described by a modified lognormal distribution (equation A7), whose parameters are given in Table 3 . The density PDF converges after the jet breaks out (jet head ≳ 3 kpc) and decouples from the ISM, proceeding along the cleared path. Figure 7. The evolution of the density PDF as the jet evolves with time and breaks out of the dense central region after a height of z ∼ 3 kpc. The density PDF converges after the jet breakout as the jet decouples from the ISM. Table 3. Coefficients of the fit to the density PDF in Fig. 7 following equation (A7). a Mean density for the PDF. b Standard deviation of variable ρ, which is related to the standard deviation in s = ln ρ as in equation (A8). c Volume-weighted mean of density for n > 10 cm −3 . This gives a measure of the mean density of the highdensity filaments. The duration of the flood-channel phase of the jet evolution depends on the mean density and filling factor of the ISM, as previously discussed in Wagner et al. ( 2012 ). Clouds with denser cores are less ablated and more efficiently impede the progress of the jet. In Fig. 8 , we present the density for Sim B (Table 2), where a jet of power 10 45 erg s −1 passes through a medium with a lower mean density ( n w 0 = 150 cm −3 ) compared to that of Sim A. We note that the jet breaks out of the warm dense gas much faster, in comparison to Sim A. Figure 8. Density {log [ n (cm −3 )]}in the x – z plane for Sim B. 4.2 Evolution of the energy bubble The confined jet creates a nearly homogeneous high-pressured energy bubble that sweeps through the ISM (see Fig. 6 ). The expanding bubble engulfs the dense filaments, driving shocks into them. The shocks become radiative, forming a skin of heated gas (∼10 5 K) surrounding the warm filaments at ∼10 4 K. The energy bubble also shears the filaments sweeping up the ablated gas to high velocities ≳1000 km s −1 . The dense filaments are themselves accelerated by the ram pressure from the bubble. However, the efficiency of acceleration depends on the density of the gas and injected mechanical power. For lower density (Sim B), the dense filaments are accelerated to speeds of ∼100 km s −1 , similar to earlier reported results of Wagner et al. ( 2012 ). In simulations with higher ISM density (Sim A) or lower jet power (Sim C and Sim D), the outward pressure from the bubble is not sufficient to overcome the inward gravitational acceleration. In Figs 10 and 11 , we show the evolution of the mean pressure inside the energy bubble and the volume of the bubble. Initially, the bubble pressure decreases more rapidly ( p ∼ t −1 ) than an adiabatic spherical bubble (with p ∼ t −0.8 ). This is likely the result of mixing with the ISM and cooling losses. Consistent with the lower pressure, the bubble expands less rapidly (volume ∼ t 1.5 ) than an adiabatic bubble (volume ∼ t 1.8 , see Appendix B). At later stages after the breakout from the confining dense ISM, the bubble expands more rapidly. 4.3 Evolution of the phase space


the analytical solution without collisional damping is in good agreement with the results of the simulations. The timescale of dynamical friction is estimated from Equations ( 14 ) and ( 15 ). If and ≫ for m p,1 ≫ m p,2 , the damping timescale due to dynamical friction has the relation as (Ohtsuki et al. 2002 )where M disk is the total mass of a planetesimal disk, is the width of the disk, and is the Hill radius for protoplanets. Note that P DF is estimated to be ∼10 for m p,1 ∼ M ⊕ and ≈ ∼ 0.1. This estimate implies a planetesimal disk with M disk ≪ M ⊕ leads to eccentricity damping for Earth-sized protoplanets in a long timescale ≫10 4 yr via dynamical friction. In addition, dynamical friction increases of planetesimals. The increase in makes τ df longer. On the other hand, the decreasing timescale for M disk due to the collisional cascade, τ cc , is estimated from Equation ( 5 ) to be (Kobayashi Tanaka 2010 )For 100 km sized planetesimals ( m c ≈ 10 22 g) with ∼ 0.1, τ cc ≲ τ df . It should be noted that dynamical friction increases during the damping, which shortens τ cc and elongates τ df as discussed above. Therefore, even if τ cc ∼ τ df initially, τ cc eventually becomes much shorter than τ df . Equations ( 17 ) and ( 18 ) show τ df / τ cc is independent of M disk and Δ a but depends on , , and m c . For = = 0.03, P DF ≈ 60 so that τ cc ≪ τ df for g, while τ df ∼ τ cc for g. Therefore, as shown in Figures 4 and 5 , e and i of protoplanets insignificantly decrease for m c = 10 16 g because of τ cc ≪ τ df , while those are moderately damped for τ cc ∼ τ df with m c = 10 19 g. Therefore, the condition with t cc ≫ τ df is required for the e damping of protoplanets. Planets formed via giant impacts have high eccentricities and inclinations. For Earth-sized planets formed in the giant impact stages, the mean eccentricity is ∼0.1 (Chambers 2001 ; Kokubo et al. 2006 ), which is much larger than the current eccentricities of Earth and Venus. The depletion timescale of a planetesimal disk with is shorter than the e damping timescale via dynamical friction (see Equations ( 17 ) and ( 18 )). Therefore, larger planetesimals are required for e damping of Earth-sized planets. We consider such large planetesimals as being produced from a giant impact. The mass ratios of the largest giant impact ejecta to parent protoplanets are ∼0.01 (Genda et al. 2015 ). Therefore, we consider g, resulting in τ cc ≫ τ df . We perform the simulation for the orbital evolution of a high-eccentricity planet with mass M ⊕ in a swarm of giant impact ejecta. Giant impact ejecta initially have similar orbits to parent planets. However, the orbital phases of giant impact ejecta, π and Ω, are eventually distributed uniformly due to perturbation from other planets. The timescale to achieve a uniform distribution for π and Ω, which is roughly given by the precession rates for π and Ω obtained from the secular perturbation theory (Murray Dermott 1999 ), is estimated as ∼10 5


BCGs at 0.5 z 1.0 to derive L TIR and the associated dust-obscured SFR, dust temperature and mass, but neither attempt to mitigate confusion noise in these bands, nor match the observed far-infrared and 24 m emission in their SED template fitting (which are not simultaneously fit for significant number of their sources).] Furthermore, the results of the template fitting show that a customized combination of components provides a better description of the BCG stacked fluxes in most instances than any single template from a pre-existing library, particularly at z 1. It is clear that an elliptical template alone is not sufficient to match any of the SEDs, as the far-infrared emission of the BCGs is one to two orders of magnitude brighter than that of a typical red and dead elliptical galaxy template. As for the star-forming fit, based on the dust scaling relations empirically derived from observations of Herschel Reference Survey galaxies of a large range of spectral type, environment and stellar mass in the local Universe (Cortese etal. 2012 ) specifically the inverse proportionality between dust-to-stellar mass ratio and the stellar mass and specific star formation rate (sSFR) in local galaxies we expect the BCG SED to exhibit a significantly lower dust-to-stellar mass ratio in comparison to a less-massive non-BCG star-forming template, which is exactly what we find. At the lowest redshifts we consider, z avg 0.185, a typical star-forming SED matches the BCG SED longward of 10m, but the BCG stellar bump rises significantly above that of the star-forming template. While these dust scaling relations were derived for local field and cluster galaxies (including those in cluster cores), we do not yet know if they apply to galaxies at higher redshifts (though we might expect them to if we assume an understanding of the physics underlying the trends). Whereas massive elliptical galaxies in the local Universe exhibit relatively low dust-to-stellar mass ratios on account of a diminished level of star formation activity with respect to local star-forming late-type galaxies, we would expect an increasing dust-to-stellar mass ratio for elliptical galaxies of a fixed stellar mass with increasing sSFR towards higher redshift, as observed in our sample (reminding the reader that we select BCGs from clusters of the same mass at every redshift, therefore the BCGs are of the same mass at every redshift based on the linear scaling of BCG stellar mass and host-cluster mass, e.g. Lidman etal. 2012 ). In fact, as we move towards higher redshift, we observe the star-forming templates begin to match the full extent of the BCG SED better and better, as opposed to just the far-IR bump at lower redshifts. Therefore, we fit the stellar emission shortward of 10m in the faint SEDs with only the Polletta 13-Gyr Elliptical model, but add to this model either of the Polletta M82 or S18 templates to fit the stellar emission in the bright SEDs. In the mid- and far-infrared


