a coronal loop in our model) is significantly lower. While our whole computational domain covers more grid points () than the Rappazzo et al. (2008) models (up to ), in their model they describe only a single loop structure (straightened out), and consequently can reach significantly higher Reynolds numbers. Table 1 Exponents for different coronal heating scaling laws as used in Eqs. ( 10 ) and ( 11 ) together with the fitting results from Sect. 5.3 . The coronal heating scaling law we fit to our model data indicates a dependency on the magnetic field that lies between the exponents given by Rappazzo et al. (2008) and van Ballegooijen et al. (2011) . We also find that the homogeneous atmospheric background in the MHD-turbulence setup of Rappazzo et al. (2008) may be problematic when estimating the coronal magnetic energy input or braiding of field lines because the Alfvén crossing time , which determines their scaling law exponents, varies strongly within our stratified atmosphere. In a recent study van Ballegooijen et al. (2014) speculate that the quasi-static behavior of the coronal magnetic field found in models like ours is due to the limited spatial resolution of the photospheric magnetic driving. They suggest that in the case of increased resolution, the heating might be wave-dominated. Certainly, with increasing resolution AC heating will also be present, but this does not automatically imply that the DC heating becomes less efficient. To the contrary, models that employ reduced MHD (allowing for a higher spatial resolution) show that MHD turbulence will lead to a DC-type heating by the build-up of current sheets also for high spatial resolution (e.g., Rappazzo et al. 2008 ). This is backed by the argument that in the coronal part of the atmosphere a field line will adapt quickly to any wave excitation from below because coronal Alfvén speeds are at least one order of magnitude faster than within the lower atmosphere (cf. Fig. A.1 and Table A.1 ). More realistic full MHD simulations with increased resolution will have to show the relative merits of AC and DC heating based on the photospheric driving. The temperature scaling laws we tested against our model field lines ( Rosner et al. 1978 ; Serio et al. 1981 ) indicate only general trends for the most heated field lines and EUV-emissive loops. This puts all attempts to set up scaling laws of the coronal heating into their context, namely that these laws are deduced from and are only applicable to a small subset of coronal field lines, namely the ones that are bright in EUV or X-rays. Non-emissive and weakly heated field lines are often not consistent with scaling laws intended for 1D loop structures. Some of their plasma parameters need to be determined differently, for example, through self-consistent 3D MHD simulations. It is an interesting question whether such observationally motivated scaling laws would benefit from new and much more precise observations of hot coronal loops. We


reflecting enhanced and variable N abundances locally in the circumstellar material (CSM) surrounding many of the individual SNRs. There are some indications that the abundances in the twice solar models begin to have some unexpected impacts on relative line intensities. For example, the twice solar models show [O iii ]/H β as already being strong at 100 km s −1 and decreasing dramatically to 200 km s −1 and above, which is exactly opposite to the lower-abundance models over this same range. Also, more salient to the above discussion, the ratio of [N ii ]/[S ii ] varies by over 40% from 100 to 300 km s −1 shocks, whereas this ratio is nearly constant for lower-abundance sets over the same velocity range. As abundances increase, the balance of energy transfer and cooling being carried by the various ions must be changing in ways that are different from the lower-abundance models. From even this cursory comparison, it seems likely that the elevated abundances may contribute both to the high ratios and to the observed scatter of line ratios we observe in M83. Figures 32 and 34 of Allen et al. ( 2008 ) show their 2× solar abundance grids projected onto the same line ratio plots as shown in the middle and right panels of Figure 10 . Allen et al. apply these models to AGN situations, where one attempts to separate shocked emission from photoionized regions, but they should apply to SNR shocks as well. The majority of the SNRs in all three galaxies plotted in Figure 10 lie within the classical shock-heated region toward the upper right in these diagrams, but a significant number of objects appear toward the lower left region nominally ascribed to H ii regions. However, note that the model grids extend significantly down into the nominally photoionized regions of the plots at lower left. (Presumably lower shock velocities might extend even further into this regime.) Here again, we see evidence that at the higher abundances assumed in these models some of the traditional expectations begin to break down. We encourage further investigation of the properties of shock models at elevated abundances that can further elucidate this interesting and so far little-explored region of parameter space. 4.2. Ramifications The high metallicity of M83 has ramifications for the massive stars that are the precursors to many of the SNRs we have observed. It has long been known that abundances affect both the momentum transfer and mass loss in the stellar winds of massive stars (e.g., Vink et al. 2001 ; Kudritzki 2002 ), though the situation is complicated (Smith 2014 ). While most such studies consider only solar abundances and below, the trends with increasing abundance are clear, with higher abundances giving rise to significantly stronger and more massive winds. Coupling this with the hot, high pressure ISM in M83 that was inferred from X-ray data (Long et al. 2014 ), one might expect this wind mass loss to be constrained to the region immediately surrounding the


The signal source comes from a quasi-monochromatic Continuous Wave HeNe laser emitting at 3.39 μm. Figure 2. Description of the experimental setup. M: injection mirrors for the infrared signal at 3.39μm; L1: focusing lens for the MIR injection into the Periodically Poled Lithium Niobate (PPLN) waveguide; L2: focusing lens for the converted signal into a fibre single mode at 810 nm; L3: collimating lens for the pump signal; P: off-axis parabola; D: dichroic mirror used to separate converted signal from pump signal; BS: beam splitter used to separate the MIR signal in two separated ways. The 3.5 mW signal is shared equally between the two interferometric arms thanks to a pellicle beam splitter BS. Over the MIR stage, a set of mirrors and objectives allow the injection of the signal into frequency converters in each arm. These converters consist of periodically poled Ti-indiffused waveguides in LiNbO 3 . The waveguides are designed to provide low-loss single-mode guiding in the MIR range. Poling periods around 22 μm enable the phase-matching for the SFG process. The entire length of the non-linear conversion section is 92 mm. The non-linear stages are powered by a distributed feedback laser laser emitting at 1065 nm to generate a wave at 810 nm through the SFG process. On each interferometric arm, the maximum power conversion efficiency is measured in the range of 3·10 −5 when each non-linear crystal is powered by a 60 mW pump power. Notice that this overall throughput includes the non-linear efficiency and the whole losses resulting from the launching and collimating stages, including the stringent spatial filtering. This current low conversion efficiency is to be improved for future application, e.g. by using pigtailed techniques as demonstrated by Büchter (Büchter, Herrmann Sohler 2011 ) The pump signal is injected backward using a taper, and is then back-reflected towards the output of the Periodically Poled Lithium Niobate (PPLN) waveguide thanks to a dichroic mirror directly deposited at the waveguide endface [Anti-Reflection (AR) at 3.39 μm and High-Reflection (HR) at 1065 nm, see Fig. 3 ]. The waveguide taper allows us to ensure a better control of the pump beam geometry leading to the optimal spatial overlapping in the non-linear crystals between the pump at 1065 nm and the signal at 3.39 μm. Figure 3. PPLN injection scheme. The pump wave at 1065 nm propagates in the reverse direction, and is coupled into the waveguide thanks to a taper. After a back-reflection by a dichroic mirror, the pump field interacts with the signal at 3.39 μm to generate the converted wave at 810 nm. We define the normalized conversion efficiency curve of the SFG process as the ratio between the converted power and the signal one as a function of the signal wavelength. This curve depends on the crystal's optical and geometrical parameters (Fig. 4 ) and can be tuned by a fine control of its temperature. The full width at half-maximum of the conversion


gravitational lensing distortion matrix ( 1 ) across the image, on the employed weight function W , and also the employed ellipticity definition. In the case of a flat weight, W ()const., and the centre of light as image centre, equations ( 9 ) and ( 13 ) yield unweighted moments. The observed ellipticity ( 10 ) and the intrinsic ellipticity ( 14 ) are then related by An advantage of based on unweighted moments is that for g 1, one may use the observed ellipticity as an unbiased estimator, for the reduced shear g , i.e. , where angular brackets denote averages over the galaxy intrinsic ellipticity distribution (which is assumed rotation invariant), regardless of the details of the intrinsic ellipticity distribution (Seitz Schneider 1997 ). Unweighted moments and ellipticities derived from them are susceptible to image noise in the outer image regions [due to the factor i j in the integral in equation ( 9 )]. Moreover, unweighted moments and ellipticities are strongly affected by errors in the separation of the galaxy light from the light of neighbouring galaxies. Ellipticity estimation from real galaxy images thus often employs down-weighting of the outer regions of the image. The drawback of such radially weighted moments is that they complicate the relation between observed and intrinsic ellipticities. For a general choice of ellipticity definition and weight function W (), and sufficiently small reduced shear g , the observed ellipticity as a function of reduced shear g can be approximated by a linear response in g : where the intrinsic ellipticity , and the shear polarizability If P can be estimated with sufficient accuracy (e.g. from the observed galaxy image itself) and is invertible, one may obtain an unbiased shear estimator by applying P 1 as a shear polarizability correction factor: If the average shear polarizability P for the observed galaxy population is known, another unbiased shear estimator can be constructed that employs P 1 as polarizability correction: The above image ellipticity-based shear estimators can be treated in a uniform manner, 7 with appropriate definitions for the observed ellipticity and intrinsic ellipticity . For example, equation ( 17 ) suggests with and from unweighted moments. For e computed from unweighted moments, one obtains (e.g. Bernstein Jarvis 2002 ) 8 A simplified version of the estimator by Kaiser, Squires Broadhurst ( 1995 , KSB) yields with and from moments with a Gaussian radial weight function, and estimated from the individual observed galaxy images. As for the shear, the ellipticities and can be decomposed into tangential and cross components with respect to a given angular direction or comoving transverse direction : with , , and . 2.4 Density and intrinsic shape correlations The intrinsic shapes of galaxies may have a preferred orientation towards nearby other galaxies and matter overdensities. The preferred orientation of galaxies towards matter overdensities may be quantified by the


