their faintness ( V > 13.5, J > 11.5). This is somewhat expected since the two catalogues are based on different methodologies and input catalogues reflecting different scientific priorities. While K2-TESS is more focused on cool SpTs (late K and M dwarfs) and mainly based on the 2MASS infrared photometry, UCAC4-RPM is focused on solar-type FGK targets, implying different selection algorithms and thresholds. In other words, the two approaches will be highly synergic in selecting the optimal targets for TESS (Stassun et al. 2014 ). 5.2 PLATO The unique optical design of PLATO (Rauer et al. 2014 ) is driven by the requirement to cover a significant fraction of the sky with a good image quality in order to achieve an unprecedented photometric precision: 34 ppm h −1 (parts per million measured over a 1 h time-scale) for the main scientific sample limited at V 11, and even better for the brightest stars of the sample at V ≃ 6 (dominated by systematic errors). The present design of PLATO implies that the array of 12 cm telescopes is subdivided into four groups, each group pointing towards a direction which is displaced by an angle θ = 9.2 deg from the centre of the overall FOV. Such strategy provides a non-uniform instantaneous coverage of a 2124 deg 2 field. The observing strategy of PLATO consists of a two-step approach in order to maximize the scientific return of the mission. PLATO will image two ‘long-duration’ (LD) fields for more than two years each, and some supplementary fields for a few months each, during the ‘step and stare’ (SS) phase. The LD phase will fulfil the main scientific objective of the mission, being sensitive to planets down to the Earth's size orbiting within the habitable zone of solar-type (FGK) stars. The SS fields will expand the accessible sky area by about one order of magnitude, giving us access to a larger number of bright nearby stars at the expense of probing a smaller range of orbital periods. A simple calculation shows that, at the end of a nominal 6.5 year mission with 2 LD and 10 SS fields, PLATO will have surveyed about two thirds of the whole sky. The PLATO Science Requirements Document 10 defines five complementary stellar samples to be surveyed, listed in decreasing priority and summarized below. P1: DSLF5 stars brighter than V = 11, monitored with a photometric noise level σ ≤ 34 ppm h −1 , to be observed during the LD phase. P2, P3: DSLF5 stars brighter than V = 8, monitored at σ ≤ 34 ppm h −1 , to be observed during the LD and SS phase, respectively. P4: cool M dwarfs (M0 or later), to be monitored during the LD phase of the mission (at V 16), or during the SS phase (at V 15). The photometric noise level for both subsamples must be below 800 ppm h −1 . P5: DSLF5 stars brighter than V = 13, to be observed during the LD phase. Samples P1, P2, P3, P5 are therefore all made of ‘solar-like’ stars brighter than V = 13. Due to telemetry limitations, PLATO will not be able to download the full images, collected

O O O B-Wavelength 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-Mission O O O O O O O O O O O O O O O O B-Survey B-Wavelength 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 B-Telescope B-Citation I-Citation I-Citation I-Citation O O B-Telescope O O B-Wavelength O O B-Telescope B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O B-Wavelength 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 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 B-Telescope 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope 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 O O O B-Dataset O O O B-Wavelength 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 B-Dataset O O O B-Wavelength 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 B-Wavelength 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 B-Dataset 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-EntityOfFutureInterest O O O B-Wavelength O O O O O O B-Telescope O O O O O O O O O O


would be one of the possible reasons for the difference between 2014 and 2016. Because the energetic electrons drift slower than the corotation and they spent more time in the inflow/outflow sectors, the drift orbit of higher-energy electron displaces more than that of the lower energy electron. However, statistical analysis indicated that the IPT and JSR did not have a strong positive correlation as expected from the hypothesis. Figure 3 indicates the scatter plot of the dusk-to-dawn ratio of JSR and IPT. Spearman’s rank correlation coefficient is −0.22 for 2014 and 0.048 for 2016. A correlation t-test at 10% significance level shows that JSR and IPT are regarded as having no correlation. The correlation between JSR and the solar wind dynamic pressure is not significant either. The energetic electrons drift slower than the corotation, which means that they may take longer to organize over all longitudes when a change in the dawn-dusk electric field occurs. The rotation period (corotation + magnetic gradient drift) of 10 MeV and 16 MeV electron are ∼10.5 hr and ∼11.0 hr at 1.5 Rj , respectively. In this study, response delays can be negligible comparing to the observation cadence. We do not consider any time lag between IPT and JSR, because the dawn-dusk electric field affects JSR and IPT at the same time. Hence, the short-term variation in the dawn-dusk asymmetry of JSR cannot be explained only by the dawn-dusk electric field. Figure 3. Scatter plot of the dusk-dawn ratio of IPT and JSR for 2014 and 2016. indicates Spearman’s correlation coefficient. Although these results did not support our hypothesis, we cannot rule out the possibility that the dawn-dusk electric field was masked by some other processes that could control the short-term variations in the dawn-to-dusk ratio of JSR. Here, we discuss the possible causalities of why the correlation is weak. Because the ionospheric potential difference induced by the field-aligned current depends on the ionospheric conductivities, the solar UV/EUV effect might appear in the dawn–dusk asymmetries of JSR. The stronger the solar UV/EUV, the weaker the dawn-dusk electric field because of higher conductivity. The third panel of Figure 2 indicates the solar UV/EUV. We cannot find a strong correlation between both dusk-to-dawn ratios and the solar UV/EUV; however, the conductivity variation should be taken into account. Because the ionospheric potential difference is the source of the electric field, the ionospheric potential map should also be taken into consideration. Dawn-dusk electric field is mapped from the ionospheric potential difference induced by the field-aligned current. As the potential difference becomes smaller at the lower latitude, the effect of the dawn-dusk electric field would be smaller in the innermost magnetosphere. The study with an ionospheric potential solver (e.g., Nakamizo et al. 2012 ) for Jovian ionosphere would give us a clue to estimate these effects quantitatively.

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


in the strength of the BLR–H β component, in addition to that observed in the Fe II strength. However, a remarkable simultaneous variation in both H β and Fe II strength is what we would expect in the case when the two emissions are strictly co-spatial, whereas we know that the BLR is stratified and that microlensing magnifies the emission from the most compact regions more strongly. Therefore, we do not exclude the microlensing hypothesis. A detailed analysis of the different BLR spectra from the two images is beyond the scope of this work and will be presented in a forthcoming paper. Therefore, in this work, we focus on how we accounted for this effect during the spectral analysis. Consequently, in SDSS J1353+1138, we extracted two distinct nuclear spectra, namely, spectrum A and B that are shown in Fig. 3 , using a 03 radius aperture centred on the emission peak of each lensed image. We proceeded to fit them separately. In both spectra we used a first-degree polynomial to model the AGN continuum that is still dominant over the stellar continuum. Unlike the BLR modelling of HS 0810+2554, the multiple Gaussian fit was not sufficient to reproduce the broader and complex profile of the broad Balmer emission lines, especially the H β line in spectrum B. In fact, even though both H β prominent wings are likely due to the Fe II emission, as discussed above, the Fe II templates employed by the code were not able to reproduce such observed emission. Therefore, we modelled both wings as part of the broad H β line profile without any focus on their physical interpretation, as we were simply interested in identifying the overall BLR spectrum in order to remove it. For the modelling of the broad Balmer emission lines observed in SDSS J1353+1138 (i.e., H β and H γ ), we used a broken power law distribution convolved with a Gaussian profile ( Nagao et al. 2006 ): where the free parameters of the fit, for each line, are the central wavelength λ 0 , the two power-law indices α and β , the normalisation F 0 , and the width σ of the Gaussian kernel. In spectrum A (upper panel), the H β and H γ were modelled separately through the line profile described in Eq. ( 1 ). Spectrum B (lower panel) required instead an additional broad Gaussian component to suitably reproduce both the more extended red wing and the broad peak ( σ ∼ 800 km s −1 ) in the H β profile. Moreover, we had to constrain the H γ line profile through that of H β . Different Fe II templates have been selected in the BLR best-models for the two nuclear spectra. To model the narrow emission line profiles, we used three Gaussian components in spectrum A, while a single Gaussian component in spectrum B, since we did not actually observe any narrow component. Then we proceeded to fit the whole data cube following the procedure described in Sect. 3.1.2 , with the main difference that in each spatial pixel, pPXF considered a linear combination of the two BLR models, weighing their relative contribution

