the telluric standard. As a last step in the data reduction process, the science spectra were divided by the response function of the corresponding standard star (examples of the final telluric corrected science spectra can be seen in Figs. B.1 and B.2 ). 4.1. Flux calibration We calibrated the continuum level of our sources to the corresponding spectroscopic standard (the collected telluric standards). For the standard stars we collected the W2 magnitudes (m) from the WISE all-sky catalogue: HR6527 (.103 mag), HR4730 (.025 mag), and HR2421 ( mag). Using these values, the continuum flux at 4.6 m of the three standard stars is respectively, 25.83 Jy, 36.62 Jy, and 42.05 Jy. There are small differences in the widths of the point spread function for the science spectra and the telluric standard spectra (we expect these differences to be due to variations in the performance of the adaptive optics system). We do not correct for these differences, but note here that the error expected from these differences in our flux calibration is 10%. Furthermore, when viewing the full spectra for each source there are inconsistent variations in continuum level at different wavelength settings (or detectors) for overlapping or neighbouring regions. These variations are at the 10% level. We apply flux shifts to the frames where this is needed to make the full spectrum fit one consistent continuum curve. 4.2. Line detection All of our observed sources have clear detections of H i recombination lines in emission: Pfund 7-5 and the Humphreys 11-6 line. For these lines, individual line profiles are shown in Fig. B.3 . The FWHM, the line centres, and the derived doppler shifts, together with the 3 error bars are shown for all sources in Table B.1 . Spectra from four of our sources (HD 163296, HD 250550, Hen 2-80, Hen 3-1227) also show clear detections of CO ro-vibrational emission lines. The CO emission from these four sources is not spatially resolved (for more details on spatially resolving emission with CRIRES see van der Plas et al. 2015 ). CO ro-vibrational emission lines could also be present in MWC 137. The spectrum shows what appears to be many wide and often blended emission lines. For the four sources with CO detections, individual CO lines were identified and extracted using wavelengths from Chandra et al. (1996) . For each source certain wavelength settings overlap, resulting in a few lines being detected twice. Furthermore, in the cases of Hen 2-80 and Hen 3-1227 we collected observations during two nights with the same wavelength settings. These doubly collected lines can be used for sanity checks and uncertainty estimates. For the further analysis we consider our line selection carefully. Some lines are contaminated by telluric residuals and some lines are blended and cannot be separated for individual profile extraction. We thus manually select the best uncontaminated and unblended lines for further analysis (Table C.1 ). Fig. 2 FWHM as a function 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 B-Instrument O O O O B-Dataset I-Dataset I-Dataset B-CelestialObject O O B-CelestialObject O O O B-CelestialObject O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O B-Wavelength I-Wavelength 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 B-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O B-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 O O O O O O O O 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 7 Be ii doublet cannot be resolved, its total equivalent widths, W ( 7 Be ii )s, in the LVC and the HVC are measured. After subtracting the combined effects of contaminations discussed above we tabulate the resulting W ( 7 Be ii ) in Table 3 . The errors of W are estimated from the S/N of the neighboring continuum. They do not include the uncertainties in the continuum placements. Table 3 Equivalent Widths of Blue-shifted Absorption Lines in Observed Novae The abundances of 7 Be in nova ejecta is estimated following the same procedure as used in Tajitsu et al. ( 2015 ). We compare the equivalent widths of Ca ii K () and 7 Be ii (, respectively) in the LVC, which show a simpler structure than the HVC. Here we need the following assumptions: (1) both the 7 Be ii and Ca ii lines are not saturated and (2) the covering factor of the absorbing gas cloud to the background illuminating source has no wavelength dependence. We notice that the LVC feature of 7 Be ii at −786 km s −1 of V5668 Sgr might be saturated. The bottom of the 7 Be ii lines in the LVC almost reaches to that in the HVC where its flat profile suggests that the absorption is saturated. The corresponding LVC component of the Ca ii K line in V5668 Sgr is shallow and the line appears to be unsaturated. The abundance of 7 Be in V5668 Sgr obtained under such a condition should be taken as a lower limit. Following Spitzer ( 1998 , Equations (3)–(48)), the ratio of column number densities, N , can be written asUsing data of the W ( 7 Be ii ) and the listed in Table 3 the column density ratios N ( 7 Be ii )/ N (Ca ii ) derived in the LVC of V5668 Sgr and V2944 Oph are 8.1 ± 2.0 and 2.5 ± 1.5, respectively. These ratios are close to that found in V339 Del at +47 days. The ionization states of each species are keys to convert the above ratios into atomic abundances. We assume that the most of 7 Be is in the singly ionized state because it still stays in hot ejecta. We also assume that Ca is in the singly ionized state. The absence of Ca i lines in the blueshifted absorption line systems supports this assumption. The difference in the second ionization potential (Be: 18.21 eV, Ca: 11.87 eV) may lead to different balances between the second and the third ionized ions and this may be a source of an error in determining the abundances. We tried but failed to detect absorption lines of doubly ionized ions of Fe-peak elements, which have intermediate second ionization potentials, consulting Kramida et al. ( 2014 ). Absorption lines of Fe iii are observed in optical range spectra of B-type stars (Thompson et al. 2008 ). This may support the assumption that all of 7 Be and Ca contained in the LVC are in the singly ionized state. Adopting this assumption, the mass fraction of 7 Be to the sum of all constituent mass components, ( 7 Be ii ), can be presented as: ( 7 Be) ∼ N ( 7 Be ii )/ N (Ca ii ) × 7/40 × X (Ca). We have obtained ( 7 Be)/ (Ca) = 1.4 ± 0.3 for V5668 Sgr and 0.44 ± 0.26 for V2944 Oph.

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


π is readily apparent. A simple way to quantify this apsidal alignment is to compare with the number fraction f even of an even π distribution. If we have N Trojans in total, since the width of each π bin is adopted to be 30 ○ , a sample size of N bin = (30/360) N per bin is expected, i.e. the mean fraction . Considering the random variations about the value of f even due to counting statistics, the uncertainty from Poisson distribution can be calculated by . Accordingly, in the upper panels of Fig. 1 , the horizontal solid and dashed lines are plotted to indicate the mean fraction f even and its 5 σ upper uncertainty, respectively. As the peak of the histograms can achieve the value of ∼0.21 (L5)–0.23 (L4), much higher than the dashed line, the clustering of π shows strong significance over 5 σ confidence level. Another key point shown in these two figures is that the number peak corresponds to the bin of π = 30 ○ –90 ○ (300 ○ –330 ○ ) for the L4 (L5) Trojan swarm, giving a difference of around +60 ○ (−60 ○ ) with Jupiter’s longitude of perihelion π J (indicated by the red line). Figure 1. Distribution of the longitudes of perihelia π (upper panels) and the longitudes of ascending nodes Ω (lower panels) of the observed Jupiter Trojans, at the epoch of 2020 May 31. Left-hand column: There are 4625 objects in the L4 region, and the values of their π are clustered around π J + 60 ○ ( π J is the longitude of perihelion of Jupiter). Right-hand column: There are 2729 objects in the L5 region, and the π clustering is around π J − 60 ○ . For reference, the horizontal solid lines are plotted in the upper two panels for the uniform distribution in π , and the dashed lines indicate the 5 σ upper uncertainty from Poisson statistics. In order to further confirm the newly found characteristic of apsidal clustering, we need to consider the evolving orbits of Jupiter Trojans at different epoch. Since the periodicity in the variation of Jupiter’s longitude of perihelion π J is ∼0.17 Myr, we propose that the 1-Myr time-scale is long enough to check the persistence of the apsidal confinement of Jupiter Trojans due to different precession rates of their π . Then the π distribution of the Jupiter Trojans after 1-Myr evolution is shown in Fig. 2 , from the integration mentioned at the beginning of this section. One can immediately notice the similar patterns depicted in Fig. 1 : (1) the longitudes of perihelia π are clustered around π J + 60 ○ and π J − 60 ○ for the L4 and L5 swarms, respectively; and (2) the number fraction of the clustered samples within a π bin could be over 0.2, which is significantly larger than f even ∼ 0.083 (>5 σ confidence level) in the case of a uniform π distribution. Therefore, the apsidal asymmetric-alignment of Jupiter Trojans should be intrinsic but not due to the observational bias. We suppose that the gravitational perturbation of Jupiter with eccentricity e J ∼ 0.05 may induce and maintain this intriguing orbital