i.e., α 0 = −0.5 and α a = 0. In Figure 3 , we show T 21 , as defined in Equation ( 2 ), for various values of α 0 and α a , with other cosmological parameters fixed at values consistent with a Planck 2015 cosmology (Planck Collaboration et al. 2016 ). As shown, the ΛCDM model ( α 0 = α a = 0), denoted by the star, is in tension with the EDGES measurement at a 99% CL illustrated by the hatched region. However, interacting vacuum models can in principle release the tension, namely, T 21 can be pushed into the hatched region by a large range of the α 0 and α a parameters. Figure 3. Illustration of the intensity of the 21 cm signal relative to the CMB temperature, T 21 (K), for various values of α 0 and α a . The color bar indicates the values of α a . The black solid curve corresponds to the case in which α does not evolve with time ( α a = 0). The intersect between the black solid curve and the vertical gray dashed line, marked by a yellow star, denotes the ΛCDM model. The hatched region illustrates the observed 21 cm signal from EDGES at a 99% CL. We then perform a Monte Carlo Markov Chain global fit for the parameters in Equation ( 12 ) using a modified version of CosmoMC 8 8 Available at https://cosmologist.info/cosmomc/ . (Lewis Bridle 2002 ) with a combined data set including, 1. the angular power spectra of temperature and polarization measurements of CMB from the Planck mission (Planck Collaboration et al. 2016 ); 2. the Joint Light-curve Analysis sample of supernovae (SNe) measurements (Betoule et al. 2014 ); 3. the Baryonic Acoustic Oscillations (BAO) distance measurements from 6dFGS (Beutler et al. 2011 ), Sloan Digital Sky Survey (SDSS) DR7 Main Galaxy Sample (Ross et al. 2015 ), Ly α forest of BOSS DR11 quasars (Font-Ribera et al. 2014 ; Delubac et al. 2015 ), and BOSS DR12 with tomographic information (Wang et al. 2017 ; Zhao et al. 2017 ); joint BAO and Redshift Space Distortions (RSD) measurements from WiggleZ (Blake et al. 2012 ) and from eBOSS DR14 (Zhao et al. 2019 ); and RSD measurements from 6dFGS (Beutler et al. 2012 ), 2dFGRS (Percival et al. 2004 ), SDSS LRG (Samushia et al. 2012 ), and VIPERS (de la Torre et al. 2013 ); 4. and the local H 0 measurement using the Cepheids, i.e., H 0 = 73.24 ± 1.74 km s −1 Mpc −1 (Riess et al. 2016 ). The results are summarized in Table 1 and in Figures 4 and 5 . To quantify the constraint on α 0 and α a from the EDEGS measurement, we show the 68%, 95%, and 99% CL contours of α 0 and α a using EDEGS alone in the lower left part of Figure 4 . 9 9 As EDEGS alone cannot constrain all of the parameters in Equation ( 12 ) simultaneously, we only vary α 0 and α a in this case while the other parameters are fixed to the values derived from the Planck 2015 measurement. As illustrated, the EDGES measurement favors an interacting vacuum model over the ΛCDM model at more than 99% CL, and this would induce a quintessence-like effective dark energy as shown in the lower left of Figure 1 . We then


( 2010 ), 8 8 The quantity f end is set to avoid higher PN tidal effects and nonlinear hydrodynamical coupling. In Hinderer et al. ( 2010 ), the fitting formula was obtained by choosing 400 Hz ≥ f end ≥ 500 Hz. The end frequency adopted in Abbott et al. ( 2017c ) is the frequency of the innermost stable circular orbit, which is above 1 kHz. and an equal mass binary with M ∼ 2.7 M ⊙ , we obtain an estimate on the tidal deformability of a star: ΔΛ 1 (1.35 M ⊙ ) ∼ 2.9 × 10 3 . Assuming a low-spin prior, GW170817 places on upper bound Λ 1 (1.4 M ⊙ ) ≤ 800 at the 90% confidence level, and an upper bound of ≤1400 if the prior is relaxed to allow for high spin (Abbott et al. 2017c ). Such constraints on Λ 1 also limit the allowed radius of NS, given the family of EOS assumed in this paper. In Figure 3 , we compare this uncertainty in the tidal deformability to the amount by the tidal deformability that has to be changed in order for a BH–NS binary to have the same leading order tidal effects as a corresponding NS–NS binary with the same masses. Figure 3. Amount by which the dimensionless tidal deformability Λ has to be increased, relative to the quantity of the corresponding NS in an NS–NS binary with the same masses, for a BH–NS binary to have the same leading order tidal effects. This is shown as a function of the mass ratio. In all of the cases, one NS is assumed have a mass of M NS1 = 1.4 M ⊙ . The different curves correspond to different choices of EOS for the NS–NS binary, and hence the different values of the radius of 1.4 M ⊙ NS in the NS–NS, as shown in the legend. For comparison, we also show the Fupper bound constraints on Λ from GW170817 assuming either a high-spin prior or a low-spin prior on the source. The highest NS radius shown (dotted red curve) saturates the former constraint on Λ, while the middle value for the NS radius (dotted blue curve) saturates the latter constraint. With N identical detections, and under the same high-spin prior, such uncertainty scales as Δ N Λ 1 (1.4 M ⊙ ) ∼ 1.4 × 10 3 N −1/2 . In reality, the component masses and source distances are different for different events, and it is possible that the best event of previous N detections dominates the constraint of NS EOS. In the above discussion, we have not accounted for the effect of spin, which is particularly important for LMBHs formed through hierarchical mergers, as they are expected to have relatively high spin ( a ∼ 0.7; Fishbach et al. 2017 ; Gerosa Berti 2017 ). 9 9 The effective spin of a most rapidly spinning pulsar known so far is ∼0.4 (Hessels et al. 2006 ). Such a spin magnitude will generate ∼0.15 mismatch between a nonspinning BH–NS waveform and a generic pretcessing waveform if the mass ratio is around 2 (see Figure 8 of Harry et al. 2014 ). The relation between distinguishable mismatch and S/N is discussed in Baird et al. ( 2013 ). 5. Multi-messenger Detection An important question is whether multi-messenger signals can help us identify an


L5 dwarfs includes 10 L4.5, 24 L5, and 2 L5.5 sources with seven detections of H in emission, and three classified as variable ( Schmidt et al. 2007 , 2015 ). In their sample, Pineda et al. (2016) included three L5 with H in emission in one of them. They inferred a fraction of emitters of 20% (15–35%; 68% confidence limit), consistent with the interval from the SDSS sample ( Schmidt et al. 2007 , 2015 ) although to date there are few sources. We also note that a large number of L dwarfs show variability in their level of chromospheric activity ( Liebert et al. 2003 ; Reiners Basri 2008 ; Schmidt et al. 2015 ; Pineda et al. 2016 ), the most striking case being the L5.5eT7 binary 2MASSI J1315309264951AB (L5.5; Hall 2002a ; Gizis 2002 ; Burgasser et al. 2011 , 2013 , 2015 ). 4.3. Radial velocity and space motion We measured the position of the H line in the 1D spectrum with the splot task under IRAF. We identified the line at 6564.11 Å with an error of 0.04 Å, while the nominal air wavelength from the NIST Atomic Spectra Database is 6562.819 Å. We should add in quadrature the error on our wavelength calibration (2.3 km s, see Sect. 3.2 ) and uncertainty due to the timespan in our observations (0.2 km s). We inferred a radial velocity of 38.0 2.9 km s (Table 2 ) after correcting for the rotation of the Earth, the motion of the Earth around the Earth-Moon barycentre, the orbit of the barycentre about the Sun, and motion of the Sun relative to the specified standard of rest. Our value is in close agreement with the mean values derived independently from the ground (39.1 0.2 km s; Detweiler et al. 1984 ) and from space with H ipparcos (39.48 0.30 km s; de Bruijne et al. 2001 ). We infer a space motion of [] = [42.92, 23.96, 0.72] km s for 2M041821 (Table 2 ), in close agreement with the space motion of the cluster centre: [41.1, 19.2, 1.4] km s ( van Leeuwen 2009 ). According to Vizier, 2M041821 should have a Gaia -band of 19.096 and should be included in the Initial Gaia Source List ( Smart Nicastro 2014 ), implying that precise coordinates and proper motions will be soon available since the second Gaia data release is expected at the end of 2017. However, based on the equation 0.244 SpT 12.6332 kindly provided by R. Smart, 2M041821 might have 20.4 mag, placing it at the faint end of the Gaia catalogue. Therefore, it is unclear at this stage whether its membership to the Hyades cluster will be settled by Gaia in the near future. Table 2 Results of our spectroscopic analysis. Notes. We quote the spectral type, spectroscopic distance, radial velocity, space motion, and ratio of the (/) luminosity for 2M041821. 4.4. Lithium absorption The lithium test was proposed in the early 1990s to distinguish between very low-mass stars and brown dwarfs ( Rebolo et al. 1992 ; Magazzu et al. 1993 ). The technique relies on the detection of lithium in absorption at 6707.8 Å for late-M and L dwarfs straddling the stellar-substellar boundary. If lithium is detected,


that are not perfectly linear too. As a consequence, the linear fittings tend to overestimate the ages of stars younger than 3 Gyr by 0.8–0.9 Gyr. By fitting the distributions of thin and thick discs with quadratic functions, we found the following solutions: From these higher order functions, we find that the average scatter is reduced to 0.5 Gyr for both [Y/Mg] and [Y/Al], which is very close to the typical uncertainties of our age determinations (i.e. 0.4 Gyr). 4 CONCLUSIONS We used high-quality HARPS spectra of 79 solar twins to obtain precise estimates of their atmospheric parameters (T eff , log g , [Fe/H] and ξ) and abundances of 12 neutron-capture elements (Sr, Y, Zr, Ba, La, Ce, Pr, Nd, Sm, Eu, Gd and Dy). The knowledge of the stellar parameters and absolute magnitudes of these stars allowed us to determine their stellar ages through the isochrone method with typical precisions of 0.4 Gyr. Our main scientific results can be summarized as follows: The thin and thick disc populations, identified through the α-elements abundances, are separated in the [X/Fe] versus age plots showed in Fig. 5 . The [X/Fe] ratios of the thin disc distribution are highly correlated with stellar age for the s -process elements (e.g. Ba), while the [X/Fe]–age distributions of the r -process elements (e.g. Eu) are nearly flat. Indeed, the slopes of the [X/Fe]–age distributions are dependent on the s -process contribution percentage of the X element (see Fig. 6 ). This indicates that, the enrichment from AGB stars is the predominant channel of nucleosynthesis of n -capture elements during the evolution of the thin disc. Despite the flat slopes traced by the thin disc stars, the nearly pure r -process elements Eu, Gd and Dy appear more enhanced in the thick disc population. This dichotomy between the thin and thick discs resembles the [X/Fe]–age distributions outlined by the α-elements, which are more abundant in the thick disc than in the thin disc due to an intensive nucleosynthesis by Type II SNe during the early stages of the Galactic disc. The sites of production of the r -process elements are not very well known at present; however it is likely that they are mainly synthesized during the mergers of massive compact objects. On the other hand, the similarity to the distributions of the α-elements suggests that the r -process elements are also produced by Type II SNe and that they could be additional tracers of intensive star formation episodes. There is a possible direct observational test that could be performed on OB associations which are regarded as a proto-type of triggered star formation, such as Orion or Sco-Cen. If Type II SNe are producing copious r -process elements, then the youngest sub-clusters should be enriched in these elements relative to the oldest stars (Cunha Lambert 1992 ). The [X/Fe]–age distributions of the thin disc stars have been fitted by linear functions. The parameters resulting from this linear fitting, listed in Table 5 ,


