and E05, PSP arrived at the perihelion of 27.8 R ⊙ (~0.13 AU) on January 29, 2020 and June 7, 2020, respectively. In Sect. 3.1 , we give an overview of the PSP measurements of solar wind density, speed, and energy flux for all available encounters including E01, E02, E04, and E05. We note that E03 observationsare not considered due to the lack of SPC observations near the perihelion. For each encounter, 12-day observations around the perihelion were used for calculations. The heliocentric distance for both E01 and E02 ranges from 35.66 to about 55 R ⊙ , and it ranges from 27.8 to about 57 R ⊙ for both E04 and E05. In Sect. 3.2 , we combine the observations from E01, E02, E04, and E05 to show the histogram distributions and the evolution of the energy flux as a function of heliocentric distance. 3.1 Overview of E01, E02, E04, and E05 Figure 1 shows an overview of the PSP measurements of solar wind density, speed, and energy flux during E01 (from October 31, 2018 00:00:00 to November 12, 2018 00:00:00 UTC). The top panel presents the electron number density ( n e ) obtained by the QTN method. In the second panel, the proton bulk speed is shown. The third and fourth panels present the solar wind energy flux ( W , from Eq. ( 2 )) and its value scaled to one solar radius (, from Eq. ( 6 )), respectively. In Fig. 1 , n α and n p were computed from n e based on n α ∕ n e = 2.5% for calculating W and . Most of the time, V p varies around 300 km s −1 , and varies around 70 W m −2 . The average values of W and are 0.045 and 77.3 W m −2 , respectively. The average value of of E01 is consistent with the long-term observations from Le Chat et al. (2012) (around 79 W m −2 ). We note that does not vary much with V p when V p increases abruptly (i.e., from November 8 to 10, 2018). Figure 2 , which follows the same format as Fig. 1 , summarizes the PSP measurements of solar wind density, speed, and energy flux during E02 (from March 30, 2019 00:00:00 to April 11, 2019 00:00:00 UTC). We deduced n p and n α with the same method used for E01to calculate both W and . We note that n e shows two successive low plateaus near the perihelion of E02 (from April 3 to 8, 2019 UT), as shown in the first panel of Fig. 2 , whereas V p shows two high peaks. This is in agreement with the well-known anticorrelation between the solar wind speed and density (e.g., Richardson et al. 1996 ; Le Chat et al. 2012 ). Both and W also show two low plateaus near the perihelion of E02 (from April 3 to 8, 2019 UT), similar to the solar wind density. Elsewhere, V p remains around 300 km s −1 and varies around 70 W m −2 . The mean values of W and during E02 are 0.032 and 59.4 W m −2 , respectively. Similarly, Fig. 3 illustrates the PSP observations during E04 (from January 23, 2020 00:00:00 to February 4, 2020 00:00:00 UTC). We used n p and n α , which were deduced with the same method used for both E01 and E02, when calculating both W and . The second panel of Fig. 3 shows that V p varies

O O B-Mission O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Mission 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 B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Mission O O 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 B-ObservationalTechniques I-ObservationalTechniques O O O O O O O O O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O O O O O O O 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 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 B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Mission O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


paper. A direct comparison with our kinematic estimate is also difficult because they do not specify at which radius the rotation velocity is measured. Our data however seem to rule out the possibility of a value of 150 km s −1 for the line-of-sight velocity: In such cases, the combined effect of rotation velocity, velocity dispersion, and instrumental smearing would have made the galaxy to spread its emission in channels with velocities well beyond those detected in our data cube (for example, in the first channel of Fig. 2 ). Livermore et al. ( 2015 ) included the data set from Yuan et al. ( 2011 ) in a broader study on the kinematics of a sample of lensed galaxies. Similarly to Yuan et al., they fitted the delensed 2D kinematic velocity map with an arctangent model of the rotation curve (Courteau 1997 ) without any correction for beam smearing and found a rotation velocity V 2.2 = 59 ± 3 km s −1 at R 2.2 = 1.32 kpc for an inclination i = 45°, where R 2.2 is the radius at 2.2 times the scalelength of an exponential disc. Although MUSE data have lower spatial resolution than OSIRIS data, our rotation curve seems to exclude such a low rotation velocity at 1.32 kpc (Figs 4 and 5 ), even after correcting for the different inclination ( V 2.2 ≃ 73 km s −1 for i = 35°). Since Livermore et al. do not report their asymptotic velocity nor turnover radius of the best-fitting arctangent function, we cannot compare the values of the flat part of the rotation curve. To constrain the velocity dispersion, Livermore et al. fitted an exponential model to the velocity dispersion map, which they derived applying a correction for beam smearing and spectral broadening. They quote a luminosity-weighted average of σ = 50 ± 10 km s −1 . This value is however strongly affected by the two inner points (see their Fig. 2 ), which appear to be dominated by residual beam smearing. Finally, we stress that the Livermore et al.'s kinematic model does not satisfactorily reproduce their data (see the residual velocity field in their fig. 1). This is likely due to a combination of the low S/N AO data, some beam smearing, and the uncertainties related to the lensing modelling. Mason et al. ( 2017 ) made use of the 3D fitting code galpak 3D (Bouché et al. 2015 ) on KMOS –λ5007 Å data. Like B arolo , this code fits 3D models to data cubes and properly accounts for beam smearing. The main difference between this code and B arolo is that, in galpak 3D , the rotation curve follows a pre-selected functional form and the velocity dispersion is always assumed to be constant across the disc. Mason et al. have observations of both M1 and M3 images. They could not fully model the M3 image because it is unresolved. M1 image is poorly detected with S/N ∼ 2 in their data, and the KMOS FOV is not sufficiently large to include the entire galaxy disc. They modelled the M1 image without any reconstruction on the source plane and found an asymptotic rotation velocity of 227 ± 32 km s −1 , an