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-EntityOfFutureInterest O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O B-CelestialObjectRegion B-CelestialObjectRegion B-EntityOfFutureInterest 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 B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O B-CelestialObject O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O B-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-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula O O B-CelestialObjectRegion O B-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O 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 B-EntityOfFutureInterest I-EntityOfFutureInterest 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


indicates that the generation of different emission bands occurs in different parts of the source with a non-uniform magnetic field and plasma density. From Fig. 1 , it is clear that each emission band has a fine structure: It consists of narrower (in frequency) elements that show a characteristic evolution in time. Each emission band begins with the appearance of a low-frequency element, which exists for a shorter time than the burst as a whole. Then there appears the next element, which is shifted towards the higher frequencies, etc. Each band contains 3–5 individual elements of the fine structure. Schematically, this evolution is more clearly shown in Fig. 2 , where the bright elements in the four emission bands from Fig. 1 are represented as dark horizontal lines. Figure 2. Schematic representation of the evolution of the dynamic spectrum (Fig. 1 ) with a fine structure of the emission bands. A fragment of the dynamic spectrum enclosed in a rectangle is analysed in Section 3 (see Fig. 7 ). A careful examination of the dynamic spectrum in Fig. 1 and similar spectra published by Hankins and Eilek leads to the conclusion that the elements of the fine structure are not superimposed on the quasi-harmonic emission bands. They actually form these bands, and the observed frequency drift of the emission bands towards higher frequencies is due to the successive change of one bright element to another, higher frequency element at a later instance of time. This fact is also indicated by Hankins et al. ( 2016 ), who analysed a large number of pulses and concluded that the drift of the emission bands towards higher frequencies is due to the appearance of new elements in the band that are delayed in time and start at slightly higher frequencies. Fig. 3 shows another, more rare type of the dynamic spectrum (Hankins, Rankin Eilek 2009 ). In the observed frequency range 8–10 GHz, the dynamic spectrum exhibits a continuous fine structure of 10 elements, rather than individual emission elements grouped into quasi-harmonic bands. Note that an insufficiently high frequency resolution does not allow an unambiguous conclusion to be drawn whether a finer frequency structure similar to that observed in Fig. 1 exists inside the observed emission bands. We also note that the interval 8–10 GHz, in which radiation with the above-mentioned structure was observed, is too narrow to definitely judge the change in the emission band spacing. It is quite possible that it remains constant. The latter will be taken into account in Section 3 when explaining the dynamic spectrum depicted in Fig. 3 . Figure 3. Rare type of the dynamic spectrum with the emission bands. This figure is adapted from Hankins et al. ( 2009 , fig. 5). Note that in both types of the dynamic spectrum, the signal lags as the radiation frequency is decreased. Hankins et al. ( 2016 ) relate this effect with the group delay of the signal directly in the local radiation source with a zebra pattern. It is

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Person O B-Person O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Citation I-Citation I-Citation I-Citation O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 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


to the dotted line in Figure 5 . The expected change of gas-phase metallicity due to this process can also be estimated using the toy model worked out in Appendix A . On the one hand, the drop of metallicity after accreting a gas mass Δ M a scales with the accreted gas mass aswhere M g 0 stands for the mass of gas already present in the object and C is a time-dependent parameter that is of the order of 1 after the accretion event (see Equation ( 26 ), with Z in ≪ Z g Z g 0 ). On the other hand, M a / τ in , and thereforeThe logarithmic derivative has been evaluated assuming Δ M a ∼ M g 0 and C ∼ 1. Its actual value can go all the way from −1 (when Δ M a ≫ M g 0 ) to 0 (when Δ M a ≪ M g 0 ). 4. Is the Correlation between Size and Gas-phase Metallicity a Result of Differences in the Depth of the Gravitational Potential of the Galaxies? The short answer to the above question is no . The long answer is elaborated in this section showing that the escape velocity and the metallicity are not correlated in the EAGLE galaxies. In order to parameterize the depth of the gravitational potential, we use the escape velocity at the half-mass radius,with Φ( R ⋆ ) the gravitational potential at R ⋆ . We model Φ as a combination of the potential due to DM, Φ DM , and the potential due to stars, Φ ⋆ ,The EAGLE database does not directly provide the depth of the gravitational potential. We infer the DM component from the DM mass and the half-mass radius of the DM assuming that the density drops with radius following a NFW profile (Navarro et al. 1996 ). The procedure is sketched in Appendix B . The stellar contribution is also inferred from the stellar mass and the half-mass stellar radius, this time assuming that the stellar density drops exponentially with radius. We follow the work by Smith et al. ( 2015 ). We assume the galaxy disks to be thin (scale height of 0.2 kpc), with the escape velocity computed in the plane of the disk. The results are rather insensitive to these assumptions since the potential is dominated by the DM component. This is also the reason why the gas mass is not included in the computation of v esc , because it represents only a minute fraction of the total mass. Figure 7 is similar to Figure 2 , but this time the symbols are color-coded with the escape velocity at the half-mass stellar radius. The spread in gas-phase metallicity is uncorrelated with the escape velocity, which is mostly set by the stellar mass. For a given stellar mass the galaxies have the same escape velocity irrespectively of the metallicity of their gas (cf. Figures 2 and 7 ). This fact is even clearer in Figure 8 . It shows Z g versus v esc for the full set of EAGLE galaxies (top left), as well as for narrow bins in galaxy mass (Δ log M ⋆ ∼ 0.3). Even though the full set shows a global trend for the gas-phase metallicity to increase with the escape velocity, this is just a construct (or a mirage) resulting from the mass–metallicity relation and the

