We also find a large extinction of A V = 1.56 mag for this target. HD 38043, sectors 1–3, 5–6, 8–13 The TESS light curve spans 357 d and includes all sectors except 4 and 7. The data are at 2-min cadence in all available sectors. The p modes appear to be dominated by two nearly equally spaced multiplets: the first contains the strongest three modes – the same ones for which frequencies and amplitudes are provided in Table 1 – with a spacing of ∼0.51 d −1 . The second is slightly lower in frequency and amplitude and has a spacing of ∼0.55 d −1 . These could be rotationally split multiplets of modes with similar but non-identical n and l. This star is highly multiperiodic at lower frequencies, consistent with g-mode pulsation, though we could not identify any clear period spacings. HD 41958, sectors 1, 4–5. 7–8, 11 The three strongest p modes have similar amplitudes (7.5–8.2 mmag). They do not have any obvious harmonic relationship, nor do they have the frequency ratio (0.77–0.78) expected of the fundamental mode and first radial overtone modes. HD 42503, sectors 5–7 The mutliperiodic nature of the light curve at frequencies near 5 d −1 is rather unusual. The frequency content does not strongly resemble that of γ Dor stars, but is also quite different from typical δ Sct stars. No radial modes could be identified from frequency ratios of the stronger peaks. The peaks at 0.99 and 2.00 d −1 are not perfect harmonics, and another peak at 3.94 d −1 also falls on this near-harmonic pattern. HD 43533, sectors 6–7 The star is a γ Dor variable and the light curve is dominated by low-frequency variability, with dozens of significant peaks below 6 d −1 , and this variability spills into the δ Sct frequency domain. Excluding this variability, which presumably does not include independent p modes, there are only a few peaks in the Fourier transform that make this a δ Sct star. All three extracted peaks are significant, with SNR>4, despite their low amplitudes. The low amplitudes perhaps suggest these peaks belong to a contaminating source, but the Gaia DR2 data show no likely contaminant. It is noteworthy that this star is located below the ZAMS compared to tracks of solar metallicity. HD 44930, sector 5 The Fourier transform is dominated by several p modes of mmag amplitude. A group of weaker peaks with frequencies between 2 and 3 d −1 might be g modes. The absence of peaks at even lower frequencies would then suggest these are l = 1, m = 1 prograde modes, which suggests the near-core region rotates rapidly. This star is in the Octans association and has a measured Δν of 6.03 d −1 (Bedding et al. 2020 ). The échelle diagram (Fig A1 ) suggests f 1 = 18.15 d −1 is the fundamental mode, even though this is not in agreement with the P–L prediction. HD 47425, sectors 6–7 The two dominant p modes are too close in frequency to be the fundamental mode and first radial overtone. Indeed, it is not possible to clearly identify radial modes by period ratios in


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


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.


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


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


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


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,


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


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


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


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


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


; 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


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


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


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


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


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


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


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


field strength can be narrowed by 10 ν Lar max{ ν Rad , ν Em }. Utilizing the fact that Fe ii λ 5362.970 Å () absorption line is fully radiative aligned for all of the orbital phases, we deduce that the upper limit field strength is ∼108 mG. Additionally, we find that the Fe i λ 5586 Å () absorption line presents a more than 3 σ detectability polarization signal at the orbital phases 0.544, 0.564, and 0.988 and that the polarization direction for all those phases aligns with the radiative pumping direction rather than the magnetic field direction. This gives us an upper limit for the field strength of ∼80 mG. The accuracy of the field strength is increased by at least two decades compared to the previous 10 G upper limit, constrained from the non-detection of the Zeeman effect. 5. Discussion GSA is the most probable and natural explanation for the discovered polarization signals of the ground-state absorption lines that are realigned to one direction as opposed to the orbital synchronization. We provide here the mean magnetic field of the photosphere surface medium that corresponds to the central part of the absorption line. Figure 2 (d) illustrates that such magnetic field is reasonable on the stellar surface. A full magnetic field tomography requires further study, which is beyond the scope of current observation precision. Higher-resolution spectral observation will enable us to study the wings in the absorption line profiles, separating the emission components from outflows. Through our analyses, we assume that the anisotropic pumping comes from the secondary (following Leone et al. 2018 ). However, when constraining the magnetic field strength, a narrower range might be achieved if accounting for the photons from the primary. We calculate the extended radiation field of the primary following Zhang et al. ( 2015 ) with the Lambert cosine law and limb-darkening (Claret Bloemen 2011 ) considered, and find that the lower limit for magnetic field strength can be ∼2 mG (see Figure 4 (a)). Additionally, we could interpret the orbital synchronization as a result of local polarized flux illuminating the medium rather than pumping from the secondary. Nonetheless, even under such an assumption, the realigned polarization direction of the two ground-state lines that we report here can still be explained by the magnetic realignment of the angular momentum on the ground state. Moreover, beyond the optical band, GSA can be implemented with multi-frequency data ranging from ultraviolet to submillimeter to trace not only the spatial but also the temporal variations of magnetic field (Yan Lazarian 2007 , 2012 ; Shangguan Yan 2013 ; Zhang Yan 2018 ). 6. Summary Polarizations of absorption lines from the ground state with a high polarization degree are discovered in the binary system of 89 Her. We conclude the following. 1. The polarization directions of the two Fe i lines show little variation across the orbital period as opposed to the polarization of