for a cold flow such that (equation B1 in Appendix B , with ω = 1). This expression provides the two solid blue curves shown in Fig. 4 , computed in two extreme cases for the location of the Alfvén surface: near the SM surface with x SM = 2, namely (lower curve) and much further out with for the upper one (as in typical near-equipartition cold flows). For a given magnetic lever arm λ (mostly determined by ξ), κ must be large enough. This rules out all super-SM solutions located at the left-hand side of these curves. It can be seen right away that the parameter space of super-A solutions for near-equipartition fields ( n = 0) will be very small, with mass loads κ smaller than 0.1, disc ejection efficiencies ξ smaller than 0.08, and magnetic lever arms larger than ∼7, in agreement with Ferreira ( 1997 ). On the other hand, MRI-like driven flows at small μ seem to allow mass loads larger than unity with small λ. These isothermal flows could be of great interest for reproducing dense outflows (ξ > 0.1) with low asymptotic speeds ( u p ∞ ∼ Ω K o r o ). In other words, a weakly magnetized disc is better suited for a massive ejection than a near-equipartition disc, not only by providing the necessary bending at the disc surface through the MRI-like mechanism, but also by bringing the Alfvén surface closer to the disc (see the discussion on the role of Ψ A in Appendix B ). Nevertheless, not all super-SM solutions located at the right-hand side of the solid curves in Fig. 4 can become super-A. For a given ξ, λ is roughly determined and so is the cylindrical radius r A = r o (λ/ω) 1/2 of the Alfvén point. But equation ( 21 ) shows that κ also depends on p and μ. For a given toroidal current density p , the SM constraint provides μ so that κ is fixed. On the other hand, p also determines the radial magnetic field component at the disc surface and thereby the initial jet bending (see Fig. B3 ). As a consequence, playing with p not only affects the disc vertical equilibrium (SM point) but also this initial jet angle. Not all couples (κ, λ) fulfil the Grad–Shafranov equation ( 30 ). If a solution is not possible, this means that there is no altitude A of the Alfvén point that can be found starting from the conditions provided at the base of the jet (SM point). Changing the value of p leads to a slight modification of κ, λ as well as the jet angle at the SM point, allowing thereby to (possibly) meet the A condition. This translates into an adaptation of the altitude A of the Alfvén point (thus the angle Ψ A ) according to the disc conditions. The necessary condition highlights this aspect. When λ is large, r A / r o is large and gravity plays a negligible role so that is satisfied whenever λ > 3 (dashed line in Fig. 4 ). But gravity cannot be neglected anymore at lower values of λ, as can be seen in equation ( 31 ). In that case, providing requires to increase sin Ψ A , namely to bring the Alfvén surface closer to the disc surface. The closer it is to the


to be aligned with its projected morphological major axis. The coincidence in PAs from the kinematics and morphology is thus generally a criterion in determining the nature of a galaxy. In practice, complications arise for a variety of physical reasons (e.g., presence of nonaxisymmetric structures, nearby companions with overlapping outer isophotes, spatially nonuniform extinction), compounded by surface brightness sensitivity and spatial resolution limitations for high-redshift galaxies. We examined the agreement between the derived kinematic position angle PA kin (Section 4.3 ) and the morphological position angle PA morph , quantified via the “kinematic misalignment” . We exclude GMASS-2540 here because it is not fully covered by the SINFONI AO data and because of its low H α surface brightness emission hampering a reliable PA kin determination. Following the same motivation as in Section 6.1 , we adopted as PA morph the PA from the H -band morphologies, when available, and from the H α maps otherwise. As noted in Section 5.4 , the PA H α and PA H are similar within 1.5 σ , and we verified that our conclusions would not be affected by instead adopting PA H α for all objects. For our sample, the mean and median ΔPA are 23 and 13 , respectively. For 73% of the galaxies, the alignment is better than 30 . Figure 8 shows the PA offsets as a function of the adopted axis ratio q and effective radius R e . Not unexpectedly, and as seen in other high-redshift samples (e.g., Wisnioski et al. 2015 ; Harrison et al. 2017 ), our galaxies broadly follow a trend of increasing ΔPA for more face-on and smaller sources. Of the 10 objects with ΔPA > 30°, eight are compact sources with distortions/extensions in their outer isophotes, asymmetric light distributions in their inner brighter regions, or little or irregular velocity structure (Q1623-BX502, Q1623-BX513, GMASS-2303, SA12-6339, ZC400528, ZC401925, ZC404221, and ZC411737). The other two sources are large, massive, and fairly face-on disks for which the misalignment can be attributed to morphological features (a noncircular ring with a clump on one side for Deep3a-6004 and clumps in a tail-like structure for ZC400569N; see Section 7.2 for more details). Figure 8. Kinematic misalignment ΔPA as a function of morphological axis ratio q for the SINS/zC-SINF AO sample. The symbols are color-coded and sized according to the effective radius R e of the galaxies. The five compact objects with ill-defined axis ratios and to which we assigned q = 0.64, corresponding to the for randomly oriented disks (Section 6.1 ), are plotted as squares connected with red dotted lines to their nominal best-fit q , shown as circles with a red arrow pointing toward the adopted value. Most of the well-resolved objects show very good agreement between their kinematic and morphological PAs, especially for the more edge-on systems. A larger proportion of the compact sources have ΔPA > 30°, reflecting ill-defined PAs due to


maximum grain size is determined by the fragmentation barrier (Eq. ( 3 )) and particles can reach centimetre sizes, but small particles are continuously reproduced. For a more massive planet, the location of the pressure maximum (and therefore the peak of mm dust concentration) occurs further away at 30, 44, and 54 AU for 1, 5, and 15 , respectively, as previously shown by Pinilla et al. (2012) . The radial range in which mm-sized grains are concentrated becomes wider. For the case, the second peak is caused by a transient density feature that in reality would be short-lived and would not function as a pressure maximum that can effectively concentrate particles. This issue has no impact on our results since we focus on the inner disk. In the regions inside the planetary gap ( AU) where the gas surface density steeply decreases outwards (and therefore the pressure gradient is negative), the maximum grain size is determined by radial drift (Fig. 2 ), and only close to the snow line ( AU) does the fragmentation barrier drop below the drift barrier due to the change in at . With the decrease in at , the maximum grain size is a few centimetres and the Stokes number of the particles at that location is much lower than unity (), thus they are better coupled to the gas, their radial drift velocities are lower (Eq. ( 2 )), and they move with at a similar speed to the gas (see also Brauer et al. 2008 ). If does not change at , the maximum grain size is dominated by radial drift, reaching values of the Stokes number of around , which would lead to very high drift velocities () depleting the inner disk on very short time scales (100–1000 yr). Therefore, when the inner disk is constantly resupplied from the outer disk, the changes of at allows replenishment of warm, small, and optically thick dust near , for which the drift velocities are slow. In the case of a mass planet, the micron-sized particles (1–10 m), are not perfectly trapped at the outer edge of the planet-gap, and they move continuously through the gap via turbulent diffusion. This partial filtration of dust grains supports a constant replenishment of dust from the outer to the inner disk, which together with variations of at extends the lifetime of a detectable inner disk reaching the life of the disk (5 Myr). In the cases of and mass planets, there is more efficient trapping of particles at the outer edge of the planetary gap, filtering all particle sizes (from 1m, which is the minimum grain size in our setup). The dust inside the planetary gap ( AU) is the dust that was initially within the gap. These particles grow, drift and fragment when they reach the snow line. Although there is a considerable amount of dust in the inner disk for all cases (1, 5, and 15 ) after 1 Myr, after 5 Myr of evolution the inner disk is practically depleted of dust for a disk hosting a and a mass planet. The dust density distribution after 5 Myr of evolution for AU is almost identical for and because the


et al. 2015b ). The contaminated regions of the SMICA map were further removed with the Galaxy, point-source, and SMICA -specific temperature and polarization masks, which leave ≈67% of the sky for the minimum-variance lensing reconstruction analysis. Given the sensitivity and angular resolutions of the Planck mission, the analysis thus results in the most significant measurement of the CMB lensing potential map to date. The online data provided by the Planck science team are in the standard HEALPix format (Górski et al. 2005 ). The spherical harmonics coefficients of lensing convergence, , are given for multipoles up to instead of the lensing potential, . We use the standard definition of lensing convergence to calculate fromWe then use the HEALPix synfast package to synthesize the lensing potential map, . The generated map has a resolution of (i.e., pixels). The projected lensing potential map is shown in Figure 1 . This reconstructed lensing potential map is used to cross-correlate with the cosmic void catalog, where the azimuthally averaged potential around each void is extracted, scaled, and then combined to constrain the void density profile. For our analysis, we shall use only those regions that pass the analysis mask (Galaxy + point-source + SMICA ). Figure 1. Lensing potential map, , constructed from Planck lensing convergence, . The gray shaded area marks the rejected pixels excluded by the analysis mask. 2.2. Cosmic Void Catalog In this work, we use the “Public Cosmic Void Catalog” (Sutter et al. 2012b ) constructed using a modified and extended version of the watershed algorithm ZOBOV , called “Void IDentification and Examination” (VIDE; Sutter et al. 2014b ). We applied the code to the SDSS Data Release 7 (Abazajian et al. 2009 ) main galaxy sample and SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 10 (Ahn et al. 2014 ) LOWZ and CMASS samples. This results in individually detected voids. The samples represent volume-limited catalogs of voids at various redshift bins. To minimize any possible evolution of the profile parameters, we choose to work with voids in individual redshift bins and do not stack voids across the bins. In order to have as many voids in a single bin as possible, we chose a high-redshift bin to increase the volume. Here, we report on the analysis using the “dr10cmass1” (, , ) and “dr10cmass2” samples (, , ), hereafter called “cmass1” and “cmass2,” respectively. We therefore stacked the Planck lensing potential map (Section 2.1 ) around the central positions of cosmic voids taken from the Sutter et al. ( 2014b ) “dr10cmass1” and “dr10cmass2” samples as two separated measurements. However, during our analysis we found that considerable numbers (106 and 303 for cmass1 and cmass2, respectively) of the voids are located in the negative lensing potential regions, which could be due to a number of reasons and warrants further investigations. We therefore restrict our analysis to 123 and


age uncertainties of these stars (that can be substantial as these solar twin stars are located on the upper main sequence). The diagonal line shows the relationship between Li and stellar age from Carlos et al. (2016) . 3.7. Li in stars with planets Since King et al. (1997) claimed a possibility that the low Li abundances in the Sun and 16 Cyg B relative to 16 Cyg A could be due to the presence of planetary companions in the former two, several studies have presented disparate results regarding whether or not stars with detected planets have different Li abundance patterns compared to those with no thus-far detected planets. Studies that support the idea that there is no difference include Ryan (2000) , Luck Heiter (2006) , Baumann et al. (2010) , Ghezzi et al. (2010) , Ramírez et al. (2012) , and Pavlenko et al. (2018) , while those that find that indeed there is a difference include Israelian et al. ( 2004 , 2009 ), Takeda Kawanomoto (2005) , Chen Zhao (2006) , Gonzalez ( 2008 , 2014 , 2015 ), Figueira et al. (2014) , Delgado Mena et al. (2014) , and Mishenina et al. (2016) . To see whether this study can add some further clues to this controversy the exoplanets website 1 ( Han et al. 2014 ) was queried on February 14, 2018. We find that 36 stars in our sample have detected exoplanets, that 18 of those have well-determined Li abundances, and that 6 have upper limit Li detections. These 18 + 6 stars are marked in red in Fig. 8 . They span a range of effective temperatures from about 5600 K to 6500 K. The bottom panel in Fig. 8 shows the differences between the Li abundance of the exoplanet stars and the mean Li abundance of other stars in the sample that have effective temperatures within ±75 K, log g within ±0.25 dex, and [Fe/H] within ±0.25 dex of each exoplanet star. Due to the low number statistics of stars with similar atmospheric parameters at higher T eff , the temperature range was expanded to ±200 K for stars with T eff > 6100 K. As stars at these temperatures have less Li depleted atmospheres, this expansion should not affect the results. The stars with detected exoplanets have on average 0.08 dex higher Li abundances than those without planet detections, with a dispersion of 0.36 dex. Using the median instead gives a Li-enhancement of 0.04 dex. These numbers are well within the uncertainties and our sample reveals no statistically significant difference in Li abundances between stars with and without exoplanet detections. Fig. 8. Upper panel : red circles mark the 18 stars in the sample that have exoplanets detected and good Li measurements. Bottom panel : difference between the A (Li) for individual stars to the mean A (Li) for stars that have no exoplanet detections and that have effective temperatures, surface gravities, and metallicities, within ±75 K, ±0.2 dex, and ±0.2 dex. For stars with T eff > 6100 K, the temperature range is expanded to ±200 K. 3.8. Li trends in the thin and thick disks It is not straightforward


