of reionization, then decreases during the late stage. When the IGM global neutral fraction drops below , on the small scales a positive cross-correlation appears. At this stage, most of the IGM has been ionized, while the neutral hydrogen in haloes starts to dominate the cross-power spectrum, producing the positive correlation seen in the small-scale power spectrum. As the remaining neutral islands in the IGM shrink and decrease in number, the halo H i come to dominate the fluctuations on larger and larger scales, as a result this positive-to-negative transition point on the cross-power spectrum moves to larger scales. Figure 4. The cross-power spectrum between the neutral fraction and the dark matter density. The solid and the dashed lines represent positive and negative values, respectively. The cross-power spectrum between the 21cm brightness temperature and the DM density are plotted in Fig. 5 . We use the two panels to show the early and late stages of reionization, respectively. We find that at the very beginning of reionization, the 21cm-DM cross-power spectrum is positive on all scales, implying that the neutral hydrogen density fluctuations still follow the DM density fluctuations, although some rare density peaks have been ionized. As more and more IGM around density peaks becomes ionized, the 21cm-DM cross-power spectrum decreases, and transits to negative starting from the largest scales. Then, the large-scale 21cm-DM cross-power becomes more and more negative. The amplitude reaches its maximum at around , and decreases again. Different from the f H i -DM cross-power, the 21cm-DM cross-power spectrum is always positive at small scales, indicating that when weighted with the local density, the small-scale 21 cm signal is always dominated by the H i in haloes. At the very late stage of reionization, the positive-to-negative transition scale increases rapidly. Figure 5. The 21 cm brightness temperature and the dark matter density cross-power spectrum. Top panel: early EoR; Bottom panel: late EoR. The solid and dashed lines represent the positive and negative values, respectively. In this plot, the 21cm-DM cross-power spectrum at z = 9.90 shows some oscillations, which are likely statistical fluctuations. To check this interpretation, we estimate the errors on cross-power spectra using the jackknife resampling method. In Fig. 5 , we plot the errors for the z = 9.90 and z = 9.00 curves. To avoid clutter, errors of other curves are not shown there. We see that indeed at z = 9.90 the error bars are larger than the oscillation feature on the power spectrum curve, so it is likely that these are just statistical fluctuations. We also check that at z = 9.00 the errors are comparable with the z = 9.90. However, at z = 9.00 the cross-power spectrum is much larger than z = 9.90. In logarithmic axes apparently its errors are less obvious than z = 9.90. We then turn to the individual contribution from the IGM and haloes to the 21cm power

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


light-to-Alfvén speed ratio is fixed at c / v Ai = 10 4 . The top panel shows the normalized real part of the wave frequency, and the bottom panel shows the normalized imaginary part of the wave frequency as functions of the normalized wavenumber k . The vertical lines in the bottom panel mark the positions of kd e = 1 for the given mass ratios. In Fig. 3 , we show the dispersion relations for the FM/W wave in quasi-parallel direction of propagation. This mode shows the typical quadratic whistler-mode behaviour at . The FM/W wave is dominated by electron dynamics unless kd i ≲ 1. With decreasing m i / m e , ω r /Ω i decreases while | γ |/Ω i increases. We attribute this behaviour to increasing cyclotron damping by electrons, which is, for the quasi-parallel FM/W wave, most efficient when n = −1 in equation ( 17 ). Thermal electrons with v ∥ ≈ − w e thus efficiently resonate with the quasi-parallel FM/W mode when in our normalization. In the electron–positron case with m i / m e = 1, a significant number of electrons resonate with the FM/W mode at ω r /Ω i = ω r /|Ω e | ≲ 1 and at kd i = kd e ≲ 1 (see fig. 2 by Gary Karimabadi 2009 ). Like in the case of the quasi-parallel A/IC wave, the resonant cut-off of the dispersion relation for ω r → |Ω e | is also present in the cold-plasma limit (Stix 1992 ). The quasi-parallel FM/W mode reaches the wavenumber range kd e ≥ 1 with | γ | ω r for all mass ratios shown in Fig. 3 . Figure 3. Dispersion relations of the FM/W wave in quasi-parallel propagation for different values of m i / m e . The light-to-Alfvén speed ratio is fixed at c / v Ai = 10 4 . The plot follows the same format as Fig. 2 . In Fig. 4 , we show the dispersion relations for the FM/W wave in quasi-perpendicular direction of propagation. The dispersion relation does not depend significantly on m i / m e for m i / m e ≳ 10. The quasi-perpendicular FM/W wave reaches the ion-Bernstein regime at ω r /Ω i ≈ 1. In the perpendicular limit ( θ → 90°), the susceptibilities for both ions and electrons include sums over all n of contributions that are each proportional to 1/( ω r − n Ω j ), leading to this resonant behaviour. As long as m i / m e ≫ 1, electron harmonics do not interfere with the ion harmonics since all contributions to decrease with increasing n . For m i / m e = 2, however, the second-order ion resonance makes a contribution to that is comparable with the first-order electron resonance. The quasi-perpendicular FM/W mode reaches the wavenumber range kd e ≥ 1 with | γ | ω r for all shown parameter combinations with m i / m e ≤ 125. Figure 4. Dispersion relations of the FM/W wave in quasi-perpendicular propagation for different values of m i / m e . The light-to-Alfvén speed ratio is fixed at c / v Ai = 10 4 . The plot follows the same format as Fig. 2 . 2.2 Dependence on light-to-Alfvén speed ratio We now investigate the dependence of the dispersion relation on c / v Ai . For this study, we fix the mass ratio at m i / m e = 100

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


and model-independent approach. To compare e red and l orb with the data, we follow the procedure of Forero-Romero etal. ( 2013 ), drawing contours in the e red l orb plane to identify those regions of the parameter space that are compatible with current observations. The contours are generated through 10 7 Monte Carlo (MC) iterations, where at each step the values of velocity, mass and distance are drawn from a Gaussian distribution within the intervals shown in Table 7 . The value of v rad was taken from van der Marel etal. ( 2012 ), r from van der Marel Guhathakurta ( 2008 ), while M MW and M M31 are consistent with van der Marel etal. ( 2012 ) and Boylan-Kolchin etal. ( 2013 ). Due to the large discrepancy existing among the and the MC was ran twice using the two different estimates. It turns out that the intervals generated with are extremely large and possess no constraining power, so that we do not consider them in the following analysis. Table 7. Values and intervals used to generate MC contours. M MW , M M31 are expressed in 10 12 h 1 M units, interhalo distance r in h 1 kpc while v rad and v tan in kms 1 . The intervals on r and v rad correspond to the 2 values of van der Marel etal. ( 2012 ), while for v tan they were chosen in agreement with (Sohn etal. 2012 ). In Fig. 2 , we bin the Mod1 objects in the e red l orb plane and compare them to the observational 95percent confidence intervals. The fraction of objects f LG that falls within those boundaries is shown in the last column of Table 8 . This quantity allows us to gauge the ability of a model to account for the observed global dynamics of the system disregarding its transient state. We note that the number for CDM varies between 0.15 and 0.19 which is consistent with Forero-Romero etal. ( 2013 ), who found a 0.08 to 0.12 fraction at the 68percent confidence interval. In the case of modified gravity cosmologies, the results largely confirm the conclusions obtained with the previous analyses of velocities. In fact, models such as FofR04, FofR05, SymmB and to a lesser extent FofR06 produce LG-like pairs within the observational boundaries at substantially lower rates than CDM. In particular, the fraction of Mod1 LGs falling within the 95percent confidence level is reduced by a factor of 3 in SymmB and around a factor of 2 in FofR04 and FofR05, showing from another perspective that the LG dynamics can only be poorly accounted for within these models. These discrepancies are explained by the increased velocity of M31, affecting the values of e red [through the kinetic energy term in equation ( 30 ) and l orb , which tend to shift the distribution farther away from the region allowed by the data]. Figure 2. LG-like pairs versus MC contours showing the 1 and 2 confidence levels. Pairs have been chosen and MC intervals have been generated using the low v tan estimate of Sohn etal. ( 2012 ). Table 8. Energy, angular momentum, spin parameter and fraction of Mod1 pairs falling within

