and the microturbulence were related according to Heinzel Anzer (2001) (see Paper I , Appendix A). Therefore, the obvious next step was to use the L and C iii lines to distinguish between kinetic temperature and microturbulence. This is only possible when two species with different masses are formed in the same emitting plasma volume ( Tandberg-Hanssen 1995 ) and are both optically thin. In this section we check whether this condition is met in the spectroscopic UVCS observations of the L, L, and C iii lines. Fig. 2 Doppler velocities of the L, L and C iii lines as a function of latitude along the UVCS slit. Note that the last three points of the L line reach Doppler velocities of several hundred km s. Fig. 3 Profiles of the L, L and C iii lines of the 12th measured point along the erupting prominence. We present a detailed Doppler velocity analysis of all the 68 points we measured along the prominence in the L, L, and C iii lines in Fig. 2 . This shows that for the majority of the points, the Doppler velocities of the C iii line are consistent with the L and L velocities within the uncertainty of the UVCS wavelength determination, which is equal to the spectral UVCS resolution of about 0.2 Å. This gives an uncertainty in the Doppler velocity of about 60 km s. The Doppler velocities of the three lines are almost consistent within the estimated uncertainties. L and L lines must have the same Doppler velocities because they are emitted from the hydrogen atoms. From this we conclude that the C iii ions also move with the same Doppler velocity as hydrogen. Therefore, the L, L and C iii lines are formed in the same or a similar emitting plasma volume with a unique kinetic temperature and microturbulent velocity. In addition, firm proof that all lines are formed in the same plasma volume is provided by the fact that the profiles of all three lines, reported in Fig. 3 in one representative case, exhibit a single peak. We note that their Doppler shifts should be proportional to . If the profiles had more than one peak, it would indicate that the prominence blobs move with different velocities in different directions, and this is not observed. 4. Kinetic temperature and microturbulent velocity The line profiles of optically thin prominences are mainly Doppler broadened as a result of the thermal motions of atoms and because of the turbulent plasma motions. The Doppler line width can then be expressed as Here is the speed of light, is the Boltzmann constant, is the kinetic temperature, is the mass of the atom, is the microturbulent velocity, and is the effective temperature. We introduced the microturbulence because in erupting prominences that are embedded in CME cores, significant nonthermal motions are expected to occur. Equation ( 1 ) shows that the carbon line is more sensitive to the microturbulent velocity and less sensitive to the kinetic temperature, as is clearly shown in Fig. 4 . Fig. 4 Panel a : FWHM of the C iii line plotted as a function

O O O O O O O B-Citation I-Citation I-Citation O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


optimize the chances of finding new systems with gas. 4.1 Flux predictions for atoms When making predictions for C i , C ii and O i masses, the conversion to fluxes is more complicated than with CO where the excitation is dominated by the CMB (see Section 3.5.2 ). Since these lines are at shorter wavelengths, the dust radiation field can become dominant (see Fig. B1 ). While the dust radiation field seen by the gas is not easy to assess, especially as most of our targets are unresolved, it is well known for β Pic. Thus, we use the same radiation field as found in Matrà et al. (in preparation) for that system. For other targets, we fit each SED individually and use the ratio of the dust fluxes at 158, 610 and 63 μm to those of β Pic to scale up or down the β Pic radiation field and so get predictions for the fluxes of each individual system for C ii , C i and O i (see Appendix B ). Note that we also take account of the optical thickness of each line in our flux calculations using the method described in Section 3.5.6 . 4.2 C <sc>ii</sc> model predictions and results We start off by comparing our C ii model predictions to Herschel observations. In Fig. 7 , we plot our predictions of C ii mass as a function of distance to the star. To do so, we use our analytical model using equation ( 11 ) to get the total carbon mass and equation ( 15 ) to get the ionization fraction and then compute . The predicted C ii masses are shown as red points in Fig. 7 . We keep the same style as the CO plot (Fig. 4 ), i.e. systems with gas detected are labelled with their names. If in addition, they have C ii detected, the label is blue (not black). NLTE detection thresholds are computed using the same code as described to compute CO population levels in NLTE (see Appendix B for details). We overplot the detection limits at 5σ in 1 h in both LTE (thin lines) and NLTE (thick lines) for Herschel /PACS (in red) where we assumed the typical sensitivity reached for non-detections (Riviere-Marichalar et al. 2014 ), for SPICA/SAFARI (in orange) and for a future far-IR mission (such as FIRS) with a 10 m aperture (in green) where the sensitivities are taken from the SPICA and FIR surveyor documentation. 4 The assumed sensitivities are summarized in Table 3 . We compute the electron density as a function of the C ii mass (using equation 14 ) with our model to compute the NLTE lines. Figure 7. C ii mass (in M ⊕ ) as a function of distance to Earth ( d ). Planetary systems with gas detections are labelled with their names. If C ii is detected, the label is in blue (black otherwise). The C ii mass lower limits worked out from observations are shown as green arrows, and for β Pic we show the mass derived from Herschel observations using Kral et al. ( 2016 ) as a green point. The red points are predictions from our model. The red downward arrows show systems that are in the blue hatched area on Fig. 1 , which cannot keep CO trapped on solid bodies. The purple points show predictions

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O B-Wavelength B-Wavelength O B-Wavelength I-Wavelength O O O B-CelestialObject I-CelestialObject O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Tag O O O O O O O O O O B-Model I-Model I-Model O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O B-Model O O O B-Model O O O B-Telescope B-Instrument O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O B-Telescope O O O O O O B-Wavelength O O O B-Telescope O O O O O O O O O O O O O O B-Telescope O B-Telescope I-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O B-Telescope O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


the same linear assumptions previously applied to yield kernel phases, analogous self-calibrating observables also exist for propagation through more complex optical systems such as coronagraphs. However, for the example configuration explored, the rapid onset of a nonlinear response indicates they may be of limited practical applicability to coronagraphic observations except in the extremely high-wave-front-quality regime. Subnanometer wave-front precision may nevertheless be achieved in future large space telescopes with high-order deformable mirrors. 2.5. Zernike Basis Taking the Jacobian of one large pixel grid by another is expensive in terms of memory; it is therefore desirable to bring down the dimensionality of either the input or target space. One way to do this is to use a Zernike basis to represent the wave front (Zernike 1934 ). One advantage of this is that we can examine only up to a certain order in Zernike polynomials if we believe that wave-front errors are negligible below a certain spatial scale. We can then differentiate just with respect to Zernike coefficients, which is much more computationally efficient and allows us to run simulations on grids that are many times larger than otherwise. Similar bases (e.g., the “hexike” basis) can be constructed for arbitrary noncircular telescope apertures. We have rerun the simple diffraction simulation from Section 2.1 with 200 Zernike modes on a 256 × 256 grid, and the coronagraph from Section 2.4 on a 128 × 128 grid using 300 Zernike modes. The calculations now take around 4 s, rather than many minutes, with peak memory use around 1.5 and 3 GB rather than 7 and 9 GB respectively. The Jacobian derived from this basis for simple diffraction is an excellent approximation to the full calculation on a grid. Given that in problems such as HST data analysis we believe that PSF variations are dominated by low-order modes (Lallo et al. 2006 ), this allows us to calculate a larger kernel space with a more accurate pupil model than has previously been possible. While it is a huge advantage in simulation speed and fidelity, this basis does not accurately represent the high-spatial-frequency sine waves corresponding to speckles far from the core of the PSF. Nevertheless, it does an adequate job representing the effects of low-order wave-front error, and this may be sufficient for many purposes, for example in optimization of optical design. 3. Discussion A phase transfer matrix constructed analytically with a discrete pupil model contains no a priori information about the pixel sampling, binning, or windowing. This means that the implicit convolutions in the plane, and therefore the associated correlation between adjacent baselines, are not taken into account. Therefore, the normally orthonormal kernel phases (calculated analytically for an infinite field of view and fine sampling) are no longer fully linearly independent. For example, Martinache et al. ( 2020 ) note that in the analysis of