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


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


of TD. In addition, the vector displacement ( of the two spacecraft is (−270.40, −47.21, −30.48) R E . It can be seen that the dot product of the TD normal (−0.098, 0.961, 0.258) and the vector displacement is negative. This means that Wind should have observed the “TD” earlier than ACE . In fact, the ACE spacecraft has observed this “TD” earlier than Wind . Thus, this DD should not be a TD. If we consider the DD to be an IS, the calculated DD propagation speed is 349.1 km s −1 in the rest frame, and the corresponding estimated time difference is 73.6 minutes, which is also different with the observed time difference (93.7 minutes). Even so, we consider that the DD should be an IS rather than a TD. As for the time deviation of the IS model, it may be caused by the following two factors. One is that the shock front may be not flat; the estimated time difference is not accurate. The other may be that not all the parts of the leading boundary of the reconnection exhaust meet the requirements of an IS, and the IS may be formed only somewhere within the boundary, with Wind and ACE crossing different parts of the leading boundary. Figure 3. Magnetic fields measured by Wind and ACE in the GSE coordinate system, where the dotted lines are for ACE , and the ACE time sequences were shifted by 94.1 minutes. 4. SUMMARY Previously, ISs were considered to be unphysical because they do not satisfy the so-called evolutionary conditions based on the theory of hyperbolic systems of conservation laws (Jeffrey Taniuti 1964 ; Kantrowitz Petschek 1966 ). Over the past more than four decades, there have been a large number of numerical investigations for ISs. In spite of evolutionary conditions, ISs are commonly observed to be stable shocks in numerical simulations (e.g., Wu 1987 ; Wu Hada 1991 ; Takahashi et al. 2013 , 2014 ), and two interplanetary ISs have been observed and reported (Chao et al. 1993 ; Feng Wang 2008 ). However, both ISs were identified through fitting the R-H relations based on one spacecraft observation. Our previous study (Feng et al. 2007 ) suggested that the analysis using a single spacecraft observation based only on the R-H relations could misinterpret a TD as an IS. In this study, we reported an IS associated with a magnetic reconnection exhaust, which was detected by the Wind and ACE spacecraft at 1 au on 2000 August 9. We investigated this shock by fitting the R-H relations and referring to the ACE observations. We fitted this discontinuity using the procedure of Lin et al. ( 2006 ) and found that the observed magnetic field and plasma data satisfy the R-H relations well. The normal Alfvén-Mach number is greater than unity in the preshock state and less than unity in the postshock state; the fast-mode Mach number in upstream and downstream regions are less than unity, and both slow-mode Mach numbers are greater than unity. The components of the preshock and postshock magnetic fields in the shock front have opposite signs. Namely,

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


RR Lyrae stars that are likely Orphan members, and we obtained . This is very similar to the value reported by Sesar et al. (2013) and also significant 12 . We explored the existence of a metallicity gradient in the Orphan stream using our nonvariable and RR Lyrae sample 13 . The depiction of the metallicity versus φ 1 can be found in Fig. 5 . In both of our samples (nonvariable and RR Lyrae sample) we do not detect any significant correlation between the sky position φ 1 and metallicity. A similar outcome holds even when we include only stars with a high probability p ( A | B ) > 0.5 for both of our samples. One of the possible reasons for this discrepancy lies in the different metallicity calibrations between our study and Sesar et al. (2013) . In our case, we rely on the new calibration of the ΔS method using metallicities determined from high-resolution spectra ( Crestani et al. 2021 ), while Sesar et al. (2013) relied on the calibration of Layden (1994) which is slightly offset compared to metallicities obtained from high-resolution spectra (see, e.g., For et al. 2011 ; Chadid et al. 2017 ). Another reason could lie in the metallicity scale, where Sesar et al. (2013) values lie on the Zinn West (1984) scale 14 , while our metallicities are on a different metallicity scale ( Chadid et al. 2017 ; Sneden et al. 2017 ; Crestani et al. 2021 ). This could shift the metallicities of Sesar et al. (2013) toward the metal-rich end by up to 0.2 dex ( For et al. 2011 ). To conclude, using our dataset we were unable to confirm the existence of a metallicity gradient in the Orphan stellar stream. Fig. 5. Stream coordinates, φ 1 , versus [Fe/H] ( top panel ), and metallicity distribution function ( bottom panel ) for likely variable andnonvariable Orphan stream members. The color-coding of each nonvariable star represents the probability of association to the Orphan stream p ( A | B ), and the green squares represent RR Lyrae stars associated with the Orphan stream in our study. The histogram in the lower panel represents the metallicity distribution of the entire sample (black line) the RGB stars (red dashed line), BHB stars (blue dotted line), and RR Lyrae stars (green lines). The red solid line represents the kernel density estimate of the metallicity distribution of the RGB stars. 5.2. Grus II as a possible progenitor In the work by K19, the previously considered candidates for the Orphan progenitors, Segue 1 and UMa II ( Fellhauer et al. 2007 ; Newberg et al. 2010 ), were excluded based on their distance and proper motions. One viable candidate for the progenitor of the Orphan stream remained, Grus II, a UFD (found in the DES by Drlica-Wagner et al. 2015 ). Grus II matches with the Orphan stellar stream in the coordinates and proper motion space. Recently, line-of-sight velocities and chemical abundances became available for several stars associated with Grus II UFD ( Simon et al. 2020 ; Hansen et al. 2020 ). The line-of-sight velocities center

O O O O O O B-CelestialObject 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 B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O B-Citation I-Citation O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O B-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 B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation 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 O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-CelestialObject O B-CelestialObject I-CelestialObject O B-CelestialObject I-CelestialObject 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 B-CelestialObject I-CelestialObject O B-CelestialObject I-CelestialObject O O O O O B-Survey O B-Citation I-Citation I-Citation I-Citation O B-CelestialObject I-CelestialObject O O O B-CelestialObject I-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O


between the best-fit values obtained from fits of the F99 law to each object’s set of color excesses (see the last column of Tables 4 and 5 ) and the values inferred from individual color excess measurement and the F99 law (see Table 3 ). In doing so these comparisons are made for each of the four color excess combinations: (top-left panel), (top-right panel), (bottom-left panel), and (bottom-right panel). Included in each panel’s sub-plots is the root-mean-square (rms) difference between the two methods. In general the values obtained by the two methods are in good agreement, as indicated by the fact that the data follow the black lines in the plots. Fig. 17 from as given in Tables 4 and 5 versus . The Poznanski et al. (2012) relation is over-plotted as a solid blue line. Empty symbols indicate upper limits on . A linear fit between the two quantities (with intercept fixed to zero) is drawn as a black dashed line and the corresponding fit expression is reported in the top-left corner of the figure. This expression has been obtained by linearly fitting all the points including the limits. We find that the optical and NIR color combinations providing the smallest dispersion among the suite of , , , and color combinations considered in this work are as follows. In the case of and time relative to the and colors exhibit minimal dispersion in , while for and time relative to the and colors exhibit minimal dispersion. Moreover, for and time relative to the and colors exhibit minimal dispersion in , while for and time relative to the and colors exhibit minimal dispersion. Discrepancies between the two methods are largely due to different spectral lines affecting the measurement from a single color combination more than the global fit value. We now compare the value derived for each object in the sample to their measurement obtained from visual-wavelength spectra (Holmbo et al., in prep.). Specifically, average values given in Tables 4 and 5 are plotted in Fig. 17 vs. . Over-plotted in the figure is the relation (solid blue line) found between these parameters by Poznanski et al. (2012) , as well as a linear fit (dashed line) to the data assuming when . The latter of these is given by . As expected there is significant scatter between the two quantities (cf. Poznanski et al. 2011 ). Returning to the CDFs shown in Fig. 14 , it is interesting to note that the SNe Ic consistently exhibit higher extinction values compared to SNe IIb and SNe Ib, and this holds independent of the assume value of . This is consistent with the findings of Anderson et al. (2015) whom used pixel statistics based on emission to study the environments of SNe by tracing on-going (16 Myr old) star formation within SN host galaxies. Anderson et al. found that SNe Ic show a statistically significant preference for being located in regions of on-going star formation, while SNe Ib are located in regions that do not as closely follow ongoing star formation. The implications are that

