2014 ; Roman-Duval et al. 2014 ). 8 For each of the tested models, Gordon et al. ( 2014 ) provide three different realizations of the best-fitting parameters. Of these, we adopt the best-fitting parameters corresponding to the expectation value of the full likelihood function for each parameter (see section 4.3 of Gordon et al. 2014 for details). The most important parameter of the BEMBB model, in terms of investigating the dust content across the SMC, is the dust surface density Σ d . To transform the dust surface densities to E ( B − V ) values for a direct comparison with our reddening map based on the background galaxies, we follow the formalism described by Whittet ( 2003 ). The relation between the total extinction at a given wavelength, λ, and the optical depth of extinction caused by the dust, τ d , is given by We can express this total extinction in terms of the extinction efficiency factor, Q ext : where N d is the column density of the dust and a is the radius of the dust grains (see section 3.1.1 of Whittet 2003 for a full derivation). The dust surface density Σ d is related to N d via where ρ d is the density of the dust grains. We can calculate the V -band extinction using the V -band extinction efficiency factor Q V , such that We adopt the following values for the remainder of the variables in equation ( 4 ): Q V = 1.4 (Chlewicki 1985 ) and, assuming ‘classical’ dust grains, a = 0.1 μm and ρ d = 3 g cm −3 (Mann Kimura 2000 ; Whittet 2003 ; Kohout et al. 2014 ). Finally, we convert A V into E ( B − V ) following the standard A V = 3.1 × E ( B − V ) (Cardelli et al. 1989 ). Note that the values of Σ d represent only the internal dust content of the SMC. Prior to fitting the HERITAGE data, Gordon et al. ( 2014 ) use the integrated MW H i velocity maps in the directions of the SMC (Stanimirović et al. 1999 ; Muller et al. 2003 ) to subtract the structured emission due to the MW. 4.2 Quantitative comparisons Fig. 6 presents the comparison between our reddening map based on galaxies with low levels of intrinsic reddening and the various reddening maps of the SMC discussed in Section 4.1 . To facilitate the comparison, we have resampled the literature maps to a 20 × 20 arcmin 2 resolution by simply taking the median reddening value of all stars/cells that fall within a given bin. This resampling of the literature maps will undoubtedly result in the loss of small-scale (less than 20 arcmin in size) features in these maps. Any large-scale morphological features, however, such as pervasive enhancements of dust along the main body of the SMC, should be preserved and visible in the maps presented in Fig. 6 . Figure 6. 20 × 20 arcmin 2 resolution reddening maps covering the SMC. Each panel refers to a different literature source. The contours in all panels represent the IRAS 100 μm dust emission. The dashed line in the lower right panel represents the footprint of the HERITAGE observations. Of the eight literature maps shown, three


similar to those presented in this paper to fully validate such methods. APPENDIX A: Implementing <italic toggle="yes">f</italic>(<italic toggle="yes">R</italic>) model in <sc>mgenzo</sc> We present here a brief overview of the modified gravity (Hu–Sawicki) model used in this paper which has been implemented via our mgenzo software. This software is a variant of the well-established enzo code and is fully described in Zhao et al. (in preparation). mgenzo has been extensively studied using several independent N -body codes including mgmlapm (Zhao, Li Koyama 2011 ) and ecosmog (Li et al. 2012 ). The mgenzo code uses the same algorithm to solve for the non-linear scalar field equations as the mgmlapm and ecosmog code. Previous results from mgenzo have been validated against other N -body and hydrodynamical simulations of the Hu–Sawicki model, including the code comparison work of Winther et al. ( 2015 ) and Hammami et al. ( 2015 ). These papers show that all these independent codes give consistent solutions for the scalar field, as well as the power spectrum and the mass function of dark matter. In detail, we can write the action of the f ( R ) model as (Capozziello 2002 ) where with . Under the quasi-static approximation, the equation of motion of the scalar field δ f R can be obtained as (Noller, von Braun-Bates Ferreira 2014 ) where , and . One can invert equation ( A2 ) to relate R to f R using where the approximation holds if the background cosmology is close to a ΛCDM+GR model and, in this case, one can approximate as At redshift z = 0, where a flat universe is assumed. Combining equations ( A4 ) and ( A6 ), one can rewrite equation ( A4 ) in terms of f R0 , which is the background value of f R at redshift z = 0, as and δ R is given explicitly as The scalar field f R can then be solved numerically by combining equation ( A3 ) with equation ( A8 ), given the model parameters f R0 and n with background cosmological parameters. The modified Poisson equation for the gravitational potential Φ can be obtained by summing the 00 and ii component of the modified Einstein equation in the Hu–Sawicki f(R) model (Hu Sawicki 2007 ), namely The dynamics of the system are determined by equations ( A3 ) and ( A9 ). Equation ( A3 ) is a non-linear Poisson equation, and it has to be solved numerically on a regular, or self-adaptive, grid using iteration methods (Oyaizu 2008 ; Zhao, Li Koyama 2011 ; Li et al. 2012 ; Puchwein, Baldi Springel 2013 ). We chose Hu–Sawicki model as it has been implemented to several simulations and, as shown in Terukina et al. ( 2014 ) and Wilcox et al. ( 2015 ), is insensitive to the form of the potential of the chameleon field. Thus our constraints are applicable to a wide class of chameleon models, and contains GR as a limiting case. Thus our test also serves as a consistency check of the LCDM model. The weak equivalence principle is not violated in this model as all matter is coupled to the scalar field universally. However,


with consistent dust/ice opacities and dust disk thermal structure. We demonstrate that the photodesorption of water ice is key in the quantitative interpretation of the peak strengths of the 45 and 63 μ m features. The water ice features originate from grains smaller than ~10 μ m. The water ice features originate predominantly at the surface snow line of the disk between 10 and 100 au, which means that they are very robust against several disk parameters such as inner and outer radii, the grain size distribution (within limits), and dust settling. However, the feature strength scales with disk dust mass in the range of typical T Tauri disks. The features also change substantially with the thickness of the ice mantle, although the strength levels off for mantles much thicker than 2.5 times the original grain sizes. Most interestingly, the features do carry an imprint of the thermal history of the ice and thus can distinguish between a warmup scenario for the water ice (where water ice is formed in cold, optically thick regions and then moves to warmer areas in the disk) and a cooldown scenario (where water ice is formed in warm areas close to the midplane snow line and then moves outwards to colder areas in the disk). The direct deposit scenario (ice stays where it was formed locally in the disk) resembles qualitatively the warmup scenario and while the peak strength change of the 45 μ m feature maynot allow a discrimination, the shift in the peak wavelengths to shorter values might be a discriminator. Given the results of our ice model series, simulations using the sensitivities for the planned SOFIA/HIRMES instrument show that the lowresolution and the sensitivity will lead to severely limited ice studies – beyond simple detection – in T Tauri disks at the distance of typical star forming regions. The 45 μ m ice feature is strong enough to be detected if it originates from warm grains with thick ice mantles that are crystalline in nature. Similar simulations for the SPICA/SAFARI instrument show that the differences in peak strengths and the wavelength shifts in the peak position can both be easily measured in samples of several hundred T Tauri disks (exposure times of 10 min). At low spectral resolution ( R = 300) weak flat ice features at 45 μ m (e.g., amorphous, direct deposit, warmup of ice) require a good continuum characterization in deep surveys. Appendix A SEDs and disk structures A.1 Disk inner radius and tapering-off radius Figures A.1 and A.2 illustrate the temperature distribution in the disk models with varying inner radius and tapering-off radius. To assess where the water ice features originate, we also show the snow line and the vertical optical depth τ = 1 contours for 45 and 63 μ m and the radial optical depth τ = 1 at 0.55 μ m. A.2 Dust settling Figure A.3 shows the 2D temperature distribution for disk models with various degrees of settling ( α turb = 10 −2 to 10 −4 ). The change in opacities is strongest in the outer


