processes. Interestingly, the relation between av Q C and av Q O of the ICME materials is different from that of the carbon-cold materials inside the ICMEs reported by Feng et al. ( 2018 ). The carbon-cold materials are defined by the carbon ionic charge state, which should be relatively lower than the solar wind mean value by three times standard deviation, with the ionic temperature lower than 10 6.05 K. It supports the distinct source or heating process of prominence materials and coronal materials in ICMEs. Further, there are three types of charge distributions inside the studied ICMEs excluding the cold material. Similar results are reported by Rivera et al. ( 2019 ) from their case study, who identified and studied the different types from the different sources in depth. Our statistical results support the stable existence of the different types of charge distributions of heavy ions during most years of a solar cycle. And the fractions of these charge distributions show clear dependence on the solar cycle. This means that the combination of the materials from different sources is common in ICMEs, but the fraction of them would change according to the solar activity. It also implies that the acceleration, the heating process, and the freeze-in height in CMEs may be different between the solar maximum and solar minimum. The source of heavy ions and the heating processes are possibly under modulation by the status of the solar magnetic field. As the most abundant heavy ions in the solar atmosphere (Asplund et al. 2009 ), oxygen ion flux in the solar wind has been systematically studied by von Steiger et al. ( 2010 ). It distributes from 10 4 to 10 6 cm −2 s −1 in the slow solar wind, and from 10 4.5 to 10 5.5 cm −2 s −1 in the fast solar wind. The peaks of the two distributions are a bit less and a bit more than 10 5 cm −2 s −1 , respectively. In the 281 ICMEs, the oxygen flux varies from 2 × 10 4 to 1.5 × 10 5 cm −2 s −1 . And it fluctuates around 10 5 cm −2 s −1 during the solar maximum, when the annual mean SN is more than 60. It could be identified that the oxygen flux in ICMEs is similar to that in the solar wind. Since the SN represents the status of the solar magnetic field, the quasi-linear relation between the O flux in the ICMEs and the SN, when the SN is less than 60, indicates that the O flux is possibly related to the status of the solar magnetic field. 5. Conclusion This statistical work analyzes the abundances and the charge states of heavy ions in the 281 ICMEs from 1998 to 2011. The mean proton speed of the ICMEs and the average charge states of heavy ions are highly related to the solar cycle. Since the SN represents the state of the solar magnetic field by nature, the proton speed and heavy ion composition of ICMEs are possibly related to the solar magnetic field. Another interesting result is the classification effect of the speed on the abundances and charge states of heavy ions. Similar to the solar wind, ICMEs could

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


one typically utilizes higher resolution grid elements in regions of higher stellar volume emissivity and dust density. Although reasonable to expect a more rapid variation of the radiation field in those regions, there is no guarantee that the spatial resolution is adequate everywhere on the grid. In the absence of iterative procedures to increase the spatial resolution during the RT calculation, the effect of the grid discretization on the numerical accuracy can only be checked by repeating the calculations at progressively higher spatial resolutions. Similarly, the finite number of angular directions of the rays that are cast from each radiation source, as well as the discretization of the scattering source function, also affect the calculation accuracy. Apart from these factors, common to all 3D dust RT codes although in different forms 6 , in DART-Ray the numerical accuracy is also affected by the estimate of the extent of the source influence volumes. This is because DART-Ray calculates the RFED contributions from each source only within this volume surrounding the source itself, thus neglecting the contributions outside it. Since this is a core characteristic of DART-Ray, we are interested in quantifying the accuracy error due to the cut off of the rays when they reach the boundary of the estimated source influence volume. We note that this accuracy error is systematic, since it will always produce RFEDs which are underestimated compared to the correct value. The ray cut off occurs when the RFED contribution carried by a ray satisfy the criterion 1 . So, once a lower limit to the RFED distribution has been estimated, the input-defined parameter is the key factor affecting the numerical accuracy of the calculation. In N14, we stated that should be low enough to preserve energy balance, in the sense that, at the end of the calculation, the total radiation luminosity that has been neglected because of the ray cut-off should be only a small fraction of the total luminosity of the model. In this case, the effect of cutting the rays is minimal because almost all the radiation luminosity has been followed in its propagation throughout the model. However, since this energy balance can only be checked at the end of the RT run, potentially several attempts had to be made to find the appropriate value for . Instead, in the following, we show how the value of the parameter can be set before an RT run such to guarantee the desired level of accuracy. We have been able to find a relation between and the accuracy of the derived RFED distribution by making a minor change in the definition of in formula 1 , compared to NA14. This is now defined as: where is the average specific intensity of the ray within the ray-cell intersection path, is the area of the emitting cell originating the ray, is the solid angle subtended by the intersected cell, is the linear size of the intersected cell, its volume and the light speed. This formula differs only slightly

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O O O O O O O O O O O O O O O O O O O B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


that the former can be used as a reliable proxy for the latter. The random theoretical 1-NNS distribution derived for an infinite media (see Appendix B for the full development) is given by: where is the mean intensity of the random process (the average surface density of stars) and is the 1-NNS. We want to compare this theoretical distribution to the 1-NNS histogram obtained from 10 000 random Monte Carlo samplings within the finite and irregularly-shaped window (see Fig. 3 ). Their respective moments are similar (see Table 2 ), with theoretical moments computed from the following expressions: where , , , , and are the mean, median, variance, standard deviation, and skewness factor (see Appendix B for their derivation). The moments from random Monte Carlo samplings were obtained from: where is the ordered sequence of the 1-NNS from the smallest to the highest value, the standard errors of the moments and the standard error of the median are taken respectively from Ahn Fessler (2003) and Kendall Stuart (1977) . Fig. 3 Probability distribution function (PDF) of the 1-NNS distributions observed in Taurus (solid blue histogram: within the limited window , that is, the three main filaments; dashed blue histogram: the entire Taurus region) and predicted for a random distribution (black histogram: for a Monte Carlo sampling within the window ; red curve: unlimited theoretical random 1-NNS distribution, see Eq. ( 3 )). Both random populations are drawn using the same mean surface density . Increasing the mean density by a factor of two leads to a shift towards the left whose amplitude is represented by the green arrow. The Monte Carlo sampling in a finite window and the unlimited theoretical random 1-NNS do not significantly differ. The 1-NNS distributions computed either in the whole Taurus or within do not significantly differ either. However, the Taurus and random 1-NNS distributions are statistically highly inconsistent, with a -value of 10 for the KS test. The spatial distribution in Taurus is clearly far from being random. We thus conclude that finite size and edge window effects do not significantly alter the distribution of 1-NNS from that obtained in an infinite medium at the level of our observational uncertainties. To prove this statement quantitatively, we use a bootstrapping technique, comparing 10 000 realizations of a) a sample of 1-NNS obtained from standard rejection sampling technique using analytical random 1-NNS distribution (Eq. ( 3 )) to b) the 1-NNS associated to random Monte Carlo samplings of 252 stars enclosed within . The two-sample Kolmogorov-Smirnov (KS) and Anderson-Darling (AD) statistical tests indicate that the two 1-NNS distributions cannot be statistically distinguished with a mean -value and standard deviation respectively of for the KS test and for the AD test. We have therefore shown that the random theoretical 1-NNS probability density function (Eq. ( 3 )) may be used as a reliable proxy to describe a 1-NNS

