could be directly understood from the second term on the RHS of Eq. ( 34 ). Also the damping due to the plasma resistivity is clearly shown by the presence of the third term on the RHS of Eq. ( 34 ). Since the viscosity is small for coronal conditions, the deceleration is not very strong in the long wavelength limit, but in the long run would gradually become significant. 3. Discussions and conclusions In the solar atmosphere MHD waves interact with the plasma. When a gradient in the density is present, a wave guide is created that guides waves leading to the appearance of collective modes. In this work a magnetized cylindrical structure whose density is higher than its surroundings has been taken into consideration. The interplay of the equilibrium twist and rotation exhibits interesting features of the nature of the torsional wave that are of interest for coronal seismology. We considered a twisted and rotating magnetic flux tube, which resembles a solar spiral or tornado, and studied the influence of its helical properties on other dissipating parameters linked to the oscillations of the torsional waves. The analytic expressions obtained for the dependence of the phase speed of the torsional wave on the equilibrium twist and rotation enabled a quantitative study of the interplay of various actors on its propagation. The comparison of the explicit expressions obtained for the phase speed of the torsional wave in the present study with the implicit version, in all cases proved adequate for the robustness of the explicit expressions. This is reflected in the figures where the numerical results are compared with analytic solutions. The full dispersion relation for axisymmetric oscillations in the long wavelength limit has been obtained by showing the joint effects of the equilibrium twist and rotation with the viscosity and gravity (Eq. ( 19 )). An explicit expression for the dependency of the torsional wave frequency in the presence of viscosity, equilibrium, and environmental conditions on the wave number has been obtained (Eq. ( 20 )). This explicit dispersion relation also gives the damping and deceleration of the torsional wave guided by solar plasma structures. The fine consistency between the full dispersion relation and the explicit expressions for the frequency, damping, and speed of the torsional wave justifies the model and results. The magnetic twist owes its efficiency on the torsional wave frequency to not only the flux-tube rotation and coronal conditions, but also to the viscosity and gravity. In a zero plasma- β structure that is non-rotating, the magnetic twist acts very weakly on the torsional wave frequency (Fig. 3 ). If in such conditions the viscosity and solar gravity become negligible, the magnetic twist, no matter how large, would be completely neutral without any effect on the frequency. The damping of the torsional wave due to viscosity in solar structures is proportional to the strength of the magnetic twist and


refer to φ w = 6 V, hν = 10.29 V (for λ ν = 121.57 nm), T d ≈ 205 K (for latitude θ = 70°), and non-thermal photoelectron distribution with A = 0.1. The parameter q is observed to increase with φ o . It is also noticed that the effect of dust charge fluctuation on the wave dispersion is pronounced for small z o values; for instance, q > 1 for z o = 30 and φ o > 0.2 (Fig. 5a ) and for φ o = 1.0 and z o 104 (Fig. 5b ). The positive plasma potential φ o infers enhanced population density of the photoelectrons in the vicinity compared to the case φ o = 0; this may induce additional shielding to the floating dust particles and effectively reduces the coupling between charged dust particles. It may result in a decrease in the phase speed and frequency of the propagating DA wave. This nature has been depicted in Figs 5(c) and (d) . The calculations corresponding to non-zero φ o are of significance to the lunar exospheric plasma, which exhibits a photoelectron sheath with a positive potential and varies with the altitude. Another interesting point evident from the wave dispersion (Figs 2 – 5 ) is the occurrence of a cut off with z o , Δ, and φ o for which ω r takes imaginary values, and it refers to a damped wave solution for the excited DA modes. Figure 5. (a) and (b) ( top panel ): Parameter q A = [(Λ ch /Ω ch ) n de ] A and (c) and (d) ( bottom panel ): wave dispersion ( ω r / k ) in long-wavelength regime ( kλ e 1) for the non-thermal distribution of photoelectrons. Left-hand and right-hand columns refer to parameters’ variation with φ o and z o , respectively. The calculations refer to the parameters φ w = 6 V, hν = 10.29 eV, T d ≈ 205 K, and A = 0.1. The black (solid), red (dash), green (dot), blue (dash–dotted), magenta (dash–dot–dotted), and brown (short dash) in the left -hand and right-hand columns correspond to the magnitude of the varying parameter z o = 30, 50, 100, 150, 200, and 250, and φ o = 0.1, 0.5, 0.8, 1.0, and 1.2, respectively. As understood from the discussion, the significant coupling between floating dust and electrons within the photoelectron sheath is a favourable condition for generating such low-frequency DA modes on the sunlit locations, and these physical conditions strongly depend on dust charge z o and constituent sheath plasma parameters (i.e. density and potential). It is of interest to comment on the influence of the solar wind on the excitation of these DA modes. The solar wind is an essential constituent configuring the electrostatic environment over Moon. Due to larger photoemission current (∼5 μA m −2 ), the surface charging over the sunlit location and sheath population (∼500 cm −3 ) is dominated by emitted photoelectrons, and the solar wind plasma (density ∼5 cm −3 and current ∼10 nA m −2 ) essentially helps in attaining dynamic equilibrium of the constituent charging currents. In the wave generation processes, the relative motion of solar wind to the photoelectron sheath plasma contributes in exciting


Thus, while large-scale structure for different types of DM can appear identical, careful attention to structure on subgalactic scales can be a powerful tool to distinguish DM models. A powerful probe of the gravitationally bound structures of dark matter is strong gravitational lensing. Given a matter over or under density, the deflection angle along the line of sight is given by an integral over the induced gravitational potential (Narayan Bartelmann 1997 ),where χ is the distance along the line of sight, χ s is the distance to the source, and is the gravitational potential. In the thin lens approximation (Narayan Bartelmann 1997 ), valid in the limit that the thickness of the lensing galaxy is small compared to the distance to the lens, this takes a simplified form,where D LS , D L , and D S are the angular diameter distances from the lens to the source, from the observer to the lens, and from the observer to the source, respectively, and z is the distance along the line of sight. From this expression one can straightforwardly compute the lensing due to any gravitational potential Ψ. The gravitational potential is in turn determined by matter density via the Poisson equation, ∇ 2 Ψ ∝ ρ . The linearity of this equation implies that the total lensing due to the separate contributions, e.g., of a halo and halo substructure, is simply the sum of the individual contributions. That is,where is the external shear due to large-scale structure, and are the lensing due to the halo and halo substructure respectively. The well studied case is the lensing due to the spherical substructures expected from hierarchical structure formation in the context of noninteracting particle dark matter. However, as mentioned in the 1 , other types of substructure can exist in models of dark matter outside the WIMP paradigm. As a prototypical example, we will consider dark matter condensates, namely superfluids, which exhibit substructure in the form of vortices. We now proceed to develop this in detail. 3. Case Study: Dark Matter Superfluidity The canonical example of a condensate dark matter model is axion dark matter. Axions were introduced as a solution to the strong-CP problem of the SM (Peccei Quinn 1977 ; Weinberg 1978 ; Wilczek 1978 ), and soon thereafter proposed as a dark matter candidate (Abbott Sikivie 1983 ; Dine Fischler 1983 ; Preskill et al. 1983 ). It was later argued that axions could form a Bose–Einstein condensate and exhibit superfluidity (Sin 1994 ; Hu et al. 2000 ; Silverman Mallett 2002 ; Hui et al. 2017 ; Sikivie Yang 2009 ; Berezhiani Khoury 2015 ; Ferreira et al. 2019 ). To emphasize the superfluid nature of axions, we can rewrite the field equations in terms of fluid equations. Being comprised of extremely light particles at an incredibly high number density, axion dark matter is well described by a coherent scalar field. Moreover, because dark matter as we observe it is cold, the system is well described by a nonrelativistic


polarization fraction. Note also that the magnetic pole and equator are the two main contributors to the surface emissions in the current configuration (see the explanations given later). We next discuss the phase-averaged quantities. The semi-amplitudes and polarization fractions are shown in the upper and lower panels of Figure 6 , respectively. Note that, rigorously speaking, the semi-amplitude is not a phase-averaged quantity, but we consider it here just for comparison. In this paper, the semi-amplitude is defined as the quantity related to the total variation of the polarization angle during the rotational period divided by four, which is expressed aswhere the supremum is taken over all possible partitions of the range for ψ . This definition coincides with that given in Taverna et al. ( 2015 ) in most cases but not always (see below). The photon energy is set to following Taverna et al. ( 2015 ). In the left column, the mode conversion is neglected on purpose for comparison with the previous work, whereas it is incorporated in the right column. The results without mode conversion are consistent with those in Taverna et al. ( 2015 ). The discontinuous suppression of the semi-amplitude on the diagonal line observed in our result (see the top left panel of Figure 6 ) but absent in their result is mainly due to the fact that our definition of the semi-amplitude is not completely the same as theirs. Figure 6. Semi-amplitudes of the polarization angle (upper panels) and phase-averaged polarization fractions (lower panels) for different configurations of a rotating neutron star. The left and right columns correspond to the cases without and with the mode conversion, respectively. The photon energy is set to . We explain this in more detail using Figure 7 , which shows how the polarization angle changes with the rotational phase for different combinations of η and γ . Figure 7. (a) Top views of the observed patches (orange circles) on the polarization-limiting surface in the middle row and the polarization directions (red arrows) at different rotational phases in the bottom row for (left), (center), and (right). The trajectories of the (extended) magnetic north pole are drawn in green. Blue arrows and black crosses in the bottom panels indicate the directions of the average magnetic fields at the different rotational phases and the position of the coordinate origin, respectively. (b) Polarization angles as functions of the rotational phase. The angle η is fixed to , whereas the angle γ is changed: . In the middle panels of Figure 7 (a), we schematically draw the top views of the observed patch on the polarization-limiting surface for , , and . The green circles indicate the trajectories of the (extended) magnetic north pole on this surface. Note that they are not exact circles in general. In the bottom panels, we give the corresponding average magnetic fields (blue arrows) and polarization directions (red arrows), which are estimated from the