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


changing from the inner to the outer an MC based on the fitting results. There is a roughly increasing trend of the tangential velocity away from the axis of the MC that continues in the ambient solar wind. However, this increase is not strictly monotonous, which may be attributed to fluctuations. 3. Possible Dependence of the Viscosity on Solar Wind Parameters 3.1. Data and Method The above analysis has shown some viscosity signature from a rough statistic. Here we study the role of viscosity further through detailed investigation of the change of the tangential velocity crossing the MC boundaries. By manually checking the change of the 1 minute averaged tangential velocity profile near the front/rear boundaries of the MCs, we further narrow down the sample by selecting the crossings during which the tangential velocity clearly increases from the inner to the outer the MC. Finally, nine crossings that we think represent the picture fairly well in Figure 1 are selected and shown in Figure 3 . A few data points indicated by the red symbols in Figures 3 (a), (b), and (d) are discarded in the following analysis because they deviate significantly away from the main trend of the crossings due to inevitable fluctuations. Figure 3. Change of the tangential velocities with time. Panels (a)–(d) show the change of the tangential velocities at the front boundary of the MC, and (e)–(i) at the rear boundary. The verticle solid line indicates the boundary of the MC. The ordinate axis is the tangential velocity, where the positive value means the anti-clockwise rotation and the negative value means the clockwise rotation. It is not clear how to obtain the viscous coefficient in the solar wind. Alternatively, we use the following formula to roughly assess the strength of the viscosity between the ambient solar wind and MC plasmain which is assumed to be a function of the viscous coefficient , and and are averaged tangential speeds in MC and solar wind, respectively. The formula follows the idea that if there is no viscosity should approach zero as well as , and if there is a strong viscosity should be equal to , leading to be infinitely large. Considering that there is more or less uncertainty in determining the boundary of an MC, we calculate the values of and based on the measurements within one and a half hours next to the boundary with the nearest half an hour ignored. The uncertainty in is propagated from the uncertainties in the averaged tangential velocities and . The averaged solar wind parameters, e.g., density, temperature, and turbulence intensity of the magnetic field, inside and outside of the boundary are also calculated within the same intervals to investigate the possible dependence of the strength of the viscosity between the ambient solar wind and MC plasma. 3.2. Results The scatter plots between and solar wind parameters inside and outside of the MC are shown in Figure 4 . The turbulence intensity of the magnetic field is estimated based on

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O O O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O O O O O O O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O O O O O O O O O O O O O O O


the following, we summarize the procedures used in this paper to simulate the auroral radio emission arising from a stellar magnetosphere shaped like a non-central dipole. To calculate the magnetic-field vector generated by an offset dipole, the magnetic-dipole moment is located in a generic grid point ( O ) within the star, identified by its spatial coordinates ( x , y , z ) in the native reference frame Oxyz , where the origin O coincides with the centre of the star, the z -axis is parallel or coincident with the dipole axis, and the x -axis lies into the plane parallel to the z -axis and containing the rotation axis. In the reference frame anchored with the offset dipole, the new coordinates ( X , Y , Z ) of the grid points are defined by the simple coordinates translation ( x x , y y , z z ). In the translated O XYZ reference frame, the Z -axis coincides with the dipole axis and the X -axis is located in the plane passing through the Z -axis and parallel to (or containing) the rotation axis. The corresponding magnitude of the magnetic-dipole moment is defined as follows: where r Z is the distance of the offset dipole from the stellar surface along the direction parallel to Z -axis, and B p is the polar magnetic-field strength, that was fixed equal to 3000G. The three components ( B X , B Y , B Z ) of the magnetic-field vector are calculated in each grid point taking into account the non-central position of the magnetic-dipole moment. In the new reference frame O XYZ , the magnetic vector components are easily calculated using the equations of the simple dipole (see appendix A.2 of Trigilio etal. 2004 ). The magnetic vectorial field is then rotated in the observer reference frame Ox y z , where the origin O coincides with the centre of the star, the x -axis is parallel to the line of sight, and the plane y z coincides with the plane of the sky. The method was described in appendix A.3 of Trigilio etal. ( 2004 ). In the reference frame ( O XYZ ) anchored with the offset dipole, it is also possible to locate the grid points falling inside the auroral cavity using the equation of the dipolar magnetic-field lines, defined by using the equation r L cos 2 , where r is the distance of the grid points to the origin O (where is located). Following the method described in Paper I , it is then possible to find those grid points that radiate auroral radio emission within a beam pattern that intercepts the line of sight and that are tuned at the assigned simulation radio frequency . To take into account the non-central position of the magnetic-dipole moment ( O O ), the distance to the centre of the star from the grid points that are able to radiate detectable auroral radio emission has to be larger than the stellar radius. The star shadowing effect has also been taken into account. APPENDIX B: OFFSET DIPOLE: SIMULATIONS The simulations of the auroral radio-emission visibility from a non-central dipolar field were performed assuming the model parameters

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


assumed to be single Gaussians, using photographic density , and solving for , and c from these lines. Then, I was solved at neighboring wavelengths for the Fe x transitions. This procedure slightly reduced the lower intensity values at the base of the lines, without changing the results significantly. We do not know widths of Fe x lines that are unblended, nor do we know the precise wavelength of Fe x lines on the wavelength scale above. Therefore, the unresolved FS can only be derived as an upper limit by comparing the observed data with the two lines, estimating for the FS splitting itself (or by a least-squares optimization outlined below). In making these comparisons, we adopted the optically thin ratio of 2.09 for the two lines from CHIANTI (Young et al. 2016 ). Some typical profiles are illustrated in Figure 3 . Figure 3. Observed profiles and fits are shown for a specified line width of 0.23 Å, of the 1603.2 Å region of the S082B data obtained above the solar limb. The solid line shows the S082B data, the dotted lines show the two components of the Fe x transitions in their optically thin ratio, and the dotted–dashed lines show the total modeled emission for the given FS splitting. The panel labeled “4 cm −1 ” shows an acceptable by-eye fit, yielding an FS splitting close to 4 cm −1 . The other panels show the fits, with residuals at least 10 times higher, for splitting values of 1, 7, and 10 cm −1 . For values of FS splitting near and below the line width ( cm −1 ) there is some redundancy between FS splitting and line width. The figure shows observed profiles over-plotted with models with a given (1/ e ) width of 0.23 Å (taken from the optimization calculation below) for four values of the FS splitting. The figure suggests an FS splitting value of , certainly cm −1 . The variances, sum of model minus data squared evaluated over the fit to a 1 Å wide band centered at the line, are 2.5, 3, and 9 times the optimal value for 1, 7, and 10 cm −1 respectively. A trade-off exists between line width and FS splitting: the larger the width, the lower the splitting needed to fit the same data. Therefore, we can place only an upper limit on the FS splitting from this analysis of cm −1 . However, we can go a step further. While the data are photographic and subject to nonlinearities in photographic density versus intensity, we nevertheless performed a formal analysis of variances by fitting the two lines and varying the strong line's wavelength, line widths and the FS splitting. Both lines were given the same width and the ratio of the intensities was fixed at 2.09. The pikaia genetic algorithm was used (Charbonneau 1995 ). Figure 4 shows the surface as a function of width and FS splitting. We adopted a constant value for the observational error across the line profiles for the calculation, because the photographic densities lie on top of a large pedestal (equivalent to a dark current). We multiplied the errors by Gaussian functions centered near

