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

O O O O O B-Formula I-Formula I-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 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 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 B-Formula I-Formula I-Formula O B-Model I-Model 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 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 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 O 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 B-Model I-Model I-Model O O O O O O O B-Model O O O O B-Model 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 B-Telescope O B-Telescope 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 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


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

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


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

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


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

B-Telescope I-Telescope B-Telescope O O O O O O O O O O O O O O O O B-Instrument I-Instrument I-Instrument B-Instrument B-Citation I-Citation I-Citation I-Citation O O O B-Telescope I-Telescope B-Telescope 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 B-Telescope O O O O O B-CelestialObject I-CelestialObject I-CelestialObject B-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula O O O B-Instrument O O B-Telescope I-Telescope I-Telescope I-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 B-Proposal I-Proposal I-Proposal O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength B-Wavelength O B-Wavelength I-Wavelength O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O B-Wavelength I-Wavelength O B-Formula I-Formula I-Formula I-Formula O O B-Wavelength 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-Software I-Software B-Citation I-Citation I-Citation I-Citation O O O B-Software I-Software I-Software I-Software O O O B-CelestialObject O B-CelestialObject O O O B-Wavelength O O O O O O O O B-Proposal I-Proposal I-Proposal O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength B-Wavelength O B-Wavelength 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 B-Observatory O O O O O O O O O O B-Telescope O O O O B-Instrument I-Instrument O O B-Telescope I-Telescope O O O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject O B-CelestialObject I-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O B-Proposal I-Proposal B-Instrument O O O O O O O O


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

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


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

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Citation I-Citation I-Citation I-Citation I-Citation 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 B-CelestialObject I-CelestialObject O B-Observatory O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Tag O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Observatory O O O O B-Model I-Model O B-Tag B-Tag B-Tag O B-Tag O O O O O O O O O O O O O O O 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


J03473-019 and J22518+317 ( Fig. 3 ) can be compared to, for example, those of fully convective J19169+051S ( Fig. 4 ) and J19511+464 ( Fig. 3 ). The only noticable feature is that fully convective stars tend to have stronger average magnetic fields represented by magnetic components of stronger strength. For instance, in the hottest partly convective star J05365+113( Fig. 3 ) we derive a very weak magnetic field with only two magnetic components (0 and 2 kG, respectively). Fig. 3 Distribution of filling factors as derived from Ti lines. The stars are sorted according to the S/N of their spectra (S/N decreases from left to the right and top to bottom). Fig. 3 continued. In our sample, we find several objects with remarkably very similar properties of their magnetic fields. For the two stars with largest υ sin i values, J01352-072 ( Fig. 3 ) and J04472+206 ( Fig. 3 ), we recover the same average magnetic fields with identical filling factors. The only difference between these stars is that J04472+206 is one spectral type cooler. Next, we find a twin of J07446+035 (very well studied M dwarf YZ CMi, Fig. 4 ), which is J23548+385 (not studiedat all, Fig. 3 ). Both stars have very similar filling factors, average magnetic field, projected rotational velocities, but slightly different spectral types. In addition, another famous M dwarf J22468+443 (EV Lac) has filling factors similar to J07446+035 and J23548+385, although its average magnetic field is noticeably weaker. We next looked for a connection between our filling factors and the geometry of large scale magnetic fields. In our sample, we have nine stars for which the geometry of their surface magnetic fields was previously derived from polarimetric measurements. In particular, Morin et al. (2010) showed that partly convective M dwarfs tend to have complex multipole fields with strong toroidal contribution, while stars that are fully convective generate dipole-dominant predominantly poloidal magnetic fields. Following this classification, in Fig. 4 we grouped M dwarfs in columns depending on whether the star has dipole-dominant magnetic field (left column) or more complex multipole-dominant field (right column). One can see that there is no obvious difference in filling factors between these two groups. A smooth distribution is found for dipole-dominant J01033+623 on one side, and multipole-dominant J08298+267 and J19169+051S on the other side. Likewise, J07446+035 and J22468+443 have almost identical filling factors but their magnetic field geometries were found to be very different. Nevertheless, there seems to be one common feature that is intrinsic to complex multipole fields as observed from filling factors, which is the appearance of strong zero-field components. This zero-field component is strongest in four out of five stars with multipole-donimant fields with an exception of J22468+443. 4.4 Magnetic field and rotation The detection of very strong magnetic fields in M dwarfs needs to be

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


is injected (brown) is different from the false positive when no planet is injected (in red, completely to the black curves on the left-hand side panels) for supergranulation (especially SGlow) alone, but it is similar when granulation and supergranulation are superposed. For GRA, ALL GRAhigh,SGmed , and ALL GRAhigh,SGlow , the red and brown curves are similar, that is, the percentage of false positives is the same whether a planet (of 1 M Earth ) is injected or not. However, the situation is different for SGmed and SGlow because when no planet is injected, the percentage of false positives is the same, even though they have very different rms RV. This is due to the fact that here the comparison of the power is made with the FAP. Because the shape of the power spectrum is the same between SGmed and SGlow, and because the FAP values are scaled with the rms, both power and FAP increases from SGlow to SGmed in a similar manner and the percentage of false positives is similar. In the case of ALL GRAhigh,SGlow , the signal is dominated by GRAhigh, hence, a level that is similar between GRAhigh and ALL GRAhigh,SGlow , while the situation is intermediate for ALL GRAhigh,SGmed . For GRAlow, the rate of false positives is very small in all cases. However, when added to supergranulation (either SGmed or SGlow), the latter dominates, and rates are very similar to those obtained when combining with GRAhigh, only slightly lower. The level of false positives here may be large because our analysis is too simplistic. When a peak is detected above the FAP, we should test the robustness of the detection to determine whether the peak is stable or not for example. More sophisticated methods will have to applied in this area in the future (see Sect. 6 ). Another representation of these results is shown in Fig. 18 , showing the percentage of false positives (sum of the two contributions described above) versus the detection rate (computed on the cases with an injected planet), which is similar to a ROC curve (but where each point corresponds to a spectral type). Each curve corresponds to one of the OGS configurations. Ideally, we would like points to be in the lower right corner. Points at the top have a high false positive level and points on the left correspond to poor detection rates. If we compare the global level of false positive here and the rms for each type of OGS configuration, we see that there is not a direct correspondence, because a granulation-like signal provides better performance due to their more suitable power spectrum (for a given rms). High-mass stars are to the left of each curve and lead to high rates of false positives and low detection rates except for granulation alone (for GRA low all points are in the lower right corner), and to a lesser extent ALL GRAhigh,SGlow . We also note that the highest level of false positives is obtained for SG alone. However, when granulation is added to supergranulation, the rms increases, but the level

