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

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


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

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


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

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope B-Wavelength O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


left. 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

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


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

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


. 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

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


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

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


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

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


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

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


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

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


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

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


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

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


(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

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


so that the sightline passes through multiple separate structures with different ionization conditions and metallicities. In contrast, Veilleux et al. ( 2005 ) suggest that large variations in metallicity and ionization conditions between clouds across an absorption profile might be a signature of outflows in addition to broad complex kinematics spanning a few hundred kilometers per second, kinematics that are not consistent with rotation, α -rich abundances, and dual-trough absorption with weak absorption between. There have been few studies thus far with detailed metallicity and kinematic analyses in order to investigate this further. To improve the metallicity measurement and better determine the structures along the line of sight, a multiphase and multicomponent modeling approach would be best. Several works have undertaken such a study and found differing metallicities in each component and/or phase (e.g., Tripp et al. 2011 ; Crighton et al. 2015 , 2016 ; Muzahid et al. 2015 , 2016 ; Rosenwasser et al. 2018 ; Zahedy et al. 2019a ) and these insights could be used to determine if outflows, inflows, tidal material, etc., are present along the same sightline. In particular, a multiphase analysis would provide insights into whether outflows are primarily traced by hot, high-ionization gas with metallicities similar to the galaxy ISM metallicity and whether the lower ions along the same sightline trace cooler, more metal-poor gas entrained by the hot outflow, which is a possible solution to the total metallicity problem suggested by Kacprzak et al. ( 2019a ) that might fit the scenario we observe here. The difficulty with this method is that it requires partitioning each ion between VP components and phases, and modeling a consistent set of VP components across transitions with similar ionization phase. This is particularly challenging when absorption is saturated and the selection of lines is limited, i.e., the only H i line observed is saturated as in the system presented here. While much of our sample has coverage of multiple H i Lyman series lines and in some cases the full series to properly do a multiphase and multicomponent analysis, the J1430+014, z = 2.071 absorber is not a good candidate for this method. Without obtaining new spectra to better cover the H i Lyman series, we would need to make assumptions on how to partition the saturated H i between components and phases, which would result in over-interpreting the absorption. Furthermore, the vast majority of metallicities in the literature are total metallicities. To study the evolution of the CGM from Cosmic Noon to today, we have focused on total metallicities here. Even though metallicity is a useful diagnostic for ruling out some scenarios of gas flow origins, especially at higher redshift where CGM mixing appears to be less efficient, a variety of properties such as kinematics and galaxy morphologies must also be considered for a more accurate picture, which we have done here.

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


major and minor axes for a particular case. Since the model is specifically constructed in such a way, the asymptotic behaviours of the density are indeed given by whereas the Taylor–Maclaurin series is where L 3 = 3ln [( a + b )/ r 0 ] − 1 and L 15/8 = 15ln [( a + b )/ r 0 ] − 8. This last series also implies that the density profile might be increasing near the origin if ( a + b )/ r 0 is chosen too small, but the examinations of and indicate that r 0 ≤ ( a + b )e −8/15 ≈ 0.5866( a + b ) is actually sufficient to guarantee the positive non-increasing density profile. Figure 4. Same as Fig. 1 except for the density profiles in equation ( 51 ) with r 0 = ( a + b )/e 8/15 . Figure 5. Density profiles along the major and minor axes for the models in equations ( 45 ) and ( 51 ). For both cases, a = 2.58 and b = 0.43 but r 0 = e −1/3 ( a + b ) ≈ 2.157 for equation ( 45 ) and r 0 = e −8/15 ( a + b ) ≈ 1.766 for equation ( 51 ). 6 THE PROLATE AND TRIAXIAL SUBSTITUTIONS One possible generalization of the Miyamoto–Nagai substitution is applying a similar transformation to the other coordinates. For instance, consider the transformation of a spherical function Φ s ( r ) to Φ gMN ( R, z ) = Φ s ( t ) where t 2 = ( c + R d ) 2 + ( a + z b ) 2 and . With Φ gMN ( R, z ) as the potential, the resulting gravity field is given by with The gravitational force points locally to a more vertically inclined direction than that to the centre if a / z b > c / R d and vice versa, whilst it points radially towards the centre everywhere (i.e. the spherical potential) if a = c = 0. The equipotential in the limit of R, z → 0 is oblate if a / b > c / d or prolate if c / d > a / b , whereas the equipotentials as R, z → ∞ become spherical. If d = 0 and c ≠ 0, we also find is non-zero finite and so the gravitational force becomes undifferentiable along any path that crosses the symmetry axis. This behaviour is understood from the fact that the corresponding density profiles are singular in this limit (like ∼ R −1 ) on the R = 0 axis. The Poisson equation indicates that the axisymmetric density profile generating the potential Φ s ( t ) can be expressed as generalizing equation ( 15 ), which corresponds to the c = d = 0 case. It is easy to observe that this density profile is also always non-negative if (actually ρ s ( r ) being non-negative and integrable at r = 0 is sufficient), and, from explicit calculation, we can furthermore demonstrate that and if (ρ s )′( r ) ≤ 0 (and ). Since , equation ( 56 ) is also regular everywhere with the Taylor-MacLaurin series unless bd = 0. 5 Here, If d = 0, on the other hand, equation ( 56 ) reduces to which exhibits an explicit R −1 -density singularity as R → 0 (i.e. the density along the symmetry axis diverges). This contrasts to the b = 0 case, for which a razor-thin disc develops. 6.1 The Miyamoto–Nagai spindle The simplest potential-density pair that results from this transformation is that due to the point mass potential Φ s ( r ) =

