always is assumed, that β is independent of r . Following the well-known spherical Jeans equation (Binney 1980 ), the radial velocity dispersion of the luminous matter in the early-type lens galaxies can be expressed aswhere β is a constant velocity anisotropy parameter. Combining the mass density profiles in Equation ( 4 ), we obtain the relation between the mass enclosed within a spherical radius r and M E aswhere by we denoted the ratio of respective Euler’s Gamma functions. Simplifying the formulae with the notation ξ = δ + α − 2 taken after Koopmans ( 2006 ), we obtain a convenient form for the radial velocity dispersion by scaling the dynamical mass to the Einstein radius: In all strong lensing measurements used, the observed velocity dispersion is reported, which is a projected luminosity-weighted average of the radially dependent velocity dispersion profile of the lensing galaxy. Its theoretical value can be calculated from Equation ( 7 ) with the assumption that the relationship between stellar number density and stellar luminosity density is spatially constant. This assumption is unlikely to be violated appreciably within the effective radius of the early-type lens galaxies under consideration. Moreover, the actual observed velocity dispersion is measured over the effective spectrometer aperture θ ap and effectively averaged by line-of-sight luminosity. Taking into account the effects of aperture with atmospheric blurring and luminosity-weighted averaging, the averaged observed velocity dispersion takes the formwhere and χ = θ ap / σ atm (Schwab et al. 2010 ); σ atm is the seeing recorded by the spectroscopic guide cameras during observing sessions (Cao et al. 2016 ). The above equation tells us that we can constrain the PPN parameter γ on a sample of lenses with known redshifts of the lens and the source with a measured velocity dispersion and the Einstein radius, provided we have reliable knowledge about the cosmological model and the parameters describing the mass distribution of lensing galaxies ( α , β , δ ). For the purpose of our analysis, the angular diameter distances D A ( z ) between redshifts z 1 and z 2 were calculated using the best-fit matter density parameter Ω m given by the Planck Collaboration assuming a flat FRW metric (Ade et al. 2014 ). Moreover, we allow the luminosity density profile to differ from the total mass density profile, i.e., , and the stellar velocity anisotropy exits, i.e., . Based on a well-studied sample of nearby elliptical galaxies from Gerhard et al. ( 2001 ), the anisotropy β is characterized by a Gaussian distribution, β = 0.18 ± 0.13, that is also extensively used in previous works (Bolton et al. 2006 ; Schwab et al. 2010 ). More recently, Xu et al. ( 2016 ) measured the stellar velocity anisotropy parameter β and its correlations with redshifts and stellar velocity dispersion, based on the Illustris simulated early-type galaxies with spherically symmetric density distributions. It is

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


conclusions of this paper are correct and valuable. The data presented here suggest another mechanism for the ECD instability. The LHD electric fields of 20 mV m −1 in B ∼ 15 nT produce ExB drift of 1300 km s −1 , comparable to the electron thermal speed. Since this field exists in narrow channels with a width of a few electron gyroradii, only electrons can participate, making ion–electron drift V d ∼ te . Incidentally, this instability attracted attention of researchers working with Hall ion thrusters, because it affects their performance (Ducrocq et al. 2006 ; Boeuf Garrigues 2018 ). In these devices, the instability is also caused by the ExB drift of electrons only, because ions have gyroradius larger than the drift channels. The theory of ECD instability that links electron–cyclotron harmonics with ion-acoustic waves and wavelengths at scales below the electron gyroradius provides convincing explanation for waves in Fig. 2(a) , which exhibit both large E ∥ and E ⊥ , and contain f ce harmonics and Doppler shifted structures smaller than electron gyroradius. 3 WHAT HEATS IONS AND ELECTRONS? We focus now on the fundamental question: What kinds of processes can increase the ion energy by 400 eV (from 50 to 450 eV), and the electron energy by 50 eV (from 20 to 70 eV), within a few seconds, or during one proton gyroperiod, as seen in Fig. 1 . Additional constraint is that heating of electrons is isotropic, while that of ions is mostly perpendicular. The mechanism of stochastic ion heating on LH waves related to condition (1 ) has been explained by Karney ( 1979 ), and on other wave structures by other authors: Cole ( 1976 ), McChesney et al. ( 1987 ), Balikhin et al. ( 1993 ), Mishin Banaszkiewicz ( 1998 ), Stasiewicz et al. ( 2000 , 2013 ), Stasiewicz ( 2007 ), Vranjes Poedts ( 2010 ), and Yoon Bellan ( 2019 ). The essence is that particles stressed by strong gradients lose adiabaticity and can be scattered along the electric field for direct acceleration by both DC and wave fields. The computed χ (Fig. 4b ) shows values greatly exceeding 1, needed to stochastically perturb proton orbits; however, significant ion heating is observed when χ > 10. Formally, the error of χ is equivalent to the error of the electric field measurements, i.e. ∼1 mV m −1 , or 10 per cent of large-amplitude fields, because of gain uncertainty in amplifiers (Lindqvist et al. 2016 ). However, in the case of ECD waves with wavelengths of the electron gyroradius, the gradient computations underestimate real values because the spacecraft separations are larger than wavelengths. In Fig. 4(c) , we show the difference in E y components measured by satellites 1 and 2. Similar differences are seen on any pair of the satellites. A difference Δ E y ≈100 mV m −1 on scales of the electron gyroradius r e ≈ 1 km in the field B = 15 nT would produce χ ≈ 4600, which could effectively demagnetize electrons and subject them to stochastic heating. Applying 10 per cent error to this value

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


each ii / jj term and ij / ji term. We start with ii / jj . For a fixed baseline that involves antenna i , there will be at most N ant additional baselines that are redundant with and do not involve gain i . From equations ( 39 ) and ( 40 ), the weighting of the covariance between two different baselines in which only one involves antenna i goes as . Thus, the presence of redundancy adds no more than N ant terms involving antenna i but not antenna j and vice versa, for each ii summand in equation ( 35 ). Multiplying this overall factor of by N ant to account for the N ant different ii sums leads to a contribution to the noise amplitude of the order of , similar to the level of the noise without redundancy. As a result, redundancy changes the modelling error amplitude by a factor of order unity in the diagonal terms. Next, we consider the ij terms in equation ( 35 ). For a given and i j , there will be at most N ant redundant baselines that do not involve the i th or j th gains, causing the weighting of each unique variance term to go as rather than in the non-redundant case. Since there are unique baselines that do not involve i or j , the overall sum of these terms goes as . As a result, the ij terms in equation ( 35 ) will have a similar magnitude as the ii / jj terms but the overall impact on the amplitude of the modelling noise described in equation ( 35 ) still changes the amplitude by a factor of order unity. We confirm these arguments with a numerical comparison between the amplitude of the modelling noise with and without redundancy taken into account for two redundant arrays of 91 and 331 hexagonally packed 14m apertures and S min equal to the naturally weighted confusion limit. We compute the off-diagonal elements of by numerically computing the beam integral in equation ( 5 ) for all with Airy beams and perform the full matrix inversions prescribed in equations ( 16 ) and ( 17 ). We compare our results to the same calculation where all off-diagonal elements of are set to zero (Fig. A1 ) and find that the difference in amplitude is essentially a factor of order unity, leading to a negligible increase in the effective . This calculation confirms our argument for HERA-scale arrays. Figure A1. We compare the amplitude of modelling noise on a short baseline when is assumed to be diagonal (orange line) and the off-diagonal terms of are explicitly included for a 91-element (dashed lines) and 331-element (solid lines) hexagonally packed array of 14m apertures. We find that even in a maximally redundant array, the effect of redundancy is to change the overall amplitude of the modelling noise by a factor of a few. This only has a small impact (10percent) on , the smallest k where the 21cm signal (black line) dominates over the modelling noise, as computed from equation ( 51 ) that ignores the effect of redundancy. APPENDIX B: The Point Source Approximation For Modelled Foregrounds For analytic tractability, we assumed that the modelled