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


We calculated a simple reduced-chi-square statistic for each DM model, finding for the YMW16 model and ∼10.2 for the NE2001 model. (The χ 2 statistic accounted only for uncertainties in the parallax distances, not in the electron-density models.) The similarity in these χ 2 values suggests the two models are comparable in their ability to predict distances to pulsars based on DM values, at least in the distance regime probed by millisecond pulsar timing parallax measurements (within ∼2.5 kpc of the Sun). Figure 4. Distances from timing parallax measurements (67% confidence) vs. distances from DM models for pulsars with significant timing parallax detections. The blue points show the NE2001 DM model distances, while the red points show the YMW16 model distances. The black dashed line shows a one-to-one relation. 4.2. Parallax Upper Limits The remaining 25 pulsars had timing parallax measurements with significances of less than 3 σ . Of these, 22 had positive parallaxes and only 3 had negative parallaxes in the formal timing fits. This is strong evidence that most of the non-detections have a true low-level parallax signal; otherwise, there would be comparable numbers of negative and positive parallax measurements. None of the negative parallaxes had large significance. We used 95%-confidence upper limits on parallax to compute 95%-confidence lower limits on distance for these pulsars. The details of this calculation are outlined in M16 . We have not attempted to correct for Lutz–Kelker bias (Verbiest et al. 2010 ), as we do not believe we have enough prior information on the spatial and luminosity distribution of the millisecond pulsar population to accurately correct for this bias (see M16 ). For the lower limits on distance, our 95% limit remains a conservative approach, in the sense that compensation for Lutz–Kelker bias would only push these limits higher. Among the pulsars with parallax upper limits, a few have significant discrepancies with previous measurements (PSRs J0636+5128, J1455−3330, J1640+1224, B1937+21). As with the pulsars discussed in Section 4.1 , the source of these discrepancies are not clear, but may result from differences in DM variation models or red-noise models. 4.3. Distance Constraints from Rotation and Orbital Period Derivatives Observed pulsar rotation period derivatives are a combination of intrinsic pulsar spin-down and kinematic terms due to the acceleration and transverse motion of the pulsar relative to the Sun (Shklovskii 1970 ; Nice Taylor 1995 ). By assuming that the pulsar is losing rotational energy, so that it has a positive rotation period derivative, an upper limit can be placed on the pulsar distance. See M16 Section 4.3 for details. Table 5 lists such “ distance” constraints, which we calculated following the procedures of M16 . In the table, we omitted distance limits greater than 10 kpc as physically uninteresting, and we did not calculate a constraint for PSR J1024−0719, as its observed rotation

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


timing solution in NGC 6624 (pulsars D, E, F, and H), as well as to validate the timing position derived for the new eccentric binary MSP (pulsar G). With the observing setup used for the two TRAPUM observations of this cluster (obs. ids 10L-trapum and 12L-trapum) reported in Section 2 , the individual beams making up the tiling have elliptic shapes with semi-axes in the range of ∼8–11 arcsec at half power, with the exact values depending on the elevation and other factors. We assume these values as the maximum uncertainty for the positions that we derive for these pulsars. The results are summarized in Table 5 , where we list the beams in which each pulsar was detected with highest S/N, and their boresight coordinates. The same is shown graphically in Fig. 9 , where the beams with localized pulsars are higlighted in grey. As can be seen, pulsars D and H are found to be the closest to the cluster centre. The eclipsing redback F and the isolated pulsar E are found at the much larger distances of ∼0.42 and ∼0.79 arcmin from the cluster centre, respectively, putting the former near the edge of, and the latter well outside, the half-power of the tied-array beam of the MeerTime observations (which used only the 1-km core antennas) of NGC 6624. This explains why NGC 6624F and E are detected with significantly lower S/N than expected in the MeerTime data as compared to the TRAPUM data, even after accounting for the different number of antennas used. Finally, the eccentric binary pulsar NGC 6624G showed up with highest S/N in beam #002. This had boresight coordinates of α = 18 h 23 m 41150 and δ = −30°21 ′ 3850. This is just ∼6.2 arcsec away from, and therefore consistent with, the corresponding timing-derived position of G. Figure 9. Tiling of the first TRAPUM observation (obs. id 10L-trapum) of NGC 6624. 60 dishes were used to synthesize 288 beams, with an overlap fraction of 80 per cent, around the nominal centre position of the cluster. The light-grey ellipses show the contours of the TRAPUM beams at their 84 per cent level of the power of their boresights, at 1284 MHz. We highlight in solid grey those beams where some of the pulsars show up with the highest S/N: the name of such pulsars are shown next to the beam number. The red ellipses show, for comparison, the L -band beam (at half power for top, centre, and bottom of the band) of one of the MeerTime observations of NGC 6624, which used only 42 antennas of the 1-km core of the array. Table 5. List of the NGC 6624 pulsars without a known position and corresponding beams where they were detected with highest S/N in the first TRAPUM observation of the cluster (id 10L-trapum). θ ⊥ is the angular distance between the beam boresight and the nominal cluster centre. 4.2.3 L-band detection of the transitional pulsar M28I M28I (also known as PSR J1824−2452I) is a redback system in M28 beloging to the rare class of transitional MSPs (see Jaodand, Hessels Archibald 2018 ; Papitto de Martino 2020 for