we find the following results: The central regions of the simulated MW mass-sized galaxies are found to be populated mainly by stars older than 10 Gyr in three of the analysed haloes (Aq-B has ∼50 per cent of its stars >10 Gyr). Most of these stars formed in situ, with a fraction of old stars in the range ∼0.10–0.35 contributed by satellite accretion. The spatial distributions of in situ and accreted stars are different – accreted stars form centrally concentrated spheroidal distributions, while the in situ components exhibit clear bar structures or elongated distributions. The predicted kinematics are consistent with these properties. In particular, the rotational velocity and velocity dispersion distributions of the central region of Aq-C resemble those reported by Zoccali et al. ( 2017 ). Both in situ and accreted stars in the central regions formed in main starbursts (in the progenitor and accreted satellites, respectively). However, accreted stars formed early, so that there is mean age difference of ∼0.5–1 Gyr between the in situ and accreted stars. The age distributions of in situ stars exhibit a tail towards younger ages. Aq-B has a more uniform star formation history for both in situ and accreted stars, since it is affected by a more recent merger event. The age distributions are consistent with the central regions being dominated by stars older than 10 Gyr. This finding is in agreement with the observational results of Santucci et al. ( 2015 ) and Carollo et al. ( 2016 ), who identified an ACS in the MW, extending out to beyond the Sun's location. The metallicity distributions of the in situ and accreted stars are slightly different. The metallicity distributions of the accreted stars are shifted towards lower abundances than those of the in situ stars, and the former have higher α-element enhancements. These trends are consistent with their formation history, since the accreted stars are formed in satellite galaxies with dynamical masses smaller than 10 10 M ⊙ (Tissera et al. 2014 ), while the in situ stars formed in the main progenitors. Regarding the old stars, they represent most of the stars in the central regions, on average. In our simulations, old, accreted stars belong preferentially to the stellar haloes within the inner 10 kpc. A mass fraction of ∼35 per cent is part of the bulge components. The accretion histories show that Aq-A and Aq-C received larger contributions from smaller satellites. On the other hand, the central regions of Aq-B and A-D experienced a greater contribution from a few massive accreted dwarf galaxies. As a consequence, the former have more metal-poor and α-element enhanced stellar populations. At a fiducial solar radius, we estimate that ∼40 per cent of the old stars are accreted. This fraction is in reasonable agreement with the recent results of An et al. ( 2015 ) for the solar neighbourhood. All the analysed central regions have a small fraction of stars younger than 0.1 Gyr, ∼3 per cent, on


bars, but in most cases are very small. Figure 3.312. Image of V417 Cen. Normalized SED profiles of S-, S+IR-, D-, and D′-type SySts. The blue dots correspond to the photometric data from the 2MASS and WISE surveys, the black lines are the BB models for each component, and the red line is the final fit only for cases with multicomponent SEDs. The errors of the data are portrayed as vertical red bars, but in most cases are very small. Figure 3.313. Image of V704 Cen. Normalized SED profiles of S-, S+IR-, D-, and D′-type SySts. The blue dots correspond to the photometric data from the 2MASS and WISE surveys, the black lines are the BB models for each component, and the red line is the final fit only for cases with multicomponent SEDs. The errors of the data are portrayed as vertical red bars, but in most cases are very small. Figure 3.314. Image of V835 Cen. Normalized SED profiles of S-, S+IR-, D-, and D′-type SySts. The blue dots correspond to the photometric data from the 2MASS and WISE surveys, the black lines are the BB models for each component, and the red line is the final fit only for cases with multicomponent SEDs. The errors of the data are portrayed as vertical red bars, but in most cases are very small. Figure 3.315. Image of V852 Cen. Normalized SED profiles of S-, S+IR-, D-, and D′-type SySts. The blue dots correspond to the photometric data from the 2MASS and WISE surveys, the black lines are the BB models for each component, and the red line is the final fit only for cases with multicomponent SEDs. The errors of the data are portrayed as vertical red bars, but in most cases are very small. Figure 3.316. Image of WISE J192140.40+155354.6. Normalized SED profiles of S-, S+IR-, D-, and D′-type SySts. The blue dots correspond to the photometric data from the 2MASS and WISE surveys, the black lines are the BB models for each component, and the red line is the final fit only for cases with multicomponent SEDs. The errors of the data are portrayed as vertical red bars, but in most cases are very small. Figure 3.317. Image of WRAY 16-312. Normalized SED profiles of S-, S+IR-, D-, and D′-type SySts. The blue dots correspond to the photometric data from the 2MASS and WISE surveys, the black lines are the BB models for each component, and the red line is the final fit only for cases with multicomponent SEDs. The errors of the data are portrayed as vertical red bars, but in most cases are very small. Figure 3.318. Image of [JD2002] 11. Normalized SED profiles of S-, S+IR-, D-, and D′-type SySts. The blue dots correspond to the photometric data from the 2MASS and WISE surveys, the black lines are the BB models for each component, and the red line is the final fit only for cases with multicomponent SEDs. The errors of the data are portrayed as vertical red bars, but in most cases are very small. Figure 3.319. Image of AS 201. Normalized SED profiles of S-, S+IR-, D-, and D′-type SySts. The blue dots correspond to the photometric data from the


H , in which the vertical component of the magnetic field is large, σ c / H . Here, the velocity is the velocity of matter in a vortex. The vortex revolution time is ≃ H /. Apparently, the numerical magnetic viscosity (inversely to the conductivity) in the calculations satisfies this condition. Also, the real conductivity of the turbulent matter is anomalous and significantly less than the classical one. Because of this, the magnetic lines above the disc are directed tangentially to the disc (Teixeira, Avara McKinney 2018 ) and the poloidal magnetic field in magnetosphere is close to radial one due to its strong compression by the plasma pressure of the disc near the central object (Kathirgamaraju et al. 2019 ; Liska et al. 2019 ). Split monopole magnetic field lines directly exit from the vicinity of the central black hole. They are involved into the rotation by the black hole and rotate with an angular velocity of Ω F , which for optimal matching is the half of the angular velocity of rotation of a black hole Ω H , Ω F = Ω H /2 (Blandford Znajek 1977 ). The rotating radial magnetic field excites in the magnetosphere a θ-component of the electric field, E θ , which, by virtue of Faraday’s law, is Here, the element of length d l is taken along the θ direction. We get The relation ( 3 ) looks like a condition ( 1 ) in ideal MHD, where instead of the fluid velocity u the azimuthal rotation velocity appears, u = e φ r sin θΩ F . The electric field ( 3 ) in the magnetosphere arises near the black hole horizon due to its rotation and is transmitted along the radial magnetic field to the magnetosphere, which extends up to the light cylinder surface r = c /Ω F sin θ. The polar field E θ in the magnetosphere is the agent that transfers the black hole rotation to the rotation of plasma of the magnetosphere and, when charged particles move in the polar direction, transfers energy to them. We emphasize here that the polar electric field E θ ( 3 ) is the result the central object rotation, and is not a consequence of MHD, which may not be satisfied in the magnetosphere. This topic is discussed in the section ‘Discussion’. Thus, in the magnetosphere there is an electromagnetic field with components Here, r L = c /Ω F is the natural size of the magnetosphere in the transverse direction. This is the radius of the light cylinder, at which the electric field is compared with the magnetic one. For a spherical distance r , the light surface is at the distance r = r L /sin θ. The value of B 0 is the value of the radial magnetic field at the distance r = r L . At the light cylinder the value of the radial field falls from the value of B 0 near the accretion disc (θ ≃ π/2) to B 0 sin 2 θ. The coefficient α is the ratio of the toroidal magnetic field to the poloidal one at the distance r = r L from the centre. Since the split monopole field and the toroidal field differently depend on the radial distance r , then at ‘small’ distances r α −1 r L the poloidal magnetic