flattening in the values at lower column densities could be an effect of completeness. The nominal function (e.g., blue curve in Figure 9 ) is calculated for 3 σ detections. If this threshold is raised to 4 σ or even 5 σ , there is relatively less effective pathlength at lower column densities. The blue curve in the left-hand panels of Figures 9 , 11 , 12 representing moves to the right by ∼0.1 dex for each 1 σ increase in significance level and the frequency of weak absorbers rises. This results in a steepening of the weak-end slope of the cumulative distribution function (less pathlength for the same number of detections), but it does not eliminate the non-power-law nature of the distributions in any case. Therefore, we believe that the turnovers seen in many of the metal absorber distributions are real, but the weak-end slopes should be treated with caution. 4.2.5. Ne <sc>viii</sc> The extreme-UV (2 s – 2 p ) doublet transition of Ne viii (, f = 0.1030, 0.0505) is often presented as a less-ambiguous tracer of collisionally ionized gas than O vi or other highly ionized, FUV metal transitions (Savage et al. 2005 ). Several compelling studies of warm-hot or multiphase gas have been made using Ne viii in conjunction with H i , O vi , and other ions to constrain gas temperature and density (Savage et al. 2005 , 2011 ; Narayanan et al. 2009 , 2011 ; Tripp et al. 2011 ; Meiring et al. 2013 ; Hussain et al. 2015 ). Unfortunately, the Ne viii doublet only redshifts into the COS/G130M band at , which limits us to the 13 highest-redshift AGN sight lines in this survey, usually without observations of the strong H i counterparts. We measure several dozen Ne viii systems, but all are at redshifts similar to the background AGNs and show the hallmarks of intrinsic, rather than intervening, absorption. They are primarily strong, blended, multi-component absorption profiles in high ions, often lacking H i absorption. There are three Ne viii detections at >3 σ in our survey that can be reasonably identified as intergalactic rather than intrinsic systems. The system detected toward PKS 0405−123 at z = 0.49494 in Ne viii and O vi by Narayanan et al. ( 2011 ) shows and . In an earlier reduction of the data allowing for the contaminating effects of fixed pattern noise, Narayanan et al. ( 2011 ) measured column densities of and . The origin of the Ne viii and O vi is consistent with collisionally ionized gas with T ≈ 5 × 10 5 K and a baryonic column density of cm −2 . Two other Ne viii detections have no corresponding absorption in any other metal or H i transition. The first is a pair of broad absorption features toward PKS 0637−752 consistent with Ne viii doublet absorption at z = 0.60552 with . Ly β and O vi λ 1032 non-detections place column density upper limits of and , respectively. A similar pair of weak absorption features in the HE 0238−1904 sight line is consistent with a z = 0.50511 Ne viii doublet: , , and . These two Ne viii -only systems provide