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


are thought to be representative for larger areas of the comet, locally there may be large deviations from the global value as detected at CG’s final landing site. Figure 18. Diurnal temperature variation for example facet in TM's FOV at 3 au. Thermal inertia: Γ = 67 Jm −2 K −1 s −1/2 . Due to an instrument failure to penetrate the subsurface layers, the depth- and temperature-dependency of the local layering remain unknown. Therefore, in this first refinement study, facet thermal inertia is assumed to be constant. The results for simulation durations of 10 d (without optimized starting conditions) are compared to those of 50 d (with and without optimized starting conditions), one orbit and three orbits. It can clearly be seen that a few comet rotations of simulation time are not sufficient to obtain a converged solution. Increasing the simulation time improves the results, especially when optimized starting conditions are used. Most facets in the TM's FOV require simulation times above 50 up to 200 d, when using appropriate initial conditions. Above a couple of 100 d, the starting conditions begin to lose importance unless the initial guess is rather far off. The limiting factor for a final in-depth TM data analysis lies in the still prevailing uncertainties for the detailed local landing environment and the final lander orientation. The preliminary shape model used in this example does not reflect the correct illumination duration on the lander itself. The model facets in the TM’s FOV are cumulatively illuminated for about the measured amount of time if not the correct time spans, pointing to the wrong lander or individual facet orientation for the preliminary DTM used. 5 CONCLUSIONS Highly resolved celestial body shapes are computationally very demanding when performing a thorough thermophysical investigation. This is especially true for highly non-convex shapes by itself or in combination with disc-integrated data. Also highly resolved local landing sites on nearly convex shapes such as expected to be obtained for Ryugu will benefit from a model that can take into account a local DTM with large detail. A method is presented for efficiently calculating converged surface temperatures and temperature-dependent quantities. While the equations applied solve for subsurface temperatures as well, the method is only applicable to surface temperatures. The software itself can be used to calculate depth profiles as well, losing the method’s advantage, however, of a reduction in computation time. The only speed-enhancing measure in that case is the implemented parallelization. The method presented adds several pre-processing steps to the actual thermophysical modelling. Some calculation steps, however, are fast – the iterative evaluation of the upper boundary condition to obtain starting conditions takes seconds to minutes depending on the size of the shape model. The calculation of illumination conditions is not fast, but is already required as input

O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O B-Instrument O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


is seen between q 24 and for the entire sample, with a correlation coefficiency of 0.33. The second panel of Figure 5 shows that metal-poor galaxies have on average warmer color than metal-rich ones, but no apparent correlation between q 24 and . Actually, the two galaxies with the highest around 0.4 show almost the largest and smallest q 24 , respectively. The above result confirms a previous finding of no relation between and f (60 μ m)/ f (100 μ m) (Wu et al. 2008 ). The last panel of Figure 5 illustrates some weak dependence of on the far-IR color , with a correlation coefficiency of 0.26. Figure 5. vs. the IR color of , , and . The red points denote metal-poor galaxies and black points are for metal-rich galaxies. The two horizontal dashed lines indicate the average values of metal-poor and metal-rich galaxies, respectively. Figure 6 investigates the dependence of on the three IR colors mentioned above. A weak correlation is seen between and , with a correlation coefficiency of −0.34. Overall, the metal-poor and metal-rich galaxies share the same range in , as already mentioned above. At the same , q 70 is smaller for metal-poor galaxies compared to metal-rich galaxies. The two metal-poor galaxies with the highest show low q 70 , but not as extremely as expected, if there is a relation. The dependence of q 70 on is very weak, with a correlation coefficiency of −0.05. At the same color, metal-poor galaxies on average occupy lower regimes compared to metal-rich ones. Among two metal-poor galaxies with the highest , only one shows a lower q 70 than the remaining galaxies. The last panel shows no strong relation between and the far-IR color , with a correlation coefficiency of about −0.2. Figure 6. Same as Figure 5 but for . Figure 7 shows as a function of the three IR colors mentioned above. The first panel indicates a weak dependence of q 100 on , with a correlation coefficiency of −0.42. At the same color, metal-poor galaxies show somewhat lower than metal-rich galaxies. SBS 0335-052E, which has the highest , does not show the lowest q 100 . In the second panel, a stronger trend is present for the with, with a correlation coefficiency of −0.53. The two galaxies with the highest have the lowest q 100 among the whole sample. In the last panel, the dependence of q 100 on is weak, with a correlation coefficiency of −0.33. Figure 7. Same as Figure 5 but for . as a function of IR color is shown in Figure 8 . An inverse relation of with is present, with a correlation coefficiency of −0.63. The relation between and is also apparent, with a correlation coefficiency of −0.43. The relationship between and is the strongest one, with a correlation coefficiency of −0.71, indicating that the low of metal-poor galaxies is associated with their high . Figure 8. Same as Figure 5 but for . In summary, for the whole sample, including both metal-rich and metal-poor galaxies, only shows good relationships with the three IR colors. Previous studies of

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


that the following correction terms are subtracted from the metallicity determined from H ii calibration given in Section 3.2 : Combining these with equations ( 5 ) and ( 7 ), they result into the following final calibrations: where x and x are determined from equations ( 5 ) and ( 7 ), respectively. We apply the above corrections to the DIG/LIER-dominated spaxels (i.e. those with emission line ratios beyond the Kauffmann line) to all galaxies in sample. Fig. 3 (bottom row) shows metallicity maps of NGC 1042 obtained from O3N2 (left-hand panel) and O3S2 (middle-panel) after correction, while the corresponding maps for all other galaxies are shown in figures (bottom rows) in the supplementary online material (Appendix A). 4.3 Residual differential metallicity after correction The metallicity maps obtained using these new calibrations for the DIG/LIER regions already show an improvement, especially in terms of much reduced metallicity contrast between H ii regions and nearby DIG/LIER regions. In this subsection, we quantify such improvement. From the corrected O3N2 and O3S2 metallicity maps of each galaxy, we estimate representative values of metallicities for H ii –DIG/LIER pairs using the same methodology described in Section 3.1.1 , and study the distribution of differential metallicities in Fig. 9 . Left-hand panel shows the distribution for [S ii ]-BPT selected H ii –DIG/LIER pairs, while right-hand panel corresponds to [N ii ]-BPT selected H ii –DIG/LIER pairs. By construction, mean differential metallicity is zero for each of the two metallicity diagnostic and for both samples. A comparison of dispersions before and after applying corrections can be found in Table 1 . Figure 9. Distribution of corrected differential metallicity (Δlog Z) of H ii –DIG/LIER pairs selected on the basis of the [S ii ]-BPT (left-hand panel) and [N ii ]-BPT (right-hand panel) diagrams. In each panel, the brown and cyan histograms represent the differential metallicity distribution from O3S2, and O3N2, respectively, after applying the correction to the DIG/LIER/Seyfert spaxels presented in Section 4.2 (equations 10 , 11 , 14 , and 15 ). σ(Δlog( Z )) denotes the standard deviation of the differential metallicity distribution. In each case, the average offsets of the distribution are zero by construction. O3N2 shows comparable metallicity dispersions for H ii –DIG/LIER samples obtained from both selection criterion, i.e. 0.04 dex for [S ii ]-BPT selection and 0.03 dex for [N ii ]-BPT selection. The dispersions are smaller than the scatter in differential metallicities before applying correction (i.e. 0.05 dex). Like O3N2, O3S2 also shows comparable metallicity dispersion for H ii –DIG/LIER samples obtained from both selection criterion, i.e. 0.06 dex for [S ii ]-BPT selection and 0.07 dex for [N ii ]-BPT selection. Although the dispersions after correction are still larger than those obtained from O3N2, the improvement is significant with respect to the dispersions