is obtained by taking the sum of the contributions from all dark matter halos We have made use of the python code colossus (Diemer 2018 ) to generate the dark matter halo mass function using the parameterized formula fitting to an N -body simulation proposed by Tinker et al. ( 2008 ), and the concentration–dark matter halo mass relation proposed by Prada et al. ( 2012 ). We have tested systematics by using Raeymaekers ( 2007 ) for N -body simulation fits for the dark matter halo mass function, and Dutton Macciò ( 2014 ) for the concentration–halo mass relation. The results show a different choice of dark matter halo population modeling will not change the final event rate by orders of magnitude. Assuming f PBH = 100%, the result of Equation ( 10 ) is shown in Figure 1 . The main contribution to the integral in Equation ( 10 ) is from low-mass dark matter halos, therefore the result depends sensitively on the lower end for halo mass. To illustrate the dependence on lower mass cutoff , we plot as a function of in Figure 1 . Also note that the integrand of Equation ( 10 ) does not depend on M PBH due to compensation between the primordial black hole number density and the cross section. To determine the lower limit of the dark matter halo mass for M PBH = 0.01/0.1/1 M ⊙ , we follow the criterion by Equation (11) of Bird et al. ( 2016 ) requiring that the dark matter halo evaporation timescale due to dynamical relaxation exceeds the dark energy domination timescale (∼3 × 10 9 yr). This choice results in the lower integral limit of Equation ( 10 ) being 0.3/3/21 M ⊙ for M PBH = 0.01/0.1/1 M ⊙ . Choosing a lighter dark matter halo cutoff would contribute more binary primordial black hole merger events if the halos would not have evaporated at present and the NFW profile is still preserved. High resolution dark matter N -body simulations are needed to precisely resolve the smallest structure of subsolar mass primordial black hole halos but this is beyond the scope of this paper. Figure 1. Event rate for binary primordial black hole merger as a function of the lower cutoff of dark matter halo mass. The markers are the event rate for M PBH = 0.01/0.1/1 M ⊙ , which are 528/140/45 Gpc −3 yr −1 , respectively. With the above choices of lower integral cutoff, as shown in Figure 1 , the event rate for M PBH = 0.01/0.1/1 M ⊙ is 528/140/45 Gpc −3 yr −1 . As a comparison, for M PBH = 30 M ⊙ , the event rate is Gpc −3 yr −1 , as computed in Bird et al. ( 2016 ). Therefore, the merger rate of subsolar primordial black holes increases by one to two orders of magnitude compared to that of 30 M ⊙ . To compare with observations, the sensitive volume, which is defined to be the orientation-averaged volume assuming a match-filtering signal-to-noise ratio (S/N) > 8 (Abbott et al. 2018b ), is Gpc 3 for M PBH = 0.01/0.1/1 M ⊙ for Advanced LIGO at its design sensitivity. Given the above estimated event rate, under our assumption of delta function mass distribution, the


spherical target and the stripped mass from the envelope as functions of time. Time is scaled with the mean pusher transit time (≈19.4 ns). The stripped mass is normalized with the total envelope mass and is identified as forward ( v z > 0) traveling mass above the mass center (MC, blue line). Also plotted is the stripped mass obtained when its velocity becomes larger than 4 km s −1 (green line). The evolution of the stripped mass and core velocity obtained with this criterion is shown by the green line in Figure 11 . Our second procedure simply counts as stripped any envelope material with coordinates above the center of mass of the target. This second method leads to the blue line in Figure 11 . As can be seen, the precise criterion to decide when the mass element has been stripped mainly affects the rising part of the curves, which is steeper with the second criterion. Nevertheless, both criteria lead to a similar asymptotic behavior. The curves show a similar overall trend to the astrophysical case presented in Figure 7 . Furthermore, by taking the ratio between the asymptotic core velocity (AACV) and the average ejecta velocity (AEV) this results in values of AACV/AEV ≈ and 1.6 × 10 –2 for the astrophysical and the laboratory simulations respectively, which fulfills Equation ( 9 ). Figure 12 shows a plot of the angular distribution of stripped mass from the two-layer companion/target. The baseline curve labeled t = 0 depicts the mass distribution function of the Cu envelope of the target before the impact (the shell in gray in the sketch) as a function of the axial angle θ (). Figure 12 shows the laboratory and astrophysics distributions at the common time . The lines for the laboratory and astrophysical simulations lie above the reference line, indicating that much of the stripped material is coming from the lower hemisphere of the target. The consequences of using planar or spherical blasts in the laboratory setting are quite evident from the figure, and support the conclusions from the simple toy model stated in Section 2 above. For curved fronts the agreement between the astrophysical and laboratory simulations is excellent. Figure 12. Distribution of stripped mass of the companion star/two-layer target envelope as a function the azimuth measured from its center of mass (CM). The curve labeled “ t = 0” is the initial mass distribution before the collision. The curves labeled “Companion Star” and “Hemispherical” refer to the astrophysical and experimental simulations respectively. For comparison, the simulation of the experiment using a planar blast wave generated with the same laser conditions (labeled “Planar”) is also presented. 5. Discussion and Conclusions We presented the results of a proposed design for a laboratory experiment at high energy density in which a spherically expanding blast wave collides with a spherical target composed of a dense core surrounded by a low-density shell. The experiment was optimized to match


because, first, the amount of early injected electrons, which has already been well cooled, will be larger, and secondly, the cooling break will appear at lower energy for a larger t age . Figure 5. Influence of pulsar’s initial rotation period P 0 on the predicted nebula extent. See Section 3.1.2 for details. 3.1.3 Braking index The braking index n determines the injection profile of electrons and its influence on the energy-dependent morphology is complex. For a large braking index, e.g. n = 3, the age of the pulsar t age is much longer than the initial spin-down time-scale τ 0 (see Fig. 1 ). The spin-down luminosity in this case decreases as t −2 except at very early time (equation 3 ). For a smaller braking index, the spin-down luminosity decreases more quickly with time for t > τ 0 . However, τ 0 will become comparable or even larger than the age of the pulsar. As a result, the global decline slope of the spin-down luminosity from the birth of the pulsar to the present day is flatter for a smaller n . Note that radiation at smaller (larger) radius mainly arises from electrons injected at later (earlier) time, so a smaller n results in a steeper decrease of the electron density profile and hence leads to a less extended morphology and vice versa. Such a tendency can be seen from Fig. 6 except at the low-energy end and the high-energy end. At the low-energy end, the extent of the PWN is mainly determined by the age of the system, so it is larger for a smaller n . At the high-energy end, the cooling time-scale of electrons is very short (within a few thousand years) so the radiating electrons are just recently injected. In other word, the spatial distribution of high-energy electrons is not sensitive to the long-term temporal behaviour of the spin-down luminosity and hence the curves for all three values of n converge at high-energy end. Figure 6. Influence of pulsar’s braking index n on the predicted nebula extent. See Section 3.1.3 for details. 3.1.4 Spectral index We assume a single power law of index p for the injection spectrum (equation 5 ). The SED shows a peak around GeV that is naturally formed due to cooling of electrons and superposition of electrons injected at different epoch, without invoking a broken power-law function for the injection spectrum. The peak in the SED roughly corresponds to the transition in the slope of the present-day electron spectrum from −3 to >−3, so the injection spectral index p can influence the peak energy in the SED. We show the present-day electron spectrum ( E e versus ) with decomposing the contributions from different injection epoch in Fig. 7 for different p . We note that the spectrum shows a hump structure around the cooling break instead of a simple broken power law. This is because the broken power-law spectrum can be formed via synchrotron or IC cooling only when the injection rate of electrons is constant, while the latter decreases with time as the pulsar spins down. Figure 7. Electron


is injected from a planar boundary of a lateral extent large enough to contain the spread of cloud debris but small compared with the wind radius, and collides with a uniform heavy cloud initially embedded in a uniform, dilute ambient gas representing the galactic medium. We denote the velocity and density of that flow by β ws and n as , respectively, but note that this flow may represent either the shocked ambient flow, if cloud crashing and cloudlets acceleration occur in that region, or the wind itself if the shock crossing time of the cloud is considerably longer than the wind expansion time t f given in equation ( 4 ). The planar approximation of the initial flow is justified by the small ratio between the cloud radius to the putative cloud’s distance from the wind’s source, as explained in the previous section. Cooling of the gas is also included in the simulations in a manner specified next. Each simulation has been run for long enough time to allow complete destruction of the cloud and subsequent acceleration of the cloudlets to high velocities. The output data of the simulation gives the spatial distribution of cloud fragments at any given time, their velocities, densities, and temperatures. These data are used to produce column density histograms in velocity space along different lines of sight, which serve us later (equation 9 ) in creating synthetic spectra that can be compared with observed BAL spectra. It also enables us to get a grasp on the general dynamical and thermal evolution of the cloud fragments, and to understand which of the following processes happen faster in different stages of the system: further fragmentation accompanied by shock heating versus cooling. 3.1 Set-up We use the pluto code (Mignone et al. 2007 ) version 4.0 in 2D Cartesian coordinates in the non-relativistic HD module on an ideal gas with an adiabatic index γ = 5/3. We performed several experiments differing in the size of the simulation box, the implementation of cooling and the ratio of densities, κ, between the cloud and the wind. In each of these experiments, the ranges of the Cartesian coordinates are of the form 0 x x max and | y | y max , the unit length is equal to 1 pc and the resolution along each Cartesian direction is 0.01 pc. The initial condition of the simulation is a static circular cloud of uniform density n c with a radius R c = 1, surrounded by a static ambient medium of uniform density n a . The cloud centre is located initially at y = 0 and x = x c > 0, as close as possible to the wind source at x = 0, but far enough to allow the bow shock created by the cloud–wind collision to remain in the simulation box at all times. The boundary condition at x = 0 is a planar flow of uniform density n ws moving at a speed of ws along the x- direction towards the cloud. On the remaining boundaries we use open boundary conditions. It is worth noting that in the absence of cooling the evolution of the system depends only on the density ratio κ =


in the analysis for Figs 8 and 9 where we looked specifically for differences in the PL relations derived from known metal-rich and metal-poor stars. Figure 11. Distance moduli for the 20 RRLs in our DZ sample as a function of [Fe/H] (spectroscopic metallicities from C05 ). The solid grey line is the distance modulus ±2σ (dashed lines) estimated using as a reference the PL relation derived by Neeley et al. ( 2017 ) and only the RRab stars in the D4 sample. Metal-poor sources are magenta squares and metal-rich are green triangles. RRab and RRc stars are encircled by blue squares and red circles, respectively. The RRLs marked with a cross are the rejected stars. The least-squares fit (black line) has been calculated in four different cases: considering the whole sample (case A, top left panel), removing the ‘closest’ star (in terms of distance from us; top right panel, case B), removing the ‘most distant’ star (case C, bottom left panel), and excluding both (case D, bottom right panel). In every case, the slope (d μ /d[Fe/H]) is consistent with zero within 1σ (see the text and Table 8 for details). Table 8. d μ /d[Fe/H] derived from the DZ sample. 5 SUMMARY AND CONCLUSION As part of the SMHASH program, using IRAC- Spitzer data we have determined a new distance modulus of the Sculptor dSph using RRLs located in the inner region of the galaxy. We obtained time-series photometry for 49 RRLs, (36 RRab and 13 RRc) at 3.6 μm. Seven stars were discarded from the initial sample mainly due to photometric contamination effects. Adopting periods from Kaluzny et al. ( 1995 ) and Clementini et al. ( 2005 ), we built light curves for the remaining 42 highest quality stars, delineating their mid-IR pulsation properties. In order to investigate the photometric properties of the sample, and to choose the highest quality subsample of stars, we created four data sets (D1, D2, D3, and D4) by removing various problematical stars (see Section 3 for details). PL relations were derived for each RRab-only and RRab+RRc ( fundamentalized ) data set, and were found to be in reasonable agreement (i.e. within 1σ) with the empirical relations published in Madore et al. ( 2013 ) and Neeley et al. ( 2015 ), as well as the revised relations from Neeley et al. ( 2017 ) and the recent PL relations derived by Muraveva et al. ( 2018b ) (Table 4 ). We adopt for Sculptor the distance modulus derived from the D4 sample, as this has the cleanest RRL selection and the best-fitting slopes are the closest to the published empirical relations that we have considered as a reference in this work. We are aware that mid-IR studies of the RRL PL are increasing (Madore et al. 2013 ; Dambis et al. 2014 ; Klein et al. 2014 ; Neeley et al. 2015 , 2017 ; Muraveva et al. 2018b ), but choose the Madore et al. ( 2013 ), Neeley et al. ( 2015 ), Neeley et al. ( 2017 ), and Muraveva et al. ( 2018b ) PLs as fiducial as they are built using the sample of RRL calibrators whose trigonometric parallaxes were