this model may not represent the true morphology, but may vary on smaller angular scales, the intensity scaling parameters per energy bin, , are re-determined for each sky region and the background. The celestial emission in this energy range is dominated by the bright 511 keV line emission from the Galaxy’s centre, modelled by a narrow bulge, a broad bulge, and a point-like source centred at ( l ∕ b ) = (0°∕0°). To this, a Gaussian-shaped disk is added to capture the faint and low surface-brightness emission beyond the bulge. The details of the spatial emission models are found in Siegert et al. (2016) , and in Appendix E . The instrumental background is modelled in a self-consistent way, using long-term knowledge about the detector behaviours, space-craft conditions, and physical origins of γ -ray emissions in the satellite ( Siegert et al. 2016 ). Based on the INTEGRAL/SPI BackGround and Reponse Data Base (BGRDB, Diehl et al. 2018 ), the background detector patterns (relative counts of the detectors to each other) are predicted as a function of energy and time. This data base includes spectral information of hundreds of instrumental γ -ray lines which are associated to different isotopes in the satellite, being excited by cosmic rays and de-exciting either promptly or delayed. The continuum background, mainly due to bremsstrahlung inside the spacecraft, is modelled in the same manner. Long-term trends of detector degradation from this cosmic-ray bombardment and radioactive build-ups are individually traced by this technique. In this energy range, eight instrumental γ -ray lines, on top of a power-law shaped instrumental continuum is used to model these background patterns ( Siegert 2017 ), to be distinguished from the expected sky emission patterns. The background scaling parameters are determined on a three-day interval (see also Siegert et al. 2019 ), corresponding to one INTEGRAL orbit. This amounts to 1083 background scaling parameters for each, the continuum and line backgrounds as a whole, for a total of 2166 background parameters. In summary, 6 (2) parameters are fitted for the celestial emission in a simultaneous (consecutive) fit of the regions of interest and the remaining Galaxy, and 2166 parameters for the instrumental background. The number of degrees of freedom in each individual energy bin thus amounts to 1 212 627 (1 212 631). 2.2 Spectral extraction 2.2.1 Full sky 511 keV signal The total spectrum of the 511 keV template map ( Fig. 2 , top two panels) is shown in Fig. 1 , together with a multi-component fit. We identify four spectral components: a narrow and a broad 511 keV line, an ortho-positronium (o-Ps) continuum, and the galactic diffuse γ -ray continuum. The derived spectral parameters are consistent with previous studies, although both, the broad and the narrow annihilation line, appear to be broader than previously measured ( Jean et al. 2006 ). This may arise from different line shapes in the disk and the bulge


SNe Ia are monitored only for a few months; if CSM is more prevalent or typically at a larger distance from the WD, we might be systematically missing the signatures of this interaction. There are additional good reasons to suspect that we might be systematically missing the interaction of CSM with SN Ia ejecta. For example, SN Ia 2006X exhibited evolution in its Na i D absorption line that was interpreted as the photoionization of more distant CSM (Patat et al. 2007 ). In a compilation of 17 SNe Ia with multi-epoch spectra, Sternberg et al. ( 2014 ) found that ∼18% exhibit time-variable Na i D. Additionally, studies of large samples of SNe Ia (20–35 events) found Na i D to be blueshifted ∼20% more often than redshifted, and argued that this was best explained by outflowing CSM from the progenitor system (Sternberg et al. 2011 ; Maguire et al. 2013b ), but see Bulla et al. ( 2018 ) for an alternative explanation. In these SNe Ia, the CSM is estimated to be 5 × 10 16 –10 18 cm away from the explosion, which means that the fastest SN ejecta would not interact until >1 yr. Additional support for late-time CSM interaction is presented by Fox Filippenko ( 2013 ), who interpreted an increase in Spitzer mid-infrared photometry for SN Ia 2005gj at 500–1000 days past peak brightness as dust heated by hot blackbody emission from new or renewed CSM interaction. Additional evidence for nondegenerate companion stars comes from detections of, e.g., “blue bumps” in the light curve in the week after explosion (Hosseinzadeh et al. 2017 ) and/or late-time H α emission from material swept off the companion star and embedded in the ejecta (Maguire et al. 2016 ; Sand et al. 2018 ). It is important to note that there is plenty of evidence that many—or even most—SN Ia progenitor systems host a degenerate binary companion and/or do not contain CSM (e.g., Hayden et al. 2010 ; Maoz et al. 2014 ; Chomiuk et al. 2016 ). In this work, we aim to put upper limits on the fraction of SNe Ia with CSM, and we are not suggesting that the systematic oversight of CSM interaction extends to all SNe Ia. There is further motivational support in searching for late-onset CSM interaction in SNe Ia from recent observations of delayed CSM interaction in some core-collapse SNe. For example, Milisavljevic et al. ( 2015 ) presented observations of SN 2014C, an SN Ib that appeared to explode into an empty cavity surrounded by CSM, which transitioned to an SN IIn as the ejecta caught up with the previously released material. Similarly, Mauerhan et al. ( 2018 ) found H α emission from the onset of CSM interaction in SN Ib 2004dk 13 years after the original explosion. Vinko et al. ( 2017 ) presented the results of a systematic narrow-band imaging survey of Type Ibc, IIb, and Ia SNe to look for H α emission due to CSM interaction years to decades after explosion. Most of their potential detections are associated with core-collapse events, but of particular relevance to this work is their


excitation temperatures) owing to atmospheric transmission and telluric lines, and would limit the detections to some energetic rotational transitions such as the 12.4 m blend observed in Pontoppidan et al. (2010a) . 5. Conclusions From the outcome of our model, we have provided a scenario that can explain the observations in the mid-IR towards a Herbig star: we considered some limitations in our description of disks around Herbig stars, and we think that these would not be problematic for the correct physical description of the mid-IR spectroscopy. Observations have been performed up to now with facilities affected by low spectral resolution and lower sensitivity. These two elements limit any possible firm conclusion about the nature of disks around Herbig stars, which can be intrinsically different from the ones surrounding T Tauri stars. Low signal-to-noise ratio (S/N) is the most likely explanation for the low detection rates of mid-IR water lines around early type PMSs. This problem also partially affects later type PMSs. T Tauri stars spectra are less noisy; however, mid-IR water line fluxes are lower, and the detection rate is only a factor two more than for Herbig stars. Better performing instruments with resolution 3000 and longer integration times are definitively needed to detect water successfully in the 1–20 m range in protoplanetary disks. Appendix A: Sensitivity limits Our analysis sample includes a selection of T Tauri and Herbig Spitzer IRS high resolution observations. BCD data products were retrieved from the Spitzer archive 4 . The data were reduced with the c2d IRS science pipeline using the PSF extraction method (see Lahuis et al. 2007 ; Lahuis 2007 , for details), which provides higher S/N spectra than the standard tapered aperture extraction used to populate the Spitzer archive. After extraction, additional defringing ( Lahuis Boogert 2003 ) was applied to remove any low-level fringe residuals. Sensitivity limits were determined by calculating the line flux for synthetic lines with an amplitude equivalent to the 1 noise level in the IRS spectrum at the respective blend wavelengths and a width comparable to the blend width at a spectral resolution of 600. Appendix B: Spectral convolution We applied Gaussian convolution and rebinning to the theoretical spectra from our models. For this task we used the ISO spectral analysis package ( Kessler et al. 1996 ), considering the three resolutions of Spitzer IRS LH/SH modules (; Houck et al. 2004 ), VLT VISIR (; Lagage et al. 2000 ). For JWST MIRI we split the range into four spectral windows: for 7.63–11.71 m, for 11.71–13.59 m, for 13.59–18.14 m, for 18.14–28.43 m, accounting for the variable spectral resolution ( Clampin 2011 ). We add noise through a random generator according to \newpage where is the computed noise and a function both of the continuum flux () multiplied for a random generator between 0 and 1 () and of the selected S/N. Here we consider 100 as claimed in