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 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 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 B-Wavelength O B-Wavelength O O O O O O O O O O B-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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O B-TextGarbage I-TextGarbage O O O O O O O O O O O O O O O B-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 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 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-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 B-CelestialObject I-CelestialObject 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-Observatory B-Telescope O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O B-Observatory I-Observatory I-Observatory I-Observatory I-Observatory I-Observatory I-Observatory O B-Observatory O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O B-Wavelength B-Wavelength O B-Wavelength O O B-Wavelength O O B-CelestialObject I-CelestialObject O O O O O B-Telescope I-Telescope B-Telescope B-Citation I-Citation I-Citation I-Citation O O O O B-CelestialObject I-CelestialObject 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 B-Identifier O O O O O O O O O O O O O B-Wavelength O O O O O O B-Identifier O O B-Software O O O B-URL O O O O O O O O B-Software O O O O O O O B-Software I-Software 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 B-CelestialObject 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 B-Wavelength O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O 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-Observatory B-Telescope O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O B-Wavelength O B-Wavelength O B-CelestialObject I-CelestialObject O O O O B-Telescope O O O B-Observatory O O O O O O O O B-Wavelength I-Wavelength B-Wavelength I-Wavelength B-Wavelength I-Wavelength B-Wavelength I-Wavelength B-Wavelength I-Wavelength B-Wavelength I-Wavelength B-Wavelength B-Wavelength I-Wavelength B-Wavelength B-Wavelength I-Wavelength O B-Wavelength B-Wavelength I-Wavelength O O


around 65% and 41%, and the uncertainties in their speeds give a likelihood of perfectly inelastic collision of around 98% and 100%, respectively. Similarly, the uncertainties in the propagation directions of the 2012 June and 2011 August CMEs give a likelihood of inelastic collision of around 65% and 77%, the uncertainties in their angular widths give a likelihood of inelastic collision of around 50% and 53%, and the uncertainties in their speeds give a likelihood of inelastic collision of around 94% and 84%, respectively. For the 2013 October CMEs, the uncertainties in the propagation directions, widths, and speeds correspond to a probability of 67% for super-elastic collision, 75% for inelastic collision, and 50% for super-elastic collision, respectively. The uncertainties in the directions of the 2011 February, 2012 March, and 2012 September CMEs give a likelihood of super-elastic collision of around 88%, 38%, and 89%, the uncertainties in their widths give a likelihood of super-elastic collision of around 73%, 43%, and 60%, while the uncertainties in their speeds give a likelihood of super-elastic collision of around 89%, 61%, and 49%, respectively. From the above values of probabilities and the values of e shown in Figures 4 – 11 , we note that the effect of the uncertainties is so large for some cases that it is difficult to ascertain a particular nature of collision for those cases. For instance, under the uncertainties considered, three cases (CMEs of 2010 May 23–24, 2013 October 25, and 2012 September 25–28) of the CMEs show the most probable nature of collision vacillating between the inelastic to super-elastic regime. Such an effect is expected for the CMEs of 2013 October 25 as its observed nature of collision was elastic, i.e., at the boundary of the inelastic and super-elastic. However, the CMEs of 2010 May show huge uncertainties in the e value in their directions, widths, and speeds. The CMEs of 2012 September 25–28 show a large deviation from the super-elastic nature due to uncertainties in the pre-collision leading edge speeds of the CMEs. Such uncertainty in the e value due to a change in the speed of the CMEs was not noted in Mishra et al. ( 2015b ). We point out that in the oblique collision scenario, even a reasonable uncertainty in the observed CME characteristics leads to a different nature of collision. The e value is found to be dependent to some extent on the relative propagation directions of the CMEs. However, this was not recognized in earlier studies that assumed the head-on collision scenario (Mishra et al. 2014 , 2015a ). We envisage that a change in the propagation directions may lead to a change in the relative contribution of the expansion speeds to the centroids speeds of the CMEs along the line joining their centroids. We did not make any attempts to understand whether the different propagation directions of the CMEs, which cause different contact areas between them, have some role in deciding the nature

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


Charlot ( 2003 ) 5 for the MILES spectral library (Snchez-Blzquez etal. 2006 ) using a Chabrier ( 2003 ) stellar initial mass function (IMF) over the range 0.1100M . The components for the base models comprised 16 ages from 1Myr to 13Gyr for each of four metallicities ( Z 0.004, 0.008, 0.02, 0.05). We note that tests with somewhat different base model sets and choice of IMF did not significantly affect continuum subtraction and so do not affect the emission-line results on which our analyses rely. Our procedure largely mirrors that performed on MUSE data of supernova hosts elsewhere (e.g. Galbany etal. 2016a ). 3.3 Emission-line fitting Emission-line fitting was performed on the spectra after subtracting the best-fitting continuum, as determined in Section 3.2 . Prior to fitting, the continuum-subtracted spectra were median filtered with a width of 120 this width was chosen in order to remove any broad residuals left by the imperfect continuum fitting, whilst leaving the narrow emission lines unaffected. The emission-line model was a composite model of single Gaussians initially centred at the wavelengths of H , [O iii ] 4959,5007, H, [N ii ] 6548,6583 and [S ii ] 6716,6731 (the two exceptions to this set-up, SNe 2002bp and 2008ge, are detailed later). The fitting was performed via the weighted LevenbergMarquardt least-squares algorithm. Such fitting is, however, susceptible to finding local minima solutions that are dependent on the initial guesses for the Gaussian parameters. In order to circumvent the dependency on initial guesses, and to restrict to physically plausible solutions we added the following caveats and steps to our fitting routine: The velocity offset of the Gaussian means were restricted to within 500km s 1 relative to the galaxys rest frame (i.e. after accounting for the redshift of the galaxy nucleus). This comfortably encloses the limits of rotational velocities seen in late-type galaxies (Sofue Rubin 2001 ) whilst preventing misidentification of lines. The velocity offset of the Balmer and forbidden lines were each tied, i.e. a single velocity offset for H and H was fit and a separate offset was fit for the other lines. The standard deviations of the Gaussians were restricted to 130km s 1 and pairs of lines for [O iii ], [N ii ] and [S ii ] had tied values for the standard deviation (in km s 1 ). In order to semibrute force locate the global minimum, a list of several initial guesses for each of the means, standard deviations and amplitudes to be fit was made. A grid was then formed of all possible combinations of these parameters to use as initial guesses for the LevenbergMarquardt fitter, which found the local minimum for each initial guess. The residual between the data and model was used as an estimator of the goodness of fit for each grid position and used to identify the best overall fit. Where the fitting process failed, we manually inspected the emission-line spectrum. In most cases, low signal to noise or