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


in the center of the sheet, and decays toward the rear of the current layer. This transpires from the shape and separation of the red equipotential contours in Figure 1 . Beyond the center, there is more energy in the stress-release motion than in the residual shear component. This means that a Poynting flux, , builds up behind the leading edge of the current front that subsequently converges, thus feeding the electromagnetic energy into the particles by maintaining . Associated with the first increasing and then decreasing stress-release motion is an inertial current, j in , pointing away from the sheet's center line. This component leads to concentrations of the current along the leading and trailing edges of the progressing sheet. Such refinements have not been incorporated in the cartoon of Figure 1 . Underlying this figure is the assumption that the current front propagates in a stationary fashion. In this case, the perpendicular potential drop equals and can be approximated byTwo aspects differ from the mechanical analogy of the fracture process: the magnetic field lines become newly connected, and part of the converted energy remains inside the fracture zone as thermal energy. However, a fraction, say about 10% of the electrons, is running through much of the parallel potential drop without losing its energy to the wave field and escapes along B , carrying perhaps up to 50% of the converted energy out of the sheet. These are the runaway electrons, candidates for producing the hard X-rays in solar flares. Figure 1. Oblique current sheet propagating with normal velocity, v n . Red lines represent equipotential contours for a quasi-stationary situation. The transverse electric field is related to the ongoing reduction of the shear field. The associated inertial current, j in , leads to current concentrations along the leading and trailing edges (not shown). The dashed magnetic field lines indicate the presence of a shear component, B ⊥ , that decays upon transit through the current sheet. An interesting problem is that of the reverse current. The question whether it is cospatial with the flux of runaway electrons has occupied many authors (Holman 1985 ). Emslie Hénoux ( 1995 ), for instance, argue against cospatial return currents. Figure 2 shows that the obliqueness of the current sheet facilitates maintaining charge neutrality. Charge neutrality requires that the flux of high-energy and low-density runaway electrons is balanced by counter-flowing low-energy background electrons. This begins outside the current sheet and thus outside the strong electric field, which would have a repulsive action on the return current, and continues all along the respective magnetic field lines. Because of the transverse propagation of the emitting current sheet, this lasts for a very limited time, τ CS , to be defined in Section 4.3 . It must be noted that the individual fluxes of runaway and reverse current electrons are by orders of magnitude higher

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


left panel but for galaxies split into redshift-independent mass bins. Bottom left panel: evolution of the logarithmic derivative of the half-mass radius r 0.5 with respect to the mass ratio m m / M s ( m is the stellar mass gained between two consecutive outputs) for non-mergers or m the mass ratio of the merger, for all galaxies with M s 510 9 M and all time outputs between z 5.2 and 1.2. Filled blue symbols indicate resolved mergers, red and light green ones represent non-merger diffuse mass acquisition, with unresolved mergers (in red) or not (in green). Whilst the evolution is linear in each case, the dependence of radius growth on the mass ratio is found to be much steeper for mergers. Bottom right panel: same plot as the top left panel, except that we have split the merger sample according to different pre-merger morphologies: discs (light blue) and spheroids (red). The steepness of the radius versus m relation appears mainly caused by minor merger disruption of the discs. The top panels show the evolution of the average half-mass radius r 0.5 as a function of redshift when we split our galaxy sample in bins of final mass (i.e. galaxy masses at redshift z 1.2; top left panel) and in bins of constant stellar mass (i.e. independent of redshift; bottom right panel). These results are consistent with the overall evolution of the sizemass relationship from observations such as Huertas-Company etal. ( 2013 ) (though our simulated galaxies are a factor of 2 larger): galaxies of a given stellar mass display much larger radii at z 1.2 than their counterparts of similar stellar mass at z 5.2; most of the growth taking place between z 3 and 1.2. More specifically, at z 1.2, galaxies with M s 10 10.5 M display an average half-mass radius two to three times bigger than their counterparts at z 3 (see bottom right panel), while one can see on the bottom left panel that galaxies reaching M s 10 10.5 M at z 1.2 have also seen their half-mass radius grow by a factor of 2 to 3 since z 3 and by a factor of 4 since z 5.2. To better investigate the role of different stellar acquisition processes in growing the size of galaxies, we compute the logarithmic derivative of the half-mass radius r 0.5 with respect to M s as a function of the merger mass ratio m for post-merger structures (bottom left panel, blue curve) and the mass increase ratio m m / M s log 10 M s , where m is the stellar mass accreted between two consecutive outputs, for galaxies only subjected to diffuse stellar accretion (green curve for pure in situ formation and red curve when including possibly unresolved mergers). This is computed for all galaxies and all time outputs between z 5.2 and 1.2 with M s 510 9 M . Note that M s or M 0.5 are equivalent for the purpose of this comparison so we use them interchangeably. The result is shown in the top left panel of Fig. 8 . Note the similarity between results for the pure star formation sample (in green) and the full sample of galaxies

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 gray scale is linear from zero to erg cm −2 s −1 sr −1 Å −1 , reversed (black is the maximum intensity) to reveal fainter emission between bright regions. The right panels show the average spectra (black) superposed with the average quiet Sun from the IRIS data studied here in red. Although the R-MHD calculation is for a network region, the region is dominated in area by non-network emission; thus, we compare with the quiet IRIS data. Note that the computed line k 2 peak separations are substantially smaller than observed. Significantly, in comparison with plage observations, these k 3 and K 3 components are far deeper in the computations. This suggests that the source function is on average larger where this feature is formed than is captured in the calculations. In Figure 9 we show spatial autocorrelation data computed from the 3D and 1D intensities of the k line, together with spatially averaged intensity profiles. Solid lines show observations, while dashed lines show computations. The autocorrelation characteristic lengths show three kinds of behavior depending on the wavelengths relative to line center. In the line wings, the images have the smallest spatial scales, with FWHM values of about 750 and 610 km. In 3D, these scales steadily increase toward the line cores, peaking near the observed peaks k 2 V and k 2 R . (In 1D these lengths decrease toward the line center before showing a small increase at k 2 V wavelengths.) Within the line core, the widths computed in 3D drop dramatically to below 700 km. Figure 9. Average profiles (top panel) are shown with autocorrelation full widths for the IRIS network and quiet regions (red and gray, respectively) in the bottom panel. The same data for the 3D and 1D calculations of Sukhorukov Leenaarts ( 2017 ), are also shown as dashed lines. The comparison of 3D and 1D images in Figure 8 is instructive in ways complementary to the interesting points made by Bjørgen et al. ( 2018 ). Figure 9 shows clearly that 3D transfer effects are important within ±1 Å of line center: the FWHM length scales are larger on average by a factor of two for the k line (15%–20% for the K line) in 3D than in 1D. The 3D features all appear “fuzzier” to the eye than their 1D counterparts, on scales of a few hundred kilometers in Figure 8 . We will speculate further on what is missing in these calculations in Section 5 . The second and fourth rows of Figure 8 show how the calculated model might be observed through filter instruments, with FWHM values of 0.1, 1, and 3 Å. Wider FWHM instruments have been used in solar physics for many years to record the Ca ii lines, and other, narrower filter widths have been developed. 11 11 See, e.g., https://www.su.se/isf/ . These panels suggest that 3D smearing effects are biggest at wavelengths within the emission cores. The differences are probably lower limits, given that the source functions for strongly scattering lines are smeared by the use of the short characteristics, which