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


of a given amount of external irradiation. Fig. 4 illustrates this. It is a disc with an accretion rate of M ⊙ yr −1 , approximately a third lower than in Fig. 3 . In this case (Fig. 4 ), external irradiation has added additional mass to the outer parts of the disc, as the equilibrium disc structure is now more massive for a given accretion rate and radius, although in this case it does not meet the criteria required for it to fragment (which requires that the local α ≳ 0.1). In this disc, the external irradiation is maintaining Q ∼ 2 with little dissipation of the GI. In reality, we should expect Q to increase beyond the marginal limit of self-gravity in the outer parts of such discs. Figure 4. Disc with M ⊙ yr −1 , 33 per cent lower than the maximum it can sustain without truncating. It is irradiated at 10 K, and this small amount of external irradiation has altered the surface density structure of the outer parts of the disc, as the equilibrium disc structure is now more massive for a given accretion rate and radius. The ‘spiky’ features on the boundary between the outer and inner parts of the disc are a numerical artefact due to a small change in surface density from the resolution limit of the grid, and are more pronounced in log space. We should bear in mind that this is a simple model in which no infall is considered. Since, in general, adding mass to the outer regions of a self-gravitating disc encourages fragmentation (Kratter et al. 2010 ; Vorobyov Basu 2010 ; Kratter Murray-Clay 2011 ; Forgan Rice 2012 ), it seems that the Jeans criterion for fragmentation may be satisfied at relatively high accretion rates (of the order of ∼10 −7 M ⊙ yr −1 ) in the presence of sufficiently small (∼10 K) irradiation. Fig. 5 shows a contour plot of the amount of external irradiation required to prevent fragmentation of the disc as a function of accretion rate and radius. Below ∼3.2 × 10 −7 M ⊙ yr −1 , in our local viscous approximation, any disc will be able to regulate itself against collapse. Above this, differing amounts of irradiation can either prevent fragmentation and totally remove spiral features from the disc, or prevent fragmentation whilst allowing spiral features to exist. As accretion rate increases, higher temperatures are required to prevent the disc from fragmenting; additionally, beyond 60 au the determining factor in whether spirals are present or not is temperature, rather than a combination of temperature and accretion rate. Figure 5. Contour plot showing the minimum temperature in (K) of external irradiation required to halt fragmentation as a function of accretion rate and radius. The shaded region with dashed contours shows where both fragmentation is suppressed and spiral features are erased. The unshaded region with dotted contours shows where added irradiation prevents fragmentation but preserves spiral structure. 3.2 Comparison with imposed constant β In our model, unlike in SPH simulations by Dipierro et al. ( 2014 )

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


∼10% at z = 18 to 23% at z = 12. While this is not an observable, it is an additional independent cross-check for our approach. 4.3. When Is <italic>dZ</italic> Important? In Figure 10 , we show the distribution of dZ as a function of physical parameters. Since dZ is most important in external enrichment, these panels indicate under what conditions external enrichment becomes important. For some stars with low [Fe/H] (≲−4), dZ is largely negative. This means that the metallicities of these stars would have been much higher if we assumed homogeneity. The clear cut at [Fe/H] ∼ −5.1 comes from our Population II star formation criterion. For stars with [Fe/H] > −5.1, we do not require carbon enhancement to form stars, whereas if [Fe/H] −5.1, we do require carbon enhancement (see Equation ( 2 )). Highly negative dZ means high (naively calculated) [Fe/H], which is therefore less likely to be carbon-enhanced and allowed to form stars. Figure 10. Distribution of dZ as a function of various physical properties of stars. (Top) For stars with [Fe/H] −4.5, external enrichment is the dominant channel. Therefore, inhomogeneity is important for such ultra-metal-poor stars. (Middle) For large, matured halos (), star formation has already begun; therefore, they are internally enriched. External enrichment is important when we consider star formation in small galaxies (). (Bottom) For star formation events at a very high redshift, external enrichment plays a role. The middle panel shows that in small halos, dZ can be largely negative. In massive galaxies (), star formation has already begun; therefore, they are internally enriched and well mixed. Combining with our former analysis of the dZ distribution, we find that the metallicity inhomogeneity is less significant in massive galaxies. The bottom panel shows that dZ is only important at high (although not the highest) redshifts. Low-redshift galaxies are homogeneous for the same reason as the massive galaxies. The highest-redshift galaxies () are homogeneous because they do not have enough time after the first star formation events to experience external enrichment. In summary, inhomogeneous metal mixing is important in low-mass halos at high redshift that are about to form EMP stars. 5. Discussion We have performed the first cosmologically representative analysis of metal mixing in high-redshift galaxies. We derived a physically motivated estimate of dZ , the metallicity difference between star-forming and all gas, and find that the distribution of dZ is very different between halos with stars and halos without stars. This bimodality can be understood by assuming that two processes are at work: internal enrichment and external enrichment. Halos without stars have not experienced any star formation events, so they can be identified as externally enriched halos. In external enrichment, the momentum of metal-rich wind is not strong. If a galaxy already has a dense gas cloud when the external enrichment takes