light. As the equilibrium temperature increases, thermal emission becomes as important as reflected light in that bandpass, leading to a smaller phase curve amplitude since both the dayside and the nightside are emitting light. Then as the equilibrium temperature increases again, the amplitude increases due to the shortening of the radiative time-scale, as in the other phase curves dominated by thermal emission. The third class of behaviour occurs at specific wavelengths that are influenced by exotic chemical effects, where the phase curve amplitude can exhibit non-monotonic behaviour with equilibrium temperature. This occurs in particular in the Spitzer 3.6- and 8-micron bands of Fig. 9 due to methane and CO opacity but will also happen at all wavelengths where a change in chemical composition with temperature leads to a significant opacity variation. For and for , the amplitude of the phase curve rises with equilibrium temperature whereas for the opposite happens. This peculiar behaviour is due to our assumption of local chemical equilibrium that leads to a spatially varying ratio between carbon monoxide and methane molecules on the planet (see also Dobbs-Dixon Cowan 2017 ). Hot Jupiters, however, are not expected to be in local chemical equilibrium since the vertical and horizontal transport of material can be much faster than chemical reactions. In such a case, the system is said to be quenched, and homogeneous chemical abundances are expected at the photosphere (Cooper Showman 2006 ; Visscher Moses 2011 ; Agúndez et al. 2014 ; Drummond et al. 2018a , 2020 ; Steinrueck et al. 2019 ). If quenching happens, and as long as CO is the dominant species (rather than CH 4 ), then the amplitude of the phase curve should be monotonically increasing with equilibrium temperature at all wavelengths dominated by thermal emission. 6.1.2 Phase curve offset The offset of the phase curve maximum is shown in the bottom panels of Fig. 9 . It always follows a bell curve, with an offset that increases with equilibrium temperature at low equilibrium temperatures and an offset that decreases with equilibrium temperature at larger equilibrium temperatures. Whereas the decrease of the offset with increasing temperature is expected based on the radiative and advective time-scales shown in Fig. 4 , the low-temperature behaviour is more puzzling, but is consistent with some of the cases explored in fig. 9 of Komacek et al. ( 2017 ) Again, the Kepler bandpass stands apart. At low temperatures, when the light curve is dominated by reflected light, the amplitude is large and the offset is close to zero because Rayleigh scattering is approximately homogeneous over the dayside of the planet. As the equilibrium temperature increases, thermal emission becomes more and more important compared to Rayleigh scattering, leading to an offset that increases with increasing equilibrium temperature. Above , the decrease of the radiative time-scale with equilibrium temperature


left. Fig. 2 Schematic overview of the features in the outer circumbinary ring detected in our SPHERE PI image. The image is centered on the location of GG Tau Aa and was smoothed for illustration purposes. Any unresolved circumstellar material may create a halo of polarization signal around the star. Because this unresolved polarized signal can affect the analysis of the immediate circumstellar environments, we subtracted these polarized signals (i.e., the total intensity halo multiplied by the degree of polarization) individually for Aa and Ab. While subtracting the polarization signal of Aa slightly increases the contrast of the fine structures in the immediate stellar environment, subtracting the polarization signal of Ab instead blurs these structures. This can be explained by the fact that the measured polarization degree of Ab is somewhat higher than that of Aa. Therefore, subtracting the polarization signal of Abadds an artificial polarization halo around Aa, which weakens the fine structures in its environment. Subtracting the (less strongly) polarized signal of Aa, however, does not noticeably affect the environment of Ab. Figure 3 shows the resulting image after subtraction of the polarization signal of Aa with annotations of the detected features. The immediate stellar environments that are affected by the diffraction pattern are masked out. In all the images, the inner region appears highly structured, as highlighted in Fig. 3 by the dotted lines. Most prominently, the “north arc”, an extended structure to the northeast of Ab observed in previous scattered light images (e.g., Krist et al. 2002 , 2005 ; Itoh et al. 2014 ; Yang et al. 2017 ), is clearly detected and appears in our SPHERE image to be composed of a double-arc structure at projected separations of ~ 0.38′′ and ~0.48′′. This double-arc structure may extend along the entire eastern side to the south, interrupted by a dark lane extending from Ab toward the east (see the dotted gray lines in Fig. 3 ). This dark lane seems to be connected to the shadow observed in the outer disk at a similar position angle (see Sect. 4.4 ). We furthermore detect two additional filament structures northwest and southwest of Ab. It is unclear, however, whether they are related to the double-arc system on the eastern side. Finally, another filament is detected immediately southeast of Aa, pointing toward the south. Fig. 3 Zoom on the inner region after subtraction of the stellar polarization on Aa. The dotted lines highlight the detected features: the “north arc”, revealing a double-arc structure (green), several filaments (light blue) and a possible shadow lane (gray dashed). See Sect. 4.1 for details. The immediate stellar environments (120 mas) are masked out. North is up and east is to the left. Figure 4 (left panel) shows the angles of linear polarization overplotted on the inner disk region. The polarization angles θ were calculated according to θ = 0.5 ×arctan( U ∕ Q ), within bins of 3