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


WD resulting from the merger of two equal-mass WDs by assuming the extreme situation of complete mixing between the two WDs and a CO core for the merged remnant. To this end, we adopted the internal distribution of carbon, oxygen, and He of the 0.58 M ⊙ WD model computed in Miller Bertolami (2016) from the evolutionary history of its progenitor star. Assuming complete mixing between both WDs, the mass fraction of He, carbon and oxygen throughout the interior of our UMCO WD model results X He = 0.017, X C = 0.363 and X O = 0.62. We mention that in this study we are interested in the advanced evolutionary stages of the WD and not the evolutionary stages shortly after the merger event, which cannot be adequately followed by our stellar evolution code. Finally, in this work we did not consider the possibility that WD mergers lead to ultra-massive ONe-core WDs, as predicted in Schwab (2021) . The reason is that we do not expect such ONe WDs to present marked differences in their pulsational properties as compared with the ONe-core models resulting from the single evolution that is explored in the present paper. 4. Evolutionary properties In this section, we compare the evolutionary properties of our UMCO WD models resulting from the two single-evolution scenarios and from the binary merger we described previously, with those predicted by the ONe-core WD models resulting from off-centre carbon burning during the single evolution of the progenitor star ( Siess 2010 ). To isolate the impact of the internal composition predicted by the possible scenarios, we adopted the same stellar mass of 1.159 M ⊙ for all of our WD sequences 4 . In addition, we assumed the same H content for all of our sequences except the merger case. In particular, it was taken as nearly the maximum allowed by evolutionary considerations for such stellar mass, log( M H / M ⋆ )≈ − 6. This limit is imposed by the occurrence of unstable nuclear burning on the cooling track for the WD mass considered. Finally, the ONe-core WD-evolutionary and -pulsational models were taken from Camisassa et al. (2019) and De Gerónimo et al. (2019) . Such models were computed with the same codes we used to compute the evolution and pulsations of our UMCO WD models (see Sect. 2 for details). The evolutions of all of our WD sequences were followed from very high luminosities, through the domain of the pulsating ZZ Ceti stars, down to very low surface luminosities. In Fig. 5 , we display the internal chemical profile of our UMCO WD models (see Sect. 3 for details), together with the chemical profile of the ONe-core WD model studied in Camisassa et al. (2019) , top panel. Specifically, the second and third panels illustrate, respectively, the chemical profiles resulting from reducing the mass-loss rates of an initially 7.8 M ⊙ progenitor star, and those from considering core rotation ( f = 0.1) in the AGB phase of an initially 7.6 M ⊙ progenitor star. The bottom panel shows the chemical profile we

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


counts and fluxes from the eregionanalyse task. They have less than 35 counts in the full band; for three of them, we even only get upper limits. The EPIC net source counts and fluxes in the full (0.2–10 keV) energy range (0.2–0.5, 0.5–2.0, 2.0–5.0, and 5.0–10.0 keV energy ranges obtained for these quasars) are summarized in Table 3 . The full-band XMM 100 arcsec EPIC mosaics of these six quasars are shown in Fig. 1 (rows 2 and 3). Table 3. X-ray net counts and fluxes for the new z > 6.4 X-ray quasars. Note . The upper limits quoted in this table correspond to the 3σ upper limits and are used only if the net counts or fluxes are smaller than their 3σ error. But only the quasars with a given value in the ‘Det.’ column have an X-ray detection. For the two X-ray detected quasars in this work, the source counts and fluxes presented in Tables 2 and 3 are from the edetect_chain task. 4 DISCUSSION For the full sample of nine quasars, we derived a set of optical and X-ray properties (see Table 4 ): The absolute magnitude at the rest-frame wavelength of λ = 1450 Å ( M 1450 ) was computed by extrapolating the J -band magnitude to the monochromatic magnitude at ( m 1450 ) assuming a power-law fit of the continuum in the UV–optical with α ν = −0.3 (Selsing et al. 2016 ). The monochromatic flux at the rest-frame wavelength of () was derived from m 1450 assuming also a power-law slope of α ν = −0.3. The X-ray luminosity in the rest-frame 2–10 keV band was computed from the count rate obtained by the eregionanalyse task on the 2–10 keV image (as done in Section 2 for the other energy ranges) and then K -correction was applied assuming a photon index Γ = 1.9. For the two detected quasars VDES J0224−4711 and PSO J159.2257−02.5438, the flux was obtained directly from their X-ray spectrum. Upper limits are used if the luminosity is smaller than its 3σ error (which is the case for all the non-detected sources) and are at the 3σ level. The hardness ratio is defined as HR = ( H − S )/( H + S ), where S and H are the number of counts in the soft (0.5–2.0 keV) and hard (2.0–5.0 keV) bands, respectively. The optical-to-X-ray slope (α ox ) is defined as where is the monochromatic flux at the rest-frame wavelength of as defined above, and the rest-frame monochromatic flux at 2 keV () was inferred from the flux in the 0.2–10 keV range assuming a photon index Γ = 1.9. Upper limits for α ox are used if the flux at 2 keV is smaller than its 3σ error. Table 4. Summary of X-ray and optical properties of the DES and new z > 6.4 X-ray quasars. Note . a Reminder: VDES J0020−3653 and PSO J036+03 have a measurement of α ox with errors because their 2 keV flux (from the 0.2–10 keV flux) is at a 3σ significance, but they are not significantly (>4σ) detected as VDES J0224−4711 and PSO J159−02. We used the compilation of X-ray observations of quasars at z > 5.5 by Nanni et al. ( 2017 ) plus the new analysis by Nanni et al. ( 2018 ) for SDSS J1030+0524 ( z = 6.28) and the observation