O O B-Formula I-Formula I-Formula O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O B-Tag O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O B-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 halo contribution We estimate the average contribution from single LRG haloes as follows. Since we have selected central LRGs for our pair catalogue, we assume that the average single-halo contribution is circularly symmetric about each LRG in a pair. To determine the radial profile of each single halo, we analytially solve for the map (indexed by pixel p ) to a model of the form where y L,i is the single-halo signal in the ith radial bin centred on the ‘left’ LRG at (−1, 0), y R,j is the single-halo signal in the jth radial bin centred on the ‘right’ LRG at (+1, 0), and p = p ( X, Y ) is a pixel on the map as shown in Fig. 3 . When solving it, we choose radial bins of size Δ r = 0.02, and we weight the map pixels uniformly. To avoid biasing the profiles with non-circular filament signal, we exclude the central region −1 X +1 and −2 Y +2. Fig. 4 shows the resulting profiles for the LRG haloes. Figure 3. Illustration to estimate the radial profile of each single halo. The y value at a pixel p, y h ( p ), is the sum of ith radial bin centred on the left LRG at (−1, 0), y L, i ( p ), and jth radial bin centred on the right LRG, y R, j ( p ) at (+1, 0). To avoid biasing the profiles with non-circular filament signal, the central region −1 X +1 and −2 Y +2 is excluded. Figure 4. Top : The circular halo profiles estimated to the map in Fig. 2 . Bottom : The radial profile of the left and right haloes shown above. Fig. 5 shows the residual y map after subtracting the circular halo profiles shown in Fig. 4 (note the change in colour scale from Figs 4 and 5 ). The bright halo signals appear to be cleanly subtracted, while a residual signal between the LRGs is clearly visible. The lower panels of Fig. 5 show the residual signal in horizontal ( Y = 0) and vertical ( X = 0) slices through the map. The shape of the signal is consistent with an elongated filamentary structure connecting average pairs of central LRGs. The mean residual signal in the central region, −0.8 X +0.8 and −0.2 Y +0.2, is found to be Δ y = 1.31 × 10 −8 . Figure 5. Top : The residual y -map after the radial halo signals are subtracted. Bottom : The residual tSZ signal along the x- and y -axes. 3.3 Null tests and error estimates To assess the reality of the residual signal and estimate its uncertainty, we perform two types of Monte Carlo-based null tests. In the first test, we rotate the centre of each LRG pair by a random angle in galactic longitude, for example, the centre of one LRG pair is rotated from [ l, b ] = [10°, 60°] to [ l, b ] = [150°, 60°]. (Keeping the latitude fixed keeps the galactic foreground level in the y map approximately fixed.) We then stack the y map against the set of rotated LRG pairs, and we repeat this stacking of the full catalogue 1000 times to determine the rms fluctuations in the background (and foreground) sky. Fig. 6 shows one of the 1000 rotated, stacked y maps: the map has no discernible structure. We can use this ensemble of maps to

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


two or more consecutive CMEs originated in the same source region. It is worth to note that the maximum fraction of free energy exhausted by one CME may be 25% ( Gopalswamy et al. 2005 ; Emslie et al. 2012 ; Feng et al. 2013 ). Finally, the speed distributions of all leading/trailing CMEs show a small but systematic tendency to have higher mean and median velocities for shorter WTs. The mean and median speed of the trailing CME are a few km s −1 higher than that of the leading CMEs, for WTs shorter than 7 h, after a WT of 10 h the differences remain constant and negligible. Nevertheless, these differences are higher (tens of km s −1 ) when we only take into account spatially-related CMEs (see Fig. 8 ). As the mean is not the best location indicator for highly skewed distributions, we also analyzed the quartiles (which are better suited to characterizing these distributions), the results are plotted in Fig. 9 . To assess the accuracy of the analysis, we applied the sign test to show that the differences between the medians of trailing and leading CMEs are statistically significant. The phases of the solar cycle where the sign-test probability (with the null hypothesis H 0 : ) is less than 0.1 are shown in Figs. 10 and 11 . These observations may be explained by the drag force models. It is clear that the magnetic field provides the necessary energy to launch and first acceleration of CMEs. Although this energy does not play an important role in the CME dynamics after few solar radii, at least for fast CMEs (such as those that form the tail of the distributions). Recently, Sachdeva et al. (2017) investigated CME dynamics using coronographic observations, and they concluded that for fast CMEs, the Lorentz force has its maximum effect at heights lower than 2.5 R ⊙ , and then, at heights of 3.5–4 R ⊙ becomes negligible compared with the drag force. In the case of slow CMEs, the Lorentz force may be significant at larger distances (up to 50 R ⊙ , but slow CMEs do not contribute to the tail of the distributions). The drag force is proportional to the drag coefficient ( C D ), the transverse area of the CME ( A ), the speed difference between the CME ( V CME ) and the solar wind ( V SW ), and the ambient density ( ρ ) ( Cargill 2004 ; Borgazzi et al. 2009 ; Vršnak et al. 2010 ). In a statistical analysis of a large number of events, the main values of A and V SW are similar for both leading and trailing CMEs. On the other hand, the leading CME may sweep the ambient medium, and the trailing CME encounters a less dense medium and therefore the drag force decreases, resulting in a faster CME. In this case, the shorter the WT, the higher the CME speed. This effect is clearly seen in Figs. 10 and 11 . 10. Conclusions We performed a statistical study of 27 761 CMEs observed by SOHO/LASCO from the ascending phase of cycle 23 to the declining phase of cycle 24, looking for long-range or memory signatures in the genesis and the first stages of evolution of

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-CelestialObject 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 B-ObservationalTechniques I-ObservationalTechniques O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Observatory O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


therefore becomes is the change of phase angle. In other words, the wave propagates forradians before producing a shock, where the bracket means a time average along the wave front. The total propagation time is proportional to , so stronger and higher-frequency waves shock earlier. 3.3. Maturation of the Shockwave To estimate the point of intersection between the wave peak and shock front, we derive their respective trajectories. First, suppose a monochromatic wave with luminosity and frequency ω is led by a compressive edge (i.e., ). The wave peak initially lags behind the wave front by a distance . The peak propagates with a speed , where is the compressed local sound speed. Assuming properties of the gas do not vary significantly under compression (i.e., constant and ), we can write the compressed sound speed in terms of the peak pressure p w . The thermodynamic expression of the mean wave energy density allows to be expressed in terms of conserved wave properties, With the kinematic expression ( 3 ), the speed of the wave peak becomes Before shock formation (), the wave front simply travels at the local sound speed c s0 . For , the exact shock velocity requires numerical calculations to describe the arrival of the remaining wave pulse. We circumvent this calculation by approximating the shock front strength with the wave peak properties (). With the following shock jump condition,we approximate the shock Mach number to be Thus, the wave peak and shock front converge at the same location , onceis satisfied. 4. Hydrodynamic Simulations To test our analytical predictions of shock formation and provide examples of shock evolution and strengthening, we turn to numerical simulations. We construct 1D planar and spherical simulations in FLASH (Fryxell et al. 2000 ), a hydrodynamic adaptive mesh refinement (AMR) code. All quiescent structures begin in hydrostatic equilibrium with a gravitational acceleration g ( r ) that is independent of fluid perturbations (Cowling’s approximation). All simulations have inner reflecting and outer diode (outflow) boundary conditions. Two structures are considered: a planar isothermal atmosphere and a n = 3 stellar polytrope. The adiabatic index is held fixed in all of our simulations. 4.1. Planar Earth Atmosphere For planar shock formation, we consider a vertically stratified, initially isothermal atmosphere of gas (FLASH’s default Earth atmosphere) with in constant gravity. Lengths in this section should be compared to the 8.8 km scale height of the model, although the results can be scaled to any similar atmosphere. Upward-travelling waves are initialized by setting the isothermal atmosphere out of equilibrium; an example of the initial waveform and its evolution is shown in Figure 1 . The initially sinusoidal wave steepens (Phase 1) and forms a shock at the wave node, after which the wave peak approaches (Phase 2) and merges with the shock front. Figure 1. Deformation of a single sinusoidal impulse in a planar,