smaller than the weaker CO lines in the planet transmission spectrum. Furthermore, in Doppler space the nature of this spurious signal is substantially different from the planet absorption, and largely canceled prior to cross-correlation. Winn et al. ( 2007 ) demonstrated that HD 189733 is a slow rotator with a rotational period close to 13 days. Thus any configuration of spots can be considered static during one single transit observation (less than 2 hr). Compared to the observer, the star moves in radial velocity by only 0.2 km s −1 during the transit (mostly due to the change in barycentric velocity), which is only 1/15 of the full width half maximum of the CRIRES IP. This means that any distortion of the stellar lines caused by unocculted spots is static in both radial velocity and time. In this case our data analysis designed to remove telluric lines (Section 3.4 ) will also re-normalize residuals from uncorrected star spots, further dampening the already small signal. However, we know from past transit observations (Pont et al. 2007 , 2008 ) that HD 189733 b usually crosses some spots during transit. In this case, the distortion of the stellar line suddenly disappears (when the spot is occulted) and reappears, generating a pulse radial velocity signal in the data, uncorrected by our analysis. The duration of this pulse is dependent on the size of the crossed spot (or region of spots). Although probably unrealistic, we discuss the worst-case scenario in which all spots are clustered in a region of radius 0.1 R S (based on the 1% coverage and spots significantly darker than the photosphere). For an impact parameter of b = 0.66, the length of the chord crossed by the planet is 1.5 stellar radii. With 39 frames observed in transit, the planet crosses 0.038 stellar radii per frame. This unrealistically big group of spots would therefore affect 2.6 frames of our data. For a spot signal 1/10 of the planet signal, occulted star spots can only contaminate 8% of the detected CO signal, or based on the detection presented in Section 5.1 . We therefore conclude that—at least in the case of HD 189733 b—the contamination due to uncorrected star spots is negligible. 3.4. Removal of Telluric Lines Telluric lines change in depth during the observations, but not in position. Therefore, the telluric spectrum is most effectively removed by modeling the flux of each data column (i.e., each wavelength channel) in time. The main cause of telluric variation is the change in geometric airmass. Changes in the IP (due to, e.g., in-slit guiding, seeing, and performances of the adaptive optics), as well as changes in the water vapor content in the Earth’s atmosphere could also affect the flux in the core of telluric lines. We initially normalize each spectrum by its median continuum level. We then model the time-variation of the flux in each spectral channel via the simple functional form:where A is the geometric airmass, and we divide through the fit. The


. 4.6. Perspectives with Gaia At the considered range of distances, Gaia will deliver exquisite parallax accuracy (%), especially because the binary effect can be adequately subtracted thanks to the knowledge of the astrometric orbital parameters presented in this study. Combined with the size of the apparent orbits and the periods, we expect the total masses to be measured with an uncertainty of 5%, following Eq. ( 1 ). For most systems, the error budget will be equally shared between the interferometric resolved astrometry and the Gaia distance. These measurements of the total masses will be completely independent from radial velocities. Gaia will also constrain the orbital photocentre displacement . This quantity can be extracted even if the orbital period is poorly sampled by Gaia because of the knowledge of all orbital parameters. It permits calculating the mass ratio : where is the (known) size of the apparent orbit and the flux ratio in the Gaia band. Interestingly, is well approximated by the (known) flux ratio in the band because hot stars have their optical and near-infrared spectra in the Rayleigh-Jeans regime. In order to test feasibility, we computed the expected photocentre displacement from the orbits derived in this study. This was done by inverting Eq. ( 5 ), guessing the expected mass ratio. We used two approaches, both relying on the calibrations from Martins et al. (2005) . We first converted the observed flux ratio into mass ratio. For a pair of main-sequence stars, the calibration is well approximated by . The exponent is even lowered for a massive, evolved primary with a less-massive main sequence secondary. In a second approach, we simply use the expected mass ratio from the individual spectral types when available (see Table 1 ). The computed are reported in Fig. 2 . The predicted displacements range from 0.1 mas to 1 mas. This is a factor ten to a hundred larger than the Gaia performances (assuming the orbital photocentre shift is measured with a similar accuracy than the parallaxes). Accounting for 5% uncertainty on the total mass (shared between the interferometric resolved astrometry and the Gaia distance, see Eq. ( 1 )), and for 1 to 10% uncertainty on the mass-ratio (shared between the interferometric flux ratio and the photocentre shift amplitude from Gaia , see Eq. ( 5 )), we expect to measure the individual masses with an uncertainty of %, independently of radial velocities. Fig. 2 Predicted photocentre displacement versus the flux ratio for the ten binaries of the sample. The mass ratios were estimated either from the flux ratio (assuming main sequence stars, filled symbols), or derived from the individual spectral types when available (open symbols). The dashed red line is for the expected Gaia performances. 5. Conclusion In this paper we report observations of spatially resolved astrometry on ten massive O-type binaries, using OLBI. This dataset is used to derive the elements of the apparent orbits. Combined