O O O B-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject B-CelestialObject B-CelestialObject O B-CelestialObject O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O B-Survey O O O O B-Identifier I-Identifier I-Identifier O B-Identifier O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O B-CelestialObject O O O O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject 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 B-Survey O O O O O O O O O B-CelestialObject I-CelestialObject O O O B-CelestialObject I-CelestialObject O B-CelestialObject 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-CelestialObject I-CelestialObject O O O O O O O O O O O O O B-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-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 B-Survey 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 B-Survey O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O B-Survey O O B-CelestialObject I-CelestialObject 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 B-Survey O O O O B-Identifier I-Identifier 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-CelestialObject O O O B-CelestialObject I-CelestialObject O O O O O B-CelestialObject 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


law may be more appropriate in these cases. Figure 9. A two parameter estimate of accreted mass fractions . The distribution of stellar mass fractions and 2D power-law slopes for the mass-matched sample of TNG100 galaxies, colour coded by the fraction of stellar mass beyond 2 half-mass radii. The full TNG100 parent sample is shown in grey points. Smaller symbols indicate galaxies for which a single power law was not an acceptable assumption, included here only for completeness (approximately ∼37 per cent of the samples require a more complex fit; see Section 6.2 for details). In general, shallower slopes correspond to higher accreted fractions, albeit with significant scatter. At fixed power-law slope, galaxies with higher stellar mass fractions in the outskirts have higher total accreted fractions. Figs 8 and 9 also raise the question of why these observations seem to be ‘missing’ stellar mass beyond 20 kpc (or, phrased differently, why TNG100 galaxies appear to be more massive and extended than DNGS galaxies at fixed stellar mass). No galaxy in DNGS has a stellar halo mass fraction above 10 per cent (when measured outside of 20 kpc), whereas the TNG100 galaxies in Fig. 9 can have up to 40 per cent of their stellar mass beyond this radius. One possible explanation is that DNGS galaxies may have low total accreted mass fractions relative to their mass-matched counterparts in TNG100. It is worth pausing to point out, however, that our capacity to ask (and answer) this question depends heavily on the validity of three assumptions: The parameters we chose to observationally estimate the accreted mass fraction (stellar halo mass fractions and power-law slopes) are able to provide an appropriate description of the outer profiles of galaxies – and, further, that these profiles contain sufficient information to characterize the assembly histories of galaxies. TNG100 reproduces observed properties of galaxies accurately enough that we should expect agreement in stellar halo properties. DNGS represents an unbiased sample of Milky Way-mass spiral galaxies. We will delve more deeply into these assumptions in Section 8 . First, however, we will proceed in Section 7 as though each of these are true, and attempt to carve out a more complete physical understanding of galaxies with low accreted mass fractions. 7 INSIGHTS FROM STELLAR PARTICLES We have seen from Figs 6 – 9 that DNGS galaxies appear to have low accretion fractions relative to their mass-matched TNG100 galaxies. The next logical question, then, is: ‘What are the assembly histories of (TNG100) galaxies with low accretion fractions?’ If, for example, this subset of galaxies shares any additional aspects of their assembly histories, we can potentially gain physical insight into our observations. In this section, we explore several different properties of our mass-matched TNG100 galaxies, combining information from the density profiles and individual stellar particles to characterize their past

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Survey 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 B-Model O O O O O O O O O O O O O O O O O O O O O O O B-Survey 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 B-Model O O O O O O O O O O O O O O O O B-Survey 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 B-Survey O O O O O O O O O O O B-Model O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O


location of the continent, especially for the fast-rotating case; for P = 5 days, this transport can increase from 7 gigatons per second (Gt s −1 ) in an aquaplanet to 14 Gt s −1 when the continent is located to both the northeast and northwest of the substellar point (not shown). This transport brings along with it the ozone and water vapor; it is unclear how the change of this transport will affect the ozone of the dayside. Therefore, AOGCMs are required to fully understand the ozone distribution on these exoplanets when a continent is present. 5. Conclusion We investigate the climate impact of a relatively small terrestrial continent on a synchronously rotating exoplanet by using an AOGCM. It is found that the climate is highly sensitive to the location of the continent, mainly because of the existence of a strong equatorial westerly jet in the ocean on such exoplanets. This jet is responsible for ∼90% of the heat transport from dayside to nightside, and the strength of this jet largely determines the global climate. When a continent blocks the equatorial westerly at the equator, the climate cools. The strongest cooling effect is obtained when it lies slightly to the west of the substellar point. On the other hand, the westerly jet strengthens and the climate warms when a continent obstructs the poleward branch of the oceanic gyre circulation. Enhanced oceanic heat transport to the nightside reduces the sea ice coverage there, and thereby reduces the sea-ice input from nightside to dayside. This reduces the planetary albedo and raises the GMST. The GMST can vary by more than 20° C simply by varying the location of a small continent. The outer edge of the HZ around an M-dwarf defined by stellar constant can change by 15% when a small continent is located at different places. Because the atmospheric circulation, atmospheric water vapor, and ocean upwelling all change with the location of the continent, the atmospheric chemistry and biosignatures may also change. Although major topographic features tend to align with the star-planet axis for synchronously rotating exoplanets (Wieczorek 2007 ; Turbet et al. 2016 ; Salazar et al. 2020 ), small continents or island arc chains may exist everywhere. Our results demonstrate that these small features can still change the global climate of a synchronously rotating exoplanet by as much as that of a round continent. We also demonstrate that it is possible to engineer the climate on such exoplanets by building a dam at appropriate locations. Appendix Model and Experimental Design A.1. Climate Model The simulations presented in this work were done with the fully coupled AOGCM CCSM3 (Collins et al. 2006 ). The model is the same as that used by Yang et al. ( 2019 ). The atmosphere and land share the same Gaussian grid, and the ocean and sea ice share the same grid. The resolution of the CCSM3 model is set to “T31_gx3v5.” In this setting, the horizontal grid spacing is approximately 3.75° by 3.75° for the