uncertainty: the propagation of the individual uncertainty spectra (left panel) and the jackknife uncertainty (right panel). Vertical ticks and labels mark the expected positions of other lines of interest, color-coded as in Figure 3 . The plotted transitions trace large-scale galactic winds and have ionization potentials of 15.0 eV (Mg ii ) and 16.2 eV (Fe ii ). (b) Same as Figure 5 (a), for transitions with ionization potentials from 13.6 eV (top panel) to 24.4 eV (bottom panel). The weighted average stack is shown in the left panel and the median stack in the right panel. (c) Same as Figure 5 (a), for transitions with high ionization potential. Transitions are plotted in order of increasing ionization potential, from top to bottom, from 28.4 to 97.9 eV. The weighted average stack is shown in the left panel and the median stack in the right panel. In Figure 5 (a), we consider the transitions of Mg ii 2796, Fe ii 2344, and Fe ii 2383. 12 12 Fe ii 2600 is unusable due to adjacent Mn ii absorption. These transitions have ionization potentials of 15.0 eV (Mg ii ) and 16.2 eV (Fe ii ) and are associated with spatially resolved, large-scale outflows in galaxies at –2 (Martin and Bouché 2009 ; Weiner et al. 2009 ; Rubin et al. 2010 , 2011 ; Giavalisco et al. 2011 ; Erb et al. 2012 ; Kornei et al. 2013 ; Bordoloi et al. 2014 ; Rigby et al. 2014 ; Rubin et al. 2014 ). In the M eg a S a ura weighted-average shape-normalized stack, these transitions have a maximum velocity of = 900 km s −1 (Table 3 .) Bordoloi et al. ( 2016 ) analyzed the velocity profiles of four regions within one of these galaxies, RCS-GA 032727−132609, and found 95th percentile velocities of 460–610 km s −1 for these transitions. Mg ii is at the extreme red end of the M eg a S a ura stack and so only four galaxy spectra went into the stack; seven galaxies contribute to the stack for Fe ii 2344 and Fe ii 2383. Knot E of RCS-GA 032727−132609 contributed to the stack for both Mg ii and Fe ii . Despite those small numbers, the maximum velocities we measure for Mg ii and Fe ii confirm and extend the conclusion of Bordoloi et al. ( 2016 ): a substantial fraction of the Mg ii and Fe ii gas column has velocities far exceeding the plausible escape velocity of their galactic hosts. 3.5. Galactic Winds as Probed by Other Low-ionization Transitions We next analyze the absorption velocity profiles of other low-ionization transitions, plotted in Figure 5 (b). The main transitions that trace the neutral gas are Ly α and O i 1302, as they have low ionization potentials (13.6 eV). However, a maximum wind velocity cannot be measured for O i 1302 because of nearby photospheric absorption lines, and Ly α is difficult to interpret due to resonant scattering. Instead, we must estimate the wind velocity from Si ii , Al ii , and C ii , which have ionization potentials of 16.3, 18.8, and 24.4 eV, respectively, and therefore trace a mixture of neutral and ionized gas. This absorption has ∼ 630–940 km s −1 in


excited state along the HT pathway. In the previous He i photoelectron study (Reutt et al. 1986 ), the IE values for the formation of the ( X 2 Π u and states were determined as 11.403 and 16.297 eV, respectively. Taking into account that the IE(N 2 ) = 15.581 eV, the first excited electronic state is expected to become accessible when E cm is greater than 0.72 eV. Compared with the distinct increase of σ HT ( v + = 0) at E cm = 0.70–1.00 eV, the σ CT ( v + = 0) only exhibits a slight decline at the same E cm range, indicating that the accessibility to the excited state only enhances the HT channel. While the σ CT ( v + = 0) curve of Figure 2 (a) is consistent with a long-range CT mechanism, the σ HT ( v + = 0) may involve an efficient coupling between kinetic energy and internal vibrational energy, enhancing the formation of N 2 H + in shorter ranges. We note that the thermal motion of neutral reactant molecules C 2 H 2 at room temperature T = 298 K can affect the kinetic energy resolution (Δ E cm ) for a given E cm value. Chantry has shown that the Δ E cm value or the Doppler width caused by the thermal motion of the target gas alone is equal to (11.1 γkTE cm ) 1/2 , where γ = m + /( m + + M ) (Chantry 1971 ). The estimated thermal broadening for the present reaction system is about one order of magnitude smaller than the E cm when E cm ≥ 1.00 eV. But the thermal broadening becomes comparable with E cm when 0.10 eV ≤ E cm 1.00 eV, and even larger than the E cm when E cm 0.10 eV. Because of the relatively large Doppler width at E cm 0.10 eV, the measured σ CT ( v + = 0) values at low E cm values shown in Figure 2 (a) could be distorted. Vibrational-state dependence. In order to investigate the effect of vibrational excitation on the chemical reactivity of ; v + ) toward C 2 H 2 , we have compared in Figures 3 (a) and (b) the respective σ CT ( v + ) and σ HT ( v + ) curves obtained at E cm = 0.03–10.00 eV with the reactant PFI-PIs prepared in the v + = 0, 1, and 2 vibrational states. As shown in the figures, after taking into account the experimental uncertainties, the σ CT ( v + ) and σ HT ( v + ) curves for v + = 1 and 2 vibrational states are found to be nearly in agreement with the corresponding σ CT ( v + = 0) and σ HT ( v + = 0) curves. Thus, we conclude that both the CT (reaction ( 2.1 )) and the HT (reaction ( 2.2 )) channels have only marginal vibrational effects. Nevertheless, the measured CT and HT cross sections seem to show weak vibrational inhibition at low E cm values and weak vibrational enhancement at high E cm values. In the range of E cm = 0.03–0.60 eV, the ( v + = 1) state shows the lowest CT reactivity. For E cm > 0.60 eV, the CT cross section is higher for reactant ion in the v + = 1 and 2 states compared to that in the v + = 0 state. For the convenience of utilizing the results obtained here for atmospheric modelings, we have listed in Table 1 all integral cross sections plotted in Figures 2 , 3 (a), and 3 (b). Figure


to test its significance and simulating 500 CPSDs from the best-fit model, scattered around within the uncertainties of the measured CPSD, we find that a similar improvement in can occur by chance with probability. We therefore conclude that this feature is not significantly detected. 4. DISCUSSION We have presented time-resolved spectral and timing analysis of NuSTAR data of GX 339−4 , taken during a HIMS in early 2015. The time-resolved approach was necessary as the source was softening significantly over the course of the observation and at the same time the prominent type-C QPO increased in frequency. From the energy spectra we concluded that the accretion disk is truncated around 9 r g , independent of the assumed geometry. This value is larger than the ISCO for a spin of () or (), as measured by Parker et al. ( 2016 ) and Miller et al. ( 2008 ), respectively. We note that using the relativistic effects to constrain the inner radius of the accretion disk still has systematic uncertainties, as all available geometries are simple approximations, as discussed in F15 . Independent of these assumptions, the data show that within the uncertainties, the inner radius is not changing over the course of the observation, despite the observed changes in spectral hardness (Figure 5 (e)). Our best-fit model assumes that the power-law continuum incident on the reflector is harder than that observed as the underlying continuum. This configuration was invoked in F15 for the hard state and later confirmed by Parker et al. ( 2016 ) in a soft state observation, and indicates a complex geometry of the corona. Using this geometry, F15 found that the iron abundance is significantly reduced compared to other models. This is not the case in the observation presented here, and all models require an iron abundance around 4–5 solar, similar to the values found by Parker et al. ( 2016 ) and García et al. ( 2015 ), using NuSTAR and RXTE data, respectively. 4.1. Truncation of the Inner Accretion Disk Using relativistic reflection models, we find that the inner radius of the accretion disk is truncated significantly outside the ISCO, at around 9 r g . This result is independent of the assumed geometry, either a standard disk emissivity profile with an index of q = 3, or a lamppost geometry. This amount of truncation is similar to the one found by Tamura et al. ( 2012 ), assuming a black hole. This result indicates that the accretion disk does not move all the way to the ISCO before the source has entered the soft state. This seems to be at odds with results finding the accretion disk to be at the ISCO in bright hard states (e.g., Miller et al. 2015 ). On the other hand, it might simply show that different outbursts behave differently. It is in theory also possible that the truncation is not a strict function of luminosity, and truncation appears again during the HIMS, given its slightly different radiation balance at the accretion disk/corona boundary (e.g., a