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


more complex calibration model may contribute to the degeneracy and, in the worst case, restore complete degeneracy. 4.5. Dependence on heliotropic coordinates The spherical coordinates , , introduced in Sect. 2.6 define the position of the solar system barycentre in the SRS. This is what matters for calculating the parallax effect, which depends on the observer’s displacement from the barycentre. On the other hand, the physical relevance of the modulation is connected with the changing illumination of the satellite by the Sun, which depends on the heliocentric distance and the heliotropic angles and that represent the proper direction towards the centre of the Sun at the time of observation. The difference between the heliotropic and barytropic coordinates is at most about 0.01 au and 0.01 rad, respectively. This is small but should be taken into account for an accurate modelling of the basic angle variations. In this context it can be noted that the expected thermal impact on the satellite scales as , whereas the parallax factor scales as . On the other hand, the scanning law is chosen to keep as constant as possible, whereas can vary at the level of 1%. If the basic angle varies as , it is no longer strictly of the form of Eq. ( 18 ). The resulting parallax bias can be estimated by means of Eq. ( 19 ). 4.6. Breaking the degeneracy? If the basic angle varies as a consequence of the changing solar illumination of the rotating satellite, we expect to see a parallax bias according to Eq. ( 19 ). However, as discussed above, the degeneracy with the parallax zero point is not perfect, and in principle this opens up a possibility to calibrate the basic angle variations from the observations. At least three different effects that contribute to breaking the degeneracy could be used: the finite size of the field of view (Sect. 4.4 ), the time dependence of due to the eccentricity of the Earth’s orbit (Sect. 4.3 ), and the difference between the barytropic and heliotropic angles (Sect. 4.5 ). Unfortunately all three effects only come in at a level of a few per cent of the variation, or less, which makes the result very sensitive to small errors in the calibration model. Moreover, the finite field of view is of little use if we have to calibrate complex periodic variations of optical distortions independently in each field of view. The best chance may be offered by the time variation of , for which the ratio of the parallax effect to the illumination strength goes as and consequently varies by % over the year. Thus the hope of breaking the degeneracy purely from the observations themselves, based on the self-calibration principle, is somewhat limited. 5. Conclusions We present an analysis of the effect of basic angle variations on the global shift of parallaxes derived from observations by a scanning astrometric satellite with two fields of view. The method of small perturbations was used to derive the changes in the four observables, the across- and

O O O O O O O O O O O O O O O O O O O O O O O O O B-TextGarbage I-TextGarbage O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion O O B-Model O O O O O O O O O O O O O O O O O B-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


equally. The fitting method is the same as the SED analysis. The results are shown in Figure 4 . The arrows indicate the 95% upper limits of those time bins, whose TS values are smaller than 5. No obvious long term variation is found, which is consistent with the emission expected from an SNR. Figure 4. Light curve of source X. The horizontal solid and dashed lines are the average flux and its 1 σ range from the whole data set. 3. DISCUSSION The spatial and spectral association between source X and the HESS observation of SNR CTB 37B suggests that source X is the GeV counterpart of this SNR. The γ -ray emission can be either from the ICS of high energy electrons or the π 0 decay due to the inelastic pp collisions. Due to the lack of non-thermal X-ray emission in the same region of the TeV γ -ray emission, Aharonian et al. ( 2008 ) argued that the TeV γ -rays may have a hadronic origin. The Suzaku observations reveal, however, both thermal and non-thermal diffuse X-ray emissions from the western part of the radio shell, which suggests alternatively a multi-zone leptonic scenario for the γ -ray emission (Nakamura et al. 2009 ). We discuss both the leptonic and hadronic models in light of the multi-wavelength data, including the Fermi -LAT ones. In the modeling, both the spectra of electrons and protons are assumed to be power laws with exponential cutoffs, , where i = e or p , and α i and are the spectral index and the cutoff energy, respectively. The distance of CTB 37B is adopted to be 13.2 kpc (Tian Leahy 2012 ), and the radius is taken to be r ≈ 20 pc which corresponds to an angular size of 51 at such a distance. The radiation field includes the cosmic microwave background (CMB), an infrared field with T = 30 K and energy density u = 1 eV cm −3 , and an optical field with T = 6000 K and u = 1 eV cm −3 (Porter et al. 2006 ). The gas density is adopted to be 0.5 hydrogen cm −3 , as inferred from the X-ray observations (Aharonian et al. 2008 ; Nakamura et al. 2009 ). For the region which is coincident with the SNR shell (region 1), no non-thermal emission has been detected (Aharonian et al. 2008 ; Nakamura et al. 2009 ). The 1–5 keV flux of the thermal emission is ∼3 × 10 −13 erg cm −2 s −1 (Aharonian et al. 2008 ). The 2–10 keV unabsorbed flux of the thermal X-ray emission from region 1 is estimated to be ∼6 × 10 −13 erg cm −2 s −1 , based on the non-equilibrium ionization model employed in Aharonian et al. ( 2008 ). This thermal flux is adopted as an upper limit of the non-thermal emission from the SNR. 3.1. Leptonic Model In the leptonic model, the radio to X-ray emission is due to synchrotron radiation of relativistic electrons in the magnetic field, and the γ -ray emission is produced through ICS in the background radiation field and bremsstrahlung in the interstellar medium. To fit the radio to TeV γ -ray data, we find α e ≈ 1.65, , a magnetic field B ≈ 100 μ G, and a total electron energy above 1 GeV W e ≈ 9.0 × 10 48 erg. The fitting