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 B-Database B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O B-Instrument O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software I-Software I-Software O O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O


were mainly from the NEOWISE database ( Mainzer et al. 2011 ) with some values taken also from Akari ( Usui et al. 2011 ) and IRAS ( Tedesco et al. 2004 ) catalogs. 4.1. Pole latitude versus size The distribution of the pole latitude β for main-belt asteroids as a function of asteroid size is shown in Fig. 4 . The distribution is strongly bimodal for asteroids smaller than 20–30 km, which can be satisfactorily explained as an effect of a YORP-driven evolution ( Hanuš et al. 2011 , 2013b ). Due to the YORP effect, small asteroids evolve towards the extreme values of obliquity. In the lower panel of Fig. 4 , we show the fraction N p / N total of the number of prograde ( β > 0) rotators in a running box over N total = 100 asteroids as a function of size. For asteroids larger than 100 km, the number of prograde rotators is statistically higher ( N p = 68, N total = 108, probability of the null hypothesis that N p = N total /2 is p ≃ 0.7% assuming binomial distribution) in accordance with the model of Johansen Lacerda (2010) who suggested that the preferentially prograde rotation of large asteroids is a result of accretion of pebbles on planetesimals in a gaseous environment. On the other hand, for asteroids in the size range 1–10 km, there is an excess of retrograde rotators ( N p = 520, N total = 1276, p ≃ 2 × 10 −11 ). For asteroids between 10 and 100 km, the number of prograde and retrograde rotators is statistically the same ( N p = 441, N total = 919, p ≃ 22%). Because most asteroids smaller than about 30 km have large absolute values of β , the prograde/retrograde analysis is not sensitive to asteroids with | β | 30°. The ratio is almost the same even if we restrict ourselves to | β | > 30° where the distinction between prograde and retrograde rotation is unambiguous even for nonzero inclination. This is not true for asteroids larger than 100 km, where for | β | > 30° we have N p = 34, N total = 55, and p ≃ 8%. Fig. 4. The distribution of pole latitudes β for all full and partial models of main-belt asteroids. The bottom panel shows the running-box (over 100 asteroids) fraction of prograde ( β > 0 deg) models (red curve) and also the fraction of models with β > 30 deg (green curve). The dashed and dotted lines show the 5% and 1% significance levels at which the null hypothesis that the prograde and retrograde asteroids are equally frequent can be rejected. The excess of small retrograde rotators in Fig. 4 is statistically significant, however, it is not clear if the reconstructed distribution of β is the same as the real one. Although we are not aware of any bias in the observations or the method that could cause the asymmetry in ± β , there could still be some nontrivial systematic effect that we have not taken into account. 4.2. Pole latitude distribution across the main belt The distribution of pole latitude β is not only dependent on the size, but also on the proper semimajor axis, namely on the proximity to resonances. For asteroids in

O O O O B-Database I-Database O B-Citation I-Citation I-Citation I-Citation O O O O O O O B-Telescope O B-Citation I-Citation I-Citation I-Citation O O B-Telescope 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-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O B-Citation I-Citation I-Citation I-Citation O B-Citation 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-Formula I-Formula I-Formula O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula B-Formula I-Formula I-Formula I-Formula 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 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 O O O 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 I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula B-Formula I-Formula I-Formula I-Formula B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula 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 B-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 O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


This is due not to continual acceleration, but instead to previously higher velocities and higher mass loss rates earlier in the model’s evolution. In Figure 4 , we show the linear (left-hand plot) and logarithmic (right-hand plot) temporal evolution of our main fiducial model as well as fiducial models with different WD and envelope masses. Black, red, and green lines represent core + envelope masses of , , and , respectively. In each plot, the top panel shows the evolution of the total luminosity, which is the sum of the luminosity at an optical depth of and the power from positron kinetic energy released by decays above the photosphere. We assume the positrons are able to thermalize and deposit their energy locally while the gamma-rays emitted during the and decays escape the wind and the surrounding SN ejecta. In practice, however, the positron kinetic energy in the optically thin region is smaller than the luminosity at the photosphere, so this contribution is not significant. Note that the luminosity from the SN Ia ejecta is not included. For comparison, the dotted line in the top panels represents the total power from radioactive decays of of initially pure under “lab” conditions. Figure 4. Evolution of winds launched from post-SN Ia surviving WD donors with envelope masses determined by the maximum bound ejecta mass. Three different models are shown, with core + envelope masses of (black), (red), and (green). The left-hand and right-hand plots use linear and logarithmic time axes, respectively. The top panel in each plot shows the sum of the luminosity at the photosphere and the luminosity from thermalization of positron kinetic energy from decays above the photosphere. The dotted line represents the total power from radioactive decays of of initially pure under “lab” conditions. Note that the luminosity from the SN Ia ejecta is not included. The middle panels track the effective temperature at the location. The bottom panels show the velocity at the photosphere (solid) and the mass-averaged velocity of material above the photosphere (dashed). The effective temperature, derived from the luminosity and radius at the surface, is shown in the middle panels. The velocity at the location is shown as a solid line in the bottom panels, and the mass-averaged velocity in the optically thin region is shown as a dashed line. The observed quasi-bolometric late-time light curve of the best observed SN Ia to date, SN 2011fe, is shown as bullets (Nugent et al. 2011 ; Tsvetkov et al. 2013 ; Kerzendorf et al. 2014 ; Shappee et al. 2016 ). The late-time flattening of SN 2011fe and other SNe Ia above simple predictions for decay within the SN ejecta has been attributed to light echoes and the decay of long-lived radioactive isotopes such as 57 Co and 55 Fe (Seitenzahl et al. 2009 ; Röpke et al. 2012 ; Kerzendorf et al. 2014 ; Graur et al. 2016 ; Shappee et al. 2016 ). Our models represent an additional contribution to the total luminosity, and