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-URL I-URL I-URL I-URL I-URL I-URL I-URL I-URL I-URL I-URL I-URL I-URL I-URL I-URL O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O B-Formula I-Formula I-Formula I-Formula O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O B-Formula I-Formula I-Formula I-Formula O O O B-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula


sample size of TNG50. For star-forming galaxies the Δ〈LLR〉 is the lowest for TNG50, followed by TNG100 and Illustris, indicating that TNG50 is the simulation that best models star-forming galaxies. Instead, all simulations struggle to accurately model quiescent galaxies, for which the Δ〈LLR〉 remains low in all cases. These trends are robust across the stellar mass bins considered. The left-hand top panel of Fig. 3 shows how the mean of the LLR distribution for simulated star-forming galaxies is the closest to SDSS for TNG50, followed by TNG100 and with Illustris being the furthest away from it. The higher LLR of TNG100 with respect to Illustris is suggestive that the improved physical model for galaxy formation adopted in the IllustrisTNG framework is overall an improvement compared to the original Illustris implementation (Pillepich et al. 2018 ). Furthermore, the unprecedented agreement with observations reached by TNG50 star-forming galaxies is also a sign that a higher resolution is key to effectively model star formation. We note, however, that all simulated data sets are still inconsistent at the 1σ level with SDSS. On the other hand, it can be seen that the improvement noted for star-forming galaxies does not seem to propagate to quiescent galaxies as well (the top right-hand panel of Fig. 3 ). We start by noting that in this case Illustris galaxies show a tail of high LLR that is consistent with IllustrisTNG at the 1σ level. However, the large variance suggests that this tail is very scarcely populated, whereas the very small variance found for the spike at low LLR is indicative that the bulk of the population of Illustris quiescent galaxies lies there, i.e. they are very far from reproducing SDSS. Yet, while there seems to be an overall improvement from the original Illustris framework to IllustrisTNG, the better resolution offered by TNG50 over TNG100 does not appear to significantly modify the overall LLR distribution for quiescent galaxies. Indeed, the distributions of the two IllustrisTNG volumes are practically consistent but at very high LLR, where the probability density of TNG50 is slightly higher. In short, what the top of Fig. 3 is telling us is that there has been a clear amelioration from the Illustris to the IllustrisTNG framework, in both the modelling of star formation regulation and of quenching, yet IllustrisTNG still produces small-scale stellar morphological details that differ from those in SDSS, and especially so for quiescent galaxies. Most importantly, while the higher resolution featured by TNG50 generates a sizeable improvement in the morphology of star-forming galaxies, this is not the case for quiescent galaxies. This is suggestive that the physics that couples small-scale stellar morphological details to star-formation quenching in the IllustrisTNG simulations warrants improvement, or that an even higher resolution is needed to accurately model the processes that lead to quiescence. 5.2 Mass dependence The