analysis to a three-dimensional (3D) turbulent dynamo with periodic boundary conditions and an equator in the middle that cuts the domain into two halves, with opposite helicity of the forcing function. Finally, we employ full-disk vector magnetograms from the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory ( SDO ) to obtain all three magnetic field components at the two-dimensional (2D) surface of the Sun, to compute magnetic helicity spectra from a sequence of synoptic maps. 2. Formalism 2.1. The Usual Magnetic Energy and Helicity Spectra In a periodic Cartesian domain, the usual magnetic energy spectrum is given by the integral over shells in wavenumber space of the Fourier-transformed magnetic energy density,where is the surface differential in Fourier space in D dimensions. In D = 3 dimensions, the surface of a D -dimensional unit sphere is . In D = 2 dimensions, is the circumference of a unit circle, while in D = 1 dimensions, corresponds to the two end points of a line. Here and in the following discussion, we measure the magnetic energy density in rather than , so the vacuum permeability factor is dropped. Furthermore, is the radius of a sphere in Fourier space, and hats denote the Fourier transform of the magnetic field, that is,The magnetic helicity spectrum is defined analogously to aswhere is the Fourier transform of the vector potential , with and . These spectra are normalized such that where angle brackets with subscript V denote volume averages. Analogously, one can define the current helicity spectrum such that , where is proportional to the current density. For the following, it is useful to remember that the magnetic energy spectrum is the Fourier transform of the trace of the two-point correlation tensorwhere angle brackets denote ensemble averaging, which could be approximated by averaging over time, and is assumed to be statistically independent of , owing to the assumption of homogeneity. Thus, following standard relationships (e.g., Matthaeus et al. 1982 ; Brandenburg et al. 2011 ), the energy spectrum is then given by , where is the Fourier transform of M ij . Likewise, the scaled magnetic helicity spectrum is given by , where is the unit vector of . (The hat on is not to be confused with the hats on or M ij , where they denote Fourier transforms over .) (Including here the factors 2 and k on the left sides of the two equations has the advantage that and thus have the same prefactors.) Note that under isotropic conditions, . Such spectra show the high-wavenumber range better than just or , and are therefore also considered in some of the following cases. The magnetic helicity spectrum can be defined analogously from a tensorial generalization of the magnetic two-point correlation tensor. This will be done in the following section, where we will also relax the assumption of homogeneity and allow the spectra to be slowly varying functions of . 2.2. Double Fourier Transform To obtain


where We find that the pairwise kSZ dipole, ξ kSZ, l = 1 , is negative in linear theory. This means that gravitational attraction predicts a slight tendency of any pair of galaxies to be moving towards rather than away from each other at large scales, where we follow the convention that if two galaxies are moving towards each other, their contribution to the pairwise velocity is negative. The linear Kaiser effect from RSDs increases the amplitude of the pairwise kSZ dipole by ∼ 20 per cent for both LOWZ and CMASS at linear regimes. On the other hand, at non-linear small scales RSDs displace galaxies away from each other, and thus, in redshift space the sign of ξ kSZ, l = 1 changes around 10 h −1 Mpc ( k ≃ 0.2 h Mpc −1 ) from negative to positive (Okumura et al. 2014 ; Sugiyama et al. 2016 ; Sugiyama et al. 2017 ). This small-scale effect of RSDs is analogous to the Finger-of-God (FoG) effect but is not the same, because we have shown that this change in sign of ξ kSZ, l = 1 appears even in the Zel'dovich approximation that does not form haloes (Sugiyama et al. 2016 ). Therefore, it could be considered that the change in sign of ξ kSZ, l = 1 is caused by non-linear velocity dispersion effects, part of which is the FoG effect. The latest kSZ measurement using the high-resolution ACT data (De Bernardis et al. 2017 ) clearly shows the expected change in sign of the pairwise velocity at ∼10 h −1 Mpc. Fig. 2 shows the theoretical predictions of the pairwise kSZ dipole and octopole in linear theory (equations 37 and 39 ) for the LOWZ sample ( f σ 8 = 0.392 and b σ 8 = 1.283), where we use the best-fitting value of the optical depth, τ E = 3.95 × 10 −5 , estimated from our kSZ measurement (Section 7.2 ). Since this figure shows the linear theory results that we use in our analysis, the change in sign of ξ kSZ, l = 1 around ∼10 h −1 Mpc does not occur unlike non-linear theories (Okumura et al. 2014 ; Sugiyama et al. 2016 ). As the shape of the pairwise kSZ power spectrum is proportional to P lin ( k )/ k , the amplitude increases at large scales. As the data improves, we will be able to investigate the pairwise kSZ signal at larger scales than ∼200 h −1 Mpc (e.g. De Bernardis et al. 2017 , fig. 3). While the data should show a baryon acoustic peak around ∼100 h −1 Mpc in the linear theory prediction of ξ kSZ, l = 1 (see blue line in the right-hand panel of Fig. 2 ), the peak is significantly broadened by non-linear effects (Sugiyama et al. 2016 ). The octopole, which is generated from the RSD effect and is free of the linear bias, is about 10 times smaller than the dipole. In future kSZ measurements such as Advanced ACTPol and CMB-S4, we will want to measure all of the multipoles up to the octopole. This full measurement will constrain cosmological parameters, especially for the linear growth rate f σ 8 and the Hubble expansion parameter H (Sugiyama et al. 2017 ). However, the data used in this work is too noisy to detect the octopole; therefore, we do


efficiently accelerate non-thermal electrons (Sironi Spitkovsky 2014 ). Magnetic reconnection is a complex non-linear process and remains the subject of intense research (Yamada, Kulsrud Ji 2010 ; Treumann Baumjohann 2015 ), so we do not pretend to capture the microscopic details of this process in our 1D fluid model. We can, however, put useful constraints on the power dissipated by magnetic reconnection which then goes into accelerating non-thermal electrons, by calculating their emission as they travel along the jet. This power is inevitably linked to the large-scale average reconnection time-scale along the jet. Our approach is intended to be complementary to the detailed numerical simulations which focus on the small-scale reconnection physics but tend to neglect the large-scale fluid flow and energy balance along the jet; in this work, we instead focus on the average large-scale fluid flow and energy balance, at the expense of a detailed treatment of the microscopic reconnection physics. Our results will help to constrain and inform dedicated numerical simulations of the macroscopic reconnection rates required by considering radiative losses and energy constraints along the jet at large scales. In most astrophysical plasmas, the amount of resistive dissipation of magnetic fields is negligible and occurs on a resistive time-scale where η is the electrical resistivity ( 36 ) and δ is the characteristic length-scale of the fluctuation in the magnetic field. This time-scale is usually far longer than the typical observed time-scale associated with the release of energy via magnetic reconnection in solar flares, for example, Priest Forbes ( 1986 ). It is found in MHD simulations and particle-in-cell simulations of reconnection that once the process of resistive dissipation or magnetic reconnection begins to occur in a region with a strong gradient in the magnetic field, the magnetic energy is released in the form of heating and bulk acceleration of an outflow of plasma from the region. This creates a low-density, low-pressure reconnection region which then draws in additional plasma from both sides of the reconnecting current sheet (the magnetic field changes rapidly across the reconnecting region and this necessitates a concentrated thin current sheet since ). The velocities of the outflow and inflow are, typically, close to the Alfvèn speed, v A , with the precise relationship depending on the geometry of the reconnecting region and the proportion of magnetic energy which can be dissipated by the process. In collisionless highly magnetised plasmas, such as jets, inflow velocities of ∼0.1 v A are typical (Sironi Spitkovsky 2014 ). From Fig. 3 , we have already constrained the jet plasma to be highly magnetized, in which case the Alfvèn speed is approximately the speed of light v A ≈ c (e.g. Gedalin 1993 ). We can parametrize the reconnection rate in terms of the power dissipated in a region in which magnetic reconnection occurs, multiplied by


The best-fit relation for Type 2 AGNs from Woo et al. ( 2016 ) is also shown (dashed line). The right panel shows the distributions of the ratio of σ [O iii ] to σ * for Type 1 AGNs: double Gaussian [O iii ] (red) and single Gaussian [O iii ] (blue). We perform regression analysis after accounting for the measurement uncertainties in both σ [O iii ] and σ * . The best fit for Type 1 AGNs is shown by the solid line in Figure 4 , while for comparison, we also plotted the best fit for Type 2 AGNs from Woo et al. ( 2016 ; dashed line). Interestingly, when the wing component is present in [O iii ] (left panel), the best fit deviates from unity (dash-dotted line), having a steeper slope of 2.79 ± 0.14 for Type 1 AGNs and 1.66 ± 0.01 for Type 2 AGNs (see Woo et al. 2016 for Type 2 AGNs). However, when the wing component is absent (middle panel), the best-fit line has a slope of 1.32 ± 0.11 for Type 1 and 1.18 ± 0.01 for Type 2 AGNs much closer to the unity relation. We also present the distribution of the velocity dispersion ratio of [O iii ] to σ * (right panel in Figure 4 ). While [O iii ] fitted with a double Gaussian is much broader than stellar lines (red histogram), for many objects, [O iii ] fitted with a single Gaussian (blue histogram) is also broader than stellar lines, suggesting that an outflow signature is significantly present. Considering that [O iii ] dispersion is a combined effect of gravitational potential ( σ gr ) and nongravitational effect, e.g., outflow components ( σ non-gr ), the measured velocity dispersion can be expressed asNote that although σ total may represent a more complex nature of gas kinematics, we simply assume that the line of sight velocity distribution of gas manifests the convolution of gravitational and nongravitational components. We expect σ [O iii ] to be a factor of 1.4 larger than σ gr if σ non-gr = σ gr . Assuming σ gr = σ * , we find that an error-weighted mean ratio of σ total to σ gr is 1.0 and 2.3, respectively, for Type 1 AGNs with single Gaussian [O iii ] and double Gaussian [O iii ]. The nonlinearity of the σ [O iii ] – σ * relation suggests that the effect of the nongravitational component is significant and outflows are common phenomena in both Type 1 and Type 2 AGNs. 3.2. Outflow Fractions To study the outflow fractions, we estimated the fraction of AGNs with double Gaussian [O iii ] in the sample. In the case of Type 1 AGNs, 89% have double Gaussian [O iii ], while only 11% have single Gaussian [O iii ]. The double Gaussian [O iii ] fraction in Type 1 AGNs is a factor of 2 larger than that of Type 2 AGNs (43%). Since the mean luminosity of Type 1 AGNs is much higher than that of Type 2 AGNs, the difference of the double Gaussian [O iii ] fraction is due to the luminosity effect. In Figure 5 , we present the fraction of double Gaussian [O iii ] as a function of [O iii ] luminosity (left panel). The double Gaussian fraction steeply increases with increasing [O iii ] luminosity, from ∼20% to