be needed to fully address this point. 4 DISCUSSION AND CONCLUSIONS WDM with a particle mass above still provides a valid alternative to the standard CDM scenario. In the previous papers of this series (Frings et al. 2017 ; Macciò et al. 2017 ) we have shown that the results of our simulations of field galaxies and satellite galaxies of the Milky Way in CDM are consistent with current observational data. In this work we investigated if the observations constrain the dark matter to be cold or if they allow for a WDM. For that we presented a sample 42 cosmological simulations of 21 haloes that were run both in CDM and WDM. As expected from the damping of the power spectrum the virial masses of the WDM haloes lie well below their CDM counterparts for masses below . Haloes at larger masses are much less affected. Like the CDM galaxies, WDM galaxies fulfil the extrapolated abundance matching relation from Moster et al. ( 2013 ) even with slightly less scatter. The critical mass for haloes to host luminous galaxies is much higher in WDM, where we find several dark haloes up to a halo mass of . Furthermore WDM seems to allow a larger range of masses where one finds both dark and luminous haloes. We found that WDM and CDM galaxies show no different behaviour in the observable velocity dispersion – size and metallicity – stellar mass relation. We have further investigated the average stellar formation times and found a possible way to distinguish the two populations: on average the WDM galaxies form slightly later, with a 〈 T age 〉 = 8.15 ± 0.70 Gyr ago while CDM galaxies have earlier formation times with 〈 T age 〉 = 10.00 ± 0.43. This result confirms the predictions from previous studies on the formation of dwarf galaxies in WDM (Governato et al. 2015 ; Chau et al. 2017 ), even though the current biases and systematic in observationally derived stellar ages (Guidi et al. 2015 ) prevent any firm comparison with observational data. Finally we found an indication that WDM barely reproduces galaxies at masses around with mean stellar ages of , i.e. that formed in the early universe before the UV background sets in. In agreement with previous work we find that the WDM haloes are systematically less concentrated than their CDM counterparts. On the other hand on small scales, about a few per cent of the virial radius, we confirm that the dark matter density slope is mainly fixed by star formation efficiency (e.g. Tollet et al. 2016 ) and not by the nature of dark matter. As a consequence at low stellar masses ( and below), our (few) data points suggest that the lower star formation efficiency in WDM galaxies might cause a slightly steeper central slope at those masses, but a larger sample of simulated galaxies is needed to firmly confirm this effect. We used four galaxies of the WDM sample and their CDM counterparts to simulate their evolution in a Milky Way potential as described above. We witnessed the lower concentrations of the WDM haloes causing the


at best, lower limits to the the true integrated fraction of escaping ionizing photons, and generally offer poor representations of the total number of ionizing photons that escape. The tables in Figure 4 show that LBGs may emit significant amounts of LyC radiation, at the level of 5%–1%, even if the optical depth at the edge is ≈10 (). By way of example, we note that Izotov et al. ( 2016a ) found an edge escape fraction f e 900 = 0.08. Using Equation ( 8 ), we derived an integrated escape fraction of f e LyC = 0.35 or 0.25 for our two cases, respectively. This suggests that the “f-escape” problem might not be as bad as it seems. The only definitive way to rule this out is through deep UV observations in the redshifted rest frame of the EUV in an attempt to observe the LyC drop-in. In the next section we address the observability of the Lyman drop-ins in the face of the steadily increasing mean optical depth of the IGM with increasing redshift. 4. Redshifted Models, Including Mean IGM Transmission We have thus far not included attenuation of the escaping LyC due to resonant scattering and photoelectric absorption (photoionization) from discrete collections of intervening clouds in the IGM. Here we use the rest frame LyC transmission models described in Section 3.1 to compute the mean transmission of the IGM as a function of the fiducial redshifts in Table 1 . The mean transmission function is derived from a mean optical depth (Paresce et al. 1980 ; Madau 1995 ; Inoue et al. 2014 ), expressed here as a numeric integral:Here, the observed wavelength is related to the rest frame wavelength by . The optical depth is . The redshift range from is in fixed increments of . The logarithm of the column densities range from in variable increments of with 0 . The differential distribution of the number of discrete absorbers with respect to H i column density and redshift, , is typically characterized by a piecewise continuous function in redshift and column density (c.f. Madau 1995 ; Inoue et al. 2014 ). There are three basic H i absorption regimes: the Ly α forest regime (LAF), ; the Lyman limit (LL) regime, , and the damped Ly α (DLA) regime, . We employ the described by Inoue et al. ( 2014 ), which uses a “Schechter-like” distribution function for the column density multiplied by a piecewise-continuous multiple power law distribution to describe the evolution in redshift. The distribution function is broken down into the sum of two different products, which in combination reasonably agrees with the evolution of H i absorption systems from the LLA to DLA regimes as detailed in the literature (Weymann et al. 1998 ; Prochaska et al. 2005 , 2010 ; Ribaudo et al. 2011 ; Noterdaeme et al. 2012 ; Fumagalli et al. 2013 ; Kim et al. 2013 ; O’Meara et al. 2013 ; Prochaska et al. 2014 ). We note that the Inoue et al. ( 2014 ) distribution function produces a mean transmission that is generally less aggressive than that produced by the distribution function


the hyperbolic method initially derived for the diffusion equation (Nishikawa 2007 ) to a 2D set of incompressible dissipative MHD equations. This completes the application to advection-diffusion and Navier–Stokes systems. The hyperbolic formulation of the resistive and viscous terms allowed us to construct a simple finite-volume scheme discretization on a rectangular grid, using an approximate Riemann solver to handle the dissipative and advective flux in the same way. For the sake of clarity, a simple second-order upwind flux formulation is chosen in this work. It is shown that our hyperbolic scheme is able to produce stationary solutions for two non-viscous reconnection problems, namely the magnetic annihilation and reconnective diffusion for which exact analytical expressions exist (Watson et al. 1998 ). The first advantage of this approach over traditional schemes is demonstrated through its consistent accuracy over a wide range of magnetic Reynolds numbers. Indeed, the spatial second order of convergence is closely obtained for the main and gradient variables as well. Secondly, the convergence towards the steady state scales only linearly with the cell width h , giving thus a O (1/ h ) acceleration over conventional schemes. Our hyperbolic method has a clear analogy with the hyperbolic divergence cleaning technique used in MHD codes to handle the divergence-free condition of the magnetic field (Dedner et al. 2002 ). Indeed, an additional numerical scalar variable is introduced in order to advect and diffuse the divergence errors to the domain boundaries. A corresponding scalar equation is also added and coupled to the magnetic field induction equation, leading thus to an hyperbolic system. As a major difference, this latter hyperbolic technique is introduced to handle a numerical term and not a physical dissipation term. It is also implemented in the true time evolution of the system contrary to our pseudo-time implementation. The next step in the development of the hyperbolic method for MHD is the extension to time-dependent solutions. Accurate time-dependent computations are possible by using implicit time integration. Indeed, efficient high-order hyperbolic schemes have been proposed for the advection-diffusion equation, with the idea to converge to successive pseudo-steady states that are solutions at successive physical time steps of the time-dependent equations (Mazaheri Nishikawa 2014 ). In order to speed up the convergence procedure iteration at each time step, the scheme presented in this work would probably require some improvements like higher order spatial reconstruction and/or an implicit pseudo-time solver (Nakashima, Watanabe Nishikawa 2016 ). Such time-dependent solutions also require some spatial or/and temporal dependences of the resistivity profile, which are essential in studies related to solar flares. We have checked that our scheme also works when a spatially localized profile is prescribed on the 1D model


objects. Therefore, in the rest of this work, we consider the A-, B-, D-, Q-, and V-type objects as possible taxonomical interlopers and eliminate them from our family. Fig. 2 Top panel : projection in the ( a , e ) domain of 5523 AstDyS asteroids in the region of the Gefion family (orange) and of 2547 members of the Gefion HCM cluster (black). Bottom panel : projection in the ( a , sin i ) domain of the same asteroids. Other symbols are the same as in Fig. 1 . Fig. 3 An ( a , sin i ) projection of the 606 asteroids in the Gefion region with taxonomic information from the SDSS-MOC4 database. The inset figure legend indicates the meaning of the symbols. Open circles indicate asteroids in the background, while filled circles correspond to asteroids of the Gefion family. The Wide-field Infrared Survey Explorer (WISE) and near-Earth object WISE 4 ( Masiero et al. 2011 ; Mainzer et al. 2016 ) were also used in this work to revise asteroid diameters and albedosin the Gefion region. We identified 896 asteroids with geometric albedo ranging between 0.0278 ± 0.0104 and 0.6200 ± 0.1510. We found 658 of them without taxonomic information. About 57.8% of those last albedos are possibly associated with an S-type (they vary between 0.12 and 0.30 with a standard deviation of 0.05). The mean albedo found in the HCM group is 0.2609 and the median one is 0.2598 with an associated standard deviation of 0.17 ( Fig. 4 ). Fig. 4 An ( a , sin i ) projection of the 658 bodies in the Gefion region with albedo information from the WISE dataset. The inset figure legend provides the meaning of the symbols. Considering a simple model with a spherical shape and a uniform density varying according to each class ( DeMeo Carry 2013 ), we find that the effective diameters ( D ) of the members in the HCM group vary between 0.82 and 71.46 km. The total mass of the family is estimated to be 0.791± 0.54 × 10 18 kg. Assuming that the objects on the left-hand side of the family are lost in the 5J:-2A MMR, our family probably originates from the break-up of an S-type asteroid with a diameter D ≈ 128 km, which is inside the allowed diameter range of 100–150 km mentioned in Nesvorný et al. (2009) . 3 Dynamical map We started our numerical exploration on the Gefion family by constructing dynamical maps of synthetic proper elements for 19 000 massless particles in the ( a , sin i ) plane and for 18 360 particles in the ( a , e ) plane. These numbers are chosen to cover an equally spaced grid in each plan. We vary the initial semi-major axis in the interval [2.69463, 2.832] with a step size of 0.0017 au. In the ( a , e ) plane, we increase the initial values of e from 0 to 0.18 with a step of 0.0015, while the initial values of the other elements are fixed to those of (1272) Gefion at the modified Julian date of 57200, which corresponds to June 27, 2015, and are available in AstDyS database. We use the Swift package ( Levison Duncan 1994 ) to integrate the particles over 20 Myr with a