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


assumed distance of 5.3 kpc. Figure 19.129. Clump BYF 57 ICO Clump BYF 57 in 12 CO J = 1 → 0, mapped in I CO . Black I 12 CO contours in each frame are every 8 K km s −1 . The 7 ′′ Mopra beam is shown in the BR corner, corresponding to a scale of 0.95 pc at an assumed distance of 5.3 kpc. Figure 19.130. Clump BYF 57 Irms Clump BYF 57 in 12 CO J = 1 → 0, mapped in I rms . Black I 12 CO contours in each frame are every 8 K km s −1 . The 7 ′′ Mopra beam is shown in the BR corner, corresponding to a scale of 0.95 pc at an assumed distance of 5.3 kpc. Figure 19.131. Clump BYF 57 VLSR Clump BYF 57 in 12 CO J = 1 → 0, mapped in V LSR . Black I 12 CO contours in each frame are every 8 K km s −1 . The 7 ′′ Mopra beam is shown in the BR corner, corresponding to a scale of 0.95 pc at an assumed distance of 5.3 kpc. Figure 19.132. Clump BYF 57 Vrms Clump BYF 57 in 12 CO J = 1 → 0, mapped in V rms . Black I 12 CO contours in each frame are every 8 K km s −1 . The 7 ′′ Mopra beam is shown in the BR corner, corresponding to a scale of 0.95 pc at an assumed distance of 5.3 kpc. Figure 19.133. Clump BYF 57 σV Clump BYF 57 in 12 CO J = 1 → 0, mapped in σ V . Black I 12 CO contours in each frame are every 8 K km s −1 . The 7 ′′ Mopra beam is shown in the BR corner, corresponding to a scale of 0.95 pc at an assumed distance of 5.3 kpc. Figure 19.134. Clumps BYF 63-80 (Region 9) Tmb(Peak) Clumps BYF 63-80 (Region 9) in 12 CO J = 1 → 0, mapped in T mb (Peak). Black I 12 CO contours in each frame are every 20 K km s −1 . The 7 ′′ Mopra beam is shown in the TL corner, corresponding to a scale of 0.45 pc at an assumed distance of 2.5 kpc. Figure 19.135. Clumps BYF 63-80 (Region 9) Trms Clumps BYF 63-80 (Region 9) in 12 CO J = 1 → 0, mapped in T rms . Black I 12 CO contours in each frame are every 20 K km s −1 . The 7 ′′ Mopra beam is shown in the TL corner, corresponding to a scale of 0.45 pc at an assumed distance of 2.5 kpc. Figure 19.136. Clumps BYF 63-80 (Region 9) ICO Clumps BYF 63-80 (Region 9) in 12 CO J = 1 → 0, mapped in I CO . Black I 12 CO contours in each frame are every 20 K km s −1 . The 7 ′′ Mopra beam is shown in the TL corner, corresponding to a scale of 0.45 pc at an assumed distance of 2.5 kpc. Figure 19.137. Clumps BYF 63-80 (Region 9) Irms Clumps BYF 63-80 (Region 9) in 12 CO J = 1 → 0, mapped in I rms . Black I 12 CO contours in each frame are every 20 K km s −1 . The 7 ′′ Mopra beam is shown in the TL corner, corresponding to a scale of 0.45 pc at an assumed distance of 2.5 kpc. Figure 19.138. Clumps BYF 63-80 (Region 9) VLSR Clumps BYF 63-80 (Region 9) in 12 CO J = 1 → 0, mapped in V LSR . Black I 12 CO contours in each frame are every 20 K km s −1 . The 7 ′′ Mopra beam is shown in the TL corner, corresponding to a scale of 0.45 pc at an assumed distance of 2.5 kpc. Figure 19.139. Clumps BYF 63-80 (Region 9) Vrms Clumps BYF 63-80 (Region 9) in 12 CO J = 1 → 0, mapped in V rms . Black I 12 CO contours in each frame are every 20 K km s −1 . The 7

O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject O B-CelestialObject I-CelestialObject I-CelestialObject O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength 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-Telescope O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject O B-CelestialObject I-CelestialObject I-CelestialObject O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject O B-CelestialObject I-CelestialObject I-CelestialObject O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength 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-Telescope O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject O B-CelestialObject I-CelestialObject I-CelestialObject O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength 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-Telescope O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject O B-CelestialObject I-CelestialObject I-CelestialObject O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength 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-Telescope O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject O O O B-CelestialObject I-CelestialObject I-CelestialObject O O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength 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-Telescope O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject O O O B-CelestialObject I-CelestialObject I-CelestialObject O O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength 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-Telescope O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject O O O B-CelestialObject I-CelestialObject I-CelestialObject O O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength 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-Telescope O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject O O O B-CelestialObject I-CelestialObject I-CelestialObject O O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength 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-Telescope O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject O O O B-CelestialObject I-CelestialObject I-CelestialObject O O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength 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-Telescope O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject O O O B-CelestialObject I-CelestialObject I-CelestialObject O O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength 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


; Chiang Youdin 2010 ; Klahr et al. 2018 ). In Schneider et al. ( 2019 ), we studied the transition from test particle to collective behavior in a levitation experiment, analyzing the free-fall velocity of grains in a cloud. We empirically found that the sedimentation velocity depends on what we call sensitivity factor F S and the closeness C of the individual particle asThe closeness C of a particle is constructed from the interparticle distances between the grain and all other particles j as N is the total number of particles. The sensitivity factor F S in Equation ( 5 ) depends on the average solid-to-gas ratio of the system:The solid-to-gas ratio is defined as the ratio between the total dust mass and the average gas mass,where m p is the mass of a single particle, V is the total volume covered by particles, ρ g is the gas density in the chamber, ρ p is the bulk density of the individual grains, and s is the particle diameter. As seen in Equation ( 5 ), Schneider et al. ( 2019 ) also empirically found that particles are only influenced by the other particles in a cloud if the average solid-to-gas ratio is above a threshold value crit ; otherwise, F s = 0 and particles sediment with v 0 . The sensitivity α connecting the solid-to-gas ratio to the sensitivity factor in Equation ( 5 ) was just a constant in Schneider et al. ( 2019 ). This description is purely empirical and was deduced from a single experiment so far. Here, we present a systematic analysis, where we varied the gas pressure, particle size, and rotation frequency of the chamber and improved the setup and data acquisition. 2. Levitation Experiment 2.1. Setup The setup of the experiment (see Figure 1 ) follows the principle used in aggregation experiments by Poppe Blum ( 1997 ) and Blum et al. ( 1998 ), but is especially based on earlier experiments on dense clouds by Schneider et al. ( 2019 ). Figure 1. Experimental setup without auxiliary parts. The vacuum chamber is evacuated to a preset pressure. Two cameras observe the particles from the front. Illumination is provided by LED modules. Particles—in this study, hollow glass spheres of different sizes and densities—are dispersed once at the beginning of the experiment, within a rotating vacuum chamber with low ambient pressure. Particles are injected using a vibrating sieve in an extension of the vacuum chamber. The gas inside follows the rigid rotation of the chamber. The vacuum chamber has a diameter of 320 mm. Inside the chamber, a ring of LEDs is used to illuminate the particles. The scattered light of the particles is detected by two non-rotating cameras. These cameras observe the particles from the front at a distance of 40 cm on a 1′′, 5 megapixel sensor with a spatial resolution in the order of 10 μ m. The frame rate is 40 fps with an exposure time of 6 ms. The field of view is 19 × 15 cm. Imaging and synchronization of both cameras are controlled by a machine vision computer. Spatial calibration was realized with a

