models consistently suggest a positive correlation between ellipticity and spin, in the sense that rounder galaxies tend to rotate more slowly. They present a similar sequence in the diagram, but the ATLAS data span a larger area in the parameter space. Our models are rounder and more slowly rotating than the ATLAS sample. This may be partly due to the fact that our galaxies are exclusively in clusters where environmental effects are more dramatic. Of the 1726 model galaxies, 138 (8%) are classified as slow rotators, which is in rough agreement with the observations. The early SAURON data appeared to suggest a separated distribution between slow and fast rotators (Emsellem et al. 2007 ), but our data do not present such a dichotomy. Figure 2. Rotation parameter vs. ellipticity. The model galaxies in our clusters at z = 0 (blue dots and contours) are presented in comparison to the ATLAS data (red dots). All measurements were performed at 1 R eff . The black dashed line shows the empirical demarcation between slow (below) and fast (above) rotators (Emsellem et al. 2011 ). We present the evolution of the galaxy rotation parameter starting from z = 3, because it is nontrivial to extract the galaxy merger history accurately from a cosmological simulation at higher redshifts where galaxy interactions and mergers occurred in a more chaotic manner. At z = 3, most of the model galaxies were fast rotators (Figure 3 ). It seems that galaxies are indeed born generally as rotating disks, as tidal torque theory suggests. Galaxy mass growth was quick in early high-density peaks that later evolve to be galaxy clusters, and thus the cluster galaxies reached a stage where dispersion is more important than rotation () already at z = 3. The peak in the rotation


of Zr 2 + initially in the excited level versus photon energy. For the online material, we provide the complete set of photoionization cross-sections from ground and excited levels of Sr, Y + , and Zr 2 + in a TOP format (The Opacity Project Team 1995 ), and the complete set of bound–bound photoexcitation transition coefficients for all the electric-dipole-allowed transitions within the same set of levels for these three parent ions. To ensure the files maintain a reasonable downloadable size, of the order of megabytes, we convoluted the cross-sections to reduce their size to around one thousand points in each initial level. The complete photoionization cross-sections, without any convolution, are available for any user under request. These cross-sections can be used for modelling the opacity of astrophysical objects, such as stellar atmospheres. 5 MODELLING OF STELLAR ATMOSPHERE Using sterne , we calculated models for the atmosphere of LS IV-14 116 assuming base parameters given in Table 6 for effective temperature T eff , surface gravity g , microturbulent velocity v turb , fractional abundances by number for hydrogen, helium, carbon, and nitrogen n i , and logarithmic abundances of heavier species relative to solar . For Sr, Y, and Zr, we used two values, one being scaled to the light metals Ca – Mn (the reference model), and the second enhanced by a factor of (+4.3 dex), which corresponds approximately to the overabundances observed in LS IV-14 116. Table 6. Model atmosphere parameters for LS IV-14 116. We construct 10 different models in three groups. All models include the photoionization cross-sections calculated here for Sr 0 , Y + , and Zr 2 + . The reference model has no enhancement in the abundances of these elements. There are four models that include abundances of Sr, Y, and Zr enhanced by +4.3 dex, each individually and all collectively. The third group of models includes a revised linelist with the calculated photoexcitation transitions of the parent ions Sr 0 , Y + , and Zr 2 + , and the ionization products Sr + , Y 2 + , and Zr 3 + . Again, Sr, Y, and Zr are enhanced by +4.3 dex, individually and collectively. In addition, two models were computed with the Zr 2 + and Zr 3 + lines included separately. Fig. 5 (top left-hand panel) shows the temperature structure of model atmospheres T versus optical depth τ 4000 for different abundances of Sr, Y, and Zr. Remaining panels show the temperature relative difference (per cent) to the reference model for various cases. Results imply that the new photoionization cross-section makes negligible difference to the total opacity, even with the high abundances adopted. The photoexcitation transitions make a modest temperature difference in the line-forming region (0.01 τ 4000 1), but only due to a number of very strong Zr lines. This difference corresponds to a temperature increase of up to . Figure 5. The temperature structure of model atmospheres with a -fold (+4.3 dex)


linear interpolation; see Fig. 2 . Based on these two cases, we expect that C ( u ) (and its derivatives) may be discontinuous at integer values of u when W is even, and may be discontinuous at half-integer values of u (i.e. values half-way between the integers) when W is odd. For W 3, visible discontinuities remain in the least-misfit gridding function C ( u ) at u 0.5 and u 1.5. This behaviour is a natural extension of the situation for W 1, and may also be understood by considering the set of three grid points on to which each visibility is distributed. According to which side of the mid-point between two grid points a baseline falls, the visibility is gridded on to a different set of three points. For example, if the baseline is u 0 0.49 (where u 0 is an integer), the visibility is distributed among u 0 1, u 0 , and u 0 1, whereas if the baseline is u 0 0.51, the visibility is distributed among u 0 , u 0 1, and u 0 2. Since the value of the gridding function at the edge of its support, i.e. C ( 1.5), is non-negligible, the way in which the visibility is distributed among the grid points is expected to change discontinuously as the baseline passes through u 0 0.5; this is because one grid point disappears from the set and is replaced by another. For W 4, these discontinuities in value and derivatives cease to be visible. In particular, the values of C ( u ) at the edge of the support u W /2 are very small. APPENDIX D: 34-SOURCE SIMULATED DATA Table D1 shows the location and flux of the 34 simulated point sources used in the numerical experiments. Sources are scattered about the phase centre with different fluxes across the full field of view. Table D1. Locations and fluxes of 34 simulated point sources. X and Y are specified in pixel numbers, and represent the distances from the image centre (0,0) to the corresponding point sources. Sources 27, 28, 29, and 30 are at four corners of the field, and are chosen to have the largest fluxes of the 34 sources. APPENDIX E: GENERATION OF THE LOOK-UP TABLE The look-up table for the least-misfit gridding function is assembled as follows: Create [0, 1) as a set of M s numbers spaced equally between 0 and 1. We refer to M s as the sampling rate in this paper. If W 11 then, for each value of , calculate a set of W gridding function values according to equation( 18 ) using matrix A , which can be used repeatedly as it is not dependent on . If W 11 then, for each value of , calculate a set of W gridding function values according to equation( B2 ) using matrix B . The B matrix must be recalculated for each , increasing the computational cost. APPENDIX F: EFFECT OF THE LOOK-UP TABLE Fig. 9 shows that, if the gridding function is calculated precisely, the RMS misfit between the DFT and the FFT is proportional to the square root of the map error ( x ), as expected from equation( 10 ). When, however, we store the gridding function C ( u ) for W /2 u W /2 in a table with WM s points over this range, and use