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


separately for the stellar subset (H ipparcos and Tycho-2 stars) and the quasars. Table 1 , experiment 1, presents the median value of the parallax errors (estimated minus true), the uncertainty of the median calculated using the bootstrap method, and the RSE 4 dispersion of the parallax errors for each of the subsets. The different columns give statistics for selections based on the individual formal standard uncertainties of the parallaxes. The median obtained for the quasar subset agrees with the corresponding stellar value to within a few as, independent of the selection of sources. Table 1 Simulation results of three different experiments comparing the parallax median between the stellar subset and the quasars. Notes. “Stars” refers to the combined subset of H ipparcos and Tycho-2 sources. In each subset, statistics are given for the selection of 90% of the sources with the smallest individual formal uncertainties and for all sources together. The values given are the median (and its uncertainty from the bootstrap method) and the RSE dispersion of the parallax errors (estimated minus true). 3.2. Spurious proper motion from variable source structure Variation in the source structure of quasars can lead to shifts of their photocentres up to the milliarcsecond level (e.g. Popović et al. 2012 ; Porcas 2009 ; Taris et al. 2011 ). Linear trends of these shifts might lead to spurious proper motions measured for quasars and stable over years to decades. Titov et al. (2011) fitted long-term proper motions for 555 quasars from VLBI observations. The total proper motion in as yr in their catalogue can be described by a log-normal distribution with mean 1.9 dex and standard deviation 0.61 dex. It is impossible to say whether these measurements give an optimistic or conservative characterization of spurious quasar proper motions on the much shorter time baselines of our simulations. Additionally, the morphology of the host galaxy might lead to a statistical increase in the centroiding error, and photometric variability of the nucleus together with the stable photocentre of the host galaxy might lead to an effect similar to “variability-induced movers” in binaries ( Wielen 1996 ). Physically all of these effects are expected to be random and therefore should only increase the dispersion of the results but not the median values themselves. We use the statistical properties of the results by Titov et al. (2011) as the basis for simulations, but apply a factor of 10 to provide a conservative assumption on the total spurious motion. The individual components of the proper motion are computed as where is a random position angle and is taken from a normal distribution with mean value 2.9 dex and standard deviation 0.61 dex. The median value of the resulting is about 800 as yr. While this spurious proper motion increases the RSE of the solution for the quasar subset, the agreement of median parallax between the quasars and the stellar subset remains at the

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


induced by turbulence (e.g. Raettig, Klahr Lyra 2015 ; Manger Klahr 2018 ) can concentrate dust particles (Barge Sommeria 1995 ; Klahr Henning 1997 ; Cuzzi, Hogan Shariff 2008 ) and seed planetesimal formation through streaming instability or gravitational instability (Youdin Goodman 2005 ; Johansen et al. 2007 ; Chiang Youdin 2010 ), whereas the growth of streaming instability can be substantially diminished by a moderate level of turbulent viscosity (Chen Lin 2020 ; Umurhan, Estrada Cuzzi 2020 ). Turbulence also influences the radial migration of planets, as well as the flow morphology and gap formation around them (Nelson Papaloizou 2004 ; Papaloizou, Nelson Snellgrove 2004 ). Therefore, understanding the origin and characteristics of turbulence in PPDs is essential to many aspects of planet formation and evolution. The lack of magnetohydrodynamic (MHD) turbulence in a PPD led to a surge in the interest of purely hydrodynamic instabilities (Lyra Umurhan 2019 ; Weiss, Bai Fu 2021 ). Among the most explored are the vertical shear instability (VSI; Nelson, Gressel Umurhan 2013 , hereafter N13 ; Lin Youdin 2015 ; Latter Papaloizou 2018 , hereafter LP18 ; Cui Bai 2020 ), the convective overstability in its linear (Klahr Hubbard 2014 ; Lyra 2014 ; Latter 2016 ) and non-linear (subcritical baroclinic instability; Klahr Bodenheimer 2003 ; Petersen, Julien Stewart 2007a ; Petersen, Stewart Julien 2007b ; Lesur Papaloizou 2010 ) phases, and the zombie vortex instability (Marcus et al. 2013 , 2015 ; Lesur Latter 2016 ; Umurhan, Shariff Cuzzi 2016b ). These instabilities set in under certain thermodynamic and structural conditions, thereby operating at distinct regions of PPDs (Malygin et al. 2017 ; Lyra Umurhan 2019 ; Pfeil Klahr 2019 ). The VSI is of particular interest as it extends a large portion of the disc (e.g. Lin Youdin 2015 ; Lyra Umurhan 2019 ). The VSI is inherited from the Goldreich–Schubert–Fricke instability (Goldreich Schubert 1967 ; Fricke 1968 ) and is initially discovered in the context of differentially rotating stars. Its importance to accretion discs was later explored by Urpin Brandenburg ( 1998 ), Urpin ( 2003 ), and Arlt Urpin ( 2004 ). The applicability of the VSI to PPDs has been demonstrated only recently in N13 . It quickly drew intensive interests (e.g. Stoll Kley 2014 ; Barker Latter 2015 ; Umurhan, Nelson Gressel 2016a ; LP18 ; Lin 2019 ; Cui Bai 2020 ; Flock et al. 2020 ; Schäfer, Johansen Banerjee 2020 ; Flores-Rivera et. al. 2020 ) and is considered to be a promising hydrodynamic mechanism in driving turbulence in PPDs. A differentially rotating disc with Keplerian profile is stable according to the Rayleigh criterion (Chandrasekhar 1961 ). The presence of vertical shear can destabilize inertial waves in a vertically global disc model (Barker Latter 2015 ). Nevertheless, a fluid element also experiences stabilizing effects from vertical buoyancy, which impedes the VSI growth. This can be overcome by