b shows the components with frequencies lower than seven cycles per pupil. This cutoff frequency has been chosen to identify the peak at around five cycles per pupil visible in the PSD of Fig. 10 (5c). It has been shown in Sect. 5 that with a FPM, the COFFEE algorithm reconstructs low-order aberrations that should be absent, this phenomenon is also visible on the PSD of Fig. 10 (5b). Fig. 11. Reconstruction error of Fig. 10 (4c). The unit are in radians. ( a ) Same reconstruction error than Fig. 10 (4c), at an optimized scale. ( b ) Orders lower than seven cycles per pupil of the reconstruction error (a), obtained with a cut on the PSD and an inverse Fourier Transform. ( c ) Difference between the phase maps (a) and (b). Patterns of a few cycles per pupil are visible and can be easily identified using a spatial filter. They correspond to the peak at around five cycles per pupil of the PSD of Fig. 10 (5c). It has been shown in Sect. 5 that with a coronagraph, the COFFEE algorithm generates extra low-order aberrations. Conversely, the reconstruction is not efficient for low-order aberrations such as the two cycles per pupil case. The reconstructed phase is very different than the theoretical one, in terms of phase pattern and RMS value (0.29 radians RMS), most of the error coming from low-frequency aberrations (see Table 1 ). This test indicates that there exist some modes that are not or badly visible by COFFEE, mainly when they are blocked by the FPM. The FPM limits COFFEE’s ability to sense and consequently reconstruct low-order modes with spatial frequencies smaller than the spatial extent of the FPM, that is, smaller than 3.5 cy/pup in our case (as a reminder, the FPM has a diameter of 7.2 ± 0.9 λ / D ). On the other hand, COFFEE shows its full capability for modes with higher spatial frequencies than the size of the FPM. 5.3. Impact of segment-level aberrations on the phase reconstruction From the previous study, we can deduce that phase patterns containing low-order variations are not properly reconstructed. Given that segment-level aberrations contain low-frequency components, COFFEE cannot fully reconstruct phasing errors, and can even add low-order background phase aberrations. To theoretically investigate this effect, we reconstruct a segment-level piston error with COFFEE. To do so, we simulate in- and out-of-focus PSFs with a segment-level phase error (piston of 1 rad PV on the central segment) in the same configuration as the HiCAT Iris-AO. These PSFs are used as inputs of COFFEE to reconstruct the phase error. The results are shown in Fig. 12 . Fig. 12. Test of reconstruction of a segment-level phase error with COFFEE in simulation only: ( a ) theoretical phase to reconstruct: a 1 rad piston is applied on the central segment, ( b ) phase reconstructed with COFFEE, ( c ) difference between the two previous phases, ( d ) cross-sections of the three phases of Fig. 12 along the vertical axis. We can notice in particular the


modes first increases as the frequency is higher. It becomes maximum at 12.3 μ Hz and decreases rapidly beyond this frequency. Group C-II is composed of four frequencies above 12.5 μ Hz, which have non-consecutive radial orders. Group C-II shows an isolated high peak of about 1 mmag at 12.85 μ Hz, which is indicated by an arrow in Fig. 6 , while the peaks at the other frequencies are only about 0.2 mmag high. It might appear that the two subgroups originate from different types of modes because the amplitude distribution is clearly different between them. With the assumption of m = −1 and the rotation frequency of 14.9 μ Hz (cf. Table 2 ), we may estimate the spin parameters of the frequencies in group C-II to be 12.9 and above, which is consistent with those of Rossby modes with k = −3 (cf. Fig. 1 ). However, we reject this mode identification of group C-II because we fail to construct the diagram with k = −3 that shows clear alignment of points on a straight line (or a smooth curve), in sharp contrast to Fig. 5 . We thus regard all of the frequencies in group C as those of Rossby modes with m = −1 and k = −2. Still, we do not understand why the amplitude structure of these modes changes suddenly around 12.5 μ Hz. If the amplitude is determined by the mode visibility alone, the envelope of the amplitude in group C-I should extend as far as about the rotation frequency of 14.9 μ Hz (cf. Saio et al. 2018 ). The reason for the isolated peak at 12.85 μ Hz also needs to be explained. While we assume that the amplitude is controlled by the physical mechanism of mode excitation and damping, the problem needs to be discussed in more detail in a separate study. We finally note that the similar amplitude distribution of Rossby modes can also be found in other stars, including KIC 3448365 and KIC 9480469 , the spectra of which are shown in Fig. A2 of Saio et al. (2018) . Fig. 6. Lomb-Scargle periodogram of KIC 3240967 around frequencies of group C. The vertical dotted lines indicate the extracted frequencies given in Table A.1 . 4.2. KIC 12066947 We analysed another γ Dor star, KIC 12066947 , based on the diagram. The amplitude spectrum of the star is shown in Fig. 7 , and the extracted frequencies are listed in Table A.2 . These frequencies were obtained by the method described in Antoci et al. (2019) , and are found in five groups, which we refer to as groups U-0, U-1, A, B, and C in the order of frequency. Group B between 26 and 38 μ Hz consists of Kelvin g -modes with m = 1, and has been analysed in Christophe et al. (2018) and Paper I. On the other hand, group A between 19 and 25 μ Hz can be identified as Rossby modes with m = −1 and k = −2, as in Van Reeth et al. (2016) . We note that in contrast to Christophe et al. (2018) , we find the peaks between 56 and 69 μ Hz (group C) to be statistically significant. This is because after more detailed analyses, we discovered that using only data from the quarters Q10–Q17, hence removing Q0 and Q1 due to


of Δ s as a function of time and Mach number. Using the driving routines from Federrath et al. ( 2010 ), we ran an additional M = 3.3 hydro simulation with 50% of the energy in compressible modes, and again found a good fit to the PDF and Δ s evolution with s 0 = 0.7 and Equation ( 7 ) unchanged. Thus τ ev is independent of M and the same for mixed and solenoidal driving, and for all cases it is significantly less than τ eddy . In fact, over the s ≈ s * ± 2 range in which we have made our measurements τ ev ( s ) varies from ≈ τ eddy /4 to ≈ τ eddy /12. Meanwhile, the effect of the Mach number is to increase the width of the PDF and shift its peak as required by mass conservation. 4. Gravity and Star Formation Calculating the rate at which stars form requires extending the model to include gravitational collapse. Current analytic models do this by assigning a critical overdensity, s crit , above which gravity overcomes turbulent motions. In this case, the normalized star formation rate per free fall time becomeswhere φ t is a “replenishment factor” that accounts for the timescale over which the log-normal is assumed to be replenished, and the efficiency factor collapse accounts for the fraction of the mass with density larger than s crit that actually collapses. Various models in the literature make different assumptions about s crit and take s ff = 0 (Krumholz McKee 2005 ), s ff = s crit Padoan Nordlund ( 2011 ) or s ff = s (Hennebelle Chabrier 2011 ; Federrath Klessen 2012 ), calibrating collapse / φ t to direct numerical simulations. Recently, Burkhart ( 2018 ) developed a model in which the log-normal PDF was combined with a high-density power-law tail in a continuous and differentiable way, which has the effect of leading to higher star formation rates for lower power-law slopes, as seen in observations and simulations. This behavior also arises naturally through a simple extension of our Markov model. If we approximate each perturbation as a constant density sphere collapsing from rest from a large initial radius, conservation of energy gives ds/dt = (24 πGρ ) 1/2 . Adding this term to Equation ( 6 ), we arrive at a Langevin equation that describes supersonic, isothermal turbulence including self-gravity:where , and are dimensionless such that and are purely a functions of is the virial parameter with R and M the cloud radius and mass, and is the turbulent driving scale in units of the cloud radius. In the left panel of Figure 3 , we compare the results of this modified Langevin equation with full three-dimensional gravoturbulent simulations (Kritsuk et al. 2010 ). These simulations drive turbulence to a steady state with and a corresponding log-normal distribution with σ s = 1.73, and then “turn-on” the force of gravity abruptly with t ff,0 = 0.7 τ eddy . Figure 3. Left panel: comparison of the Markov results from Equation ( 9 ) with numerical results for the evolution of the PDF of isothermal supersonic turbulence plus gravity. Each


at ∼0.1 arcsec, as illustrated in Fig. 14(d) . Below R ∼ 0.05 arcsec, the effect of absorption becomes very important and complicates the picture, however with no significant impact on the present argument. We checked that this result remains true when considering only one quadrant (north-west, south-west, north-east, or south-east; see Fig. A2 of the appendix) of the sky plane. A natural interpretation of these results is to make the line width, rather than the wind velocity, responsible for the production of large Doppler velocity wings. As thermal broadening cannot produce such large line widths, turbulence must be invoked. The picture would then be of a shell surrounding the zone where stellar pulsation dominates and extending up to ∼10 au, hosting a very turbulent regime. Indeed, such a possibility was mentioned earlier by Kamínski et al. ( 2016 ) in relation with the possible presence of very broad AlO line profiles. According to the standard picture of acceleration by transfer of momentum from dust grains to molecules of gas (Höfner Olofsson 2018 ), this is a region that hosts important shocks. At 10 au, the escape velocity from one (two) solar masses, values commonly accepted for Mira A, is ∼13 (19) km s −1 and the density is such that the velocity acquired by a gas molecule after its interaction with a dust grain is immediately thermalized. Such important turbulence has been observed in a different context by Falgarone Phillips ( 1990 ) and discussed by Gillet et al. ( 1998 ) in the case of pulsating stars. If such a scenario were confirmed, it would require revisiting in its context the cases of the other mentioned AGB stars, L 2 Pup, EP Aqr, and R Dor, which is, however, beyond the scope of this work. In the same spirit of seeking a description of high Doppler velocity wings in terms others than a simple acceleration of the wind, Homan et al. ( 2018a ) have suggested a possible contribution of inelastic collisions in a mixed granular particle fluid. They were first, to our knowledge, to underline explicitly the need for a reliable description of such high-velocity wings and for an explanation of their relative importance in SiO emission with respect to CO emission Finally, we note that the models used by Wong et al. ( 2016 ) and Khouri et al. ( 2018 ) fail to reproduce the large Doppler velocities displayed in Fig. 14 . Indeed, these models do not account for important turbulence. If important turbulence is present between 5 and 10 au from the star, causing a broadening of the SiO line profile at the level of 20 km s −1 full width, this raises the question of the validity of models that ignore it at shorter distances and may significantly impact the conclusions reached by Wong et al. ( 2016 ) and Khouri et al. ( 2018 ) in the close neighbourhood of the star. 9 SUMMARY AND CONCLUSIONS The above study of the morpho-kinematics of the circumbinary envelope of the Mira AB pair at distances between ∼100 and ∼350 au from the stars