al. 2007 ), photodesorption (Bertin et al. 2013 ), and cosmic ray induced photodesorption (Hasegawa Herbst 1993 ). These three switches are set to ‘on’, with the photodesorption yield set at 1 × 10 −4 . 2.2 Network The nautilus reaction network used in this study has been expanded to include more complex chemical species and intermediates that lead up to C 2 H 4 O 2 isomers, as well as dimethyl ether. The base network of gaseous reactions is taken from the KIDA network (Wakelam et al. 2012 , http://kida.astrophy.u-bordeaux.fr/ ). The granular reaction network is from the nautilus package, with additional thermal grain-surface reaction pathways leading to C 2 H 4 O 2 isomer precursors from Garrod Herbst ( 2006 ). Used initially in hot core models, these reactions have been included here to provide likely thermal pathways to COMs in competition with radiolysis. Other notable additions include new gas-phase reactions for acetic acid and glycolaldehyde from Skouteris et al. ( 2018 ). The full list of additional reactions is contained in the supplementary material , Tables S1–S3 (available online), with important reactions discussed in Sections 3.1 , 3.3 , and 3.2 . Species with the first letter ‘J’ are those on the surface of the ice mantle, while species with a ‘K’ lie within the bulk of the ice, which, after the simulation has completed running (10 7 yr), contains close to 100 monolayers of ice. Additional binding energies E D for the four principal molecules studied were taken from Garrod ( 2013 ) and are listed in Table 3 . The diffusion barriers ( E b ) for all granular species are 0.4 × E D for ice surface species, and 0.8 × E D for bulk species. 2.3 Radiolysis The method used for radiolysis was first developed by Shingledecker Herbst ( 2018 ). It describes four different results that follow an incoming cosmic ray or secondary electron interacting initially with a target species A, for which we use a ‘’. The subsequent results can be described by the following equations, which represent different paths to ions and suprathermal neutrals, the latter denoted with an asterisk: The first process leads to the ionization of A, while the second process describes the formation of suprathermal fragments B and C with an intermediate suprathermal A formed via dissociative recombination of the A ion. The third process describes the direct formation of an intermediate suprathermal species followed by its fragmentation into non-excited products, while the last process describes the formation of suprathermal A, which does not subsequently fragment. In order to implement both generation of suprathermal species, and fast suprathermal reactions into the rate-equation based model used, we can derive a pseudo-first-order rate coefficient by multiplying a cross-section (σ e ), in cm 2 , with a cosmic ray flux (φ) ,in cm −2 s −1 . In order to obtain a cross-section, we start with a stopping power cross-section S ( E ), which is defined through the loss of kinetic


flux from near the heliotail. Figure 3 can be directly compared to Fig. 9 of Funsten et al. (2015) , who analyzed the symmetry of the IBEX ribbon; however, note that Funsten et al. plot the IBEX ribbon flux and location as a function of angle from the ribbon symmetry axis, which lies within 40 of the plane (0 azimuth in our Fig. 3 ). The IBEX ribbon flux appears to maximize close to the symmetry axis for 0.71 and 1.11 keV, relatively close to the plane (within 30), similar to our results at low ENA energies for the case of slow SW, and high ENA energies during fast SW – both in the absence of an asymmetric SW. At higher energies, the IBEX ribbon flux appears bimodal, likely due to the asymmetric SW, which is excluded in our study. Nevertheless, in all cases, our results appear to be symmetric about the plane. This suggests that, besides the possible influence of the latitudinal asymmetry of the SW, the hydrodynamic interaction of the SW with the LISM, centered on the trajectory of the heliosphere through the interstellar gas, is an important ordering process for the ribbon flux, as also found by Funsten et al. (2015) . 3.2.2. Comparing simulated and IBEX ribbon geometry Fig. 3 Simulated ribbon flux from locations along the elliptical fits, as a function of azimuthal angle about the circularity plot center (negative to positive angle is counterclockwise in Fig. 2 ). In the left panels we show the ribbon flux at each energy (different rows) for the slow, intermediate, and fast SW (solid curves), as well as the heliolatitude location of the ribbon (dashed curves). The shaded regions correspond to locations of the ribbon lying within 35 heliolatitude. Notice that the left -axis is in scaling. In the right panels we show the components of the ribbon flux that originated from outward-propagating, primary ENAs born in the IHS, the supersonic SW (SSW), and the total. Fig. 4 Simulated angles between the line-of-sight view from IBEX and the local interstellar magnetic field vector, at distances of 20 au ( left ) and 200 au ( right ) from the heliopause (HP). We show the locus of points defined by (black dots), fit a circle to that locus of points (black curve), and plot the center of the fitted circle (black dot near the center of the plot). The frame of reference of these plots is the same as those shown in Fig. 2 . Table 2 Weighted averages of geometric properties. Notes. The IBEX data are from Funsten et al. (2013) . All results in this table are weighted over energy and circle/ellipse fits. The aim of this analysis is to determine if there is a significant dependence of the ribbon’s geometric properties on the SW speed and ENA energy. Since the draping of the LISM magnetic field is a function of distance from the heliopause (e.g., Grygorczuk et al. 2011 ; Pogorelov et al. 2011 ; Zirnstein et al. 2015a ), the energy of the parent SW and ENA distribution may affect the distances at which the majority of ribbon ENAs (observed at 1 au) originate. We


configuration of the non-Gaussianity vs. the sound speed in a nonminimal derivative model in which both the nonminimal coupling and potential are E-model. The left panel corresponds to N = 60, and the right panel is for N = 70. The stars show the maximum values of the sound speed in each case. Table 3 Constraints on the Sound Speed and Tensor-to-scalar Ratio Obtained from 95% CL of Planck2015 TT, TE, EE+lowP Data Note. These constraints are corresponding to a nonminimal derivative model in which the nonminimal coupling is a constant and the potential is E-model. Table 4 Constraints on the Sound Speed and Tensor-to-scalar Ratio Obtained from 95% CL of Planck2015 TT, TE, EE+lowP Data Note. These constraints are corresponding to a nonminimal derivative model in which both the nonminimal coupling and potential are E-model. 5. Summary The aim of this paper was to study the nonminimal derivative model in the context of α -attractor. In this regard, we have considered a two-fields action in which both the fields and their derivatives are nonminimally coupled to the gravity. We have used the conformal gauge to convert the two-fields model into a one field, which its derivative (and not the field itself) is nonminimally coupled to the gravity. After obtaining the the background equations of this NMDC model, we have studied the linear perturbations theory. By adopting the ADM formalism, we have studied both the scalar and tensor perturbations in this setup and found some important perturbation parameters such as the power spectrum, scalar spectral index, and tensor-to-scalar ratio. After that, by introducing the types of the general functions and U ( ψ , φ ), and using the conformal gauge, the NMDC function and potential have been obtained. In this paper, two types of NMDC function have been considered: and . We have shown that in both cases, there is an attractor line in large N and small α limits that the r − n s trajectories tend to, while in the the single-field α -attractor model, there is an attractor point in these limits. In fact, the presence of attractor line instead of attractor point is due to the nonminimal derivatives coupling that causes the scalar spectral index of this model to be a functions of two parameters, α and M . In the limit , one recovers the attractor point as is usual in α -attractor models. We have numerically studied the linear perturbation in two cases with constant NMDC coupling and E-model NMDC coupling (in both cases the potential is considered to be E-model). With these choices, the power spectrum of the perturbations in NMDC model can get the observationally viable value (almost 2.4 × 10 −9 ) in some ranges of χ and α . Also, in this model, the r − n s plane lies in the background of Planck2015 TT, TE, EE+lowP data for all values of M (or χ ) and in some ranges of α , for both N = 60 and N = 70. We have obtained some constraints on the free parameter α which lead to the values of the scalar spectral index and


(b) Group 1 (red line) and Group 2 (blue line) events; (c) Group 3 (red line) and Group 4 (blue line) events. To reveal the reason for this difference, the intermittent structures are grouped according to the intensity and direction changes of magnetic field. The intensity changes are determined by a normalized parameter , where and B 0 is the average of the magnetic field strength of the whole sheath. The directional changes are also divided into two groups: Δ θ > 45° and Δ θ ≤ 45°, as current sheets with Δ θ > 45° are categorized to strong currents in Borovsky Denton ( 2011 ). Thus, the intermittent structures are grouped into the following four categories: (1) and Δ θ > 45°; (2) and Δ θ ≤ 45°; (3) and Δ θ > 45°; (4) and Δ θ ≤ 45°. Figure 2 (b) shows the associated proton temperature of intermittent structures with significant magnetic field intensity changes (). A substantial enhancement (10%) of the normalized proton temperature can be found regardless of the value of Δ θ , revealing that local heating is prominent near these coherent structures. Near the intermittent structures without large changes in magnetic field magnitude (), local enhancement is still prominent (nearly 8%) near current sheets with large shear angles (Δ θ > 45°), but is not significant near current sheets with small shear angles (Δ θ ≤ 45°), as shown in Figure 2 (c). However, 10,831 of the total 12,426 intermittent structures identified fall into Group 4, so the average enhancement of normalized proton temperature is only 3%, as shown in Figure 2 (a). As shown in Figures 2 (b) and (c), the normalized proton temperature suffers a significant enhancement near current sheets with Δ θ > 45° (red lines). We then analyze the association between the temperature enhancement and the scale of such current sheets. The superposed-epoch analysis is performed for strong current sheets identified under four different time lags. Figure 3 shows that the temperature enhancement becomes more prominent as the spatial scale (≈ τ · V sh ) of the current sheets decreases. Meanwhile, the heating effect is more localized near thinner current sheets. When the time lag is 3 s, the normalized proton temperature has already dropped 7% at a distance of 10 5 km, but it almost remains the same at this distance when the time lag increases to 120 s. This result suggests that the intermittent heating mainly occurs at thin current sheets instead of large-scale ones. Figure 3. Averages of normalized proton temperature conditioned on the distance from strong current sheets (Δ θ > 45°) at different timescales. 4. Summary and Discussion A total of 12,426 PVI events have been identified in the sheaths of 71 MC events observed by the WIND spacecraft, with the criterion of PVI ≥ 3. Superposed-epoch analysis of normalized proton temperature associated with the PVI peaks identified shows that the averaged temperature enhancement is not prominent near the current sheets in the MC sheath, which is different