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


to contextualize this nebula, we measured the SB Ly α profile through the standard NB images, similar to previous works ( B16 , A19 ). We computed the circularly averaged profile from the pseudo-NB image obtained by collapsing the MUSE data cube using the maximum spectral size of the 3D mask as the width, which in the case of our Ly α emission is 30 Å. We then performed an exponential fit and a power-law fit above the 2 σ noise limit, i.e., SB of ≈0.5 × 10 −18 erg s −1 cm −2 arcsec −2 , that returns a normalization parameter (at a radius of 10 pkpc) of log 10 ( C p , r 10 ) = −15.8 and a slope α of −2.4, compatible with other Ly α SB profiles obtained with MUSE. More details on the fitting process are provided in Appendix B of B16 . The red line in Figure 7 shows the circularly averaged values computed in units of SB × ((1 + z )/4) 4 with an extent of more than 100 pkpc from the QSO. We chose these units because we wanted to perform a consistent comparison of the J0952+0114 SB profile with the other Ly α systems in the literature and therefore avoid any redshift dependence and cosmological dimming effects. Figure 7 also shows the comparison with previous works as the median profile of the MUSE QSO nebulae we published in Borisova et al. 2016 (purple line, see also Appendix C ) and the best exponential fit to the QSO MUSEUM sample ( A19 , blue line). As discussed later in Section 5 , the outer parts (beyond 10 pkpc) of the J0952+0114 SB profile are very similar to what we found in other giant fluorescent nebulae around QSOs at z ≈ 3. The innermost regions are brighter due to the presence of the PDLA; however, this could reflect the difficulty of tracing the nebula into the center of typical objects (without PDLAs). Figure 7. Ly α surface brightness (SB) profile of the J0952+0114 nebula as a function of the projected physical distance from the QSO. The circularly averaged profile is plotted with the red solid line. Other Ly α SB profiles are also plotted for comparison. In particular, the median SB profile of the MUSE Ly α nebulae from B16 is shown in purple with the dashed lines marking the 10th and 90th percentiles. This median profile has been rescaled to z = 3. The best exponential fit (and its dispersion) of the SB profiles from the QSO MUSEUM is plotted with the solid blue line (light blue area, Arrigoni Battaia et al. 2019 ). 4.4. He <sc>ii</sc>/Ly<italic>α</italic> and C <sc>iv</sc>/Ly<italic>α</italic> Map Ratios Ly α λ 1216, C iv λ 1550, and He ii λ 1640 are some of the brightest rest-frame UV lines employed to better constrain the nature of ionized gas in emission. In particular, the ratios of these lines, i.e., He ii /Ly α and C iv /Ly α , are particularly useful for insights into the physical properties of the emitting gas, such as the ionization parameter, density, and metallicity (Villar-Martin et al. 1997 ; Arrigoni Battaia et al. 2015 ; Prescott et al. 2015 ; C19 and references therein). Differently from previous works, in

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


optically thin, and uniformly expanding shells as the source of emission in the line wings, since they produce a top-hat line profile without individual emission peaks (e.g., Zuckerman 1987 , pp. 185–209; Cid Fernandes Terlevich 1994 ; Tenorio-Tagle et al. 1996 ; and also the Appendix ). However, the two-hump emission can be caused by a non-spherically symmetric shell or a shell having internal absorption (the other alternatives are analyzed and discarded in Section 5.2 ). Even though the observed amplitudes are similar, the blue component of each pair tends to be larger than the red component. Figure 9 shows the ratio between the areas of the red and blue components, and in all but one case, this ratio is one or smaller, considering error bars. Moreover, if one of the components is missing, it tends to be the red one. These two facts suggest a dusty expanding shell model, where the receding cap of the shell is obscured by the approaching cap (see the Appendix and Figure 17 ). These issues are discussed in detail in Section 5.2 . The color code employed in Figures 9 – 15 assigns a color to each galaxy, and then the different symbols of the same color correspond to the various pairs of secondary components in that galaxy. Figure 9. Area ratio between the blue and red emission of paired components vs. mean strength of the secondary components relative to the central component, i.e., area ratio vs. ε . Each point corresponds to one pair in one of the galaxies, as indicated in the inset—each galaxy has a color, and different symbols with the same color correspond to different weak components of the same galaxy. When only one component exists, it tends to be the blue one (they are marked with an asterisk in the inset). We show unpaired components as having an area ratio equal to zero. Except for ML32, the ratio is consistent with one or smaller. There is no obvious trend in the observed scatter plot. Using the equations in Section 3.3 , we have estimated the mass, mass loss rate, and kinetic energy associated with all the weak components in the H α wings (Section 3.2 , Figure 3 ). The mean values, as well as the errors, are given in Table 4 . The velocities and the ratio between the secondary components and the central component, ε , are provided directly by the multi-Gaussian fit described in Section 3.2 . In the case of paired components, the velocity is the mean of the absolute values of the two velocities, and ε is the total ε of the pair. The estimates also depend on the temperature and electron density of the emitting plasma, as well as on the relative thickness of the shell, , and the filling factor, f . Table 4 Parameters for the Weak Components in the H α Wings a Notes. a The errors in this table represent the standard deviation across the starburst (for velocity, ε , and area ratio) or errors for the value obtained from the mean H α line of the starburst (for the rest). b The number added to the galaxy name identifies each of the pairs of

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


are fully available in the machine-readable version. We present one catalog for each band, containing the 1730 SDSS+ATLAS cluster galaxies for which the pipelines ProFound + ProFit work. 4. Results We aim to shed light on the formation of S0 galaxies in clusters. In particular, we focus on understanding the relative importance of environmental processes acting in the cluster core and preprocessing acting in the cluster outskirts. We study the g − i colors separately for bulges and disks up to ∼2.5 R 200 , including the infalling cluster regions where galaxies are mainly in groups or isolated. We explore the color–magnitude relations for the two galaxy components. To understand the impact of the environment, we investigate the dependence of the bulge and disk g − i colors on the projected cluster-centric distance R / R 200 and the local galaxy density. We disentangle backsplash and infalling galaxy populations in the PPS. Finally, we compare the results for double-component galaxies with single-component disk-dominated galaxies. 4.1. Color–Magnitude Relations We aim to understand whether the bulge, disk, or both are responsible for the global galaxy color–magnitude relation observed in clusters. The study of the bulge and disk color–magnitude trends helps us to assess the mechanisms that drove the evolution history of the two components. We explore the extinction- and k -corrected bulge and disk g − i colors for the 469 double-component galaxies within 2.5 R 200 and with reliable bulge and disk measurements as described in Section 3.3 . Figure 9 shows the g − i color distributions for the bulges and disks. The disks are mainly shifted toward bluer colors with respect to the bulges. The median g − i offset separating the two distributions is 0.11 ± 0.02 mag. We find that 67% ± 2% of the galaxies have a bulge that is redder than the disk, while for the remaining 33% ± 2%, the bulge is bluer than the disk. Figure 9. Histogram in g − i color for bulges and disks of the 469 double-component galaxies within 2.5 R 200 . The dashed lines represent the median values. Disks are shifted toward bluer colors with respect to bulges by 0.11 ± 0.02 mag. We investigate the g − i color–magnitude relations for double-component galaxies and for bulges and disks in the left and right panels of Figure 10 , respectively. The total absolute magnitude of the galaxy M g has been estimated using , where D L is the luminosity distance measured using the cluster redshift. The k -correction and Milky Way extinction corrections are applied. We fit the g − i color–magnitude values using the Hyper-fit software, which takes into account the random uncertainties associated with the data (Robotham Obreschkow 2015 ). Figure 10. Color–magnitude diagrams for the 469 double-component galaxies within 2.5 R 200 (left panel) and the bulges (red and magenta) and disks (blue and light blue; right panel). In both panels, M g is the total absolute magnitude of the galaxy. The