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


Galactic latitude. The significance of this result can be assessed by a straightforward reduced χ 2 statistic: where ( x Bes , x MOA ) refer to the (model, observed) microlensing quantity. σ is the observational uncertainty within the field, and N fld is number of fields. The observational uncertainty within the field is calculated using formula from Han Gould ( 1995 ). The reduced χ 2 contribution of each MOA-II field are shown in Table 5 and Fig. 11 . The gb21 field is excluded due to the limit of the Besançon extinction maps. The model optical depth is in agreement with MOA-II data within 3σ MOA for most fields. The reduced χ 2 of resolved source and DIA sources optical depth are 2.4 and 2.0, respectively. Figure 11. The reduced χ 2 contribution of optical depth (a) and microlensing event rate per star (b) of resolved sources (left) and DIA sources (right). Table 5. Field-by-field contributions to the reduced χ 2 () between the Besançon model and the MOA-II data for the optical depth and microlensing event rate per star. The event rates show higher reduced chi-squared contribution than the optical depths. The Besançon resolved sources and DIA source results have values of 2.6 and 2.2, respectively. The low Galactic latitude area ( b 3°) of both parameters provide the bulk of the disagreement (see Section 5.1 ). In field gb1, there is a long time-scale event (gb1-3-1, t E = 157.6 d) which contributes more than half of optical depth in that field. This event provides a hotspot in MOA-II optical depth and average time-scale maps (Section 5.2 ). In order to check the reliability of reduced χ 2 test, the reduced χ 2 of field gb1 without gb1-3-1, gb1 Cut , is calculated. The result in Table 5 shows that the gb1 Cut field provide a better reduced than original gb1 field. Finally, we cut the events which have crossing time longer than 100 d which locate in 5 field; gb1, gb9, gb10, gb13 and gb 14. The new reduced chi-squared, , of optical depth (2.3 for resolved sources and 1.8 for DIA sources) and event rate per star (2.2 for resolved sources and 2.0 for DIA sources) is reduced. However, fields which locate around inner bulge except field gb6 still show high reduced chi-squared compare to high Galactic latitude field. Therefore, high reduced chi-squared region around inner bulge do not effect by long time-scale event, but show the mismatch of optical depth and event rate per star between the Besançon model and the MOA-II data at low Galactic latitude area. 6 MICROLENSING MODEL PARAMETRIZATION The MOA-II team parametrize the observed spatial microlensing distribution using a polynomial function. We can do likewise for our simulated maps. We model the structure of the optical depth, average time-scale and event rate maps shown in Fig. 5 using a 10-parameter cubic polynomial fit in l and b . The model function can be written as where x is the microlensing observable (rate, time-scale or optical depth). The best-fitting models are shown in Fig. 12 and

B-CelestialRegion I-CelestialRegion O O O O O O O O O O O O O O O O O O B-Model O O B-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O B-Survey O O O O O O O O O O O B-CelestialRegion I-CelestialRegion O O O O O O O O B-Model O O O O O O O O O O B-Survey O O O B-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-ObservationalTechniques O O O O O O O O O O O O O O B-Model O O O B-Survey O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O B-ObservationalTechniques O O O O O O O O O O B-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion O B-CelestialRegion I-CelestialRegion O O O O O O O O O O O O O O B-CelestialRegion I-CelestialRegion O O O O O O B-CelestialObject B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O B-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialRegion O B-CelestialObject B-CelestialRegion I-CelestialRegion O O O O O O O O O O O B-CelestialRegion I-CelestialRegion I-CelestialRegion O O O O O O B-CelestialRegion I-CelestialRegion O O O O O O O O O O O O O O O O O O B-CelestialRegion B-CelestialRegion B-CelestialRegion B-CelestialRegion O O B-CelestialRegion O O O O O O O O O O O O O O O B-ObservationalTechniques O O O O O O O O O O O O O B-ObservationalTechniques O O O O O O O O O O O B-CelestialRegion I-CelestialRegion O O O O O O O B-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O B-Survey O O B-CelestialRegion I-CelestialRegion I-CelestialRegion O O O O O O B-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