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


et al. 2018 ). In the X-ray, events up to 10 32 erg (10 32.7 erg bolometric) have been detected (Güdel et al. 2004 ). The Microvariability and Oscillation of Stars ( MOST ) satellite (Walker et al. 2003 ) performed the most comprehensive previous measurement of the Proxima flare rate. MOST observed Proxima for 37.6 days, observing 66 white-light flare events, the largest of which was 10 31.5 erg in the MOST bandpass (∼4500–7500 Å). No superflares were observed; extrapolating the cumulative flare frequency distribution (FFD) obtained by Davenport et al. ( 2016 ) from the MOST flare sample out by 1.5 dex predicts that ∼8 × 10 33+ erg events in the MOST bandpass occur per year. To search for superflares and other short-timescale phenomena, the Evryscope (Law et al. 2015 ) is performing long-term high-cadence monitoring of Proxima, along with every other bright star in the Southern sky. In 2016 March the Evryscope detected the first-known Proxima superflare. Although no M-dwarfs are usually visible to the naked eye (e.g., Shields et al. 2016 ), Proxima briefly became at least a magnitude-6.8 star during this superflare, at the limit of visibility to dark-site naked-eye observers. 2. Evryscope Flare Discovery and Observations We discovered the Proxima superflare as part of the Evryscope survey of all bright southern stars. The Evryscope is an array of small telescopes simultaneously imaging 8000 square degrees of the sky every two minutes (Law et al. 2015 ). The Evryscope observes essentially the entire Southern sky above an airmass of two, at two-minute cadence in g ′ and at a resolution of 13′′ pixel −1 . The system has a typical dark-sky limiting magnitude of g ′ = 16 and tracks the sky for 2 hr at a time before ratcheting back and continuing observations, for an average of ∼6 hr of continuous monitoring each night on each part of the sky. The Evryscope image archive contains 2.5 million raw images, which is ∼350TB of data. A custom pipeline analyzes the Evryscope data set at realtime rates (Law et al. 2016 ). Each image, consisting of a 30 MPix FITS file from one camera, is calibrated using a custom wide-field solver. After careful background modeling and subtraction, forced-aperture photometry is extracted based on known source positions in a reference catalog. Light curves are then generated for approximately 15 million sources across the Southern sky by differential photometry in small sky regions using carefully selected reference stars and a range of apertures; residual systematics are removed using two iterations of the SysRem detrending algorithm (Tamuz et al. 2005 ). In extremely crowded fields, such as for Proxima (−2° galactic latitude), we re-run the pipeline for particular targets, optimizing the aperture sizes to avoid nearby stars. As a very large event, the Proxima Superflare was discovered in routine by-eye checks of interesting targets in the Evryscope data set. Smaller flares are discovered and characterized with an automated

O O O O O O B-Wavelength O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O B-Telescope I-Telescope I-Telescope I-Telescope I-Telescope O B-Telescope O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O B-CelestialObject O O B-Telescope O B-CelestialObject O O O O O O O O O O O O O O O O O O B-Telescope O B-Wavelength I-Wavelength 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 B-Telescope O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O O B-Telescope B-Citation I-Citation I-Citation I-Citation O O O O O O O B-CelestialObject O O O O O O O O B-CelestialRegion I-CelestialRegion O O O O B-Telescope O O O B-CelestialObject O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-CelestialObject O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O O B-CelestialObject O O O O O B-Telescope O O O O O O O B-Telescope 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-Telescope O O O O B-CelestialRegion I-CelestialRegion 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 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 B-Telescope 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-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialRegion I-CelestialRegion O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O B-CelestialObject B-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 B-CelestialObject O O O O O O O O O O O O B-Telescope O O O O O O O O O O O


mixes with nearby gas, producing a sharp peak in the PDF at the high metallicity end. More efficient diffusion tends to push this peak to lower metallicities. This trend is produced by enriched gas losing its metals more rapidly. However, this also depends on the recent star formation history, and is not a monotonic trend with diffusion strength. This peak is not present in Nodiff. Instead, there is a high-metallicity tail, consisting of the small number of particles that have been enriched by very many feedback events. The difference between the metal distributions has no clear impact on the distribution of cooling times, presumably because the number of particles in the high-metallicity tail is small. In general, the gas properties of Shear do not seem to stand out as particularly distinct among the other simulations. The differences between the simulations thus appears to depend only on the strength of diffusion, even when the diffusion coefficient is calculated in different ways. This suggests that diffusion can be accurately calibrated by adjusting the pre-factor, and that it is not necessary to introduce a more complex method for calculating the diffusion coefficient. 3.3. Spatial Distribution of Metals The spatial distribution of metals at t = 750 Myr is plotted in the second column of Figures 3 and 4 . This distribution is strongly affected by the choice of diffusion algorithm. Without any diffusion, the metal distribution is very clumpy as there is no mechanism to smooth out the metals. Highly metal-enriched particles can therefore move over large distances without losing their metals. Metal-rich gas in the Nodiff model at clearly has a large vertical extent, while Disp is more localized (Figure 4 ). We have plotted the mean metallicity, and [O/Fe], in vertical and radial bins in Figure 7 at intervals of 250 Myr to examine more clearly the difference between the diffusion algorithms. The radial metallicity bins are annuli that extend 2 kpc above and below the disk plane, and the vertical metallicity bins are pillboxes of radius 5 kpc. While many observed dwarf galaxies appear to have flat or near-flat metallicity gradients (Crnojević et al. 2010 ; Koleva et al. 2011 ), all of our simulations show significant slopes. This is likely a result of our feedback being weak, resulting in gas (and hence star formation) that is centrally concentrated. Stronger feedback at higher resolution can produce more distributed star formation ( K14 ). This dependence on feedback means that the simulated spatial distributions of metals can not be directly compared with observations, but only compared with other models with similar feedback strength. Figure 7. Metallicity distributions at t = 250, 500, 750, and 1000 Myr (from top to bottom). First column: metallicity as a function of height above the disk plane. Second column: Metallicity as a function of radius. Third column: [O/Fe] as a function of height above the disk plane. Fourth column: [O/Fe]

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


errors for are 3%–7%. Because there is no physical motivation to assume that the prior distribution of the pressures is uniform, we also tested the inversion with priors that are uniform in the logarithm of pressure. The results of this test, with identical data as above and the Gaussian regularizer included, are shown in the bottom panel of Figure 2 . The top panel of Figure 2 shows that assuming a uniform prior introduces a preference toward higher pressures. On the other hand, assuming that the prior is uniform in the logarithm of pressures biases the results toward lower pressures. The inversion is particularly sensitive to this bias in the low-mass/low-density region of the EoS, where we lack data. Our Gaussian regularizer helps reduce this bias, as shown in the middle and bottom panels of Figure 2 , in which the results are similar for the two types of priors when the regularizer is also included. In the absence of a regularizer, the freedom introduced by using five polytropes in the parameterization combined with this sensitivity to prior distributions could lead to significantly skewed results, or even the false inference of a phase transition with a perceived high statistical confidence. It is therefore important to use a Gaussian regularizer on the second derivative, with a characteristic scale , to avoid this sensitivity to over-fitting. In Figure 4 , we explore potential correlations between the inferred parameters for this test. Specifically, we show the correlations for the inversion using uniform priors and the Gaussian regularizer (i.e., the middle panel of Figure 2 ). There are slight anti-correlations between adjacent inferred pressures, due to fact that, even with the addition of the regularizer, we are still over-parameterizing our model while trying to fit the effectively single-polytrope EoS SLy. Overall, however, the pressures that are not adjacent are uncorrelated with one another. Özel Psaltis ( 2009 ) showed that, for a three-polytrope parameterization, parameterizing with the pressures as free parameters instead of the polytropic indices reduced the correlations between the inferred values. Figure 4 shows that the low levels of correlations are maintained here. Figure 4. Correlation plots for the inferred pressures at our five fiducial densities. The inversion was performed using uniform priors and a Gaussian regularizer (). The red diamonds mark the pressures of the true EoS (SLy) that we are trying to infer. There are slight anti-correlations between adjacent pressures (e.g., P 1 and P 2 ), but the non-adjacent pressures are relatively uncorrelated. The triangular shape of the P 4 vs. P 5 correlation is due to the causality requirement, which is shown as the red line. In order to ensure that the Bayesian inference works well for other underlying EoS and that the regularizer does not adversely limit our ability to detect potential phase transitions, we tested the method on a number of different EoS as well. As an