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


half of the mass that has become unbound during the preceding orbit. The simulations used by Fujii et al. ( 2006 ) followed the orbital evolution of a self-consistent satellite galaxy (without dark matter). As they point out in their paper, since dark matter subhaloes are more extended than satellite galaxies, they typically experience more mass loss and thus should be susceptible to even stronger self-friction. In this paper we use idealized numerical experiments to study the nature of self-friction acting on dark matter substructure. Our main goal is to characterize the relative contribution of self-friction to the total drag force experienced by subhaloes as a function of orbital properties and the mass ratio between the sub- and host halo. The rest of the paper is organized as follows: in Section 2 , we discuss our numerical methods and simulations. Our results are presented in Section 3 and then discussed and summarized in Section 4 . Throughout, we adopt a Hubble parameter , which corresponds to a Hubble time of 13.97 Gyr for a flat universe with Ω Λ = 0.73. 2 METHODS To investigate the effects of self-friction, we perform numerical simulations of an N -body subhalo orbiting within an analytical host halo potential. We provide a brief description of the methods here and refer the reader to van den Bosch Ogiya ( 2018 , hereafter BO18 ) for full details on the numerical simulations and analysis methods. The host- and subhaloes are both assumed to initially be spherical NFW profiles (Navarro, Frenk White 1996 ) with concentrations c host and c sub , respectively. The host halo is represented by a static analytical potential. Throughout this paper, R and r are used to indicate radii with respect to the centre of the host halo and subhalo, respectively. The virial masses and radii of the two systems 2 are indicated by M host and R host , in the case of the host halo, and M sub and r sub in the case of the subhalo. Note that for the latter, these relate to the initial, unperturbed subhalo, prior to being introduced to the tidal field of the host halo. Positions and velocities of particles in the subhalo are initialized assuming an isotropic distribution function, f ( E ), using the method of Widrow ( 2000 ). In order to roughly account for the tidal mass loss that the subhalo would have experienced when approaching its initial position from an infinite distance, the initial distribution of particles is truncated at the instantaneous tidal radius of the subhalo (King 1962 ), given by Here, R is the (initial) distance from the centre of the subhalo to the centre of the host halo, m ( r tidal ) is the mass of the subhalo within r tidal , M ( R ) is the mass of the host halo within R , and Ω is the (initial) angular speed of the subhalo (Taylor Babul 2001 ; Zentner Bullock 2003 ; Peñarrubia Benson 2005 ; van den Bosch 2017 ). Note that we do not account for this truncation in the distribution function, which instead is computed under the

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


criterion, and a maximum of five features, as this set of hyperparameters performed best for V19 (see also Appendix D ). After training the random forest on the oversampled training set, we apply it to the 10 sets of features (from the 10 random posterior draws) for each transient in the test set to get 10 sets of classification probabilities. We then average the 10 sets of classification probabilities for each transient and adopt the classification with the highest probability. 4. Results and Validation Applying our classification pipeline to the test set described in Section 2 yields 1257 photometrically classified SNe Ia, 521 SNe II, 298 SNe Ibc, 181 SNe IIn, and 58 SLSNe. 26 26 To exactly reproduce our results, a seed of 0 must be used in the pseudorandom number generators during feature extraction, oversampling, and classification. Table 3 gives the full list of classifications, and Figure 5 shows a sample of photometrically classified light curves. These are among the largest samples of each of these classes of SNe in the literature from a single survey. In the remainder of this section, we assess the performance of our algorithm in general and discuss how to use these classifications in practice. Figure 5. Sample observed (circles) and model (lines) light curves of photometrically classified SNe. Downward-pointing arrows indicate 3 σ upper limits from nondetections. The left column shows the highest confidence classification in each class, and the right column shows the median-confidence classification. Notice that in three of the lower confidence classifications, the light curve is poorly sampled on either the rise or the decline because it was discovered close to the boundaries of the observing season. Table 3 Classification Results (This table is available in its entirety in machine-readable form.) Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available. 4.1. Cross-validation We first validate our classifier using leave-one-out cross-validation with the SNe in our training set. For each iteration of the cross-validation, we retrain the classifier on all but one of the SNe in our training set (still using the median parameters) and then use it to classify 10 sets of features derived from the posterior parameter distributions for that SN. We then average the 10 sets of probabilities to determine the cross-validation classifications listed in Table 4 . Figure 6 shows the resulting confusion matrices. Figure 6. Confusion matrices of our validation results. Each cell lists and is colored by the fraction of each class, with the raw number in parentheses. The top matrix aggregates by true label, so its diagonal shows completeness. The middle matrix aggregates by predicted label, so its diagonal shows purity. The bottom matrices are the same results but with all four non-SN Ia classes grouped together as CCSNe. N is the total size of the training set, A is the

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


(Planck Collaboration I 2016 ), is implemented in order to constrain the Λ( H ) models. Up to now, for these models only the set of the CMB shift parameters have been used in order to test the dynamical vacuum scenarios close to recombination. Then, we combine CMB in an overall likelihood analysis with other cosmological probes (SNe type Ia, BAOs, H 0 ) in order to extract the probability distribution (via Monte Carlo MCMC method) of the solutions for a large set of cosmological parameters, as well as, to search for deviations from the concordance ΛCDM model for which Λ( H ) = const. The structure of our paper is as follows: in Section 2 we provide a brief introduction of the running vacuum cosmology and we present the most popular Λ( H ) models that have appeared in the literature. In Section 3 , we discuss the methodology and the cosmological data that we utilize and we perform a detailed statistical analysis aiming to provide the corresponding best-fitting values and contour plots for the current Λ( H ) models. Finally, we discuss our results in the conclusions. 2 BACKGROUND EXPANSION IN RUNNING VACUUM MODELS In this section, we briefly describe the main features of the dynamical vacuum models for which Λ is not constant but evolves with cosmic time. This is perfectly allowed by the cosmological principle embedded in the FLRW metric (Perico et al. 2013 ). In general, if we model the expanding Universe as a mixture of perfect fluids N = 1, 2, ... then the total energy momentum tensor is given by where is the four-velocity field. In this case the components of are written as where the quantities p T and ρ T are the total pressure and energy density in the comoving frame , respectively. The next step is to apply the covariant local conservation law for the mixture, namely ∇ μ T μν = 0. Inserting equation ( 1 ) into the latter expression and with the aid of the relation (which comes from the fact that for any four-velocity vector, we have ) we arrive at (Grande, Pelinson Sola 2009 ): For a Friedmann–Lemaître–Robertson–Walker (FLRW) metric, it is easy to check that for a comoving frame (), one obtains: and thus equation ( 3 ) reduces to where is the Hubble parameter and a ( t ) is the scale factor of the Universe normalized to unity at the present epoch. For the rest of the paper we focus on the spatially flat FLRW metric. In the aforementioned discussion, we did not address the physics of the fluids involved. The total density ρ T receives contributions from non-relativistic matter (cold dark matter and baryons) ρ m = ρ b + ρ dm ( p m = 0), radiation ρ r ( p r = ρ r /3) and vacuum ρ Λ ( p Λ = −ρ Λ ). In this context, the index N specifies the specific components of the cosmic fluid, namely {dm, b, r , Λ}. Assuming that baryons and radiation are self-conserved, namely the corresponding densities evolve in the nominal way ρ b = ρ b0 a −3 and ρ r = ρ r0 a −4 the overall conservation law ( 5 ) becomes or Note that Q is the interaction term