This channel is more common for those models with strong mass segregation effects, i.e., m BBH ≫ m ⋆ . Figure 7 shows an example of the evolutions of the BBH’s inner and outer orbits in model M2. The outer orbit of the BBH first gradually migrates from the outer parts of the cluster ( a 2 ∼ 10 5 au) into the inner regions ( a 2 ∼ 10 3 au). Along the way the binary–single encounters become more and more frequent. Each binary–single encounter changes the inner orbit slightly, as the incoming field star is much lighter than the components of the BBHs, i.e., m A , m B ≫ m ⋆ . From the top right panel of Figure 7 , we can see that the encounters gradually increase the e 1 of the BBH up to ∼0.8–0.9, and the SMA of the BBH also increases up to about 2 au. When the pericenter of the BBH’s outer orbit approaches to about tens of r t , the KL effects become important, which can increase e 1 rapidly. Note that simultaneously the binary–single encounters also change the inner orbits. Under these two effects, the inner orbit of the BBH finally reaches to a very high eccentricity, and eventually the BBH merges owing to GW radiation. Figure 7. Example of evolutions of BBH’s inner and outer orbits. Left panels: evolutions of the outer orbit of the BBH. The dashed cyan line in the top left panel shows the tidal radius for the BBH with a 2 = 2 au. In the bottom left panel, the evolutions of Ω 2 and I 2 are mainly driven by vector RR. Right panels: evolutions of the inner orbit of the BBH. The dashed lines in the top right panel show the GW timescales. “BySn” means the position after the binary–single encounter; “KL” means the position after the KL oscillations. The filled blue square symbol marks the starting position of the BBHs in each panel. The filled blue star symbol in all panels marks the position where the BBH is merged. The initial condition of the model is given in model M2. The bottom panels of Figure 7 show the evolutions of the orbital orientations of both the inner and outer orbits of the BBH. The orientation of the outer orbit evolves under vector RR and the KL effect (bottom left panel of Figure 7 ). The orientation of the inner orbit is changed cumulatively during multiple binary–single encounters and becomes quite rapid during the KL precesses (bottom right panel of Figure 7 ). The rapid oscillations of the inner orbital orientations can help to trigger the merging of BBHs by the KL effect. For example, before merging, I 2 ∼ π and I 1 ∼ π /2, the relative inclination between the inner and outer orbits is close to π /2, which can help to enhance the eccentricity oscillations and merging of the BBHs (Wen 2003 ). Figure 8 shows another example of the BBH’s evolutions in model M2. In Figure 8 , the SMA of the BBH always tends to decrease owing to multiple binary–single encounters. This is because the BBH is mostly remaining in the hard binary regions, and the binary–single encounters always decrease the SMA for a hard binary. A hard binary


is to get the power spectrum. The power spectrum obtained for the fiducial model is depicted in Figure 4 . To get the power spectrum, the 21 cm brightness temperature distribution, , is Fourier transformed and then the dimensionless power spectrum is obtained using the following prescription: The spherically averaged power spectrum is obtained by averaging Δ 2 ( k ) over all possible angles:where is the cosine of the angle that wavevector k makes with the line-of-sight direction. Figure 4. Power spectrum of 21 cm brightness temperature distribution for three redshifts. The power spectrum obtained is of expected magnitude (see, e.g., Mesinger et al. 2011 ) and also seems to show the expected trend with respect to the redshift. 2.5. Salient Features of the Method This method of generating 21 cm maps has the following features: 1. A simple and intuitive method where excursion set formalism is used only for getting the collapse fraction. 2. An explicitly photon conserving method where one can compute the mean neutral hydrogen fraction once one knows, the mean collapse fraction () and the other two reionization parameters ( n ion and n rec ). 3. The expression for mean neutral hydrogen fraction is: . 4. Method is fairly fast. It takes about 3–4 minutes to propagate 10 million photon rays and generate a temperature cube (64 × 64 × 64) on an ordinary intel core i5 machine with 8 GB memory. 5. It is precise even with a small number of photon rays as it automatically assigns more rays to more overdense regions or more luminous objects. 2.6. Stability Analysis To check if the reionization procedure is giving a convergent answer, two tests were performed. In the first test, the step size was halved, twice, from the value chosen earlier, that is, it was made to be 0.025 and 0.0125 of the grid cell size. And, in the second test, the number of photon rays was doubled, again twice, to 20 million and 40 million. The effect of these two procedures on temperature maps and power spectrum is summarized in Tables 1 and 2 respectively. In the case of temperature maps the quantity listed is , where is the absolute value of the difference in brightness temperature measured with respect to the fiducial case, that is, with respect to step size of .05 and ray count of 10 million case. In this case, indicates the average over all the grid cells. Table 1 Percentage Change in Temperature Maps with Respect to the Fiducial Case Table 2 Percentage Change in Power Spectrum with Respect to Fiducial Case As seen from Table 1 , the change in δT b averaged over the whole grid cell is small (≲5%). Also the increment in going from the double to the four times case is smaller than going from the fiducial to the double case. In the case of changing step size, the percentage change is nearly the same. In the case of the power spectrum, in Table 2 , the quantity listed is , that is a fractional change in 21 cm power spectrum averaged over all k values. The smallness of values in the


that halos with M 10 9 M ⊙ were suppressed if located inside an ionized patch of the IGM (Iliev et al. 2007 , 2012 , 2014 ; Ahn et al. 2012 ; Dixon et al. 2016 ). Our ability to distinguish the progress and impact of reionization locally here has enabled us, not only to demonstrate the causal connection between reionization and low-mass halo suppression, but also to show that the time at which local reionization takes place is correlated with local matter overdensity and with the corresponding local variations of the halo mass function. In addition, we found that, with the exception of suppressed low-mass halos, the SFRs and gas-to-dark matter ratios of halos of any given mass are higher in regions that reionized earlier. For the low-mass halos, after their local reionization, when suppression takes place, curves of SFR and per halo vs thereafter decline by following a universal curve which is independent of re . We also found that relatively rare, highly overdense and, consequently, highly developed regions, which were the first to reionize, produced the vast majority of stars during the EOR, while not consuming more ionizing radiation than regions that reionized later. These early-reionizing regions must have exported a surplus of ionizing radiation, therefore, which helped to reionize and/or maintain the reionization of the late-reionizing regions. Future observations of high-redshift galaxies which look for the inhomogeneous distribution of suppressed and gas-poor low-mass dwarf galaxies and partially-suppressed dwarf galaxies of intermediate mass predicted here will be an excellent probe of the EOR. Since the CoDa I simulation used a constrained realization of the initial conditions that represents the Local Universe, we can also apply the results found here to predict relic signatures of suppression in the present-day galaxies of the Local Universe. For example, the neighbourhoods of MW and M31 were found in CoDa I to have reionized at roughly the same redshift, a bit earlier than the global average reionization redshift, a result which was also found by CoDa I-AMR as described in Aubert et al. ( 2018 ). CoDa I-AMR used an improved calibration of subgrid star formation efficiency so as to finish global reionization by = 6.1, making it easier to relate simulation redshifts directly to observations. In Aubert et al. ( 2018 ), the reionization redshift field was based on the redshifts when each cell first reached X ion = 0.5 (rather than X ion = 0.9 as used here). As structure formation changes the comoving positions of mass over time, the time when a mass element first reaches a location that is 50 per cent ionized is defined as its reionization redshift, . The average reionization redshift of the mass elements that constitute MW and M31 at = 0 were found to be for both, while . The spread of reionization times within each galaxy was as large as ∼400 Myrs (max – min), with a 2σ spread of ∼100 − 150 Myrs. Our results here suggest that the


arise from a broad range of temperatures at a given density (spanning up to ∼0.5 − 1 dex) as they are coming to the end of the rapid cooling phase, and they have not yet reached thermal equilibrium. Emission from molecules and low-ionization states such as [O i ] and [C ii ] that trace the 100 phase also cover a broad range of temperatures at each density, rather than simply tracking the thermal equilibrium temperature as a function of density. This is likely due to turbulent shock heating. We find that, in our simulations, the dense () gas clouds that condense within the outflowing shell after it cools typically have velocity dispersions up to a few tens of km s −1 . The shocks resulting from this turbulence can heat the gas up to a few thousand K. The photoionization models also assume that the ions and molecules are in chemical equilibrium. To test this assumption in our simulations, we computed the equilibrium abundances of each gas particle at fixed density and temperature, and then repeated the radiative transfer calculations using the equilibrium abundances. The most notable difference is in the [O iii ] line, which is ≈7 − 8 times higher when we set the abundances to equilibrium than when we use non-equilibrium abundances. Other emission lines also show modest deviations when we assume equilibrium abundances, in particular [Ne v ] (up to 80 per cent), [N ii ] (up to 62 per cent), [O iv ] (up to 60 per cent), [N iii ] (up to 44 per cent), [S iii ] (up to 39 per cent), [N ii ] (up to 35 per cent), H (up to 31 per cent), H (up to 29 per cent), and CO (up to 26 per cent). The remaining lines differ by 20 per cent when we use equilibrium abundances. 3.3 Comparison with observations We now compare the predictions from our simulations to observations of outflows in AGN host galaxies. Fig. 7 compares the line luminosity ( L line ) divided by the bolometric AGN luminosity ( L AGN ) plotted against L AGN for a subset of the infrared lines (the full sample can be found in Appendix A ). We divide by L AGN on the y -axis to reduce the dynamic range; a simple linear scaling between L line and L AGN would thus manifest itself as a horizontal trend in these plots. For the simulations ( RFG18 ; grey symbols), our radiative transfer calculations include only one quadrant of the spherical outflow (see Section 2.2 ). We therefore multiply the resulting luminosities by four to obtain the luminosity of the whole outflow. Figure 7. Line luminosity ( L line ) divided by bolometric AGN luminosity ( L AGN ) plotted against L AGN . Our simulations from RFG18 are shown by the grey symbols. In the left column, showing a subset of mid-infrared (IR) lines, we compare to the observations in Veilleux et al. ( 2009 ; V09 ; squares), which we divide according to the AGN classification as PG QSO, ULIRG Sy1, ULIRG Sy2, and ULIRG LINER, as indicated by the colour. In the right column, showing a subset of far-IR lines, we compare to the observations in Herrera-Camus et al.