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


groups as an extra fractional uncertainty, f , on all data points. 10 10 We use this statistically robust approach instead of assuming a fixed fractional uncertainty of 3%–5% at each frequency as done by Dobie et al. ( 2018 ). We use emcee (Foreman-Mackey et al. 2013 ) to perform a MCMC analysis to determine the posteriors of the model parameters. We use a logarithmic flat prior on s (−1.5 log s 1.5) because by definition s must be positive and the data do not provide any constraints once s becomes sufficiently large (corresponding to a sharp break that occurs over a time interval much smaller than our sampling time). We use flat linear priors on all other parameters: 10 t b 1000 days, 1 F ν , b 1000 μ Jy, −20 α 1 , α 2 20, and 0 f 1. Figure 1. Up-to-date X-ray, optical, and radio light curves of GW170817 (solid circles; open circles are the new data presented in Dobie et al. 2018 ). The data are clearly indicative of a decline at ≳200 days. Also shown are our structured jet models from Margutti et al. ( 2018 ); see Xie et al. ( 2018 ) for full details of the simulations. Both jets have an ultra-relativistic core with E K,iso = 6 ×10 52 erg within an opening angle θ jet = 9°. The solid lines are for a model with n = 10 −5 cm −3 , θ obs = 17°, e = 0.1, and B = 0.0005, while the dashed lines are for n = 10 −4 cm −3 , θ obs = 20°, e = 0.02, and B = 0.001. Our new radio, optical, and X-ray observations continue to support these models. We find and , with days, indicative of a clear transition from a rising to a declining light curve; see Figure 2 . We can reject a non-declining light curve (i.e., α 2 ≥ 0) at 7 σ confidence level. These results are consistent 11 11 We repeat our MCMC analysis for the subset of radio data presented in Dobie et al. ( 2018 ), with α 1 , α 2 , t b , F ν , b , s , and f as free parameters, and find that t b and α 2 are more loosely constrained: t b = 190 ± 30 days and . A value of α 2 ≥ 0 can be ruled out at 3.0 σ confidence level. with the analysis of Dobie et al. ( 2018 ), but provide a much stronger indication of a break due to the longer time baseline of our observations. Both successful structured jet models and pure cocoon models are consistent with the observed α 1 . Unlike the simplest analytic models, which predict α 2 ≈ −2.2 (Sari et al. 1999 ; Nakar Piran 2018 ), the Xie et al. ( 2018 ) successful structured jet simulations predict a shallower initial post-peak decline (Figure 1 ). Therefore, our derived α 2 does not strongly discriminate between successful structured jet and pure cocoon or dynamical ejecta models, although the latter are mildly disfavored (Lamb et al. 2018 ). Of the two Xie et al. ( 2018 ) models shown in Figure 1 , our most recent data at 273 days and 289 days mildly favor the dashed model, which in comparison to the solid model implies a higher circumbinary density of 10 −4 cm −3 , a lower fraction of the shock energy imparted to electrons ( e = 0.02), and an observer viewing angle

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


excluded in this work due to their CMD locations. Figure 1. Locations of the stars in the 7 deg 2 APOGEE field of NGC 6553. The solid circle indicates cluster tidal radius ( R t ). Non-members outside 1.5 R t are the grey crosses. Stars inside 1.5 R t are colour-coded, according to the colour bar shown in Fig. 2 . Cluster members and non-members are labelled by filled circles and crosses, respectively. Figure 2. [Fe/H] versus radial velocity. Symbol meanings are the same as in Fig. 1 . Figure 3. Differential reddening-corrected CMD of NGC 6553 from PSF photometry of VVV imaging, supplemented with bright stars from 2MASS. The cluster fiducial sequence is indicated as a red solid line. The grey dots are stars within 1.5 R t (tidal radius), and the black dots are stars within the half-light radius. APOGEE targets inside 1.5 R t are colour-coded as in Fig. 1 . Cluster members and non-members determined in this paper are labelled by filled circles and crosses, respectively. See text for more details. From the coordinate information, these 10 cluster members have no overlap with the spectroscopic studies of NGC 6553 published after the year 2006, which include Alves-Brito et al. ( 2006 ), Zoccali et al. ( 2008 ), Gonzalez et al. ( 2011 ), Johnson et al. ( 2014 ), and Dias et al. ( 2015 ). Most of the APOGEE spectra for our sample have signal-to-noise ratio (SNR) higher than 80, except the second star in Table 1 . Each star in our sample has a single one hour visit, so the SNR is correlated with the stellar brightness. The SNR plays an important role in estimating the uncertainties of element abundances (Majewski et al. 2015 ). Three stars are labelled as ‘PERSIST_HIGH’ and six are labelled as ‘PERSIST_MED’. Persistence, where a significant fraction of accumulated charge is released over a long period of time, is particularly strong in one of the detectors (1.51–1.58 μm) used in the SDSS III/APOGEE survey (Nidever et al. 2015 ). However, by comparing the results from spectra containing persistence pixels versus those without, Holtzman et al. ( 2015 ) suggest that persistence does not dramatically impact the parameters in DR12 data. Table 1. Basic parameters for cluster members of NGC 6553. Notes . a Differential reddening corrected magnitude. b Measurement error. c PERSIST: spectrum has a significant number (>20 per cent) of pixels in the high (or medium) persistence region. d N_WARN: parameter value is within half grid spacing of the synthetic spectrum grid edge for nitrogen. SN_WARN: SNR70. From APOGEE measurements, our 10 cluster members show a mean RV of −0.14 ± 5.47 3 km s −1 . Our mean RV agrees with the other determinations: 4 ± 7.1 km s −1 (Cohen et al. 1999 ), 1.6 ± 6 km s −1 (Meléndez et al. 2003 ), −1.86 ± 2.01 km s −1 (Alves-Brito et al. 2006 ), −2.03 ± 4.85 km s −1 (Johnson et al. 2014 ), and 6 ± 8 km s −1 (Dias et al. 2015 ). In addition, the APOGEE data yield a mean [Fe/H] of −0.15 ± 0.05. This GC has diverse metallicity results from

O O O O O O O O O O O O O O O O O O O O B-CelestialRegion I-CelestialRegion 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 B-CelestialObject I-CelestialObject O B-Model I-Model O B-Survey 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 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 B-CelestialObject I-CelestialObject O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O B-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 B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O B-Citation I-Citation B-Citation 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 I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-Dataset I-Dataset 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 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 B-Citation I-Citation I-Citation I-Citation O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O B-Citation O O O O O O O O O O O O O O O O