O O O O O O O O O O O O O O O O O B-Dataset I-Dataset I-Dataset O O O O B-Software I-Software I-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 B-Wavelength O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O B-Wavelength O B-Wavelength O O O O B-Software I-Software 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


initial selection of compact group candidates. They emphasize that the large angular size of the isolation region for low-redshift systems artificially removes them from a catalog. Figure 8 of Barton et al. ( 1996 ) shows that groups with larger isolation regions have smaller sizes for groups selected from the CfA redshift survey. Here, again the limiting apparent magnitude for the definition of the isolation radius is the limiting apparent magnitude of the catalog rather than a limit three magnitudes fainter than the brightest group member. Eliminating the isolation criterion includes these nearby groups at the expense of including compact group candidates that are substructures in massive systems. However, the compact group candidates within massive systems or in dense regions can be removed after the initial selection. In contrast, the low-redshift systems cannot be recovered. The probability of rejection as a result of the isolation criterion can increase with decreasing redshift depending on the details of the application. The lowest redshift compact group candidates have larger angular size and a correspondingly more extensive isolation region than more distant compact group candidates. Figure 7 (a) shows the difference between the redshift distribution of the MLCG systems and the SDSS DR6 compact groups. Because McConnachie et al. ( 2009 ) remove r 14.5 galaxies, they might miss some nearby groups, thus accounting for the difference. To test this conjecture, Figure 11 plots the redshift distribution of the MLCG systems containing only galaxies in analogy with the SDSS DR6 sample. Although we remove 407 MLCG systems containing bright members, we still identify plenty of compact groups in the local universe ( z 0.05) where SDSS DR6 compact systems are absent or rare. Figure 11. Redshift distribution of the MLCG systems containing only galaxies with (open histograms) compared with the SDSS DR6 compact groups (filled histograms, Sohn et al. 2015 ). Because we do not apply an isolation criterion in the selection algorithm, we also include compact group candidates in dense surroundings (see Figure 10 ). Indeed, the fraction of the MLCG systems in dense environments ( N C > 7) is larger than for the SDSS DR6 compact groups at all redshifts. Interlopers may occur more often in high-density regions, thus producing some of the MLCG systems with inflated line-of-sight velocity dispersions. Barton et al. ( 2007 ) emphasize that a study of some aspects of galaxy evolution in tight pairs and compact groups requires specialization to relatively low-density environments. As in pair studies, candidate systems in dense surroundings can be removed after the general group selection. 5.2. Environmental Effects The diverse local environments of compact groups have been discussed previously (e.g., Ramella et al. 1994 ; Ribeiro et al. 1998 ; Andernach Coziol 2005 ; Mendel et al. 2011 ; Díaz-Giménez et al. 2012 ; Pompei Iovino 2012 ; Díaz-Giménez Zandivarez

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With that purpose, we have selected seven regions where the dust-to-gas ratio is larger than the mean expected value for the diffuse ISM, and for consistency, we keep the same names as in Paper I : H1, H2, H4, L1, L2, L4, and M1. In regions H1–H4, the gas density value ρ is greater than 1 σ ; in regions L1–L4, it is lower than 1 σ ; and in region M1, the gas density reaches intermediate values. In all cases, conspicuous filaments of charged dust are formed aligned with the magnetic fields. We want to note that the computational domains for coagulation simulations are squared domains that contain the original regions, so their limits are slightly different from those in Paper I ; the properties of these regions are summarized in Table 1 . Table 1 Properties of the Selected Regions Note. Regions selected from the turbulence simulation (Paper I ) to study the performance of the dust coagulation algorithm. In all cases, they are taken to be squared regions of a fixed length as given in the table, and with a uniform resolution in x - and y -directions. Given a region, we extract the gas properties and particle positions and set them inside a new domain with normalized limits [0, 1] × [0, 1]. The boundary conditions are outflow to ensure that the divergence-free constraint holds, ∇ · B = 0. This implies that some mass of dust will be inevitably lost, but we will take this fact into account when discussing the performance of the algorithm. The initial dust population is homogeneous, with a common radius of 0.05 μ m, a charge of Z d = −17, and an internal solid density . As explained in Section 2 , the computational test particles have to be considered as the centroids of a squared cloud with linear size 2 b that depends on the dust content. At the initial stage, all the clouds have the same linear size, typically 1.4 times the pixel size; this means that the clouds span a region of 2 × 2 pixels. The system is then left to evolve an arbitrary amount of time that differs from simulation to simulation. The final time is subjectively set following the condition that dust particles have moved enough to produce substantial coagulation, but they have not been completely swept away from the domain. A typical value is (∼3 × 10 −3 Myr; see Table 1 ), which, when compared with the global simulation (), is ∼7% of the total time. Hence, we expect that the phenomena observed in the simulations presented here are representative of the evolution of the global system (Paper I ) at short timescales. Besides, if we compare this time with the typical lifetime of a molecular cloud (∼10 6 Myr; Hartmann et al. 2001 ), it is evident that the timescales treated in this work are so small that we can consider that the final size distributions are representative for a molecular cloud at any stage of its evolution, provided that the ambient conditions (temperature, ionization fraction, magnetic field strength, and density) are maintained. 3.1. Evolution of the Size

O O O O O O O O O O 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 O O O 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 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 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 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 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 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


(95 au). Blackbody dust at ∼135 K, as found in the longest wavelength source peaking at ∼40 μ m of our HD 36546 SED (Figure 2 ) would have to be located at ∼20 au from a 20 primary. Allowing for the superheat ratio = 100 K/71 K = 1.41 found by NIRDS for dust in the HR 4796A (A0.5V) ring at ∼75 au from its primary (Lisse et al. 2017 ) moves this location out to ∼40 au, closer to the Curie et al. estimate. The remaining discrepancy between the spectral and imaging radial distance estimates might be due to our poor current characterization of the MIR–FIR SED peak; to our lack of understanding of the superheat behavior of the HD 36546 outer dust (values of out to 5–15 have been reported by Rodriguez Zuckerman 2012 and Vican et al. 2016 ); or to the different sensitivities of scattered light ( surface area*albedo) versus thermal emission ( surface area*emissivity* T 4 ) measurements of circumstellar dust in a thick disk, which will weight closer-in dust thermal emission most highly (Watson et al. 2009 and references therein). Using the T ∼ 570 K fit to the continuum underlying the warm SED excesses in Figure 2 , we find that the dust component creating the ∼8 μ m peaked emission would have to lie somewhere near 1.1 au for pure blackbody behavior, or near 2.2 au for superheated grains with . Either estimate is well within the Currie et al. coronographic masking region, so no direct comparison is possible. 5. Conclusions (1) The HD 36546 primary is a nearly unextincted early A star, not a late B star. Our modeling favors A1.5V +/−1 subclass, which is slightly later than the A0V classification found from optical spectra (Currie et al. 2017 ). Both optical and near-IR spectra rule out spectral types earlier than A0. The best-fit photospheric models require very low or no extinction, implying that HD 36546 is in front of the 1–2 Myr old Taurus–Auriga star-forming region as seen from Earth, and that there is little to no in-system extinction of the primary star. (2) There are no detected 2.1–2.5 μ m CO emission lines due to fluorescing circumstellar gas, no HBr γ lines due to accretion, and no He i 1.083 μ m, Fe ii 1.256/1.644 μ m, or S(1) 1-0 2.121 μ m emission lines due to strong wind outflow. No emission lines due to neutral PAHs are present at 3.29 μ m. (3) From 0.7 to 4.0 μ m, the SED is not “flat” or “filled-in” by inner-disk hot dust as in YSOs or transition disks. There are the beginnings of warm dust excess flux in the 4.5–5.0 μ m region, agreeing with archival JHKLM photometry of the system (triangles in Figure 2 ) showing a rise in M-band and WISE W2. (4) There are indications of an unusual local maximum in the SED at 6–9 μ m. A similar feature was seen in the A3V, ∼10 Myr old debris disk system HD 131488 and at lower SNR for the similarly bright HD 121191 system (A8V, ∼10 Myr) by Melis et al. ( 2013 ) using T-ReCS. The Mittal et al. ( 2015 ) Spitzer /IRS disk survey contains another good spectral match, the HD 148657 (A7V, 12 Myr) system. The