SMBH. The forward shock region is shown as the purple area. The cocoon is not depicted. On the other hand, within the duration of these two short-term processes, e.g., t m and t vis , the disk wind radius may reach v d ( t vis − t m ) ∼ 10 14 − 10 16 cm above the disk, where v d is the disk wind velocity that is of the order of the escape velocity, for the circumbinary disk, and is the radius of the circumbinary disk at the decoupling. In reality, not only the circumbinary disk but also mini-disks around two SMBHs contribute, which would make the wind bubble more complicated. For simplicity, we assume the density profile of the winds at the decoupling to obtain the density distribution of the wind bubble at larger distances,where is the mass accretion rate onto the binary system, χ ∼ 1 is introduced to take into account the contribution of mini-disks, and η w represents the fraction of accreted mass converted to the disk wind. According to the simulations, for SANE (Standard And Normal Evolution) models, the parameter η w may vary from 10 −4 to 10 −1 (Jiang et al. 2019b , 2019a ; Ohsuga et al. 2009 ) when the mass accretion rate changes from sub-Eddington to super-Eddington. In MAD (Magnetically Arrested Disk) models, η w can reach 10 −2 to 10 −1 (Akiyama et al. 2019 ). With v d ∼ v esc ( R d ,dec ), we have , where , β d ,−1 ≡ v d /(0.1 c ), the parameter is defined as the ratio of , and the Eddington value (assuming a radiation efficiency of 0.1). After the coalescence, a powerful jet driven by the spin energy of the newly formed SMBH can appear, subsequently propagating in the pre-merger wind bubble. Considering a sub-Eddington accretion rate with the MAD configuration, we estimate the jet kinetic luminosity to bewhere η j ∼ 0.3–1 is the ratio of the accretion energy converted to the jet energy (Tchekhovskoy et al. 2011 ). Following the standard jet propagation theory (e.g., Bromberg et al. 2011 ; Mizuta Ioka 2013 ), we write down the dimensionless parameter that represents the ratio of the energy density of the jet and the rest-mass energy density of the surrounding mediumwhere θ j is the jet opening angle, is the isotropic-equivalent luminosity. Since the quantity lies in the regime , we expect that the jet is “uncollimated” for our fiducial parameters. 6 6 However, jet collimation, which was assumed in Yuan et al. ( 2020 ), would be achievable for the super-Eddington accretion accompanied by disk winds with η w ∼ 0.1–0.3. This situation is similar to that in choked jet propagation in the circumstellar material (Senno et al. 2016 ; Nakar 2015 ), and β h is evaluated from . In the relativistic limit, the jet head Lorentz factor is (Senno et al. 2016 ), and we have Γ h ∼ 2 in our fiducial case with . Note that the jet head radius is , and is introduced to represent time measured in the central engine frame, which can be converted to the observation time T via (that is in the relativistic limit) for on-axis observers. Furthermore, to ensure


This leads to a fraction of ∼30 per cent of the nova progenitor systems which harbour evolved secondaries. Given that the nova progenitor systems with evolved secondaries have relatively higher mass transfer rates compared with nova progenitor systems with MS donors, nova progenitor systems with evolved secondaries should have more frequent outbursts. Therefore, the contribution of novae with evolved donors to the total nova rate should be larger than the fraction of corresponding binary systems, 30 per cent. Recently, Williams et al. ( 2016 ) conducted a more accurate statistical analysis of their preceding results and came to the conclusion that of nova eruptions in M31 galaxy are RG-novae. 4.5 Correlation between mass-specific nova rate and morphological type of galaxy Observations give contradicting results regarding the dependence of the mass-specific nova rate on the Hubble type of the galaxy. Some observational studies (e.g. Ciardullo et al. 1990 ; Shafter et al. 2000 ; Ferrarese et al. 2003 ; Williams Shafter 2004 ) claimed that there is no strong dependence of mass-specific nova rate on the Hubble types of galaxies: the majority of galaxies have around 2 ± 1 × 10 −10 L ⊙, K −1 yr −1 . However, there are several galaxies which may have a higher mass-specific nova rate e.g. the SMC, LMC, M33 and others (Della Valle et al. 1994 ; Della Valle 2002 ; Neill Shara 2005 ; Alis Saygac 2014 ; Mróz et al. 2016 ; Shara et al. 2016 ). The mass-specific nova rate of elliptical-like galaxies at 10 Gyr in our calculation is around (1 − 2) × 10 −10 M ⊙ −1 yr −1 . This is consistent with Williams Shafter ( 2004 ), since the total stellar mass-to-light ratio M ⋆ / L K ∼ 1.0, slightly depending on the colour of the galaxy (Bell de Jong 2001 ). However, for spiral-like galaxies, we obtained a mass-specific nova rate 10–20 times larger. It would seem then that our results are inconsistent with measurements of Williams Shafter ( 2004 ). However, one crucial point to understand this discrepancy is the incompleteness of nova surveys. For example, the nova rate of M31 in the analysis of Williams Shafter ( 2004 ) is significantly lower than the nova rates of Darnley et al. ( 2006 ). As we discussed above, a more reliable value should be ≈97 yr −1 , giving a luminosity-specific nova rate ∼7.0 × 10 −10 L ⊙,K −1 yr −1 , which is a factor of 3–4 larger than the value in Williams Shafter ( 2004 ). In our model for M31, we find a mass-specific nova rate of ≈(7 − 14) × 10 −10 M ⊙ −1 yr −1 , which is consistent with the above number. In our model of spiral-like galaxies, we assume the SFR to be constant, which is almost certainly oversimplified in the general case. As shown in Figs 1 and 2 , if there was an initial spike of SFR, certain fraction of total mass of ‘realistic’ spirals sits in old population which does not contribute much to the current nova rate. This will lead to a smaller value of luminosity-specific nova rate (cf. Table 1 ). 4.6 Novae with short