based on the Lick indices and the abundance ratios. In Section 4 , our results are summarized and discussed. In Section 5 , conclusions are given. 2 OBSERVATIONS AND DATA REDUCTION Our sample consists of 37 galaxies, the full spectroscopic sample of the SMAKCED project. For each of them, we obtained data suitable for a detailed stellar population study, with relatively high spectral resolution and high S/N ratio. Two galaxies in the sample (VCC1684 and VCC2083) were not included, since no ages could be determined because of lack of observed Balmer lines. The spectroscopic data were obtained at three different telescopes. A total of 26 dEs were observed at the 4.2-m William Herschel Telescope (WHT) using the double-arm ISIS spectrograph, of which the blue-arm covered the wavelength range 4200–5000 Å and the red-arm covered the wavelength range 5500–6700 Å. A total of 10 dEs were observed at the 2.5-m Isaac-Newton Telescope (INT), using the IDS spectrograph covering the wavelength range 4600–5600 Å, whereas the remaining three dEs were observed at the 8-m Very Large Telescope (VLT), using the FORS2 spectrograph that covers the wavelength range 4500–5600 Å. Table 1 summarizes the main properties of these 37 dEs (see also T14 ). Table 1. Properties of the SMAKCED dEs. Column 1: galaxy name. Columns 2 and 3: right ascension and declination in J2000, respectively. Columns 4 and 5: r -band magnitude (in the AB system) and half-light radius by Janz Lisker ( 2008 , 2009 ), respectively. Column 6: velocity dispersion. The data were reduced following the standard procedure for long-slit spectra using the package reduceme (Cardiel 1999 ). Details on sample selection, observations, and data reduction are presented in T14 . 2.1 Line-strength measurements Observed spectral data can be studied either by fitting the full spectrum or by focusing on selected line indices. In this work, we study selected line indices. We measured Lick indices (Worthey et al. 1994 ) in the Line Index System (LIS)-5 Å flux calibrated system (Vazdekis et al. 2010 ). The new LIS has numerous advantages over the Lick system. It is defined at three different resolutions, namely 5.0 Å, 8.4 Å, and 14.0 Å. As such, it is particularly useful for analysing small galaxies and globular clusters. As the resolution of the Lick/IDS library (FWHM ∼ 8–11 Å) is much lower than what is available with our high resolution spectra, we broadened the spectra to the LIS-5 Å system. The LIS-5 Å system choice expresses a factor of 2 improvement in resolution over Lick/IDS system. Also, the fact that the LIS system is flux calibrated makes it easier to reproduce data from other authors. The spectra were broadened to the LIS-5 Å system, taking into account the velocity dispersion of the spectra. This ensures that every galaxy spectrum has the same spectral resolution, which is important and necessary to compare them with each other. We measured a total of 23 Lick indices (Faber et al. 1985 ; Gorgas et al.


correlations between the p -values for each formation channel provided in Table 1 and the half-mass relaxation time, t rh . Fig. 8 shows that there is no strong correlation between the p -values obtained for the mass-transfer channel and the cluster half-mass relaxation time. If such a correlation were present, 2 one interpretation would be that the initial BS velocity distribution immediately after formation is not Maxwellian, but instead evolves towards a dynamically relaxed state over a relaxation time. This would, in principle, be more consistent with the collisional hypothesis, since the binary mass-transfer hypothesis predicts that BSs descended directly from internal evolution within (relatively) old binaries that have had plenty of time to relax towards a Maxwellian velocity distribution. Thus, the results from this component of our analysis are most consistent with a mass-transfer origin for the majority of the BSs in our samples, since the observed BS velocity distributions are typically consistent with having formed from a dynamically relaxed population. However, as already discussed, this is insufficient to fully exclude the collisional channel, because collisions among the dynamically relaxed binary population would yield the same Maxwellian velocity distribution of the collision products in very relaxed clusters. As shown in Table 1 and Fig. 8 , the 2+2 collisional velocity distributions best match the observed BS velocity distributions for the post-core collapse GCs in our sample, namely NGC 6624, NGC 6681 and NGC 7099. The latter being our strongest candidate for having a large fraction of BSs formed via 2+2 collisions. This provides good independent evidence to support the claim of a strong contribution from collisions to BS formation in NGC 7099, as found by Ferraro et al. ( 2009 ). 4 SUMMARY AND DISCUSSION In this paper, we have performed a thorough statistics-based search to answer the question: What are the origins of BS stars in GCs? The BS catalogue of Simunovic Puzia ( 2016 ) provides us with observational measurements for BS velocities (from their proper motions) and masses (from isochrone-fitting and assuming they are single isolated objects). We compare these observed BS masses and velocities to analogous theoretical predictions for BSs formed from MS–MS collisions during single–binary (1+2) and binary–binary (2+2) interactions, obtained via a suite of numerical scattering experiments performed with the FEWBODY code (Fregeau et al. 2004 ). The results of this analysis are ultimately consistent with the BS samples having been derived from a dynamically relaxed population. At face value, this appears to favour the mass-transfer (and/or binary merger) hypothesis for BS formation. This is because the p -values obtained from Kolmogorov–Smirnov tests suggest that the observed BS velocity distributions most closely resemble Maxwellian velocity distributions, adjusted to account for the slightly higher masses of the


side and top histograms show that our SINFONI targets (red-hatched histogram) form a fair sub-sample of the full CARLA sample (blue-shaded histogram) in radio power, UV luminosity, and BH mass, even though the SINFONI sample covers a more limited range in redshift. A list of the targets and relevant observational information in our quasar sample is given in Table 1 . Table 2 summarizes the main parameters determined for the six broad-line radio galaxies from Nesvadba et al. ( 2011 ) that were used in our analysis. The available parameters include H α-based BH mass estimates and Eddington ratios that were determined in a similar fashion to the analysis performed on the CARLA quasars in this paper. Table 1. Sample information. Note . a Redshifts are from SDSS. Table 2. Broad-line radio galaxies from Nesvadba et al. ( 2011 ). Notes . a Redshifts based on H α taken from Nesvadba et al. ( 2011 ). † Radio luminosity at 325 MHz taken from De Breuck et al. ( 2000 ). ‡ Radio luminosity at 500 MHz taken from Wylezalek et al. ( 2013 ). 2.2 Observations We used SINFONI at UT4 of the VLT at the European Southern Observatory (ESO) to observe a sample of 35 high-redshift quasars. The purpose of the project was to obtain NIR spectra probing the rest-frame optical region around H α in order to obtain more accurate BH masses for quasars selected from the CARLA survey and SDSS. The data were taken over 6 yer (2009–2015) as part of programmes 095.B-0323(A), 094.B-0105(A), 093.B-0084(A), 092.B-0565(A), 091.B-0112(A), 090.B-0674(A), and 089.B-0433(A) (PI: Jaron Kurk). Except for 089.B-0433(A), all programmes targeted radio-loud quasars from CARLA. The 089.B-0433(A) targets were selected from SDSS on the basis of their very high (C iv -based) BH masses but are not part of the CARLA sample (see Section 2.1 ). We used the SINFONI K band (1.95–2.45 μ m) with the spatial scale of 125 × 250 mas (without adaptive optics). This setup delivers a spatial aperture of 8 × 8 arcsec 2 with a spectral resolution of ∼400 km s −1 , allowing a robust sky subtraction. The observational strategy includes on-source dithering (ABBA pattern) in order to optimize the exposure time on the source and sky subtraction, and a telluric standard star for telluric band removal and flux calibration. We took 14–16 individual exposures of 300 s each, resulting in total integration times of 4200–4800 s. 2.3 Data reduction The data reduction was performed using the SINFONI pipeline v2.9.0 (Modigliani et al. 2007 ) with the Reflex interface. The pipeline creates master calibration images and applies them to the observations, starting with a non-linearity map constructed from the flat-field frames. A master dark frame is created from the dark frames and the hot pixels are mapped. Individual flat-field images are combined into a master flat. Optical distortion and slitlet distances are computed, and the dispersion solution for the wavelength calibration is determined from arc spectra. Finally,


neutrinos in spatial and temporal coincidences were reported by the IceCube neutrino telescope around this burst. A similar powerful burst GRB 130427A with energy of erg was detected by several satellites and ground-based telescopes (Ackermann et al. 2014 ; Maselli et al. 2014 ; Vestrand et al. 2014 ) and although searches for TeV–PeV neutrinos were performed, no excess were found above background. Gao et al. ( 2013b ) stated that the neutrino non-detection could constrain the values of the bulk Lorentz factor, emitting radius and the energy fraction converted into cosmic rays . They found that almost independently of the bulk Lorentz factor, the energy fraction between electrons and cosmic rays lies in the range . Although a robust analysis could be required, a simple proof can be done for GRB 160625B following a similar procedure. Form our results obtained in early afterglow can be seen that the energy fraction given to accelerate electrons and amplified the magnetic field at the end of the prompt phase is and , respectively. Taking into consideration the energy conservation condition , then the energy fraction converted into cosmic rays would be limited by . This result is very similar to that found by Gao et al. ( 2013b ) for GRB 130427A and might explain the lack of high-energy neutrinos around GRB 160625B. 7. Kann et al. ( 2010 ) studied the optical photometry data in a total of 42 GRB afterglows. They found that 10% of the afterglows presented optical peaks followed by a fast decay which are usually associated with a reverse-shock flash. Several authors have claimed that this kind of afterglow, as observed in GRB 080319B (Racusin et al. 2008 ), GRB 130427A (Ackermann et al. 2014 ; Vestrand et al. 2014 ), GRB 050904 (Kann et al. 2007 ), GRB 120711A (Martin-Carrillo et al. 2014 ), and GRB 990123 (Akerlof et al. 1999 ), among others, are only present in the most luminous bursts. Given that GRB 160625B has been one of the most powerful bursts detected which exhibited an optical flash with a fast decay, this burst seems to confirm this statement and belong in the same category. Table 2 Parameters found of the Early and Late Afterglow Table 3 Quantities Derived with our Leptonic Model for the Early and Late Afterglow Note. Quantities for the early afterglow are calculated at 150 s and for the late afterglow at . At the jet-break time ( s), the jet opening angle and the bulk Lorentz factor are and 6.9, respectively.) 5. Conclusions We have described the non-thermal multiwavelength observations of GRB 160625B collected with Fermi -LAT, Swift -XRT and several optical ground observatories. The multiwavelength observations of the early afterglow are consistent with the afterglow evolution in a stellar wind medium. The optical spectral index is consistent with the synchrotron radiation while GeV γ -ray flux with SSC emission dominated by the high latitude emission. In this event, a strong correlation between GeV γ -ray and optical fluxes