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


(top), central detectors of sparse observations (middle), and from mapping observations (bottom) are shown in blue, orange, and violet, respectively. Lines found by the FF employ round markers while those found by the low SNR search routine through line identification use triangular markers (see Section 3.1 ). The |SNR| cutoff in each case is shown by the dotted black line. The axes in each case have been set to the same scale to allow comparison. 5 CONCLUSIONS The extensions of the FF to include spectral observations from off-axis detectors in sparsely sampled single-pointing observations is detailed. An additional 30 720 spectral features with a |SNR| greater than 6.5 are aggregated into the SAFECAT by the inclusion of the analysis and extraction of features from the off-axis detector spectra. We developed a set of postcards to highlight and summarize results from these off-axis detectors in each observation that are of a similar format to the mapping postcards described by Paper I and are available from the ESA Herschel legacy area (see footnote 6). We have also extended the automated SPIRE FF routine ( Paper I ) to identify the atomic or molecular transition that corresponds to the features extracted from HR observations of the SPIRE FTS. This identification of atomic/molecular transitions is done by matching the spectral features to a template of 307 atomic fine structure and molecular features that are commonly found in SPIRE FTS observations. Line identification is reliant on the radial velocity estimates included in the catalogue by Paper II and is able to successfully match 77.3 per cent, 93.1 per cent, and 95.2 per cent of spectral features found by the FF from central detectors of sparse single-pointing observations, off-axis detectors, and mapping observations, respectively, to their atomic/molecular transitions. We find this line identification to be particularly effective at identifying the CO rotational ladder from J = 4–3 to J = 13–12 and the [N ii ] 3 P 1 – 3 P 0 transition in SPIRE FTS observations. The identification of all 15 atomic/molecular species in SPIRE FTS spectra from mapping, off-axis detectors in sparse observations, and central detectors in sparse observations is shown in Fig. 14 . Note that isotopologues and ionization states have all been grouped together for each species. Figure 14. The line identification of all 15 atomic/molecular species contained in the template for mapping and sparse SPIRE observations. The information provided by the line identification is also used to uncover low SNR features that fall below the |SNR| ≥ 5 cutoff that exists nominally in the FF ( Paper I ). This low SNR search routine adds an additional 1516 for the central detectors of sparsely sampled single-pointing observations and 1234 for the off-axis detectors. An additional 370 lines are added by this routine from mapping observations of the SPIRE FTS. APPENDIX: LINE MATCHING TEMPLATE A note on the quantum numbers

O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Dataset O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O O O O O B-Organization B-Telescope O O O O O O O O O O O B-Instrument B-Software O O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O B-Instrument I-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument I-Instrument O O O O O O O O O O O O O O O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength O B-Wavelength I-Wavelength I-Wavelength O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength O O B-Instrument I-Instrument O O O O O O O O O B-Instrument I-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 B-Instrument O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O B-Software O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument I-Instrument O O O O O O O O O O


size equal to the sum of the number of HDs and CRs. This results in 118 HDs, 47 CRs, and 165 NDs (see Table 1 ). We show the distribution of the three samples in the plane in the right-hand panel of Fig. 1 , which is a zoom-in figure with galaxies with and . As can be seen, all three sub-populations have roughly similar sSFR, with CRs being slightly lower than the other two. In addition, we have also checked and confirmed that the total halo masses of the three galaxy samples are roughly within the same range. Table 1. Number of galaxies in different samples. Columns (1): All z = 0 central galaxies from the IllustrisTNG simulation; also the parent sample of Columns (2)−(5). Column (2): late-type galaxies; Column (3): selected hot disc galaxies (HDs); Column (4): selected counter-rotating disc galaxies (CRs); and Col.(5): control-sample normal disc galaxies (NDs). See Section 2.2 for definition and selection criteria. In Fig. 2 , we show the distributions of the three orbital fractions ( f cold , f hot , and f ccd ) for general late-type galaxies and the three selected samples (HDs, CRs, and NDs). As can be seen, the three samples exhibit distinctive differences in cold, hot, and counter-rotating cold orbital fractions: NDs, which host the highest fractions in f cold , also possess the lowest fractions in f hot and f ccd , while HDs indeed have lower fractions in f cold and f ccd , and CRs have the lowest fractions in f cold and moderate fractions in f hot . This also demonstrates that the three types of galaxies are intrinsically different from each other. Figure 2. Distributions of f cold , f hot , and f ccd (from left to right, see Section 2.1 for definitions) for late-type galaxies (black), NDs (blue), HDs (red), and CRs (green). Black dashed lines represent f cold = 0.4, f hot = 0.31, and f ccd = 0.2, which are used to classify NDs, HDs, and CRs, respectively. 3 WHAT DO THEY LOOK LIKE? 3.1 Morphology of stars and gas To discuss the visually apparent differences in morphologies between HDs, CRs, and NDs, we first present in Fig. 3 the stellar and H i mass density maps from both edge-on and face-on views for typical HDs (the first 2 columns), CRs (the middle 2 columns), and NDs (the latter 2 columns). As can be seen, the two NDs have the flattest stellar and gaseous disc morphologies with their spin axes well-aligned. In comparison, however, both CRs have less flat stellar and gaseous discs, the spins of which exhibit very large misalignment (∼180°); the two HDs possess much thicker stellar discs and display the least established gaseous discs among all three types. Interestingly, very often the optical images of NDs and CRs show clear extended spiral patterns which are absent in the HD samples. Figure 3. Examples of two HDs (ID: 582800, 512569), two CRs (ID: 486917, 532146), and two NDs (ID: 462986, 606707) from left to right. For each example, we show from the top to the bottom rows: (1) the face-on view of the stellar mass density map,