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


described via perturbations. Although isotropy has been directly tested (Blake Wall 2002 ; Bernui, Oliveira Pereira 2014 ; Bengaly 2016 ; Schwarz et al. 2016 ; Tiwari Nusser 2016 ; Bengaly et al. 2017 ; Bernal, Cardenas Motta 2017 ; Javanmardi Kroupa 2017 ), homogeneity is much harder to probe by observations (see e.g. Clarkson Maartens 2010 ; Maartens 2011 ; Clarkson 2012 ). As is well known, the smaller the scale we observe, the clumpier the universe appears. However, non-uniformities, such as groups and clusters of galaxies, voids, walls, and filaments, are expected in a Friedmann–Lemaître–Robertson–Walker (FLRW) universe according to cosmological simulations. In such a background, a transition scale is also expected, above which the patterns composed by these structures become smoother, eventually becoming indistinguishable from a random distribution of sources. This homogeneity scale r h has been identified and estimated at 70–150 Mpc h −1 , using data from several galaxy and quasar surveys (Hogg et al. 2005 ; Scrimgeour et al. 2012 ; Nadathur 2013 ; Alonso et al. 2015 ; Pandey Sarkar 2015 ; Laurent et al. 2016 ; Sarkar Pandey 2016 ; Ntelis 2017 ), although other authors have claimed no evidence for it (Sylos Labini, Montuori Pietronero 1998 ; Sylos Labini 2011 ; Park et al. 2017 ). In the context of the ΛCDM paradigm, an upper limit for the homogeneity scale was estimated by Yadav, Bagla Khandai ( 2010 ) to be r h ∼ 260 Mpc h −1 . Tests of homogeneity of the matter distribution by counting sources in spheres or spherical caps are not direct tests of geometric homogeneity, i.e. of the Cosmological Principle. Source counts on spatial hypersurfaces inside the past lightcone cannot be accessed by this method, since the counts are restricted to the intersection of the past lightcone with the spatial hypersurfaces. Instead, source counts provide consistency tests: if the count data show that the matter distribution does not approach homogeneity on large scales, then this can falsify the Cosmological Principle. Alternatively, if observations confirm an approach to count homogeneity, then this strengthens the evidence for geometric homogeneity – but cannot prove it. A test of homogeneity of the galaxy distribution that does probe inside the past lightcone has been developed by Heavens, Jimenez Maartens ( 2011 ) and Hoyle et al. ( 2012 ) – but this test is unable to determine a homogeneity scale. When a length-scale r h is used to probe homogeneity, a further assumption is made – a fiducial FLRW model is assumed a priori, in order to convert redshifts and angles to distances. In order to circumvent this model dependence, one can use an angular homogeneity scale θ h (Alonso et al. 2014 ). It was shown by Alonso et al. ( 2015 ) that the θ h determined from the 2MASS photometric catalogue is consistent with ΛCDM-based mock samples within 90 per cent confidence level. In this letter , we make tomographic measurements of θ h in the Luminous Red

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


ejecta, we assume the nucleosynthesis pattern following the recent numerical results for the postmerger ejecta which show significantly low production of lanthanide elements and give the mass fraction of 1.64 × 10 −2 for Y (Fujibayashi et al. 2018 ). We first propose that the degree of Eu enhancement indicated by [Eu/Fe] for individual stars (−0.7 ≲ [Eu/Fe ≲ +2) could be basically determined by the different levels of Eu enrichment of gas via associated merger events (cNSNSs or cBHNSs) with widely varying masses ( M tid ) of tidally driven dynamical ejecta (10 −4 M ⊙ ≲ M tid ≲ 0.1 M ⊙ ). Considering the [Eu/Fe] distribution of halo stars, we identify two components: a Gaussian distribution in the range of −0.7 ≲ [Eu/Fe] ≲ +1.3 with a peak around [Eu/Fe] ≈ + 0.3 and an extending Eu-rich tail up to [Eu/Fe] ≈ + 2. Then, considering the predicted mass range of dynamical ejecta, cNSNS and cBHNS are likely to be responsible for producing the former and latter distributions, respectively. Approximate mass values of the mass of tidally driven dynamical ejecta are shown in the upper part of the figure, implying that the average value for cNSNSs should be a few times 10 −3 M ⊙ . If cBHNS should produce more Eu than cNSNS due to larger tidal mass ejection, the Y/Eu plateau could be connected to such events. Considering very low production of light r -process elements in the tidally dominated dynamical ejecta of cBHNSs, owing to a low Y e (≲0.1) (Roberts et al. 2017 ), we argue that Y in r-II stars originates from the postmerger ejecta. The Y/Eu plateau implies that the production ratio of Y to Eu is quite similar in individual cBHNS events. As each element owes its origin to nontidal postmerger ejecta and tidally driven dynamical ejecta, respectively, the masses of the two type of ejecta are suggested to scale linearly with each other. This linearity may also hold even if the postmerger ejecta of cBHNSs produce Eu due to a smaller Y e resulting from lower neutrino irradiation (Fernández et al. 2017 ), though there are complexities in the influence of the neutrino treatment (e.g., Caballero et al. 2012 ; Wu et al. 2017 ). The required condition of a similar mass ratio of light r -process elements to Eu among the postmerger ejecta of cBHNSs needs to be investigated (see also Kyutoku et al. 2015 ). On the other hand, the trend of an increasing [Y/Eu] with decreasing [Eu/Fe] at the low [Eu/Fe] regime is likely to reflect the diversity of nucleosynthesis in cNSNSs with various mass asymmetry in our scheme. The tidal interaction tends to be efficient for asymmetric binaries, and M tid becomes large. At the same time, shock interactions are not very efficient for dynamical mass ejection in asymmetric binaries. Thus, the average values of Y e become lower for more asymmetric binaries (e.g., Sekiguchi et al. 2016 ). These combined effects could explain the observed Y/Eu trend. According to this view, cNSNSs with massive (≳0.01 M ⊙ ) tidally driven dynamical