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


have discussed the mechanisms that lead to the formation of instabilities in both the upstream and downstream medium when the magnetic field makes a large angle with the direction of the flow. We should note here that when we increase the angle even further beyond 70° this effect disappears since the component of the particle velocity parallel to the flow becomes smaller than the drift velocity if the thermal plasma, which eliminates the upstream current. The question remains as to why this result was not obtained with a hybrid code. By comparing our simulations with these earlier models we come to the conclusion that there are two factors that contribute to the different outcome. The number of particles . Although the absolute number of particles used in hybrid codes is far larger than what we use for the PI[MHD]C simulations, only a small fraction of the particles in hybrid simulations actually are suprathermal. Combined with the fact that for an oblique magnetic field only a fraction of the non-thermal particles are able to move upstream because of their pitch angle, we conclude that the hybrid simulations lacked the necessary number of particles to create the current that causes the disturbance of the upstream magnetic field. The size of the physical domain . The size of the simulated domain in the direction perpendicular to the shock-normal is six times larger in our model than in the original hybrid simulation. This allows us to capture the long wavelength that corrugates the shock and sets in motion the process that disturbs the upstream magnetic field. The smaller domain used by the hybrid simulation makes this impossible. We have tested our code with a physical domain similar to that used by Caprioli Spitkovsky ( 2014a ) and find that indeed the long wavelength never appears and so is the magnetic field amplification. These points demonstrate the opportunity that the PI[MHD]C method affords us. Because it is designed primarily to simulate large-scale structures, is less computationally expensive than PIC or hybrid methods and enables us to run the simulation in the frame of reference of the shock, it allows us to simulate a large volume of space, using a larger number of suprathermal particles, which in this particular case proved to be necessary. 2D3V PIC simulations of perpendicular and oblique shock configurations have been performed by Kato Takabe ( 2010 ) and Wieland et al. ( 2016 ), respectively. These studies verify that fast Alfvénic Mach (low magnetization) number shocks are mediated by the Weibel instability. These studies only report on electron thermalization but find pieces of evidence for the development of a proton non-thermal tail possibly connected with a shock surfing process in the perpendicular shock configuration. We confirm with Caprioli Spitkovsky ( 2014a ) that protons are accelerated at oblique shocks with an angle θ B = 45°. However, we argue that particle acceleration also proceeds at larger angles through

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


of the local inventory, nearby solar-type stars provide particular insight from high signal-to-noise, high-resolution spectroscopy, such as stellar masses and ages. Most or possibly all of the scatter in the barium-to-iron abundances among the Population II and intermediate-disc stars, as we learn in this work, is subject to former mass transfer from white dwarf companions, and, if accounted for, discloses a very different perspective on the underlying core-collapse supernovae nucleosynthesis. Likewise, non-single sources cause false stellar parameters and hence scatter or potentially even false trends in the derived elemental abundances, if their individual components are not treated as such, which is often commonplace. There are numerous examples in the literature, and sources like the intermediate-disc star HD 117635 in P1 or the Population II star HD 34297 in Fig. 1 below in this work, just two of them. On the other hand, it is frequently found that towards the metal-rich end the Population I and II disc star sequences progressively coalesce with their iron versus α-chain elemental abundances. This is – for many reasons – important to know, and it may be of some relevance that the stars of P1 and the present, extended sample, as we see, do not comply with a systematic trend of this kind in terms of their magnesium and iron enrichment. Figure 1. Modelling of the Fe i line λ6200.321 in the composite spectrum of the spectroscopic binary HD 34297 ( P ≃ 2 yr) with its Aa and Ab components being Doppler-displaced at Δ v r (Aa–Ab) =+28.9 km s −1 in this 2017 November 28 observation. Stellar parameters for the spectrum synthesis (dark blue) are as given in the legend. The light blue-dotted curves denote abundance changes of Δ[Fe/H] = ±0.10 dex. Individual line profiles of the Aa and Ab components are given by the red-dotted curves. In Sections 2 and 3 we briefly discuss the characteristics of the underlying spectroscopic observations and the model atmosphere analyses. The very centrepiece of our work follows in Section 4 with the analyses and related key aspects of the Population II and intermediate-disc stars. As in P1, these comprise about one-third of the final 42 pc ancient star sample and several findings as they become apparent at the present, intermediate stage of the survey will be the subject of Section 5 . Population I stars, which in the course of the analyses are identified as such, and hence not part of the survey, are presented in the Appendix. 2 OBSERVATIONS With reference to a Gaia -based 42 pc parent sample, our strategy to cover an unbiased, complete subset of more than a hundred ancient solar-type Population II (τ ≥ 12 Gyr) and intermediate-disc stars (τ ≃ 10 Gyr) within that volume has been described in detail in P1. The spectroscopic observations that we present in this second work on the survey were all secured in 2017 with the FEROS échelle spectrograph (Kaufer et al. 1999 ) at the La Silla Observatory in Chile, most of them

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O B-CelestialObject I-CelestialObject O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O B-Citation O O O O O O O O O O O O O O O O O O O O B-Instrument O O B-Citation I-Citation I-Citation I-Citation O O O B-Observatory I-Observatory I-Observatory O B-Location O O O


be plausible for an isolated black hole accreting from the interstellar medium (see, e.g., Maccarone ( 2005 ) and references therein). At the same time, in this context there is an indication that the observed X-ray spectrum of source XMM0838+24 does not coincide with predictions for various forms of radiatively inefficient accretion flows that are expected to have a power law spectrum with a photon index 1.4–2.5 (see, e.g., Narayan et al. 1998 ; Ball et al. 2001 ). High-resolution X-ray and deeper optical/NIR imaging and spectroscopic observations are required to shed light on the association of XMM0838+24 and its host galaxy and thus derive its X-ray luminosity. In this study we do not attempt to analyze X-ray spectra of XMM0838+24 and XMM1226+12 in detail because given their faint X-ray fluxes it would not provide any selectivity to discriminate conventional X-ray object types. However, we compare their X-ray colors from the XMM-Newton source catalog to a sample of known AGNs and ESO 243–49 HLX–1. In Figure 6 we overplotted two “corner” states of ESO 243–49 HLX–1 and our HLX candidates on hardness diagrams of the known AGN population from Lin et al. ( 2012 ). Clearly, broadband properties of ESO 243–49 HLX–1 do not allow its unambigous separation from AGNs. At the same time, selected HLX candidates are situated aside from ESO 243–49 HLX–1 and most AGNs due to systematically harder HR2 and HR3 colors. This, however, does not favor any particular interpretation of the nature of the candidates. Figure 6. The X-ray color–color diagrams for known AGN (from Lin et al. ( 2012 ), black dots), selected HLX candidates (this paper, gray stars) and two spectral states of ESO 243–49 HLX–1, high luminosity consistent with steep power law and low luminosity hard power law states (gray triangles). X-ray colors are taken from the 3XMM-DR5 catalog and are defined as HR , where f i is the X-ray flux in i -th XMM-Newton band (band 1 is 0.2–0.5 keV, band 2 is 0.5–1.0 keV, band 3 is 1.0–2.0 keV, band 4 is 2.0–4.5 keV, band 5 is 4.5–12 keV). As claimed by Lin et al. ( 2012 ) systematic uncertainties of these colors can reach 0.1 which is below symbol size for ESO 243–49 HLX–1 and HLX candidates. 5.2. Base Sample Properties We compute the number density of the HLX candidates from our base sample. From a total of 98 HLX candidates we expect to have at least 21 true HLXs. Given the searched volume and solid angle this gives us an HLX number density of 1 object per ≈2 × 10 5 Mpc 3 . This is approximately a factor of several thousand less frequent than ULXs (Swartz et al. 2011 ). We can normalize this density to galactic halos. In total there are 33,879 SDSS galaxies falling in the 3XMM-DR5 footprint (total observed part of the sky) that we included in our off-nuclear cross-match procedure. Hence, the density of our HLX candidates is about 6 × 10 −4 per galaxy. If they are all accreting IMBHs, this is too large a density for a population of “naked” IMBHs that