X1, the most well known of these systems, periodic occultation of the source due to the precession of the warped inner disc results in a luminosity not proportional to the accretion rate and as a consequence the torque luminosity correlation is not good (Klochkov etal. 2009 ). We have seen that the dimensionless torque near the equilibrium is qualitatively different from the predictions of the existing models. Across the torque equilibrium the torque is concave-up in its dependence on the fastness parameter, whereas the existing models (Ghosh Lamb 1979b ; Li Wang 1996 ) predict concave-down (convex) relation. The torque has a cubic dependence near the torque equilibrium and the general qualitative behaviour can be represented by superposition of two hyperbolic functions and is shown to be very different from the existing analytical models. These qualitative differences indicate either that an important ingredient of the discmagnetosphere interaction is not captured in these models or that one or more of our assumptions in constructing the torque are not justified. An assumption implicit in our construction of the torque is the proportionality of the inner radius with the Alfvn radius, R in R A , yet it is possible that is not a constant but depends on the fastness parameter. This condition will be relaxed in a future study, but we would like to mention that our comparison of the dimensionless torque with the existing torque models of Ghosh Lamb ( 1979b ) and Li Wang ( 1996 ) is self-consistent in the sense that these authors also find to be constant, independent of the fastness parameter. Another assumption that can be questioned is the proportionality of luminosity, and hence the flux received, to the accretion rate. There could be two ways this assumption may fail: it is possible that the inner disc is warped and obscures some of the X-ray flux as is the case in Her X1. This possibility is recently suggested by Beri, Paul Dewangan ( 2015 ) relying on the pulse-phase dependence of the emission lines. Yet we note that the object shows a very smooth torque evolution near the torque equilibrium with a very satisfactory torqueflux correlation (Camero-Arranz etal. 2010 , 2012 ) as opposed to the case in Her X-1. This is probably because we are seeing the system face on: we do not see the Doppler modulations, yet we do know the orbital period through optical modulation of the companion (Chakrabarty 1998 ). There is another way the linear relation between the accretion rate and the luminosity could break down. Yi, Wheeler Vishniac ( 1997 ) suggested that the torque reversals from spin-up to spin-down could be a consequence of transition of the flow in the disc from a Keplerian flow to a sub-Keplerian flow. A torque reversal from spin-up to spin-down is then associated with a spectral transition from soft- to hard-state (Vaughan Kitamoto 1997 ; Yi Vishniac 1999 ). Such spectral transitions, in the case of black holes, are associated with transition


external stream, they nevertheless dominate the broad-band opacity at FUV, optical, and IR wavelengths if they are present. They also dominate at EUV wavelengths (), if the hydrogen neutral fraction is less than ≈0.001. The strong coupling assumption means that all the radiative forces applied to the dust grains are directly felt by the gas also. 2.1 Bow shells supported by radiation and wind The internal pressure is the sum of wind ram pressure and the effective radiation pressure that acts on the bow shell. The radiative momentum loss rate of the star is L / c and the wind momentum loss rate can be expressed as where η w is the momentum efficiency of the wind, which is 1 in all cases except WR stars (Lamers Cassinelli 1999 ). If the optical depth at UV/optical wavelengths is sufficiently large, then all of the stellar radiative momentum, emitted with rate L / c , is trapped by the bow shell. At the infrared wavelengths where the absorbed radiation is re-emitted, the grain opacity is much lower, so the bow shell is optically thin to this radiation. Combined with the fact that the UV single-scattering albedo is only ≈0.5, this means that the single-scattering limit is approximately valid, and we adopt it here. We define a fiducial bow shock radius R * in the optically thick, radiation-only limit by balancing stellar radiation pressure against stream ram pressure at the bow apex along the symmetry axis from the star: which yields We now consider the opposite, optically thin limit. If the total opacity (gas plus dust) per total mass (gas plus dust) is κ (with units of ), then the radiative acceleration is Therefore, an incoming stream with initial velocity, v ∞ , can be brought to rest by radiation alone at a distance R ** where yielding On the other hand, we can also argue as in the optically thick case above by approximating the bow shell as a surface, and balancing stellar radiation pressure against the ram pressure of the incoming stream. The important difference when the shell is not optically thick is that only a fraction 1 − e −τ of the radiative momentum is absorbed by the bow, so that equation ( 2 ) is replaced with In the optically thin limit, 1 − e −τ ≈ τ, so these two descriptions can be seen to agree ( R 0 → R ** ) so long as which we will assume to hold generally. We define a fiducial optical depth, With these fiducial values established, we return to the combined radiation plus wind scenario. Adding the stellar wind ram pressure term from equation ( 1 ) allows us to write the general bow shell radius in terms of the fiducial radius as where x is the solution of Since this is a transcendental equation, x must be found numerically, but we can write explicit expressions for three limiting cases: The first case, x ≈ (1 + η w ) 1/2 , corresponds to a radiation bow shock (RBS); the second case, x ≈ 2τ * , corresponds to a radiation bow wave (RBW); and the third case, , corresponds to a wind bow shock (WBS). The two bow shock cases are


the host galaxy potential. The average difference between AGNs and SF galaxies is 0.16 dex. Note that even among the objects with single Gaussian [O iii ], we clearly detect the systematic difference of the ratio between AGNs and SF galaxies (the average difference is 0.11 dex). 3.2. [O <sc>iii</sc>] Velocity Dispersion versus Luminosity We investigate how the [O iii ] kinematics are related to [O iii ] luminosity for AGNs and SF galaxies in Figure 5 . There is an increasing trend of σ O iii with increasing luminosity in AGNs, though the trend is very broad. The increasing trend is also present among composite objects while the the luminosity range of [O iii ] is an order of magnitude narrower. These trends show that gas outflows are stronger in AGNs with higher luminosity, indicating that AGN energetics are responsible for the outflow kinematics. In contrast, we find no clear increasing trend among SF galaxies. On average σ O iii is lower in SF galaxies, while the range of σ O iii is as broad as that of AGNs. Since the average stellar mass of AGNs and SF galaxies is very different, as we pointed out in S.2.2, we plot the same comparison after limiting stellar mass between 10 10 and 10 10.5 (bottom panels in Figure 5 ). Again, we find that AGNs and SF galaxies show different trends, suggesting that these different trends are not due to the difference in mass scales between AGN and SF galaxy samples. Figure 5. Comparison of [O iii ] velocity dispersion with [O iii ] luminosity, respectively, for AGNs (left), composite objects (middle), and SF galaxies (right), using the entire sample (top) and the stellar mass-limited sample (bottom). The colors represent the number density in each bin with Δ x = 0.03 dex and Δ y = 0.01 dex. 3.3. [O <sc>iii</sc>] Velocity–Velocity Dispersion Diagram In Figure 6 , we combine the velocity and velocity dispersion of [O iii ] to investigate the difference of gas kinematics between AGNs and SF galaxies. We find a dramatic contrast between AGNs and SF galaxies in terms of the range of gas velocities. While SF galaxies are concentrated at the lower center with a limited range of velocity shift and velocity dispersion ( σ O iii ∼150 km s −1 ), AGNs show a much larger distribution, including AGNs with extreme kinematics (i.e., and σ O iii > 400 km s −1 ). Figure 6. [O iii ] Velocity–velocity dispersion diagrams, respectively, for AGNs (left), composite objects (middle), and SF galaxies (right), using the total sample (top) and the stellar mass-limited subsample (bottom). The average σ O iii is 175.1 ± 76, 125.3 ± 49.9, and 73.2 ± 28.6 km s −1 , respectively, for AGNs, composite objects, and SF galaxies, indicating that AGNs have more than a factor of two broader [O iii ] than SF galaxies. Also, the dispersion of the σ O iii distribution is significantly different with a factor of ∼3 broader distribution in AGNs. Note that the σ O iii distribution is skewed toward high values, indicating the presence of extreme


in determining the fractional abundance of atomic hydrogen in dark clouds. The main results are listed below. (i) The CR dissociation rate, ζ diss , is primarily determined by secondary electrons produced during the primary CR ionisation process. These secondary electrons can efficiently dissociate H 2 and represent the only source of atomic hydrogen at column densities higher than ≈10 21 cm −2 , regulating the ratio in dark clouds. (ii) ζ diss entering the balance Eq. ( 4 ) is not equal to the ionisation rate ζ ion , as assumed in some previous work. We find that the ratio ζ diss ∕ ζ ion varies between ≈0.63 and ≈0.7, depending on the column density range, while ζ ion is a decreasing function of the column density. (iii) Even given the uncertainties in the values of H 2 formation rate, temperature, total hydrogen volume density, and IS UV radiation field for each cloud, only a CR proton spectrum enhanced at low energies (such as our model ) is capable of reproducing the upper values of measured f H under the assumption of steady state. We note that neither model nor model is able toreproduce the entire set of observational data: the spread in the values of f H at any given column density must be attributed to time dependence or to individual characteristics of each cloud. For example, tangled magnetic field lines and/or higher volume densities would result in a stronger CR attenuation and thereforein a lower f H . (iv) An accurate description of H 2 dissociation in dense environments is essential because many chemical processes (such as CO hydrogenation and its depletion degree onto dust grains, or formation of complex organic molecules) critically depend on the abundance of atomic hydrogen. Appendix A Equilibrium distribution of protons and Hfast atoms at low energies Because of the process of electron capture at low energies, CR protons interacting with H 2 are efficiently neutralised, creating fast H atoms. In parentheses we list the cross section of the respective process. At the same time, H fast atoms reacting with H 2 yield The electron capture by protons, reaction ( A.1 ), and the reaction of H fast self-ionisation, reaction ( A.3 ), are catastrophic processes, since the respective projectile particles disappear after such collisions. The reactions of H 2 ionisation and dissociation by H fast atoms, reactions ( A.2 ) and ( A.4 ), respectively, are continuous loss processes, where the projectile kinetic energy decreases only slightly after each collision. The efficiency of continuous energy losses is generally characterised by the projectile stopping range (see, e.g. Padovani et al. 2009 ). For our calculations, is taken from Rudd et al. (1983) , is adopted from Phelps (1990) and Kunc Soon (1991) , is computed by Stier Barnett (1956) , van Zyl et al. (1981) , and Phelps (1990) , and is taken from Dove Mandy (1986) and Esposito Capitelli (2009) . In Fig. A.1 , we plot the cross sections and the inverse of the proton