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


baryon fraction. Once M g is specified, the gas density is normalized such that, 2.3 Ionization balance In this paper, we consider models that may represent the most metal-poor DLAs currently known. Given the presumably minimal level of recent star formation in these systems, it is reasonable to assume that the local sources of ionizing photons are sub-dominant relative to the extragalactic background. In what follows, we have therefore assumed that the surface of the most metal-poor DLAs is illuminated solely by the Haardt Madau ( 2012 ) ultraviolet/X-ray background radiation from quasars and galaxies with intensity J 0 (ν). We also explore simple power-law models for the ionizing background, which are equivalent to the ‘ table power law slope α ’ command within cloudy , where f (ν) ∝ ν α . We assume that the distributions of gas and dark matter are spherically symmetric. Under this assumption, gas at a distance r from the centre of a dark matter halo is irradiated by background photons from all directions. The radiation field is therefore attenuated by a different amount depending on the density distribution of the gas along a given direction. If J 0 (ν) represents the unattenuated radiation field at a frequency ν, and 2πsin (θ)dθ/4π is the fraction of sky with an optical depth τ(ν, r , θ), then the intensity of the radiation field at a distance r from the centre of the cloud is given by where μ = cos θ, and i corresponds to every element/ion stage that we consider in this work. Unfortunately, our calculations are computationally too demanding to include every ionization stage for all elements with atomic number 30 (unlike cloudy ). We have therefore incorporated only the most abundant metals that are commonly observed in metal-poor DLAs, including H i , D i , He i , He ii , C i –C iv , N i –N iv , O i –O iv , Mg i –Mg iv , and Si i –Si iv . We have adopted the photoionization cross-section, σ i (ν), of each element using the compilation by Verner et al. ( 1996 ). At a distance r from the centre of the halo, the column density of species i in the direction θ can be calculated by integrating the volume density of species i, n i ( R ), from a radial distance r to the virial radius 2 (i.e. integrate along the path defined by the dashed line in Fig. 1 ): where equation ( 12 ) is used for 0 ≤ θ ≤ π/2 and equation ( 13 ) is used for π/2 θ ≤ π. The rate of primary ionizing photons at a given radius from the cloud centre of each species is then where h ν i is the ionization energy 3 of ion i . Each radiation field considered in this work is finely interpolated around the ionization energy of each ion to ensure numerical accuracy in the integrations. Figure 1. The coordinate system used to calculate the angular dependence of the column density of each species at a given radial coordinate (see equations 12 and 13 ). The rate of collisional ionization, Γ ci ( T ), is incorporated in our models using the Dere ( 2007 ) rate calculations.

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


range of 60–80 kpc. Similar numbers have been found by Zhang et al. ( 2019 ) from the analysis of about 300 galaxy clusters at redshift 0.2 z 0.3. These authors described the BCG+ICL radial profile by using a triple Sérsic model and found a dominant core in the innermost 10 kpc, a bulge between 30 and 100 kpc and the ICL that dominates the distribution beyond 200 kpc, but already outside 100 kpc the profile transitions from the BCG to the ICL. They suggested that this transition is a potential cut between the two components, in good agreement with Pillepich et al. ( 2018 ) who noticed that simulated halos more massive than 5 × 10 14 M ⊙ have more ICL mass outside 100 kpc than within. All the values of the transition radius, i.e., the radius at which the ICL starts to become the dominant component, reported above are comparable with the range predicted by our model. We stress again that a wide range of possible values of R transition is preferable to a narrow one for the reasons discussed above. It strongly depends on the morphology of the BCG, on the amount of ICL with respect to the other components, and on the dynamical state of clusters, which reflects the merging history of the BCG+ICL system and thus its evolution with time. 5. Conclusions Following the analysis done in our recent paper (Contini Gu 2020 ), we have further improved our model by assuming that the radial mass distribution of a BCG+ICL system can be described by the sum of three profiles: a Jaffe profile for the bulge, an exponential disk, and a modified NFW for the ICL. We have taken advantage of a wide sample of simulated galaxy groups and clusters from our state-of-the-art semianalytic model to study the innermost ∼100 kpc of BCG+ICL systems. Unlike the model used in our previous study, the new one offers the opportunity to go below 100 kpc since bulge and disk are treated separately. The main goals of this study were to confirm that our model can reproduce several observed relations between the stellar mass at a given radius and the total BCG+ICL/halo mass, at different redshift and, give an idea of where the transition between the BCG and the ICL happens, i.e., when the ICL component starts to dominate the total distribution. In light of the analysis done and the overall discussion, we conclude the following: 1. The radial mass distribution of a BCG+ICL system can be described by the sum of three profiles: a Jaffe profile for the bulge, an exponential disk, and an NFW-like profile for the ICL. The model can reproduce several observed scaling relations between the BCG+ICL stellar mass within a given aperture and the BCG+ICL/halo mass, at different redshift with an overall precision below 0.05 dex at z = 0 and 0.3 dex at z ≳ 0.5 along the wide stellar mass/halo mass ranges probed. 2. In good agreement with recent observational studies, our model predicts that R transition , i.e., the radius at which the radial distribution of BCG+ICL systems transitions from the BCG to the

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


; Boylan-Kolchin etal. 2012 ), and rotation curves (van der Marel Kallivayalil 2014 ). 2.4 Likelihood from <italic>V</italic>max distributions Here, we summarize the statistical method for comparing the observational and simulated V max distributions. It is identical to that of Jiang van den Bosch ( 2015 ) except where noted below. The goal is to determine the probability that the Milky Way satellite V max function can be drawn from the distribution of simulated functions. We will establish the statistical scatter between the simulated V max functions, and calculate the mean deviation between the measured Milky Way V max function and the simulated systems. The size of the measured V max function deviation relative to the size of the scatter will tell us about how readily the Milky Way V max function is realized in each of our models. The first step is to define the variation within the set of V max for a given halo mass-dark matter modelgalaxy formation model combination. The n most massive satellites of the i th simulated halo are selected, and their values of V max are sorted into descending order. The V max distribution is then { V i , 1 , V i , 2 , V i , 3 V i , n }; here we have omitted the max subscript for clarity. We can define the difference between this i th halo distribution with respect to the j th halo distribution thus: and if there are N realizations of the model in question, the mean Q for the i th distribution, , is Similarly, if we substitute the i th simulated V max distribution to instead be { V MW, 1 , V MW, 2 , V MW, 3 V MW, n }, i.e. the observed V max distribution of the Milky Way satellites, then we obtain Q MW : The probability that a V max function with Q MW could be drawn from the parent distribution is then P ( Q MW ), where P is the cumulative distribution of . We expand on the method described above to describe how we select satellites. The luminosities calculated for the satellites enable us to take account of the fact that the brightest satellites, for which the velocity dispersions have been measured with the highest precision, need not necessarily reside in the most massive haloes. Therefore, we consider two options for selecting our top n satellites to be matched to observations: (i) select the n brightest V -band satellites and (ii) select the n highest V max satellites. We compare the results from these two approaches in Section 3.1.3 . 2.5 Sterile neutrino matter power spectra In addition to CDM, we consider keV-scale, resonantly produced sterile neutrino dark matter. The latter constitutes part of a larger particle physics model called the neutrino minimal standard model (MSM), which explains neutrino oscillations and baryogenesis in addition to yielding a dark matter candidate, see Boyarsky, Ruchayskiy Shaposhnikov ( 2009 ) for a review. The keV sterile neutrino behaves like WDM, in that it free streams out of small perturbations in the early Universe. The resulting matter power spectrum