luminosity function for bright galaxies and numerous papers (e.g., Vogelsberger et al. 2014 ; Crain et al. 2015 ) detail their success. So, whether the CDM paradigm is right or wrong, the physical processes that they implement give them a luminosity function, above and below the L * break, that matches real data. We have looked at the publicly available output from these groups to see if their results do or do not match observations on statistical expectations with regard to the Tremaine Richstone ( 1977 ) t 1 statistics. We use r -band magnitudes throughout this study. 3.1. EAGLE Simulation The EAGLE simulation is a publicly available (McAlpine et al. 2016 ) suite of cosmological hydrodynamical simulations (Crain et al. 2015 ; Schaye et al. 2015 ). It assumes a standard Λ cold dark-matter cosmology from the Planck-1 (Planck Collaboration et al. 2014 ), Ω m = 1 − Ω Λ = 0.307, Ω b = 0.04825, h = 0.6777, σ 8 = 0.8288, and n S = 0.9611. The simulation suite is run with a modified version of the GADGET-3 N -body Tree-PM smoothed particle hydrodynamics (SPH) code (Springel 2005 ), and includes an updated formulation of SPH, new time stepping, and sub-grid physics (see Schaye et al. 2015 , for details). In this study, we use RefL0100, which has a cosmological volume of (100 comoving Mpc) 3 and a baryonic mass resolution of . We refer the readers to the introductory papers Crain et al. ( 2015 ) and Schaye et al. ( 2015 ) for complete descriptions of the sub-grid physics models. We bin EAGLE simulation results into different size galaxy groups from smallest (12–24 objects), with stellar mass greater than , to more massive systems, with 75–150 galaxies (see Table 1 ). The red lines in Figures 1 and 2 show the average magnitude gap between first-brightest and second-brightest galaxies, , in each group and the brightness of the first-brightest galaxy . Overall, simulated galaxies in EAGLE show a ∼1.7 mag gap between first-brightest and second-brightest galaxies, which is similar to the gap reported by van den Bosch et al. ( 2007 ) with 2° Field Galaxy Redshift Survey data. Figure 1. M 12 presented in the EAGLE simulation (red) and in the “randomized” data (blue). Figure 2. Average first-ranked r magnitude as a function of number of galaxy members in the EAGLE simulation. Table 1 EAGLE Simulation Note. a Average halo mass of the first-brightest galaxies in solar mass. Next, we put all the groups in one bin and randomly repopulate each group from the collective bin, keeping the same number of galaxies in each galaxy group or cluster (See Table 2 ). By construction, this keeps the overall luminosity function invariant. Then, we recompute , and σ ( M 1 ) for each of Figures 1 and 2 . Table 2 EAGLE “Randomized” Simulation Note how the gap is systematically larger in the original () than in the randomized groups (), and the first-brightest galaxy is brighter by over a magnitudes in each original set of galaxy groups than in the randomized versions of


the case of mass transfer from the primary to the secondary star before the secondary expands. Figure 1. Radii (solid lines) and core masses (dashed lines) of the two stars in the binary system, (blue) and (red) as function of time. We assume that merger takes place when the secondary experiences its large and rapid expansion. Figure 2. Like Figure 1 , but for the (blue) and (red) binary system. In Figures 3 and 4 , we present the stellar models of the stars in the two binary systems we study here when the lower-mass companion experiences its large and rapid expansion. We assume that merger occurs during this phase. Figure 3. Structures of the binary systems (upper) and (lower) when the lower-mass companion experiences its large and rapid expansions at . In Table 1 we present the following stellar parameters for the two stars at the time when the more massive star (primary star) finishes its rapid expansion: luminosity, L , effective temperature, T eff , stellar masses, M * , core mass, M core , stellar radius, R * , core radius, R core , and binding energy of the envelope, E bind . In Table 2 we present the same quantities, but for the case when the secondary star finishes its rapid expansion. We assume that a merger takes place then (later we will discuss alternative merger times). Table 1 Properties of the Giant Primary Star and the Pre-giant Secondary Star When the More Massive (primary) Star Finishes Its Rapid Expansion Note. At this phase, the core of the secondary star is not relevant for our study, and we do not present its properties. The gravitational energy that the two cores release when they merge; namely, when their separation is , is given by Equation ( 10 ). The ratio of this energy to the binding energy of the two envelopes, isThis is the typical ratio for the and binary system (using the data from Table 2 ). For the M ZAMS,1 = 31.5 M ⊙ and binary system this ratio is 0.8 (using the data from Table 2 ). As the efficiency of channeling the gravitational energy of the merging cores to envelope removal is α CE 1, when the cores merge there is still bound envelope, but a large fraction of the envelope is leaving the system, and a fraction might form an extended envelope. Table 2 Properties of the Giant Stars When the Lower-mass Star in the Binary System Finishes Its Rapid Expansion Note. We assume that in many cases merger takes place during this time (see Figures 1 and 2 for the models). 4.3. The ILOT Properties Using these results and Equation ( 10 ), we can crudely estimate the total radiated energy in the ILOT. Very crudely, in many ILOTs the typical ratio of radiated to kinetic energy is E rad ≈ 0.1 E kin (e.g., Kashi Soker 2010 ). We take about half of the envelope to be ejected at the escape speed, , and the radiation to carry a fraction of of that energy. For an ejected mass of , we find . This is the general median value of the radiated energy of ILOTs (e.g., Kashi 2018 ). The photon-diffusion time from an ejected mass of


of luminosities for the LMC reported in Table 1 . Concerning the mass-loss rates, Riebel et al. ( 2012 ) find that the C-stars in the LMC with the highest degree of obscuration are injecting into the interstellar medium carbonaceous dust with a rate of ∼10 −7 M ⊙ yr −1 . This is translated into an overall mass-loss rate of ∼2 × 10 −5 M ⊙ yr −1 . 2 This quantity is significantly smaller than the result reported in Table 1 , which is in much better agreement with the results published by Gullieuszik et al. ( 2012 ), van Loon ( 2006 ) and Groenewegen et al. ( 2007 ). On the chemical side, we have seen that the conclusions we may draw for the SMC and LMC are different. In the former case, we showed that within the context of our description of the AGB and dust systems, the colours of the C-stars exhibiting the highest degree of obscuration are reproduced only if the amount of carbon accumulated at the surface exceeds ∼0.5 per cent of the total mass. This C abundance corresponds to a C/O ratio above 3. The IR colours of the most obscured LMC C-stars are however less sensitive to the surface carbon abundance than their SMC counterparts. The uncertainties affecting the degree of carbon enrichment are still significant, which is confirmed by the differences between the monash (surface carbon mass fraction slightly below 0.02, C/O ∼ 10) and aton ( X (C) ∼ 0.01, C/O ∼ 3) models. The most obscured C-stars in the MCs are very faint in the optical domain but much brighter in the near-IR. Thus, the best observational way to test the different nature (i.e. progenitor masses) of the obscured C-stars in the SMC and LMC would be to obtain follow-up high-resolution () near-IR ( JHK bands) spectroscopy of these stars. This can be done with actual instrumentation (e.g. CRIRES at European Southern Observatory/VLT). From such spectra, one could get the CNO elemental abundances, which are expected to be different in both types of stars (see e.g. Ventura et al. 2015b ). On the other hand, an analysis of the chemical composition of planetary nebulae (PNe) in the MCs would provide important complementary information on the chemical enrichment of C-stars in these galaxies. This is because only small surface abundance changes are expected from the final AGB phase to the PN stage. For example, Ventura et al. ( 2015b ) showed that the most C-enriched PNe in the LMC display carbon abundances below X (C) ∼ 0.01, in agreement with the 2.5 and 3 M ⊙ aton models and with the 2.25 M ⊙ monash model (see the bottom-right panel in Fig. 1 ). The extension of this type of analysis to a much wider sample of PNe in the LMC (and also to the SMC PNe) will help us to understand whether this upper limit in the carbon abundance is real, or due to the limited sample of PNe examined. 7 CONCLUSIONS We use Spitzer IR data of C-stars in the MCs to improve our understanding of the evolution of AGB stars with masses below ∼3 M ⊙ , which become carbon stars through repeated TDU events. We focus on