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


s −1 ). Figure 2 shows the integrated intensity maps of C 18 O ( J = 1–0) (cyan contours) and 13 CO ( J = 1–0) (color) observed with the NRO 45 m telescope for the entire region of HCL2 (Sunada Kitamura 1999 ). A prominent straight structure is seen in the northern part of HCL2 in the C 18 O map, which also has been pointed out by Narayanan et al. ( 2008 ) and Goldsmith et al. ( 2010 ). Interestingly, the velocity of the blueshifted component detected in the OH 18 cm transition ( km s −1 ) corresponds to that of C 18 O, exhibiting the straight structure, whereas the velocity of the redshifted component seen in OH ( 6–10 km s −1 ) corresponds to that of the southwestern extended gas in the 13 CO map. These two structures are interfacing with each other, suggesting a compressive motion as the origin of the straight structure (Figure 20 ). Such a compressive motion is consistent with the decreasing velocity from southwest to northeast across the straight structure observed in 13 CO and C 18 O. In addition, the existence of an [H i ] cloud in the northeast of TMC-1FN is suggested by the archival data of the Galactic Arecibo L-band Feed Array H i (GALFA-H i ) Survey maps (Peek et al. 2011 ). Furthermore, the 6–10 km s −1 component traces a diffuse warm gas, whereas the 5.5 km s −1 component traces a cold and dense core illuminated by the FIR radiation from dust grains, according to our statistical equilibrium calculation. It is likely that the 5.5 km s −1 component traces cold cores surrounded by the warm envelope gas in HCL2. Figure 20. Schematic illustration of the cross section of TMC-1FN along the line of sight. The cold (∼20 K) and dense core (5 km s −1 ) is formed by compressive motion of the extended warm gas (6–10 km s −1 ). We observe the source from the right-hand side. The 6.5 and 8.2 km s −1 components show the 1612 MHz line absorption, in spite of the FIR pumping effect seen in the 5.5 km s −1 component. This can be explained by the proposed picture of TMC-1FN (Figure 20 ). A warm envelope gas traced by the 6.5 and 8.2 km s −1 components is likely to be illuminated by fainter FIR radiation than the gas traced by the 5.5 km s −1 component. The OH column density for the 6.5 and 8.2 km s −1 components is also lower. According to the results in Appendix C , the FIR intensity at 160 μ m is estimated to be ∼400 and 100 MJy sr −1 at positions 0.5 and 1.0 pc distant from the center of the TMC-1FN filament, respectively. The OH column densities are determined to be 3.6 × 10 14 cm −2 and 1.4 × 10 14 cm −2 for the 6.5 and 8.2 km s −1 components, respectively (Table 3 ). As described in Section 4.1.7 , our calculation shows that the FIR pumping effect is negligible for an OH column density lower than 10 15 cm −2 and I 160 lower than 100 MJy sr −1 . On the other hand, the 1612 MHz line indeed appears in absorption for I 160 lower than 4 × 10 3 MJy sr −1 , if the OH column density is 3 × 10 14 cm −2 (Figure 15 (d)). Hence, even though there might be

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


represent the 1.3-mm (G09-83808, NGP-190387) and 3-mm (SGP-261206) continuum emission, at 5, 6, 7, 8, 9 × σ. Near-IR emission is seen clearly, coincident or near-coincident with the 1.3- or 3-mm continuum emission. At the depth of the VIKING observations (limiting magnitude, K AB ≃ 21.2), we do not expect to detect dust-obscured distant galaxies. The sources coincident with G09-83808 and SGP-261206 show, therefore, that these two DSFGs are amplified gravitationally by the foreground galaxies seen in the near-IR images. The galaxy in the foreground of SGP-83808 has z spec = 0.778, obtained using X-shooter on the VLT (Fig. 5 ), and is magnified by 8.2 ± 0.3, a factor determined using high-resolution ALMA continuum imaging (see Oteo et al., in preparation-a). The three galaxies revealed by the deeper Gemini imaging of NGP-190387 are considerably fainter, with K AB = 21.0, 22.3, 21.4, yet they are not coincident with the z = 4.42 DSFG and likely constitute a foreground lensing group. Towards G09-81106 we have detected two emission lines, CO(4–3) and CO(5–4), at 83.36 and 104.19 GHz (Fig. 3 ), both at z = 4.531. There is no suggestion of gravitational lensing for G09-81106, either via the presence of unusually bright near-IR galaxies in the field, or via its submm morphology as seen in high-resolution ALMA continuum imaging (Oteo et al., in preparation-a). Towards G09-83808 we have detected two faint emission lines, at 82.02 and 98.39 GHz (Fig. 3 ), corresponding to CO(5–4) and CO(6–5) at z = 6.026 ± 0.001 and 6.028 ± 0.001, respectively, so an average of 6.027 ± 0.001. These lines were also noted by Zavala et al. ( 2017 ) in a spectrum obtained using the Large Millimeter Telescope. G09-83808 is near-coincident with a foreground galaxy, seen clearly in near-IR imaging from the VIKING survey (see Fig. 4 – Edge et al. 2013 ), indicative of gravitationally lensing. This foreground galaxy has a spectroscopic redshift of 0.778, obtained using X-shooter on the 8-m Very Large Telescope (VLT; see Fig. 5 ). A lens model based on the morphology determined by high-resolution ALMA continuum imaging predicts a gravitational amplification of 8.2 ± 0.3 (Oteo et al., in preparation-a). Figure 5. Top: Spectrum of the lensing galaxy in the foreground of SGP-83808, as seen in the optical arm of VLT/X-shooter after integrating for 4 × 20 min on 2013 March 17. Below: The 1D spectrum, in grey, extracted using a simple box-car summation [090.A-0891(A), PI: Christensen]. To identify the lens redshift we binned these data heavily (see Modigliani et al. 2010 ; Christensen et al. 2012 ; Kausch et al. 2014 ), as illustrated in black, with the error spectrum shown in green, then fitted the redshift by χ 2 minimization using a 5-Gyr stellar population model (shown in red) from Bruzual Charlot ( 2003 ). We find z spec = 0.778 ± 0.006. Strong absorption features are labelled. The flux units are 10 −17 erg s −1 cm −2 Å −1 . For NGP-284357, we find at least two emission lines, at

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


to test this connection more rigorously, but the match is poor, being both too blue and too broad (Fig. 11 ) compared to even the earliest spectra of SN1998bw or SN2002ap (Patat et al. 2001 ; Kinugasa et al. 2002 ), or of the spectrum of SN2008D (Modjaz et al. 2009 ) during its shock-cooling phase. 9 As of yet we have no convincing explanation for the origin of this feature, other than that it implies very fast (nearly relativistic) ejecta. Figure 11. Comparison of an early spectrum of AT 2018cow to the early spectrum of SN 2008D (Ib) and two SNe Ic-BL (top row), and of a later-time spectrum to SN 1998S (IIn) and two tidal disruption events (bottom row). The extremely blue, smooth continuum bears little resemblance to SN Ib/c, even after attempting to subtract the blue continuum. (A power-law plus a constant have been subtracted from AT 2018cow; the reference SN spectra have been subtracted by a constant only. The strength of the features in the SNe after subtraction has been suppressed by a factor of 2.) The later-time spectra are dominated by weak emission features of hydrogen and helium; these features are also present in IIn SNe but are much narrower compared to what is seen in AT 2018cow. These features are seen in known TDEs with similarly broad widths, although typically much greater strengths. The identities of the features seen in later spectra (H and He in broad emission) are secure. In spite of this, these later spectra bear no obvious resemblance to any class of known supernova. The strongest similarities are to Type IIn supernovae (which can also remain hot for several weeks after explosion, and are emission-dominated by definition): in the bottom panel of Fig. 11 , we plot AT 2018cow versus an early spectrum of SN 1998S from Fassia et al. ( 2001 ), which shows a similar blue continuum and most of the same H and He transitions. However, the lines in AT 2018cow are not narrow for most of their evolution ( ∼ 6000 km s −1 , versus a few hundred km s −1 for SN 1998S). Thomson scattering within ionized matter could broaden a line enough to wash out the narrow component, but this would not produce the net redshift in the emission component that we observe. The H and He thus must be in the ejecta itself (and seemingly preferentially in receding ejecta given the net redshift). In fact, the best spectroscopic analogues to AT 2018cow are not supernovae at all. Our spectra bear a striking resemblance to tidal disruption events: the high temperatures, presence of helium and hydrogen features in emission, and moderate velocities all match what is observed for TDEs. The spectral features in AT 2018cow are substantially weaker than in the examples of TDEs that we are aware of (bottom panel of Fig. 11 ; comparison spectra are from Holoien et al. 2014 , 2016 ), but the resemblance to a TDE is much stronger than to any supernova. We summarize the key observational features of AT 2018cow in Table 3 . 5 INTERPRETATION 5.1 Supernova models: A