and the radio core is typically within 10%. The apparent displacement vectors of C7 have an anisotropic distribution and show asymmetry in the jet direction with tendency to be longer along the jet axis. These effects are most likely due to resolution-dependent core shift or opacity effects. We developed a statistical tool for estimating the mean and variance of the displacements of the core and C7. We find that the displacements of C7 (isotropic component) and the core (anisotropic component) have an almost commensurate contribution to the apparent displacements of C7. The estimates of statistical characteristics of displacements are close to true values for short observation intervals ( 35 days). The rms of displacements of the core and C7 decreases 1.5−2 times during the stable jet state compared to those during the swinging activity of C7. The contribution of the core and C7 to the apparent motion of C7 remains of comparable importance during both states of activity. The rms of the spatial displacements of the core is a factor of four larger than those of the C7. During the jet stability period, the motion of the C7 on time scales of months is complex, showing swinging motion with reversals of the direction, and superluminal speeds. The trajectories of C7, smoothed over time scales of a few years, show a clock-wise loop motion with mean subrelativistic speed (0.16 ± 0.008) c . Long-term monitoring with high cadence (less than or about a month) VLBA observations at 15 GHz is needed to study the dynamics of the C7. Accurate and low positional uncertainties of the C7 are crucial for identifying the dominant contribution of the intrinsic motions of the core and C7 to the apparent motion of C7. We confirm that the excitation of transverse waves moving along the jet is generated by the motion of the C7, which acts as the nozzle to the jet. The excitation of transverse waves with relatively large amplitudes (≳0.2 mas) are associated with excessively large apparent displacement vectors (> 0.08 mas) of the nozzle. Quasi-sinusoidal stable waves with small amplitudes (≲0.02 mas) are generated by the reversal motion of the nozzle within the angular distance of ≈0.02 mas (0.03 pc), which matches nicely with the amplitudes of the excited waves. The on-sky distribution of flux densities of C7 reveals a statistically significant brightening of the emission upstream and transverse to the jet. The observed brightness asymmetry is not dependent on the epoch and it is, rather, associated with a regular change of the jet viewing angle at the location of the C7 (or the nozzle). The asymmetry of the brightness can be reproduced by a toy model of C7. The model assumes an axisymmetric twisted jet velocity field for the C7 and a jet viewing angle of 8°, while the intrinsic flux density and speed of the jet are unchanged. More sophisticated models are necessary to recover the jet viewing angle of the BL Lac and parameters characterising the velocity field of the jet.


of K2-140b in Livingston et al. ( 2018 ) was based on simple mass–radius relation. It was not the intention to give accurate mass determinations, rather to select appropriate targets for follow-up observations. This highlights the importance of RV measurements to determine precise planetary masses. The planet mass derived by G18 using RV measurements is in agreement with the presented results within 1σ. The main difference between the subsequent analysis and the parameters for K2-140b from G18 is the orbital eccentricity. An accurate estimate of this parameter is important since it affects the derived argument of pericentre, stellar mean density, semimajor axis, and thus the derived equilibrium temperature. G18 found a non-zero eccentricity for K2-140b of using 12 CORALIE and 6 HARPS RV measurements. The analysis presented in this paper favours in contrast a circular orbit solution. In order to check whether this is a direct result from the additional 13 RV measurements the relation for an expected eccentricity error σ( e ) (Zakamska et al 2011) is used: where K is the radial velocity amplitude, N is the number of RV observations, and σ obs is the average RV error of the observations. The G18 RV data with K = 111.2 m s −1 , σ obs = 23.6 m s −1 , and N = 18 do not constrain the orbit eccentricity better than σ( e ) = ±0.21. The KESPRINT RV data with K = 102 m s −1 , σ obs = 12.8 m s −1 , and N = 13 constrain the orbit eccentricity to σ( e ) = ±0.15. Combining both data sets ( K = 106 m s −1 , σ obs = 19.1 m s −1 , and N = 31), the orbit eccentricity is constrained to σ( e ) = ±0.14. Thus it was concluded that the more accurate KESPRINT RV measurements improved the eccentricity detection. Moreover, a combined fit using the light curve and the RV data achieves better accuracy in the eccentricity. The eccentricity found by G18 might be driven by the uncertainties of the individual RV measurements and their distribution along the RV curve. The significance of their result was here tested statistically by Monte Carlo simulations. One hundred thousand simulated RV data sets were created by sampling a best-fitting circular orbit solution at the timestamps of the CORALIE and HARPS observations. Gaussian noise at the same level of the G18 measurements was added. A least-squares fit to these simulated data also allowed an eccentric solution. There is a probability of ∼12 per cent that an eccentric solution with e ≥ 0.12 may be found if the true orbit is actually circular. The same analysis was repeated by combining the FIES RV data with those from G18 . Once again, simulated data created from the best-fitting circular orbit model can mimic an eccentric orbit with a probability of 6 per cent. The new analysis shows that the previously claimed eccentric orbit is not statistically significant. In contrast, the BIC that distinguishes between an eccentric or circular solution prefers the circular orbit. The results highlight the difficulty in distinguishing


younger objects suggests a much shallower gradient: we derive slopes equal to and dex kpc for the SFRs and all the associations younger than 100 Myr (i.e. SFRs + YOCs), respectively, through a linear fit based on the orthogonal distance regression method and taking into account the error bars on both the axes. In other words, comparison with the old clusters analysed by Jacobson et al. suggests a flattening of the gradient at very young ages. The results on the evolution of the Galactic metallicity distribution is still based on a small number of metallicity determinations and limited to clusters covering a range of 2 kpc in around the Solar location, thus they cannot be taken as conclusive. However, it is in agreement with and, crucially, extends to younger ages, previous estimates of the evolution of the radial metallicity gradient based on the study of open clusters ( Carraro et al. 1998 ; Friel et al. 2002 ; Magrini et al. 2009 ; Andreuzzi et al. 2011 ; Cunha et al. 2016 ). On the other hand, this result is at variance with other studies based on observations of field stars (e.g. Nordström et al. 2004 ; Casagrande et al. 2011 ; Anders et al. 2017 ). As mentioned already, however, the main difficulty of using field stars to trace the chemical pattern of the Galaxy and its evolution over time is that their ages and distances are not as well constrained as for open clusters, and that field star samples are normally older than 1 Gyr, thus not allowing the study of the latest phases of disc evolution. Whilst the Gaia mission ( Perryman et al. 2001 ; Gaia Collaboration 2016 ) and asteroseismology are allowing and will continue to allow a big step forward in the determination of the distances and ages of field stars, the second problem still remains a major and intrinsic limitation. Fig. 5 Radial metallicity distribution of all the clusters included in the iDR4 catalogue. Their Galactocentric radii and metallicities are reported in Tables 2 and 4 . Red circles indicate star forming regions, blue circles denote young clusters in the age range between 10 and 100 Myr, while intermediate age clusters are shown as black symbols. 5.1. Comparison with literature results and the metallicity distribution at young ages from other tracers In a recent paper Netopil et al. (2016) investigated the metallicity distribution of a sample of 172 clusters, using a homogenised compilation from the literature. They suggested that young clusters (defined in that paper as those younger than 500 Myr) may be characterised by lower metallicities than the older ones, at least in the region between 7 and 9 kpc from the Galactic centre; at the same time, they confirmed the presence of a negative gradient for these clusters. We mention, however, that their sample did not include any clusters younger than Myr located in the inner Galaxy. Fig. 6 Comparison between the metallicity distributions of SFRs and YOCs by our analysis (red and blue dots, respectively) and those of