Sky Survey (Skrutskie et al. 2006 ) with an overall accuracy of 012–015. To account for the measured absolute offsets of ∼023 and ∼057 in the NUV and FUV image astrometry, respectively, we used a grid of reference stars detected in a ∼12′′ radius around PSR B0540−69 to register the MAMA images onto the astrometry reference frame of the WFPC2 images with an accuracy of better than 001. We used the NUV and FUV images with the recalibrated astrometry as a reference for the pulsar identification. 3. Results 3.1. Imaging and Photometry Figure 1 shows the NUV- and FUV-MAMA images of the PSR B0540−69 field obtained after the processing described in the previous section. We clearly detected PSR B0540−69 in both the NUV and FUV images at a position coincident with its optical coordinates computed by Mignani et al. ( 2010b ): (0009), (005). 21 21 The errors refer to the average of the pulsar coordinates computed on four independent WFPC2 data sets, see Mignani et al. ( 2010b ) for details. Ours is the first detection ever of PSR B0540−69 in the UV, which also makes it the fifth isolated pulsar, among the ∼2300 known, that has been detected in the near-IR, optical, UV, X-rays, and γ -rays, after the Crab and Vela pulsars, PSR B0656+14, and Geminga (the fourth among radio pulsars 22 22 Geminga (PSR J0633+1746) has not yet been unambiguously detected as a radio pulsar despite many searches, see Maan ( 2015 ) and references therein. ). We also detected the PSR B0540−69 PWN in our NUV image (Figure 1 , left), with a structure and extent similar to what is observed in the optical and near-IR (Mignani et al. 2010b , 2012 ). The PWN is at most barely visible, however, in the FUV image (Figure 1 , right). The bright emission knot in the PWN detected at ∼17 southwest of the pulsar in HST /WFPC2 images (De Luca et al. 2007 ) is also visible in the STIS/NUV-MAMA observation, aligned with the major axis of the PWN. Since our paper is focused on the pulsar, a coherent multi-wavelength spectral and spatial analysis of the PWN and its features will be the subject of a subsequent paper. Figure 1. STIS NUV-MAMA (left) and FUV-MAMA (right) images (9650 s each) of the PSR B0540−69 field taken with the F25QTZ filters. The images are aligned in R.A. and decl., with north to the top and east to the left. The image size is 9′′ × 9′′. The pulsar is the source at the center of the nebula, clearly visible in the NUV-MAMA image. The intensity scale of the two images (in counts) is color-coded in the two horizontal bars at the bottom of each image. In both cases, the minimum/maximum of the scale have been adjusted to favor the identification of the pulsar and other stars in the field. For a better visualization, both images have been smoothed with a Gaussian function using a kernel of 2 pixel radius. For both the NUV and FUV images, we computed the pulsar fluxes through aperture photometry employing the tools in the IRAF 23 23 IRAF is distributed by the National Optical Astronomy

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


six ARs. Each time interval is limited to a duration when the corresponding AR is between −60° and +60° with respect to the central meridian to avoid extreme magnetic field projection effects (Bobra et al. 2014 ). Table 1 includes also the onset time and the associated GOES class of the flares occurred in each AR, based on the GOES solar flare catalog. 9 9 https://hesperia.gsfc.nasa.gov/ Furthermore, Table 1 gives information on the dominant evolutionary phases of the ARs, and on how long their δ -spots were observed. Table 1 Summary Table of the Properties of the Studied Six ARs: NOAA Number and the Study Period of AR, Information about the Investigated Flares, Dominant Evolution Phase of the ARs Note. The last coulomb shows the time interval when δ -spot(s) appeared in an AR. 3. Data Analysis The emergence and shearing components of the magnetic helicity of the six ARs are calculated using Equation ( 1 ). The total magnetic helicity flux for a given AR was generated by summing the emergence and shearing components. The three helicity injection rates for each AR were obtained by integrating the helicity flux over the entire area of the AR. The three helicity flux components are further normalized by their respective largest absolute value in order to facilitate comparison on similar scales. The normalized emergence, shearing, and total helicity fluxes are shown in the top panels of Figures 2 – 3 . In the upper panels of Figures 2 – 3 , the blue line is the emergence term, the red line the magnetic helicity flux associated with shearing motions at the photosphere, and the black line is the total magnetic flux. Figure 2. Time analysis of three flaring ARs, namely (a) AR 11166 (b) AR 12192, and (c) AR 11890. The top panels show time series of the normalized emergence (EM, blue), shearing (SH, red), and total (Total, black) helicity fluxes. The red vertical lines mark the onset time of flares. The second through fourth rows show the wavelet power spectrum (WPS) of the normalized emergence, shearing, and total helicity fluxes, respectively. Rather than plotting power directly, the color bars visualize the logarithm of the ratio of the power to the expected power for Gaussian-distributed white noise and significance compared to noise. The x -axis of each WPS is the observation time, and the y -axis is the period, both in hours. On the WPS plots, the black lines bound the cone-of-influence, i.e., the domain where edge effects become important. The plots to the right of each WPS are the corresponding global wavelet spectra (power averaged over time, similar to a Fourier power spectrum). The orange dashed lines mark the one σ confidence in global wavelet spectrum analyses. Figure 3. Same as Figure 2 , but for the three non-flaring ARs, namely (a) AR 12645, (b) AR 12470, and (c) AR 11785. By inspecting the top panels of Figures 2 – 3 (a)–(c), we can see that the normalized shearing and total helicity flux components show similar evolution trends in

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O B-Telescope O O O O O O O O O O O B-Dataset I-Dataset I-Dataset I-Dataset O O B-URL O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-CelestialObjectRegion I-CelestialObjectRegion 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 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 B-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 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 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 B-CelestialObjectRegion I-CelestialObjectRegion O B-CelestialObjectRegion I-CelestialObjectRegion 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


, d v1 ) and ( V v2 , d v2 ) (not shown here). Figure 8. Left-hand panel: 2D distribution ( V v3 , d v3 ). There is a linear trend that is correctly described by the linear relation given by equation ( 16 , dashed line). Right-hand panel: the correlation disappears after correcting the LOS displacements with this equation. This is a statistical demonstration of the v-RSD off-centring effect. From this analysis, we arrive at the third important conclusion of this work: void centres shift preferentially along the LOS when they are mapped from r - into z -space, and this displacement can be statistically quantified by means of equation ( 16 ). These results give support to the v-RSD off-centring effect postulated in Section 4.5 . 5.3 Cross-correlations Since the ratio (or equivalently δ R v ) characterizes the change of volume in voids, the statistical analysis of Section 5.1 gave support to the t-RSD expansion effect postulated in Section 4.2 . On the other hand, as the displacement and velocity characterize the movement of voids, the statistical analysis of Section 5.2 gave support to the v-RSD off-centring effect postulated in Section 4.5 . It only remains to test if both effects are statistically independent by looking for cross-correlations between these quantities. Fig. 9 shows the 2D LOS distributions (left-hand panel) and (right-hand panel). The horizontal lines are the theoretical predictions (dashed) and (solid). No correlations can be seen, giving support to the postulated independence. It is worth mentioning that the analogue POS distributions (not shown here): , , , and show a similar behaviour. These results allow us to interpret the large-scale dynamics of the whole region containing the void (v-RSD) as decoupled from the dynamics of the galaxies at scales of the void radius (t-RSD). This also suggests that potential distortion patterns in observations due to these two effects can be treated separately. This is the fourth important conclusion of this work. Figure 9. 2D distributions (left-hand panel) and (right-hand panel). The horizontal lines are the theoretical predictions (equation 7 , dashed) and (equation 10 , solid). No correlations can be seen in both panels, suggesting that the t-RSD expansion effect and the v-RSD off-centring effect are statistically independent. 6 IMPACT ON THE VOID SIZE FUNCTION This section has a double intention. On the one hand, we will finish the analysis of the last section incorporating the additional AP change of volume not treated yet. On the other hand, we will study the impact of all the z -space effects on the void size function. For this reason, we turn now to the FC void catalogues, fully affected by z -space systematics (see Table 1 ). 6.1 Generalities of the <xref ref-type="bibr" rid="bib69">VSF</xref> modelling We start with some generalities concerning the VSF modelling. The real-space VSF can be modelled using the excursion set formalism combined with the spherical expansion of matter