for the SR effect in H and K. To convert stellar fluxes to magnitudes, we set the zero-point magnitude to the instrumental zero-point (one ADU/s in H and K, are 25.2 and 24.8 magnitudes, respectively). To double check our calibration, we compared H and K magnitudes of 26 sources (located r ≥ 3 ′′ from R136a1) common between our catalogue and the VLT/MAD (Campbell et al. 2010 ) in H and K. 2 We cannot compare our zero-points with the MAD/H and K magnitudes in the central 2.8 ′′ region because of the completeness issue and the very low AO correction (SR ∼ 15–30 per cent) of their data. Fig. 2 shows the completeness and contrast problem of the previous data, leading to an inability to distinguish certain sources. By way of example R136a6 (H19) and H26 3 – are very close in terms of brightness (flux ratio of about 90 per cent) and location (separation of about 70 mas). These bright O-type stars are most easily detectable in our data compared with others (Figs 2 and A2 ). Cases like these close bright stars, bring confusion even in the HST spectroscopic analysis (Bestenlehner et al. 2020 ). The K magnitude of R136a1 and R136a2 (11.15 mag and 11.43 mag) increased about 0.08 and 0.11 mag, compared to their K mag in the first epoch (11.07 mag and 11.32 mag). The brightness of R136a3 and R136b in K (11.45 mag and 11.67 mag) is consistent with the first epoch K data (11.44 mag and 11.66 mag). R136c in the K (11.31 mag) is 0.17 mag brighter than in 2015 (11.48 mag), making this source the second brightest in our K catalogue. In previous studies, R136c shows indications of binarity based on its strong X-ray emission (Portegies Zwart, Pooley Lewin 2002 ; Townsley et al. 2006 ; Guerrero Chu 2008 ) and possible low-amplitude RV variations (Schnurr et al. 2009 ). Comparing the brightness of common detected sources within two epochs, the K magnitude of 56 per cent of the sources has changed more than twice their photometric errors. 4 To make sure that this is not due to Starfinder photometry analysis (which is based on the reference input PSF), we have used daophot algorithm for this analysis as well. The variation of the K magnitude of these sources still remains. 5 The K mag of about 67 per cent of the sources located outside of the core ( r > 3 ′′ ) has changed more than twice their photometric errors. Since the observations were made in different nights and the AO correction in the outer part of the FOV is not as good as its centre, this inconsistency is probably an observational effect; otherwise, it is originated from physical reasons like variables or multiple systems with periods less than 3 yr. 4 COMPLETENESS We produced 6.2 × 10 4 artificial stars (500 per magnitude) in H and K, in order to determine the completeness as a function of magnitude. These artificial stars are created using the same PSF as we used for source extraction process. They are added to the original image one by one (500 times per magnitude) and the same photometric tools and

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


between sunspot numbers and flare occurrence as a function of the solar cycle has been extensively examined, revealing a surge of renewed solar activity occurs a few years after the cycle maximum ( Fritzová-Švestková Švestka 1973 ; Švestka 1995 ). In a correlation analysis of flare occurrence and sunspot number, Temmer et al. (2003) noticed that the flare occurrence lags behind the sunspot number. For solar cycle 23, Bai (2006) found high flare activity in the late declining phase of the cycle. Not only was an increased flare activity noted but many low-latitude coronal holes were repeatedly observed during the declining and minimum phases of solar cycle 23 ( Abramenko et al. 2010 ). In addition, Gopalswamy et al. (2003) determined that the occurrence rate of coronal mass ejections (CMEs) peaked two years after the cycle maximum, and in the analysis of Kilcik et al. (2011) , the maximum speeds of CMEs also peaked approximately at that time. Recently, Lee et al. (2016) reported that the occurrence rates of major flares and front-side halo CMEs are higher during the descending phase of solar cycle 23 as compared to other phases of the cycle. The recent rejuvenation in the Sun’s large-scale magnetic field during solar cycle 24 starting in the second half of 2014, was pointed out by Sheeley Wang (2015) . They concluded that this was the result of systematic flux emergence in active regions, whose longitudinal distribution greatly increased the Sun’s dipole moment. The role of horizontal shear flows in building up magnetic stress in flare-productive active regions was already noticed by Harvey Harvey (1976) . Horizontal shear flows are not only responsible for magnetic stress but are also drivers for magnetic reconnection ( Yurchyshyn et al. 2006 ). Yang et al. (2004) measured the horizontal flows in active region NOAA 10486 before an X10 flare and found shear flows with local correlation tracking (LCT; November Simon 1988 ) of up to 1.6 km s −1 along the polarity inversion line (PIL). These strong shear flows were correlated with white-light flare kernels in the optical range. Strong horizontal shear flows, which decrease with height in the atmosphere, were also observed by Deng et al. (2006) in the same active region. Based on photospheric flows and the flux around the PIL, Welsch et al. (2009) derived indicators for the occurrence of flares. Many case studies established crucial links between photospheric shear flows, build-up of free-energy in a stressed magnetic field topology, and major flares (e.g., Tan et al. 2009 ; Liu et al. 2010 ). More recently, Beauregard et al. (2012) and Wang et al. (2014) analyzed the horizontal flows in the active region NOAA 11158 in relation to an X2.2 flare. The photospheric signatures produced by this major flare were rather diminutive. On the other hand, during the impulsive phase shear flows around the PIL showed a sudden decrease and a change in the intrinsic rotation of the two main sunspots. Recently,