objects, the models were applied to the set of Spitzer , Herschel , and ALMA fluxes. We used the Spitzer and Herschel /PACS flux values as published in Lim et al. (2010) , but updated the Herschel /SPIRE fluxes, accounting for (i) a new reduction pipeline (HIPE version 8.2) and destriping methods ( Fornasier et al. 2013 ) and (ii) the availability of new Makemake observations from June 2010, in addition to the Nov./Dec. 2009 data presented in Lim et al. (2010) . Averaging the two epochs, the new SPIRE fluxes are 12.5 1.3 mJy, 9.5 1.3 mJy, and 4.7 1.5 mJy at 250, 350 and 500 m, respectively. In the first model (“Makemake-alone”), a standard NEATM fit was performed on the 3-band Herschel /PACS and the Spitzer 71.42 m fluxes, ignoring the Spitzer 23.68 m flux, with as the only free parameter. As before, the model was then applied to other wavelengths to determine the corresponding spectral emissivities. The best fit solution, shown in the left panel of Fig. 7 , has 9, but even though the diameter and geometric albedos are fixed, the error bar on is large (; see Table 5 ), a consequence of the strong effect of the phase integral uncertainty for a bright object. Our ALMA flux measurements then imply a 1.03 relative mm emissivity. In a second model (“Makemake + moon”), the two Spitzer and the three Herschel /PACS measurements were fit with the sum of emission from Makemake and its moon. This model had initially four parameters, and (, and ) for its moon, for which we adopted 0.3 (to allow for possible light curve variation). However, the system was somehow degenerate and best fit solutions tended to call for very large values of (3–4), while values larger than 2.7 are unphysical (see e.g., Fig. 4 of Lellouch et al. 2013 ). was then fixed at a maximum value of 2.64. Even then, the problem remained somewhat under-constrained, leading to broad ranges for (, and ) of the moon (Table 5 ). More worryingly but consistent with the previous studies ( Lim et al. 2010 ; Parker et al. 2016 ), the solution range of remained unphysical (0.34) suggesting that Makemake’s moon alone might not entirely explain the 24-m flux. Since the temperatures scale as (), a possible way to alleviate the problem would be to invoke a bolometric emissivity much lower than 1 for Makemake’s moon, but we note that restoring physically reasonable values of (say ) would then require . In any case, with this “Makemake + moon” model, we infer a 1.05 relative mm emissivity for the system. In a third model, the 24 m flux excess from Makemake’s system was attributed to dust emission. For this we adopted the dust absorption coefficients of Li Draine (2001) , giving, for example, m kg at 23.68 m, and specified a dust grain temperature of 54.6 K, which corresponds to the instantaneous equilibrium of a sun-facing surface with zero albedo at Makemake’s 52 AU distance. This choice is somewhat arbitrary as small grains could be poor radiators (hence warmer than the above value), and/or radiating


We found that the best-fitting soft-excess flux predictions are off by at least a factor of two from the values measured by Tripathi et al. ( 2021 ), except for the extinction curve of Czerny et al. ( 2004 ) with E ( B − V ) = 1.0. In this case, the estimated soft excess flux in the 0.3–2 keV is within the range of the fluxes measured by Tripathi et al. ( 2021 ) from the five AstroSat observations. The best-fitting inner radius and accretion rate are 126 R g and of the Eddington rate, respectively. This suggests that the inner disc in IC 4329A could be covered by a warm, optically thick layer, whose emission is consistent with the optical/UV SED and could also explain the observed soft-excess we detect in this source. 5 DISCUSSION AND CONCLUSIONS We present the results from the analysis of UV images of IC 4329A obtained with AstroSat / UVIT observations. These are the highest resolution and deepest images of IC 4329A ever acquired with any telescope in the near and far-UV bands. The UVIT images enabled us to calculate the galaxy radial profile, and unambiguously separate the AGN emission from the extended emission of the host galaxy by fitting the profiles with the appropriate functions. We derived the intrinsic AGN continuum flux after de-reddening for both the Galactic and internal extinctions, and correcting for the contribution of emission lines. The active nucleus is not detected in the FUV band, and we were able to put a conservative 3σ upper limit on the AGN flux in this band. When combined with the AGN flux in the NUV and 5100 Å (taken from past observations), we found that the far-UV/optical, intrinsic emission of the active nucleus in IC 4329A, requires no disc emission below ∼80–170 R g . The superb spatial resolution of UVIT is crucial in this case, specially in the FUV. If we had performed simple aperture photometry in the FUV image, using a 5–10 arcsec radius (as is typically the case), we would have ended with a flux measurement at least seven times larger than the 3σ upper limit we have determined in this band. Since the host galaxy in most templates is assumed to emit very little at these short wavelengths, this measurement would have been assumed to be intrinsic of the active nucleus, and this false result would have critically altered the shape of the intrinsic AGN SED at short wavelengths. X-ray reflection spectroscopy can independently probe the inner accretion discs via the relativistic iron Kα line near ∼6.4 keV and the strength of the reflection. Using XMM-Newton observations of IC 4329A, Nandra et al. ( 2007 ) derived a low-disc reflection fraction of R f ∼0.3 ( R f is defined as the ratio of the X–ray intensity that illuminates the disc to the intensity that reaches the observer; R f = 1 corresponds to a semi-infinite slab subtending 2π solid angle at the X-ray source). Using NuSTAR observations, Brenneman et al. ( 2014 ) detected a moderately broad iron line with a Gaussian σ ∼0.36 keV in addition to narrow iron Kα,


interact gravitationally and radiative cooling is left on. This density threshold is set to 10 per cent of the star formation threshold, which is ρ SF = 0.13 cm −3 for the arepo simulations and ρ SF = 0.33 cm −3 for the Sherwood simulation. By looking at volume-weighted spherically averaged density profiles of haloes, we estimate that these density thresholds correspond to an average distance of 0.7 R vir for the arepo simulations and 0.4 R vir for the Sherwood simulation. There is of course some scatter between individual haloes, however. The Illustris, HVEL and FAST simulations all include AGN feedback, but the Sherwood simulation does not include black holes. We do not however expect this to change our results significantly [see, for example, Tescari et al. ( 2011 ) and Suresh et al. ( 2015 ), who find that AGN are not very important for metal enrichment at high redshift]. 2.1.3 UV background Illustris, HVEL and FAST were all run using the Faucher-Giguère et al. ( 2009 ) model of the UV background. A correction for the self-shielding of gas from the UV background is also incorporated into these simulations, based on the Rahmati et al. ( 2013 ) model; however, this is only included below z = 6. The Sherwood simulation was run using the Haardt Madau ( 2012 ) UV background, which turns on at z = 15. Note that throughout this work, unless specified, we used the Haardt Madau ( 2012 ) model of the UV background for computing the ionization state of the gas. The original UV background of the simulations will still be important when considering, for example, the temperature of the gas in the simulations. We do investigate the effect of changing the shape and amplitude of the UV background on the metal-line absorbers we model in Section 4.2 . Ideally, we would use a more realistic inhomogeneous UV background, such as in Finlator et al. ( 2015 ), but it is reassuring in that work they find that there is only a factor of ∼2 difference between the neutral fractions calculated using their model and the Haardt Madau ( 2012 ) background. 2.2 Feedback and the high-<italic>z</italic> IGM/CGM Galactic feedback is generally invoked to reconcile the shapes of the dark matter halo mass function and galactic stellar mass function (e.g. White Frenk 1991 ). For our purposes, the feedback is important both as a means of regulating the number of stars produced (and hence the amount of metals) and also for distributing these metals throughout the IGM. In the left-hand panel of Fig. 1 , we show the galaxy stellar mass function of the different simulations at z = 6 for haloes resolved by at least 100 dark matter particles. Here we compare to observations of the stellar mass functions at z ∼ 6 (Stark et al. 2009 ; González et al. 2011 ) but note that the Illustris run has already been compared with observations across a wide range of redshifts z = 0–7 in Genel et al. ( 2014 ). The HVEL model shows an increase in galaxies with low stellar masses, as the constant fast