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of galaxies with high SFRs/luminosities to the CSFRD/total IR luminosity decreases much flatter. This discrepancy reflects the tension between the SFRFs of the EAGLE reference model and IR constraints. The later imply larger number densities of objects with SFR ∼ 10–100 M ⊙ yr −1 (Section 4.1 ) at z 2, and the disagreement with the L100N1504-Ref run increases with time. In Section 6 we will see the important role that feedback plays on keeping the number of these extremely high star-forming objects low at these redshifts. 5 THE CONTRIBUTION OF HALOES WITH DIFFERENT MASSES TO THE SFRF AND CSFRD In this section we present the contribution of haloes with various masses to the CSFRD (Fig. 4 ), the number density of haloes of different masses at different redshifts (Fig. 5 ) and their contribution on the SFRF (Fig. 6 ) in the EAGLE L100N1504-Ref run. Figure 4. CSFRD contribution of haloes with different masses in EAGLE. Below redshift 5 objects with masses M halo = 10 11–12 M ⊙ dominate through their high efficiencies besides their low numbers (Fig. 5 ). Figure 5. Left-hand panel: evolution of the number of haloes with different masses in the L100N1504-Ref. Haloes with low masses are numerous even at high redshift while higher mass objects (e.g. M halo ∼ 10 11–13 M ⊙ ) form with high rate up to redshift z ∼ 1.5. Right-hand panel: percentage of star-forming haloes at different masses. Haloes with M halo ∼ 10 11–12 M ⊙ are typically star forming at all redshift. Figure 6. The contribution of dark matter haloes to the SFRF (black stars) for redshifts z ∼ 8.0 (top left-hand panel), z ∼ 4.0 (top right-hand panel), z ∼ 2.0 (bottom left-hand panel) and z ∼ 0.1 (bottom right-hand panel). Galaxies with SFR ≥ 1 M ⊙ yr −1 reside in large haloes M halo ∼ 10 11–12 M ⊙ even at z ∼ 4.0. These haloes represent only ∼1 per cent of the total star-forming population at this era. In the local Universe the number of massive haloes M halo ≥ 10 11 M ⊙ is significantly higher than that of z ∼ 4. They dominate almost entirely the SFRF at SFR ≥ 0.1 M ⊙ yr −1 . Behroozi, Wechsler Conroy ( 2013 ) and Moster, Naab White ( 2013 ) argued that haloes near 10 12 M ⊙ are the most efficient at forming stars at all redshifts with the baryon conversion efficiency ( M ⋆ / M baryon ) dropping rapidly at both higher and lower masses. In addition, the stellar to halo mass ratio also peaks at 10 12 M ⊙ (Behroozi et al. 2013 ). However, in the paradigm of hierarchical structure formation, small haloes form earlier than larger ones, which need some time to emerge. In Fig. 4 we see that at z ≥ 5 the CSFRD is dominated by relatively small haloes of mass M halo = 10 9–10 M ⊙ . 5 The left-hand panel of Fig. 5 reveals that the number of objects of this mass interval is high. In addition, the right-hand panel of the same figure, where we present the percentage of star-forming haloes at different masses (i.e. n haloes, SFR > 0 / n haloes, total ), shows that a large percentage (>50 per

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


10 and 15 per cent, respectively. Figure 2. Distribution of the resultant distance uncertainties of the catalogued PGCCs. In Fig. 3 , we compare our newly derived extinction distances with the kinematic values deduced by Zhang et al. ( 2018 ). In general, the newly estimated extinction distances differ significantly from the kinematic ones. Amongst the sample objects, 10 clumps have similar kinematic distances ( d Z18 ∼ 0.46 kpc), as they all have similar radial velocities (8.0 or 3.0 km s −1 ). However, their directly measured extinction distances range from 0.21 to 0.51 kpc. It is quite possible that the peculiar and non-circular motions of the clumps may have significantly affected the calculation of their kinematic distances (Liszt Burton 1981 ; Gómez 2006 ; Reid et al. 2009 ). For some PGCCs, such as G176.17-02.10 and G177.14-01.21, the differences between the two sets of distances are very large. The kinematic distance probabilities of those clumps derived with the Bayesian Distance Calculator (see table 1 of Zhang et al. 2018 ) are very small (less than 0.5), indicating that those kinematic distances are poorly constrained. Figure 3. Comparison of our extinction distances with their kinematic values from Zhang et al. ( 2018 ). In the left-hand panel, the black dash line denoting complete equality is used to guide the eyes. 5 DISCUSSION The improved distance estimates allow us to revise some of the distance-dependent physical properties of the cores of the PGCCs, such as their radii, masses, and the virial parameters. We update those physical parameters by simply rescaling the results of Zhang et al. ( 2018 ). For example, effective radius R eff of a Planck core is proportional to distance d , R eff ∝ d . Thus the revised radius is evaluated as Similarly, the revised mass M ′ is given by We note that these updates also lead to changes of other parameters, such as the virial parameter, which is given by Fig. 4 plots the space distribution of these 61 PGCCs in the X – Y space with both the original kinematic distances and our updated distances, where the distance changes are indicated. According to the formula (3) and (4), we present the changes of these physical quantities in Fig. 5 . From the histograms in the left-hand panel of Fig. 5 , we find that on the whole the radii and masses calculated with the new extinction distances tend to be smaller than those of Zhang et al. ( 2018 ), by respectively ∼ 17.9 and 32.6 per cent. This leads us to conclude that to understand the local molecular structures, accurate distances are necessary. We use an MCMC algorithm to fit the mass–radius relation for both sets of distances. The new distances yield a slope of 1.95 ± 0.09, comparable to 1.93 ± 0.09 obtained with the kinematic distances. In spite of the significant changes, the slope is largely unaffected. The result is understandable, considering that a change in the distance measurement leads to changes in both mass and size estimates. Since the

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


of all bodies to zero. We also fixed the orbital period of the planet–moon barycenter to 287.378949 days (the best fit from TK18 ). We elected not to vary the period of the planet–moon barycenter because it is poorly constrained from a single transit observation. A longer period would cause a longer transit duration for the planet, but this could equivalently result from a smaller impact parameter, a larger star, or a massive moon that significantly perturbs the planetary orbit. We used the following priors: the stellar radius was normally distributed, R * ∼ N (1.81, 0.17) R ⊙ (see the next section). The planet radius was uniform from 8 to 14 R ⊕ . The planet transit time was uniform over the timespan of the observations, and inclination was uniform from 0° to 90°. The planet mass was log-normally distributed, M p ∼ 10 2.5±0.5 M ⊕ , based on the expectation for Jupiter-radius objects from Ning et al. ( 2018 ). For the moon model, we allowed the transit time to vary uniformly over the entire visit. The moon period was uniform between 1.6 and 260 days. These limits span the duration of the HST observations (so there is one possible moon occultation event), to the orbit at 0.5 the Hill radius, based on the stability limit for prograde moon orbits (Domingos et al. 2006 ). The Hill radius calculation assumed that the planet and stellar masses are 1 M Jup and 1.37 M ⊙ . The moon mass varied uniformly from 0 to 30 M ⊕ . The longitude of the ascending node was also uniform from 0° to 360°. The moon inclination was uniform from 0° to 90°, and was defined relative to the line of sight. We assigned zero prior probability to scenarios where the moon did not transit or experienced a grazing transit. We made this choice to put an upper limit on the radius of a fully transiting moon; for grazing transits or non-transits the moon radius could be arbitrarily large. 3.1.1. Stellar Parameters For both the moon and no-moon scenarios, we used a quadratic stellar limb-darkening law and fixed the coefficients to the prediction for a 5700 K, solar metallicity PHOENIX model from Espinoza Jordán ( 2015 ); u 1 , u 2 = [0.216, 0.183]. We estimated the host star parameters using the Gaia second data release (DR2) parallax (Gaia Collaboration et al. 2016 , 2018 ) along with UBV photometry from Everett et al. ( 2012 ) and JHK photometry from the Two Micron All-Sky Survey (Skrutskie et al. 2006 ). We employed the isochrone python package (Morton 2015 ) with the Dartmouth isochrone grid (Dotter et al. 2008 ) to obtain posterior constraints on the stellar parameters. The resulting parameters indicate that Kepler-1625 has stellar mass M ⊙ , radius R ⊙ , and age Gyr. In our analysis, we fixed the stellar mass to the best-fit value (1.37 M ⊙ ), and used a Gaussian prior on the radius, R * ∼ N (1.81, 0.17). 3.2. Instrument Systematics Model There are two systematic trends in the data. One is the orbit-long ramp, attributed to charge traps in the detector filling up over the orbit