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


drive heat conduction in the disc. Fig. 6 shows that, even in 3D, the heat flux is negligible in regions in which P saturates. From our EMHD simulation, we thus deduce that the average impact of the non-ideal effects in the compact, SANE disc studied here might be close to what one would obtain by setting P 0.25 b 2 and q 0. We also note that our results critically depend on the treatment of the mirror instability in the EMHD model. We assume that when driven above the threshold of the mirror instability, P saturates at nearly exactly the instability threshold P mirror , through an increase in the effective collision rate in the plasma. Our results are only physical if this approximation captures the global behaviour of the plasma on length-scales much larger than the Larmor radius. While current particle-in-cell simulations broadly support this model (Kunz etal. 2016 ), comparisons of the EMHD model with more detailed local simulations of a plasma at the mirror instability threshold will be required to test this assumption. 4.4 Stress tensor and angular momentum transport In previous sections, we showed that the pressure anisotropy in the EMHD simulations of SANE discs is, in a time-averaged sense, P b 2 /4. In Section 2 , we also argued that the associated shear stress, , is effectively of the same form as the magnetic shear stress, . As far as the shear stress is concerned, the pressure anisotropy P and the magnetic energy density b 2 are interchangeable. Additionally, for 1, the magnetic energy density and isotropic magnetic pressure do not play a particularly important role in the dynamics of the accretion flow. Accordingly, we may expect similar steady-state accretion flows to be reached in EMHD and IMHD if . Our simulations appear consistent with this interpretation of the impact of the pressure anisotropy: in the SANE configuration, we find similar density and temperature profiles for the EMHD and IMHD models, but with a weaker magnetic field in the EMHD model, e.g. the plasma parameter satisfies EMHD (1.21.4) IMHD . We can have a more direct look at the component of the stress-energy tensor responsible for angular momentum transport in the disc, . We show radial profiles of (averaged over time and azimuthal angle, integrated over the polar angle and normalized by the gas pressure) in Fig. 10 . The first notable result is that the total stress is nearly identical for the IMHD and EMHD simulations. However, in the IMHD model, the entirety of the stress is due to the magnetic field. In the EMHD model, outside the ISCO of the black hole, (7075)percent of the r component of the stress is due to the magnetic field and (2530)percent to the pressure anisotropy. While this fraction of the stress due to the pressure anisotropy is slightly larger than one might have expected based on the simplistic model of a constant ratio P b 2 1 4, the properties of the stress tensor are broadly consistent with the view that in EMHD the pressure anisotropy

O O O 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 B-Model I-Model O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula 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 B-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 B-Model I-Model O B-Model I-Model O O O O O B-Formula I-Formula I-Formula I-Formula 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 B-TextGarbage I-TextGarbage O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O B-Model 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 B-Model O B-Model I-Model O O O O O O O O B-Model I-Model O O O O O B-Model O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O B-Model I-Model O O O B-Model I-Model O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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


have this feature, because we masked them out during the second iteration of the PSF construction process. As our PSF model cannot model all the particular features of a given individual star, after the subtraction process, some residuals are left. They correspond mainly to the central region due to the saturated pixels and the internal reflections. In the same way, the diffraction spikes of each star will remain as residuals since the PSF models do not have diffraction spikes. All of these effects can be seen in Fig. 10 , where we show a colour composite ( g, r , and i ) image of the central part of the Coma Cluster field in three different panels. Top panel shows the original image with the scattered light of near and bright stars contaminating the central parts of the galaxy cluster. In the middle panel, we show the scattered light field model of the brightest stars. In this particular case, we have modelled all stars brighter than 13 mag in the G band of Gaia DR2 Catalogue. The bottom panel shows the stars subtracted image. After the removal of the scattered light field, the low-surface brightness features of the Coma Cluster and its intracluster light are ready to be explored. Figure 10. Colour composite image of the central region of the Coma Cluster as seen by SDSS (R.A. (J2000) = 12:59:48.658, Dec (J2000) = +27:58:49.443), using g, r , and i filters. The background of the image (in grey) corresponds to the sum of g, r , and i SDSS band images. The images have been rebinned to 2 arcsec per pixel and convoluted with a Gaussian kernel of 3 pixel width to enhance the low-surface brightness features of the data. Upper panel: SDSS original image. Note the enormous contamination produced by the brightest stars in the central part of the Coma Cluster. Middle panel: scattered light field of all stars brighter than 13 mag in the G band of Gaia DR2 Catalogue. Bottom panel: scattered light field subtracted image. 4 DISCUSSION AND CONCLUSIONS We present extended SDSS PSFs (8 arcmin in radius) for all five SDSS filters. We describe the methodology we have used to obtain these large PSFs and we show a particular example of how the PSFs can be used to remove the scattered light field produced by the brightest stars in the images. Our approach of deriving PSFs can be applied to other telescopes and instruments to obtain extended PSFs. This work shows that the PSFs have complex bidimensional structures as it can be seen in Fig. 6 . In that figure we plot the radial profiles produced by de Jong ( 2008 ) with a maximum radius of ∼46 arcsec for the g, r , and i SDSS filters together with the radial profiles of the PSFs of this work. The reader can see that the agreement between these two works is rather good. Compared to de Jong ( 2008 ), we enlarge the model of SDSS PSFs an order of magnitude in radius. In addition to this, we also provide their 2-dimensional structures. The PSFs models presented in this work can be used to remove the scattered light of

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


than the canonical value of 1.4. Fig. 12. Parallax over error ( π / σ π ) ve. RUWE of the three new groups of YSOs identified in this work, compared to sources with resolved protoplanetary disks (DSHARP, Andrews et al. 2018 ) and known binaries in Upper Sco ( Tokovinin Briceño 2020 ). 5. On the origin of the new YSOs with disks The previous section has shown that the new disk-bearing YSOs that are candidate members of the US and V1062 Sco comoving groups are relatively well characterized with respect to proper motion, on-sky spatial distribution, distance distribution, and age. Tables D.1 and E.1 list the source designations and disk type for US and V1062 Sco, respectively. The remaining YSOs in our sample (Table A.1 ) are likely composed of sources from both Lupus and UCL, as they present properties that are common to both of these populations; the emerging picture is that the youngest of these YSOs are likely Lupus members, while the older sources are likely part of UCL. Comparison of our new disk-bearing sources in Table A.1 with the YSOs identified by Damiani et al. (2019) yielded 37 out of 60 matches: 45% of the sources were found to belong to the UCL diffuse group D1, and 35% to the UCL diffuse group D2 (further divided into 27% from the D2a sub-group and 8% from the D2b sub-group). Of our new disks in US, 12/19 were identified as belonging to either the diffuse population in Upper Sco USC-D2 (32%), to UCL-D1 (32%), or to UCL-D2a (5%). Regarding the new disks in V1062 Sco, 14/19 were also previously identified by Damiani et al. (2019) as candidate members of the V1062 Sco/UCL-1 compact group. We discuss in this section the region morphology and kinematics to explore the origin and connection between Lupus, UCL, US, and V1062 Sco. 5.1. Evolution of the 3D spatial distribution We attempt to reconstruct the 3D distribution of the new disk-bearing YSOs and the Lupus clouds to better determine how the Lupus and UCL stellar groups are related. Figure 13 shows in the upper (middle) row the Galactic Latitude (Longitude) as a function of distance for these sources. Each row has three panels, corresponding to the three iscohronal age groups. These panels also include a schematic representation of the Lupus clouds (the central Galactic coordinates were taken from Hara et al. (1999) and the width of the filled ellipses are merely representative and not to be taken to scale). The distances to Lupus 1, Lupus 2, Lupus 3, and Lupus 4 were derived from the distances to their previously known members ( Dzib et al. 2018 ), and for clouds with no known associated YSOs we use the distances calculated by Zucker et al. (2019) (we exclude the clouds Lupus 7 and Lupus 8, due to the lack of distance estimates). To constrain the origin of a YSO, we explore its travel radius, specifically, the projected distance traversed by a source since its birth assuming a 1D velocity of 1 km s −1 . We represent the area corresponding to the travel radius as dotted-line