ρ instead. aswith B ∥ being the LOS component of the magnetic field. Beck et al. ( 2003 ) derived how an (anti)correlation between ρ and B changes this measurement of the mean magnetic field strength, which is exact for uncorrelated fields. For anticorrelated fields Equation ( 4 ) underestimates the true LOS B . This effect can be observed in Figure 4 (c), where the mean PDFs of the LOS B x (over the 512 2 available LOSs) are shown. With increasing anticorrelation from , , , , to the derived values of 0.1640(8), 0.1589(12), 0.1584(12), 0.1558(8), and 0.1533(11), respectively, deviate further from the real value 0.1667. More strikingly, the PDF of is much more peaked with a standard deviation of 0.058(3) compared to , , , and with 0.103(5), 0.104(4), 0.125(12), and 0.116(5), respectively. 3.4. Supersonic Simulations The supersonic simulations , , and exhibit a very similar behavior to their subsonic counterparts. All of the simulations reach a stationary regime after ≈2.5 T with the same , but different of 2.84(13), 1.96(19), and 1.62(7), respectively. Again, a higher for similar in the saturated regime implies less-effective magnetic field amplification in the case. Similarly, the ratio of compressive versus rotational power in the kinetic energy spectrum decreases from to to . However, the differences are less pronounced compared to the subsonic regime given that there is overall more power in compressive modes as expected from the supersonic regime. The dynamical alignment between velocity and acceleration field in the supersonic regime is virtually identical to the corresponding subsonic simulations shown in Figure 3 (b). Quantitative differences between both regimes are first observed in the ρ – B correlation, as illustrated in Figure 4 (d). and exhibit virtually no correlation with correlation coefficients of 0.04(5) and −0.09(7) whereas still shows a weak anticorrelation with a coefficient of −0.23(3). The logarithmic density PDFs of the supersonic simulations in Figure 4 (e) follow the same trend observed in the subsonic simulations. With decreasing power in the acceleration field the PDFs get a more pronounced negative skew. Finally, derived LOS magnetic field strength measurements are again systematically affected as shown in Figure 4 (f). The derived value in the simulation of 0.630(12) is closest the real value of 2/3 and the PDF is most peaked with a standard deviation of 0.229(17) whereas and underestimate the magnetic field strength with 0.562(19) and 0.544(15), respectively, and generally broader PDFs with deviations of 0.39(2) and 0.46(4), respectively. 4. Discussion 4.1. Unrealistic Large-scale δ-in-time Forcing While the idea of a δ -in-time forcing is appealing on first sight due to its random, uncorrelated nature, we argue that it is unrealistic for two reasons. First, no large-scale process (on some length scale L p ) in nature evolves instantaneously. 8 8 Small-scale processes, such as energy injection from supernovae


to estimate the host-galaxy reddening and preferred dust extinction law. First, following Goldhaber et al. (2001) , we measured the stretch factor s that multiplies the temporal axis of the light curve providing the best match of the Hsiao et al. (2007) SN Ia template to the observations. In our case, we restricted the fit to the first 15 days, to avoid the dependence of the light curve on secondary parameters and the light excess detected for SN 2016hnk at later times, and obtained an s = 0.59 ± 0.04. The modified decline rate Δ m 15, s ( B ) is then defined as the magnitude difference between the peak and the reference epoch, 15 days × s (measured in the template), divided by the s factor [Δ m 15, s = , which in our case is = = 1.803 ± 0.200 mag. The measured value of Δ m 15, s ( B ) determines the theoretical model from Höflich et al. (2017) that is used as a reference to correct the B - and V -band light curves, the B versus ( B − V ) and V versus ( B − V ) diagrams, and the ( B − V ) evolution of SN 2016hnk. In the CDMagic fit we fixed the to the value previously obtained with SN OO P Y and the distance modulus measured from the assumed cosmology ( μ = 34.195 mag), and only left as free parameters E ( B − V ) and R V . While the color excess is estimated from the shift between the uncorrected (as observed and Milky Way dust-corrected) and the corrected points that best match the template, the R V is measured from the direction of this shift in the color-magnitude diagrams. In Fig. 9 we show, as an example, the absolute V and vs. B − V diagram, including a number of SNe Ia from the Carnegie Supernova Project I (CSP-I; Krisciunas et al. 2017 ) and the 1991bg-like SN Ia 2005ke (empty triangles) for reference, models from Höflich et al. (2017) with different stretch factor (green lines), and SN 2016hnk data before (blue) and after corrections (red). We obtained an E ( B − V ) of 0.45 ± 0.08 mag, consistent with previous methods, and an R V = 2.1 ± 0.6, which we use hereafter; however, we note that our results are not significantly dependent on the particular choice of R V . Fig. 9. Representative panel for the CDMagic method, where a simultaneous fit in the B - and V -band light curves, the B vs. ( B − V ) and V vs. ( B − V ) diagrams, and the ( B − V ) evolution, is performed. More details are given in, for example, Fig. 13 in Höflich et al. (2017) . We show the absolute V -band vs. ( B − V ) diagram populated with eight normal SNe Ia from the CSP-I ( Krisciunas et al. 2017 ; SNe 2004ef, 2005eo, 2005el, 2005iq, 2005ki, 2005M, 2006bh, 2006D; in differnet symbols), the SN Ia 1991bg-like 2005ke (empty triangles), and the uncorrected (blue) and corrected (red) SN 2016hnk data points. Models from Höflich et al. (2017) are shown in green for reference; the two arrows are the reddening vectors representing the direction to which the data points are shifted when affected by R V = 3.2 and R V = 1.0. SN 2016hnk corrected data points lie on top of the


spiral-wave wind is here defined as the ejecta computed with the Bernoulli criterion discussed in Section 2.4 , and computed at times after which the dynamical ejecta have saturated. Table 4 Summary Table of the Spiral-wave Wind Properties of Long-lived Remnants Note. The columns contain the following information, starting from the left. Equation of state, mass ratio, available resolutions, inclusion of subgrid turbulence, time of the simulation end, mass of the spiral-wave wind, mass-loss rate via spiral-wave wind, mass-averaged electron fraction, terminal velocity, and finally rms angle for spiral-wave wind. For these four quantities we give the mean value among the resolutions and 1 σ deviations. For binaries for which only one resolution is present, the error is assumed to be 20% of the value. Figure 9 shows the total unbound mass of the wind as a function of time. The wind is monitored after the mass flux of the dynamical ejecta (computed according to the geodesic criterion) has saturated. Mass outflows due to the spiral-wave wind continue throughout the duration of the simulations with no indication of saturation. Indeed, while injection of mass and angular momentum from the high-density core of the remnant into the disk decreases with time as the system becomes more stationary, the mass ejection is expected to continue for as long as the spiral waves persist. Because the m = 1 modes are not efficiently damped (Paschalidis et al. 2015 ; Radice et al. 2016a ; Lehner et al. 2016b ; East et al. 2016a ), the ejection can in principle continue for the timescales that the system needs to reach equilibrium or to collapse to a BH (Section 3 ). Figure 9. Cumulative mass of the spiral-wave wind from long-lived remnants. The wind persists on timescales of ms with mass fluxes ∼0.33–1.23 M ⊙ s –1 . The largest wind masses are obtained for asymmetric binaries such as BLh q = 1.67 and LS220 q = 1.4, which in about ∼50 ms unbind ∼0.02 M ⊙ at a rate of ∼0.5 M ⊙ s –1 . We find that models with softer EOS achieve higher mass flux at lower mass ratios, i.e ., the mass flux of BLh* q = 1.66 is achieved by LS220* with q = 1.22. This might be attributed to softer EOS models having a stronger m = 1 mode in the remnant (see Section 7 ). However, if these remnants collapse, the spiral-wave mechanism shuts down and the outflow terminates. Thus the total mass ejected via spiral-wave wind depends directly on the lifetime of the remnant in addition to the binary parameters, EOS, and mass ratio. Thermal effects play an important role in determining the outflow properties, because high thermal pressures result in more extended disks with material that is easier to unbind. The highest temperatures in our simulations are found for the BLh EOS. On longer timescales than those simulated, the spiral-wave wind from the remnants with stiffer EOS might be larger, also in relation to the larger disk masses (Section 3 ). Overall, the spiral-wave wind from the long-lived remnant


or the ansae (symmetric enhancements at the ends of the stellar bar) observed in the inner bar. Fig. 1 shows a 3.6 m S 4 G image of NGC 1291 where these stellar structures are visible. Figure 1. S 4 G 3.6 m images of NGC 1291. The left-hand panel shows the main outer structures described in Section 2 , i.e. the outer ring, outer disc, lens, and outer bar. The blue square represents the MUSE 1 arcmin × 1 arcmin field of view. The right-hand panels show a zoom-in (upper panel) and contour (lower panel) images highlighting the central photometric structures, i.e. inner disc, inner bar, and central bulge. They correspond to the actual field of view observed with MUSE, which is slightly offset with respect to the centre of the galaxy. North is up and East is left. 3 TIMER OBSERVATIONS OF NGC 1291 The TIMER project is a survey employing the MUSE integral-field spectrograph to study the central 1 arcmin × 1 arcmin of a sample of 24 nearby ( d 40Mpc) barred galaxies with nuclear rings and other central structures such as nuclear spiral arms, inner bars, and inner discs (see Paper I ). One of the project’s main goals is to study the star formation histories of such structures to infer the cosmic epoch of the formation of the bar and the dynamical settling of the main disc of the host galaxy. The methodology was demonstrated with a pilot study of NGC 4371 (Gadotti et al. 2015 ). The corresponding observations of NGC 1291 were performed during ESO Period 97 (2016 April to September) with a typical seeing on the combined data cube of 1.1 arcsec (spaxel size = 0.2 arcsec), mean spectral resolution of 2.65 Å (full width at half-maximum), and spectral coverage from 4750 Å to 9350 Å. NGC 1291, being one of the closest galaxies in the TIMER sample, the MUSE 1 arcmin × 1 arcmin field of view (FoV) corresponds to a (almost) square region of ≈2.5 kpc on a side (i.e. 1 arcsec corresponds to 42 pc). The MUSE pipeline (version 1.6) was used to reduce the data set (Weilbacher et al. 2012 ), correcting for bias and applying flat-fielding and illumination corrections, as well as wavelength calibration. The exposures were flux-calibrated through the observation of a spectrophotometric standard star, which was also used to remove telluric features. Dedicated empty-sky exposures and a PCA methodology were employed to remove signatures from the sky background. Finally, the exposures were also finely registered astrometrically, so that the point spread function of the combined cube is similar to that in individual exposures. More details can be found in Gadotti et al. ( 2018 ). 3.1 Stellar kinematics The fully reduced data cube was spatially binned using the Voronoi scheme of Cappellari Copin ( 2003 ) to achieve a signal-to-noise ratio of approximately 40 per pixel on each spatial bin. We used the penalized pixel fitting ( ppxf ) code developed by Cappellari Emsellem ( 2004 ) to extract the stellar kinematics from the binned spectra, masking emission lines and using the