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


wings. If we compare epochs I and II, we can see that the magnified blue wing fades while the red wing enhances. This supports that the separation between the approaching and receding parts of the microlensed region of the BLR is of about a few light-days. In several cases, mainly affecting the shelf-like feature at ∼ λ 1610 and several blends of Fe ii and Fe iii , the impact of microlensing and microlensing variability (see Tables 2 – 5 ) is mag, comparable to the typical microlensing magnification amplitudes observed in the X-ray continuum. It is important to notice that the spectral features mainly affected by intrinsic variability are also the C iv wings, some blends of Fe ii and Fe iii , and the shelf-like feature at ∼ λ 1610. In contrast with microlensing, we have not observed marked asymmetries induced by intrinsic variability in the line profiles. This result supports (within the statistical significance of our relatively limited sample) the hypothesis that the small region sensitive to microlensing is not systematically affected by extinction, beaming, or any other mechanism that may selectively enhance one part of it. Consequently, the asymmetric enhancements observed, in either the blue or red parts of microlensed line profiles, likely originate from an anisotropic distribution of microlensing magnification in the source plane. 3. Discussion 3.1. Microlensing and Kinematics The main result of the previous sections is that the cores of C iv , C iii ], and Mg ii and the wings of the last two lines are only weakly affected by microlensing. However, the wings of C iv can be strongly affected. In other high-ionization emission-line features, such as the Fe iii λλ 2039–2113 blend and the shelf-like feature at ∼ λ 1610, the whole feature may be globally affected by high-magnification microlensing. To discuss these results with more detailed kinematic information than the separation between core and wings, in Figure 6 we have overlapped the averaged line profiles corresponding to C iv , C iii ], Mg ii , and Fe iii λλ 2039–2113. The wings of Mg ii correspond to relatively low velocities as compared with other lines. This is consistent with the weak impact of microlensing on this line. Regarding C iii ] and C iv , the red parts of these lines match very well, except at the lowest intensity level, where the shelf-like feature at ∼ λ 1610 is present in C iv (the blue side of C iii ] is blended with Al iii , Si iii , and Fe ii , and no reasonable comparison can be made). In spite of this remarkable kinematic coincidence, the C iv line can be strongly affected by microlensing, whereas C iii ] seems to be rather insensitive to this effect (see, e.g., the cases of SDSS J1004+4112 and SDSS J1339+1310). In addition, they have a different degree of ionization (C iv is of high ionization and C iii ] of low ionization). These results suggest that both lines are mostly generated in the same region, but that there is also a contribution, exclusive to 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 B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-CelestialObject I-CelestialObject 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


red giant clump (RGC), with its known de-reddened color and magnitude, in the CMD serves as a reference for the color and magnitude calibration. In the first step of the method, we estimated the combined (instrumental) flux from the source stars, F S, p = F S 1 , p + F S 2 , p , and the companion/primary flux ratio, q F, p , by fitting the KMTC photometry data set processed using the pyDIA code. Here the subscript “ p ” denotes the passband of observation. The measured values are ( F S, I , F S, V ) = (0.07751 ± 0.00060, 0.00909 ± 0.00032) and ( q F, I , q F, V ) = (0.0471 ± 0.0023, 0.0110 ± 0.0084). We note that the value of q F, I , which is derived from the pyDIA reduction, is slightly different (less than 1 σ ) from the value presented in Table 3 , which is derived from the pySIS reduction, because they come from different reductions of the data. Then, the flux values from S 1 and S 2 were estimated by respectively. From the measured flux values in the I - and V -bands, we estimated the colors and magnitudes of S 1 and S 2 to be ( V − I , I ) S 1 = (2.289 ± 0.043, 20.827 ± 0.010) and ( V − I , I ) S 2 = (3.868 ± 0.831, 24.143 ± 0.053), respectively. In Fig. 9 , we mark the locations of S 1 and S 2 with respect to the RGC centroid in the instrumental CMD that was constructed using the pyDIA photometry of the KMTC data (gray dots). Fig. 9. Locations of the primary and companion source stars with respect to the centroid of the RGC in the instrumental CMD (gray dots). The determinations of the source positions and the construction of the CMD are based on the pyDIA photometry of the KMTC data set. We also present the Hubble Space Telescope CMD ( Holtzman et al. 1998 , brown dots) to show the source locations on the main-sequence branch. Although the V -band flux of S 2 has a relatively large fractional (magnitude) error, it is strongly constrained to be faint in an absolute sense. In particular, we find (i.e., a 4.4 σ difference). This serves as a second line of evidence that the 2L2S solution is correct. If, for example, we had somehow missed a 3L1S solution, and the derived 2L2S solutions were merely mimicking it, then q F, I − q F, V should be consistent with zero because there is only one source with just one color. However, according to Eq. ( 4 ), this possibility is excluded at 4.4 σ . In the second step, we calibrated the color and magnitude. With the measured instrumental color and brightness of the source, ( V − I , I ), and the RGC centroid, ( V − I , I ) RGC = (2.473, 16.918), together with the known de-reddened values of the RGC centroid, ( V − I , I ) RGC, 0 = (1.060, 14.509) ( Bensby et al. 2013 ; Nataf et al. 2013 ), the reddening and extinction corrected color and magnitude of the source were estimated by where Δ( V − I , I ) denote the offsets in the color and brightness of the source from the RGC centroid measured on the instrumental CMD. This results in In Table 5 , we summarize the values of ( V − I , I ) RGC , ( V − I , I

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


HWHM versus albedo. The modeled HWHM for 67P is located close to satellites of Mars, Phobos and Deimos, suggesting a similarity in the optical properties and structure of their surfaces, such as size of particles and porosity. The variation of the enhancement factor, against geometric albedo does not follow a recognizable trend (lower panel of Fig. 5 ). However, it shows two collections of data points, the values of the enhancement factor for all bright bodies studied in Rosenbush et al. (2002) are lower than 1.6, while for all dark objects they do not go beyond 1.8. It is notable that Phobos and Deimos including 67P do not resemble any group of data points. Another comparative study can be done for 67P and existing data for Centaurs and Kuiper belts objects (KBOs) ( Belskaya et al. 2008 ). Since these bodies are observed in the small phase angle range, for the comparison we only adopt the local phase curve of 67P at nm in the same phase angle range as those objects. The best-fit value of the phase coefficient in mag/deg for 67P is plotted together with the measured phase coefficients of KBOs and Centaurs (Table 1 of Belskaya et al. 2008 and references therein) with respect to the albedo (see Fig. 6 ). Fig. 6 Phase coefficient versus albedo for Centaurs, classical Kuiper belt objects (KBOs), and trans-Neptunian objects in band together with comet 67P/CG at nm. Figure 6 shows that 67P with the phase coefficient, , is located in Centaurs regions. The two particular Centaurs with similar phase coefficient to 67P are (54 598) Bienor and 1999 TD10. Centaurs are believed to have a greater steepness in their phase curve than other solar system bodies ( Bauer et al. 2003 ; Rousselot et al. 2005 ). 5.2. Comparison with laboratory measurements of the phase curve at small phase angles We also compared our results with laboratory measurements that study the dependence of the photometric characteristics of particulate surfaces on the surface properties, that is, albedo, grain size distribution, and porosity. There are not many experimental studies at very small phase angles. The measurements that are made in the opposition-effect region were carried out by Jost et al. (2016) for icy particles with a high-albedo close to unity and by Psarev et al. (2007) for low- and high-albedo samples. We found that the laboratory reflectance data from carbon soot at the wavelength of 630 nm in the phase angle range of 0.008–1.5 ( Psarev et al. 2007 ) show a behavior that is very similar to the measured local phase curve from the Imhotep-Ash region of 67P at nm. The local phase curve we extracted was normalized at to make it comparable with normalized laboratory measurements (see Fig. 7 ). In Fig. 7 two samples, the ultra-dispersed quartz and the carbon soot, behave similarly for the phase angles >0.2 (the limit we determined for the local phase curve of 67P from OSIRIS close-flyby images). However, light scattering by quartz sample is defined by its very special