of C/O is roughly uniform, unlike for unconstrained chemistry where it is double-peaked (Line et al. 2013 ). In chemical equilibrium, specifying the elemental abundances allows all of the molecular abundances to be computed, with no parametric freedom, given a temperature and pressure. We are agnostic about the terms “cloud” and “haze” and use them interchangeably for this study. 7 7 These terms are either used to distinguish between size (Earth science convention) or formation origin (planetary science convention), and there is no consensus within the exoplanet community on their usage. We implement the simplified cloud model introduced by Lee et al. ( 2013 ) and used by Lavie et al. ( 2017 ), which describes a monodisperse population of spherical cloud particles with radii , cloud volume mixing ratio and a single composition (represented by the parameter Q 0 ). Refractory and volatile cloud species have and ∼10, respectively. This cloud model accommodates both small and large particles, and correctly reproduces the limits of Rayleigh and gray scattering. It is based on the notion that curves of the extinction coefficient have a roughly universal shape (Pierrehumbert 2010 ). 3. Results We begin by presenting a pair of retrieval models that make the common assumption of log-uniform priors (Figure 3 ). For the measured emission spectrum of WASP-12b, we use the published data of Stevenson et al. ( 2014 ) as stated in their Table 3. For the model with unconstrained chemistry, we set log-uniform priors on the six mixing ratios. For the model with equilibrium chemistry, we set log-uniform priors on the elemental abundances of carbon, oxygen, and nitrogen. As an improvement over the work of Stevenson et al. ( 2014 ), we include clouds in our analysis as part of the retrieval (i.e., the cloud parameters are not fixed to preset values). The other parameters also have log-uniform priors, except for Q 0 , which has a (linearly) uniform prior. Figure 3. Posterior distributions of fitting parameters for cloudy retrieval models with unconstrained chemistry (top panel) and equilibrium chemistry (bottom panel) with log-uniform priors. has physical units of m 2 kg −1 , while is given in m. The rest of the parameters are dimensionless. In Figure 3 , the first thing to notice is that the cloud parameters display degeneracies that match our physical intuition: the mixing ratios are degenerate with cloud composition, particle radius, and number density. In particular, it is possible to set bounds on the cloud particle radius, but the cloud composition is essentially—and unsurprisingly—unconstrained. When we include only CO, CO 2 , CH 4 , and H 2 O in the retrieval, we reproduce the result of Line et al. ( 2014 ) and Stevenson et al. ( 2014 ) that unrealistically high abundances for CO 2 are obtained (not shown). (Heng Lyons 2016 have previously elucidated this implausibility using validated analytical formulae.) Such high abundances of CO 2 drive the


the eccentric disc at the centre of M31. In order to test whether the finding that σ z /σ R > 1 depends on our assumption that the velocity ellipsoid is aligned on cylindrical coordinates, we have repeated our analysis assuming that the velocity ellipsoid is aligned on spherical coordinates (see section 2.4 of Cappellari 2020 ). We found that models with σ θ /σ r > 1 are clearly favoured, which on the plane z = 0 corresponds to σ z /σ R > 1. Thus, the alignment of the velocity ellipsoid does not affect the results discussed here. There are two questions in relation to our finding that σ z /σ R > 1. The first is why are such values favoured by our models? Comparison of Fig. 9 with Fig. 13 shows that the reason is that a small value of b (i.e. a large σ z /σ R ) is needed to reproduce the drop in the observed μ obs near the centre (| l | ≲ ), which is present both in the APOGEE data and the SiO maser data (see middle row in Fig. 9 ). In Fig. 9 , which shows model 3 with b = 0.45, the drop is well reproduced, while in Fig. 13 , which shows the same model but for b = 1, the drop is not well reproduced. The ‘NSD only’ models favour a slightly larger value of b compared to the ‘NSD+NSC’ models because the absence of the NSC component in the middle lowers the velocity dispersion in the central regions compared to the outer parts. The ring models also favour a larger value of b (consistent with b ∼ 1, see Fig. A2 ) because the density is essentially zero for , and therefore those regions do not contribute to the integrals in equations ( 11 ) and ( 12 ). Assuming that the drop in the data is real (which ought to be confirmed with better data), this suggests that indeed b 1, or that our assumed tracer density population is not representative of the population from which the kinematics are drawn. We note that the observed kinematics directly constrain only the v R and v φ components of velocity: our constraints on the v z component come from the integral ( 11 ) of ρ and Φ along z . If the potential or density were much flatter than we have assumed, then the σ z given by ( 11 ) would increase and we could fit the observed kinematics with larger values of b . It is currently unclear whether such a strong flattening would be detectable given the extreme and strong differential extinction. Figure 13. Same as Fig. 9 , but for a model that is identical to model 3 except that b = 1. Note that the drop in second moment velocities at | l | ≲ is reproduced less well than in the model shown in Fig. 9 . Assuming that σ z /σ R > 1 then the second question is how would stars get such large vertical oscillations? In the solar neighbourhood stars are formed from gas clouds that move on almost closed orbits, beginning their lives with random velocities of the order of a few . There are a number of dynamical processes that inevitably cause these random velocities to increase over time (see Sellwood 2014 for a recent review). Each of these heating mechanisms has a different


PN G233.010.1: ring-like PN. More images can be found in Saurer Weinberger (1987) . PN G236.010.6: object poorly studied, morphology type one-side (see Ali et al. 2000 ) with radial filaments. More images can be found in Hartl Weinberger (1987) . PN G236.701.6: our image shows two areas of lower brightness that are not visible in the H image of the MASH catalogue. PN G239.612.0: round with internal structure and intense patches. More images can be found in Fredrick West (1984) . PN G239.613.9: Balick (1989) classified this PN as elliptical (early-middle subtype). Additional images can be found in Schwarz et al. (1992) . PN G243.837.1: Boffin et al. (2012a) performed a morphological analysis of this PN. PN G247.504.7: there is an HII region towards the SW, and it is unclear whether it is part of the PN or is the optical counterpart of the molecular cloud BRAN 63. PN G249.305.4: ring-like PN with a very faint CSPN. It shows several irregularities in the brightness of the ring. PN G249.807.1: this seems to be two overlapping PN. It is difficult to explain the homogeneous and extensive overdensity of material towards the NW. PN G250.401.3: classical bipolar PN with an arc towards the NW. It is also visible in the [N ii ] images of Kerber et al. (2000) . PN G257.500.6: poorly studied planetary nebula with intriguing morphology. The PN displays a ring-like structure of low surface brightness towards the NE and a emission region towards the SSE that is difficult to explain. It probably is a bipolar PN. This object requires a more detailed study. PN G258.015.7: Gonçalves et al. (2002) show an [N ii ] image, but it is not as deep as ours. In both cases the huge jet-like features are clearly visible. Additional images can be found in Corradi et al. (1996 , 1999) . PN G259.100.9: it is difficult to perform a morphological classification of this Type I PN. A complete analysis of this object was made by Jones et al. (2014) . Our [N ii ] image does not show any differences with the [N ii ]+H published in that article. A H image is presented by Górny et al. (1999) . PN G260.703.3: the H image of MASH catalogue displays a more extended HII region than our image. According to its morphology, it would not be a PN. It could be a filament of the supernova remnant (SNR) Puppis A ( Goudis Meaburn 1978 ). PN G261.603.0: Corradi Schwarz (1995) classify this Type I PN as a possible/probable bipolar. Our [N ii ] image shows a well-defined bipolar morphology with a pronounced waist, thus we confirm this classification. It is not evident from our image if the two saturated regions define the torus of the waist. If this were the case, the waist would not be perpendicular to the bipolar lobes. To answer this question, it is necessary to perform a detailed spectroscopic study. PN G261.908.5: this Type I PN has been classified by Peimbert Torres-Peimbert (1983) as a filamentary bipolar. More images can be found in Vázquez (2012) , Bohigas (2003) and Dufour (1984) . PN