net yield of the chemical element X per stellar generation, y X , and the yield of X from Type Ia SNe, m X , Ia . Other fundamental assumptions in the model are given by the DTD for the Type Ia SN rate and the prescription for the SFR law. An observational constraint for the calibration of the gas infall history is given by the radial profile of the present-day total surface mass density, tot ( r , t G ), which is very difficult to retrieve from an observational point of view. In this work, we apply our model to reproduce the observed chemical abundance patterns at the solar neighbourhood, where r S 8kpc; hence, we normalize the infall law, as given in equation ( 12 ), by requiring the following constraint: where we assume t G 14Gyr, a single infall episode, and tot ( r S , t G )54M pc 2 , which represents the present-day total surface mass density at the solar neighbourhood (see also Micali, Matteucci Romano 2013 , which refers to the work by Kuijken Gilmore 1991 ). The best model is defined as the one capable of reproducing the observed trend of the [O/Fe] versus [Fe/H] chemical abundance pattern, which represents the best observational constraint for the chemical evolution models of the MW. Our best models are characterized by the following values of the free parameters: L 2Gyr 1 , for our best model with the linear SchmidtKennicutt law, and SFR 0 2M pc 2 Gyr 1 , for our best model with the non-linear SchmidtKennicutt law; the infall time-scale for the gas mass growth of the MW disc is 7Gyr; the mass loading factor is 0.4. Finally, the best models assume the single-degenerate scenario for the Type Ia SN rate. We remark on the fact that the predicted [Fe/H]-[O/Fe] relation in the MW is fitted by construction using fixed values for the key free parameters L (or SFR 0 ), and . It is worth noting that the values of our best parameters are in agreement with previous recent studies (see e.g. Minchev, Chiappini Martig 2013 ; Nidever etal. 2014 ; Spitoni etal. 2015 ); in particular, a typical infall time-scale 7Gyr and star formation efficiency 1Gyr 1 are necessary to reproduce also the observed age-metallicity relation and the metallicity distribution function of the G-dwarf stars in the solar neighbourhood (Matteucci 2001 , 2012 ; Pagel 2009 ). Once the best set of free parameters is determined, we fix them and explore the effects of assuming different DTDs for the Type Ia SN rate and different prescriptions for the relation between the SFR and the surface gas mass density, gas ( r , t ). In this way, we can demonstrate the flexibility of our method for solving the chemical evolution of galaxies by taking into account the major systematics in the theory. 3 THE OBSERVED DATA SET The data set for the observed [Fe/H][O/Fe] and [Fe/H][Si/Fe] relations in the solar neighbourhood is shown in Fig. 1 (a) and Fig. 1 (b), respectively, where the data from different works are drawn with different colours. Our set of data includes both MW halo stars from


luminosity of 3D H α clumps ranges from ∼10 per cent–95 per cent, while the contribution to H α luminosity from individual 3D clumps ranges from less than 1 per cent to ∼90 per cent. This large range results from the short time-scale of star formation traced by H α and thus the clumpiness of H α emission. Most individual 3D clumps contribute less than 10 per cent to total H α luminosity, while only one or two largest clumps contribute most of the H α flux. The gas in H α clumps is not bound, with virial parameters (equation 1 ) larger than 1 by orders of magnitude. 4.4 Origins of giant stellar clumps Gravitational instability can induce fragmentation of the galactic disc, thus leading to growth of clumps. Stability criterion to linear axisymmetric perturbations for gaseous discs can be described by the Toomre parameter (Safronov 1960 ; Toomre 1964 ): where κ is the epicycle frequency, σ is the velocity dispersion, and Σ is the mass surface density. A disc is unstable if Q ≲ 1. Observations (e.g. Puech 2010 ; Girard et al. 2018 ) found that clumpy galaxies are marginally stable, with Toomre Q ∼ 1. Most H α clumps in high-redshift galaxies are located in regions where Q is low (Genzel et al. 2011 ; Wisnioski et al. 2012 ; Mieda et al. 2016 ). In galaxy formation simulations (Inoue et al. 2016 ; Oklopčić et al. 2017 ) gas clumps also coincide with regions of Q 1, albeit with large scatter of Q value. Inoue et al. ( 2016 ) also found that stellar clumps coincide with regions of low stellar Q . In Meng et al. ( 2019 ) we studied the distribution of Q in our simulations, accounting for different phases of the gas and stars. Such multicomponent Q more accurately describes the linear stability criterion in realistic galaxies. We found that strong feedback from young stars disperses gas around them, leading to spatial anticorrelation of dense gas and stars up to 50 Myr old. Here we analogously find that locations of 2D UV clumps do not coincide with the regions of low Q . This is because low Q regions closely trace high gas density, while rest-frame UV clumps trace young stars. The average value of Q in 2D UV clump regions ranges from 2.1 to 3.6, which is larger than the median value of Q = 0.5–1.0 weighted by molecular gas mass in Meng et al. ( 2019 ). For H α clumps Q = 1.4–3.3 is closer to the gas values, as expected for very young stars. The discrepancy in location of gas and young stars is also seen in the simulations of Oklopčić et al. ( 2017 ), where they find that the gas clumps coincide with the location of instantaneous star formation, but not of the SFR averaged over more than 10 Myr. If clumps form out of instability of a self-gravitating disc, the wavelength of the fastest growing perturbation is The effective radius of a fully formed clump may not exactly correspond to this scale, but it can still be used as a rough guide. If we take λ T /2 for R clump , and approximate the disc rotation velocity profile as flat, then , and we obtain


within these haloes, we can quantify the expected rate of DCBH mergers that will be detectable by LISA due to SMS multiplicity. 2 NUMBER DENSITY DISTRIBUTION OF DCBHS In order to obtain the abundance of DCBH seeds, we use the results of A12, D14 and H16. We focus on two scenarios with J c = 30 J 21 1 and 300 J 21 respectively, where J c is the critical Lyman–Werner (LW) flux required to induce DCBH formation. The exact value of J c that can facilitate DCBH formation in an ACH is still unknown. What complicates the matter further is that a single value of J c is not representative of the chemothermodynamical processes that lead to the formation of a DCBH, namely the photodestruction of H − and H 2 (Wolcott-Green Haiman 2012 ; Sugimura, Omukai Inoue 2014 ; Agarwal Khochfar 2015 ; Agarwal et al. 2016 ). Therefore, we use abundance estimates from the literature and employ two values of J c as our extreme limits. In doing so, we are implicitly assuming that other process may either augment or replace the effect of an external LW field to produce similar results (e.g. streaming velocities, see Tanaka Li 2014 ; Hirano et al. 2017 ; Schauer et al. 2017 , or rapid accretion, see Yoshida et al. 2003 ). Thus, J c = 30 J 21 can be viewed as a scenario in which DCBHs are relatively common and would result in a sufficient number of massive seeds for the entire MBH population. On the other hand, J c = 300 J 21 would result in a number density of heavy seeds that could only seed a subpopulation of massive black holes (perhaps the highest redshift quasars) and can thus be viewed as a scenario where large initial mass black holes are rare. We now describe our steps going from the theoretical estimates of abundance of DCBH seeds to the observed number of events. Using the models and predictions from the redshift distributions of the newly formed DCBH seeds per unit comoving Mpc 3 found in A12, D14, H16 we calculate a ‘rate’ of formation at time-step ‘i’ in units of cMpc −3 where N new is the number of newly formed DCBH sites identified in the simulations for a given value of J c , and d V denotes the comoving volume normalization. To get the DCBH formation rate per unit time per unit redshift from any given redshift in the observer’s frame of reference (i.e. as seen at z = 0), we follow Magg et al. 2016 (equation 8) where R z is the comoving distance at a given redshift. In Fig. 1 we plot the number of DCBH seeds per unit time per unit volume i.e. equation ( 1 ), generating a fit using a second-order polynomial. The fit is obtained from the estimate for the number density of DCBHs based on J c = 30 J 21 (in blue filled circles, A12 , D14 , and H16 ), and can be written as where t is the age of the Universe at which the rate is computed. The number density of pristine ACHs scales approximately as J (D14, Inayoshi Tanaka 2015 ), hence rescaling from J c = 30 to J c = 300 requires a normalization factor of 10 −5 . This is shown using the red filled circles. The


Saturn's bow shock one of the strongest in the Solar System (e.g., Russell 1985 ), and such occasions occur under rare solar wind conditions where the near-Saturn Interplanetary (solar) Magnetic Field (IMF) strength drops to ∼0.1 nT and the shock Alfvén Mach number increases to order 100. On such occasions Cassini has witnessed electron acceleration at a quasi-parallel shock crossing (Masters et al. 2013 ), and provided evidence for shock reformation controlled by specular ion reflection (Sulaiman et al. 2015 ). The electron acceleration result indicates that there may not be an electron injection problem at high Mach number quasi-parallel collisionless shocks, in agreement with some theories (e.g., Amano Hoshino 2010 ). Here we reveal the full picture of suprathermal electrons at Saturn's bow shock revealed by Cassini . We show that the sum of all Cassini electron observations made during hundreds of shock crossings is consistent with electron acceleration theory that involves interactions with whistler waves excited by the reflected thermal electrons just upstream of the shock. The implication for the strong shocks surrounding young SNRs is that they may be able to inject thermal electrons into an acceleration process under any upstream magnetic field orientation. 2. SURVEY OF SUPRATHERMAL ELECTRON SIGNATURES AT SATURN'S BOW SHOCK The Cassini spacecraft has been in Saturn orbit since 2004 July. During the orbital tour the spacecraft has crossed Saturn's bow shock hundreds of times. The location of the shock is highly variable, and the boundary moves at speeds much greater than that of the spacecraft (Achilleos et al. 2006 ). As a result, multiple shock crossings are typically made on an inbound/outbound pass of any orbit where the spacecraft enters the region of space defined by the range of possible shock locations. Two of the sensors carried by instruments mounted on the three-axis stabilized spacecraft are particularly relevant for a survey of electron acceleration at Saturn's bow shock. The first is the Electron Spectrometer (ELS) of the Cassini Plasma Spectrometer (CAPS), which detects electrons in the (lower) energy range 0.5 eV to 26 keV (Young et al. 2004 ). The second is the Low Energy Magnetospheric Measurements System (LEMMS) of the Magnetospheric Imaging Instrument, which detects electrons in the (higher) energy range 18 keV to ∼1 MeV (Krimigis et al. 2004 ). Both ELS and LEMMS have a limited field of view (FOV). In addition, measurements of the local magnetic field vector made by the fluxgate magnetometer of the Cassini dual-technique magnetometer (MAG; Dougherty et al. 2004 ) provide an essential diagnostic of shock structure. This study is motivated by recently reported observations made by Cassini at a single (quasi-parallel) shock crossing, where suprathermal electrons were detected (Masters et al. 2013 ). The high-energy electron signature of this event is most pronounced in data taken by the more sensitive LEMMS