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-TextGarbage I-TextGarbage I-TextGarbage O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O 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 B-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Dataset I-Dataset I-Dataset O O O O O O O O O O O O O O B-Tag I-Tag I-Tag 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 O O


A MannWhitney U test of the distributions about this relation does not rule out at 95percent confidence the null hypothesis that the two redshift sub-samples have the same parent population. We do, however, acknowledge that weak evolution of the relation of equation ( 1 ) cannot be ruled out by our data, and this should be investigated with deep X-ray survey data and/or further deep X-ray observations of carefully selected samples. 2.3 Using pressure to predict X-ray luminosity We have demonstrated that we can reliably predict the ICM pressure at a single distance within the group/cluster surrounding an FRII radio galaxy. To be able to predict the overall group/cluster richness, we need to be able to translate this pressure measurement into an estimate of cluster mass and/or X-ray luminosity. We therefore examined whether the universal cluster pressure profile of Arnaud etal. ( 2010 , hereafter A10 ) could be applied to FRII environments. We first examined the sub-sample of I17 for which reliable spectral temperature estimates were available. Our pressure profiles have large uncertainties, and were obtained from either beta or double-beta model fits to the surface brightness profiles (see I17 ). The environments are also mainly galaxy groups ( L X 10 44 ergs 1 ), and so lower in mass than the sample of A10 ; however, Sun etal. ( 2011 ) have shown that the universal profile also applies on galaxy group scales. Fig. 2 (right-hand panel) shows that our scaled pressure profiles are in broad agreement with the A10 profile shape and normalization. We therefore tested whether the universal cluster pressure profile could be used to translate our single-radius pressure estimates, from our radio predictions, into cluster mass and X-ray luminosity. We used the profile of A10 (equations 1113 of that work) and our input values of distance and P ext to estimate M 500 for each radio-galaxy environment. We then applied the L X M 500 relation of Pratt etal. ( 2009 ) (using the relation for L X R 500 ) to obtain a predicted L X for each radio-galaxy environment. Finally, we compared our radio-predicted X-ray luminosities with the measured X-ray luminosities for our sample from Ineson etal. ( 2015 ). Fig. 3 (left-hand panel) shows the remarkable agreement between our radio-predicted X-ray luminosities and the measured values across more than three orders of magnitude in X-ray luminosity (from poor groups to moderate clusters) our method appears to predict ICM X-ray luminosity to within roughly a factor of 2 based only on the measured properties of the embedded radio galaxy. We have included four additional FRII sources from the sample of I17 for which external pressure distributions could not be measured, but which meet the morphological selection criteria, leading to a sample of 31 objects, as listed in Table 1 . Figure 3. Left-hand panel: the predicted group/cluster X-ray luminosities determined from the radio-measured pressures for the morphologically

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


data presented here from the ion trap measurements are not of the bare species itself because of the slight perturbation induced by the weakly bound helium atom; however, the shift is expected to be small. Laboratory data on the band at and the weak features near for are shown in Figure 2 and indicate that the helium causes a shift on the electronic transition of of around . Considering the width of the absorption band profiles, for comparison with astronomical data, the spectrum of (Figure 1 ) can be considered to be that of the bare cation. In Table 1 , the band maxima of the absorptions shown in Figure 1 are listed. Figure 2. Electronic spectra of below 10 K. Data are shown for two of the bands presented in Figure 1 . The similarities between the spectra indicate that the shift on the electronic transition of due to the presence of the helium is small. Therefore, the spectrum of may be regarded as that of for comparison with DIB data. A linear offset has been applied to the vertical axis of the data shown. Table 1 Absorption Maxima of the Bands Shown in Figure 1 and Compared with the Gas-phase Prediction Reported by Steglich et al. ( 2011 ) Note. a Weak absorptions with intensities lower than 20% of the band at are not listed. Steglich et al. ( 2011 ) predicted the gas-phase transition energies of based on their matrix data using a model (Gredel et al. 2011 ) to account for the polarizability of the different rare gases used. The present work enables a direct evaluation of this model and their results are also given in Table 1 . The predicted values are found to be in accord with the gas phase; however, the large error bars () indicate that the extrapolation is not quite good enough for an unambiguous comparison with DIB data, especially if the latter are weak (). For this, gas-phase measurements as done here on are required. In the context of astronomical detectability it is important to determine the oscillator strength f of the individual transitions, in particular for the strongest band in the spectrum. This is because the theoretically calculated values are not expected to be very accurate because of the nature of the method that had to be used (TD-DFT). Furthermore, these f values correspond to the the whole electronic absorption system(s). To obtain the oscillator strength for the origin band at , its Franck–Condon factor relative to all the other transitions has to be estimated, as carried out by Steglich et al. ( 2011 ). Thus, it is more reliable to measure absolute absorption cross sections directly in the ion trap, as previously demonstrated by measurements on the fullerene cations (Campbell et al. 2016a , 2017 ). Absorption cross-section measurements were carried out at the wavelength of the band maxima of the two strongest absorptions in the spectrum. Plots showing typical exponential fits to the data are shown in Figure 3 . The characteristic fluence, , was found to be 0.8 and at 8281 and , respectively. These values correspond