O O O O O O O O O O O O O O O O O O O O O O B-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O B-Model O O O O O O O O O O O O B-Model O O O O O O O O O B-Model O O O O O O O O B-Model I-Model B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest B-Model I-Model O B-Citation I-Citation I-Citation I-Citation I-Citation B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O B-Dataset I-Dataset I-Dataset I-Dataset B-Dataset O B-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation O O O B-Wavelength O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Wavelength O O O B-Survey I-Survey I-Survey I-Survey B-Citation I-Citation I-Citation I-Citation O O O O B-Model I-Model I-Model B-Citation I-Citation O O O B-Model I-Model I-Model B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


results, the most important one being that due to the photoelectric charging. This is further illustrated below. Two typical runs, though limited to 100 grains for each a value and with integration times of only 0.1 Myr for clarity, are illustrated in Figs. 4 and 5 . The spread of the orbits into broom-like structures is entirely due to the turbulence; if v turb is set equal to 0 the orbits collapse to a single vertical line. It is obvious from these figures that the choice of initial conditions for the velocity is important for the orbits, although the fraction of grains falling into the star as a function of grain radius is not as dependent on these conditions. Fig. 4. The orbits of grains over 10 5 yr, from a point indicated by an “ x ” in black along the z axis at a distance of 10 4 AU from the star (which is at the origin of the coordinate system), and with different grain radii a as indicated by the different colours. The dust grains were given an initial velocity identical to the gas free-fall velocity. The turbulent mean speed was set to 0.1 km s −1 . We note that the scales of the x and y axes are different from that of the z axis. Fig. 5. The orbits of grains over 10 5 yr, from a point indicated by an “ x ” in white along the z axis at a distance of 10 4 AU from the star (which is at the origin of the coordinate system), and with different grain radii a as indicated by the different colours. The initial velocity of the dust grains was set to zero. The turbulent mean speed was set to 0.1 km s −1 . We note that the scales of the x and y axes are different from that of the z axis. The main results of these numerical experiments are displayed in Fig. 6 . Here we have plotted a quantity called “the defect”, D ( a ), of the run, as a function of a for different choices of the defining parameters. D ( a ) measures the fraction of grains that leave the proto-solar cloud as a result of the radiative cleansing. It is defined as where N l is the number of dust grains lost inside 100 AU, and N 0 is the corresponding number lost in a run with identical parameters with the exception that the stellar luminosity L is set equal to zero. In this way, we try to correct for the fact that even at zero luminosity some of the gas may depart at high turbulence speeds from the stellar neighbourhood. It is seen from the figure that the variation of D with a is smoothed when v turb increases, from a very steep change when a passes the limiting value in Eq. ( 9 ) for small turbulence, to a less steep variation. We also note that an increased inflow of gas decreases the deficit at a given a , as does a change of the initial condition from v ( r 0 )=0 to setting v ( r 0 ) equal to the free fall velocity of the gas flow. Also, the coulomb forces diminish D but not drastically so. None of these effects is unexpected. Obviously, these variations of the deficit with the different parameters are not very dramatic: the conclusions concerning the cleansing effects in

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


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


of the blended line intensities of Fe xiii and Fe xii in the analysis of EIS spectra, we applied the same method to the Fe xvii line complex around λ 204.6 Å in the LHD spectra to unblend the Fe xiii and xii line intensities. The results are summarized in Figure 5 . The time evolution of the electron density for low-temperature LHD peripheral plasmas is plotted in Figure 5 (a), where the electron density ( n e ) is estimated to be log n e (cm −3 ) ∼ 10.5–11.8 after the NBI controls, slightly higher in the later phases of discharge. The estimated electron densities are somewhat lower than those measured by Thomson scattering at t = 4.3 s and t = 4.9 s (see Figure 2 of Murakami et al. 2014 ), but these line intensity ratios of Fe xii and xiii are located in the range that is close to the high-density limit, and the apparent large difference in the absolute n e values derived from Fe xii and Fe xiii does not affect the estimation of the blended Fe xiii/xii line intensities much, and therefore is negliglible in the following analysis results. Figure 5. (a) Electron densities for the LHD plasma plottted against time since the discharge of shot 107,802. The line types are the same as in Figure 4 (b). (b) Reduced Fe xvii line ratios by unblending the contributions of the Fe xii and xiii lines. The horizontal thin dotted line indicates the line intensity ratio averaged at the eight epochs in discharge 107,802. Error bars show photon noise ranges only. We take this contribution of the Fe xiii emissions to the emission line intensity at 204.6 Å into account and plot the Fe xvii λ 204.6/ λ 254.8 ratios against time after the start of discharge in Figure 5 (b). No lines are assumed to be blended in the Fe xvii λ 254.8 line, and a common electron density is assumed for the Fe xii/xiii emitting plasmas. The measured ratio is reduced to 20%–30% as a result of subtracting the Fe xiii line contribution, and the average value (∼1.12) is very close to the theoretically predicted constant vlaue of ∼1.1, although the temporal variation, henceforth, the temperature dependence of the line ratios, could not be completely eliminated in this analysis. The average value at the four epochs ( t = 4.8–5.4 s) is rather close to ∼1.3, when the line complexes at 204.6 Å are the strongest and the electron temperatures are the lowest during the discharge. 4. Discussion and Summary The Fe xvii line intensity ratios obtained from the solar active region in Section 2.3 and the LHD experiment are plotted against electron temperature in Figure 6 , in which the revised sensitivity proposed by Del Zanna ( 2013 ) is adopted for the EIS radiometric calibration. The LHD experimental results clearly show that the Fe xvii line branching ratio of λ 204.6/ λ 254.8 is close to the theoretical value of ∼1.1, which means that the revised in-orbit EIS sensitivity calibration (Del Zanna 2013 ; Warren et al. 2014 ) makes the solar data consistent with the laboratory data. The apparent