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


1999 ). The cycle duration is believed to be controlled by the meridional flow. Fig. 7 shows also the ratio of the cycle period to advection time. The ratio – though not constant – is of the order one and varies moderately. Figure 7. Cycle period for marginal dynamos (a) and the period ratio to the advection time (b). V b is the meridional velocity at the inner boundary r i at the latitude of 45°. Fig. 8 shows estimations of the Rossby and dynamo numbers. The Rossby number is position-dependent. The estimations of Fig. 8 were done for the radius r one pressure scaleheight above the base of the convection zone, i.e. for the radius r where r − r i = H p . The Rossby number Ro ∼ 2 of Fig. 8 agrees with estimation of van Saders et al. ( 2016 ). The two numbers in Fig. 8 are often used to parametrize observations or theoretical computations of magnetic activity. The two parameters of this figure vary moderately but are not constant. This implies that stellar activity can be only crudely parametrized by a single parameter. Figure 8. (a) The Rossby number estimated for the rotation periods of equation ( 2 ). (b) The marginal dynamo number ( 4 ) estimated with the isotropic part η of the eddy diffusivity at middle depth in the convection zone. 5 CONCLUSIONS Asteroseismic measurements of stellar ages revealed a dramatic decrease in the rate of stellar spin-down and magnetic activity for ages beyond about a half of the main-sequence life (Metcalfe et al. 2016 ; van Saders et al. 2016 ). This paper suggests an explanation for the violation of gyrochronology by a switch-off of the global dynamo for a rotation period exceeding the critical value estimated by equation ( 2 ). The switch-off should not be abrupt. Dynamo theory explains the observed variations in amplitudes and periods of solar cycles by fluctuations in dynamo parameters (cf. Choudhuri 2011 ). The fluctuations will cause a star to wander between the parameter regions of (supercritical) dynamo of ‘normal’ magnetic activity and (subcritical) dynamo of fading activity if the rotation period is close to its critical value. The dynamo models with fluctuating parameters reproduce the statistics of grand solar minima (Usoskin, Solanki Kovaltsov 2007 ) only if the dynamo number is close to its marginal value (Moss et al. 2008 ; Olemskoy Kitchatinov 2013 ; Karak, Kitchatinov Brandenburg 2015 ). It may be appropriate to note that observations of total solar eclipses in the Maunder minimum did not find an extended solar corona (Eddy 1976 ) indicating a relatively small co-rotation radius and inefficient spin-down. Unfortunately, the concept of dynamo switch-off at the critical rotation period cannot be supported by dynamo modelling because of uncertainties in key dynamo parameters. The uncertainties can, however, be reduced using this concept. Equation ( 5 ) for α-parameter or similar equation for the dynamo number can be used to estimate the dynamo parameter values for a star of given rotation

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O B-Formula I-Formula I-Formula O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-ObservationalTechniques O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-ObservationalTechniques O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O B-CelestialObject O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


are associated in a binary system with a large mass ratio. This suggests the existence in the Kepler LEGACY sample of a sizeable fraction of binaries. This is supported by the fact that N17 detected two SB2s in their sample of ten stars from snapshot observations only. It would not be surprising considering the ubiquity of companions in solar-like stars (e.g., Duquennoy Mayor 1991 ). This aspect certainly deserves further investigation (i.e. a dedicated RV monitoring). As guidance for further ensemble seismic modelling of Kepler main-sequence stars, our comparison with the results of (semi-)automatic methods suggests that the study of Buchhave Latham (2015) is a valuable source of effective temperatures and metallicities. For the elemental abundances, the works of Bruntt et al. (2012) and Brewer et al. (2016) appear to be of similar quality for most elements. However, our results tend to be in closer agreement with those of the latter study. We confirm that the ASPCAP effective temperatures used for the APOKASC catalogue are systematically too cool for dwarfs. This is not completely unexpected given that the pipeline is naturally optimised for red giants ( García Pérez et al. 2016 ). The consequence is that a grid-based modelling that makes use of the SDSS photometric T eff scale may be more reliable for relatively unevolved Kepler targets, as already claimed by Serenelli et al. (2017) . However, one can see, in Fig. 12 , the existence of a systematic discrepancy between the SDSS T eff values and those of Brewer et al. (2016) . We find evidence in our sample that the APOKASC metallicities for dwarfs (solely based on ASPCAP) are typically underestimated by ∼0.1 dex. A similar conclusion is reached when considering the data of Brewer et al. (2016) . Correcting for such a bias would lead to a fractional improvement of a few percent in the stellar properties quoted in the APOKASC catalogue (e.g., ∼5% in age; Serenelli et al. 2017 ). As illustrated by our new seismic analysis of KIC 9965715 , even larger changes can be expected if the quality of the classical parameters is mediocre. 10.2. Stellar ages from chemical clocks beyond solar analogues We find that the quality of stellar ages empirically determined from abundance data is currently limited by the precision of the calibrations, which is typically 1.5–2 Gyr when venturing away from stars closely resembling our Sun. Constructing more complex relationships that take into account a dependency on one or two stellar parameters does improve the situation, if only slightly. For instance, incorporating T eff as an additional variable globally improves the agreement between the abundance- and seismic-based ages for the APOKASC stars studied by Brewer et al. (2016) . The calibrations presently available appear significantly less precise than what can be achieved for stars akin to the Sun (precision often below 1 Gyr), but some abundance ratios may hopefully prove more suitable than others outside

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


fractional rms variability spectrum and the best-fit model in Figure 12 (right). The fractional variations in the normalization of the illuminating continuum and reflected emission are and , respectively. 7. Summary and Discussion We present the first results from our XMM-Newton observation of the NLS1 galaxy PG 1404+226. Here, we investigated the large-amplitude X-ray variability, the origin of the soft X-ray excess emission, and its connection with the intrinsic power-law emission through a detailed analysis of the time-averaged as well as time-resolved X-ray spectra, and frequency-averaged ( ν ∼ [1.4–100] × 10 −5 Hz) X-ray fractional rms spectrum. Below we summarize our results. 1. PG 1404+226 showed a short-term, large-amplitude variability event in which the X-ray (0.3–8 keV) count rate increased exponentially by a factor of ∼7 in about 10 ks and dropped sharply during the 2016 XMM-Newton observation. The hard X-ray (1–8 keV) Chandra /ACIS light curve also showed a rapid variability (a factor of ∼2 in about 5 ks) with an exponential rise and a sharp fall in 2000 (Dasgupta et al. 2005 ). The rapid X-ray variability had been observed in a few NLS1 galaxies (e.g., NGC 4051: Gierliński Done 2006 ; 1H 0707–495: Fabian et al. 2012 ; Mrk 335: Wilkins et al. 2015 ). However, the UV ( λ eff = 2910 Å) emission from PG 1404+226 is much less variable () than the X-ray (0.3–8 keV) variability (). 2. The source exhibited strong soft X-ray excess emission below ∼1 keV, which was fitted by both the intrinsic disk Comptonization and relativistic reflection models. The EPIC-PN spectral data revealed the presence of a highly ionized ( ξ ∼ 600 erg cm s −1 ) Ne x Ly α absorbing cloud along the line of sight with a column density of N H ∼ 5 × 10 22 cm −2 and a possible O viii Ly α emission line. However, we did not detect the presence of any outflow as found by Dasgupta et al. ( 2005 ). 3. The modeling of the RGS spectrum not only confirms the presence of the Ne x Ly α absorbing cloud and O viii Ly α emission line but also reveals an O viii Ly β emission line. 4. The time-resolved spectroscopy showed a significant variability in both the soft X-ray excess and primary power-law flux, although there were no noticeable variations in the soft X-ray excess temperature ( eV) and photon index of the primary power-law continuum. 5. In the disk Comptonization scenario, the rapid X-ray variability can be attributed to a variation in the source luminosity as indicated by the time-resolved spectroscopy. However, the modeling of the X-ray fractional rms spectrum using the “one-component disk Comptonization” model cannot reproduce the observed hard X-ray variability pattern and indicates a reflection origin for the soft X-ray excess emission (see Figure 12 , left). 6. In the relativistic reflection scenario, the observed large-amplitude X-ray variability was predominantly due to two components: an illuminating continuum and smeared reflected emission; both of them are