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-TextGarbage O O O O O O O O O O O O O O O O O O O O O O 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 B-ObservationalTechniques O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Citation I-Citation I-Citation I-Citation O B-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-TextGarbage I-TextGarbage O O O O O O O O O O O O O O


gravitational influences, it is possible to include the Yarkovsky drift. The orbfit has additional programs for determination of the orbits of Solar system bodies and could compute their positions on the celestial sphere. Also, orbfit has tools for the computation of Lyapunov exponents and proper elements (analytic and synthetic). 2.2 <sc>mercury</sc> The mercury package (Chambers Migliorini 1997 ) includes different algorithms, and it is written using the fortran 77 programming language. The mercury package is publicly available at https://github.com/4xxi/mercury . mercury has the following N -body algorithms: second-order mixed-variable symplectic integrator, general Bulirsh–Stoer integrator, conservative Bulirsh–Stoer, Everhart's RA15 (RADAU) algorithm and Hybrid symplectic/Bulirsh–Stoer integrator. For the purpose of our analysis, we chose the explicit Hybrid symplectic integrator (Chambers 1999 ) that could compute close encounters. Symplectic integrators (for complete theory of symplectic integrators, see e.g. Sanz-Serna 1991 ; Yoshida 1993 ) do not have a long-term build-up of energy error, and they are significantly faster with problems in which most of the mass is contained in a single body. The idea behind symplectic integrators is to split the Hamiltonian () of a system into pieces, each of which can be solved on its own. Symplectic integrator use a fixed time-step that makes calculating close encounter difficult due to the necessity of changing the step size. One of the possible solutions is to use a smaller step size or to split the perturbing terms, and to set a different step size for each term (SYMBA integrator; Duncan, Levison Lee 1998 ). Chambers ( 1999 ) described an alternative solution – a hybrid integrator that has symplectic and non-symplectic components. That alternative solution keeps the best properties of both symplectic and non-symplectic integrators. 3 METHODOLOGY AND DATA To study the limitations of the BIM, first a fictional family is going to be created based on the Veritas asteroid family. In this respect, all adopted values of the fictitious family are the same as of Veritas. Families are formed from the disruption of the target asteroid during a high-velocity impact. Escape speed ( v esc ) is much smaller than orbital speed ( v orb ≈ 15–20 km s −1 ), and, consequentially, all the orbits of family members are similar immediately after their creation. To create the initial orbital distribution of the simulated family members, we have used Gauss equations. These equations describe changes in the osculating elements due to the components of the ejection velocity: where a , e , i , f and ω are the semimajor axis, eccentricity, inclination, true anomaly and argument of perihelion, respectively; na is the mean orbital velocity; and δ V T , δ V R and δ V W are the components of ejection velocity along the direction of the motion, the radial direction and perpendicular to the orbital plane, respectively. The

O O O O O O O O O O O B-Software 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-Software O O O O O O O O O O O O O O O B-Tag O B-Software I-Software B-Citation I-Citation I-Citation O O O O O O O O O O B-Software I-Software O O O B-Software I-Software O O O O B-URL O B-Software O O O B-Model I-Model O B-Model I-Model I-Model I-Model B-Model I-Model I-Model B-Model I-Model B-Model I-Model B-Model B-Model O B-Model I-Model I-Model O O O O O O O O O O B-Model I-Model I-Model B-Citation I-Citation O O O O O O O O O O O O O O O O B-Citation I-Citation O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-TextGarbage O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model B-Citation I-Citation I-Citation I-Citation I-Citation 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 B-EntityOfFutureInterest I-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O O O O O O B-EntityOfFutureInterest O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


value . This gives 3785 proper motion slices. A slice then contains all stars for which holds. The number of stars per slice strongly varies and depends on the total proper motion. The maximum number of 44 000 stars is at (, ) = (), whereas the number of stars is less than 150 at the borders of our square. About 90% of all slices contain less than 6000 stars. These slices represent a seven-fold overlap of the proper motion plane, with the effect that the same over-density on the sky may appear in neighbouring slices, but not necessarily with the same signal-to-noise ratio. (b) In the second step we searched for over-densities in the proper motion slices. For each star in a proper motion slice, we counted all its neighbours within a radius of 0.5 deg (called sky circle) and determined the surface density (stars/square degree). Surrounding each star’s sky circle we chose an area of 9 sq. deg, where we determined the background surface density . We only retain stars if / of their sky circle is larger than 3.0 and their is larger than 5 per square degree. If the angle between two stars is less than 0.5 deg, each of them is in the other’s sky circle. We discard the one with the lower . This cleaning goes on until only “isolated” sky circles are left, which we call Level-0 centres. As our system of proper motion slices represents a seven-fold overlap of the sky, a Level-0 centre in slice could have the same or a neighbouring Level-0 centre in slice . If they are within the radius of a sky circle and the difference of their actual proper motions is less than 1.5 mas/yr, only the Level-0 centre with higher / is retained. These survivors are called Level-1 centres; they are disjunct and are possible candidates of new open clusters. Of course, many of the Level-1 centres could be related to known open clusters. Therefore, we cross-matched them with the MWSC clusters ( Kharchenko et al. 2013 ) and with the most recent cluster list DAML02 VERSION 3.5 of 2016 Jan. 28 ( Dias et al. 2002 ). We discarded all the Level-1 centres within 0.7 deg of a known cluster, if the radius of the known cluster was larger than 0.2 deg. If the radius of a cluster in MWSC or in DAML is smaller than 0.2 deg, it cannot be identical to one of the objects found here. About 200 Level-1 centres surviving this process (called Level-2 centres) were then subject to a photometric check of their existence as clusters. Table 1 New open clusters. 3.2. Photometric steps. (a) We first made a quick and coarse check in the CMD of the stars in a sky circle around a Level-2 centre using TOPCAT 2 ( Taylor 2005 ). A Level-2 centre was selected for a more careful treatment if stars with showed a tendency towards building a part of a main sequence or a turn-off region. The Level-2 centres were immediately rejected if, on the CMDs, their stars showed a random distribution, mostly at the limiting magnitude of Tycho-2. So, we could quickly check the Level-2 centres found in the previous step. Fig. 1

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-TextGarbage I-TextGarbage O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Dataset I-Dataset O B-Citation I-Citation I-Citation I-Citation O O O O O O B-Dataset I-Dataset I-Dataset I-Dataset I-Dataset 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 B-Dataset O O B-Dataset O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 I-Software O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Dataset O O O O O O O O O O O O O O O


to be the main reason for our different conclusions. 7.4. [α/Fe]–[Fe/H] relations As shown in Fig 7 , the intrinsic scatter of the [ α /Fe]–[Fe/H] data is large as a result of the complex galactic gas and metal distribution, and stars may form outside the main progenitor halo ( Jeon et al. 2017 ). Our mean galactic metal evolution track assumes that all the gas is always well mixed and thus cannot explain the metal abundance of individual single stars. The best-fit model that applies the IGIMF theory is comparable with the solutions given by Lacchin et al. (2020) , which are shown as the dashed and dash-dotted lines in Fig 7 , especially for metal-rich stars. The highest [ α /Fe] value at the metal-poor end of the plots from Lacchin et al. (2020) is lower than our results and fits the data not as well as our model, however. The highest [ α /Fe] value should be the IMF-weighted [ α /Fe] value of all the massive stars with Z = 0 and a lifetime shorter than the first time step, δ t = 10 Myr, that is, the IMF-weighted thin solid line within the red shaded region of Fig. 8 . Because the IMF-weighted value should be higher than the lowest value in the red region, it is clear that the initial [Mg/Fe] should be higher than 0.5, which agrees with our result and disagrees with Lacchin et al. (2020) . Fig. 8. Stellar metal yield ratios of stars with different mass and metallicity given by Kobayashi et al. (2006) . The yields from Kobayashi et al. (2006) for massive stars are connected to the yields for low- and intermediate-mass stars as given by Marigo (2001) . The yields for M * > 40 M ⊙ are the same as the yields for M * = 40 M ⊙ stars. The red shaded region with log 10 ( M *, initial [ M ⊙ ]) > 1.3073 indicates zero-metallicity stars with lifetimes shorter than 10 Myr, according to Yan et al. (2019) . The [ α /Fe] plateau can be enhanced by a more complicated gas-flow model, a larger stellar-mass bin, or a larger model time step. A non-simultaneous star formation combined with local stellar wind pollution can also complicate the model prediction, which requires more elaborate hydrochemical simulations. We note that the metal-poor part of the [ α /Fe]–[Fe/H] relations is affected by the small number of stars that are formed at the earliest time steps. This shows that the metal-poor part is not reliable because of the small number of massive stars that affect it, the uncertainty of the stellar winds of these massive stars, and whether or not they explode as supernovae. Stars that are more massive than 40 M ⊙ share the same adopted stellar yield table, which is certainly not the ideal setup to discuss the chemical abundance of the extremely metal-poor era of a galaxy. 7.5. Star formation history The tested SFT in Lacchin et al. (2020) is generally longer than our best-fit models. Because the gas flow and star formation criteria in the chemical evolution model are uncertain, the best-fit SFH is not conclusive. Here we compare it with the independently