the ICME structure and how the structure controls the geomagnetic activity. These results are summarized and discussed below, which illustrate the importance of multi-spacecraft remote-sensing and in situ observations for understanding the physical processes of CME propagation and space weather forecasting. 1. This study compares STEREO stereoscopic wide-angle imaging observations with multi-point in situ measurements at Mercury and Earth, which places a strong constraint on CME Sun-to-Earth propagation. The CME kinematics determined from the triangulation technique predicts well the shock arrival time at MESSENGER with an error of about 1 hr in this study. A reasonable accuracy is also obtained when we compare the predicted arrival time and speed with the in situ measurements near the Earth. From the Sun to Earth, the CME undergoes an impulsive acceleration, a rapid deceleration, and then a gradual deceleration out to 1 au, which agrees with the conclusions of Liu et al. ( 2013 , 2016 ). We find that the rapid deceleration ceases at ∼50 before the CME reached MESSENGER (∼0.47 au), which is different from the coronagraph findings in Gopalswamy et al. ( 2001a ). Combining this case with the three events in Liu et al. ( 2013 ), we suggest that fast CMEs are likely to terminate deceleration before reaching 100 from the Sun, which should be noticed in kinematics models of fast CMEs. This work once again proves the reliability of the stereoscopic triangulation technique in determining the kinematics of earthward CMEs in the inner heliosphere. 2. Our comparison between wide-angle imaging observations and the interplanetary type II radio burst indicates important clues on the source region of the type II burst. The study reveals that the consistency between the shock distance derived from the type II radio burst and the CME kinematics determined by the triangulation method requires an unusually high solar wind electron density. The type II radio burst was probably produced from a high-density region. This discrepancy and the slow increasing distance of the CME-driven shock derived from the type II radio burst can be explained by the shock interacting with nearby streamers (e.g., Reiner et al. 2003 ; Cho et al. 2007 ; Feng et al. 2012 ). Another possibility is that the type II radio burst was generated by the shock flank region with lower heights (Claßen Aurass 2002 ; Knock et al. 2003 ). Because only one spacecraft detected the type II radio burst, it is not possible to determine the position of the source region using the radio triangulation method of Martínez-Oliveros et al. ( 2015 ). This result implies uncertainties in the determination of CME kinematics using type II radio bursts alone. 3. We reconstruct the ICME structure near the Earth in order to connect it with the solar source observations and to understand how the structure contributes to the geomagnetic storm. The flux-rope inclination angle and chirality at 1 au are consistent with those


43 , otherwise the matter is swallowed by the BHs before the merger. The bounding energy of this matter is only a fraction of the rest mass energy of the matter, This ratio is much smaller than the wind efficiency w 0.1 of a super-Eddington accretion disc, so that such matter is easily blown away by the disc wind. As long as a possible dead disc is ionized by the ISM accretion (that occurs unless we consider low n and high v ), we have encountered an unlikely set-up. Note that a fraction of the matter M m should accrete on to the BHs before the merger, otherwise a fine-tuning is needed because the time t b is much larger than the event duration t acc . The accretion is super-Eddington, even if only a fraction of the matter accretes, and should be accompanied by a strong disc wind as suggested by numerical simulations (Ohsuga etal. 2005 ; Jiang, Stone Davis 2014 ; Sadowski etal. 2014 ). Therefore, it is difficult to keep the matter near the BH before the merger and the BH mergers unlikely accompany observable prompt electromagnetic counterparts. 7 SUMMARY AND DISCUSSIONS We suggest possible connections between the BH mergers observed by GWs and the high-energy sources of TeVPeV particles in our Galaxy. The GW observations give a lower limit on the number of merged and hence highly spinning BHs as , and the spinning BHs produce relativistic jets by accreting matter and magnetic fields from the ISM. We calculate the luminosity function, the total power and the maximum acceleration energy of the BH jets, and find that the BH jets are eligible for PeVatrons, sources of CR positrons and TeV unIDs. The BH jets form extended nebulae-like PWNe. If they are observed as TeV unIDs, additional 300 nebulae will be discovered by CTA. We quantify the uncertainties of the estimate for the total power of the BH jets within a factor of 10 3 , which is much better than before the GW detections, by considering the initial BH spin, the velocity distribution depending on the formation scenario, the accretion profile changed by the wind and the feedback by the outflow (Table 2 ). The uncertainties will be reduced by the GW observations, in particular, of the BH spins. It is also important to clarify the feedback by the wind from the sub-Eddington accretion disc on the BondiHoyle accretion. Our considerations on the BH accretion and jet imply that the electromagnetic counterparts to BH mergers including the Fermi GBM event after GW150914 are difficult to detect with the current sensitivity. The accretion from the ISM can evaporate the cold neutral dead disc around the BH. A slight accretion before the merger can also blow away the surrounding matter if any. These should be considered as constraints on dead disc models for prompt electromagnetic counterparts of the BHBH merger. Although we do not go into detail in this paper, there are several sites of particle acceleration for a BH jet. First, the BH magnetosphere acts as a particle accelerator like pulsars if a gap