times. No physical prescriptions govern these behaviors, only the universe’s observed SFH and the end-states of a set of real objects. In this sense, the G13 “model” is not a model at all, but a realization of possible lognormal SFHs for a sample of galaxies. As such, all physics must be inferred from the resulting distribution, or read into the form of the SFH. Sections 3.2 , 3.3 , and 4 revisit this point. Note: Given its mass limit, G13 does not describe the SFHs of local dwarfs (though neither does it contain any). Unlike giant systems (Rodighiero et al. 2011 ), these are known to grow via stochastic bursts (Weisz et al. 2014 ) which a single lognormal cannot capture. Hence, the following discussion is likely not applicable to them. Our principal interest lies in understanding what shapes the longer-term growth modes of galaxies that have consistently dominated the universe’s mass and budget (Section 2.1 ). 2.3. Previous Descriptive Successes In G13 , we showed that the model naturally reproduced the population of galaxies O13 (and subsequently Dressler et al. 2016 ) found to have both late-peaking and narrow SFHs, something impossible to do using τ or delayed- τ SFH parameterizations (Figures 2 and 9 ; O13 ). This encouraged us that the G13 model represented not only an improved description, but perhaps a physically meaningful worldview. More encouragement has come as the model continues to reproduce a range of observations it was neither constrained by nor intended to describe. We explore most of these results below, but review here what we have demonstrated to date: 1. Constrained only by the cosmic SFRD and input galaxies, G13 (Figure 7 ) showed that the model faithfully reproduced distributions at four epochs at . As O13 did for τ /delayed- τ models, G13 showed that Gaussian SFHs failed this test badly. 2. Turning the distributions into modeling constraints and refitting for each galaxy’s , G13 (Figure 13 ) showed that the model reproduced the – relation (the “Star Formation Main Sequence,” or “SFMS”) from Daddi et al. ( 2007 ). 9 9 The agreement with distributions achieved by the initial model suggests that the SFMS could have been reproduced without turning these into constraints. We have not performed this test, however. 3. Similarly constrained at , Abramson et al. ( 2015 ) showed that the model reproduced the evolution of the stellar mass functions of star-forming and non-star-forming galaxies at . This was despite the fact that no mass-sensitive constraints were ever imposed except via the intrinsic mass distribution of the input data. These achievements by no means make the G13 model uniquely successful: others are equally capable (e.g., Sparre et al. 2015 ). However , as G13 entails no explicit treatment of any physical process, we are spurred to investigate what makes this simple mathematical description an accurate expression of complex, poorly understood underlying physics. 2.4. New Challenges Here, we test the G13


the inner initial region of the debris disc is chosen as to coincide with the appropriate tidal radius given the NS and WD properties. However, the exact structure of the debris disc is more complex than our simplified models and we therefore checked the dependence of slightly by moving the disc position inwards or outwards (see R 0 / r t in Table 2 ). As we show, the results depend on the chosen inner positions, but the overall behaviour is robust and is not strongly dependent on the exact choice. Closer-in debris discs are more effective in allowing for material to accrete into close-in orbits before outflows become efficient enough to quench further accretion. The overall ejected mass and total energetic are therefore determined by both the overall NS and WD mass and the inner radius of the disc; these are well reflected in Table 2 . Overall the nuclear energy deposited increases with increasing density and with Helium content. These provide more favourable conditions for nuclear burning. The density is determined by the total mass of the debris disc (the disrupted WD), the inner radius ( r d ), the disc scale height, and to some extent the disc composition that affects the EOS (see equation 3 ). As can be seen in Table 2 , the nuclear energy produced follows these various trends; it increases with increasing WD mass and Helium content, as well as with decreasing disc scale height and inner radius. The tidal radius, which determines the inner radius, depends on both the NS mass and the WD mass, as well as on the WD composition, and hence more massive NSs (giving rise to larger tidal radii) correspond to lesser production of nuclear energy. The pure Helium WD case (not shown) is the only case where no nuclear burning is observed. This may appear counter-intuitive given the lower temperatures and densities required to ignite Helium, however such WDs have a lower mass and are much puffier, hence the effective density of the debris disc they produce is far lower than that of CO WD debris disc, explaining the result. As discussed above, our results suggest that only a small fraction of the WD debris disc is effectively ejected during the modelled evolution, while most of the material expands to produce a more isotropic configuration, but stays bound to the NS. The long-term evolution of such expanded debris ‘atmosphere’ is beyond the scope (and computational capabilities) of the current study focusing on the immediate outcomes of the merger following the disruption of the WD. As already noted, nuclear burning is not the main driver of the outflows in NS–WD mergers, and only a small fraction of the WD debris disc experiences any nuclear burning. Hence, the majority of the ejected unbound material (identified through the comparison of the kinetic and potential energy of each mass element) shows the same composition as the original WD, i.e. C/O composition (and He in the hybrid WD cases). However, most of the unbound material is ejected through


ones (Figure 8 ). Overall, Figure 11 does not suggest any significant trends in the mass error with respect to merger history, percentage of incomplete data, or percentage of unbound particles. Thus, except in extreme cases, these quantities may not play a role in underestimating the mass. In the following section, we explore the possibility that the inner GC analogs are influencing the model fit, as suggested in Section 5.1.3 . 5.3. Sensitivity to Inner Tracers Our studies of the MW, and in particular the sensitivity analyses in Papers 2 and 3 , found an increased mass estimate when inner GCs were not included in the analysis. We repeat this kind of analysis here by removing the inner GC analogs from the MUGS2 galaxies, and recalculating the mass estimate M 200 . Each galaxy in the MUGS2 simulation is unique in shape and spatial distribution of GC analogs. In order to remove inner GC analogs in a consistent way across all galaxies, we find the scale radius r s of each galactic disk via a simple exponential fit, and then remove GC analogs within 7.5 r s . The MW’s scale radius is roughly 2 kpc, so in our own Galaxy this cut is akin to removing GCs within r gc = 15 kpc of the Galactic center. It should be noted that the galaxies already had GC analogs removed within 3 r s in the original analysis. The new mass estimates after removing the inner GC analogs are shown in Figure 12 . In general, the estimates are better but at the cost of wider Bayesian c.r. The true M 200 values lie within the Bayesian c.r. in 13 out of 18 cases—a slight improvement from 8 out of 18 (Figure 9 ). Three regulated galaxy masses that were previously underestimated are now captured within the uncertainties. The mass estimate for g 15807, previously a large outlier, is also notably improved. Figure 12. Results from the sensitivity test: mass estimates after selecting tracers outside of r = 7.5 r s ). True values are shown as blue diamonds, estimates are dark purple circles, and the 95% c.r. are shown as errorbars. In light of this result, and evidence presented in Section 5.1.3 , we suggest that the combination of the GC analog number density profile, the percentage of complete data at small r , and the incomplete data at large r are the culprits of the mismatch between the predicted and true mass profiles. To test this hypothesis, one could rerun the analysis in a future sensitivity test, gradually increasing the number of proper motion measurements at large distances. We leave this to a future work. 5.4. Discussion The underestimation of the total mass appears to be a systematic bias in our method, as it applies to these MUGS2 galaxies—especially the regulated variety. Although it may be tempting to extrapolate results from these blind tests to our previous MW results using GCs in Paper 3 , it is important to make this kind of inference cautiously, for a few reasons: (1) The GC analog populations are dissimilar to the MW, and the MUGS2 galaxies, in the end,


is no longer achieved and no solutions are found. (For more details on the Grad–Shafranov solver, refer to Paper I .) 3 RESULTS We next present results from various runs for the magnetosphere, as it adapts to the internal evolution. In the leftmost panel of Fig. 1 , we show the 2D projection of the magnetic field lines (on the r θ plane) at several snapshots throughout the evolution of the sample field defined as model A in Section 2.2 . In this case, the initial field is dipolar, with a toroidal component of relative strength , confined within the critical field line defined by P c = 0.5 P o . Crucially, a value of P c P o allows for a toroidal field to be present in the magnetosphere at the start of our simulation. Figure 1. Left-hand panel: snapshots of the projection of field lines in the meridional plane for model A at three different times: the initial field configuration at t = 0 is shown with dotted lines; the field at t = 1500 yr is shown with dot–dashed lines; and the field at t = 1579 yr (the last time-step before the magnetosphere saturates) is shown in solid lines. The star is shown in grey, and the distances are rescaled by the stellar radius. The critical field line at t = 1579 yr (confining the magnetospheric currents) is shown thicker. Note the accelerating expansion of the field lines over the last two snapshots. Middle and right-hand panels: 3D field lines for the initial magnetic field (at t = 0) and for the last snapshot before reaching the critical point (at t = 1579 yr), respectively. We find that, starting with an initial toroidal field occupying part of the magnetosphere, it gradually increases in amplitude over the course of the evolution. Consequently, the strength of magnetospheric currents, total energy, helicity and twist in the magnetosphere steadily increase over time, and the field lines stretch outwards as the simulation progresses. This continues until the toroidal field reaches a maximal amplitude, beyond which simple field configurations with lines connected to the interior are no longer feasible solutions of the Grad–Shafranov equation (see Paper I ), and thus the magnetosphere reaches what we refer to as a critical point . For the particular model presented here, this happens at approximately t max ≈ 1579 yr. It is important to notice that t max is not very sensitive to the exact twist at which the reconnection event occurs because, once the twist is significant (∼1 rad), the evolution proceeds very rapidly. At this moment, we expect the magnetosphere to undergo a violent rearrangement on the Alfvén time-scale, resulting in the expulsion of some or all of the excess energy stored in the toroidal component. After this rearrangement, the evolution will continue, starting from the new initial state, and the process is repeated. Thus, one would expect recurrent outbursts or flares throughout the evolution, each resulting in the expulsion of a fraction of the available energy. The amount of energy