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


from the spine. Previously published high-resolution images show that filaments consist of numerous very fine threads. On the other hand, panel (a), which is a cutout from the full-disk image, has the spatial resolution about 1′′–2′′. Therefore, the barbs seen here are understood to be groups of smaller threads below the spatial resolution. The directions of the polarization signals in panel (b) coincide with the H α spine and barb structure very well. The direction somewhat varies from part to part of the filament, but it is approximately parallel to the H α spine or barbs in any part. This result confirms previous deductions that the structure in filaments is confined to follow the magnetic field. Plasma motions in filaments have been observed to be along the fine threads (Lin et al. 2003 , 2005 , 2008 ), and also verify the field-aligned nature of the threads of filaments. Because the polarization directions of the filament in Figure 2 (b) are roughly aligned with either the spine or barbs, the average polarization direction for all of the filament structure without differentiating between the spine and barbs can be defined; it is shown by a dashed line in the inset at the lower-right of panel (b). The green line shows the direction of the axis of the filament, which represents the average direction of the polarity inversion line seen in panel (b), which is approximately along a straight line. In the case of the filament in Figure 2 , these two lines intersect at an angle of 180. In this case, the average polarization direction deviates from the filament axis by −180. The deviation angle is defined as an acute angle and a positive value corresponds to the counterclockwise deviation; in this case, the deviation is clockwise. This deviation angle is considered to be the deviation angle of the magnetic field vector with respect to the polarity inversion line. As mentioned in Section 1 , it is known that H α structures in filaments shows a chiral nature (see e.g., Zirker et al. 1997 ; Martin 1998 ). As in the case of the filament shown in Figure 2 , where the filament has barbs along the sides of the filament that bend downward to the right and make acute angles to the right side of the filament axis, the chirality is “right-bearing” (dextral). The alternative chirality is “left-bearing” (sinistral). The spine/barbs structure and the deviation by an acute angle of the average polarization direction with respect to the axis of the filament are schematically illustrated at the bottom of Figure 2 . It is known that right(left)-bearing filaments are dominant in the northern (southern) hemisphere, and actually the filament is located in the northern hemisphere as shown in Figure 1 . The magnetic field direction shown in Figure 2 (b) has the 180° ambiguity, and it cannot be solved only with our polarization measurements. However, Martin et al. ( 1994 ) revealed that the direction of the magnetic field can be interpreted as shown in 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 B-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-CelestialObjectRegion B-CelestialObjectRegion O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O


O O O O O O B-Wavelength O B-Wavelength O O O O O O O O O O O O O O O O O O O O B-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 B-Wavelength O O O O O O O O O O O O O O O O B-Wavelength O B-Wavelength I-Wavelength I-Wavelength O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O B-Wavelength O B-Wavelength I-Wavelength B-Citation I-Citation I-Citation I-Citation O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation O O B-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O B-Observatory O O O O O O O O B-Wavelength O O B-CelestialObject I-CelestialObject O B-Observatory O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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-Model I-Model I-Model I-Model I-Model O O O B-URL O O O O O O O O O B-Organization I-Organization I-Organization I-Organization O O B-URL O B-Dataset I-Dataset I-Dataset O O O O B-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula O O O O O B-Model O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O B-URL I-URL I-URL I-URL O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O B-Wavelength I-Wavelength O O O B-Model I-Model B-Model O O O O O O O O O O O O O O O O O O O B-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion O O B-URL O O O B-Dataset I-Dataset I-Dataset I-Dataset I-Dataset I-Dataset B-Dataset B-Citation I-Citation I-Citation I-Citation O O O O B-Software 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 B-Model I-Model I-Model O O O O B-CelestialObject I-CelestialObject O O O O O O O O B-Software O O B-Software I-Software I-Software I-Software 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 B-Model I-Model I-Model I-Model I-Model I-Model I-Model I-Model I-Model O B-Model I-Model I-Model I-Model I-Model O O O B-URL O O O O B-Software O O O


from this distribution to infer a simulated distribution for the X-ray non-detected sources (see Figure 8 ). This result provides additional support for the need for a large population of CT AGNs to explain the black hole mass density while adhering to constraints imposed by the cosmic X-ray background (Comastri et al. 2015 ). It should be noted the distributions presented here are derived from modeled X-ray data with certain assumptions (e.g., source redshift, photon index, lack of intervening dust on larger scales), and that a more thorough treatment is required to understand the underlying distributions. A detailed analysis of such modeling is left for future work. 4.4. X-Ray Stacking Analysis As an additional test of our ability to select heavily obscured AGNs with no X-ray counterparts, we performed an X-ray stacking analysis using stackfast . 10 10 http://www.dartmouth.edu/stackfast/ For this analysis we chose to focus strictly on sources within the Chandra footprint, as Chandra yields the highest S/N of our three X-ray observatories. The stackfast software uses pre-reduced Chandra ACIS data products based on individual observations to match against a set of input sources. The pre-reduction stage allows stackfast to work much more efficiently than other stacking methods, as the data are only sorted and screened once, at initialization; the result is a set of stackable X-ray events containing position, energy, grade, and exposure times for each source within the master set of Chandra observations. For each of the sources in our sample, we extracted photon counts and exposure times in both soft (0.5–2 keV) and hard (2–7 keV) energies, and estimated X-ray fluxes and luminosities (see Table 6 ). Fluxes are computed using count-rate-to-flux ratios characteristic of Chandra ACIS-I responses in Cycle 12 (in approximately the middle time frame of the observations in our stacking analyses), and assuming a power-law spectrum with typical Galactic absorption ( = cm) and photon index Γ = 1.4. This spectral shape is broadly consistent with the observed ratios of hard and soft source counts in our stacking analyses as shown in Table 6 . The count-rate-to-flux ratios adopted are 1.11 × 10 erg cm count (0.5–2 keV count rate to 0.5–2 keV flux) and 3.04 × 10 erg cm count (2–7 keV count rate to 2–10 keV flux). We obtained uncertainties in the stacked flux by bootstrap resampling of the input sources. This yields uncertainties on the average flux for the sample, which reflect the distribution in input fluxes and are typically larger than Poisson photon counting uncertainties. Additional details regarding stackfast can be found in earlier implementations of the code (e.g., Hickox et al. 2007 ; Chen et al. 2013 ; Goulding et al. 2017 ). Table 6 X-Ray Stacking Data and Results Note. X-ray stacking results for energy ranges of 0.5–2 and 2–7 keV. For each energy range, we present exposure time, photon counts, and flux and luminosity estimates. The flux and