best fit for Model 1 (χ 2 /ν = = 1.02) and Model 2 (χ 2 /ν = = 1.02) yield radii of 2.1 and 5.2 R, respectively. We have also performed another fit letting relxilllp represent both incident and reflected spectra alone (Model 3: diskbb+relxilllp ), in such a way that we can leave the reflection fraction free. The best fit (χ 2 /ν = = 1.02), which sets the inner radius at 1.7 R, provides a reflection fraction of R = 0.26. The power-law index – now unique for both incident and reflected spectrum – is Γ = 1.78. Other parameters, which are common to Models 1 and 2, have not changed much from the values quoted previously. In regard of spin and inclination, Fig. 6 presents the MCMC output distribution for these two parameters for the cases where R in was left free in Models 1, 2, and 3. For all three models, the spin behaviour differs very little from that of relconv(reflionx) , displayed in the bottom panel of Fig. 5 : it reaches the hard limit but is only poorly suggestive it might be ≳ 0.5 (1 σ); any value is still possible within 3 σ. As for the inclinations, they all coincide to be in the range of ∼ 60–85° (2 σ); values below ∼ 55° can be excluded with 3 σ confidence for Models 1 and 2, whereas for Model 3 this same confidence region encompass a broader range, with marginally lower inclinations. Model components, model fitted to the data, and its residuals for Model 2 are displayed in Fig. 7 . Aside from providing the best constraints on spin and inclination, the reason we elect to show this combination is that it includes the comptonization component, in which best-fitting values of τ and kT e are – as formerly discussed – in a more likely interval for 1E 1740.7−2942. For a comprehensive description of the model variables and dependencies, we also present, in Fig. 8 , the joint distributions of selected parameters for Model 2. Figure 6. MCMC output distribution for parameters spin and inclination for combinations relxill+comptt (Model 1; upper panel), relxilllp+comptt (Model 2; middle panel), and relxilllp alone (Model 3; bottom panel). The black plus symbols indicate the best-fitting values. Confidence contours of 1 (magenta), 2 (bluish green), and 3 (blue) σ are shown. The colour figure can be viewed online. Figure 7. Model components (upper panel), model fitted to the data (middle panel), and its residuals (bottom panel) for Model 2. Note: Vertical axis of bottom panel is in (data-model)/error , equivalent to , so magnitudes of XMM (blue), NuSTAR (magenta), and INTEGRAL (bluish green) residuals are comparable. The colour figure can be viewed online. Figure 8. Joint distribution of selected parameters for Model 2, calculated from the MCMC output. The red plus symbols indicate the best-fitting values. Confidence contours of 1 (magenta), 2 (bluish green), and 3 (blue) σ are shown. Note: Parameters and their units are: N H (× 10 22 cm −2 ), T 0 (keV), kT e (keV), h ( R g ), i (degrees), R in (R), (log erg cm s −1 ). τ and a are dimensionless.


redshift z 2 to the present day, the black holes switch to the low-accretion regime again, remaining in a self-regulated state in which both the stellar and AGN feedback balance cooling. The relative importance of AGN over stellar feedback depends on halo mass. While stellar feedback dominates in haloes up to the size of the Milky Way, more massive haloes are mainly regulated through AGN feedback. The stellar mass fraction as a function of halo mass (Fig. 9 ) clearly shows the decrease in star formation efficiency with halo mass at the massive end, in good agreement with observations. We find it useful to compare the stellar mass including the diffuse intracluster light in the high-mass end in observations and theory. In this way, we are less sensitive to the choice of the aperture within which stellar masses are estimated. At the high halo-mass end, the data shown here are in reasonable agreement with Kravtsov, Vikhlinin Meshscheryakov ( 2014 ) who pointed out the importance of outer stellar profiles in high-mass haloes in this type of analysis. Additionally, we plot both the halo mass from the full physics simulation as well as the halo mass of the corresponding halo in the dark matter only run, where the latter, i.e. the dashed line and open circles, should be compared to the results from abundance-matching. Fig. 4 shows the ratio of these two masses as a function of halo mass. In particular at around M 200, c 10 13 M , it turns out to be crucial to take this effect into account. Figure 9. Stellar mass fraction as a function of halo mass for the high-resolution simulation. The stellar mass is calculated as the mass of all star particles within 10 stellar half-mass radii that do not belong to a subhalo. The black line is the corresponding fit to observations from Behroozi etal. ( 2013a , b ) including the intracluster light. We use the simulation values of b and m for both simulation and literature data. The dashed line and open circles correspond to the same simulation data, but the halo mass M 200, c is taken from the corresponding halo in the dark matter only simulation (see Munshi etal. 2013 , for a discussion). One of the conjectured effects of AGN is that they can prevent the most massive galaxies from being blue and star forming, instead making them red and having an old stellar population. We use BV colour and mean stellar age (Fig. 10 ) as a measure for the efficiency of the feedback in the low-accretion state to accomplish this. To probe the relevance of the kinetic feedback mode for this, we compare our fiducial simulation with a simulation without the kinetic mode. The panels of Fig. 10 clearly show the need for this efficient mode to get red and dead galaxies with old stellar populations on the massive end of the galaxy population. Figure 10. Top panel: BV colours as a function of stellar mass within twice the stellar half-mass radius. The red dots are from the fiducial simulations. The blue dots represent the haloes in the run


(e.g. Desert et al. 1990 ; Draine Li 2001 ; Compiègne et al. 2011 ). The grain structure and optical properties were therefore calculated by considering their composition and size, and the resulting spectra are directly relationed to these properties. In order to facilitate comparison with previous models and studies, we distinguish three sub-populations of a-C grains: a-C1: a-C nanoparticles with a ≤ 0.7 nm, which would be equivalent to the smallest PAH grains in Desert et al. (1990) , Draine Li (2001) and Compiègne et al. (2011) and represent ~10% of the mass for all models; a-C2: a-C with 0.7 a ≤ 1.5 nm, which would be equivalent to the largest PAHs in Desert et al. (1990) , Draine Li (2001) and Compiègne et al. (2011) ; very small grains (VSG): larger a-C particles with a > 1.5 nm, which would be equivalent to the VSG as defined in Desert et al. (1990) , the smallest carbon grains with graphite optical properties in Draine Li (2001) , and the small amorphous carbon grains (SamC) in Compiègne et al. (2011) . Fig. 5 Upper panel : measured FWHM in VISIR long-slit spectra. The ozone atmospheric absorption band is delimited by the grey shaded area. The positions of aromatic (blue) and silicate crystalline (red) main features are shown as dashed lines. The estimated 3 σ error on the FWHM is 2.5 10 −3′′ . The purple points are the measures for HD 100546. The same reference star (HD 91056, green points) as was used for photometriccalibration was used and is assumed to reflect the angular resolution response of the atmosphere combined to the telescope or instrument. Bottom panel : ratio between HD 100546 and standard star FWHM shown in the upper panel. The raw ratio obtained by crude division of the FWHMs was smoothed it with a three-pixel-wide boxcar having the spectral width of the actual spectral sampling in order to reduce pixel-to-pixel irregularities. The estimated 3 σ error on the ratio is about 1.2% (~0.02). Fig. 6 Top panel : 8.6 μm (brown) and 11.3 μm (magenta) aromatic emission bands and 10.4 μm (black) continuum emission plotted according to the distance to the star. The 1∕ d 2 function is also plotted (black dotted). Bottom panel : 8.6 μm/10.4 μm and 11.3 μm/10.4 μm band ratios plotted according the distance to the star. The transparent grey box on the left represents the distance up to which the cavity is extended in POLARIS simulations, ~ 0.12′′ (13 au). At large distances, the variations in the band-to-continuum ratios are not significant. The error bars on the band-to-continuum ratio are about 5%. The dust mass fraction of each THEMIS dust population and a-C sub-population, that is, the population dust mass M X to the total dust mass M total ratio, q X = M X ∕ M total are, q a-C1 ~ 10%, q a-C2 ~ 7%, q VSG ~ 6%, q a-C:H/a-C ~ 8% and q a-Sil/a-C ~ 69%. Finally, for simplicity, we considered only amorphous silicate grains in our model, while several signatures from crystalline silicates have clearly been observed towards HD