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


orders, which yields a sufficient number of data points for our analysis and still benefits from a low-dimensional covariance. The fact that we do not find a decrease of parameter uncertainty with increasing number of orders shows that the first few orders indeed contain all the relevant information (see Fig. 7 for more details). The measured data points for both angular intervals are presented in Fig. 8 . Unlike correlation function measurements, these Υ data points cannot be interpreted easily. However, it is clear that in the large-scale interval the model (see Section 2 ) is a very good fit to the data regardless of the cosmological parameters used. 4 This is not the case for the smaller scale interval, where one of the clustering data points is several σ away from the best-fitting model. Clearly, the assumption of linear bias on these non-linear scales is not valid for the clustering data. This is partly due to the small uncertainties in these measurements as well as the fact that we neglect the model uncertainties. As can be seen in Fig. 9 , a change of b of about 5 per cent within this interval would already be enough to reconcile the data with the model. If model uncertainties had been included in this figure, it is likely that data and model would be in line again. Another possible explanation of the discrepancy between data and model in this case could be that the fiducial cosmology is wrong. Furthermore, we also investigate if an indication for a scale-dependent bias can be found in the γ t (θ) data in Fig. 10 and find no such preference. Figure 7. Left: the measured parameter values as a function of maximum Υ-order n for b and r . No significant difference in the values is visible, from which we conclude that the data compression is indeed working and only a few orders contain all the information from the measured signals. Right: the parameter uncertainty in per cent for b and r , again as a function of n . Here, we do not find a significant difference, which again shows that the data compression of Υ( n ) is robust. Figure 8. The top panels show the measured Υ gm and Υ gg and the best fit using one of the two cosmologies. The magenta and dark blue lines are the connections between the predicted data points using the Planck or the CFHTLenS cosmology. In the bottom panels, we show the residuals (Υ obs − Υ model )/ΔΥ obs , where ΔΥ obs is the uncertainty in the measured Υ. Left: measurements for the 3-20 arcmin interval. Clearly, on these scales the model we adopt to describe the galaxy bias is not a good description of the data shown here, especially the clustering data. For more details, see Section 3.4 Right: measurements for the 20-70 arcmin interval. Figure 9. Top: the angular correlation function within the small-scale interval, the corresponding model for b = 1, and the best-fitting model. This best-fitting model has been determined from a joint fit of Υ gm and Υ gg . Bottom: the square root of the ratio between the

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


of signal-to-noise ratio (S/N), and found it to be well described by a power-law function, . is about 0.01 mas in the innermost jet region where , and 0.1 mas downstream of the jet where , corresponding to 1/50 and 1/5 of the beam size, respectively. Therefore, we consider the upper limit of the imaging error to be because the jet radii are measured where the jet is detected when (see also Homan et al. 2002 , Appendix A for similar analysis). Note that we assume the time variability of the jet radius is negligible. 3.3. Radius Profile of the Jet Figure 2 shows the distribution of jet radius ( r ) as a function of the deprojected distance to the core ( z ), which we refer to as the radius profile of the jet. The jet viewing angle ( θ ) for deprojection is uncertain within an upper limit of 47° (Jones Wehrle 2002 ). We adopt θ = 19° derived from a detection of a sub-parsec scale counter-jet (Sudou et al. 2000 ). An independent model of the spectral energy distribution (SED) suggests a consistent result of θ ≃ 18° (Chiaberge et al. 2003 ). We use the deprojected length scale ( mas −1 ) along the jet throughout the rest of the paper. Note that the jet radius, as defined perpendicular to the jet axis, is not affected by projection effects. Figure 2. Top panel: the radius profile of the NGC 6251 jet in units of Schwarzschild radius ( r s ) and parsecs, using archival VLBA data at 15 and 5 GHz (green and blue triangles), and our EVN(-i, ii, iii) data at 1.6 GHz with three weighting schemes (violet square, cross, and circle). The single (orange solid line) and double (brown solid line) power-law models are fitted to the profile, where we show the case of the sharpness parameter n = 100 here. Statistics ( f -test) shows that the data are better fitted by double power-law models (with all n ) than by a single power law (see also Section 3 ). Furthermore, the double power-law model is also supported by the VLA data (gray plus signs) and VLBI cores (gray triangles and squares), as discussed in Section 4.1 . Note that the VLA data and VLBI cores are not included in the regression analysis. Middle and bottom panels: the relative residuals of the jet radii for the single () and double () power-law models. The single power law shows a systematic deviation at the two ends of the distance scale, while the double power laws (i.e., for all n ) show uniformly distributed relative residuals on all distance scales. We conclude that the jet structure is described by a parabolic shape upstream () and a conical shape downstream () with a transition located at a characteristic distance z 0 = (1–2) × 10 5 r s (brown dashed line), which is fairly close to the sphere of gravitational influence (SGI) of the SMBH (, black dashed line) in order of magnitude. 3.4. Collimation Profile by Power-law Models Collimation profiles are generally described by power-law functions with some local features, as a manifestation of the global evolution of jet structure. We perform