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


PSFs (right). Both images are on the same logarithmic scale with a lower threshold of . The theoretical PSF is calculated for the central monochromatic wavelength of 3.94 microns. The retardance in the simulation was set to radians, thereby creating the leakage PSF “0.” The observed image is saturated on the first diffraction ring and on the central core but is corrected to the unsaturated flux level. A small asymmetry of the intensities of the wind-driven halos of the star inside the dark holes is seen between the two coronagraphic PSFs (“+” and “−”). Instrumental ghosts are indicated with arrows and are not related to the coronagraphic optic. Further investigation showed that these ghosts can be removed from the dark hole by setting the rotator to an angle of 30°. 3.1. Data Reduction To remove hot, dead, or flaky pixels in each image, we subtracted a median-filtered image with a 3 × 5 pixel box from the cleaned and centroided image cube to generate an image where the outliers clearly stand out. The 3 × 5 box is chosen because the outlying pixels tend to have structure in the direction of the readout and not perpendicular to it. The data points that deviate more than 1000 counts are replaced by the local value of the 3 × 5 median. Four sets of sky reference frames are taken between on-target observations. The sky frames were median-combined for every one of the four sets. Each of the previously taken frames on target were subtracted by the first consecutive median-combined master sky frame. After the background subtraction, the median of a cosmetically clean part of the chip is subtracted in order to remove any residual background offset. A theoretical diffraction pattern consistent with the geometry of the telescope and wavelength of observation is used as a fiducial. This theoretical PSF is then fit to the central leakage PSF by minimizing the chi-squared residuals between the theoretical PSF and the leakage PSF, with x , y , radius (), and intensity as the free parameters of the fit. All images of the data cubes are coregistered by shifting the images to the central pixel of the frame with the previously fit x and y values using a bilinear interpolator. The radius of the leakage PSF fit is used as a subframe quality indicator. The few images (39) that have fitted radii significantly smaller ( pixels) or larger ( pixels) than the diffraction limit are excluded. The best 91% (5200) of the images are selected after sorting the frames by radius from smallest to largest. Both criteria remove the frames where the seeing conditions temporarily worsened or where the AO system lost its lock. After these selections, the images are reordered to original chronological order and binned by four frames, corresponding to 4 s integration time per binned frame to reduce memory consumption and computational time. Instrumental ghosts due to internal reflection of the refractive optics are present in the image; see Figure 2 . Several of these ghosts are

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


on different methods. A simple radial profile (black line within gray boundaries) nicely fits our results and the previous estimates in the range 1.1−2.0 R ⊙ . 3. Coronal magnetic field The upstream Alfvénic Mach number M A and the magnetic field strength B can be derived from the standoff distance Δ r ≡ r sh − r cme between the shock front r sh and the CME leading edge r cme by employing a model adapted by Gopalswamy Yashiro (2011) but originally developed for the bow shock of the Earth. Physically, the shock Mach number M and the radius of curvature r cme of the nose of the driver control the standoff distance. The ratio δ between Δ r and r cme can be expressed as δ ≡ Δ r / r cme = 0.81[( γ − 1) M 2 + 2]/[( γ − 1)( M 2 − 1)], (e.g., Farris Russell 1994 ) where γ is the adiabatic index (we assume γ = 4/3 and γ = 5/3 as two possible values). This expression allows the applicability of the model to the low- M regime provided that M is substituted for the fast magnetosonic Mach number ( Fairfield et al. 2001 ). In the inner corona, v A substantially exceeds the sound speed meaning that M can be confidently replaced by M A . It then follows that , implying that M A (and thus the coronal magnetic field strength B , given the upstream electron density profile n e ) can be obtained at any given time by measuring δ . We point out that the above method is based on a model by Farris Russell (1994) , further extended by Russell Mulligan (2002) , which was specifically designed for the bow shock of the terrestrial magnetosphere. As such, the evaluation of the standoff distance in that model is intended to be strictly valid for the nose of a CME. It is then important to discuss how appropriate such a model is for a coronal CME-driven shock, for which, moreover, as in our case, the standoff distance is calculated not at the nose but at the flanks of the shock. In order to check the validity of the model in the coronal environment, Schmidt et al. (2016) used a 3D magnetohydrodynamic code to test the accuracy of the Gopalswamy Yashiro (2011) method by applying it to a simulation of a real CME event, where the standoff distances between the driven shock and the CME could be determined within the simulation box. As a result, the predicted magnetic field strength profile agreed very well (within 30% between 1.8 and 10 R ⊙ ) with the magnetic field strength profile found in the simulation domain, thus providing strong support for the Gopalswamy Yashiro (2011) method in a coronal environment. As for the second issue, that is, the reliability of the model when the standoff distance is evaluated at the flanks of the shock surface, it is obvious that in the general case of a fast moving CME the shock surface would be better represented by a 3D oblate surface. In that case, our model would yield unreliable results away from the CME nose. In our specific case however, since the translational motion of the CME away from the Sun is negligible with respect to its