could regulate SFRs to some extent (Shi et al. 2011 , 2018 ). 4.2 Theoretical models to explain the relation between σgas and SFR There are two dominant models for the origin of the turbulence: star formation feedback or gravitational instability of the gas (Krumholz Burkhart 2016 ). Both models predict that the velocity dispersions will correlate with their SFRs. The work of Krumholz Burkhart ( 2016 ) gives the details about these two models. In Fig. 8 , we overlaid the gravitational-instability model (left-hand panel) and star-formation-feedback model (right-hand panel). The gravitational-instability model gives SFR as following (Krumholz Burkhart 2016 ): where v c is the rotational velocity, f g is the gas fraction, ε ff = 0.01 is the SFR per free-fall time, φ P = 3 is a factor that accounts for the presence of stars in the disc, and a Coulomb logarithm-like term ln ( r 1 / r 0 ), which measures the radial extent of the star-forming disc ( r 1 = 10, r 0 = 0.1). From equation ( 3 ) we find that a gravitational-instability model has a strong dependence on the gas fraction. The star formation feedback model gives the SFR as following (Krumholz Burkhart 2016 ): where Q g is the Toomre parameters of the gas, φ ≈ 1 and are constants of order unity that parametrize various uncertainties, P * / m * = 3000 km s − 1 is the momentum per unit mass (Faucher-Giguère, Quataert Hopkins 2013 ). We found that the star formation feedback origin for the turbulence predicts that a velocity dispersion rises more steeply with the SFR, and it does not depend on the gas fraction. For the comparisons with our observations, we give the plausible range of f g and Q g following with the works of Krumholz Burkhart ( 2016 ) or Johnson et al. ( 2018 ). We also used the rotation velocity v c = 90–190 , which spans the plausible range for local and high z galaxies. From Fig. 8 (right panel), we find that a star-formation-feedback model provides a rather poor match to the observation, while the gravitational-instability model shows better agreement with the observations. Johnson et al. ( 2018 ) also test two analytic models but found that both provide an adequate description of the data, and need further observations to rule out either model. In the work of Krumholz Burkhart ( 2016 ), they also compared with observations and found that gravity is the ultimate source of ISM turbulence, at least in rapidly star-forming, high-velocity dispersion galaxies for which our test is most effective. Figure 8. The relationship between SFR and gas velocity dispersion. In the left-hand panel, lines show the predictions of the gravitational-instability model (equation 6) for f g = 0.2, 0.5, and 1.0, as indicated in the legend. Lines in the right panel show the prediction of the star formation feedback model (equation 8) for Q g = 0.5, 1.0, and 2.5. The solid lines are for a circular velocity v c = 140 km s −1 (the median rotation velocity of local and high z galaxies), and the


regular observations of SN 1987A continued for the purposes of monitoring the evolution of the interaction with the ER and to develop a clear picture of the evolving relationship between the IR emission at these wavelengths and emission at optical and X-ray wavelengths (Dwek et al. 2008 , 2010 ; Arendt et al. 2016 ). This paper reports on the complete set of Spitzer ’ s IRAC observations of SN 1987A and its ER. Section 2 briefly describes the observations and additional mosaicking procedures. The complete mid-IR light curves from Spitzer IRAC and MIPS photometry are presented and modeled with a simple empirical function in Section 3 . The final light curves extend a little over 4 yr (in eight epochs) beyond the results presented by Arendt et al. ( 2016 ). In Section 4 we employ high-resolution mapping and deconvolution that are enabled by the long-term repeated observations of SN1987A at a wide range of position angles. We model the marginally resolved ER to identify the separate evolution of the N, S, E, and W portions of the ER. Section 5 provides further discussion of some of the results, and the findings are summarized in Section 6 . The Appendix describes a strongly variable source that is unassociated with SN 1987A, but was serendipitously located within the field of view of the IRAC observations. 2. Data 2.1. Standard Post-basic Calibrated Data (pBCD) Mosaics and Photometry The initial targeted IRAC observations of SN 1987A employed 12 s frame times using the small-scale Spiral16 dither pattern. Guided by those results, subsequent SN 1987A observations continued the use of 12 s frame times, but switched to the slightly shallower medium-scale Reuleaux12 dither pattern, resulting in 125 s of total exposure (10.4 s of signal integration per 12 s frame time). These observations were repeated at roughly 6 month intervals. The basic calibrated date (BCD) individual frames were automatically mosaicked into pBCD images on 06 pixel scales. The SN brightness was measured from the pBCD mosaics using aperture photometry. Because the SN is not well resolved from nearby stars (Star 2 and Star 3 as designated by Walker Suntzeff 1990 ), the source aperture includes the SN and these stars, and estimates of their flux density (extrapolated from the observations by Walborn et al. 1993 ) are subtracted from the reported result for SN 1987A (Table 1 ). Table 1 SN 1987A Flux Densities Notes. Flux densities are in millijansky. Flux densities of [0.41, 0.26, 0.16, 0.09, 0.01] mJy have been subtracted at [3.6, 4.5, 5.8, 8, 24] μ m to account for the emission of Stars 2 and 3 in the aperture. This correction was not included in Table 1 of Arendt et al. ( 2016 ). a Day number 0 = 1987 Feb 23. b Spitzer astronomical observation request (AOR) number. c Spitzer program ID number. Bold numbers indicate programs specifically targeting SN 1987A. (This table is available in machine-readable form.) A machine-readable version of the table is available. Additional