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


is a potential avenue for direct comparison of the observations to the predictions of MHD simulations. The magnetic field lower limits found in each region are consistent with the values found by H13 . This peak value is consistent with the H13 value of +8 μ G. Our data strengthen their finding that the RMs along the narrow, decelerated H α ridge in region 5 are much stronger and opposite in sign compared to the surrounding RMs, suggesting a compressed ambient field which has a preferred direction. Due to the high density of RMs on and next to the Smith Cloud, we can model the morphology of the magnetic field. As seen in Figures 5 and 6 , an arch of positive RMs extends above and around the head of the Smith Cloud. This cap of RMs suggests a magnetic field that has been compressed by the ambient field as the Smith Cloud travels toward the Galactic plane, assuming that the cloud is falling into the disk (see Section 1 ). Under the assumption that is roughly constant, since RM is proportional to , the small negative RMs over the body suggest that the perpendicular component of the magnetic field is stronger than the parallel component, while the large positive RMs surrounding the cloud indicate that the parallel component dominates. To the right of the major axis of the cloud, the RMs are predominately positive, indicating a weak magnetic field perpendicular vector component pointing toward the observer. To the left of the Smith Cloud, strong negative RMs dominate. These strongly negative RMs indicate weak magnetic field perpendicular vector components pointing away from us. This picture is qualitatively consistent with strong parallel magnetic field vector lines along the sides of the Smith Cloud. This suggests a magnetic field that is draped, or laid over the ionized gas of the Smith Cloud, where the field has been compressed near the tip of the cloud (Dursi Pfrommer 2008 ). This configuration of a draped magnetic field surrounding the Smith Cloud is consistent with the idea that the neutral gas in the Smith Cloud is shielded from the hot ISM by a magnetic barrier between the surrounding medium and the gas; this has been seen in 2D simulations by Konz et al. ( 2002 ) and in 3D simulations by Grønnow et al. ( 2017 ). Grønnow et al. ( 2017 ) found that a magnetic field of a few μ G associated with an HVC within 10 kpc of the disk corresponds to an ambient field that has been “swept up” by the cloud, which is consistent with H13 and our observations. The Grønnow et al. ( 2017 , 2018 ) models also support the idea that a magnetic field could keep the cloud intact as it travels through the Galactic halo by delaying hydrodynamic instabilities and stripping of the gas. With this draped magnetic field barrier, the Smith Cloud could travel through the ISM while keeping the gas near the head and body intact. To test if this geometry could produce the observed RMs, we create a toy model of a possible magnetic field configuration surrounding the

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


of the system is maintained. When a dust grain is placed on a highly eccentric orbit by radiation pressure, it may create a local pressure maximum but not linger in a nearby circular orbit where it can stabilize the gas through drag backreaction. This may provide a second possible explanation for the difference between runs D and F discussed above, especially given the higher mass of dust used in run F, which may lead to drag backforces that are strong enough to destabilize gas from a circular orbit. In Figure 12 , we show the dust surface density every 50 orbits for 400 orbits. We find that the photoelectric instability sets in quickly, but has no obvious secular effect on the global structure of the disk. The behavior is dominated by transient clumps and arcs that appear and disappear on timescales of orbits to dozens of orbits. Figure 12. Dust surface density over time for run F. The photoelectric instability arises quickly and is continuously redistributing dust into nonaxisymmetric structures throughout the disk over the full course of the simulation. Though the radial distribution of the dust varies nonsecularly over time, the 2D dust structure is consistently dominated by clumps and arcs that form and dissipate on short timescales of ≈1–10 orbits. In order to confirm that the dust structures seen in run F (Figure 8 ) are conclusively attributable to the photoelectric instability, we run two additional models: one without photoelectric heating, and one with an increased dust resolution to ensure model convergence (run I). For run I, we double the number of dust superparticles while reducing the mass of each superparticle by half in order to maintain the same overall dust mass. The run without photoelectric heating shows no clumping behavior, and instead yields a smooth, structureless dust distribution, as one would expect. Run I, on the other hand, shows the same clumping behavior as seen in run F, suggesting that the resolution we use in runs A–F is sufficient. Gas and dust surface densities after 400 orbits are shown in Figure 13 . Figure 13. Gas (left panel) and dust (right panel) surface densities after 400 orbits for run I, which is a high-dust resolution (2× superparticles) duplicate of run F (). The dashed circle indicates (100 au). Doubling the number of superparticles yields substantially similar gas and dust spirals and clumps, suggesting that 800,000 superparticles are sufficient for capturing the effect of the PeI in the presence of radiation pressure (for the chosen grain size distribution). In run H, we duplicate run F (Figure 8 ) but double the birth ring width to verify that the dust clumping behavior of run F does not require a narrow birth ring. Dust and gas surface densities after 400 orbits for run H are shown in Figure 10 . We find that the enhancement in the dust-to-gas ratio produced by the photoelectric instability is weaker in run H compared with run F (see Table 1 ), but the qualitative results—nonaxisymmetric,