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


taken with the Broadband Filter Imager, and the chromosphere, using the H α 6563 Å line obtained with the Visible Imaging Spectrometer (VIS). The passband of the TiO filter is 10 Å, centered at 7057 Å, while its temporal resolution is about 15 s with a pixel scale of 00343. Concerning VIS, a combination of 5 Å interference filter and a Fabry–Pérot etalon is used to get a bandpass of 0.07 Å at the H α line. Its field of view (FOV) is about 70′′ with a pixel scale of 00323. To obtain more spectral information, we scan the H α line at 11 positions with a 0.2 Å step following this sequence: ±1.0, ±0.8, ±0.6, ±0.4, ±0.2, 0.0 Å. The time used in each scan is 23 s. Both high-order adaptive optics (Cao et al. 2010 ) and a speckle reconstruction postprocessing method (KISIP speckle reconstruction code; Wöger von der Lühe 2007 ) are employed to achieve diffraction-limited resolution images. IRIS data are taken in a very large, coarse 64-step raster mode, with a step size of 035, step cadence of 31.8 s, and a raster cadence of 2036 s. The exposure time at each step is 29 s. Several strong emission lines are recorded, such as Si iv 1402.77 Å, Si iv 1393.7 Å, C ii 1334.53 Å, and Mg ii k 2796.35 Å. The cadences of the SJI in the passbands of 1400, 2796, and 2832 Å are all 112 s. The spatial resolution is about 033, and the FOV is 224 × 175′′ and 175′′ × 175′′ corresponding to the 64-step raster mode and the SJI. All of the spectra and images used in the analysis are level 2 data, including dark current subtraction and flat-field and geometrical corrections (De Pontieu et al. 2014 ; Tian et al. 2014 ). Hinode/SP data are acquired in a fast mode with an FOV of 81′′ × 81′′, a step size of 0297, and a raster cadence of 1080 s. Additionally, in order to analyze the corona response to our event, we have used SDO data, including the EUV and UV passbands from the AIA (Lemen et al. 2012 ) with cadences of 12 s and 24 s, respectively. The spatial register between the GST and SDO is first done by coaligning the AIA 1600 Å images with the GST/TiO data, and then coaligning the TiO data with the H α images at different wavelength positions. We use the AIA 1600 Å, IRIS 2832 Å, and SP continuum images to align the SDO , IRIS, and SP data. The uncertainty of the coalignment is about one AIA pixel (06). Figure 1 contains the context image of the LBs and fan-shaped jets on the sunspot of AR 12127 that we analyze in the subsequent section. The figure shows data from GST, IRIS, and SDO /AIA after the alignment process. Figure 1. Context images of the LBs and fan-shaped jets on the sunspot of AR 12127 obtained on 2014 August 1 around 17:27 UT. The different panels show (a) the photosphere through TiO images from GST, (b) the chromosphere via Ha LOS velocity obtained with GST/VIS, (c) the TR through SJI 1400 Å images from IRIS, and (d)–(i) the corona response observed with the different filters of SDO /AIA. R1 illustrates the LB region, to be analyzed in Figure 3 . L1 represents

O O O B-Instrument I-Instrument I-Instrument O O B-CelestialObjectRegion O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength O O O O B-Instrument I-Instrument I-Instrument B-Instrument 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 O O O O O O O O O B-Instrument I-Instrument 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 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-Citation I-Citation I-Citation I-Citation O O O O O O O B-Software I-Software I-Software I-Software B-Citation I-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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument I-Instrument O O B-Wavelength I-Wavelength O O B-Wavelength I-Wavelength O O O O B-Wavelength I-Wavelength O O O O B-Instrument O O O O B-Wavelength B-Wavelength O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation 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 B-Observatory O O O B-Wavelength O B-Wavelength O 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 B-Telescope O B-Observatory O O O O O O B-Telescope B-Wavelength I-Wavelength O O O B-Telescope O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O B-Telescope B-Wavelength I-Wavelength B-Instrument B-Wavelength I-Wavelength O O O O O O O B-Observatory O B-Telescope O B-Instrument 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 B-Identifier I-Identifier O O O O O O O O O O O O B-Telescope B-Telescope O B-Observatory B-Telescope O O O O O O O O O O O O O O O O O O B-Identifier I-Identifier O O O O O O O O O O O O O O O O O O O B-Telescope O O O O B-Wavelength O O O O B-Telescope O O O O B-Instrument B-Wavelength I-Wavelength O O B-Telescope O O O B-CelestialObjectRegion O O O O O O O B-Observatory B-Telescope O O O O O O O O O O O O O O


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O B-Telescope I-Telescope I-Telescope I-Telescope I-Telescope B-Telescope O O O O O B-Location I-Location I-Location O O B-Location I-Location I-Location I-Location O O O O O O B-Wavelength B-Wavelength B-Wavelength B-Wavelength O B-Wavelength O O 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 B-Instrument O O O O O B-Wavelength I-Wavelength 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 B-Instrument O O O O O B-Wavelength I-Wavelength O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O B-Wavelength 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 B-CelestialObject I-CelestialObject B-CelestialObject O B-CelestialObject B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O B-Wavelength I-Wavelength O O O O B-Citation I-Citation I-Citation I-Citation O O B-Instrument O O O O O O O O O B-Instrument O O O O O O O O O O O O B-Software I-Software B-Software I-Software O O O O O O O O O O B-TextGarbage O O O O O O B-Instrument O B-Instrument 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-Telescope O O O B-Telescope I-Telescope I-Telescope I-Telescope B-Telescope O O B-Citation I-Citation I-Citation I-Citation 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 B-TextGarbage I-TextGarbage I-TextGarbage O O O O O O O B-Telescope O O B-Wavelength B-Wavelength B-Wavelength O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey 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 B-Tag I-Tag B-Tag I-Tag O B-Tag


the outermost regions of clusters. For example, Fig. 8 shows a snapshot of the plane ( J z , R ) for model KF05, with the potential escapers highlighted in green. It is evident that almost all of the outer cluster stars beyond approximately 0.5 r J are potential escapers. This result is in general agreement with the findings of Küpper et al. ( 2010 ), who first showed that the behaviour of the surface brightness and velocity dispersion radial profiles are significantly affected by the presence of an outer population of potential escapers. Figure 8. The same as the last panel of Fig. 5 , but with the unbound particles highlighted in green. The fraction of unbound particles as a function of the fraction of the mass remaining in the cluster for all our locked models is illustrated in Fig. 9 . As discussed in Fukushige Heggie ( 2000 ) and Baumgardt ( 2001 ), initial conditions set by sampling, for example, a King model may include a fraction of stars which are unbound when an external tidal field is added. This is the case for our KF1 model. For this model, we show the evolution of the fraction of potential escapers both with and without this population of primordial potential escapers. All the other models do not have any primordial potential escapers. Figure 9. The fraction of unbound particles as a function of fraction of mass remaining in the cluster for all locked models. For KF1, there are two separate lines for including primordially unbound particles and excluding them. Fig. 9 also shows that the fraction of potential escapers increases significantly over time reaching a fraction of the remaining mass equal to about 15 per cent by the end of our simulations. Such a behaviour is qualitatively consistent with the findings reported by Baumgardt ( 2001 ), in which tidally perturbed models (initialised as critically filling King model W 0 = 3, i.e. characterized by a much higher fraction of primordial potential escapers, about 15 per cent) possess approximately 20 per cent of potential escapers during the final stages of evolution. We have examined the evolution of the fraction of prograde and retrograde particles within the populations of bound and unbound particles in models KF1 and KF025, as representative of the two filling regimes (see Figs 10 and 11 , respectively). The larger fraction of retrograde particles in the population of unbound particles is the result of the two effects discussed in Section 3.2 : the preferential escape of prograde particles and the fact that, in the transition from bound to unbound, some particles move on more eccentric/radial orbits becoming retrograde as they move outwards. Figure 10. The time evolution of model KF1 of the fraction of retrograde stars within the entire system, and within energetically bound and unbound particles. The bottom panel is a zoomed in version. The red line shows the fraction of unbound particles that do not include the primordially unbound stars. Note that the black solid lines