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


of passive materials, e.g. the lens frame and satellite housing. The sensitivity was calculated as follows: where is the exposure time, set at 100 ks. The results for the sensitivities are shown in Fig. 9 b. The best sensitivities are achieved for cases 2 and 3. Finally, to compare the three focal spots, it was resorted to the S/N , as in Guidi et al. (2011) , where is the signal count within a specified encircled area with radius , is the background of the area, and is the useful volume of the detector. For a Laue lens, the size of the detector determines its field of view for off-axis sources. Here, an on-axis source was simulated and the noise of the detector was considered proportional to the focal spot size. In particular, was chosen to enclose 90% of the diffracted photons (see Table 3 ) in the focal plane and the signal within this area. Thus, the background was taken proportional to the volume of the detector, which faced the incoming X-rays with a surface as large as the encircled area. Because of different focalization properties, the obtained S/N for the three cases were significantly different. As a result of the simulation, the quotient between the S/Ns for the three cases turned out to be as follows: Thus, QM crystals are also the most efficient in terms of the signal-to-noise ratio. The comparison worked out in this paper is based on a photon beam with energy centred at 200 keV. This is mainly because of the high diffraction efficiency of Ge in this energy range. The obtained results also hold for different energies. For low energy, such as 100 keV, Si crystals can be used. For photons with energy greater than 600 keV, the diffraction efficiency of Si and Ge crystals decreases. With the aim of focusing such high energy photons at high efficiency, crystals with high , such as silver, gold, lead, etc. ( Barrière et al. 2009 ), are needed. These materials cannot be fabricated as perfect crystals, but only as mosaic crystals. Thus, CDP and QM crystals would be not available if high material are used, and a comparison between these types of crystal would be impossible. In this case, it would be important to take into account that metal crystals have particular mechanical and chemical properties, which make them very difficult to cut, align, and carry out the gluing and polishing process. In this paper, a comparison between different types of diffracting crystals has been worked out. Actually, the feasibility of a Laue lens depends on several criteria that have to be taken into account. With regard to the crystals, important parameters are the availability of crystalline materials, reproducibility of the crystal manufacturing, and alignment and mounting of the crystals on the lens frame. Moreover, in the context of a space-borne Laue lens, additional criteria must be considered, such as payload, mechanical robustness to shocks and vibrations, and long-time reliability with respect to chemical and temperature cycling. A simulation for

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


sky positions of voids, if any, is at the sub-K level, which is negligible. We present results using the SEVEM map in practice. A common mask UT78 is applied to both the temperature and lensing maps (Planck Collaboration X 2016 ). The lensing situation offers less choice, as only a single convergence map is available: the 2015 lensing data are released directly in the form of the spherical harmonic transform of the (masked) field (Planck Collaboration XV 2016 ). 3.1 The optimal radius of the filter Corresponding to each void centre, the CMB signal is taken to be the average temperature T (or ) within a circular aperture r R filter minus the same quantities averaged over an annular aperture , where R filter is the size of the compensated top-hat filter. We will call the filtered temperature and lensing convergence T and , i.e. To maximize the ISW signal, Cai etal. ( 2014 ) showed that the optimal choice was R filter 0.6 r v , using mock void catalogues defined via haloes from N -body simulations. Using our HOD mocks, we re-investigate this scale factor for a possible dependence on void radius. We find that R filter 0.7 r v gives slightly higher amplitudes for the stacked filtered T signal as well as for the lensing signal for voids with 100 r v 150 h 1 Mpc. The corresponding outer radius of the filter is r v . For simplicity, we will use this size of the filter throughout out analysis, even though it may not be the optimal choice for all ranges of voids. 3.2 Stacking with all voids We now look at the results of stacking the CMB sky at the DR12 void locations. Because the predicted signal varies with void radius, as does the fidelity of the void catalogue, we divided the results into different bins of void radius. We sorted the voids in decreasing order of radius, and measured the average filtered T and imprints for several logarithmically spaced bins of r v . The results are shown in the top row of Fig. 2 . The filtered temperature T is negative at large void radii. The deepest temperature dip is approximately 6K between r v 100 and 150 h 1 Mpc, with a significance of 2.4. T crosses zero at r v 90 h 1 Mpc and remains slightly positive at smaller void radii. We can understand the presence of positive filtered temperature as an indication of voids-in-clouds, i.e. voids living in overdense environments. The gravitational potential at the scale of the void for a void-in-cloud is negative; i.e. it is a potential well rather than a potential hill as intuitively expected for a void. The dominant linear ISW effect thus yields a positive temperature perturbation (Cai etal. 2014 ). We also find that the simulated ISW signal crosses zero, though at a similar void radius of 30 h 1 Mpc. This indicates that the stacked signal for the CMB temperature qualitatively resembles an ISW signal in a CDM universe. For the largest voids, the observed T shows consistency with zero at r v 150 h 1 Mpc, which confirms our speculation from simulations that these objects

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