turn depends on much of the physics of the cloud. Section 2 reviews briefly the details of the particle heating model grid and discusses the physical and chemical properties of the grid. Section 3.1 explores the effect of a large quantity of cold clouds on the composite model spectrum for BCGs. Section 3.2 discusses the effects of optical depth on the predictions for the BCG line ratios and Sections 3.3 and 3.4 explore the effect of turbulence and magnetic fields. Some words of caution about the models are given in Section 3.5 . A discussion and predictions for future observations are presented in Section 4 . 2 MODEL The particle heating model used in this paper is essentially that described in F2009 for optically thin emission from warm ionized gas adapted to include physics pertinent to very cold clouds. The model is motivated by spectra from extended emission-line regions in BCGs which show spatially coincident emission from molecular, atomic and ionized gas, suggesting that the total emission in the filaments is from clouds with a range of densities and temperatures. F2009 parametrize the contribution of the different phases to the total volume as a weighted sum of ‘cloudlets’ of different densities but constant pressure. The weighting function, α, is taken to be a power law in the cloud density, and hence the cloud density function will be this power law. The line emissivity ( in erg cm −3 s −1 ) summed over the distribution of clouds is where n i are the specific densities and we simulate the grid in density bins of 0.1 dex from log 10 ( n ) 0 to 6. The pressure in the ionized filaments has been measured by Heckman et al. ( 1989 ) and is similar to the X-ray derived pressure of the ICM. Throughout the paper we will refer to ‘hot gas’ as X-ray emitting ( T ≳ 10 6 K) gas, ‘warm gas’ as ionized, optical emitting clouds ( T ∼10 000 K) which emit strongly in Hα, ‘cool gas’ as T ∼ 1000 K gas which emits strongly in H 2 12 μm and ‘cold gas’ as gas with temperatures T ≲ 100 K, which emit in the strong fine structure lines of [C ii ] λ157 μm , and many molecular emission lines. F2009 use the Hα and H 2 12 μm emission-line ratios to determine α for the Perseus cluster (a constant pressure of ∼10 6.5 is used for the Perseus cluster). They find α = −0.35 can reproduce all emission lines from the warm ionized ( T ∼ 10 000 K) gas to within a factor of 2 (but see Johnstone et al. 2012 for a discussion of the Hα flux in the Perseus cluster). This value of α implies the majority of the volume is filled by hot ionized gas with only a minor contribution from the more massive, cold clouds. Hα emission is predominantly from ∼10 4 K gas while the H 2 12 μm emission line is from gas ∼10 3 K. The authors point out that the data available at the time are not able to constrain a large reservoir of very low temperature clouds. However, extrapolation of α to low-temperature clouds gives good agreement with mass estimates from CO emission lines though these may be


applied to the data of the Apatity Neutron Monitor ( http://www.nmdb.eu/nest/search.php/ ); the results, reported in the third panel of Figure 3 , show a periodicity that seems to coincide with the observed one by PAMELA. To try to explore the origin of this quasi-periodicity, a raw periodgram (95% Kolmogorov–Smirnov confidence level) of the first two rigidity spectra, 0.4–0.65 GV and 0.65–15 GV, has been carried out. The results are presented in the fifth panel of Figure 3 . Peaks appear around 580, 450, 370, 320, and 230 days. The 580-day periodicity is possibly linked to an ∼600-day periodicity reported in Valdés-Galicia et al. ( 1996 ), which could be associated with fluctuations in the southern coronal hole area and in large active regions. The seasonal ∼370-day cosmic-ray variation is caused by the Earth’s rotation (Forbush 1954 ). The 230-day peak was also found in El-Borie et al. ( 2011 ) as a 0.7-year periodicity during the A > 0 solar cycle (1992–2000). The last periodicity, ∼450 days, was already described in Valdés-Galicia et al. ( 1996 ) as a possible 1.2-year periodicity but its origin is not reported. The nature of the ∼450-day periodicity could be related to quasi biennial oscillations or QBOs (Vecchio et al. 2012 ; Laurenza et al. 2012 ). QBOs have been detected as a prominent scale of variability in GCRs, but they could just be more an effect of superposition of other periodic/quasi-periodic processes and not stochastic perturbations. Higher QBOs have been observed during solar maxima with respect to solar minima (Bazilevskaya et al. 2015 ); this could explain a higher signal in the descending phase of PAMELA proton data (see Figure 1 ) and could be related to different drift effects in different polarities of the HMF. In the past, numerous periodicities between 0.5 and 4 years have been correlated to QBOs (Kato et al. 2003 ; Rybák et al. 2001 ; Kudela et al. 2002 , 2010 ; Benevolenskaya ( 1998 ) and it is very difficult to disentangle their effects from others. In this work, a different hypothesis is proposed for the 450-day periodicity as a study case: a Jovian origin, more exotic but largely proposed in the past. It is well known that the planet Jupiter possesses a very intense magnetosphere due to the combination between its strong magnetic field, about 10 4 times larger than that of the Earth, and the weakness of the solar wind at 5 au. Evidence that Jupiter could generate high-energy particles has been shown for electrons (Teegarden et al. 1974 ; Simpson et al. 1974 ), and more recent studies revealed that the impulsive and quasi-periodic bursts observed in Jupiter’s duskside magnetosphere also contain protons and helium nuclei in the range 0.7–10 MeV/nucleon (Zhang et al. 1995 ). Moreover, an indication that acceleration mechanisms can operate in magnetospheric environments has been found on Earth, where trapped particles are shown to be accelerated to relativistic energies by local acceleration acting in the heart


polarized emission at intermediate and high Galactic latitudes. In extrapolating the foreground contribution at the various frequencies, we take the Planck 353 and 30 GHz and WMAP--band color corrections into account to properly include the real frequency response of the instruments ( Planck Collaboration IX 2014 ; Planck Collaboration V 2016 ). We recall that synchrotron and dust maps of Fig. 3 report the actual value of the spectra in the bandpower in those pixels corresponding to regions where we have a signal detection above 3, and the upper limit on it in all the other pixels. Nevertheless, we treat detections and upper limits in the same way by rigidly extrapolating the complete maps in frequency. To distinguish among different cases, we divide the sky regions into four classes, depending on whether we reach detections or upper limits for synchrotron and dust, and in the following figures, we use different colors to distinguish them. Classes are defined in Table 2 . Figure 4 shows the minimum foreground amplitude (sum of synchrotron and dust contributions) recovered in each sky patch after frequency extrapolation, together with the associated error. Amplitudes are expressed in terms of , computed by dividing the total minimum amplitude of foreground emission in K by the value of the CMB primordial modes power spectrum with tensor-to-scalar ratio in the bandpower, which is equal to K. Therefore, a value of , for example, means a foreground contribution at the level of a CMB GWs signal with . For regions belonging to class (1), maps in Fig. 4 use colored pixels to report the estimated values of and the associated errors. For each map we also report the histogram of the retrieved values. Uncertainties are calculated as the quadratic sum of the statistical errors coming from the white noise in the sky maps and the errors coming from the uncertainties on the frequency scaling parameters. For regions in classes (2), (3), and (4), we are able to put only upper limits on , which are shown in Fig. 4 . We also report the errors on these upper limits, which as before, are the quadratic sum of the statistical errors (included only if we have a detection of at least one of the two kinds of signal) and the frequency scaling ones. Figure 5 shows the map reporting, for each region, the frequency at which we find the minimum of foreground emission, together with the associated histogram. In this map, we again distinguish the four classes of regions using different color scales. For class (1), since we are dealing with detections, the value of each pixel represents the actual frequency where the minimum of foreground emission is reached. For classes (2) and (3), the reported value represents the frequency at which we set the upper limit on in the corresponding region. This frequency should be seen as an upper (for class (2)) or a lower limit (for class (3)) on the real frequency at which the foreground emission reaches its actual minimum. For class number


strong negative gas-phase metallicities from the center toward the stripped tails, consistent with an inside-out formation in isolation, followed by a outside-in removal of gas upon infall into the cluster (e.g., Bellhouse et al. 2019 ; Franchetto et al. 2020 ). Our galaxies show offset H α -flux peaks, extended tails of nebular emission, and bow-like and asymmetric velocity maps reminiscent of those seen in jellyfish galaxies. However, the tantalizing alignment of these features with the merger axis is broadly incompatible with galaxies infalling into the cluster radially and, unlike jellyfish galaxies, we actually find consistent evidence against radial metallicity gradients. We can draw comparisons between detailed studies of infalling galaxies in local clusters. For example, Chemin et al. ( 2006 ) conducted a detailed kinematic analysis of 30 typical spiral galaxies in the 1.2 × 10 15 M ⊙ Virgo cluster, located at a distance of just ∼16.5 Mpc. The bulk of their sample is located outside the core of the cluster, specifically at relative velocities and radii larger than our sample (see the phase–space diagram in Figure 5 ). Chemin et al. ( 2006 ) found evidence for disturbed H α kinematics, but the offsets between the peak of the stellar light and the H α are of the order of 0.2–0.4 kpc, which is smaller than what we observe in our galaxies (0.6–1.9 kpc). Outside of its core, the Coma cluster (7 × 10 14 M ⊙ , located at ∼100 Mpc) is dominated by disturbed galaxies with tails of H α emission (Gavazzi et al. 2018 ). Three Coma galaxies are located to the cluster center as close as our galaxies Sausage 6–9 (Figure 5 ). However, these three galaxies are undergoing extreme ram pressure. With only one galaxy powered by SF and two by AGN, there is little to no H α within the stellar disk and the bulk of H α is found outside the galaxies, streaming out in long tails (Yagi et al. 2010 ). Observations of both Coma and Virgo indicate that infalling galaxies can present tails of H α emission and perturbed kinematics, but the H α gas is removed from the outside in, while the peak of the emission, close to the nucleus of the galaxies does not get displaced. Figure 5. Phase–space diagram for the cores of the Sausage, Virgo, and Coma clusters, highlighting kinematically disturbed H α galaxies. We show our five galaxies with respect to the properties of the closest subcluster (as derived from weak lensing and dynamics in Jee et al. 2015 ), together with data from Chemin et al. ( 2006 ) on the Virgo cluster and Gavazzi et al. ( 2018 ) for the Coma cluster. Our galaxies are embedded deep within the ICM. Unlike galaxies at similar cluster-centric radii and relative velocities in Coma and Virgo, which are almost completely devoid of H α within the disk, the Sausage galaxies show H α throughout the stellar disk, with large offsets between the peak of H α and the stellar light. Considering that our galaxies are deeply embedded in the hottest parts of the ICM (see