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


with ) based on their line properties alone. We compare the results from the simulations to what is expected when using the negative image FDR as reference. For the latter, we estimate the probability of an emission line with of being false by taking , where is the number of emission lines with found in the negative data, while is the number found in the positive (“real”) data. This means that for equal numbers, there is a 100% probability that the line is produced by noise. Alternatively, if there there are twice as many positive lines as negative ones, we assume that there is a 50% probability that each positive line is real. A comparison between simulations and negative image FDR probabilities for each cluster is shown in Fig. 4 . We see that using the negative image FDR as a reference for estimating the probability of a line being false returns a much noisier and sharper probability distribution for all of the clusters. At a given S/N value, it can strongly under- or overestimate the probability since it is dominated by small number statistics. Using simulations allows us to more accurately assign probabilities and understand the true detection rate at low . To confirm weaker real emission lines, we investigate the NIR and 1.1 mm counterparts of all of our candidates. Fig. 4 Probability of an emission line with a given of being produced by noise for the five clusters. Solid curves correspond to the probabilities given by the simulations, while dashed curves correspond to the probabilities estimated from the negative data. 3.3. Association with optical/NIR counterparts Clearly galaxies with high SFRs are likely to be detectable both with HST and/or ALMA in continuum and in molecular emission lines. Because of this, we expect that an emission line candidate co-spatial to a NIR detected galaxy should increase the probability of this candidate being real and thus use the NIR images for this purpose. However, the lack of a NIR or 1.1 mm counterpart does not necessarily imply that the emission line is noise. A galaxy that remains undetected both in HST/160 and ALMA continuum at could still have a at and at , based on spectral energy distribution fitting. In such cases, it should still be possible to detect CO, [NII], or [CII]lines. For instance, we find that CO can be detected at from CO lines when a high CO excitation level () is present in combination with strong dust extinction (). Detections of [NII]and [CII]lines can be made to lower SFRs and extinctions () at . Thus, some weak line candidates that lack NIR counterparts could still be real. Unfortunately, in such cases, confirmation and identification of line candidates will only be possible with deeper mm observations, which is beyond the scope of this study. Thus, we restrict our analysis of weak emission line candidates to those with nearby optical/NIR detected sources. Based on the number and spatial distribution of NIR detections in the FFs, a given random position within any of

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O B-Telescope O B-Observatory O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O B-Wavelength O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O B-Telescope O B-Observatory O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O B-Wavelength O O O O O O O O O O B-Wavelength O O O O O O O O O O O


a L ~10 3 L ⊙ low-mass YSO cluster (e.g. Estalella et al. 1993 ; Quanz et al. 2007 ). Four of the YSOs, namely VLA1-4, are known to be associated with thermal radio jets ( Anglada et al. 1994 ). Based on the previous, lower angular-resolution observations of C 18 O (1–0), Umemoto et al. (1999) estimated the enclosed gas mass over the ~ 0.5-pc-scale parent molecular gas structure to be ~120 M ⊙ . Contrasting to the aforementioned OB cluster-forming regions, the bolometric luminosity of L1287 is not contributed by the nuclear burning of OB stars, but instead is contributed by the accretion luminosity of the low-mass protostars, including two known FU Orionis objects 1 RNO 1B/1C( Staude Neckel 1991 ; Kenyon et al. 1993 ; McMuldroch et al. 1995 ; Quanz et al. 2007 ), and a L ~ 600 L ⊙ Class 0/I YSO IRAS 00338 + 6312 ( Anglada et al. 1994 ). Earlier observations resolved bipolar CO outflow(s) aligning in the NE-SW direction ( Snell et al. 1990 ; Yang et al. 1991 ; Fehér et al. 2017 ), although the identification of the powering source(s) remains uncertain. Table 1 SMA observations summary. In this paper, we report the ~ 1′′ (~ 930 AU)-angular-resolution observations with the Submillimeter Array (SMA) 2 , covering the inner ~0.25-pc region of L1287. By examining the resolved 1.3 mm dust continuum emission and various molecular line tracers of dense gas, warm gas, shocks, and outflows, our aim is to elucidate how the gas flows converge from parsec scales (e.g., due to gravitational collapse) down to ~ 1000 AU scales, and how they are dynamically forming the low-mass YSO cluster. We also provide a more definite identification of the powering source of the previously reported molecular outflows. The details of our observations are presented in Sect. 2 . The observational results from the dust continuum and molecular line emission are given in Sect. 3 . In Sect. 4 we present an analysis of fragmentation, dense gas kinematics, and powering sources of the previously reported CO outflows. Our conclusions are given in Sect. 5 . 2 Observations and data reduction 2.1 Submillimeter Array observations We performed five tracks of SMA observations at ~1.3 mm wavelengths towards the inner ~0.25-pc region of L1287 between August 2013 and July 2014, which are summarized in Table 1 . The pointing and phase referencing centers of the observationsare RA(J2000) = 00 h 36 m 46.65 s , Dec(J2000) = + 63°28′57.90′′. The projected baselines of these observations range from ~4 to ~ 140 k λ . The system temperature T sys for all the observations was around 150 K. The observations were obtained with the 230 GHz receiver, with 4 GHz bandwidth in each of the upper and lower sidebands. The correlator consisted of 48 chunks, each with a bandwidth of 104 MHz. The frequency was centered at 231.3 GHz at chunk 35 of the upper sideband (USB). This configured the correlator with the lower sideband (LSB) covering from 216.48 to 220.46 GHz and the USB from 228.46 to 232.43 GHz. These