panel, the upper right-hand panel and the lower panel of Fig. 3 , respectively. For simplicity, here we consider only four bins. For low z , β is always consistent with a constant value. For SDSS, the 1σ upper bound of β in the last bin deviates from the results given by the full SDSS subsample at 2σ CL, showing that the SDSS subsample favours a decreasing β at high red shift. This conclusion is consistent with the results of Marriner et al. ( 2011 ). For SNLS, the 1σ upper bounds of β in the third and fourth bins deviate from the results of the full SNLS subsample at 1.6σ and 3.3σ CL, respectively. So compared with SDSS, the SNLS subsample favours a time-varying β with a larger decreasing rate. It should be mentioned that this conclusion differs from the results of the full SNLS3 sample (Wang Wang 2013a ). This means that the SNLS3 data set may contain unknown systematic uncertainties (Betoule et al. 2014 ). Figure 3. The 1σ confidence regions of β given by the three subsamples: low z (upper left-hand panel), SDSS (upper right-hand panel) and SNLS (lower panel). The grey region and the grey dashed line are the 1σ region and the best-fitting result given by the full low- z , the full SDSS and the full SNLS subsamples, respectively. The red, green, blue and yellow regions correspond to the 1σ regions of the first, second, third and fourth bins, respectively. In Fig. 4 , we compare the 1σ confidence regions of β given by the JLA without HST data (left-hand panel) with the results given by the full JLA sample (right-hand panel). We can see that the HST subsample only affects the evolution behaviour of β at high red shift. For the case without HST , the 1σ upper bound of β in the last bin deviates from the results given by the full sample at 3.9σ CL. For the full JLA sample, the 1σ upper bound of β in the last bin deviates from the results given by the full JLA sample at 3.6σ CL. This indicates that the HST subsample can slightly slow down the rate of decrease of β at high red shift. Figure 4. The 1σ confidence regions of β given by the JLA without HST data (left-hand panel) and the full JLA sample (right-hand panel) at red-shift region [0,1]. The grey regions and the grey dashed lines denote the 1σ regions and the best-fitting results given by the full samples, respectively. The red, green, blue and yellow regions correspond to the 1σ regions of the first, second, third, and fourth bins, respectively. Next, we discuss the impact of a varying β on parameter estimation. For simplicity, here we consider the standard cosmological model: the ΛCDM model. As shown in Fig. 2 , β prefers a higher value at low red shift and a lower value at high red shift. So we assume that β is related to the red shift by a simple piecewise function: where β 1 and β 2 are two model parameters. In Fig. 5 , using only the full JLA sample, we plot the one-dimensional (1D) marginalized probability distributions of Ω m 0 for constant β and varying β( z ). It can be


groups: good ( LR > 0.25), fair (0.05 LR 0.25), and bad ( LR 0.25). In addition, as a cross-check we calculated the simple probability of chance coincidence, according to Downes et al. (1986) . We then assigned a preliminary rank, rejecting most of the cases with bad scores. A primary single counterpart is either a physical solitary association, a single non-bad association, or exceptionally the best of the rejects that has been “recovered”. When several candidates above the threshold exist, the one with the best estimator is considered the primary counterpart, and all the others secondaries. The detailed procedure can be found in XXL Paper XXVII. 2.4 Optical photometry The BCS covers ~50 deg 2 , fully covering XXL-S. Optical data in the griz bands were obtained with the Mosaic2 imager mounted on the Cerro Tololo Inter-American Observatory (CTIO) 4m Blanco telescope, reaching 10 σ point source depths of 23.9, 24.0, 23.6, and 22.1 mag (AB) in the four bands (for more details see Desai et al. 2012 ). The DECam ( Flaugher et al. 2015 ) mounted on the Blanco telescope also observed XXL-S (PI: C. Lidman) in the griz bands (4850−9000 Å). The limiting magnitudes in each band (defined as the third quartile of the corresponding magnitude distribution) reach 25.73, 25.78, 25.6, and 24.87 mag (AB). More details of the observations can be found in XXL Paper VI and in Desai et al. (2012 , 2015 ). 2.5 Optical spectroscopy A significant effort has been made to obtain spectroscopy of both northern and southern XXL fields, either with large spectroscopic surveys, for example SDSS, VIPERS ( Scodeggio et al. 2018 ), GAMA ( Baldry et al. 2018 ), ESO Large Program ( Adami et al. 2018 , a.k.a. XXL Paper XX), or smaller scale spectroscopic observations, like the William Herschel Telescope (WHT) spectroscopic follow-up program ( Koulouridis et al. 2016 , XXL Paper XII). The southern field has been chosen for this study due to the homogeneity of its spectroscopic follow-up data, which is based uniquely on a number of observing runs with the multifibre 2dF+AAOmega facility on the AAT; instead, the northern field is based on a compilation of different surveys with different instruments, limiting magnitudes, selection biases, and solid angles.The first set of AAOmega runs occurred in 2013, and is described in Lidman et al. (2016 , hereafter XXL Paper XIV). The second set of runs occurred in 2016 and is described in XXL Paper XXVII. As noted in XXL Paper XIV, priority was given to cluster galaxies over AGN in the 2013 observations. In the 2016 set of observations, AGNs had the highest priority. Hence, the coverage of the AGNs is, perhaps apart from the smallest scales, uniform. It should also be remembered that there is always a lower fibre separation limit, which for the AAOmega case is , corresponding to ~0.2 h −1 Mpc at the median redshift of our sample. However, since any given region within the XXL area was targeted multiple times with 2dF, the number of objects lost


are able to identify galaxies , which have internal and external properties different from dark matter subhalos in several respects. Stellar components tend to be more compact than their dark matter counterparts, and thus better survive the strong background tidal force exerted by their host halo. The background potential, however, is largely governed by the dark matter component. Sometimes, satellite galaxies may even lose their associated dark matter component through tidal disruption as they orbit within the group. In our search for galaxies, we thus start from the stellar distribution, which is then used as a seed to explore the distribution of the other particle species. We first identify the N s nearest star particle neighbors of each star particle and measure local densities using the W 4 smoothed particle hydrodynamics (SPH) density kernel (Monaghan Lattanzio 1985 ). We build a neighborhood network using chains of N n -nearest neighbors at each particle position. This means that all particles have their own neighboring connections. This coordinate-free method suppresses the ambiguities that arise in building the density field, and it reduces the number of parameters required by the galaxy-finding algorithm. Second, we search for the peaks in the stellar mass density field at each particle position. These peaks are local maxima with respect to their own N n neighbors. To alleviate the identification of spurious local peaks due to Poisson noise, we adopt two approaches. One approach is to merge multiple peaks if their distance is less than l merge . The other approach is to set both the minimum number of stars and the minimum stellar mass in the core region. Here, a core region is a volume identified by progressively lowering the density threshold down to the point where the isodensity surface encloses another peak. This is similar to the watershed method. At this point, particles within the isodensity surface are considered to belong to a galaxy candidate centered on the enclosed peak. Third, after extracting core particles related to a density peak, we apply density cuts to group the remaining (noncore) particles utilizing the watershed method. Around each density core, we search for noncore particles whose densities are between the i th and i + 1th density thresholds. We gather those particles to build a “shell” group. By definition, a shell group should surround other density groups. Accordingly, all particles are split into core and shell groups. Finally, to complete the membership decision, we check the tidal boundary of each galaxy candidate, as well as the total energy of particles within the boundary. Even though a particle may be bound to a galaxy, it is not considered a member unless it is within the tidal radius. Figure 6 shows the most massive halo in HR5 identified using the variable FoF approach at z = 0.76. Even with varying particle mass, the derived distributions of dark matter (top left) and gas (bottom left) are