et al. (2011) . These swirls are obviously caused by the turbulent plasma motions in the surface layers of the convection zone. However, the Hydro simulation shows a higher density of swirls than the MHD simulations. This is because the magnetic fields hamper the formation of vortices in the convective layers of the simulation. The photosphere of the MHD 200 G time instant harbors an almost homogeneous structure of vertically oriented swirls and only a few swirl arches are present near the τ 500 = 1 surface. In the MHD 50 G case, the vertical swirls are clustered in funnel-shaped structures and the arches are more prominent than in MHD 200 G. Different from these two cases, vertical swirls are essentially absent in the Hydro simulation, while swirl arches are omnipresent in the photosphere. Again, these results well agree with and confirm earlier results of Moll et al. (2011 , 2012) . A similar behavior is observed in the chromosphere: the stronger the initial magnetic field, the more abundant the vertical swirls are. However, we observe that the strongest swirls appear at the top of the MHD 50 G simulation. This suggests that too strong magnetic fields can possibly inhibit the formation of strong vertical vortices in the chromosphere. In the Hydro simulation, we see a quasi-isotropic distribution of swirls at chromospheric levels, which are most probably related to hydrodynamic shocks taking place in this region of the field-free solar atmosphere (see, e.g., Moll et al. 2012 ). Therefore, not all swirls found at chromospheric levels are necessarily related to the magnetic field, even though the magnetism clearly plays a cardinal role in the generation of vertical vortices. The above more qualitative assessment is confirmed by the quantitative analysis of Fig. A.2 , which shows for each simulation a bi-dimensional histogram of the inclination angle cos( θ ) of the swirling strength vector at each height z . The angle θ is defined through being the angle between the swirling strength vector λ and the unit vector in the vertical direction . Therefore, horizontally oriented swirls are binned close to cos( θ ) = 0, while vertically oriented swirls are close to cos( θ ) = 1. We choose to plot the histogram of cos( θ ) instead of θ in order to easily recognize isotropy. In this way, an isotropic angle distribution at a certain height z is characterized by a flat distribution in the histograms of Fig. A.2 . In the convection zone, that is, for z ≲ 0 km, all three simulations show a flat distribution, which confirms the nearly isotropic distribution of swirls in that region. Also, as estimated before, there are on average more swirls in the Hydro simulation (panel c) than in the MHD 50 G (panel b) and the MHD 200 G (panel a) simulations. Near the optical surface, that is, around z = 0 km, there is a sudden break of isotropy. Two families of vortices can be spotted. First, a cluster of horizontally oriented swirls (cos( θ )≈0), visible in all three


to the total flux. Thus we believe the signal to belong to the visual companion star, which has a temperature of 5430 K. A rotation period of 4.6 d is fairly rapid for a star of T eff = 5430 K, which may imply a young age for the system, consistent with our bagemass analysis in Section 6 . 5 COMBINED MCMC ANALYSIS We use a Markov chain Monte Carlo (MCMC) approach to fit the combined photometric and radial velocity data, as well as investigate the RM effect. We follow methods very similar to Temple et al. ( 2018 , 2019 ), whereby we conduct both an RM analysis and a tomographic analysis and adopt the better constrained solution. The RM analysis involves detecting the line profile distortions as an apparent overall shift in radial velocity measurements (e.g. Triaud 2017 ), whereas the tomographic analysis requires one to directly map the motion of the distortion caused by the occulting body across the line profiles as a function of phase (e.g. Brown et al. 2017 ; Temple et al. 2017 ). The code we use is described by Collier Cameron et al. ( 2007 , 2010 ) and Pollacco et al. ( 2008 ). The combined photometric and RV fitting determines the orbital period P , the epoch of mid-transit T c , the planet-to-star area ratio ( R p / R ⋆ ) 2 , the transit duration T 14 , the impact parameter b , the stellar reflex velocity semi-amplitude K 1 , and the barycentric system velocity γ. We use the value of T eff obtained in the dilution correction as input, and interpolate four-parameter limb darkening coefficients from the Claret ( 2000 , 2004 ) tables in each step using the current value of T eff . We use the stellar radius obtained in Section 4.2 (1.17 ± 0.08 ) as a prior to constrain stellar parameters. In the fit we present, we have assumed that the orbit is circular, as one would expect a hot Jupiter to circularize on a time-scale shorter than its lifetime (Pont et al. 2011 ). However, a further fit was carried out to test this assumption, leading to an upper limit of e 0.27 (95 per cent confidence). We display the photometry and best-fitting transit model in Fig. 2 . Figure 2. The WASP discovery photometry (top) and follow-up transit light curves (bottom) with the best-fitting model shown in blue (see Section 5 ). The data for the three follow-up light curves, prior to the dilution correction, are available online as supporting material . The RM fit and Doppler tomography give values for v sin i ⋆ , λ, and the system γ-velocity. We use the calibrations of Hirano et al. ( 2011 ) to fit the RM effect. For Doppler tomography, we assume a Gaussian profile for the perturbation to the stellar-line profiles and fit the intrinsic full width at half maximum (FWHM) of the perturbation, v FWHM . Both methods also provide an additional constraint on the impact parameter b , although the tomographic method fits this quantity more directly. We estimate the start value for γ by fitting a Gaussian profile to the CCFs. We also apply the spectral v sin i ⋆ as a


can differ from a standard average value, depending on stochastically sampled explosions that have enriched a given galaxy. In addition, inhomogeneous mixing of gas results in different element abundance ratios in the next generation of stars. The same is true for other element abundance ratios, such as [Mg/Ca] or [Na/Mg]. Since there are model predictions of explosions of Pop iii stars, producing low [Na/Mg], we suggest them to be responsible for the low [Na/Mg] detected in MP stars. We failed to fit abundance patterns of any of our sample stars with a single nucleosynthesis event, however, we suggest that a small number of SN ii explosions including those with low [Na/Mg] contributed to the abundances found in the investigated stars. A comparison of observed relative [El/Mg] abundance ratios with nucleosynthesis predictions should be performed with a caution. We note that our sample stars are too metal rich to be fitted with yields from only one explosion. For each selected model, its metallicity is about [Fe/H]≃ −3, which is lower compared to that of the sample stars (−2.5 [Fe/H] −2.1). Magg et al. ( 2020 ) estimated analytically a limit for the dilution of metals produced by a single SN and recommended to account for not only element-to-element abundance ratios, but also the absolute abundance values when fitting stellar abundance patterns with nucleosynthesis yields. In their calculations, the following assumptions were adopted: the SN being alone and isolated, the explosions being spherical and well-mixed, and the surrounding medium being homogeneous. The latter assumption is not always fulfilled (see for example Chiaki Tominaga 2020 ). We also note that to date there is no a metal-poor star, whose extensive abundance pattern is reasonably well fitted with the yields from a single nucleosynthesis episode, despite many attempts that were made (see for example, Tominaga et al. 2007 ; Placco et al. 2015 ; Hansen et al. 2020a ). 5.3 Neutron-capture elements in classical and ultrafaint dwarf galaxies In the majority of EMP stars, n-capture elements are represented by Sr and Ba. A number of the Galactic studies reported on a large scatter of [Sr/Ba], of about 2 dex, which decreases with increasing [Ba/H] (Honda et al. 2004 ; François et al. 2007 ; Andrievsky et al. 2011 ). In classical dSphs, abundances of Sr and Ba at the lowest metallicity are at or below the lowest values in the MW halo, however, the [Sr/Fe] and [Ba/Fe] ratios increase toward the solar ratio as [Fe/H] increases, similarly to that for the MW halo (Cohen Huang 2009 , 2010 ; Jablonka et al. 2015 ; Mashonkina et al. 2017b ). Very low abundances of Sr and Ba were reported for the majority of UFDs (Frebel et al. 2010 ; Simon et al. 2010 ; Gilmore et al. 2013 ; Koch et al. 2013 ; Koch Rich 2014 ; Ji et al. 2016c , a ; Nagasawa et al. 2018 ). In the UFDs, the [Sr/Fe] and [Ba/Fe] ratios do not rise with metallicity, they scatter around a mean floor level of −1 and −0.7,


directions of Sgr A* were 0.056 and 0.060 mas yr −1 respectively. Figure 5. Comparison of the stability of the reference frame as measured by the average differences between the positions and velocities in the radio and IR. The agreements of the maser positions (left) and velocities (right) in the IR are compared to those in the radio. The ellipses represent 1 σ , 2 σ , and 3 σ uncertainties. For the Keck/NIRC2 data, the uncertainty in the distortion correction of 1 mas that dominates the IR error was subtracted so as to show the improvement in the methods used in this paper to construct the reference frame. Using the NACO imager on VLT, Plewa et al. ( 2015 ) reports a stability of ∼0.17 mas in position and ∼0.07 mas yr −1 in velocity. Their analysis used eight masers because their mosaicked field covered 42 arcsec × 42 arcsec. However, their maser sample did not include IRS 7. IRS 7 is a supergiant and its SiO maser features originate from a much larger maser emission region than the other masers used (Reid et al. 2003 ) by a factor of ∼2, which is reflected in larger uncertainties in the star’s radio positions and proper motions. To see how much effect this one star has on the IR reference frame, we construct the reference frame without IRS 7. Excluding IRS 7, we obtain combined positional and velocity uncertainties of 0.17 mas and 0.031 mas yr −1 respectively. The velocity stability of our sample of six masers, without IRS 7, is still a factor of 2 better than the one reported by Plewa et al. ( 2015 ). This is because IRS 7 has less influence on the overall reference frame due to the very large errors assigned to its radio velocities. The maser sample used by Plewa et al. ( 2015 ) also had one less epoch of the radio observations. Furthermore, their IR observations included data through 2013, while our IR data extend four additional years. As explained in Section 5 , the IR data and the method used to create the reference frame presented in this paper were modified significantly compared to those used in Yelda et al. ( 2010 ). The comparison of the reference frame of Boehle et al. ( 2016 ) with that of Plewa et al. ( 2015 ) is likely more appropriate, because both use the maser data through 2013. 5. Discussion We have presented an improved astrometric reference frame that utilizes 13 years of IR observations of radio-emitting SiO masers in the vicinity of the Galactic Center. Since our previous work in Yelda et al. ( 2010 ), several modifications have been made in the construction of the reference frame including: (i) using 13 epochs of maser data (2005–2017) instead of six epochs (2005–2010) used by Yelda et al. ( 2010 ); (ii) using an improved PSF-fitting package, AIROPA, instead of StarFinder v1.6 (Diolaiti et al. 2000 ) used in Yelda et al. ( 2010 ); (iii) using a new method to mosaic 9 or 13 dither positions for each epoch of observations. Yelda et al. ( 2010 ) stitched together one field at a time, building up the starlist by one