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


misalignment angles in 3C sources are known to extend up to values of about 12° or more ( Leahy Williams 1984 ). We thus consider the interpretation of the S5 0836+710 large-scale morphology as an FR II radio galaxy at a small viewing angle as realistic. 4.3. Derivation of the jet parameters The total jet power for a relativistic jet is parameterized as (see, e.g., Perucho et al. 2017 ): where is the jet specific enthalpy, Γ j is the jet Lorentz factor, ρ j is the jet rest mass density, v j is the jet velocity, c is the speed of light, B φ is the toroidal field in the observer’s frame, γ j is the ratio of specific heats of the jet gas, and A j is the jet cross-section. The first term in Eq. ( 2 ) includes the kinetic, internal, and rest-mass energy contributions, and the second term stands for the magnetic energy of the jet. We can assume (see Appendix B ) that the jet is kinetically dominated and in the cold regime (i.e., its magnetosonic Mach number is high). Furthermore, taking into account that the advance speed as measured by LOFAR is also so slow, the velocity of the bulk plasma flowing into the hotspot can be assumed to be only mildly relativistic at most (see also Appendix C for the relativistic derivation). Under these conditions, the magnetic and pressure terms can be neglected and Eq. ( 2 ) simplifies to Across a strong shock, the hotspot pressure is (e.g., Landau Lifshitz 1987 ) In this equation, we need to define the jet radius at the hotspot, R j, h , which can be approximated as the hotspot radius. Because we do not know whether the southern radio structure includes the hotspot and part of the lobe or if it is the hotspot, we considered half of the whole region as the jet radius (4.5 kpc) and half of the fitted component, which represents the brightest region within the hypothetical lobe (2.5 kpc). Although the polarization seems to favor the latter interpretation (see the previous section), we study both cases here. Furthermore, we need an estimate for v j at the hotspot, v j, h . As we show in the following paragraphs, any reasonable input value is sufficient because we define an iterative method to derive its convergence value. When the hotspot pressure is obtained, we can use equipartition between the nonthermal particles and the magnetic field, as reported for FR II hotspots (see e.g., Hardcastle Worrall 2000 ), to obtain a value of the magnetic field at the interaction site. The value of the magnetic field prior to the reverse shock can be constrained by assuming conservation of the magnetic flux from the 1.6 GHz jet to the interaction site 3 . Applying the magnetohydrodynamcis (MHD) jump conditions at the reverse shock that give rise to the hotspot, allows us to derive a new estimate for v j, h . Setting a convergence criterion for this parameter at a precision of 10 −3 , we can determine the relevant parameters of the problem. We applied this method to four different sets of hotspot velocity and radius: the possible

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


different cell sizes in the CMDs, they are fixed each time, i.e. they do not vary across the CMDs. From our experience in cleaning the field star contamination in the cluster CMDs, we have identified some situations which still need our attention. It frequently happens that some parts of the CMDs are more populated than others, so that fixing the size of the cells in the CMDs becomes a difficult task. Small cells do not usually carry out a satisfactory job in CMD regions with a scarce number of field stars, while big cells fail in populous CMD regions. Thus, relatively bright field red giants with small photometric errors could not be subtracted and, consequently, the cluster CMD could show spurious red giant features. A compromise between minimizing the residuals left after the subtractions of field stars from the cluster CMDs and maximizing the cleaning of field stars is always desirable. In this paper, we present a comprehensive multiband photometric analysis of Haffner9 from BVI and Washington CT 1 photometry. The cluster has been previously studied from 2MASS and BVI photometry. However, a relatively lower photometric accuracy and shallower limited magnitude, in combination with a not much pinpointed treatment of field decontamination led those studies to discordant results. In Section 2 , we describe the collection and reduction of the available photometric data and their thorough treatment in order to build an extensive and reliable data set. The cluster structural and fundamental parameters are derived from star counts and CMD and colourcolour (CC) diagrams, respectively, as described in Section 3 . The analysis of the results of the different astrophysical parameters obtained is carried out in Section 4 , where implications about the stage of its dynamical evolution are suggested. Finally, Section 5 summarizes the main conclusion of this work. 2 DATA COLLECTION AND REDUCTION We used CCD images 1 obtained on the nights of 2004 December 18 and 19 with a 2048 2048pixel Tektronix CCD attached to the 0.9-m telescope (scale 0.396 arcsecpixel 1 ) at Cerro Tololo Inter-American Observatory (CTIO, Chile). Its field of view (FOV) is 13.6 13.6arcmin 2 . We used the Washington C (Canterna 1976 ) and KronCousins R filters. The latter has a significantly higher throughput as compared with the standard Washington T 1 filter so that R magnitudes can be accurately transformed to yield T 1 magnitudes Geisler ( 1996 ). We used a series of bias, dome and sky flat-field exposures per filter to calibrate the CCD instrumental signature. We also utilized images for the Small Magellanic Cloud cluster Lindsay106, which was previously observed at La Silla (ESO, Chile) with the C and T 1 filters (Piatti etal. 2007 ). Lindsay106 was used here only as control cluster, i.e. to verify the quality of the present CTIO photometry. Table 1 shows the log of the observations with filters, exposure times, airmasses and seeing estimates. A large number (typically 20) of

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


and the lack of a large additional population of variable sources beyond those identified with the CRATES catalogue. 4.4 Differential source counts Differential source counts have been intensively studied (e.g. de Zotti et al. 2005 ; de Zotti et al. 2010 ; AMI Consortium et al. 2011 ), having important implications for models of cosmic evolution (e.g. Condon 1984 ; Massardi et al. 2010 ) and provided the first clear evidence against the Steady State Theory (Pooley Ryle 1968 ). However, for the purposes of C-BASS analysis, we calculate the differential source counts to provide an additional cross-check on the statistical properties of our bright-source population. Given that we are concerned with the statistical properties of our catalogue at flux-densities , where the C-BASS catalogue is largely complete, we do not consider correction factors to the differential source counts necessary at lower flux densities to account for catalogue incompleteness and varying flux-density sensitivities across the sky. Sources are put into flux-density bins of width . For each bin, source counts are determined against a central flux density, S c , taken to be the geometric mean of flux densities in that bin. The differential source counts for a given flux-density bin are then given by where N c is the number of sources in the flux-density bin, A is the sky area to which the catalogue corresponds, and Δ S is the bin width. Errors are estimated for the source counts by assuming Poisson statistics. We only consider bins with N c ≥ 9 so as to maintain a SNR ≥ 3 for each bin. The differential source counts for C-BASS North in total intensity, applying the CG30 mask, are plotted in Fig. 12 , alongside the differential source counts for the GB6 catalogue. We can see that at low flux densities the C-BASS source counts are significantly lower. This is to be expected from the increasing catalogue incompleteness at these lower flux densities. From the differential source counts, we can again see the catalogue completeness level from the point at which the source count turn-off ends and we have good agreement between the C-BASS and GB6 counts, i.e. over flux densities . It is worth noting here that the errors obtained from assuming Poisson statistics are likely to be somewhat optimistic. These do not account for false positives in the source catalogues, or errors arising from incorrect binning due to uncertain flux-density estimates. These effects become significant at lower flux densities, where the proportion of false positives in the catalogue is greater, and our photometry methods become less reliable. Figure 12. Differential source counts calculated using the C-BASS northern sky total intensity catalogue, plotted alongside the differential source counts for the GB6 catalogue. Source counts were calculated applying the CG30 mask. We also plot as grey-scale the fitted model source counts corresponding to 100 posterior samples for the C-BASS and GB6 models. At low-flux