polynomial to each run. 2.2 APO and prompt Additional observations were obtained on 2017 March 4, using the Agile photometer on the 3.5 m telescope at Apache Point Observatory, and on 2017 May 5 and 2017 May 6 using the 60 cm robotic Prompt8 telescope at CTIO. The APO observations consisted of 515 30 s integrations obtained through a BG39 filter, and the Prompt observations consisted of 253 and 300 30 s integrations obtained through a Baader Clear (C) filter. The APO and Prompt data were reduced following our standard procedures (see e.g. Chote et al. 2014 ; SZ16 ) to extract aperture photometry, with one exception: the polynomial fit to remove long-period trends was omitted as there was insufficient data to separate the effect of differential extinction from the long-period variability intrinsic to GW Lib. 2.3 Hubble Space Telescope Quasi-simultaneous Hubble Space Telescope (HST) far-ultraviolet (UV) spectroscopy of GW Lib was obtained using the Cosmic Origins Spectrograph (COS; Green et al. 2012 ) on the nights of 2017 August 31, September 6, and September 13, near the end of the NGTS observation window. The first two observations occurred during bad weather at Paranal, so simultaneous observations were not possible. The weather was clear during the final run, but GW Lib set past the NGTS elevation limit less than 2 min before the HST observations started. The time-tag COS data were reduced following the procedure from TO16 to create ultraviolet light curves. Data were binned into 5 s sub-spectra, which were then background-subtracted and the Ly α and OI airglow lines at 1216 and 1302 Å were masked. Each spectrum was then binned in the spectral direction to create individual photometric points with a 5 s cadence. We present limited results from this data set where they provide important context to the NGTS observations, but defer the full analysis to a future publication (Toloza et al. in preparation). 3 LONG PERIOD VARIABILITY Photometry demonstrating the long-period behaviour was extracted using a 2.5 pixel aperture and all calibrations. Points more than 5σ from the nightly mean (42 in total) were rejected, and then the data were smoothed with a running 40 min mean (roughly 190 points) to reduce the scatter introduced by noise and the 20 min signal. The resulting 34-week long light curve is presented in Fig. 1 . Figure 1. The full 7.5 month NGTS light curve of GW Lib, smoothed with a 40 min boxcar filter to emphasize the long-period behaviour. Each fortnight is offset vertically by 0.5 units, and the observation duty cycle for each fortnight is listed in parentheses below the start date. The regular gaps in the light curve are due to the day/night cycle; the gaps on February 1–2 and August 11–15 were due to technical issues; the remaining gaps are nights when NGTS was not operating due to cloud. Several nights are marked with indicative periods to highlight the detection of the previously observed long-period modulations. The time windows


al. ( 2015 ). We do not expect our L62 results to match the obervational data, since the TNG model was tuned for the TNG-L25N512 test simulations using the galaxy properties mentioned above (as well as the BH mass–stellar mass relation and the galaxy size at redshift z = 0; Pillepich et al. 2018a ) and it has been demonstrated that the stellar properties of galaxies depend on the simulation resolution in the TNG model (see appendix A of Pillepich et al. 2018a , b , for details). Figure 8. Stellar and gaseous galaxy properties at z = 0 (unless otherwise stated). Upper left: Stellar-to-halo mass ratio as a function of halo mass. The stellar mass is measured within 30 kpc from the halo centre. Upper right: Galaxy stellar mass function measured within 30 kpc from the centre of the halo. Bottom left: The halo gas fraction within r 500 c as a function of the total halo mass. Bottom right: Star formation rate density as a function of redshift. Different colours represent different gravity models as specified in the legend. The solid colour lines show results from our L25 simulations, while the dashed coloured lines are from our L62 boxes. All lower subpanels show the relative differences between the galaxy properties of nDGP and GR models. In all panels, we compare our results with the IllustrisTNG results at three different resolutions (Pillepich et al. 2018a ): TNG-L25N512 (the solid grey curves), TNG-L25N256 (the grey-dashed curves), and TNG-L25N128 (the grey-dotted curves). The blue solid line in the upper panels shows the results from the TNG100 simulation (Pillepich et al. 2018b ). The light grey symbols represent observational measurements from Behroozi, Wechsler Conroy ( 2013 ), Baldry et al. ( 2012 ), Bernardi et al. ( 2013 ), D’Souza, Vegetti Kauffmann ( 2015 ), Giodini et al. ( 2009 ), and Lovisari, Reiprich Schellenberger ( 2015 ). The upper left-hand panel of Fig. 8 shows the stellar-to-halo mass ratio multiplied by the inverse of the baryon fraction (Ω b /Ω m ), as a function of the total host halo mass ( M 200 c ) for our six full-physics simulations at z = 0. The stellar mass was measured within 30 kpc from the halo centre. First, we note that the L62 simulations (the dashed coloured lines) are in good agreement with the TNG-L25N128 (the grey-dotted line) run at the high-mass end, but is lower than the TNG-L25N256 (the grey-dashed line) and TNG-L25N512 (the grey solid line) results, which is as expected given the resolutions of these runs. Our L25 runs (the solid coloured lines) predict higher stellar mass fractions than the TNG-L25N512 (the grey solid line), despite the fact that these simulations have the same resolution. The differences are due to the combination of the different initial condition realizations we used to run our simulations (i.e. cosmic variance) and the small number of high-mass objects in the small boxes. Note that the final TNG100 run (the blue solid line; Pillepich et al. 2018b ) also has disagreements with the


coordinate. The photon ring is the gravitationally lensed image of the (unstable) photon orbit. Because the absolute values of angular momenta of the co- and counter-rotating photons on the photon orbit around highly spinning BHs (i.e., blue and red curves in Figure 2 (a)) are distinctly different, the impact parameter is significantly different between them. This results in the positional shift of the photon-ring center in the observer screen (Bardeen 1973 ). On the other hand, photons emitted by the innermost accretion flow produce an SSA-thick ISCO ring and the ISCO ring does not show such a significant positional shift of its center (green and purple curves in Figure 2 (b)). This is because these rays deviate from the photon orbit near the BH and the resultant impact parameter does not strongly depend on the sign of angular momentum of photons. Then, the positional offset between the center of the photon ring and that of the SSA-thick innermost region forms the “dark crescent” in the resultant image. The dark crescent appears in the opposite side of relativistically beamed bright region. Figure 2. Trajectories of photons forming the photon ring (top) and the SSA-thick ISCO ring (bottom), in the vicinity of the Kerr BH with a * = 0.998. The viewing angle is i = 30°. Each trajectory is projected onto the equatorial plane of the Boyer–Lindquist coordinate (we note that we define ( x eq , y eq ) ≡ ( r sin θ cos φ , r sin θ sin φ )). The solid/dashed curves represent the SSA-thin/SSA-thick regions along the rays. The positions of the rays on the observer screen are represented by the dashed lines in Figure 4 . Because the horizontal shift of the photon ring increases with BH spin (as well as the ISCO radius for matter decreasing with BH spin), the larger and clearer dark crescent appears when the BH spin is higher: the dark crescent appears in the models with a * = 0.998 and 0.75, while it is not found around the BH with a * = 0.5 in our shadow images. We can find a clearer dark crescent for the model with i = 30° than for i = 15°, because of a more prominent horizontal shift of the photon ring by the frame-dragging effect in the case with larger viewing angle. In Figure 3 , we present the intensity images (top) and τ SSA (bottom) in the observer’s screen at 230 and 350 GHz for i = 30° and 15° in the model with a * = 0.998. This is the first example explicitly displaying τ SSA in the observer’s screen. These spatial distribution maps of τ SSA on the observer screen enable us to understand the formation of the dark crescent in the BH shadow image. By comparing the intensity and τ SSA map at 230 GHz, we can confirm that the bright inner ring is formed via the emission from the SSA-thick innermost accretion flow. We note that the photon ring is τ SSA ≳ 1, because the rays pass close to the photon orbit, which results in the large emission gain and the formation of the bright photon ring. At ν = 350 GHz, the right side of both the photon ring and