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


in Appendix B . The final result is plotted in Fig. 5 and the derived parameters are listed in Table 5 . The final rms is small with only 90 m s −1 . Our revised orbital parameters are in rather good agreement with the literature, within 1.5 σ ( Groenewegen 2013 ; Gorynya et al. 1995 ; Evans et al. 1990 ; Abt 1959 ). Fig. 5. Result of our combined fit of the orbital and radial pulsation velocity for FF Aql. Left panel : fitted (solid lines) and measured primary (blue dots) orbital velocity. Right panel : fitted (solid line) and measured (blue dots) radial pulsation velocity. Table 5. Pulsation and orbital parameters of the FF Aql system. Notes. Parameters are the same as in Table 4 . a 1 : semi-major axis of the Cepheid’s orbit relative to the centre of mass. f ( M ): the mass function. (a) Not fitted. (b) Uncertainty not given by the authors. (c) Gorynya et al. (1995) . We noticed a slight difference in the systemic velocity between our estimate and that from Gorynya et al. (1995) . This might be linked to the wide companion, however, this might also be from other non-astrophysical effects. We should be cautious when studying long-term variations of v γ , unless a clear pattern is observed. Differences in v γ of the order of 0.5–1 km s −1 might be caused, for instance, to the way RVs are determined (cross-correlation, bisector, ...), the mask used, and the instrument zero points. In this paper we did not perform such a long-term study as this is out of the scope of this paper and would require a complete analysis of all available literature data. U Car. The companion orbiting this Cepheid is below our detection level. Our datasets enable us however to exclude any companion with a flux ratio higher than 0.4%, which would correspond to a spectral type earlier than B2V (see Table 3 ). Y Car. Our possibly detected companion has a flux ratio of ∼0.94% and would correspond to a ∼A0V spectral type, which is in rather good agreement with the ∼B9V derived by Evans (1992c) . Although additional data are still necessary to confirm, this possible detection seems in a very close orbit as we measured a projected separation of ∼2.5 mas (∼3.5 au), as for S Mus. We first estimated the 3 σ detection limit using all observables and removing the possible companion (because we have a detection), and second using only the CPs but without removing it (because there is no detection). We noticed that the closure phases alone provide a contrast limit lower than 4 mag (see Table 3 ), which explains the non-detection with only this observable. With all observables we add more constraints in this case, which provide contrast limit of 5 mag (5.1 mag within 25 mas). This enables us to exclude at 3 σ any companion with a spectral type earlier than A0V. YZ Car. The faint companion orbiting this Cepheid is not detected from our observations. Our 3 σ detection limits (see Table 3 ) show that any companion with a spectral type later than B3V would not have been detected with

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


tailed and, more importantly, (b) that the chosen statistical sample represents the global statistics well, at least, in terms of statistical power. Therefore, if we randomly select a pixel inside our sampling area from one observation, the probability to observe a value above the background mean is or . 10 10 is the probability to observe values outside the limits. Half of this should account for the probability to observe values that exceed only the upper limit of . Therefore, a is adopted as a realistic occurrence probability of a stochastic observation in a single experiment. Considering also that the signal at the position of the A HST star is the only consistently present signal in all our NIR images (i.e., three independent experiments), then the probability that it results from random background noise fluctuations should be or . Since this is negligible, we can safely consider that the presence of an underlying point source, which systematically “drives” the flux within the green circle above the limit in repeated observations, is the origin of the observed NIR signal of Figure 5 . However, are the photometric properties of the NIR detections consistent with the visual photometric properties of the A HST star? 4.2. Photometric Calibration of the NIR Detections The V and I magnitudes of the A HST star are measured with aperture photometry on the and HST images (Section 2.2 ). They are and mag, respectively. On the contrary, due to the low S/N of the Subaru data, aperture photometry is not an option for estimating the NIR magnitudes of the detections. Alternatively, their , and K S magnitudes are estimated by taking the ratio of the sum of the peak fluxes of G.S.1 and G.S.2 to the peak fluxes of the NIR detections, 11 11 Point sources of different brightness observed simultaneously with the same telescope are convolved with the same PSF as long as their separation is smaller than ∼30 arcsec (i.e., isoplanatic angle). Consequently, the ratio of the fluxes at any point across their PSFs and the ratio of their integrated fluxes will (ideally) be approximately equal and, therefore, any of these measurements should be representative of their true brightness difference. usingwhere is the peak flux of each guide star, is the peak flux of each detection, and is the Subaru magnitude of the G.S. that we derived in Section 2.1.1 . This yields , and mag for the detections in each NIR band. The uncertainties are calculated according to the relationwhere we assume a 10% uncertainty in the measurement of and a 30% uncertainty in the measurement of the, more uncertain, . Having magnitude estimations, we can attempt to constrain the V − I , visual–NIR, 12 12 I.e., , and . and NIR 13 13 I.e., , and . colors of the NIR detections/A HST star and, therefore, its spectral type and luminosity class. 4.3. An Extragalactic Supergiant or a Galactic Dwarf? There are two possibilities for the nature of the A HST star. It can be either a distant supergiant

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O B-Wavelength O O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject O O O O O B-Wavelength O O B-Wavelength O B-Wavelength O O O B-CelestialObject I-CelestialObject I-CelestialObject O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O O O B-Wavelength O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O B-CelestialObject O B-CelestialObject O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O O O O O O O B-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-Telescope O O O B-CelestialObject O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-TextGarbage I-TextGarbage O O O O O O O O O B-Wavelength O B-Wavelength O B-Wavelength O O O O O O O B-Wavelength O O O O O O O O O B-Wavelength B-CelestialObject I-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject I-CelestialObject O O O O O O O


the course of the observations (typically 33 d for Campaign 0). Eclipsing binaries and ellipsoidal variables of high amplitude are avoided. If we consider only stars where the harmonic is visible, then 86 out of 265 (32 per cent) 09–B9 stars are rotational variables. In addition, if we add stars with just a single isolated peak (no harmonic), then 142 out of 265 stars (54 per cent) are rotational variables. Balona et al. ( 2015 ) has already shown that rotational modulation is probably present in many late B stars in the Kepler field. This study shows that this effect is likely to be present in early B stars as well. Indeed, the large fraction of B-type rotational variables in the K2 data is probably an underestimate because these data are less precise and of much shorter duration than the Kepler data. The only test that is available for rotational modulation is to compare the rotational velocity obtained from the photometric period (using an appropriate stellar radius) with the rotational velocity derived from spectroscopic line broadening measurements. This could be done successfully for the A stars (Balona 2013 ) because of the large number (875) of stars with known periods and radii derived from multicolour CCD photometry. Unfortunately, there are too few B stars in our sample to use this statistical test. Moreover, stellar radii cannot be estimated with sufficient precision. There are only seven stars in Table 2 with known values of the projected rotational velocity. Rotational modulation implies some kind of surface brightness inhomogeneity. The nature of such a ‘spot’ cannot be determined at present. However, it is difficult to conceive of starspot formation without the presence of a magnetic field. We therefore suggest that magnetic fields are probably present in stars with radiative envelopes. According to Cantiello Braithwaite ( 2011 ), dynamo action in a subsurface convection zone in such stars might generate a magnetic field. In this case magnetic spots of size comparable to the local pressure scaleheight can manifest themselves as hot, bright spots. A theory of dynamo action in radiative envelopes which involves differential rotation has been developed by Spruit ( 1999 , 2002 ) and Maeder Meynet ( 2004 ). In this theory, a magnetic instability in the toroidal field wound up by differential rotation replaces the role of convection in closing the field amplification loop in conventional dynamo theory. Zahn, Brun Mathis ( 2007 ) has verified that an instability is generated, but concludes that a dynamo cannot be sustained by this effect. Arlt Rüdiger ( 2011 ) found that feedback by the Lorentz force diminishes differential rotation and brings field growth to a halt in a few thousand years for intermediate mass stars. It seems that we still do not have an acceptable explanation for the generation of a magnetic field in radiative envelopes. One way to circumvent the generation of magnetic fields in radiative envelopes is to suppose