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


Einstein radius, and σ SIS is the velocity dispersion of the star in the periphery of the lens galaxy due to the lens mass distribution in the SIS model. In general, σ SIS does not equal the observed stellar velocity dispersion σ 0 (White Davis 1996 ). To express the difference, researchers use a phenomenological free parameter f e defined by the relation σ SIS = f e σ 0 (Kochanek 1992 ; Ofek et al. 2003 ; Cao et al. 2012 ), where (0.8) 1/2 f e (1.2) 1/2 . In this case, the systematic error is caused by σ 0 as σ SIS , the deviation of the SIS model, the effects of secondary lenses (nearby galaxies), the line-of-sight contamination (Ofek et al. 2003 ), etc. The uncertainty of Equation ( 5 ) can be written by (Liao et al. 2016 )In Equation ( 6 ), and are the fractional uncertainties of σ sis and θ E , respectively. To test the CDDR, the left term of Equation (ref5), R A ( z l , z s ), should be expressed as the ratio of luminosity distance, . We transform R A ( z l , z s ) into the ratio of comoving distance ( D C ) or dimensionless distance H 0 D C / c . In a flat space, the dimensionless distance satisfiesBy using the equation, R A ( z l , z s ) can be written as In a nonflat space, the expression of R A ( z l , z s ) is more complicated; one can refer to Räsänen et al. ( 2015 ). Fortunately, most cosmological tests today support a flat cosmic space (Planck Collaboration et al. 2016 ). In this work, we test the CDD relation in a case where we assume that spacetime is flat. To test the CDDR, Equation ( 1 ) is rewritten by the parameterization of the deviation:Combining Equations ( 9 ) and ( 10 ), R A ( z l , z s ) can be written asBy using Equation ( 4 ), of Equation ( 11 ) can be rewritten aswhere the absolute magnitude of the SNe Ia subsample is offset, z l is the redshift of the lens, and z s is the redshift of the sources. 3. Method and Results In this section, we introduce a distance-deviation consistency method of data selection and show the result. 3.1. Method of Data Selection: A Distance-deviation Consistency Method To test the CDDR, D L and D A at the same redshift z need to be provided simultaneously. However, redshifts of subsamples from the SGLS and the SNe Ia are different. To take full advantage of the data, one needs to pair the subsamples efficiently. In this section, we provide a distance-deviation consistency method to pair subsamples, which outperforms the conventional method. The redshift-difference of subsample pairs in this work is not fixed, and it decreases with the redshifts to ensure the distance deviation of the sources stays the same. The relation between Δ z and coordinate distance with a cosmology model readswhere R h = ct and flat ΛCDM model with Ω m = 0.31 (Planck Collaboration et al. 2016 ) are used. By setting Δ d c / d c equal to 5% and combining Equation ( 13 ), Δ z ( z ) can be calculated:where the distance formulas of the two cosmology model, ΛCDM and R h = ct are used. The R h = ct cosmological model was

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


are sub-Keplerian by ≈20%, in good agreement with other studies (e.g., Wade Horne 1988 ). Note that for q ≳ 0.25, the 3:1 resonance lies beyond ≈0.9 R L 1 and the outer disk radius is then limited by the largest non-intersecting orbits allowed by three-body interactions (Paczyński 1977 ). Under these circumstances the dependence of the outer disk radius on q is very weak (Frank et al. 2002 ) and therefore a nearly constant evolution of DP/FWHM versus q is expected for q ≳ 0.25. For practical purposes, in Figure 3 we display the variation of DP/FWHM versus q in logarithmic units. A least-squares linear fit yieldswith a Pearson correlation coefficient r = 0.95. To estimate the error in q implied by this relation, we computed the difference with respect to the true observed values for our 11 SXTs. The distribution of differences can be approximated by a normal function with σ ( q ) = 0.015. This indicates that mass ratios can be realistically obtained from Equation ( 6 ) with a typical ∼25% uncertainty. Figure 3. Correlation between q and the parameter DP/FWHM in log units and the best linear fit. 4. ORBITAL EFFECTS The spectra that we used to produce the DP/FWHM– q correlation are orbital averages. This is party because individual spectra rarely possess enough signal-to-noise for the technique to be applicable. But also because orbital means average out possible asymmetries in individual spectra from, for example, hot spots or disk eccentricities that could potentially bias the determination of q . At this point we decided to explore the impact of line asymmetries in the results of our technique. Since this can only be tested on data with sufficient signal-to-noise, we have focused on the 154 high-quality GTC spectra of XTE J1118+480 obtained along four different orbits over two years. We have performed Gaussian fits on every individual spectrum and computed mass ratios using Equation ( 6 ). The distribution of q values is found to peak at q = 0.024 (the bottom panel in Figure 4 ), with 68% of the values contained between q = 0.021 and 0.045. This indicates that if q were to be obtained from a single individual spectrum, the typical uncertainty would be about ∼56%. Figure 4. Bottom: histogram of q values derived through Equation ( 6 ) from 154 GTC spectra of XTE J1118+480. Top: variation q with the V / R parameter of the H α profile (see the text for details). In order to trace the effect of line asymmetries we also extracted the V / R parameter from each spectrum, with V / R defined as the ratio of equivalent widths between the blue and the red part of the H α profile. The two halves of the line are set from the rest wavelength till ±2500 km s −1 . For example, indicates a line with the red part stronger by 20% while implies a symmetric profile. A plot of q versus V / R (see top panel in Figure 4 ) seems to show a trend, with asymmetric profiles preferring slightly lower q values, although the large scatter prevents from drawing a firm