bias evolution scheme of Basilakos Plionis (2001 , 2003) , which is based on linear perturbation theory and given by ( Basilakos et al. 2011 ) with The constants (the present day bias factor) and depend on the host dark matter halo mass and for the CDM model are given by where ( Basilakos et al. 2012 ). This bias evolution model has been thoroughly tested and found to rate very well in reproducing -body simulation data ( Basilakos et al. 2008 ) as well as fitting observational data ( Papageorgiou et al. 2012 ). Fig. 1 Redshift evolution of the comoving clustering length for the two different parametrizations of clustering evolution. For the case of our model (Eq. ( 13 )), shown as black and blue curves, the different evolution behaviours shown correspond to the indicated parameters ). The specific values of these parameters have been chosen such as to resemble the and models of the traditional parametrization of Eq. ( 7 ), shown in red, which correspond to the constant in comoving coordinates clustering (for ) and to the stable clustering models (for details see the text). We therefore see that through the dependence of the bias factor on the dark matter halo mass, one expects a different clustering evolution for dark matter halos of different mass for the same values of and . In order to appreciate our parametrization of the clustering evolution we present in Fig. 1 the evolution of the comoving clustering length for models that have been purposely selected to resemble some based models. As can be seen the model with is equivalent with the constant in comoving coordinates clustering model () up to very large redshifts (). No other ( combination can provide such an equivalence up to such high redshifts. However, as we can again see in Fig. 1 , one can find () combinations that correspond to the comoving clustering model, but up to , as the example shown with . In fact one can derive the degeneracy between the and parameters such that the clustering evolution is constant in comoving coordinates (), but up to , since beyond this redshift the equivalence is unattainable. In Fig. 2 we present the corresponding 1, 2, and 3 contours in the ) parameter space of the solution that provides the above equivalence with the model. The range is dictated by the uncertainty that we have imposed on , which is taken to be of , typical of current accurate measurements. The degeneracy is clear and it can only be broken if we either impose a value of , for example from the expected slope of the power spectrum on these scales, or from an independent estimate of the mass of the dark matter halos in which the tracers (in our case X-ray selected AGN) reside. Fig. 2 Contour ranges of 1, 2 and 3 in the parameter plane for the case where our clustering evolution scheme corresponds to the constant in comoving coordinates model (imposed up to in this example). The strong degeneracy of the parameters is evident. Similarly, larger values of provide clustering evolution


in the whole COSMOS field) to a control sample of 109 normal star-forming main sequence galaxies. We have performed an additional visual merger identification among the main sequence population and applied the classical Gini- M 20 classification to select galaxies with merger-like shapes. Our main results are summarized as follows: First, starburst and main sequence galaxies have different clumpiness histogram distributions: the former dominate in the high clumpiness regime, while the latter are mostly found at lower clumpiness. Given the merger nature of intermediate- z starbursts, this suggests that mergers are likely responsible for the formation of bright clumps and for the increase of the clumpiness with respect to normal star-forming isolated disks. Secondly, the majority (76%) of morphological mergers (according to Gini- M 20 based criterion by Lotz et al. 2008 ) are starburst galaxies. However, 57% of starbursts are not classified as mergers from their i -band morphology. This suggests that the Gini- M 20 merger selection is highly incomplete, likely due to multiple effects, including the galaxy inclination, the impact parameter, the dust attenuation, and the rapid fading of merger signatures after the coalescence. Furthermore, a larger difference among the clumpiness distributions is obtained both when comparing morphological mergers to not merger systems. In particular, Gini- M 20 mergers, regardless of their level of SFR, have a median clumpiness a factor of three higher compared to the rest of the population, and are almost entirely responsible for the high clumpiness tail observed among our sample. We also find a positive correlation between the clumpiness and the distance from the main sequence, for morphologically selected mergers. From hydrodynamical simulations of merger galaxies with initial conditions typical for our redshift range, we also confirm that mergers can significantly enhance the clumpiness compared to isolated main sequence systems, by a similar amount to that observed in real images. Different spin-orbit couplings of colliding galaxies can fully explain the scatter of the clumpiness observed in our sample (from 0 to 20%). Afterward, for a sample of 21 SBs with previous Magellan-FIRE spectra, there is a mild correlation between the clumpiness and the equivalent width of Balmer and Paschen lines, suggesting a possible clumpiness evolution during the merger, decreasing from early-intermediate to later, post-coalescence stages. X-ray detected AGNs are preferentially found in low-clumpiness systems, suggesting a possible evaporation or destruction of clumps induced by AGN feedback. However, other effects (including galaxy inclination, rotation, attenuation, and impact parameter) are likely responsible for the low correlation strength (≃2 σ ). Finally, using four high-resolution images in different optical or near-IR bands, available for three clumpy starbursts identified in the COSMOS-CANDELS field, we suggest that


analysis is beyond the scope of this work and will be discussed in Paper III. The results presented herein provide a statistically significant list of values and histogram distributions for reference and baselines in future work. Given the large statistics in this investigation, the beam/strahl fits for selection criteria Criteria UP are now the most comprehensive attempt to parameterize the beam/strahl electron velocity moments in the ambient solar wind. These results are useful for multiple modeling and simulation studies in addition to comparison with inaccessible regions like the intracluster medium. Further, these results will provide a statistical baseline for the Parker Solar Probe mission and the future Solar Orbiter and IMAP missions. Appendix A Definitions and Notation As in Paper I , in this appendix the symbols and notation used throughout will be defined. For all direction-dependent parameters we use the subscript j to represent the direction, where j = tot for the entire distribution, j = ∥ for the the parallel direction, and j = ⊥ for the perpendicular direction, where parallel/perpendicular is with respect to the quasi-static magnetic field vector, (nT). The generic subscript s is used to denote the particle species (e.g., electrons, protons, etc.) or the component of a single particle species (e.g., electron core). For the electron components, the subscript will be s = ec for the core, s = eh for the halo, s = eb for the beam/strahl, s = eff for the effective, and s = e for the total/entire population. Below are the symbol/parameter definitions: – one-variable statistics – X min ≡ minimum – X max ≡ maximum – – – X 25% ≡ lower quartile – X 75% ≡ upper quartile – σ ≡ standard deviation – σ 2 ≡ variance – fundamental parameters – ε o ≡ permittivity of free space – μ o ≡ permeability of free space – c ≡ speed of light in vacuum (km s −1 ) = – k B ≡ the Boltzmann constant (J K −1 ) – e ≡ the fundamental charge (C) – plasma parameters – n s ≡ the number density (cm −3 ) of species s – m s ≡ the mass (kg) of species s – Z s ≡ the charge state of species s – q s ≡ the charge (C) of species s = Z s e – T s , j ≡ the scalar temperature (eV) of the j th component of species s – the temperature ratio (N/A) of species s and s ′ of the j th component – the temperature anisotropy (N/A) of species s – V Ts , j ≡ the most probable thermal speed (km s −1 ) of a one-dimensional velocity distribution (see Equation 1 (c)) – ≡ the drift velocity (km s −1 ) of species s in the plasma bulk flow rest frame – C s ≡ the sound or ion-acoustic sound speed (km s −1 ) (see supplemental PDF file in Wilson et al. 2019b , for definitions) – V A ≡ the Alfvén speed (km s −1 ) (see supplemental PDF file in Wilson et al. 2019b , for definitions) – V f ≡ the fast mode speed (km s −1 ) (see supplemental PDF file in Wilson et al. 2019b , for definitions) – Ω cs ≡ the angular cyclotron frequency (rad s −1 ) (see Equation 1 (d)) – ω ps ≡ the angular plasma frequency


the site S234. The data were observed with the Giant Metrewave Radio Telescope (GMRT) facility on 2016 December 8 (Proposal Code: 31_025; PI: L. K. Dewangan). The radio data reduction was carried out using the AIPS software, in a similar manner to that given in Mallick et al. ( 2012 , 2013 ). The synthesized beam size and the rms noise of the final 610 MHz continuum map are 56 × 46 and 120 μ Jy/beam, respectively. It is expected, specifically at low frequencies, that a sufficient amount of background emission will increase the antenna temperature while observing the source. Hence, we corrected the final GMRT map at 610 MHz for system temperature (see Omar et al. 2002 ; Mallick et al. 2012 , 2013 ; Baug et al. 2015 ). More details about the procedure adopted for correction of system temperature can be found in Mallick et al. ( 2012 , 2013 ). 2.2 Archival Data Sets The multi-wavelength data sets are also retrieved from different surveys (e.g., the NRAO VLA Sky Survey (NVSS; λ = 21 cm; resolution = 45′′; Condon et al. 1998 ), the Five College Radio Astronomy Observatory (FCRAO) 12 CO (1–0) and 13 CO (1–0) line data ( λ = 2.6, 2.7 mm; resolution ∼45′′; Heyer et al. 1998 ; Brunt 2004 ), the Herschel Infrared Galactic Plane Survey (Hi-GAL; λ = 70, 160, 250, 350, 500 μ m; resolutions = 58, 12′′, 18′′, 25′′, 37′′; Molinari et al. 2010 ), the Wide Field Infrared Survey Explorer ( WISE ; λ = 3.4, 4.6, 12, 22 μ m; resolutions = 61, 64, 65, 12′′; Wright et al. 2010 ), the Warm- Spitzer IRAC 3.6 and 4.5 μ m photometric data (GLIMPSE360; λ = 3.6, 4.5 μ m; resolution = 2′′; Whitney et al. 2011 ), the UKIRT NIR Galactic Plane Survey (GPS; λ = 1.25, 1.65, 2.2 μ m; resolution ∼08; Lawrence et al. 2007 ), the Two Micron All Sky Survey (2MASS; λ = 1.25, 1.65, 2.2 μ m; resolution = 25; Skrutskie et al. 2006 ), and the Isaac Newton Telescope (INT) Photometric H α Survey of the Northern Galactic Plane (IPHAS; λ = 0.6563 μ m; resolution ∼1′′; Drew et al. 2005 )). One can learn more details of these data sets and their analysis procedures in Dewangan et al. ( 2017e ). 3 Results 3.1 Extended Features in the Direction of l = 1717–1741 To explore the extended and embedded features toward l = 1717–1741, we have employed the submillimeter image at 250 μ m, a radio continuum map at 1.4 GHz (having an rms sensitivity of ∼0.45 mJy/beam; Condon et al. 1998 ), and 12 CO ( J = 1–0) line data (having a velocity resolution of 0.25 km s −1 and an rms sensitivity of 0.25 K; Heyer et al. 1996 , 1998 ). These data enable us to depict cold dust, ionized gas, and molecular gas in the sites. Figure 1 (a) displays the submillimeter image at 250 μ m overlaid with the 1.4 GHz continuum emission contours. Figure 1 (b) shows the 12 CO emission contour map at [−17.75, −1.0] km s −1 . We have labeled at least six objects (i.e., S237, S234, IRAS 05253+3504, IRAS 05231+3512, IRAS 05220+3455, and V582) in Figures 1 (a) and (b). The submillimeter image traces a spherical shell morphology of the site