a with σ = 0, Ω m = 0.26, and Ω r = 8.4 × 10 −5 . We see that k cr decreases in time and reaches the minimum at a M = [Ω m /2(1 − Ω m )] 1/3 ≃ 0.56. The super-interaction effect appears in a very small region (large k ) in the very early time of the universe. In addition, the larger the ν is, the wider the influences of dark energy to the matter density perturbation will be. Consequently, the size of the super-interaction regime enlarges in the cosmological evolution and finally reaches the scale , 2.8 × 10 −2 , and 2.8 × 10 −1 ( h Mpc −1 ) at a = a M for ν = 10 −2 , 10 −4 , and 10 −6 , respectively. Figure 1. The critical scale factor a cr as a function of the wavenumber k with σ = 0 and ν = 10 −2 (solid line), 10 −4 (dashed line), and 10 −6 (dotted line), where the boundary conditions of Ω m = 0.26 and Ω r = 8.4 × 10 −5 are used. 4 EVOLUTIONS OF MATTER DENSITY PERTURBATION AND POWER SPECTRUM The Hubble radius d H ≡ H −1 increases during the evolution of our universe. More and more density perturbation modes of δ k with the wavenumber k enter the horizon, in which k 2 = a 2 H 2 with a = a k . Explicitly using Ω m = 0.26, Ω r = 8.4 × 10 −5 , and H 0 = 70 km s −1 · Mpc, we find that k = 10 −3 and 0.25 ( h Mpc −1 ) go to the horizon at a k ≃ 0.03 and 1.24 × 10 −5 , respectively. Following a similar procedure to that discussed in the literature (Borges et al. 2008a ), we can recover P ( k ) in the ΛCDM model with the BBKS transfer function within 10 per cent accuracy by taking the initial density perturbation to be the scale invariance when all modes are located at the super-horizon scale, i.e. at a ≪ a k , where n s is the spectral index, given from the inflationary epoch. From the above discussion, it is reasonable to choose ln a = −18 to be the initial time in our work. We note that from equation ( 26 ), the super-interaction effect appears at the scale deep inside the horizon , indicating that the ΛCDM initial condition is applicable to the RVM. In this section, we analyse the evolution of δ m from equation ( 25 ) for two cases: (i) σ = 0 and (ii) σ ≠ 0, and numerically solve δ m ( a ) and P ( k ). (i) σ = 0. At the super-interaction regime ( k ≫ k cr ), the friction in equation ( 25 ) plays the most important role in the evolution history of δ m . Thus, with 0 ν ≪ 1, the growth of δ m is frozen with , and the matter power spectrum is suppressed by the dark energy perturbation. From equations ( 17 ) and ( 18 ), one can derive that and θ m ≃ 0 at k ≪ k cr , showing that δρ Λ = ρ Λ δ Λ 0. When entering the super-interaction scale, the second term on the right-hand side of equation ( 21 ) dominates, and the momentum perturbation of θ m becomes of the order of , implying that the RVM heats up the cold dark matter for a large value of k . As a result, the particles propagate inside the super-interaction divide, and the growth of δ m is frozen. In Fig. 2 (a), we show the evolution of as a function of the scale factor a with k = 0.25 ( h Mpc −1