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


obtained by using (green), (red), and (blue). We make the following observations from this plot: β BF versus f / b falls nicely on a straight line with slope 1 (the solid line). However, note that the relation β BF = f / b (the dashed line) does not exactly hold: we have checked that the actual value of β BF depends on the s min used, decreasing as smaller s min is used; the results here are for . The trend suggests that, roughly speaking, the reconstruction simply spits out the ‘input’ β value, and therefore has no predictive power regarding β, unless we look beyond R ( s ). The two ( f, b ) pairs that give similar β = f / b ≈ 0.375 produce very similar β BF : this is a consequence of the f – b degeneracy mentioned above. For comparison, we include the best-fitting β BF values obtained using R ′ ( s ) as filled circles, using the same colour scheme. Because there is no reconstruction and therefore no input ( f, b ), we simply plot the points at a fixed horizontal coordinate f / b = 0.376 (the theoretical value). We note that β BF obtained in this way is indeed larger than the theoretical value, but this is well within the 1σ uncertainty indicated by the grey error bar; at this stage, we cannot accurately assess the impact on β BF due to the small sample size or the simulation resolution, which is beyond the scope of this work. As mentioned above, a small (per cent-level) error in R ′ ( s ) leads to a larger error in β BF . Figure 12. Upper left : The best-fitting β BF values obtained using the estimator R ( s ) and the reconstructed galaxy catalogues, for seven choices of input parameters f and b supplied to the reconstruction pipeline (crosses). R ( s ) is measured as the weighted average between and s max = 98.9 (green), 90.2 (red), and (blue), respectively, and the error bars are the standard deviations obtained from 15 realizations for the case of as the error bars for remaining s max values are similar. The filled circles are the same, but obtained from the estimator R ′ ( s ): since there is no reconstruction in this case, these data are plotted against the theoretical value β = f / b = 0.376. The dashed line represents β = f / b , whilst the solid line is a line of slope 1.0 to guide the eyes. Lower left : , the constant value fitting ξ 2 [ x ( k ) ]( s ) between and the three s max values s max = 98.9 (green, densely dashed), 90.2 (red, dashed), and (blue, sparesly dashed), respectively, for the same seven choices of input ( f, b ). The vertical dotted lines mark the best-fitting β BF at which is closest to zero, and the error bars are again the standard deviations of the 15 realizations. Right-hand panels : the estimator E4 (upper) and E3 (lower) for the seven choices of reconstruction parameters ( f, b ), with their corresponding values of β indicated in the legend and increase with the sparsenesses of the curves [β increases from to the top (bottom) to the bottom (top) line in the upper (lower) right-hand panels]. Note that

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


domain to a 4 kpc × 4 kpc × 24 kpc region of the Galaxy. The Galactic magnetic field model of Jansson Farrar ( 2012a ) has azimuthal variations in strength and direction of the field. We chose the galactocentric azimuthal angle to roughly agree with that of the point of impact 70 Myr ago shown in Nichols Bland-Hawthorn ( 2009 ), Figure 3 . The minihalos are necessarily constrained by the size of the domain and fill spheres of 2 kpc radius (the domain half-width). In Figure 1 , the minihalo barycenters are indicated by the “ X ” markers, and their simulation domain half-mass radii (distinct from r e ) are shown as black circles. Figure 1. Initial conditions for each simulation along slices through the y = 0 plane. log 10 of hydrogen number density is represented by the continuous color scale. log 10 of magnetic field strength is represented by contours. The dark matter barycenter is marked with an “ X ” and a circle at the half-mass radius. From left to right, the panels show Runs 1–6, as in Table 1 . 3. RESULTS All six clouds behave similarly as they fall through the halo. This can be seen in Figure 2 which shows the clouds at epoch t 1 (35 Myr), just before impact. As they pass through the halo, the clouds lose material due to ram pressure stripping. By epoch t 1 the clouds with minihalos have lost 16%–18% of their original baryonic mass, while those without have lost ∼36% (see Table 1 ). During this stage, the effect of the weak magnetic field is merely to become swept up and wrapped around the cloud. This is similar to the behavior in the 2D MHD simulations of Konz et al. ( 2002 ). Figure 2. Same as Figure 1 , but for epoch t 1 , equivalent to t = 35 Myr for all runs. Figure 3. Same as Figure 1 , but for epoch t 2 , equivalent to t = 52 Myr for Runs 1 and 2 and t = 45 Myr for Runs 3–6. Each of the clouds approaches the disk with a similar velocity (∼300 km s −1 ). However, the dark matter confined clouds are more compact and contain more baryonic mass and so carry larger kinetic energy densities than the dark-matter-free clouds. The collision of the cloud with the Galactic disk occurs at 36 Myr for those runs with a minihalo, and 37 Myr for the dark-matter-free runs. At the moment of collision, the minihalo separates from the cloud gas and continues, unhindered, through the Galactic disk. During the collision, the gas cloud ceases to exist as it mixes with and transfers momentum to the disk gas. This results in a hole in the disk and a long-lived, bubble-shaped structure filled with moderately dense (∼0.1 to ∼3 H cm −3 ), cool gas (∼1000 K) below the disk, as shown in Figure 3 at 52 Myr for Runs 1 and 2 and 45 Myr for Runs 3–6 (epoch t 2 ). These structures are composed of a mixture of gas from both the cloud and the disk, with the majority of their mass originating from the disk. Tenorio-Tagle et al. ( 1986 ) found similar structures in 2D hydrodynamic simulations of dark-matter-free clouds colliding with the Galactic thin disk. Over

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


750 and HARP 1028. These flare-productive active regions produced at least one flare of intensity greater than M5. Middle panel: power index evolution for HARP 1464 and HARP 1621. These flare-productive active regions produced flares of intensity between M1 and M5. Lower panel: power index evolution for HARP 1019 and HARP 1318. These active regions showed no flare productivity. Vertical lines in the graphs indicate the occurrence of flares with intensity greater than M1. In addition to exhibiting, on average, a lower value for the power index, flare-quiet regions tend to show much more variability in the temporal evolution of the index. Figure 5 (bottom) shows one such trend—where the index tends to drop off over several days. A second trend is shown in Figure 7 , where NOAA 11274 shows periods when the power index rises to 1. However, these periods of time are short. In contrast, there is no sudden spike in the index value for any of the flare-productive regions as they track across the solar disk. Instead, flare-productive regions exhibit a large power index for many days, both before and after they produce solar flares. This suggests that the flare potential of any active region could be determined a few days in advance of the production of a large solar flare and the occurrence of solar flares does not reduce the future flare potential. Figure 6 shows the results in the form of histograms for all 53 HARPs. The range of index values (1.0–2.5) is similar to that in previous studies (Abramenko Yurchyshyn 2010 ). The dotted histogram shows the power index values taken by flare-quiet active regions. The power index distribution for these flare-quiet regions is quite broad and peaks around 1.6. The dashed histogram indicates the results for flare-productive active regions that produced flares of magnitude M1–M5. This distribution is much narrower, with fewer values below 1.5, and peaks around 1.8. However, the high-value tail does overlap with the flare-quiet distribution. Finally, the solid histogram shows the power index values taken by flare-productive active regions that produced at least one flare of intensity greater than M5. In this case, the power index mostly lies above 2 with a maximum at around 2.2. Figure 6. Histograms of power index values for all 53 HARPs. The dotted line indicates a histogram for 25 flare-quiet active regions. The dashed line shows a histogram for 19 flare-productive active regions that produced flares of intensity between M1 and M5. The solid line indicates a histogram for nine flare-productive active regions that produced at least one flare with intensity greater than M5. Figure 7. Power index evolution of a non-flaring active region HARP 803 (NOAA 11274). Flare-quiet regions tend to show much variation in the power index values. The above classification of HARPs was performed based on the maximum intensity of any flare from the region. However, the flare productivity can be measured more carefully in terms of