specified by the photon index Γ of the underlying power law. Under the assumption of isotropic emission, this provides the bolometric luminosity, L bol . We express the luminosity as the Eddington ratio: the ratio of L bol to the Eddington limited luminosity, L Edd . The latter is determined as L Edd = (2.1 ± 0.5) × 10 45 erg s −1 using a black hole mass of (14 ± 4) × 10 6 M ⊙ (Peterson et al. 2004 , see also Grier et al. 2012a ) as well as a solar hydrogen abundance of X = 0.71. The Eddington ratio's uncertainty is dominated by systematics. The relation of Zhou Zhao ( 2010 ) introduces a substantial systematic uncertainty from the spread in the observations that they employed. Including this uncertainty and the uncertainty in the Eddington luminosity, the mean 1σ uncertainty in log L bol / L Edd is 0.77. Without these systematic uncertainties, and only including the uncertainties in Γ and the 2–10 keV luminosity, the mean error in log L bol / L Edd is 0.10. As the in-band flux is well measured, the uncertainty is mostly set by the error in Γ. We are interested in the correlation between parameters of a single source, so we omit the systematics from the uncertainty reported in each data point. The systematic error would only shift the observed trends with Eddington ratio. 3 SIMPLE POWER-LAW FIT Previous analyses of these observations required a complex spectral model that includes ionized absorption at energies ≲3 keV as well as photoionized reflection (e.g. Parker et al. 2014 ; Wilkins Gallo 2015 ). Before we apply a similar detailed spectral model in Section 4 , however, we first fit the data with a simple power law. The observed correlation of the photon index Γ and the X-ray flux (Sarma et al. 2015 ), suggests that we can gain some insight into the qualitative behaviour of the source with a simple spectral model. Following Parker et al. ( 2014 ), we fit a power law to the spectra in the energy intervals 3–4, 8.5–10, and 40–50 keV. This avoids absorption at low energies as well as the Fe Kα line and the Compton hump, which are prominent reflection features. These fits provide a relatively clean look at the underlying power law. We include absorption by the Galactic interstellar medium using the Tübingen–Boulder model (Wilms, Allen McCray 2000 ) with an equivalent hydrogen column of N H = 3.6 × 10 20 cm −2 (Kalberla et al. 2005 ), and we use solar abundances as reported by Grevesse Sauval ( 1998 ). A cosmological redshift is applied (Section 2.3 ). The spectral fits are performed using xspec v.12.8.2 (Arnaud 1996 ), and all presented errors in the fit parameters are at 1σ. For each spectrum, we determine Γ and the 3–10 keV power-law flux. We reproduce the logarithmic relation of Γ and the X-ray flux with a break at higher fluxes (Sarma et al. 2015 ), which has also been observed in other AGN (e.g. Perola et al. 1986 ; Done, Madejski Życki 2000 ; Shih, Iwasawa Fabian 2002 ), and we will quantify this relation with the detailed spectral


in the downstream. In PIC simulations of nonrelativistic shocks, Bohdan et al. ( 2020 ) found similar values of while Park et al. ( 2015 ) found even more effective thermalization with . This heating via plasma processes of the thermal electrons requires to be large. In Figure 6 , we show as a dashed vertical cyan line, representing the value found by Crumley et al. ( 2019 ) (). This value of would overshoot that radio data by orders of magnitude. Observations of supernova remnants also find the ratio to be between 0.03 and 1, albeit the velocities in those cases are much lower (Ghavamian et al. 2013 ; Vink et al. 2015 ). Very small values of help alleviate the constraint on . However, small values of are problematic in the sense of UHECR acceleration. The dotted–dashed horizontal lines shown in Figure 6 correspond to minimum values of required for UHECR acceleration. They are shown for different values of the best-fit rigidities, similarly to Figure 3 . The lower limit on is calculated using aswhere is the internal energy of the downstream. The lines are plotted for completely stripped iron using acceleration efficiency (thin) and (thick). It is possible that the magnetization decreases with distance to the shock front (e.g., Lemoine et al. 2013 ), something which is not considered in the present work. Inspection of Figure 6 shows that, while , the radio flux is only weakly dependent on . Therefore, for these values of , our conclusion would not change if a varying magnetization was included. As previously mentioned, is suggested by PIC simulations (Sironi Spitkovsky 2011 ; Park et al. 2015 ; Crumley et al. 2019 ; Bohdan et al. 2020 ). The constraints shown in Figure 6 are valid for the microphysical parameters at the forward shock. In principle, the reverse shock could be different from the forward shock, which means that could be sufficiently small in the forward shock as to not overshine the radio, while large enough at the reverse shock for UHECR acceleration to be possible. As both the reverse and the forward shocks are transrelativistic, this might imply that , but this also depends on the magnetization around the two shocks, which can be different. One can estimate as follows. Assuming cosmic ray acceleration occurs during the first shell crossing of the shock, the shell crossing radius is estimated as , where is the shell width and is the central engine duration that we set equal to T 90 (Nakar Piran 2004 ). With an initial Lorentz factor of , the ratio of the ejecta density to the circumburst density is . Thus, the Lorentz factor of the downstream of the reverse shock as seen from a laboratory observer can be estimated as , where has been used (Panaitescu Kumar 2004a ; Zhang Murase 2019 ). 14 14 This approximation for is not very accurate in this case, but it has been used to show the parameter dependence. A more precise value is given by . The magnetic field is calculated as . The value of sufficient to accelerate UHECR can be


and remain the same also in the saturated stage. The PDFs in the saturated stage are more intermittent than in the kinematic stage, but the PDFs both in the kinematic and saturated stages are more intermittent for the case than for any of the cases (compare the x -axis values and the heavy tails at higher values in Figs 5a and 8c ). However, the growth rate and the structure of the magnetic fields in the kinematic and saturated stages, even for the case, are unaffected by the configuration of the seed field. The overall conclusions, even with changes in the plasma parameters, remain the same as before: the structure and strength of the seed magnetic fields do not affect the growth rate, final saturation level, shape of the magnetic power spectrum, and the statistical structure of the small-scale dynamo generated magnetic fields. Thus, the detailed properties of the seed field or even their various generation mechanisms are relatively unimportant when studying evolved magnetic fields that were amplified by the turbulent small-scale dynamo. 4 DISCUSSION From our results, we show that the seed magnetic field information is lost (within a few eddy turnover times, as seen in Figs 2a , 6a , 7a , and 8a ). Then, the dynamo-generated magnetic field reaches a statistically similar state for all three seed fields, which is determined by the properties of the turbulence (such as Re and ) and magnetic resistivity (or equivalently Rm). This also shows that the small-scale dynamo is very efficient in amplifying (given that Rm is greater than its critical value, Rm (crit) ) any non-zero seed field. 4.1 Small-scale magnetic fields generated by the tangling of the large-scale field If Rm Rm (crit) , the small-scale dynamo is inactive. However, for the case with non-zero mean seed field (UniRm100), small-scale magnetic fields can still be generated by the tangling of the large-scale (or mean) uniform seed field (see appendix A in Seta et al. 2018 , for discussion on various mechanisms by which small-scale magnetic fields can be generated). Such a mechanism is only applicable in systems, such as spiral galaxies, where the large-scale field is maintained by other processes, i.e. α − Ω large-scale dynamo (Krause Rädler 1980 ; Shukurov Sokoloff 2008 ; Chamandy et al. 2014 ) or cosmic ray driven dynamo (Parker 1992 ; Hanasz et al. 2004 ). In our simulations, the large-scale uniform field is maintained at all times because the MHD equations (equations 1 – 4 ) preserve the net seed magnetic flux in a triply periodic numerical domain. We demonstrate the growth of small-scale magnetic fields by the tangling of the uniform seed field in Fig. 9 by choosing Rm = 100 Rm (crit) (≈165). In Fig. 9(a) , we show the evolution of magnetic and turbulent kinetic energies for models with all three seed field cases (UniRm100, PLRm100, and ParRm100). The magnetic energy only grows (linearly) for the case UniRm100 and decays for the other two cases (PLRm100 and ParRm100). Figure 9. Same


11 . For the most massive bin, the HSE mass is biased low at a constant level of about 24%. This bias drops with decreasing halo mass, with the mean bias in the radial range being , and 10% for the three lower-mass bins. These findings are in good agreement with the HSE mass biases for halos found in previous NR simulations (Kay et al. 2004 ; Nelson et al. 2012 ). Here we have assumed full information on both the density and temperature profiles in Equation ( 9 ). Incomplete knowledge on either of these quantities has the potential to further bias the HSE estimate. Figure 11. Bias between the HSE mass estimate and simulation mass at z = 0. Each line traces the median relation, with the red (black) error bars showing the 25th and 75th percentiles of the highest-mass (lowest-mass) bin. We show the result down to only , as the relation becomes dominated by noise on smaller scales. We can obtain a better understanding of the HSE mass bias by measuring the nonthermal pressure for each individual halo. Following Battaglia et al. ( 2012a ), we focus here on bulk flows, which should capture the major contribution to nonthermal support. We compute the corresponding kinetic pressure based on mass-averaged velocity fluctuations:The velocity fluctuations are made with respect to the baryon center of mass, , and mass-averaged velocity, , within R 200 :The resulting kinetic pressure profiles are shown in Figure 12 as the fraction of the total pressure. These are compared to the fitting function from Battaglia et al. ( 2012a ), which is based on the Shaw et al. ( 2010 ) power-law fitting function with an additional mass dependency that scales as . Figure 12. Fraction of the kinetic pressure with respect to the total (kinetic plus thermal) pressure for each of the four mass bins in the NR run at z = 0. The light-shaded solid lines trace the fitting function from Battaglia et al. ( 2012a ), which is based on power-law slopes of 4/5 in radius and 1/5 in mass. The fitting function is computed using the median halo mass in each bin. We show the 25th and 75th percentiles of the highest-mass (lowest-mass) bin as the red (black) error bars. The fitting function does a good job at matching our simulation results for but dramatically underestimates the kinetic pressure on smaller scales. In this case, a broken power law with a shallower slope on small scales would be more appropriate. We expect the NR results to be accurate for since bulk flows on these scales will be gravitationally sourced and mostly unaffected by cooling and feedback processes occurring on smaller scales (Battaglia et al. 2012a ; Nelson et al. 2014 ). Indeed, the fitting function in Figure 12 was calibrated against simulations with cooling and feedback. Earlier works have shown that kinetic pressure is greater in less relaxed systems that have undergone recent major mergers (Jeltema et al. 2008 ; Piffaretti Valdarnini 2008 ; Lau et al. 2009 ; Nelson et al. 2014 ). The rise of the kinetic