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


include in our list lines with intensity values that are above some fraction (typically 50%) of the maximum value. Of course, the choice of this threshold is arbitrary, but we find it works well for our needs, and can be easily modified as needed. In a companion paper (A. Gal-Yam, O. Yaron N. Knezevic 2019, in preparation), we describe in more detail our survey of other methods to compile line lists from the NIST databases and other tests and applications of this method. With the line lists in hand, we attempt to determine for each spectrum the expansion velocity by matching features to ions with numerous transitions (see. e.g., Figure 1 ). Once we have determined a convincing value for the expansion velocity, we inspect other ions using the fixed velocity (i.e., we assume explicitly that the photosphere is narrow). Figure 1. High S/N red spectra of the nearby SLSN-I PTF12dam (left; from Nicholl et al. 2013 ) and Gaia16apd (right; from Yan et al. 2017b ). Both spectra (black curves) have been binned and host narrow emission lines have been excised; the original spectra are shown in blue. Uncorrected Telluric features in the spectrum of PTF12dam are marked. The spectrum of PTF12dam shows pronounced lines of O i and C ii with distinct sharp absorption troughs, all at the same expansion velocity of V exp = 11,000 km s −1 ; O ii lines probably begin to shape the spectrum blueward of 5000 Å while C iii may also contribute. The same is true for Gaia16apd (right) though absorption lines are of lower contrast and have higher expansion velocity, V exp = 14,000 km s −1 . 2.1. Application to Peak Spectra of SLSNe-I We begin our examination of SLSN-I peak spectra by inspecting high signal-to-noise ratio (S/N) spectra of nearby events. In particular, we begin by focusing on the red side of the optical range ( λ > 5000 Å). This wavelength range has been relatively neglected in studies of SLSN-I spectra as it does not contain strong features, and is redshifted out of visible-light spectra of SLSNe at moderate or high redshifts, which are typical for SLSNe. Figure 1 (left) shows our analysis results for a high S/N spectrum of PTF12dam from Nicholl et al. ( 2013 ) obtained on 2012 May 24, 25 restframe days prior to peak according to the analysis of Vreeswijk et al. ( 2017 ). This and all other spectra discussed here are available from WISeREP (Yaron Gal-Yam 2012 ). 5 5 http://wiserep.weizmann.ac.il/ Multiple features consistent with O i and C ii lines all align using a single expansion velocity of V exp = 11,000 km s −1 ; these two ions explain most features in this wavelength range. C iii may explain two weak features, and may also contribute to the observed spectrum. O ii has a distinct line spectrum with a multitude of lines all with very similar intensities. While a few single lines seen around 6500 Å appear to be negligible compared to the stronger C ii lines, accumulations of multiple overlapping O ii lines begin to shape the spectrum bluewards of 5000

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O B-Database I-Database O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O B-Citation I-Citation I-Citation I-Citation O O B-CelestialObject O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O B-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 B-Wavelength I-Wavelength 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 B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength 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 B-CelestialObject O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-Database B-Citation I-Citation I-Citation O O O B-URL O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Wavelength


of star formation, with the younger and older parent stellar population dominating the brighter and fainter PNe respectively. Indeed Valenzuela et al. (2019) showed theoretically that the shape of the PNLF at the faint-end is quite sensitive to the distribution of masses of the PN central stars, which is a product of the SFH in any galaxy. In Bhattacharya et al. (2019b , hereafter Paper I), we observed a rise in the faint-end of the PNLF in the central 16 sq. deg. of M 31 conceivably linked to the SFH of M 31. Owing to the homogeneous spatial coverage and photometry of the current imaging survey, we detect PNe associated with all the stellar populations in a 54 sq. deg area centred on M31. Thanks to the sensitivity and accuracy, we can quantify the imprints of the variations of these stellar populations on the PNLFs in distinct regions. In Sect. 2 , we describe our PN survey of M 31 and set the geometrical boundaries around any regions with RGB overdensities where the PNLFs are measured. In Sect. 3 , we obtain the PNLFs, compute the parameters that best describe them, and carry out the quantitative comparisons via statistical methods. In Sect. 4 , we correlate the stellar population parameters with the properties of the PNLFs at both their bright and faint ends in the different subregions. In Sect. 5 , we discuss the implications of our results on the origin of the M31 inner halo substructures. We draw our conclusions in Sect. 6 . 2. Survey of Planetary Nebulae in M31 2.1. Survey characteristics In Paper I, we identified PNe candidates in a 16 sq. deg. uniform imaging survey of the disc and disc–halo interface of M 31 using the MegaCam wide-field imager ( Boulade et al. 2003 ) mounted on the 3.6-meter Canada-France-Hawaii Telescope (CFHT). M 31 was observed through a narrow-band [O III ] filter ( λ c = 5007 Å, Δ λ = 102 Å, on-band) and a broad-band g -filter ( λ c = 4750 Å, Δ λ = 1540 Å, off-band). An additional 38 sq. deg. were obtained in late-2019, providing uniform coverage of the inner halo of M 31 and its substructures reaching a uniform sensitivity down to fluxes equivalent to m 5007 = 26.2 mag over the entire area. Details of these observations are presented in Bhattacharya (2020) and Bhattacharya et al. (in prep.). The zero points for each of the [O III ] and g -band frames in AB magnitudes, normalised to a 1 s exposure, are Z [O III ] = 23.4 and Z g = 26.5. The photometry was calibrated using observations of spectrophotometric standard stars. The photometric uncertainty (err m , 5007 ) is well below 0.01 mag at m 5007 = 22.5 mag; it increases to err m , 5007 ∼ 0.15–0.2 mag at m 5007 = 26.2 mag. The PN identification in each of these pointings was also carried out as described in Paper I using the on-off band technique developed and validated in Arnaboldi et al. (2002 , 2003) , later optimised for large imaging surveys by Longobardi et al. (2013) . The PNe are identified as point-like sources with an excess [O III ] – g colour. The