modern stellar atmosphere models were compared to the disentangled spectra of each component of HD 54662 AB in order to estimate their physical parameters. A previous quantitative spectroscopic study of the system components was performed by MMR18 using the cmfgen code (Hillier Miller 1998 ). Regarding the projected rotational velocities, using the Fourier Transform method (Simón-Díaz Herrero 2007 ) MMR18 determined 158 and 43 for the genuine 12 primary (A) and secondary (B) components, respectively. These values perfectly agree with our determinations of v sin i (see Table 6 ). However, we differ with the former authors regarding the macroturbulent velocity: while MMR18 attributed to component B a macroturbulence of 35 in order to match the observed line profiles with the synthetic spectra, we estimated a macroturbulence of 40 for component A and fixed this parameter to zero for component B, since we found no reason to modify its value when checking the broadening of the synthetic line profiles. The values computed in this work for the effective temperatures ( T eff ) and surface gravities (log g ) of the components are consistent, within the uncertainties, with the current calibrations for O stars in the Milky Way, including the classical calibration by Martins et al. ( 2005 ), as well as the most recent ones by Simón-Díaz et al. ( 2014 ) and Holgado et al. ( 2018 ). MMR18 also determined T eff , as well as helium abundances ( Y He ) for both stars. While our estimates of log g and Y He are in good agreement with their values, our T eff determinations result in slightly higher values than theirs (Δ T eff 1500 K). We re-analysed both stars using the line broadening parameters estimated by MMR18 . We obtained good agreement for component A, in contrast to component B. Moreover, the broadening of the fastwind synthetic lines using MMR18 ’s v sin i and v mac values cannot reconcile the broadening of the lines observed in our disentangled spectra. Therefore, line broadening only cannot explain the differences in T eff with MMR18 . In Section 3.1 , we mentioned that the presence of residuals in the Balmer lines originated from the disentangling process may affect the surface gravity determination. As explained in Section 5 , for our analysis we used the least affected lines (H γ and H ε) in order to minimize this effect. Regarding the He lines, some profile distortions which could be playing a role are also observed, in particular in the He i λ 4388 Å line, mostly for the primary component. In any case, Fig. 6 shows that the synthetic composite spectrum resulting from the addition of the individual models for the A and B components reproduces well the observed spectrum of the system. We then conclude that potential differences in the shape of the lines of the individual spectra due to different disentangling processes may be the cause of the disagreement between our determinations and those from MMR18 . Note also that, unlike the results presented


(the second average). This means that the short-term effects in the time-scale of the outer binary’s period are incorporated into the double-averaged Hamiltonian, but the short-term effects in the time-scale of the inner binary’s period are neglected. Thus, the application conditions require that the elements of the test particle are slow variables in the time-scale of the inner binary’s orbital period (i.e. the secular frequencies of the elements need to be much smaller than the mean motion of the inner binary). It is evident that the modified approach broadens the application range compared to the classical double averaging. As for the computational efforts about the classical and modified double-averaged models, we report in Table 1 the time required by the numerical integration of different-order models over a time span of 1.5 × 10 4 yr for the Sun-perturbed Uranus–Caliban system (the initial conditions and time span are the same as the ones of Fig. 6 ). It is observed that, compared to the classical approach, the modified version requires additional computation time. Therefore, when the application conditions of the classical approach are satisfied, the classical averaged model is preferable because in this case the periodic corrections considered in the modified approach become negligible but the computation time increases. Table 1. Computation time for the numerical integration of different-order averaged models about the Sun-perturbed Uranus–Caliban system. The initial conditions and time span are the same as the ones of Fig. 6 . The computation time about the full model over the same period is 9.720 s. In some physical systems, such as Jupiter’s irregular satellite systems, the strong perturbation coming from the disturbing body (the Sun) could make the elements of test particles no longer slow variables in the time-scale of the inner binary’s orbital period. In this case, the short-term effects appearing in the first average could accumulate and produce significant errors to the secular evolution. To overcome this problem, the short-term effects would need to be incorporated also in the first average (over the inner binary’s orbital period). 6 CONCLUSIONS In this work, we developed a modified double-averaging approach, which was used to formulate a more accurate Hamiltonian in comparison to the secular Hamiltonian formulated by the classical double averaging. To test the modified approach, the resulting double-averaged Hamiltonian was applied to a variety of hierarchical triple systems, covering planetary, and stellar scales. In this approach, the disturbing function appearing in the Hamiltonian is averaged twice in order to eliminate the short-term oscillations induced from the orbital motions of inner and outer binaries. When the perturbation coming from the disturbing body is relatively strong, the short-term effects neglected in the classical double averaging may accumulate over long time-scales. This leads to the