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


interlopers, selection biases, and metallicity diagnostics. These errors can easily overwhelm the chemical enrichment signal as a function of environment, particularly at high redshifts. In addition, the diverse definition of environment makes comparisons across different studies ambiguous (Ellison et al. 2009 ; Peng Maiolino 2014 ). Cosmological simulations with a full three-dimensional formation history of cluster galaxies are a powerful tool to overcome observational biases and understand the physics of the environmental dependence of the chemical evolution (Davé, Finlator Oppenheimer 2011 ; Bahe et al. 2016 ; Genel 2016 ). In this Letter, we explore the MZR evolution as a function of the formation history of galaxy groups and clusters in IllustrisTNG, a large-scale cosmological simulation. Using a novel method of separating progenitor cluster galaxies into accreted and infalling categories, we report for the first time a clear systematic signature of ‘chemical pre-processing’ in cluster galaxies over the past 10 Gyr. We show the effectiveness of pre-enriched gas inflows in driving the chemical evolution of cluster galaxies out to twice the virial radius. 2 METHODS Our results are based on the IllustrisTNG simulations (Marinacci et al. 2017 ; Naiman et al. 2018 ; Nelson et al. 2018 ; Pillepich et al. 2018a ; Springel et al. 2018 ). The galaxy formation model is an updated and extended version of the Illustris model (Vogelsberger et al. 2013 ; Torrey et al. 2014 ). Details of the model modifications are described in Weinberger et al. ( 2017 ) and Pillepich et al. ( 2018b ). We use the TNG100 simulation that has a volume of ∼(100 Mpc) 3 and m b = 9.4 × 10 5 M ⊙ h −1 , where m b is the baryonic mass per particle. From the TNG100 simulation, we select all haloes with M 200 c ≥10 13.0 M ⊙ h −1 , where M 200 c is total mass enclosed within R 200 c (the radius within which the mean density is 200 times the critical density of the Universe at the halo redshift). This leads to a selection of 127 galaxy clusters and groups at z = 0. The mean cluster halo mass of our sample is 10 13.4 M ⊙ h −1 . We define the boundary of a cluster as twice the R 200 c of the cluster halo, which is similar to the splashback radius (Diemer et al. 2017 ). Out of all friends-of-friends (FOF) subhaloes associated with the cluster at z = 0, all galaxies whether centrals or satellites residing within twice the R 200 c make up our cluster member galaxy sample. Note that we exclude flybys and satellite galaxies in the process of splashing back at z = 0 from our analysis. We restrict this analysis to a stellar mass range of 10 9 –10 10.5 M ⊙ h −1 . The lower stellar mass cut is to minimize numerical uncertainties such that there are at least 1000 stellar particles per galaxy (a single star particle in TNG100 has a mass of about 10 6 M ⊙ h −1 ). We impose the upper mass cut of 10 10.5 M ⊙ h −1 to reduce contaminations from active galactic nuclei (AGN) activities (Pillepich

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


detected magnetic patches with red and blue lines (panel c). The intensity is normalized with the average intensity. The white and black magnetic fields indicate the positive and negative magnetic fields, respectively. The magnetic field is distributed in a network with a scale of several 10 Mm, and the structure of supergranulation can be seen. We note that although the maximum value of the colour bar for the magnetic field is 300 G, the maximum magnetic field strength exceeds 1000 G. The red and blue contours in panel (c) indicate positive and negative magnetic patches, respectively. Figure 3. The radiative intensity (panel a), the vertical magnetic field strength (panel b), and the detection of magnetic patches (panel c). The intensity is normalized by the average intensity I ⊙ . Panels (b) and (c) show the vertical magnetic field at τ = 0.01 surface. The red and blue lines indicate positive and negative magnetic patches, respectively. Fig. 4 shows the vertical magnetic field convolved with PSF and the detected features. The figure shows the raw simulated magnetic field (panel a), the magnetic field with the PSF of the Hinode /SOT (panel b), and the magnetic field with the PSF of SDO /HMI (panel c). SDO /HMI (panel c) shows the most diffused patches, and the field strength is weak on average. Figure 4. Magnetic field strength convolved with different kinds of PSF. The simulated raw magnetic field data (panel a), data convolved with the PSF of Hinode /SOT PSF (panel b), and data convolved with the PSF of SDO /HMI (panel c). Fig. 5 shows the probability density function (PDF) of the magnetic flux at the photosphere. Orange, green, and blue lines indicate the magnetic flux in the original raw data, the data with the PSF of Hinode /SOT, and the data with the PSF of SDO /HMI, respectively. The black line indicates the fitting result for a range that clearly shows the power-law distribution. The slope increases with increasing resolution, i.e. the raw simulation data show a steeper slope than the data with Hinode and SDO PSF. The power-law index of the PDF with Hinode ’s PSF (green line) is –1.848, consistent with Parnell et al. ( 2009 ), which showed –1.85 for the power-law index with the Hinode observation. This suggests that the simulated magnetic field data reproduce the real Sun nicely and support the appropriateness of the model in this study. Figure 5. The probability density function (PDF) at the photosphere. Orange, green, and blue lines indicate the PDF of the raw simulation data, the data with Hinode /SOT’s PSF, and the data with SDO /HMI’s PSF, respectively. The black lines are the fitted lines for their power-law distribution. Fig. 6 shows the results of our analysis for the detected magnetic field depths. |〈 B z 〉| means the absolute value of the vertical magnetic field averaged over each magnetic patches. We divide the horizontal axis into 100 bins. Each bin has the same size in logarithmic and linear scales for magnetic flux

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


and , our CDF is, analogously with Eq. ( A.2 )and using Eq. ( A.1 ), (The use of is merely a matter of convenience for the integration limits.) The basis functions, that is, any CDF caused by all objects having given fixed and , are now easy to write in closed form. They are obtained by replacing and in the integrands by the fixed and , setting , and using the integration limits to describe the inequalities between and to define the piecewise function . This replaces the integral by a sum of such basis functions each multiplied by the corresponding weight of the and bin. The resulting basis functions are given in Sect. 2.1. The above assumption of most orbits to be close to the ecliptic plane is only approximate, and one can always define populations (especially those of near-Earth asteroids) for which it is not true even approximately. Thus the validity of this assumption should be checked for the targets used. However, as we show in Sect. 4, the assumption works quite well (given the large model error budget in any case) with typical asteroid populations for which there is some concentration of viewing geometries sufficiently near the ecliptic plane. Appendix B: Ill-posedness caused by two-point variation observables As earlier, we consider the case when is (approximately) the same for the pair. Now we have, for two rotation phases and , so, with , that is, (due to symmetry, we only need to consider the interval ), we define iso- contours in the plane (for given ) by so, to have viable solutions for from , we must have , , and so exist for given only if ; that is, Denoting our CDF is thus Again, we can include the -distribution by expanding the integral in the same way as with Eq. (A.4). The basis function for a given in the two-point brightness scatter case is, from Eq. ( B.1 ), Although the -integral can be given in terms of elliptic functions, this is best computed by evaluating the double integral numerically. The maximum value of is obtained at : Our basis functions are closed-form expressions of those computed by Monte-Carlo sampling in Szabo Kiss (2008) . These can be used to determine the -distribution, although we found the accuracy inferior to the solution based on the variation observable , which was to expected. In principle, we can expand to for a -grid in the same way that were expanded to . However, a notable difference between the two-index basis functions of - or - data is that the all reach their maxima at the same point since the two-point comparison can always contain two equal brightnesses for any and . Thus the -curves of the of a given form a curve family with the same abscissae for the minimum () and maximum (); that is, members of the family can easily be mimicked by a superposition of other members unlike in the case of . A number of simulations indeed confirmed that are not usable for solving the inverse problem in practice; that is, -information is not recoverable from -data. Adding prior assumptions on the