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


S = S t (and ). In Table 6 we present the statistical results of a linear least-squares analysis for the toy model ensemble, both prior to and after time-randomization, for , 0.010, and 0.020. These results can be compared directly against the results from Section 4 and Table 4 . As can be seen in the table, for a large value of there is a significant difference in the width of the measured slope histogram between the original time-ordered data and the randomized data, with the distribution of the original time-ordered data being significantly broader than that of the randomized data. In all three model cases, the width of the measured slope for the randomized data remains similar to that for both the time-ordered and randomized data obtained by the JCMT Transient Survey to date, suggesting that the uncertainty assumptions of the toy model are reasonable. As the magnitude of decreases, the measured slope distribution for the time-ordered data becomes narrower. The trends seen here are entirely as expected since the strength of the input slope within the toy model is proportional to and becomes directly measurable in the time-ordered data as the secular signal becomes greater than the uncertainty in the individual measurements. For the randomized data, the input slope is significantly disrupted and thus there is little signal remaining to influence the histogram. The observed trend is similar for the histograms of measured slope in units of the measured slope uncertainty. For large values of this width becomes significantly larger than unity for the time-ordered observations while the randomized distribution remains close to 1.1 (which is also the value obtained by the Transient Survey ensemble). Table 6 Secular Variability Analysis: Histogram Widths in the Toy Model Notes. a Standard deviation of S measured for all members of the ensemble (see the text). b Standard deviation of measured for all members of the ensemble (see the text). The toy model can be extended in order to predict the detection power of the JCMT Transient Survey after its full three years of observation. By increasing the number of observations to 30 and the time period to three years, we show in Table 6 that the difference in ensemble histogram widths between the time-ordered and random observations becomes much stronger for each value of . We thus conclude that at present we can rule out a Gaussian distribution of secular variations linear in time with but that a distribution with would be undetectable today. After the full three years of the survey, we expect to either measure or rule out distributions with . In each of these toy models, the normal distribution of linear slopes prevents there being a significant population of sources with large brightness variations, such as those observed by the JCMT Transient Survey (Table 5 ). This suggests that the five observed sources are indeed rare, statistical outliers. It should be recognized, however, that the toy models are

O O O O O O O O O O O O O O O O B-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 I-Survey I-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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 I-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 O O O O O O O B-Survey I-Survey I-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 O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey I-Survey I-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 B-Model I-Model O B-Software I-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O B-Wavelength O B-Wavelength O O O B-Telescope B-Instrument O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject B-CelestialObject O O O O O O O O O B-Wavelength O B-CelestialObject O O O O O O O O O O O O O O O O O O O B-Telescope B-Instrument O O B-Software B-Citation I-Citation I-Citation I-Citation O O B-Model I-Model I-Model O O O B-Model O O O O O B-Model I-Model O O O B-Wavelength 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-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O B-URL O O O B-Model I-Model 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 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 B-CelestialObject O O O O O O O O O O O O B-Instrument I-Instrument I-Instrument B-Instrument B-Citation I-Citation I-Citation I-Citation O O O B-Telescope I-Telescope I-Telescope O O O B-Proposal I-Proposal I-Proposal O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O B-CelestialObject O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


of the X-ray flux (see e.g. Patruno, Wijnands van der Klis 2009b ), which can hinder the detection of relative weak spin derivatives (see e.g. Galloway et al. 2002 ; Burderi et al. 2006 ; Riggio et al. 2008 ; Bult et al. 2019 ). Here, we report on the phase-coherent timing analysis of the AMXP IGR J17591–2342 (Sanna et al. 2018d ), first detected by INTEGRAL on 2018 August 10 (Ducci et al. 2018 ) and extensively monitored by the NICER instrument during its outburst. Moreover, we investigated the evolution of the spin pulse delays within the framework of magnetically disc-threading theories in which the material torque (dependent on mass accretion rate) as well as the disc-threading torques exerted by the magnetic field are taken into account (see e.g. Rappaport et al. 2004 ; Kluźniak Rappaport 2007 ). For the first time in phase-coherent timing analysis of AMXPs, we modelled variations of the frequency spin derivative taking into account instantaneous values of the mass accretion rate by following the X-ray flux evolution. Recently, a similar approach has been successfully applied to the timing of the X-ray pulsar GRO J1744–28, a slowly spinning (∼2 Hz) NS accreting from a low-mass companion (Sanna et al. 2017b ). The obtained results show that, at least in this case, the standard theory of accretion on to NS works very well also for fast rotators and allowed an accurate determination of the magnetic field strength that is in the range of the values expected for this class of sources. Finally, we report on the updated source ephemerides and we discuss the properties of the X-ray pulsation as well as its temporal evolution. 2 OBSERVATIONS AND DATA ANALYSIS NICER (Gendreau, Arzoumanian Okajima 2012 ) started monitoring the X-ray transient IGR J17591–2342 on 2018 August 15 (MJD 58345) up to 2018 October 17 (MJD 58408.2) for a total of 37 dedicated observations. We processed the available NICER observation using the nicerdas pipeline (version V004a) retaining events in the 0.2–12 keV energy range, for which the pointing offset was 54 arcsec, the dark Earth limb angle was >30°, the bright Earth limb angle was >40°, and the ISS location was outside of the South Atlantic Anomaly (SAA). Moreover, we removed short intervals that showed background flaring in high geomagnetic latitude regions. As a result of the filtering process we retained a total exposure time of ∼101 ks. The spectral background was obtained from a blank-sky observation of the RXTE-6 region. We did not detect any Type-I thermonuclear bursts during the observations analysed in this work. For each observation we modelled the energy spectrum with an absorbed blackbody component plus a thermally comptonized continuum ( Tbabs(bbody+nthcomp) in Xspec) and we extracted the source unabsorbed flux in the energy range 0.5–10 keV (see Fig. 1 ). Finally, we barycentred the NICER photon arrival times with the barycorr tool using the JPL DE-405 Solar system ephemeris and adopting the

O O B-Wavelength O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O B-CelestialObject I-CelestialObject B-Citation I-Citation I-Citation I-Citation O O O O B-Telescope O O O O B-Citation I-Citation I-Citation I-Citation 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-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O B-Wavelength O B-CelestialObject I-CelestialObject 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 B-Wavelength O O O O O O O O O O O O B-Telescope B-Citation I-Citation I-Citation I-Citation O O O O B-Wavelength O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O B-Software I-Software B-Identifier I-Identifier O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O B-CelestialObject O O O O O O B-Mission O O O O O B-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion 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 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-Model O B-Software O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O B-Software I-Software O O B-Dataset I-Dataset I-Dataset I-Dataset I-Dataset O O O