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


distribution is the same as for the monodispere case. For the broad distribution between 10 −8 and 10 −4 bar, the single-scattering albedo of the Gaussian distribution () is always higher than that of the monodisperse case (), see the right two plots of Fig. 5 . The increase for the initial broadening around 10 −7 bar is wavelength independentand peaks at ( Fig. 5 , bottom right). The second peak in the increase of the albedo from the monodispserse case occurs at about 10 −5 bar, and this time is wavelength dependent with a significantly lower increase of only a factor of 2 for λ = 0.1 μ m, as opposed to increases by a factor greater than 4 for all longer wavelengths. This is because in this region and the fraction of cloud particles in the Rayleigh scattering regime ( Q sca ∝ λ −4 ) varies for each wavelength for a broad size distribution. Although an increase of half an order of magnitude in albedo seems substantial when the total extinction of the atmosphere is calculated, the peak extinction is dominated by regions with high mass fractions of cloud particles ( ρ d ∕ ρ ). The mass fraction of cloud particles peaks around the millibar level in the atmosphere, which does not significantly overlap with regions of high nucleation rates ( Fig. 5 , bottom left) where the local size distribution is broad. The size distribution therefore has little effect on properties such as optical depth ( Fig. 9 ). Wakeford Sing (2015) also found that for a log-normal distribution, the cumulative effect of transmission spectra of clouds is dominated by larger particles in the distribution. An asymmetric distribution, such as the log-normal distribution, has a greater number of large particles than the Gaussian distribution considered here, and may produce greater deviations from the monodisperse case. It has been found recently to have an effect on retrieved cloud particle size ( Benneke et al. 2019a ). We note, however, that none of the size distributions used in retrieval approaches are based on a consistent cloud model, and therefore no conclusion can be drawn about the shape of the particle size distribution from such retrieval approaches. 5 Optical effects of non-spherical particles To determine the effect of non-spherical cloud particles, we return to the T eff = 1800 K, log ( g ) = 3.0 atmosphere with compact monodisperse cloud particles. When a distribution of hollow spheres is used, as described in Sect. 2.5 , the albedo generally decreases compared to the compact monodisperse case ( Fig. 6 , top right). This is due to the high f hol end of the hollow sphere distribution, where the cloud particles have a large surface area (which is not conserved across the distribution of hollow spheres) and thus increase absorption ( Min et al. 2003 ). Furthermore, Fig. 9 shows that for the compact case (red line), the inclusion of non-spherical particles leads to an increase in optical depth in the silicate features between 10− 20 μ m. This result is in good

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


where m p = (4/3)ρ s 3 is the particles mass orbiting with velocity A is the particle’s cross section, and is the unit vector pointing to the direction of the radiation. The particles are assumed to be spherical with uniform density equal to 1 g cm − 3 . For transparency we give the explicit form of ω H is Haumea’s rotational frequency, n H is the mean motion about the Sun, and i is the obliquity of the dwarf planet to its orbital plane. The gravitational effect of the Sun is not included in this model because it is fifth order of magnitude weaker than that of Haumea at the distance of the ring. However, Haumea’s orbit is assumed to be circular with a period of 284 yr which is included in the time dependence of the RP. Since the obliquity of the dwarf planet is about 14 deg this implies a long-term modulation in z -component of the RP. In other words, the initial position of the Sun in our calculations is the negative x direction and Haumea’s obliquity stays in this direction during the whole integration. The effect of planetary shadowing (which blocks the stellar radiation impinging on the ring) is neglected since the ring is currently not shadowed because it is in the equatorial plane of the planet which is tilted with 13.8° ± 0.5° to the orbital plane (Ortiz et al. 2017 ). Furthermore, even for longer integration, only a small fraction of the ring will be hided during Haumea’s journey around the sun. We use a 4th order Runge–Kutta numerical scheme with a fixed step size that keeps the relative energy error below 10 −8 . Equation ( 5 ) is integrated for different times in order to cover different dynamical regimes. That is, the simulations are performed for T = 10 3 , 2.5 × 10 4 , and 3.5 × 10 5 rotation periods, yielding ca. 1, 10, 1000 yr, respectively. The calculations also have been done for grain sizes, 1, 1.75, 2.5, and 5 m. The dynamical analysis involves two different setup of initial conditions. In the one hand, when studying the fine resonant structure, particles are placed equidistantly along a line ( x -axis) in radial distance 1 r 11. On the other hand, an initial ring is defined, θ ∈ [0; 2] and r ∈ [0; 5], in order to follow the particle dynamics in general. In both cases grains are initially on circular Keplerian orbits in the equatorial plane of Haumea. 3 RING CHARACTERISTICS Our first analysis explores the lifetime of the particles around the dwarf planet. The grain dynamics yields three different end-states for the particles: (i) Escape : When the semimajor axis of a particle becomes larger than 25 r s (≈ 25575 km) it is taken to be ejected. Ejections occur due the close encounters with Haumea when the particles are perturbed to hyperbolic orbits. (ii) Collision : In our model a collision occurs when the particle approaches the dwarf planet closer than its volume-equivalent radius, 816 km (0.74 r s ) (Ortiz et al. 2017 ). (iii) Bounded motion : When a particle, until the end of the integration, neither collides nor escapes