The standard approach has been to compare measurements of different statistics to cosmological hydrodynamical simulations (Zaldarriaga et al. 2001 ; Theuns et al. 2002b ; Viel et al. 2009 ; Lidz et al. 2010 ; Becker et al. 2011 ; Garzilli et al. 2012 ; Rorai et al. 2013 , 2017a , 2017b ; Iršič Viel 2014 ) to deduce the thermal parameters (e.g., T 0 , γ or ) that best describe the IGM thermal state. As a larger number of high-resolution spectra of quasars have become available at higher redshifts , the same approach has been applied to study the thermal state of the IGM at these redshifts, where the Ly α forest is more sensitive to the timing and nature of hydrogen reionization (Theuns et al. 2002b ; Hui Haiman 2003 ; Cen et al. 2009 ; Furlanetto Oh 2009 ; Becker et al. 2011 ; Viel et al. 2013a ; Lidz Malloy 2014 ; Garzilli et al. 2015 ; Nasir et al. 2016 ). In the light of the new Planck constraints on reionization, as well as the increasing number of quasars discovered at high- z (e.g., Bañados et al. 2014 , 2016 ; Matsuoka et al. 2016 ), it is pertinent to revisit what Ly α observations with current and upcoming facilities can tell us about reionization. This work aims to explore in detail the possibilities of using the Ly α forest 1D flux power spectrum at high- z to constrain H i reionization. For this we have used a new method that has recently been introduced by Oñorbe et al. ( 2017 ). It builds on the Haardt Madau ( 2012 ) model, but enables one to vary the redshifts of and reionization, as well as their associated heat injection, allowing one to consistently simulate a more diverse range of reionization histories. This allows for a much comprehensive and consistent exploration of the space of thermal parameters than previously done. We present here the results of the 1D flux power spectrum at high- z of a new set of hydrodynamical simulations that also improve the resolution used in previous studies at these redshifts. Additionally, we compare these power spectra with some recent measurements at these redshifts (Viel et al. 2013a ). The structure of this paper is as follows. In Section 2 we describe the characteristics of our hydrodynamical simulations and the different reionization models studied in this work. Section 3 presents the thermal evolution of the different reionization models obtained from the cosmological hydrodynamical simulations. In Section 4 we compare the 1D flux power spectrum of each model at as well as with the best available observations. We discuss in Section 5 the relevance of our findings in the context of current observational and theoretical limitations. We conclude by presenting a summary of our results and an outlook in Section 6 . In the Appendix we perform a set of convergence test for the optical depth and the 1D flux power spectrum at . Throughout this paper we assumed a flat ΛCDM cosmology with the following fundamental parameters: , , , h = 0.67038, , and . These values agree within 1 σ with the


effect of photoionization feedback may be further reduced for realistic accretion disc spectra, compared to the case of the single power-law spectrum usually assumed in most works (Takeo et al. 2019 ). As mentioned in Section 3 , for accretion rates satisfying the DPT condition, photon trapping due to electron scattering is also naturally realized. In the case of DPT, radiation feedback at radii larger than the dust sublimation radius is effectively suppressed, while the entire accretion disc radiation may be efficiently trapped. Under such extreme trapping conditions, most of the infalling matter may be accreted (Volonteri et al. 2015 ). Since the accretion rate leading to DPT is much larger than the Eddington rate, it should be associated with super-Eddington accretion and a rapid build-up of the BH mass. For instance, adopting the DPT accretion rate as the minimal value, the enhancement factor could be of a few orders of magnitude compared to the Eddington-limited value. It is known that photon trapping also modifies the emergent spectral energy distribution. Higher energy photons originating in the inner accretion flow are more efficiently trapped than lower energy photons produced from the outer regions. As a result, the peak frequency of the spectral energy distribution shifts towards lower energies, and the active galactic nucleus (AGN) spectrum becomes softer with increasing accretion rate (Ohsuga, Mineshige Watarai 2003 ). In the case of DPT, the whole disc radiation can be efficiently trapped, and the overall luminosity output may be considerably reduced, leading to faint AGNs. This may not be the case for photon trapping due to electron scattering, where only the inner parts of the accretion disc remain trapped (unless the accretion rate is extremely high). Since UV/optical photons are trapped within the dusty accretion flow, the central AGN will be obscured. In this context, X-ray photons would be even more readily trapped than UV/optical photons, and thus super-Eddington accretion will be likely obscured at both X-ray and UV/optical wavelengths (Wyithe Loeb 2012 ). In our picture, DPT accretion is indeed associated with significant obscuration, with large column densities expected at early times. Cosmological hydrodynamic simulations also suggest heavy obscuration on different physical scales around the growing BHs in the early Universe (Trebitsch, Volonteri Dubois 2019 ; Ni et al. 2020 ). Assuming a standard radiative efficiency of ε ∼ 0.1, it has been estimated that the obscured fraction at z > 7 could be of the order of (Davies, Hennawi Eilers 2019 ). In fact, much of the early growth of massive BHs could be obscured, and a large number of such obscured quasars may be missed in current optical surveys (Hickox Alexander 2018 ; Inayoshi et al. 2020 , and references therein). On the other hand, obscuration by dusty gas may cause higher energy photons to be reprocessed into lower energy photons, leading to an increase in the


projected orbital arrangements in motion in Figure 17 . Figure 5. Smoothed representation of the pole vision image of the circularized orbit distribution shown in Figure 4 (f). We subtracted the distribution expected from 39 randomly oriented orbits. Here the 39 orbits are generated, assuming a sin i uniform distribution for the inclinations, and a circular uniform distribution of the longitude of ascending node after setting e = 0 and a = const. As in Figure 4 (f), the black lines indicate the directions of the disks and the white line the direction of the Galactic plane. The two orbital disk systems are well separable (see above) but rather thick. Furthermore, the orthogonal X-shaped disk structure becomes apparent only in alternating zones in the position angle histogram (see Figure 8 ) and in Ω diagrams as well (see Figure 6 ). This leads to the fact that they cannot easily be recognized in polar diagrams as used by, e.g., Gillessen et al. ( 2017 ) in their Figure 12 or Yelda et al. ( 2014 ) in their Figure 21. In Figure 6 , we show the inclination of the stars as a function of the longitude of the ascending node Ω. The color indicates their membership in either the red or the black disk. It becomes clear that the two disks cannot easily be identified as the angular momentum vectors of the disk members point in opposite directions. Comparing Figure 8 and Figure 6 , one can also see that the two disks can be better separated by evaluation in the position angle histogram instead of evaluating the longitude of the ascending node Ω. Figure 6. The inclination as a function of the (LOAN) longitude of the ascending node Ω. However, compared to Figure 6 , the inclined and face-on representations of the disk members as shown in Figure 4 are better grouped together, because the direction of the angular momentum vector is not relevant in this representation. Here, looking at circularized orbits as described above is more successful in searching for face-on orbits that bunch close to the circumference of the sky-projected distributions as in Figures 4 (g) or (h). In Figures 7 (a) and (b), we show the inclinations of the two stellar systems. On the right-hand side of Figure 7 , we show the distribution of inclinations for all stars within the central acrseconds for which we can provide Newtonian orbital fits. In particular, the distributions for the two disks do not follow a sin i distribution as one might have expected for a fully randomized scenario. There is a clear clustering of inclinations around a mean value of ∼90° with the bulk of the higher inclined stellar orbits contained within an interval width of 50° (red disk with bulk between 80° and 130°) or even a width of only 40° (black disk with bulk between 70° and 110°). In comparison to the expected width of about 100° for a sin i distribution, this implies that the two separate disk are highly biased toward high inclinations. There are also no stars with inclinations in the intervals 0°–20°


every system, the highest mass is generally achieved when pebble accretion is included. While the systems in which pebble accretion is neglected fail to build super-Earths with our input parameters, the formation of such planets becomes possible when pebble accretion is included. While the number of active embryos decreases when pebble accretion is included (see Fig. 6 ), their masses increase drastically. 4.3 Active number and total mass Figure 6 shows the total number of embryos and the total mass that is in embryos over time for the setups from Figs. 2 – 4 . We also give the fraction of total embryo mass M Emb over the mass that was given to the planetesimaldisk after 1 Myr ( M D ) for each setup. The first embryos always form in the systems in which pebble accretion is enabled. However, the number of active embryos during the simulation is almost a factor of 2 below the number of embryos in the systems without pebble accretion. The mass in embryos differs even more strongly than the active number of embryos for the corresponding systems. The fraction M Emb ∕M D consistentlyincreases for higher total masses and steeper Σ P -profiles, respectively. In the systems in which pebble accretion is included, it can exceed unity. This means that the mass in planetary embryos can be higher than the mass that is transformed into planetesimals through pebble accretion. 4.4 Orbital separation In Fig. 7 we compare the mean orbital separation of embryos over time for the systems from Figs. 2 – 4 . The orbital separation is expressed in units of the embryos Hill radii. The mean orbital separation after 1 Myr converges to ≈ 10R Hill for each setup. The simulations in which pebble accretion is included show a smoother and more stable behavior over time than the systems in which pebble accretion is neglected. The explanation of these differences lies in the fact that the first embryos can start growing farther apart from each other in the runs that only consider planetesimal accretion. Therefore numerous embryos are needed in order to converge for a characteristic orbital Hill spacing. Fig. 2 Time over semimajor-axis evolution of the N -body simulation in LIPAD. The time and location at which an object has first reached lunar mass is indicated by the black dots in the plot. The subsequent growth of the embryo is tracked and connected with the gray lines, and its mass is given by the color bar. The mass in planetesimals after 1 Myr is given by 6 M ⊕ in these runs, the planetesimal surface density slope is varied (Σ P ∝ r −1.0 , Σ P ∝ r −1.5 , and Σ P ∝ r −2.0 ). Left panels : system without pebble accretion. Right panels : system in which pebble accretion is included. The red line indicates the time after which the analytic model presented in Voelkel et al. (2021) states that embryo formation is possible. Fig. 3 Time over semimajor-axis evolution of the N -body simulation in LIPAD. The time and location at which an object has first reached lunar mass is