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


function layers can be concatenated together to form a deep CNN. This is usually followed by a fully connected layer also known as a dense layer, which is then finally connected to the output layer. The output layer for a classification problem is the amount of class labels we have in our data. Additionally for deep CNNs, a dropout layer is typically added after the max-pooling operation, which randomly drops off a certain percentage of the preceding nodes. This is done so that the neural network learns to better generalize its performance across the entire data. This is used as a regularization technique to avoid overfitting. CNNs are also trained using back-propagation. However, in practice, since it is computationally difficult to calculate the gradient of the loss function for all images in the training data, we typically divide the data into mini-batches and use the stochastic gradient descent algorithm. Figure 2. Schematic diagram of a typical CNN. Here the input image is a grey scale image of size 48×48 and the output contains two nodes for the binary class labels. 8 and 16 filters of size 4×4 were used for the convolutional layers. These act as feature extractors that identify import patterns in the input image. This diagram was created using an open source tool called NN-SVG 5 (LeNail 2019 ). 2.4 Generative adversarial network (GAN) GANs are a class of machine learning algorithms (Goodfellow et al. 2014 ) in which two neural networks are trained simultaneously with opposing goals. They act against each other as adversaries in a minmax two-player game. A generative model G is tasked with generating new data that capture the distribution of the input data. A discriminator model D is tasked with classifying samples as either REAL (that belong to the original data distribution) or FAKE (samples generated by G ). Assuming is the value/loss function, we are interested in then the first term in equation ( 2 ), is the expectation of the logarithm of D ’s predictions when an input is from the real data sample. D ’s goal is to maximise this term. The second term represents one minus the expectation of the logarithm of D ’s predictions when data generated by G is passed on to to D . The goal of D is to maximize the second term but the goal of G is to minimize this term. This sets up the adversarial framework. In the ideal case, the generator perfectly samples the distribution of the input data distribution, and the discriminator output equals to 1/2. In practice however, we use a minibatch stochastic gradient descent method and train the generator and the discriminator alternatively. The algorithm and the proof for the convergence of the algorithm can be found in Goodfellow et al. ( 2014 ), however for the benefit of the reader, we briefly summarize the training of this network in algorithm 1 . Algorithm 1: Minibatch stochastic gradient descent algorithm used for training a GAN. GANs have been used successfully in a wide range of tasks ranging

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


Like black holes, this distribution is relatively flat. Figure 6. Distribution of periods for NSLC binaries detectable by Gaia . Blue is the fiducial model, orange is low αλ, green is the kick model with the same momentum as neutron stars, and red is kicks with the same velocity. For completeness we have also included in Appendix C the distribution of distances from earth (Fig. C1 ), apparent magnitudes of the luminous companions (Fig. C2 ), ratios between the semimajor axes and distances (Fig. C3 ), and radial velocity amplitudes (Fig. C4 ). 5 CONCLUSIONS In this work we give some predictions for the detection of binaries with a single luminous companion with Gaia . Similar endeavours exist in the literature, but two novel ideas that we introduce in this paper are that (i) similar methods can be used to detect neutron star luminous companion systems (which are expected to be more numerous) and (ii) the data from Hipparcos can be used to constrains the theoretical models. Our fiducial model predicts a few dozen BHLC detections with Gaia , and about one detections with Hipparcos . The last result is consistent with non-detection by Hipparcos , due to uncertainties in the models and statistical fluctuations. All other variants of the fiducial model have similar properties. The corresponding predictions for NSLC binaries are hundreds to thousands with Gaia and a few with Hipparcos . We emphasize that the numbers reported here only apply to binaries where the Chandrasekhar mass is beyond the dark companion’s mass error margin. One of the challenges in this kind of work is estimating the uncertainty. This is because this work is largely based on poorly understood physics and empirical models calibrated with incomplete data. One way to get an estimate for the uncertainty is to explore the sensitivity of the results to changes in the different model parameters. This was done in Yamaguchi et al. ( 2018 ), and the conclusion was that while the number of BHLC binaries might change by a factor of order unity, the shapes of the distribution functions do not. The results from Gaia , as well as future observations, are necessary to refine these models and improve their precision. To date, there are no reports of quiescent neutron stars (i.e. neither pulsars nor accreting) in binaries. As for BHLC binaries, there is one reported detection of a ≥2.5 M ⊙ mass black hole candidate with a red giant companion (Thompson et al. 2018 ). We note that another isolated black hole candidate with mass of about four solar masses was detected in the globular cluster NGC 3201 (Giesers et al. 2018 ). This discovery is less relevant to this study, because stars in a cluster are thought to have formed in a relatively short period of star formation, whereas we are interested in the case where star formation proceeds continuously. Another important difference is that we neglect gravitational interaction between stars that are not mutually bound, which is justified

O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Telescope 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 B-Telescope 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 B-Telescope O O O O O O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula 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 B-CelestialObject I-CelestialObject 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


As described in Sections 3.6 and 3.7 , the H 2 and PAH emission, indicating the location of the PDR, encircles the western border of the H ii region. A curved morphology of the radio continuum emission in the western periphery further suggests a stalling effect for the ionized gas against the PDR in that direction. As shown by Pellegrini et al. ( 2012 ), the [S ii ]/[O iii ] ratio map can be used to distinguish density-bounded, radiation-bounded, and blister-type H ii regions. Pellegrini et al. ( 2012 ) found that the optically thick nebula with highly ionized gas (low [S ii ]/[O iii ] ratio; appears dark in ratio map) is usually surrounded by an ionization transition zone with a higher [S ii ]/[O iii ] ratio (appears as lighter gray scale). We made an [S ii ]/[O iii ] ratio map of the central part (∼10′ × 10′) of the Sh2-112 H ii region, which is shown in Figure 8 (bottom left panel). The ratio map consists of bright and dark features. We notice a pronounced ionization transition zone (bright region) toward the south of the massive star, where H α emission is traced. This ionization transition zone appears to be surrounded by a relatively diffuse feature in light gray. In the southwestern direction, the ratio of [S ii ]/[O iii ] reveals the presence of ionized gas (dark feature) in the region, which is spatially correlated with the IBL. The distribution of the ionized hydrogen, H 2 , and 13 CO emission indicates that the IBL structure is seen edge-on. An example of this kind of edge-on geometry is the Orion bar, which is located in a blister-type H ii region, the Orion Nebula (Goicoechea et al. 2018 ). In our case, the bright S ii emission could actually be on the surface of the H ii cavity. Therefore, from the above analysis, it seems that Sh2-112 is an example of a blistered H ii region that is ionization-bounded on the high-density sides (western direction) and density-bounded on the low-density sides (eastern direction). The intensity gradient of the radio emission (see 610 MHz emission contours in Figure 7 (b)) supports that the ionized gas is escaping from the H ii region toward the low-density ISM in the eastern direction. Based on radial velocity measurements of the H α (i.e., −9.7 km s −1 ) and CO (i.e., −12.2 km s −1 ) emissions, Israel ( 1978 ) also suggested that the ionized gas in the Sh2-112 region is probably undergoing a champagne flow. Thus, the structure of the radio continuum, dust extinction, 13 CO, and [S ii ]/[O iii ] ratio maps; the spatial distribution of the young stars; and the NIR-to-MIR images of the H ii region indicate that Sh2-112 is a blistered H ii region in which the ionized gas is possibly undergoing a champagne flow. In Figure 9 , we show the AKARI 160 μ m image superimposed by Planck 353 GHz contours (left panel) and a simple geometry of the H ii region (right panel). Based on the distribution of the cold dust emission and young stars, we suggest that the massive star possibly formed on the eastern

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