this is 0.3 ≲ f h ≲ 0.4 for halo masses M 12 ∼ (0.5−2) at redshift z ≳ 2 (Roca-Fàbrega et al. 2019 ), while observations of M 12 ∼ (1−10) haloes at z ≳ 0.1 suggest f h ∼ 0.2−0.3 (Singh et al. 2018 ). We define f h,0.3 = f h /0.3. Δ( R v ) is the ratio of the density at R v to the mean density in the halo, . For a singular isothermal sphere Δ( R v ) = 1/3, while for an NFW halo with concentration c = (5, 10, 20), Δ( R v ) ∼ (0.24, 0.19, 0.14), respectively. We write Δ 1/6 = Δ( R v )/(1/6). Assuming cosmological parameters Ω m = 0.3 and , we obtain for the stream density at R v where δ 100 = δ/100 and . For a hydrogen mass fraction of X = 0.76, this yields a hydrogen number density in the stream at R v of We hereafter write . The stream radius at R v can be constrained using the mass flux through the stream, where is the total mass accretion rate on to the halo virial radius, and f s is the fraction of baryonic accretion along the gas stream. Cosmological simulations suggest f s ∼ (0.2−0.5) with a typical value of f s = 1/3 (i.e. three significant streams; Danovich et al. 2012 ). In the Einstein de Sitter (EdS) regime (valid at z > 1), the accretion on to the virial radius is well approximated by (Dekel et al. 2013 ) with halo-to-halo variance encapsulated by the normalization s ∼ (0.5−2). Combining equations ( 15 ), ( 23 ), ( 25 ), and ( 26 ), we obtain with . Together with equation ( 16 ), we have Note that this is larger by a factor of ∼2 than the corresponding equation (68) in Padnos et al. ( 2018 ), which seems to be due to a typo, as it is consistent with their equation (67). Using equation ( 21 ) for δ, we see that and is independent of redshift. More massive haloes are thus fed by relatively narrower streams compared to their virial radii. We hereafter substitute . The hydrogen column density perpendicular to the stream axis is N H, 0 = n H, 0 R s . Using equations ( 24 ) and ( 27 ), this yields For haloes at z ∼ 2, this is large enough for the streams to be largely self-shielded against the UV background if the neutral fraction is x H i ≳ 10 −3 . In collisional ionization equilibrium (CIE), this is true for (e.g. Goerdt et al. 2010 ), i.e. Θ s ≲ 2. Of course, streams may still be susceptible to local sources of UV radiation, such as star formation in satellite galaxies located along the stream, or starbursts/AGN activity in the central galaxy. To summarize, given the halo mass and redshift, the precise temperatures of the stream and halo gas, Θ s and Θ h , respectively, determine the density contrast, δ. The stream Mach number, M b , is then interchangeable with η, the ratio of stream-to-virial velocity. The stream density is then determined by , the normalization of the hot halo gas density near R v . Finally, the ratio of stream radius to virial radius is set by , the normalization of the gas accretion rate along the stream. For η ∼ 1, , and , a stream at z = 2 has , (0.05−0.28), and (0.03−0.16) for δ = 30, 100, and 300, respectively.


reduced to a negligible percentage (Magliocchetti etal. 2002 ; Mauch Sadler 2007 ). We then distinguished between AGN-powered galaxies and star-forming galaxies by means of equation ( 1 ) for z 1.8 and by fixing log 10 P cross ( z )23.5 [W Hz 1 sr 1 ] at higher redshifts. This procedure identifies 704 AGNs (corresponding to 33percent of the total radio population) and 1419 star-forming galaxies. With respect to our earlier work, these numbers imply an increase of a third of sources in both the AGN and the SF samples and allow us to draw conclusions on the properties of radio-selected sources with and without an FIR counterpart on much more solid grounds. Also, note that, due to the adopted selection criteria and thanks to the depth of the VLA-COSMOS survey, the AGN samples are complete with respect to radio selection at all redshifts z 3.5, i.e. the considered sample includes all radio-emitting AGNs selected at 1.4 GHz in the COSMOS field and endowed with a redshift determination z 3.5. 272 sources classified as AGNs and 901 sources classified as star-forming galaxies also show up in the Herschel maps. The redshift distribution of radio-selected AGNs is presented in Fig. 1 . The filled histogram shows the distribution of all AGNs, independent of their FIR emission, while the dashed (red) histogram represents that of those AGNs which also appear in the Herschel maps. The bottom panel highlights the ratio between these two quantities. Errorbars correspond to 1 Poissonian estimates. As already seen in Magliocchetti etal. ( 2014 ), also in the present case we have that the redshift distribution of radio-selected AGNs presents a marked peak at a redshift z 1. However, the better statistics of the present data allow us to identify a prominent tail which extends up to z 3.54 and which in Magliocchetti etal. ( 2014 ) only showed up as a secondary peak centred around z 2.5. There is no functional difference between the distribution of the parent AGN population and that which corresponds to AGNs with an FIR counterpart. One is the scaled version of the other, and the ratio between these two quantities is roughly constant and equal to the value of 0.5 throughout the whole redshift range probed by our data. Figure 1. Redshift distribution of COSMOS-VLA radio-selected AGNs with fluxes F 1.4GHz 0.06mJy. The AGN sample is complete up to z 3.5. The solid line represents all sources irrespective of their FIR emission, while the dashed line indicates those objects which are also FIR emitters. The bottom panel highlights the ratio between the two quantities. Errorbars correspond to 1 Poissonian estimates. Some more information on the sources under exam can be provided by investigations of the distribution of their radio luminosities, both in the presence and in absence of FIR emission. This is shown in Fig. 2 , whereby the left-hand plot shows the distribution of sources at all redshifts, while the one on the right-hand side that of sources divided into


Fig. 1 were obtained with the 1.6-m telescope of the National Laboratory for Astrophysics (Brazil) on 2011 May 31 (Ivanova et al. 2018 ). The instrumental setup and data processing are presented in detail in Cavichia, Costa Maciel ( 2010 ) and Ivanova et al. ( 2016 ). Table 1 summarizes the characteristics of our observations: the date of observation (the mid-cycle time, UT date), the geocentric ( ∆ ) and heliocentric ( r ) distances, the phase angle of the comet ( α ), the position angle of the extended Sun–comet radius vector ( φ ), the filter (photometry) and grid (spectroscopy), the total exposure time during the night ( T exp ), and the mode of the observation. Table 1. Log of the observations of comet 29P/Schwassman–Wachmann 1. 3 MORPHOLOGY OF THE COMA As can be seen in Fig. 1 , the λ4277/39 Å filter transmits the radiation of CO + ions and the continuum, whereas the transmitted radiation flux through the λ5309/169 Å filter may truly be considered as the continuum, without CO + ions. Thus, to derive the pure ion image, we subtracted the composite image of the continuum that was obtained in the SED537 filter from the combined CO + image, controlling the particular light transmission of each filter and various continuum levels. We used values of reddening obtained from the spectral observations of comet 29P presented by Korsun et al. ( 2008 ) and Ivanova et al. ( 2016 , 2018 ). The images of the comet in the two filters were centred using the central isophotes, which was closest to the maximum brightness of the comet. The panels on the left of Fig. 2 present the intensity maps of the isolated CO + coma after subtraction of the continuum intensity from the observed intensity in the CO + band, and the panels on the right present the images of the dust coma of comet 29P. Figure 2. Isolated CO + (a, c, e, g) and dust (b, d, f, h) coma of comet 29P derived from observations on November 8, 2007, December 4, 2008, March 29, 2009 and December 26, 2009. All images are scaled to erg cm −2 s −1 Å −1 . The values near the white contours, corresponding to the column density at a cometocentric distance about 20 000 km, are presented in Table 2 . The sunward (⊙), north (N) and east (E) directions, and the cometary motion vector (V) are shown. The isolated CO + coma is clearly observed on all the dates of observation presented here (see Fig. 2 ): it is compact, asymmetric relative to the optocentre, and always elongated in the sunward direction, although this elongation does not coincide exactly with the direction to the Sun. The CO + coma observed on 2007 November 8 was only slightly elongated in the sunward direction, while on 2008 December 4 the comet had a very compact and strongly elongated CO + coma in the solar hemisphere to at least 60 000 km. On 2009 March 29, the comet had a small asymmetric coma with strong sunward elongation. In contrast to the CO + coma, the dust coma, formed by sunlight scattered from dust particles, was more extended and


the positions on the SED of the observational wavelengths for various instruments of interest here: 250, 350, and 500 μ m for the SPIRE instrument on board Herschel ; 450 and 850 μ m for the SCUBA-2 instrument at the James Clerk Maxwell telescope; ∼1100 μ m for AzTEC at the LMT; 1400 μ m for SPT ; and 850, 1400, and 3000 μ m for ALMA . We have also highlighted the 5 σ detection limits for such instruments (attained in the deepest large-scale surveys undertaken so far or in the near future): S 250 ≈ 35 mJy, S 350 ≈ 40 mJy, and S 500 ≈ 50 mJy for SPIRE; S 450 ≈ 8 mJy and S 850 ≈ 2 mJy for SCUBA-2 ; S 1100 ≈ 1 mJy for AzTEC ; S 1400 ≈ 20 mJy for SPT ; and S 850 ≈ 0.42, S 1400 ≈ 0.11, and S 3000 ≈ 0.02 mJy for ALMA (500 hr on 100 arcmin 2 ). The accurate determination of the spectroscopic redshift for a large sample of dusty galaxies is a major problem. In order to probe the bright end of the SFR function at z ≳ 3, a strategy could be to preselect high-redshift sources using flux/color criteria from surveys conducted with Herschel or SCUBA-2 , and then perform a more accurate photometric (or even spectroscopic) redshift determination with observations on source by, e.g., AzTEC and ALMA . Commonly used preselection criteria (e.g., Dowell et al. 2014 ; Asboth et al. 2016 ) for high-redshift sources based on Herschel photometry involve looking for “350-peakers,” which are defined as sources with S 350 / S 250 ≳ 1 and S 500 / S 350 ≲ 1, or “500-risers,” which are defined as sources with S 350 / S 250 ≳ 1 and S 500 / S 350 ≳ 1. Actually, the uncertainties in the flux measurements make the distinction between peakers and risers quite loose; moreover, at z ≳ 4, the channel at 250 μ m refers to rest-frame wavelengths λ ≲ 50 μ m, where details of the SED due to different dust properties and a possible contribution from an AGN component can be relevant. Thus, here, we mainly focus on the color S 500 / S 350 . In Figure 9 (bottom panel), we plot its evolution with redshift and compare it with the measurements from ALMA /ALESS by Swinbank et al. ( 2014 ), finding reasonable agreement within the large uncertainties. Sources with S 500 / S 350 ≳ 0.8 are high-redshift z ≳ 3 candidates. However, the rather high limiting fluxes of Herschel cannot probe the SFR function much above z ∼ 5, since even sources with SFR ψ ≳ 10 3 M ⊙ yr −1 are too faint to be detected. To go much beyond z ≳ 4, the preselection based on the color S 850 / S 450 from SCUBA-2 photometry is much more efficient. In Figure 9 (bottom panel), we plot its evolution with redshift and compare it with the measurements from SCUBA-2 by Koprowski et al. ( 2016 ), again finding reasonable agreement. It can be seen that the color condition S 850 / S 450 ≳ 0.6 can be exploited to preselect candidate galaxies at z ≳ 4. In Figure 10 , we show our predictions for the differential counts at 500 and 850 μ m for the red sources preselected according to the color criteria discussed above. At 500 μ m, the