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


XTE J1752-223 discovered by the Rossi X-ray Timing Explorer ( RXTE ) and Swift satellites on 2009 October 23 (Markwardt et al. 2009b ) suggested that it is a black hole candidate (Markwardt et al. 2009a ; Nakahira et al. 2009 ; Remillard et al. 2009 ; Shaposhnikov et al. 2009 , 2010 ). Three days after the X-ray discovery, a bright optical counterpart was found by the Magellan Baade telescope (Torres et al. 2009b ). Also, a bright near-infrared (NIR) counterpart was identified immediately (Torres et al. 2009a ). Afterwards, a bright radio counterpart was discovered by the Australia Telescope Compact Array (ATCA) with a flux density of at both 5.5 and (Brocksopp et al. 2009 , 2010 ). The radio light curves of XTE J1752-223 at 5.5 and were measured by ATCA, the European VLBI (Very Long Baseline Interferometry) Network (EVN), the Very Long Baseline Array (VLBA), and the Expanded Very Large Array (Brocksopp et al. 2009 ; Yang et al. 2010 ; Miller-Jones et al. 2011 ). Furthermore, the X-ray outbursts during 2009 October and 2010 July were obtained by the Monitor of All-sky Image (MAXI), RXTE , and Swift (Nakahira et al. 2010 ; Shaposhnikov et al. 2010 ; Curran et al. 2011 ). The long baseline observations of XTE J1752-223 are shown in Figure 1 , in which four jet features marked as A, B, C, and D have been reported by Yang et al. ( 2011 ). Component A appeared first, and then components B1 and B2 emerged, which suggests that components farther from the core can be seen earlier than components nearer the core. Moreover, components A and B were observed after the peaks of the radio light curve. It is of interest to understand such a connection between jet features and light curve. Figure 1. The positions of the components A, B, and D of XTE J1752-223 from the VLBA images (Yang et al. 2011 ) for each observing epoch. Note that components B and C in Yang et al. ( 2011 ) are written as B1 and B2 here. NRAO 150, discovered in the radio band by Pauliny-Toth et al. ( 1966 ), is a prominent quasar from the millimeter to radio band at redshift z = 1.52 (Agudo et al. 2006 ). Observations of this source by VLBI from 2001 October to 2004 April and by VLBA from 1997 June to 2002 June have exhibited a moving core–jet structure as shown in the left panel of Figure 2 . The core–jet structure consists of three components, Q1, Q2, and Q3. The evolution of the relative position of these three components is plotted in the right panel of Figure 2 , where Q1, Q2, and Q3 moved in a counterclockwise direction with respect to the core. The projected angular speed of these components can be up to , which is the first superluminal motion found within the innermost region () of the jet in NRAO 150 (Agudo et al. 2007 ). Figure 2. The ridge line structure of the jet of quasar NRAO 150 and the evolution of the position of components Q1, Q2, and Q3 from left to right (Agudo et al. 2007 ). In this paper, the observations of the kinematics of XTE J1752-223 and NRAO 150 are

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


descent, that is good for learning acceleration, but can lead to missing the loss minimum), and max_depth (greater values correspond to a large complexity of the trees, and can lead to overfitting). Moreover, GB algorithms usually allow the use of a stop criterion, responsible for the termination of the learning when an overfitting occurs (the so-called, early_stopping parameter). It is expressed via the number of constructed trees, after which the quality of the metric no longer increases. Usually this parameter ranges between 10 and 1000 trees, depending on learning_rate . If the early stopping criterion is met, the GB algorithm accepts the number of trees, satisfied to the best score. Paying particular attention to the early_stopping parameter is the best way to avoid as much overfitting as possible. To quantify, how the quality of the classification changes over the iterations, for XGBoost and CatBoost, it is necessary to define a quality metric. Defining this metric allows one to express the changing of the classification quality against the complexity of the GBDT algorithm and can be easily used to control the overfitting. Widely used quality metrics are accuracy, precision, recall, and F1-score; however, these metrics are sensitive to the imbalance in number of training sources among different classes. Therefore, we decided to use Matthews correlation coefficient (MCC, Matthews 1975 ) which is instead insensitive to this imbalance. Finally, a good way to decrease the number of stars and galaxies classified by the algorithm as quasars is to apply a weight to the loss function of these two classes. In fact, this trick, applied to CatBoost, helped us in the paper to improve the final purity of the quasar selection with a minimal decrease in the completeness of the training set. In particular, we weighted the loss function for the STAR and GALAXY samples in the following way: where w i = 1 if source is a QSO and w i = 4 if source is STAR or GALAXY . A.2. Random Forest Another method of ensemble learning with decision trees is based on the use of an RF ( Breiman 2001 ) algorithm. This was the choice adopted in KiDS DR3 by N19. The basic idea of RF is that a set of decision trees can fit a robust classifier by averaging their decisions. From the performance side, the RF constructs a large number of decision trees and then uses the majority vote among them. The main pipeline of the single decision tree includes the following steps: (1) generation of different samples from the training set with the same size, but using random subsets of all the objects. The repetition of some objects among different subsamples is required to make the sample complete (so-called, random subsample with replacement); (2) let the decision tree learn on the “random subsample with replacement”, generated at step (1), but using randomly selected features. The RF therefore consists of many learning processes, each performed on a single decision tree using different

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


that the near-isothermal density profiles were found to be broadly consistent with MOdified Newtonian Dynamics (MOND). With this greater sample of total- mass profiles that cover a greater stellar mass range, new tests of MOND and the general mass-discrepancy–acceleration relations can be made. In order to make useful comparisons between simulations and observations, it is necessary that exactly the same measurements are made for each. Currently, there is great difficulty in achieving this, since observational measurements are best constrained in the inner regions of galaxies, while the resolution limitations of cosmological simulations mean that measurements for simulated galaxies are best constrained at radii greater than ∼0.5 R e . This means that while care can be taken to make measurements in the same way, the underlying data are fundamentally different. 8 SUMMARY AND CONCLUSIONS We measure total-mass density slopes for 21 fast-rotator ETGs of the SLUGGS survey (Brodie et al. 2014 ), including a greater number of galaxies in the low-mass range than the previous study by Cappellari et al. ( 2015 ). These measurements are made by conducting dynamical mass modelling on 2D kinematics that extend to large radii. We apply the jam mass-modelling technique (Cappellari 2008 ), using two different parametrizations of mass distribution to recover the total-mass density profiles for individual galaxies. We determine that the best fits of the model kinematics to the input kinematics of each galaxy are produced by the model in which the total mass is separated into its stellar and DM components, where the DM distribution is parametrized as a double power law (as given by equation 2 ). We find that the measured total-mass density slope values are robust to slight variations within the applied modelling, whereas the separation of stellar and DM is much more degenerate, and susceptible to such variations in the modelling. In order to be consistent with Cappellari et al. ( 2015 ), we measure γ tot values for each galaxy by fitting a power-law slope to the stellar plus DM profile in the radial range 0.1–4 R e , and find an average total-mass density slope of γ tot = −2.24 ± 0.05 for our sample of 21 galaxies, identifying no discernable trend with stellar mass. We collate measurements of total-mass density slopes from multiple observational studies, for a comprehensive overview of the γ tot behaviour across a broad range of stellar masses, utilizing an array of data-types and measurement techniques. Overwhelmingly, the studies all tend to produce consistent results when including the central regions, as shown in Fig. 6 . This is despite the fact that the data utilized have varying radial extents for individual galaxies – an indication that these slopes do not display much variation with radius. We find that there tends to be very little trend with stellar mass, and that the slight shallowing of total-mass density slopes we see at lower stellar masses may not

O O O O O O O O O O O O B-Model I-Model I-Model B-Model 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 B-Survey O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 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 B-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O B-TextGarbage O O O O O O O O O O O O O B-Model O O O O O O O O O O B-Model I-Model I-Model O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Model O O O O O O O O O O O O O B-Model O O O O B-Citation I-Citation O B-Citation O O O O O O O B-Citation O O O O O O O O O O B-TextGarbage O O O O O O O O O B-Model O O O O O O O O B-Model O O O B-Dataset O B-Dataset I-Dataset O O O O O O O O O O O O O O O O O O O O O O O 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-Tag I-Tag O O B-Dataset I-Dataset 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 B-CelestialObject B-TextGarbage I-TextGarbage I-TextGarbage I-TextGarbage 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