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


accuracy and precision of the density and the potential depends on the choice of the parametrized density model used. Both the Gamma and the Einasto profiles produce nearly unbiased density-potential pairs when compared to observables, while the Einasto profiles are most sensitive to how the halo centers are defined. As noted in the Introduction, Serra et al. ( 2011 ) attribute the lower numerically integrated potential (Equation ( 3 )) compared to the NFW potential (Equation ( 4 b )) to mass outside the cluster that is not accounted for by the NFW profile shape. We show that the opposite is true. The NFW model density profile overpredicts the true density profile outside r 200 and thus overpredicts the true gravitational potential via the Poisson equation by 10%–15%. 3.3. Mass and Redshift Dependence Next, we examine how the edge varies as a function of halo mass and redshift. In this case, we use a new sub-set of the Millennium simulation with the 100 most massive halos halos smaller than 1 × 10 14 M . The minimum mass of this new subset is M , i.e., a factor of 10 smaller than the previous sample. We measure the spherically averaged density profiles and infer the escape edges via the potential from Equation ( 6 ). The edges are measured using the same algorithm as applied to the more massive subset studied previously. We find no statistical or systematic difference between the high mass and low mass halo data sets. The density profile predicts the escape edge via the Poisson equation to the same level of accuracy and precision for over two orders of magnitude in cluster halo mass. We study the low mass clusters at four different simulation snapshot outputs, corresponding to , and 0.75. We keep the 100 most massive halos in each snapshot as provided by the “millimil” subset of the Millennium data. At , the deceleration parameter goes from negative to positive. As the cluster density profiles evolve with redshift, we fit the profiles separately for each halo at each redshift. Instead of physical coordinates, we use radial coordinates with respect to the r 200 of each cluster for the profiles, due to the fact that the cluster sizes also evolve with redshift. In Figure 4 we show that within r 200 , the edge can be accurately predicted from the density and Poisson equation to z = 0.75. However, outside the virial radius, the edge is increasingly underpredicted compared to the model, as a function of increasing redshift. We find the same result when using the mean background density as opposed to the critical background density when defining the cluster masses and radii. Figure 4. The variation in the fractional difference between the measured v esc edge and the predictions from the density profile from redshift 0 to 0.75. The light (dark) gray bands represent the 67% (90%) scatter of the individual halos. We can explain this by the growing influence of the halo gravitational potential well on the dynamics of the infall regions around the

O O O O O O O O O O O O O O O O O O O O O B-Model O O B-Model I-Model 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 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-Model I-Model 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-Model I-Model I-Model I-Model 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 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 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 B-Dataset I-Dataset 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 B-Model I-Model 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


regions described in Section 4.3 . In Figure 6 , we present again the oxygen abundance and ionization parameter gradients and color-code the data points based on the different groups defined in Figure 5 . Figure 6 further demonstrates the azimuthal variation visible on the oxygen abundance map (Figure 3 ). The H ii regions that belong to the spiral arms have systematically higher oxygen abundances than the other regions at the same galactocentric distances. The upstream regions have oxygen abundances in between the main spiral and downstream H ii regions. A total of 73 of the 96 (76%) main spiral H ii regions are above the best-fit abundance gradient. In contrast, only 13/76 (17%) of the downstream H ii regions are above the best-fit abundance gradient. The distributions of the residuals, after the best-fit radial gradient is subtracted, are statistically different (Figure 6 histogram). Two-sample Kolmogorov–Smirnov tests suggest that the null hypotheses that the residuals of the spiral-downstream, spiral-upstream, and downstream-upstream regions are drawn from the same distributions can effectively be ruled out (, , and , respectively). Figure 6. Oxygen abundance (left panels) and ionization parameter (right panels) gradients in NGC 1365. Each color point corresponds to one H ii region in Figure 3 . The different color symbols correspond to the different groups of H ii regions shown in Figure 5 . The black solid lines are the overall best fits. The red, blue, and green dashed lines are the linear best fits to the “Spiral,” “Downstream,” and “Upstream” H ii regions, respectively. The bottom panels show the residuals, i.e., after subtracting the black solid lines. The best-fit parameters are tabulated in Table 2 . We also perform the same least-squares linear fits to the spiral arm, downstream and upstream H ii regions. The best-fit oxygen abundance gradients shown in Figure 6 demonstrate the systematic differences between the different groups of H ii regions. The best-fit parameters are tabulated in Table 2 . It is worth pointing out that the majority of the upstream H ii regions (21/27; 78%) are in between the best-fit gradients defined by the spiral arm and downstream H ii regions. In Figure 7 , we present the azimuthal variations more clearly by subtracting the best-fit radial gradient from the oxygen abundance map. If there are no azimuthal variations, the residual map should present only random fluctuations. However, Figure 7 shows that the residuals correlate strongly with the spiral pattern. Figure 7. Oxygen abundance map after subtracting the best-fit radial abundance gradient (i.e., Figure 6 ). The azimuthal variations of oxygen abundance are now clearly visible. To summarize, while overall there is a negative oxygen abundance gradient in NGC 1365, we find pronounced azimuthal variations. The H ii regions on the spiral arms present, on average, about 0.2 dex higher oxygen abundance than the downstream H ii regions. The upstream H ii

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