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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-CelestialRegion I-CelestialRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Mission 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 B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Citation I-Citation I-Citation 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 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-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


NW part of RCW 57A. This could be the plausible reason behind the low-density material observed in the NW region. The observed large-scale loops in the NE possibly formed due to the newly formed material as a result of the expanding I-fronts driven by the embedded massive protostars of RCW 57A. A high-velocity outflow signature is discernible close to eastward from the center, while the same feature is absent westward as shown in Figure 11 (b). This could be attributed to the confined ionized gas flow toward the west from the center, possibly due to the presence of a dense clump (thin black contours in Figure 7 ). The high-velocity component is only seen toward the east, which implies a dearth of dense material there, and hence, the ionized gas expanded with relatively more velocity. de Pree et al. ( 1999 ) and Purcell et al. ( 2009 ) have also shown that the H ii region expands more freely toward the east and is bounded on the west. 5.2. Column Density Profiles: Filament Width and <italic>B</italic>-field Support We fitted a Gaussian to the mean column density profiles spread over ∼5 pc radii, and the resultant FWHM, corresponding to the filament characteristic width, is found to be 1.55 ± 0.09 pc. However, a constant filament width of ∼0.1 pc was determined for the central dense sections of the filaments of nearby star-forming regions in the Herschel Gould Belt survey by fitting a Gaussian to the inner sections (radii up to 0.3–0.4 pc) of the filaments (Arzoumanian et al. 2011 ). Therefore, we fit a Gaussian to the inner 1 pc width of the clubbed mean column density profiles of the NW and SE regions, and the resultant σ and FWHM are found to be 0.21 ± 0.08 pc and 0.50 ± 0.18 pc, respectively. Within the error, the filament width (0.50 pc; green lines in Figures 12 (a) and (b)) of RCW 57A is higher than the constant filament width of ∼0.1 pc (Arzoumanian et al. 2011 ). Filament widths larger than 0.1 pc (spanning over 0.1 –1 pc with typical widths of ∼0.2–0.3 pc) have also been witnessed in a number of studies (e.g., Hennemann et al. 2012 ; Juvela et al. 2012 ). However, the filament width of RCW 57A has not been resolved because of the limited resolution (364 corresponds to 0.42 pc as shown by the cyan lines) of the column density map. The mean power-law index p = 2.02 ± 0.05, derived from the Plummer-like profile fitting for RCW 57A, is consistent with other studies (Arzoumanian et al. 2011 ; Juvela et al. 2012 ; Palmeirim et al. 2013 ; Hoq et al. 2017 ). A similar value of this index ( p = 2) is expected if the filament is supported by B -fields (Hennebelle 2003 ; Tilley Pudritz 2003 ), in accordance with our observational results supporting the active role of B -fields in the formation and evolution of filaments, as described in Section 5.3 below. 5.3. Evolutionary Scenario of the Filament and Bipolar Bubble Based on the morphological correlations among the (i) dense filamentary cloud structure seen in the submillimeter (in the 0.87 mm

B-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion 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-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Tag 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 B-Survey I-Survey I-Survey I-Survey O O O B-Model 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 B-Model O O O O O O O O O O O O O O O B-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 B-CelestialObject I-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 O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O B-CelestialObject 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 B-Formula I-Formula I-Formula I-Formula I-Formula O O O B-Model I-Model O O B-CelestialObject I-CelestialObject O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O B-Citation I-Citation O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O B-Wavelength I-Wavelength


the matter power spectrum (left-hand panel) and reduced bispectrum (right-hand panel), defined as S ( k ) ≡ T ( k ) BCM / T ( k ) GrO for T ( k ) = { P ( k ), Q ( k )}, at z = 0. Solid, dashed, dash–dotted and dotted lines are computed with simulations of box side and 768 3 , 512 3 , 384 3 , and 256 3 particles, respectively. Colours are referred to different halo mass bins, expressed in decimal logarithm of , with which the baryon corrections have been computed, according to the legend. APPENDIX B: FOLDING OF THE PARTICLE DISTRIBUTION Measuring the three-point clustering with the classical Fourier estimators can be very expensive in terms of memory and CPU, especially when using covering larger dynamical ranges. In fact, it is easy to see that, being k Ny = π N g / L box the Nyquist frequency of the grid, increasingly large number of grid points N g are required to get a given accuracy at a fixed wavenumber, when using progressively larger simulation boxes L box . Additionally, when using “interlacing” to suppress aliasing, the number of grids used must be doubled (Sefusatti et al. 2016 ). However, since our measurements are limited by discreteness noise (and not cosmic variance), we can obtain accurate estimates of Fourier statistics on small scales by folding the density field (Jenkins et al. 1998 ; Colombi et al. 2009 ). The idea is to fold the particle distribution by re-applying the periodic boundary conditions assuming a new boxsize L ′ = L / f , where we call f the number of foldings. If L ′ is large enough to assure that the modes inside the new box are uncorrelated, we can measure in principle the clustering from a new effective fundamental wavenumber up to a new effective Nyquist frequency, given by . For instance, by folding the box four times, we will get to Nyquist frequency four times higher. In Fig. A3 , we apply this technique to our simulation, folding the particles up to six times, and reaching a with a 64 3 and a 128 3 grid for the power spectrum and the bispectrum, respectively. Even using a TSC scheme on interlaced grids, we note that it is safer to use the measurements up to in the bispectrum. Also, the measurement of the largest modes of the folded box are noisy because they are sparsely sampled; for this reason, it is convenient to discard these modes, taking for instance wavenumbers . Figure A3. Left-hand panels: Matter power spectrum measured in a 64 3 (interlaced) mesh, folding the box up to six times, following the technique explained in the text (coloured dots). For comparison, the matter power spectrum measured with a 696 3 mesh and not folding the box is plotted as a black solid lines. The equivalent Nyquist frequencies for each folded box is plotted as a solid line. In the bottom panel, we display the ratio between the power spectrum measure with a 64 3 and a 696 3 mesh. Right-hand panels: Similarly to the left-hand panels, we display the measured bispectra using a 128 3 mesh and the folding of the box, and