the same procedure as used for generating the LAXPC PDS. NuSTAR observations of 2015 October 22 show a single broad peak at ∼1 mHz with 1024 bins per interval, whereas two clearly resolved peaks at ∼1 and 2 mHz are visible in the PDS with 512 bins per time interval. In the NuSTAR PDS of 2015 October 30, QPO peaks at ∼1 and 2 mHz are detected using 1024 bins as well as 512 bins per interval. We have, therefore, used 512 bins per interval for both of the NuSTAR observations to generate PDSs, as shown in Figure 5 . The NuSTAR PDS of 2015 October 30 also shows the presence of 12 and 27 mHz QPOs with a coherence factor and rms (%) of 8 and 3% and 4 and 3%, respectively. A summary of the characteristics of the ∼1 mHz and ∼2 mHz QPOs from LAXPC and NuSTAR are presented in Table 3 . Figure 5. PDSs (in the units of (rms mean −1 ) 2 Hz −1 ) of 4U 0115+63 obtained for the outburst from NuSTAR in the 3–79 keV energy band ((a), (e)). PDSs in the 3–80 keV energy band of LAXPC 10 (b), 20 (c), and 30 (d). Arrows indicate ∼1 mHz and ∼2 mHz QPOs in the PDSs of NuSTAR and LAXPC detectors. Table 3 Summary of the Characteristics of the ∼1 mHz and ∼2 mHz QPOs Observed from LAXPC and NuSTAR To investigate the energy dependence of the QPO characteristics, PDSs were extracted in the 3–15, 15–30, 30–50, and 50–80 keV bands for each of the LAXPC units. This was achieved by extracting data from Layer 1 for 3–15 keV, Layers 1 and 2 for 15–30 keV, and Layers 1–5 for the 30–50 and 50–80 keV energy bands. PDSs in the units of (rms mean −1 ) 2 Hz −1 are generated with 10 s binning and by subtracting Poissonian noise. Prominent QPOs are observed at ∼1 mHz and ∼2 mHz in the energy bands up to 50 keV. Above 50 keV the 1 mHz and 2 mHz QPOs are insignificant. Details of QPO characteristics like frequency, rms amplitude, and quality factor are summarized in Table 3 . The coherence factor ( ν / δν ) lies in the range 7.6–11.1 for the ∼1 mHz QPO and 2.8–6.0 for the ∼2 mHz QPO, respectively. It can be observed from Table 3 that the coherence factor of the ∼1 mHz QPO decreases from 3–15 keV to 15–30 keV and then increases at higher energies. rms amplitude (%) of the ∼1 mHz QPO increases from 3–15 keV to 15–30 keV and then decreases at higher energies. It may be noticed that the coherence factor increases with energy for the ∼2 mHz QPO and rms amplitude (%) of the ∼2 mHz QPO increases until 30 keV and then decreases at higher energy. 3.1.1. ∼1 mHz and ∼2 mHz QPOs from <italic>RXTE</italic>/PCA Observations PCA/ RXTE Standard 1 mode light curves (10 s binned) in 2–60 keV, generated using the FTOOLS task “lcurve” in HEASOFT for of all of the observations showing ∼mHz QPOs, are presented in Figures 6 (a), (b), and (c). It may be noted that during the 2004 observation, three PCUs were on, while in 2008 observations two PCUs were on, and the count rates in the figures reflect this. In the 2011 light curve in Figure 6 (c), the jump in the count rate in the middle of the light curve is not


data. Section 3 shows an example of SIR and presents the identification criteria for SIRs and shocks. Section 4 presents the statistical distributions of the properties of SIRs and their associated shocks, and compares the results with those at 1 au. The last section concludes with a summary of the contributions. 2. <italic>MAVEN</italic> Data The MAVEN spacecraft carries nine sensors that measure the solar wind and the plasma and neutral environment at Mars. In this work, we use data from the following three instruments: Solar Wind Ion Analyzer (SWIA; Halekas et al. 2015 ), Magnetometer (MAG; Connerney et al. 2015 ), and Solar Wind Electron Analyzer (SWEA; Mitchell et al. 2016 ). SWIA is an electrostatic analyzer that measures 3D distributions of ions from 25 eV to 25 keV. When MAVEN is in the solar wind, SWIA provides the solar wind parameters with a cadence of 4 s. MAG measures the three components of magnetic field with 32 Hz cadence. We use 4 s resolution MAG data that are extracted from the full resolution measurements and are in one-to-one correspondence with SWIA data. SWEA provides the energy and angular distributions of 3–4600 eV electrons with 2 s time resolution. We utilize the MAVEN data in Mars Solar Orbital (MSO) coordinates, in which X points from Mars toward the Sun, Y points in the opposite direction of the Mars orbital velocity component perpendicular to X, and Z completes the right-handed system. 3. Observations of an SIR during 2016 August 2–3 Figure 1 shows solar wind plasma and magnetic field data from MAVEN during 2016 August 2–3 encompassing a typical SIR event. The SIR is clearly identified by the signatures including a compression of IMF ∣ B ∣, an increase of proton speed V p , an increase of proton number density N p , an enhancement of proton temperature T p , and a significant enhancement of total perpendicular pressure P t (e.g., Guo et al. 2015 , 2016 ; Wang et al. 2018 ). P t is defined as the sum of the magnetic pressure and plasma thermal pressure perpendicular to the magnetic field (Gosling et al. 1987 ). Note that SWIA does not have the capability to discriminate ions based on mass, and thus the plasma parameters are calculated assuming that all ions are protons. SWEA does not provide direct measurements of solar wind electron temperature and density. In the calculation of P t , the electron contributions are not included and the proton temperature is assumed to be isotropic. An SI in the SIR, characterized by a decrease in proton density and a simultaneous increase in proton temperature, can be discerned at about 13:25 UT on August 2. A pair of forward–reverse shocks bounding the SIR are observed at about 03:44 UT on August 2 and at about 07:37 UT on August 3 respectively. Figure 1. MAVEN observations of an SIR at 1.52 au during 2016 August 2–3. From top to bottom: the MAVEN spacecraft altitude, pitch angle distributions of electron (∼282 eV), electron energy spectra, ion energy spectra, proton speed ( V p


difference in realization may cause a bigger difference in the mass evolution (however, still very small) than using the same realization but with a different code. Figure 7. Comparison of models performed with different N -body codes. The blue and orange lines are the differences in the remaining bound masses between models 18 and 19 on one hand (performed with φ grape and ph4 , respectively) and 17 on the other (performed with nbody6++ ). The light green lines are similarly the differences between models 17A and 17B on one hand and 17 on the other that only differ in random seed. These models are in our weak tidal field eccentric orbit and have N = 10 5 stars. No gravitational softening was used. The small and seemingly random residuals indicate that there is no systematic difference in these models. Despite the differences between nbody6++ , φ grape , and ph4 , we find that the evolution of N = 10 5 clusters in weak tidal fields is nearly identical from one code to the next. 3.3 Softened models Gravitational softening is a technique to ease the computation of N -body simulation. In ‘Plummer’-type softening, the gravitational force between two bodies is modified from ∼ r −2 to ∼( r 2 + a 2 ) −1 , where a is called the softening length. For r ≫ a , the modified force approaches the true Newtonian force, but otherwise it approaches a constant. This hinders the formation of bound systems on scales ≤ a which otherwise have small time-steps and are difficult to integrate unless a regularization technique is used. Modifying the gravitational force in such a way has implications for hyperbolic encounters as well, the effect is decreasing the Coulomb logarithm and thus increasing of the two-body relaxation time. 3.3.1 Model with <italic>N</italic> = 105 Model 22 is the softened equivalent of model 17 presented in Section 3.1 . The two models evolve in a very similar way, and most quantities (total mass-loss, Lagrange radii) match when 17 is ‘slowed down’ by a factor of 1.18. Between 0.2 and 5 Gyr (roughly the time of the core collapse), model 17 experiences 461 kicks and 8593 sweeps, while model 22 experiences 129 kicks and 6620 sweeps. The softer potential causes a significant reduction in the number of kicks (as expected given the treatment of close encounters) and a moderate reduction in the number of sweeps. 3.3.2 Model with <italic>N</italic> = 106 Model 6 is the softened equivalent of model 1 presented in Section 3.1 . It behaves unexpectedly. While it is similar to model 1 , one would expect a somewhat lower mass-loss rate due to the gravitational softening, as seen when comparing models 22 and 17 . However, the result is the opposite. The difference in kick rate is especially stark: Between 0.2 and 5 Gyr, model 1 experiences 558 kicks and 14 530 sweeps, while model 6 experiences 5369 kicks and 16 607 sweeps. This ∼tenfold increase in the kick rate (as opposed to a decrease by a factor of 3.6 when softening is added in


an sGRB that can be observed along its axis. This successful jet with its cocoon, which is sometimes called the “structured jet,” is scenario E in Figure 2 of Mooley et al. ( 2018b ), and it is similar to the one considered by Lazzati et al. ( 2018 ) and Margutti et al. ( 2018 ). In the second simulation the jet is launched for a short duration and is choked before breaking out of the ejecta. In both cases the cocoon does not affect the UV/optical emission on a timescale of half a day, but we show that the shock breakout of the successful jet can potentially generate the γ -ray signal (Figure 4 ). In both simulations there are afterglow parameters (ISM density and microphysics) for which the observed radio and X-ray emission is produced as shown in Figure 3 . Figure 4. Shock breakout γ -ray light curve (top panel) and spectrum (bottom panel) from the successful jet simulation. The blue thin line is the spectrum during the peak, while the red thick line is the spectrum during the tail. 4. Was There a Relativistic Jet in GW170817? A relativistic jet is necessary to produce an sGRB. Therefore, the question whether a relativistic jet can successfully break out of a neutron star merger ejecta and in particular whether a jet broke out in this event is interesting. In GW170817 we consider the option of a successful jet as possible but less likely. First, it does not explain the early optical light. Second, and more importantly, to explain the observed radio emission, either the jet should be much weaker than the cocoon, so that its contribution is unimportant, or it should be so powerful that its contribution begins only at very late time, at least months after the merger. Without fine-tuning, the jet is not expected to have much less energy than the cocoon (Nakar Piran 2017 ), while a very powerful jet produces a very luminous sGRB, and these are known to be extremely rare (Nakar 2007 ; Wanderman Piran 2015 ). However, this is only circumstantial evidence. Unfortunately, a weak successful jet does not contribute to the observed emission, and therefore we may never know whether it existed or not. A powerful jet, however, might be detectable. If it is powerful enough, it may be detectable while being still off-axis. In that case the radio light curve should rise sharply and then decline as a power law, after a short plateau. This unique prediction of the jet signature is the easiest to identify. A less powerful jet may contribute to the radio light curve, but its contribution may not be easily identified (see, e.g., Figure 3 and Lazzati et al. 2018 ; Margutti et al. 2018 ), since a continuous rise to a peak followed by a decay can arise either from a successful or from a choked jet (see Figure 3 and Nakar Piran 2018 ). Additional information, especially in the radio near the time that the afterglow flux peaks, may provide the key to resolve this question. First, the radio image of the source is expected to be resolved soon. Figure 5 shows the images