in steps of 1′′ (a total field of view 15 × 119). The roll angle of the slits is –45° to the N–S direction on the Sun. Here, we focus on FUV spectra from both channels containing ∼1333–1337 Å (C ii lines), ∼1342–1344 Å (continuum), ∼1348–1351 Å (Fe xii line), ∼1353–1356 Å (Fe xxi and O i lines), and ∼1399–1406 Å (Si iv line), and on the NUV channel containing four spectral regions: 2791–2806 Å (Mg ii h and k lines), 2813–2816 Å, 2825–2828 Å, and 2831–2834 Å. IRIS also recorded SJIs for four passbands with a step of 2′′ and a total field of view 120 × 119: 1330 Å (C ii transition-region filter), 1400 Å (Si iv transition-region filter), 2796 Å (Mg ii k chromospheric filter), and 2832 Å (Mg ii wing photospheric imaging). 2.2. Solar Flare on 2014 March 29 An X1 flare observed on 2014 March 29 occurred in the active region NOAA 12017 with the GOES 1–8 Å flux starting to rise impulsively at 17:45 UT and peaking at 17:48 UT. IRIS started to observe the active region three hours before the flare, and the observations lasted a few minutes after the flare peak with the NUV exposure time of 8.00 s before 17:46:04.78 UT and 2.44 s after 17:46:13.98 UT, and a 75 s raster cadence (see e.g., Heinzel Kleint 2014 and Kleint et al. 2015 , 2016 ; Liu et al. 2015 ; Young et al. 2015 for detailed descriptions of IRIS observations of this flare). In contrast to the previous flare, the gradual phase was detected only at its beginning, and the flare loops are barely visible. Moreover, the slit rasters cover only the less pronounced parts of the loop system. We add this X-type flare because it was widely studied in the literature; however, our detailed analysis is focused mainly on IRIS spectra from the flare of 2015 June 22. To show the time lag between the flare ribbons and loops, light curves from a small part of the flare ribbons (red) and their corresponding loop tops (blue) in 1400 and 2796 Å are plotted in Figure 2 . It is seen that the loop tops peak about 3 minutes later than the ribbons in both 1400 and 2796 Å channels. Figure 2. Time lag between the flare ribbons and loops for 2014 March 29. Light curves from a small part of the flare ribbons (red lines) and their corresponding loop tops (blue lines) in 1400 and 2796 Å. Black lines represent the integral emission from the whole flare. Note that the sharp blue peak between 17:45 and 17:46 is due to leakage of saturated emission from the ribbon. 2.3. The Radiometric Calibration In our analysis, we used IRIS -calibrated data (Level 2 data), which are corrected for dark current, flat field, and geometry effects, and are wavelength calibrated. The radiometric calibration was performed in the following way. Intensities in the IRIS data are given in Data Number (DN) or counts (DN s −1 ). We perform radiometric calibration of the observed intensities to absolute units [erg s −1 cm −2 sr −1 Å −1 ]. To convert intensities to absolute units, we used the following calibration procedure:where I abs is the absolute


in Section 5 . To facilitate discussion, we define as a reference value. In order for MI to be disfavoured by less than 3σ, must be lowered by with fixed degrees of freedom. Hence, it would likely require a combination of (1) a different definition of r bar , (2) different values for the mass-to-light ratios, possibly including radial dependence, (3) removal of statistical outliers, and (4) other effects. Regarding point (1): There is an unaccounted bias in that the bins are defined by r bar , a point that is affected by uncertainty. The impact of this bias can be roughly estimated by moving r bar one point towards smaller (larger) radii. Doing so yields a reduction in χ 2 relative to , however with the accompanying degrees of freedom . The reduction in degrees of freedom (galaxies) are due to the criterion of at least two points at small radii. Considering the reduced chi square changes from to after the shift to smaller radii, it can be concluded that although the shift in r bar greatly affects the χ 2 it only slightly reduces the statistical disfavouring of MI. Regarding point (2): The dependence on the mass-to-light ratios may significantly affect g bar and consequently both the expected value of MI and the specification of r bar . The fixed mass-to-light ratios used here ( and ) are not optimal for all galaxies. This is clear from the rotation curve plots in Appendix C , where for some galaxies v bar > v obs for limited radial range (e.g. as is the case for CAMB and NGC 4217). To roughly gauge the effect of radically different mass-to-light ratios, we take (corresponding to galaxies dominated by DM at all radii, Lelli et al. 2017 ), yielding an increase in the χ 2 relative to (the result become slightly more significant). This is, however, just an example and one can imagine changing individual mass-to-light ratios and uncertainties potentially having a great impact on the result. Regarding point (3): Fig. 5 shows the distribution of residuals. Of the galaxies with | R i | > 4 UGC11455, NGC 4217, NGC 3109, ESO563-G021, and D631-7 have quality flag 1 whereas CAMB have quality flag 2 (listed in the SPARC data base). This indicates that the disfavouring of MI is not rooted in bad data (Fig. B1 in Appendix B shows residuals after discarding all galaxies with quality flag larger than 1). That being said, as mentioned in point (2), the fixed mass-to-light ratios used are too large in case of NGC 4217 and CAMB and possibly also affect the innermost radii of UGC11455 and ESO563-G021. It can also be argued that the high residual value in case of ESO563-G021 is at least partially rooted in a peculiar selection of points (e.g. see Fig. C1 in Appendix C ). Hence, although data are of good quality, for several of the significant outliers, there are valid arguments that could at least partially explain the high residuals. To be conservative and test the dependence on the outliers, we proceed to discard all galaxies with | R i | > 4. Doing so yield a


The x -axis in the line profiles gives the lambda channels and the y -axis is the intensity in arbitrary units. Both [S ii ] lines at 6717 Å and 6731 Å are detected. The decomposition of each profile is indicated by the thin lines. The resulting profile is shown as hollow circles and with numbers. The dotted line represents the sum of all fitted components. We assume the brightest component of the line to be the main velocity component of the SNR. It is marked with a 0 in Fig. 6 . For each emission line, we can also identify two extreme velocity components. We shall refer to these as V min and V max . These are marked with a 2 and a 4, respectively. Table 3 reports the velocity components of the [S ii ] λ6717 Å line. Column 1 is the region ID. Columns 2, 3 and 4 indicate the main and extreme velocity components ( V min and V max ) corrected for the local standard of rest (LSR). Column 5 gives the difference in velocity between the extreme velocity components. Column 6 lists the distance of each region in arcmin to the geometrical centre of the SNR. Column 7 lists the [S ii ]/H α line ratio and finally column 8 indicates the associated filament to which each region belongs. As one can see from Fig. 6 and Table 3 , the radial velocity profiles are, in general, composite, implying large motions as expected in a SNR. They show at least three velocity components. The brightest one corresponds to the systemic motion of the SNR, while two faint velocity components are seen at extreme velocities. The several velocity components found in the velocity profiles of the filaments are probably due to the SNR shock expansion, as well as to contamination due to the interaction of the SNR gas with dense interstellar clouds that could be associated with the H ii regions located to the north and south-west of the remnant. Note the existence in the SNR velocity profiles of a velocity component also identified with those of regions located in the Perseus arm, as we will discuss below. The velocities of the main component vary from −34 to −89 km s −1 . Taking the average of all the velocities of the main components in Table 3 , we obtain a LSR velocity of −59 ± 17 km s −1 as a first estimate of the systemic velocity of the SNR. The averages for the extreme velocity components, in all the boxes where velocity profiles were extracted, are V min ∼ −122 km s −1 and V max ∼ +152 km s −1 . Another way of obtaining the systemic velocity is to average the extreme velocity components ( V min and V max ). Doing this, we obtained a systemic velocity V LSR = −50 ± 6 km s −1 . For some regions, we find an additional velocity component averaging 1 km s −1 . This latter velocity component agrees with the component found by Roberts ( 1972 ) in the theoretical H i profile of the TASS model at 12° pitch angle ( V LSR = 0 km s −1 ) in the direction of SNR CTB 109. Roberts ( 1972 ) attributed this component to gas located very close to the Sun in the Orion spur. Fig. 7 shows a


flux ratio . The sum of the model primary and rescaled secondary spectra was then rectified to a unit continuum. We then repeated the CCF and tomography analysis of this model set of spectra in the same way as was done with the observed spectra to derive a relationship between reconstructed secondary CCF peak height and the assumed flux ratio at 1525 Å. Interpolating the observed CCF peak height in this relation led to a monochromatic flux ratio estimate of at 1525 Å. This flux ratio is related to the ratio of stellar radii bywhere is the monochromatic surface flux ratio of the stars and is equal to in the continuum at 1525 Å for the adopted temperatures of the two stars in the TLUSTY models. Using the above relation, the resulting radius ratio is , where the uncertainty includes the range of associated with the error in . Koubský et al. ( 2000 ) estimate that the Be star mass and mean radius of 60 Cyg are and , respectively. If we adopt these values, then the mass, radius, and gravity of the subdwarf are , and , respectively. This estimate of the companion mass places it above the Chandrasekhar limit of , so it is possible that the subdwarf may become a neutron star in the future. If so, then 60 Cyg may be a progenitor of a Be X-ray binary system. The estimated gravity of the subdwarf is higher than the limit in the TLUSTY grid that we used in deriving the best-fit . The relative strengths of the spectral features in the model spectra depend on the ionization balance in the model, so if we had used a higher model, we would probably arrive at a slightly higher estimate of and a somewhat lower value of R 2 . It is remarkable that among the now five known Be+subdwarf systems that 60 Cyg and 59 Cyg are separated by about one degree on the sky. The stars are not known as cluster members, but they may be affiliated with other early-type stars in their vicinity. We formed a list of stars with B spectral classifications from the catalog of Skiff ( 2014 ) that are situated within 2 deg of the midpoint between 59 Cyg and 60 Cyg, and then collected proper motions from the Gaia Collaboration et al. ( 2016 ) and parallaxes from Leeuwen ( 2007 ) for these stars. Table 3 shows those selected with proper motions and parallaxes within of those of 59 Cyg (HD 200120) and 60 Cyg (HD 200310). This collection of six objects may form part of a hitherto unknown co-moving group of equal age stars. If so, then 59 Cyg and 60 Cyg may be at a similar stage of binary evolution because of their common origin and age. Table 3 Co-moving Stars in the Vicinity of 59 Cyg and 60 Cyg Note. The spectral classifications are from the collection by Skiff ( 2014 ), proper motions and are from the Gaia Collaboration et al. ( 2016 ), and parallaxes are from van Leeuwen ( 2007 ). The V magnitude and radial velocity data are from SIMBAD, with the exception of the systemic velocities for 59 Cyg (Peters et al. 2013 ) and 60 Cyg (Koubský et al. 2000 ). We found no evidence of the