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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-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


perpendicular to the mean magnetic field. The spectral hardness does not arise because the particle energy spectrum itself is hard, i.e., with , but rather because the distribution is anisotropic. Within the nonthermal tail of accelerated particles, lower energy electrons tend to be more aligned with the local magnetic field than higher energy electrons, so their synchrotron emission is comparatively weaker. This energy-dependent anisotropy has the effect of hardening the synchrotron spectrum. 3 3 We expect similar conclusions to hold for electrons accelerated by reconnection with a strong guide field, even in a nonturbulent environment. Indeed, in our simulations of magnetically dominated turbulence, the acceleration of particles attaining the strongest anisotropy is primarily due to reconnection (Comisso Sironi 2019 ). In laminar reconnection, the guide field would play the role of the mean field of our turbulent setup. Our results have important implications for the interpretation of the hard radio spectra of pulsar wind nebulae (PWNe), where the observed radio spectral index is typically (Gaensler Slane 2006 ; Reynolds et al. 2017 ). In the notable case of the Crab Nebula, the radio spectral index is (Hester 2008 ; Bühler Blandford 2014 ). Turbulence, which develops as an effect of MHD instabilities in PWNe (Porth et al. 2014 ), has been suggested to accelerate the radio-emitting electrons (Lyutikov et al. 2019 ; Xu et al. 2019 ). However, these studies simply invoked a hard particle spectrum () over some energy range, without addressing from first principles the origin of the accelerated particles. We have shown that producing hard radio spectra does not necessarily require an acceleration mechanism that transfers most of the available energy to a small fraction of particles (which is the case when ). Instead, hard synchrotron spectra may be produced by a relatively soft population of nonthermal particles with an energy-dependent anisotropy. Finally, note that our assumption of neglecting the effect of synchrotron cooling on the particle evolution is well justified in PWNe, where the cooling time of radio-emitting electrons is longer than the age of the system. For the Crab Nebula, it is generally quoted that the hard spectral slope persists over six orders of magnitude in frequency (for an extended discussion, see, e.g., Bietenholz et al. 1997 ). Since the hard range of our synchrotron spectra extends over four decades, contributions from turbulent regions with moderately different properties would be required. While a detailed comparison to the Crab Nebula radio emission is left for future work, we mention that in our model we would imply that (i) the total number of radio-emitting electrons is at least one order of magnitude higher than in the case with isotropic electrons. More precisely, the number of radio electrons increases by a factor of (ii) the initial magnetization of the plasma is relatively low and/or the predissipation

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


defined as AGNs all galaxies beyond the left line in the BPT ([NII]/H α ) diagram. In specific cases we refer only to “pure” AGNs, namely galaxies above the curve defined by Kewley et al. (2001) in the BPT ([NII]/H α ) diagram. Also, galaxies classified as PAS or PSB (and RET in the WHAN diagnostic) are always held together. Fig. 3 Nuclear diagnostic diagrams for the whole HRS sample limited to emission-line objects with S ∕ N > 3. In the left BPT diagram panel , the broken separation line between AGNs (red) and TRAN (pink) galaxies is from Kewley et al. (2001) , while the dotted separation line between TRAN (pink) and HII region-like nuclei (blue) is from K03. In the second BPT diagram panel , the extreme starburst classification line is from Kewley et al. (2001) , while the separation between LINER (pink) and SEY (red) is from Kewley et al. (2006) . We note that the pink filled symbols refer to different types of objects in the three diagrams. The third panel reports the BPT diagram for the minority of galaxies (101) with [OI] in emission. In the WHAN diagram the separations between the different classes are from Gavazzi et al. (2011) . Fig. 4 Integrated diagnostic diagrams for emission-line objects with S ∕ N > 3. Brokenseparations in the diagrams are the same as in Fig. 3 . Despite the different populations and classification criteria, the WHAN and the BPT nuclear diagnostics give consistent results (see Table 2 ). Hereafter, two different percentages are always reported, one is the value resulting from one of the [NII]/H α or [SII]/H α BPT diagrams and the other is from the WHAN diagram. Between 53 and 64% of the nuclear spectra are HII region-like nuclei. The remaining percentage is divided between AGNs (21–27%) and PAS (15–21%). The “pure” AGNs are half of the AGNs percentage: 7–13%. These are galaxies ionized by a SMBH. Restricting to the 254 LTGs alone, the statistics is altered (see right columns of Table 2 ): the HII-regions increase to 67–77%; the AGNs become 21–27%; and the PAS spectra decrease to 2–7%. The latter class includes two PSB galaxies: HRS-116 and HRS-195. These two objects show a late-type morphology, with a central bulge and spiral arms, but the SF activity has been stopped suddenly. Also HRS-164 is a LTG with a PAS spectrum: its morphology shows a strong barred structure in the center, but it is an old and red object. A comparison between the nuclear and integrated spectral classifications can be performed among the subsample of HRS galaxies with available nuclear and integrated classification (see Figs. 5 , 7 , and 8 ); the subsample is reported in Table 3 . This comparison provides information about how the excitation properties of galaxies change from the center to the outskirts. As can be seen in the three figures, AGNs represent 18–26% in the nuclear spectra; while in the integrated they decrease to 4–11%. HII-regions are 59–71% in the nuclear classification, becoming 69–84% among the integrated spectra. PAS

O O O O O O O O O O O B-ObservationalTechniques B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O B-ObservationalTechniques B-Wavelength I-Wavelength O O O O O O O O O O O O O B-ObservationalTechniques I-ObservationalTechniques O O O O O O O O O O O O B-Dataset I-Dataset O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O B-ObservationalTechniques I-ObservationalTechniques O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O B-Citation O O O B-ObservationalTechniques I-ObservationalTechniques 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 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 B-ObservationalTechniques I-ObservationalTechniques O O O O O O O O O O O O B-ObservationalTechniques I-ObservationalTechniques O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-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-ObservationalTechniques O O B-ObservationalTechniques I-ObservationalTechniques I-ObservationalTechniques 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 B-Wavelength I-Wavelength B-ObservationalTechniques I-ObservationalTechniques O O O O O O B-ObservationalTechniques I-ObservationalTechniques O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O