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


governed by the equilibrium with SI clathrate hydrates of CO 2 (Levi et al. 2017 ). For convenience, we have cast into a cubic polynomial form the first and second dissociation constants of carbonic acid, as derived from the revised-HKF equation of state:where P is in GPa and K is in molal. For each isotherm, the polynomial is valid for the pressure range spanning from the surface of the ocean to the ocean floor. The coefficients for the polynomials are tabulated in Table 4 . Table 4 Polynomial Coefficients to Be Used with Equation ( 55 ) In Figure 14 , we give the speciation of the carbonate system as a function of depth, for the 280 K isotherm. We find that freely dissolved CO 2 is the most abundant form of DIC, in water-planet oceans, at any depth. This is opposite to the case of Earth, where freely dissolved CO 2 is the least abundant DIC component in the ocean (Zeebe Wolf-Gladrow 2001 ). Also, we find no substantial difference between the concentrations of hydrogen complexes, H + , and bicarbonate (both are represented by the red curve). Carbonate and hydroxide ions are found to exist in the ocean only in trace amounts. We note that the errors we have suggested above for the values of K 1 and K 2 do not have any considerable effect on our results. Figure 14. Speciation of the carbonate system as a function of depth in the ocean. Here we consider the ocean thermal profile to be an isotherm, set at 280 K. The black curve is the concentration of freely dissolved CO 2 . The red curve is the concentration of H + and . The green curve is the concentration of . The cyan curve is the concentration of OH − . The curves terminate at the pressure representing the bottom of the ocean, for the given isotherm. From Figure 14 we see that the different chemical species making up the carbonate system have a concentration gradient with depth. We argue that these concentration gradients with depth are stable against vertical mixing in an ocean world. First, we wish to point out that the concentration of freely dissolved CO 2 , the most abundant component of the DIC, is constant to a good approximation throughout the ocean. This is a consequence of the nature of solubility when in equilibrium with the clathrate phase, rather than due to efficient vertical mixing in the ocean (Levi et al. 2017 ). Thus, the concentration gradients with depth are most pronounced for the chemical species that are least abundant. If a parcel of ocean water migrates from the ocean floor upward, this parcel would be supersaturated with carbonate with respect to the shallower depth. The value for K 2 decreases with decreasing pressure. Consequently, carbonate would transform to bicarbonate, and then to freely dissolved CO 2 . However, this newly formed CO 2 is added to an ocean likely saturated with CO 2 , at equilibrium levels with respect to its clathrate hydrate phase (Levi et al. 2017 ). Therefore, the additional dissolved CO 2 forms grains of clathrate hydrates, which tend to

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


the importance of the presented ion acceleration in these systems. In terms of the long-term evolution of the acceleration process, in the turbulent environment of accretion disks, we expect many successive δB / B ∼ 1 amplifications and decreases of the field (see also Verscharen et al. 2016 ). So a more realistic picture of this process should consider the acceleration presented in this work occurring many times as the plasma is gradually accreted. We will study these aspects of the acceleration process in future investigations. Appendix A 1D Shear Setup The goal of our 1D shear runs is to simulate a shearing plasma, assuming that its properties depend only on the direction parallel to the mean background magnetic field . This is equivalent to assuming that the wavevectors captured in the simulations satisfy . Since, in a shearing plasma, the direction of evolves with time, the orientation of the wavevectors that can be consistently resolved needs to evolve accordingly. Our 1D setup is built upon the “shearing coordinates” setup presented by Riquelme et al. ( 2012 ). This setup was designed so that the simulation domain follows the shearing flow of the plasma, which is given by the shear velocity (). Figures 1 (a) and (b) illustrate the way the shape of the domain evolves as seen by an inertial observer at t = 0 and t > 0, respectively. Formally, the shearing coordinates ( x ′, y ′, z ′, t ′) are defined in terms of the regular, inertial coordinates ( x , y , z , t ) aswhere , , 19 19 Notice that, in the limit , the expression is equivalent to v = − sx , as we assume in Figures 1 (a) and (b). Since ensures that , this expression was adopted in Riquelme et al. ( 2012 ) in order to deduce the equations that describe the dynamics of the plasma in the shearing coordinate system. However, both in Riquelme et al. ( 2012 ) and in this paper, we are interested in the plasma dynamics in the regime . c is the speed of light, and s is the shear rate of the plasma. Our 1D domain is defined by y ′ = 0, and it is shown by the blue lines in Figures 1 (a) and (b). These figures show how the length and orientation of the 1D domain change over time. This in turn changes the orientation of the wavevectors that can be captured within the domain. In addition, there is an initially homogeneous magnetic field, , pointing parallel to the 1D domain at t = 0. Magnetic flux conservation ensures that will always be parallel to the 1D domain at t > 0, as also depicted in Figures 1 (a) and (b). Therefore, if the problem of interest is dominated by waves that propagate parallel to , our 1D simulations will be able to capture the essence of the phenomenon. In order for our 1D simulations to consistently satisfy , we need to replace x ′ with a new coordinate, , which we define asIndeed, if we assume and sy ′ ≪ c , the partial derivatives with respect to the spatial coordinates in the inertial frame areThus, if we impose the 1D condition, namely, that the fields depend only

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line properties.) In our initial line list, we use the former model, adopting the tuned of −0.224 from DM12 . This blended feature is addressed more fully in the next section. We use this initial line list to generate synthetic spectra of the benchmark stars without any Be to compare to the observed spectra, as shown in Figure 3 . The solar spectrum clearly requires the inclusion of Be absorption to fit the observed spectrum at the location of both Be ii lines. In the modeled solar spectrum, the contentious Mn i line at λ 3131.037 Å is clearly visible in the blue wing of the Be line at λ 3131.065 Å. The Mn i line is stronger in the red giant spectra and is well fit with the larger adopted from DM12 . All three benchmark observations show excess absorption predicted by the models, especially below λ 3130.0 Å. Most concerning is that the Arcturus model is a poor fit to the spectrum in the contentious blue wing of the λ 3131.065 Å Be line. Some tuning of the gf -values is therefore required. 4.2. Tuning the Line List The poor fit seen at λ ≲ 3129.6 Å has little effect on the Be abundance analysis, but we did trace the problem to two Fe lines: λ 3129.102 Å (Peterson Kurucz 2015 ) and λ 3129.619 (VALD K14). Removing these lines (which we achieved by changing the by the arbitrarily large factor of −10) produces a much better fit to the spectrum. The focus of the remainder of astrophysical tuning is on a narrow wavelength region around the redder Be ii line, which is the more isolated of the two lines. Despite the relative isolation, there are still significant blends including the contentious Mn i noted earlier as well as a contribution in the red wing of the line by Zr i at λ 3131.109 Å. In the solar spectrum, this line is weak (∼1.5 mÅ equivalent width), but the equivalent width is at least an order of magnitude larger in red giant stars. Furthermore, Figure 3 shows that a nearby Cr i line is poorly fit in the solar spectrum and is nearby enough to potentially affect the neighboring Be blend. The synthesized Cr i line at λ 3131.212 Å is too weak in the spectra of all three benchmark stars. Its was increased by 0.60 dex in order to match the observed solar spectrum. Figure 3. Comparison of synthetic spectra generated with the newly compiled line list (solid lines) compared to observations (dotted lines), assuming no Be in the stellar atmospheres. The dashed vertical lines show the location of the Be ii lines, and the dotted–dashed vertical line marks the Mn i line at λ 3131.037 Å, using the tuned of −0.224 from DM12 . The solar spectrum (top, archival Subaru spectrum of Vesta) is clearly not well fit when Be is absent from the model. The spectrum of Pollux (middle) shows a generally good fit at wavelengths above ∼3130.5 Å, whereas the model for Arcturus (bottom) has conspicuous missing absorption just blue ward of the λ 3131.065 Å Be ii line. As we considered additional changes to the line list in the blended Be feature, we generated spectra

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