Telescopio Canarias (GTC) to obtain data on two further objects. Finally, we re-observed one S2 object with the second-generation Low Resolution Spectrograph (LRS2-B Chonis et al. 2014 ) at the Hobby-Eberly Telescope (HET). The high-quality data from LRS2-B allowed us to derive elemental abundances. The seven stars for which we have acquired data are listed in Table 2 . Table 2. Coordinates and stellar parameters from low-resolution analysis. This table is an example in which are included stars with further follow-up high-resolution spectroscopy. All the identified S2 members are shown in the appendix in Table B1 . Notes . is the average of the S/N of the entire low-resolution spectra. Inst. is the instrument used in the high-resolution observations. 3.1 VLT observations Three of our targets (J0026 + 0037, J0049 + 1553, and J0206 + 0435) were observed with UVES at the 8.2- m VLT Kueyen Telescope in three observing blocks (OBs) of 1 h in service mode during two different nights, 2019 August 2 and August 28 under program ID 0103.B–0398(A). A 12 slit was used with 1 × 1 binning in grey sky conditions and an airmass of ∼1.4. Our settings used dichroic and provided a spectral coverage between 330 and 680 nm. We corrected each spectrum for the barycentric velocity. The average signal to noise per pixel in the spectra was ∼15, 30, and 35 at 390, 510, and 670 nm, respectively. The resolving power for this set up is R ∼ 45 000 for the blue part of the spectrum (330–452 nm) and R ∼ 41 500 for the red (480–680 nm). The seeing was 095 during the first and second OB and 105 in the third one. The data were reduced using the REFLEX environment (Freudling et al. 2013 ) within the ESO Common Pipeline Library. Two more targets (J0007–0431 and J2345–0003) were observed with X-SHOOTER during 2019 August 29 and September 24/26 under program ID 0103.B–0398(B). Due to the relative faintness of these targets, three OBs of 1 h each were allocated but only one per target was finally carried out. The second target has an additional half-time exposure that was aborted due to weather restrictions. We combined both spectra after barycentric corrections. Grey time, a maximum airmass of 1.3, and seeing of 1 were the observational conditions. We used slit widths of 08, 09, and 09 (for UVB, VIS, and NIR) leading to R ∼ 6200, 7400, and 5400, respectively. The average S/N obtained per pixel in stare mode was 30, 45, and 40 at 390, 510, and 670 nm, respectively. The data were reduced by the ESO staff and retrieved through the phase 3 query form. 3.2 GTC observations The observations with HORuS 1 on the 10.4-m GTC were performed in two different periods. Two 1800-s exposures of J0808 + 2418 were taken during the commissioning of the instrument in 2018 December 12. In addition, four 1800-s exposures for each of J0808 + 2418 and J0929 + 4105 were taken in queue mode in the period 2019 November 18 to December 18 under program 133-GTC130/19B. HORuS uses a 3 × 3 integral field unit


this study as the approach leads to reasonable results for the limited energy range considered. Fig. 2 Sketch of the simulation setup as detailed in Dunzlaff et al. (2015) . The four different exit possibilities are colour-coded: the Sun (yellow), the Jovian magnetosphere (orange), the Heliopause (blue), as well as the option that the phase space trajectory is terminated by reaching a predefined end time (green). We note that the figure is not to scale. As described in great detail by e.g. Kloeden Platen (2011) , the stochastic nature of diffusion is treated within the SDE method as a Wiener process with ζ being a vector of Gaussian distributed random numbers. The resulting set of four integral equations, as they are derived by Strauss et al. (2011b ), is solved iteratively by applying the Euler-Maruyama scheme. This leads to a random walk type solution which is terminated if a spatial or temporal boundary is reached, as shown in Fig. 2 for various possible exit positions. A time-backward phase-space trajectory can either terminate at the assumed position of the heliopause (blue line), the Jovian magnetosphere (orange line), or after a pre-specified number of steps have been made without an encounter with either of the formerly mentioned structures (green line). As discussed in Sect. 2.2 , in the low-MeV energy range Jovian electrons dominate the spectrum. The solar population therefore can be assumed to be negligible during quiettimes, and thus trajectories exiting at the Sun are discarded. Galactic electrons, on the other hand are considered via the local interstellar spectrum according to Potgieter Vos (2017) , although the transport of the Galactic population into the inner heliosphere is much more sensitive to the drift effect, which is not considered here. Instead of solving Parker’s TPE directly to obtain a time-dependent distribution function f ( r , t ) covering thewhole phase space, the SDE method provides a chain of point-like solutions both in space and time. The solutions must be sampled at a large number of phase-space points to approximate a spatial solution covering the phase space of interest. In order for the computational results to be comparable with spacecraft data, the time-backward setup is solved as derived and discussed by e.g. Kopp et al. (2012) . A comparison between the time-forward and time-backward setup, made using a simpler 1D model, can be found in the review by Strauss Effenberger (2017) . The left panel of Fig. 5 shows histograms of the so called exit energy 1 (i.e. the energy of which pseudo-particles leave the computational domain) at times of good magnetic connection between the Jovian magnetosphere and the observational point, in contrast to Fig. 5 b, which illustrates the energy distribution for an observational point in opposition to the Jovian source. The distributions in Fig. 5 b are much broader. This, of course, is in agreement with Fig. 5 a being dominated by the much more efficient parallel


mean water abundance is 5 × 10 −5 n H . The accreting D/H ratio is inferred from the observed CH 2 DOH/CH 3 OH ratio (see Table 2 ) as α m = 1.1 × 10 −3 , assuming that the initial (statistical) deuteration of CH 2 DOH in the ice is conserved during the hot core phase. The post-evaporative gas-phase chemistry is also entirely neglected (full details can be found in Faure et al. 2015a ). The results of the model are plotted in Fig. 5 : it is found that the observed CH 2 DOH/CH 3 OD ratio of 3.2 ± 1.5 can be reproduced for a solid s-HDO/s-H 2 O ratio in the range ~8 × 10 −4 −2 × 10 −3 . Therefore, while the CH 2 DOH/CH 3 OD ratio of 3.2 ± 1.5 is consistent with a statistical deuteration, the occurrence of H/D exchanges cannot be excluded. In particular, it should be noted that H/D exchanges can explain the range of values depicted in Fig. 4 , that is CH 2 DOH/CH 3 OD ratios in the range ~0.1−10. To our knowledge, this is currently the only mechanism able to explain the nonstatistical deuteration of methanol in both low- and high-mass protostars. Fig. 5 Gas-phase abundance ratio of the deuterated isotopologs, CH 2 DOH/CH 3 OD, as function of the initial (cold) water ice deuteration. The dotted line corresponds to the analytic solution CH 2 DOH/CH 3 OD = 0.004/(HDO/H 2 O), see Faure et al. (2015a ) for details.The ratio observed toward NGC 7538-IRS1 is represented by the orange hatched zone. 5 Conclusions To summarize, we investigated the deuteration of methanol in the high-mass star-forming regions NGC 7538-IRS1 using IRAM-30m observations. Our study shows that the fractionation degree of deuterated methanol is low in this source. From the numerous (≥10) detected lines, we estimate a CH 2 DOH/CH 3 OD relative abundance ratio of 3.2 ± 1.5. Although our findings are commensurate with statistical deuteration at the icy surface of grain mantles, we cannot exclude H/D exchanges between water and methanol at the present time. Further observations of water and HDO are required to address this point. Appendix A Spectroscopic and observational line parameters Tables A.1 – A.4 list the spectroscopic and observational line parameters for the observed CH 3 OH-A, CH 3 OH-E, 13 CH 3 OH, CH 2 DOH, CH 3 OD-A and CH 3 OD-E transitions. Table A.1 Methanol. Table A.2 Methanol. Table A.3 13 C methanol. Table A.4 Deuterated methanol. Appendix B Partitionfunction of CH3OD Table B.1 gives the respective CH 3 OD-A and CH 3 OD-E rotation partition functions we use in the present study. Table B.1 Rotational partition function for CH 3 OD. Appendix C IRAM-30m observations overlaid with our LTE modeling for 13 CH3OH, CH3OD-A and CH3OD-E Figures C.1 – C.3 show a montage of the detected 13 CH 3 OH, CH 2 DOH, CH 3 OD-A and CH 3 OD-E transitions (see Tables A.3 and A.4 for the observational line parameters) along with our LTE modeling. Fig. C.1 Montage of detected transitions associated with the methanol 13 C isotopolog