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


with the yellow shades. The light-gray shades represent the 3 σ noise levels. The dark-gray shades present the wavelength range of bright sky lines and bad pixels. Left: HETDEX Fiber positions atop the broadband images taken with CFHT/MegaCam or HST/WFC3. The red, blue, green, and yellow circles present the positions and the sky coverage of the fibers used for the measurements of the LAE spectra. Figure 17. Same as Figure 11 , but for the H i radial profile around LAE1–4 in the the extreme QSO overdensity EGS–QO1 (red circles). The blue and black circles are the H i radial profiles of LAEs in the blank fields: the blue circles are the remaining 22 EGS LAEs that reside outside of the EGS–QO1 (i.e., EGS outside), and the black circles are the COSMOS LAEs. A significant H i transmission underdensity is identified around LAE1–4, which is similar to the one around the QSOs in EGS–QO1 (Figure 15 ). We find that one of the four LAEs, LAE4, shows triple-continuum components over the scale of a 10 pkpc radius circle on the HST F814W/F160W images of the EGS, indicative of a triple merging system (middle/bottom panels of Figure 18 ). LAE4 is located at (R.A., decl.) = (14:19:13.02, +52:49:11.2) near the center of the ionized bubble of EGS–QO1 (bottom panel of Figure 13 ). The average Ly α redshift of LAE4 over the HETDEX fibers is , and the total Ly α luminosity over the fibers is erg s −1 . The top panel of Figure 18 presents the spectrum of LAE4, summed over the fibers, which is the same as the one in Figure 16 . The spectrum of LAE4 has a broad Ly α emission line whose FWHM is ∼1100 km s −1 (about 3 times broader than the instrumental resolution), possibly suggesting a type I AGN (e.g., Kakuma et al. in preparation). 24 24 Other AGN features of high-ionization emission lines, C iv and He ii , are not detected in the LAE4 spectrum shown in Figure 16 . This is probably because the LAE4 is optically faint (∼25 mag) and its metal lines are too faint to be identified. The bottom panel of Figure 18 presents the positions and the sky coverage of the fibers used for the measurements of the LAE4 Ly α redshift and total luminosity and indicates that three fibers cover the triple-continuum components with the blue, green, and yellow circles. The spectra of these three fibers are shown on the right-hand side in Figure 18 . All of the three fiber spectra of the blue, green, and yellow circles have Ly α emission lines at , suggesting that the three objects probably reside at the same redshift. Moreover, these three fiber spectra have broad Ly α emission lines with an FWHM of ∼1000 km s −1 . Although each of these fibers does not separately cover one of the triple-continuum components, whose blending due to the HET image quality and large fiber diameter may produce apparent broad lines, these broad Ly α emission lines found in the different positions over the triple-continuum components imply that the LAE4 system could be a merging type I AGN doublet or

O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O B-Telescope O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O B-CelestialObject O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O B-Wavelength O O O O O B-CelestialObject O O O O O O O O O B-Survey B-Wavelength O O O O O O O O O B-CelestialObject O O O O O O O O O O B-CelestialObject O O O O O O O O O O B-Wavelength B-CelestialObject O O O O O O O O O O O O O O B-Telescope B-Wavelength O O O O O O O O O O O O O O O O B-CelestialObject O O O B-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion O O O O O O O O B-CelestialObject O O O O O O O O B-Wavelength I-Wavelength O O B-CelestialObject O O B-Instrument O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O B-CelestialObject O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O B-CelestialObject O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O


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


Figure 8. Galaxy stellar mass function at z = 0 for simulations with different black hole feedback parameters, including (i) no feedback (grey), (ii) v out = 10 3 km s −1 and (blue; fiducial simulation), (iii) v out = 10 4 km s −1 and (green), and (iv) v out = 10 3 km s −1 and (red). Error bars show cosmic variance estimates computed as the standard deviation over the eight sub-octants of the simulated volume. Black points connected by a dashed line show the observed stellar mass function from Baldry et al. ( 2012 ). Quasar mode feedback alone is not sufficient to reproduce the observed galaxy mass function, either at low or high masses. 4.4 Mass dependence of black hole feedback effects Fig. 9 shows in more detail how the effects of black hole feedback depend on galaxy stellar mass. We cross-match galaxies between simulations based on the unique ID of the particles they contain at z = 0. Each galaxy is matched to the galaxy that contains the largest number of common star particles, which we use to compute the stellar mass of galaxies in simulations with black hole feedback relative to the no-feedback simulation. Figure 9. Mass-dependent effects of galaxy-scale black hole feedback. Left: ratio of the stellar mass of galaxies at z = 0 in simulations including black hole feedback to the stellar mass of the corresponding galaxies in the no-feedback simulation as a function of stellar mass. Different colours indicate simulations with different outflow velocity and momentum flux. Solid lines and shaded regions indicate median and 10 per cent–90 per cent percentile ranges. Right: same as left for black hole masses. Black hole feedback appears to be more effective in galaxies with mass M ⋆ ∼ 10 10 M ⊙ for outflows with velocity v out = 10 3 km s −1 , while the mass suppression efficiency increases to higher mass galaxies for simulations with v out = 10 4 km s −1 . The overall effect of feedback on the growth of black holes and galaxies is qualitatively similar. Black hole feedback in our simulations with v out = 10 3 km s −1 is more effective at suppressing star formation and black hole growth in galaxies in the mass range M ⋆ ≈ 10 9 –10 11 M ⊙ at z = 0. This trend with M ⋆ , already present at z = 2, suggests that black holes in lower mass galaxies have not coupled enough energy to affect their host galaxies from the time of seeding down to z = 0 (which may be sensitive to our seed model), while outflows with v out = 10 3 km s −1 may not be sufficient to unbind gas in galaxies at the highest masses. With the same momentum flux and v out = 10 4 km s −1 , the results are similar at low M * but the mass suppression efficiency keeps increasing towards high masses, giving a ∼60 per cent reduction of the stellar mass of galaxies with M ⋆ ≳ 10 11.5 M ⊙ by z = 0. As expected, our simulation with v out = 10 3 km s −1 and yields the strongest suppression of stellar growth at all masses, but the efficiency follows a trend with M ⋆ similar to that of the

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


rays, and calibrate the absolute flux to reduce the raw SAMI observations (Allen et al. 2015 ). Each galaxy field was observed in a set of approximately seven 30 minute exposures that are aligned together by fitting the galaxy position within each hexabundle with a two-dimensional Gaussian and fitting a simple empirical model describing the telescope offset and atmospheric refraction to the centroids. The exposures are then combined to produce a spectral cube with regular 05 spaxels, with a median seeing of 21. More details for Data Release 1 and Data Release 2 reduction can be found in Green et al. ( 2018 ) and Scott et al. ( 2018 ), respectively. 2.2. Sample Selection The GAMA group sample includes all galaxy associations with two or more members, so to ensure the robustness of our group sample, we first select all SAMI observed galaxies that belong to GAMA halos with at least five members to ensure that they have a robustly estimated velocity dispersion (Robotham et al. 2011 ). Moreover, only galaxies classified as cluster members by Owers et al. ( 2017 ) are taken as cluster galaxies. This gives us an initial sample of 574 galaxies (out of a potential 2502 observed by GAMA) in 205 groups in the GAMA regions and 861 galaxies in eight clusters. Stellar population measurements are compromised for 100 galaxies because nearby galaxies or stars affect their observation (van de Sande et al. 2017 ). In addition, we also exclude three more galaxies whose g − i colors suggest contamination from other objects in the field of view and eight galaxies whose annuli do not reflect the shape of their isophotes and/or the central bin is not well aligned with the peak of their flux map (since they could lead to a biased gradient). In this paper, we are particularly interested in whether the evolution of central and satellite galaxies has an environmental dependence. We focus on the passive central galaxies to ensure a like-to-like comparison in determining how their central and satellite status affects their stellar population gradients. We use the SAMI spectroscopic classifications presented in Owers et al. ( 2019 ) to select a homogeneous sample. The galaxies are classified as star-forming, passive, or H δ -strong using the absorption and emission line properties of each SAMI spectrum. We select 843 passive galaxies; of these, 98 are central and 745 are satellite galaxies (Figure 1 ). Figure 1. Distribution of g − i color with stellar mass as a function of galaxy classification for the galaxies included in SAMI v0.11. Unselected passive galaxies are shown as green crosses. Galaxies selected in the final sample are shown as red crosses, and nonpassive galaxies are shown as black crosses. The dotted line is the stellar mass cut at ; galaxies below this mass are excluded from the final sample. To ensure the stellar population measurements we use are reliable, we exclude all galaxies with masses less than , owing to the low signal-to-noise ratio (S/N) and