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


generating these artificial leakage parameters, it was ensured that no off-diagonal elements of the Mueller matrix exceeded 1.5 conversion between Stokes parameters at any frequency channel, while reaching this maximum percentage in at least one frequency channel. This limit was chosen based on the following test. From our sample, we chose all pulsars that did not show any RM(φ) variations (e.g. J1048–5832 and J1709–4429). Our assumption was that the imperfections of the receiver could not generate more RM(φ) variations than were already observed. The limit was therefore chosen as the maximum value that did not create additional apparent variations in RM(φ). The systematic uncertainties because of receiver imperfections were quantified for each pulsar by randomly generating 100 receiver imperfections obeying the above description, which then were used to distort the pulsar signal in the process of polarization calibration. 3 For each of these 100 different distortions, we calculated values for RM profile , RM scatt , RM(φ), and Δ( V / I )(φ). The standard deviation of these values was quoted as the systematic uncertainty in Table 1 . The systematic uncertainties determined for the RM(φ) and Δ( V / I ) are displayed for each pulsar, for example in Fig. 1 , in the third and fourth panels as a 1σ contour grey-shaded region overplotted over the RM(φ) values (green in the online version). 4 RESULTS Pulsars described in Sections 4.1 and 4.2 and in Table 1 , for which the phase-resolved RM profile had never been investigated previously in the literature, are marked with an asterisk (*). The plots for the 98 pulsars have been included in the online supplementary material , in Figs A1–A26 and an example is displayed in Fig. 1 . All plots were aligned, so that the total intensity peaked at pulse longitude 180°. For the six pulsars from the sample, which had both a main pulse (MP) and an interpulse (IP), we aligned the MP peak at pulse longitude 90°, and hence the IP peaked around pulse longitude 270°. The results from the analysis described in the Section 3 can be found in Table 1 . The resulting RM(φ) profiles allowed us to classify the pulsars as follows. Pulsars that had were classified as showing significant RM(φ) variations, and they are discussed in more detail, on a case to case basis, in Section 4.1 . Six pulsars, which were initially classified as showing significant RM(φ) variations, were removed from this section based on their high systematic uncertainties. A total of 42 pulsars, of our sample of 98, were classified as showing significant RM(φ) variations. For all cases where we saw RM(φ) variations, we observed deviations from the expected λ 2 dependence (as quantified by , but also by inspecting PA versus λ 2 directly), implying that Faraday law fails to describe the full frequency dependence of the PA, and there must be another frequency and pulse longitude dependent effect present. Therefore, the results obtained from the panel, where

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


structure than in the spot. Moreover, the smearing due to the point-spread function of the telescope may dilute into the bright structure part of the magnetic signal belonging to the surrounding umbra and penumbral filaments. However, the average estimated errors for the vertical and horizontal component of the field in the structure are about ±35 G and ±70 G, respectively. Thus, the strong horizontal field of about 2000 G appears to be a robust result. The presence of such a significant horizontal component of the magnetic field allows us to exclude the field-free configuration typically observed in LBs. Conversely, it supports the possibility that the magnetic field of the flux rope forming the filaments around the sunspot may have a counterpart in the middle of the sunspot umbra, where it appears to end in the cospatial chromospheric images. This would also provide an explanation for the detection of opposite polarity in the structure with respect to the umbra, as well as an alternative interpretation for the opposite polarity of an apparently filamentary LB with respect to its hosting umbra observed by Bharti et al. ( 2007 ). Note that this phenomenon is different from the magnetic reversals found by Lagg et al. ( 2014 ) and Felipe et al. ( 2016 ) in LBs, due to the bending of the field lines along the atmospheric stratification of the structure. Moreover, this scenario is confirmed by the portions of the bright feature characterized by both upward and downward plasma motions along it, which are compatible with plasma flows along the helical field lines of a flux rope. Actually, the length of each portion of the filamentary structure with coherent plasma motion is of about 5′′, which could correspond to the pitch of a helically twisted flux tube. Therefore, we guess that this bright filamentary structure is not a filamentary LB, but it is due to the accumulation of plasma coming from higher solar atmospheric levels into the photosphere. The presence of stably inclined fields belonging to the flux rope, which are touching part of the sunspot umbra, would set in radiatively driven penumbral magneto-convective mode (Jurčák et al. 2014 , 2017 ). Indeed, high-resolution observations have shown that plasma fallen from chromospheric layers can lead to the formation of penumbra in sunspots (Shimizu et al. 2012 ; Romano et al. 2013 , 2014 ). Furthermore, penumbral-like structures, i.e., so-called orphan penumbrae, have been reported as a photospheric counterpart of a chromospheric filament (Kuckein et al. 2012a , 2012b ; Buehler et al. 2016 ). Observations of similar bright filaments inside the umbra, called UFs, have been recently reported by Kleint Sainz Dalda ( 2013 ). They found that UFs were characterized by a horizontal flow opposite to the Evershed flow and they also found from coronal images the presence of bright coronal loops that seemed to end in UFs. To interpret such phenomena, Kleint Sainz Dalda ( 2013 ) conjectured two different

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


2010 ; Bahramian et al. 2021 ). In addition, very hard spectra in a bright hard state have been observed in a couple of NS LMXBs (Parikh et al. 2017 ) and BH LMXBs including V 404 Cyg (e.g., Kimura et al. 2016 ), V4641 Sgr (e.g., Maitra Bailyn 2006 ), and Swift J1858.6−0814 (Hare et al. 2020 ). All these sources have a strong short-term flux variation by a more than order of magnitude (e.g., Kitamoto et al. 1989 ; Revnivtsev et al. 2002 ; Wijnands et al. 2017 ), also in agreement with the present case. In addition, partial covering absorption is sometimes required in these sources, especially in high-flux phases (Kimura et al. 2016 ), consistent with Swift J0840.7−3516 in a bright phase. We note that the photon index of Swift J0840.7−3516 after the decay, ≲2, is reminiscent of a BH rather than an NS LMXB, which usually shows a larger value, Γ ∼ 3 (Wijnands et al. 2015 ), although the NS LMXB EXO 1745−248 showed a similar hard spectrum in quiescence (Rivera Sandoval et al. 2018 ). On the other hand, an NS LMXB would rather be favored, in that a very small radius of the thermal component, 1–2( D /8 kpc) km, consistent with emission from an NS surface, was obtained from the NuSTAR+Swift/XRT+NICER spectrum in a faint phase. This holds even if the observed power-law component was entirely produced by Comptonized disk photons. Assuming conservation of the number of photons and an isotropic scattered emission (Kubota Makishima 2004 ), and using the intrinsic disk photons estimated from the best-fit diskbb+cutoffpl model, we obtain the inner disk radius as ∼3( D /8 kpc) km (where i = 60° is assumed). Similar thermal emission likely emitted by the NS surface can be seen in NS LMXBs at low X-ray luminosities below ∼10 35 erg s −1 but not in a more luminous hard state, where the power-law component dominates the X-ray flux (e.g., Sakurai et al. 2014 ; Shidatsu et al. 2017 ). The thermal component in Swift J0840.7−3516 was observed at a consistent luminosity; the second rapid decay from 10 5 s since the discovery, in which this component was found, started at ∼10 35 ( D /8 kpc) 2 erg s −1 . Even if an LMXB scenario works for all the properties raised above, the observed absorption feature is difficult to explain. Although ionized Si and S lines from disk winds are sometimes seen at similar energies (e.g., Ueda et al. 2009 ), they are much weaker than the present case and always with strong iron K α lines at ∼7 keV. Assuming the observed feature to be the redshifted Fe K edge, we obtained z = 1.1. If this is the gravitational redshift caused by a Schwarzschild stellar-mass BH, the feature should be produced at ∼1.3 R S , where R S is the Schwarzschild radius. It is unclear that an absorber with such a small size can exist in the vicinity of a BH. Another possibility is that the observed feature is a different blueshifted line produced by an outflow at a relativistic speed, like baryonic jets observed in SS 433. However, it is unclear whether such

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