scales linearly with the gas mass density and is proportional to the logarithm of the ratio of the spatial extents of the forming wake and the shock’s stand-off distance. 7.2. Minimum spatial interaction scale The numerical experiments allow us to compute the total dynamical friction acting on the body and also to investigate the individual contributions to the dynamical friction induced as a function of the distance to the perturber. The outcome of this analysis reveals that the region within the stand-off distance of the shock does not contribute to the dynamical friction of a gaseous medium (see Fig. 5 and associated main text for details). At radii smaller than the stand-off distance, a spherically symmetric stratified atmosphere forms around the moving body, which (because of its symmetry) induces no net gravitational pull or pressure force. Only at radii above the stand-off distance does a wake of higher density form behind the moving body and induce a gravitational drag force. Hence, in the well-known formulae by Ruderman Spiegel (1971) or Ostriker (1999) , it is the stand-off distance of the shock that determines the minimum length scale required in the so-called Coulomb logarithm : The formation of a spherically symmetric atmosphere (with radius ) around a gravitating object implies that the hydrodynamical drag force vanishes in contrast to the non-gravitating case, but for very high Mach numbers the shock moves very close to the object so that . In this case, no spherically symmetric envelope around the object forms and the hydrodynamical drag becomes important again. 7.3. Relating the stand-off distance to the accretion radius In a second step, to allow an easy computation of the stand-off distance for general dynamical friction problems, we derived the relation of the shock’s stand-off distance to the common definition of the accretion radius, depending only on the mass and velocity of the perturber. The stand-off distance is directly proportional to the accretion radius and the proportionality constant only depends on the Mach number and the adiabatic index of the gas: Additionally, the geometrical radius of the moving body yields a lower limit for the stand-off distance . Via an analytical estimate of the stand-off distance and further fitting of the remaining free parameters, we gave an approximate relation of the dependence of the shock’s stand-off distance on the adiabatic index of the gaseous medium with and values of and . 7.4. Updated formula of dynamical friction Finally, we combined the derived scaling relations and the finding on the stand-off distance to give an update of the well-known formula of dynamical friction acting on a body of mass moving at supersonic speed through a gaseous homogeneous medium of mass density , where denotes the extent of the wake and can be obtained using the derived formulae above. Appendix A: Hydrostatic equilibrium stratification As mentioned in the text, behind the shock front and


ejecta and a shock-heated ISM (Park et al. 2003 , 2012 ; Uchida et al. 2015 ). It is also notable that N49 is in an overionized state (Uchida et al. 2015 ) and is interacting with dense molecular clouds on the eastern side (Banas et al. 1997 ; Yamane et al. 2018 ). Due to the interaction with molecular clouds, the thermal X-ray emission of N49 is particularly bright on the southeastern rim. N49 is an attractive object since Kaastra Mewe ( 1995 ) pointed out that the effect of RS can show up if an SNR has such a spherically asymmetric structure. Here, we present a high-resolution X-ray spectroscopy of N49 with the Reflection Grating Spectrometer (RGS) on board XMM-Newton. The obtained G-ratio of O vii He α and other line ratios as well imply a nonnegligible contribution of RS in N49. Throughout the paper, errors are given at a 68% confidence level. We assume the distance to N49 (LMC) to be 50 kpc (Pietrzyński et al. 2013 ). 2. Observation and Data Reduction N49 was observed with the XMM-Newton satellite (Jansen et al. 2001 ) in 2001 (Obs.ID 0113000201) and 2007 (Obs.ID 0505310101). The observation in 2007 was performed with a roll angle which placed N49 and a nearby SNR, N49B, along the dispersion direction of the RGS, making it difficult to extract RGS spectra of N49. We thus analyzed only the data obtained in 2001. For our spectral analysis, we used the RGS (den Herder et al. 2001 ) and the European Photon Imaging Camera MOS (Turner et al. 2001 ) data. We reduced the data using XMM Science Analysis Software version 16.1.0. The RGS data were processed with the RGS pipeline tool rgsproc . To discard periods of background flares, we applied good time intervals based on the count rate in CCD9, which is the closest to the optical axis of the mirror and has the least X-ray counts from the source and most affected by the background flares. The resulting effective exposure time is 11 ks for both RGS1 and RGS2. Since the second-order spectra are of low statistical quality, we analyzed only the first-order spectra. Figure 1. EPIC-MOS image (0.4–8.0 keV) of N49. The cross-dispersion width of the RGS (5 arcmin) is in between the white solid line. The spectral extraction region is enclosed by the white dashed line. N49B is another SNR near N49. 3. Analysis We analyzed the spectra using version 3.04.0 of the SRON SPEX package (Kaastra et al. 1996 ) with the maximum likelihood C-statistic (Cash 1979 ; Kaastra 2017 ). The RGS spectra were fitted simultaneously with those of MOS1 and 2. To account for the spatial broadening of the source, we multiplied spectral models with the SPEX model lpro , to which we input the MOS1 image of the source. Our models have two absorption models: one for the Milky Way and the other for the LMC. The column density of the former was fixed to (Dickey Lockman 1990 ) whereas that of the latter is left free. The elemental abundances for the LMC absorption were fixed to values found in the literature (∼ 0.3 solar; Russell Dopita


final abundances at some specific values of A that differ by up to two orders of magnitude from the other networks. This shows the importance of using detailed balance to compute inverse rates. We again see good agreement in Figure 9 between the three networks in the proton and helium abundance evolution (left panel of Figure 9 ). But there are a handful of mass numbers at which SkyNet with detailed balance produces final abundances that deviate from the other networks by up to two orders of magnitude (right panel of Figure 9 ). This indicates that it is vital to compute the inverse reaction rates correctly with detailed balance in this scenario. However, the average fractional abundance errors shown in Table 1 are still at the few percent level, and the differences between SkyNet and WinNet or XNet are comparable to the differences between WinNet and XNet. We note that the errors between SkyNet without detailed balance and WinNet or XNet are smaller if screening is turned off. This indicates that screening is somewhat important in this case and we expect the discrepancy between the different codes to increase if screening is turned on due to the different screening implementations. The effect is especially noticeable when comparing SkyNet to XNet with self-heating turned on, because in this case XNet uses the temperature computed from SkyNet, but if screening is switched off, the error between the two codes decreases from 1.1% to 0.086%. SkyNet’s screening implementation is presented in Section 4 . WinNet uses a single fit of the two-body screening factor by Chugunov et al. ( 2007 ) across all screening regimes. XNet computes the two-body screening function provided by Graboske et al. ( 1973 ) for weak and intermediate screening and the one provided by Dewitt Slattery ( 1999 ) for strong screening. XNet then uses a selection rule to select one of the three screening regimes without interpolating between them. 6.2.3. Hydrostatic Carbon–Oxygen Burning In order to compare the self-heating methods implemented in the three networks, we perform a hydrostatic burn at constant density. We keep fixed and start with T = 3 GK and the initial composition consists of half and half (by mass). As a baseline comparison, we also perform non-self-heating runs, where we keep the temperature fixed at 3 GK. The increase in the errors between the networks with self-heating enabled compared to with it disabled must then be due to the difference in the self-heating implementations in the codes. We use a mid-size network containing all nuclides from the full network (Section 6.2.1 ) with . This results in a network with 1530 species and 20,000 reactions. Figure 10 shows the results of this test case with self-heating and screening turned on. We find good qualitative agreement between the three networks, but quantitatively, the differences between XNet and the other two codes are much larger than in the previous test cases. These discrepancies come from the different