O O O O O O O O O O B-Survey O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Dataset I-Dataset I-Dataset O B-Dataset I-Dataset I-Dataset O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O B-Survey O O O O O O O O O O O O O O O O O O O O O O O O B-Survey O O O O O B-Survey O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O B-Survey O O O O O B-CelestialRegion I-CelestialRegion O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-Wavelength O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O B-Survey O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O B-Wavelength O O O O O O O O O O O O O O O B-Dataset I-Dataset O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


while the dark matter distribution in the interior of the halo hardly changes at low redshift (Prada et al. 2006 ; Diemand, Kuhlen Madau 2007 ; Cuesta et al. 2008 ). Recently More, Diemer Kravtsov ( 2015 ) proposed that the best physically based definition of halo radius is the ‘splashback radius’ R sp ≈ 2 R 200m , where there is typically a sharp drop in the density; using this definition, there is actually more halo mass increase than for R vir , R 200m , or R 200c . What is actually relevant to star formation of the central galaxy in the halo is the amount of gas that enters the halo and eventually reaches its central regions. Wetzel Nagai ( 2015 ) have used adaptive refinement tree (ART) hydrodynamic galaxy simulations with a best resolution of about 0.5 kpc to show that infalling gas decouples from dark matter starting at about 2 R 200m and roughly tracks the growth of M 200m . Thus, they argue that pseudo-evolution is relevant to the accretion of dark matter, but not to that of gas. Further evidence that the gas falling into the central regions of haloes roughly tracks the halo MAR is provided by Dekel et al. ( 2013 ), who used a suite of ART hydrodynamic zoom-in galaxy simulations with M vir /10 12 M ⊙ = 0.1 to 2 at z = 2 and best resolution of 35 pc, and found that the gas inflow rate is proportional to the halo MAR, with about half the gas penetrating to 0.1 R vir at redshifts from z = 4 to 2, and with the fraction increasing from z = 2 to 1. Analysis of a subsequent suite of ART hydrodynamic zoom-in galaxy simulations with better resolution and feedback showed that these simulated star-forming galaxies grow stellar mass at the same rate as the specific halo mass increase (Tacchella et al. 2015 ; Zolotov et al. 2015 ). A similar result has been reported in González-Samaniego et al. ( 2014 ) for galaxies formed in haloes of . Star-forming galaxies are known to show a tight dependence of SFR on stellar mass, which is known as the ‘main sequence’ of galaxy formation (Daddi et al. 2007 ; Elbaz et al. 2007 ; Noeske et al. 2007 ; Salim et al. 2007 ), in analogy with the tight dependence on stellar mass of the properties of stars on the stellar main sequence. Dark matter haloes also have an MAR that is roughly proportional to their mass, and we show in Section 2.1 of this paper that the dispersion of the halo MAR at a given halo mass is 0.3 to 0.4 dex, similar to the dispersion of the SFR on the main sequence. It was this equality that originally motivates us to examine more closely the connection between mass accretion and star formation. Our analysis is limited to the connection between distinct haloes and central galaxies only. One reason is that subhaloes lose mass via tidal stripping, resulting in negative values of accretion rates (see e.g. van den Bosch, Tormen Giocoli 2005 ). Satellite galaxies are also affected in other ways by their proximity to central galaxies. Therefore, studying the connection between subhalo mass accretion

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


in our model to reproduce the free–free continuum spectrum flattening near 2 mm and the surface brightness depression at the center in the continuum and mm-RRL maps. We estimate average electron temperatures of T e ~ 8000–11 000 K and densities in the range n e ≈ 10 7 –10 6 cm −3 in the ionized core of MWC 922. A density radial law n e ∝ r −2.7 , and a smooth variation with the latitude (decreasing from the disk outer boundary to the poles) is inferred. The density radial law could be slightly shallower than adopted, as suggested by the H39 α cubes, which show that the emission from this transition arises at slightly larger distances from the center than predicted by our model. We deduce a mass-loss rate of the fast bipolar wind of Ṁ fast ~ few × 10 −6 M ⊙ yr −1 . Assuming that a slow wind is also present at intermediate latitudes (i.e., bridging the ionized surface of the rotating disk and the fast bipolar wind), we obtain a mass-loss rate of Ṁ slow ~ few × 10 −7 M ⊙ yr −1 . The dynamical age of the winds traced by our observations is a few decades at most, with the innermost layers of the fast wind (at ~29–51 au) ejected just ~1.5–2.6 yr ago. The total ionized mass deduced from the free–free continuum emission at millimeter wavelengths is M H II ~ 2 × M ⊙ . The dominant mass component in the close environment of MWC 922 is probably that probed by the ~160 K dust millimeter continuum emission, from which we deduce ~ 8 M ⊙ . In Sect. 5 we discuss the evolutionary status of MWC 922 from different perspectives and provide a number of arguments that favor a post-main sequence stage. We believe that MWC 922 could be a ~15 M ⊙ blue giant (with T eff ~ 20–30 kK and L ⋆ ~ 5.9 × 10 4 L ⊙ ) located at d ~ 3 kpc that has recently left the main sequence (~10 Myr ago) and is probably undergoing a phase of mass exchange with an unseen companion. Appendix A Additional figures The Band 3and Band 6 continuum emission maps of MWC 922 obtained with 15 and 30 mas-resolution, respectively,are shown in Fig. A.1 . We note the X-shaped morphology, reminiscent of that of the near-IR andmid-IR nebulosities around MWC 922 (Sect. 1 ). The predictions from our model, which is described in Sect. 4 and is schematically represented in Fig. 6 , are shown in Fig. A.2 with the same angular resolution. The equatorial plane of the disk is oriented along PA ~ 45°. The velocity-channel maps of the H30 α and H39 α lines towards MWC 922 are presented in Figs. A.3 and A.4 , respectively. In Fig. A.5 a summary of the observational results for the weak non- α mm-RRLs detected in MWC 922 together with our model predictions is offered. In Figs. A.6 and A.7 we summarize the comparison between data and model for the H30 α and H39 α transitions with super-resolution (15 and 30 mas, respectively). For H30 α , we also display the predictions given by a model where rotation has been suppressed in the fast wind to show that when there is no rotation of the fast wind, the peaks of the red- and

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