role of the hydrodynamic effects, we compare a 3D hydrodynamic simulation, published in Nawaz et al. ( 2016 ), to a ballistic jet model (Gower et al. 1982 ) for the precessing jet source Hydra A in Fig. A1 . Model parameters are given in Table A1 . It is clear that even for this comparatively low-power jet, the curvature induced by precession dominates the observational appearance for most of the region where the jet is observed. It is therefore reasonable to take curvature as signature for precessing jets. Figure A1. Different methods of modelling the precessing jet in Hydra A. (a) VLA image of Hydra A. (b) Hydrodynamic simulation of a jet with parameters empirically matched to Hydra A. (c) Ballistic jet model (Gower et al. 1982 ) for Hydra A. Even though Hydra A has a weaker jet than the powerful jet sources discussed elsewhere in this article, the jet path is over most of its length well modelled by the hydrodynamic simulation as well as the ballistic model. This suggests that precession effects are indeed observable in real radio sources. Panels (a) and (b) were adopted from Nawaz et al. ( 2016 ). Table A1. Parameters for the jet models compared in Fig. A1 . a Ω t ref in Gower et al. ( 1982 ). APPENDIX B: RADIO MAPS FOR THE COMPLETE SAMPLE We provide here all the radio maps of our complete sample. Shown is Stokes I in Jy beam −1 . The mapping of the flux levels onto the colour map is non-linear and has been adjusted carefully for each map to ensure lobe and jet structures are well visible. Equatorial coordinates are given on the maps. Observing frequency, resolution, redshift, and precession indicators are given in the individual figure captions. The features of precessing jets are indicated on each map if applicable. Figure B1. 3C 20, 8.41 GHz, resolution: 11, redshift: 0.174. C: Curved jet structure on the eastern side. E: Lobe brightness asymmetry/jet at edge of lobe on the western side. R: Multiple terminal hotspots on the eastern side; wide terminal hotspot on the western side. S: S-symmetry. Additionally, interaction with ambient medium. Figure B2. 3C 22, 8.56 GHz, resolution: 075, redshift: 0.938. C: Curved jet. E: Misaligned lobe axis on the eastern side. Lobe brightness asymmetry on the western side. S: S symmetric jets. Figure B3. 3C 33.1, 4.85 GHz, resolution: 2948 × 2472, redshift: 0.18. C: Curved eastern jet. E: Misaligned lobe axis on the eastern side. S: S-symmetric jets. Jet enters lobe on southern side. Jet bends with brightening, possibly related to jet–cloud interaction. Southern tip-of-lobe hotspot lies along the continuation of inner southern jet. The innermost part of the jets is aligned with the lobe axis [solid black line, position angle (jet side) indicated]. Figure B4. 3C 41, 8.46 GHz, resolution: 02, redshift: 0.795. C: Curved southern jet. E: Misaligned lobe. R: Wide terminal hotspots on both sides. S: S-symmetric jet–hotspots. Southern jet (yellow dotted line) misaligned with lobe axis (solid white line) by


light images with HST /STIS at 260 au, and estimated the mass of a potential planet to be 0.4 M jup (based on some simple analytical derivation). Isella et al. ( 2016 ) also detected a small dip in the integrated CO brightness profile at ≈22 (see their Figure 1, or Figure 5 in Liu et al. 2018 ). In our model, the gap appears in scattered light for a planet mass larger than 2 M jup , but remains undetected in the synthetic CO maps. The final profile of a planetary gap establishes itself on a viscous timescale (thousands of orbits with a viscosity of 10 −3 ), however, and the gap width and depth in our models are only lower limits. The effect of the planet appears fainter in the 13 CO channels maps than in the 12 CO maps, even if the planet is located in the midplane. This is due to optical depth and vertical temperature gradient effects: the 12 CO is coming from a vertically narrow and warm layer above the midplane, while the 13 CO is originating from a deeper, thicker layer, where the disk is almost vertically isothermal, resulting in a uniform emissivity that washes out some of the kinematics signal. Are we seeing the signature of an embedded planet? Can we exclude wishful thinking? The strongest evidence is that the perturbation to the disk kinematics is highly localized in both space and velocity. This excludes any mechanism that merely produces axisymmetric rings in disks. This excludes, for example, ice lines (Zhang et al. 2015 ), self-induced dust traps (Gonzalez et al. 2015 ), instabilities (Takahashi Inutsuka 2014 ; Lorén-Aguilar Bate 2015 ), and zonal flows (Flock et al. 2015 ). A spiral wave could in principle result from the disk self-gravity, but multiple, large-scale spirals would be expected in that case (e.g., Dipierro et al. 2015 ), which the localized deviation seen in HD 163296 would seem to exclude. The localized nature of the kinematic perturbation, that it occurs close to the gap found by Grady et al. ( 2000 ), and the similarity to the signatures predicted by our hydrodynamic models is strong evidence for a young protoplanet in a gas-rich disk. However, confirmation with direct imaging is the only way to be sure. The relatively large planet mass and its known location in the disk means direct imaging follow-up might be able to detect it, depending on how embedded it is in the disk. So far, no point source has been detected at the location of the potential planet with near-IR adaptive optics systems. A 2 M Jup planet is consistent with the upper limits (for an unobscured planet) obtained by adaptive optics systems, such as SPHERE (Muro-Arena et al. 2018 ) and Keck L’ (Guidi et al. submitted). Using the formalism developed in Pinte et al. ( 2018 ), we find that the velocity kink is located at a distance of ≈260 au, and an elevation above the midplane of ≈70 au. Assuming that the potential planet is located in the midplane, it would be at a projected distance of 2.3 ± 02 and PA = −3° ± 5° from the star, where we


that sometimes show a periodic structure (one of the most famous example is the Guitar nebula, see e.g. Chatterjee Cordes 2002 , 2004 ; van Kerkwijk Ingle 2008 ). While at present the structures in the vicinity of the bow-shock head are reasonably well understood, the same cannot be said of the structures in the tail (Brownsberger Romani 2014 ; Klingler et al. 2016 ; Pavan et al. 2016 ). The possibility that the dynamics of PWNe can be strongly affected by the mass loading was discussed by Bucciantini and Bandiera ( 2001 ) and Bucciantini ( 2002c ). There the authors have shown that a non-negligible fraction of neutral atoms is expected to penetrate in the bow shock through shocked ISM, and then interact with the pulsar wind, modifying the predicted dynamics. These first models provide a good description of both the hydrogen penetration length-scale and the Hα luminosity. In Morlino, Lyutikov, and Vorster ( 2015 ) a quasi-1D steady-state model has been proposed to investigate the effect of mass loading on the tail morphology of BSPWNe. If a significant fraction of neutral atoms from the ISM penetrate into the bow shock, they can undergo ionization essentially by interacting with the UV photons emitted by the relativistic plasma of the nebula. The resulting protons and electrons interact, in turn, with the wind thorough its magnetic field, leading to a net mass loading of the shocked wind in the tail. The newly formed protons and electrons are at rest in the rest frame of the ISM. Moreover they originate from the cold neutrals of the ISM, which carry negligible thermal energy. Hence they do not add momentum or internal energy to the flow (they however add their rest mass energy). Given that momentum and energy are conserved, the rise in rest mass energy density causes the wind to slow down and the pressure to rise, resulting ultimately in a lateral expansion. This effect indeed produces a shape which resembles the head-and-shoulder morphology. Nevertheless the analytic model by Morlino et al. ( 2015 ) has few shortcomings: being 1D it does not account for the fluid dynamics in the lateral direction, the ISM ram pressure is neglected despite the supersonic motion, and, being stationary, it cannot capture possible instabilities. In this paper we extend this model by means of 2D relativistic HD axisymmetric simulations, with the aim of validating the head–shoulder morphology of BSPWNe predicted by the aforementioned work, and extending it beyond its limitations. Although magnetic field might influence the dynamics of the flow, its response to mass loading, and the expected opening of the tail, in order to avoid a further level of complexity we limit this work to pure HD. This paper is organized as follows: in Section 2 the numerical tool and setup are described; in Section 3 we present and discuss our findings. Conclusions are then drawn in Section 4 . 2 NUMERICAL SETUP The typical length-scale of BSPWNe is the so called stand off distance d


transfer, to atmospheric chemistry and dynamics, and they influence—if not control—aspects such as the surface temperature and, thus, the potential habitability of a terrestrial planet (Marley et al. 2013 ). Understanding the impact of clouds is thus instrumental for the study of planetary climates. Clouds composed of carbon dioxide (CO 2 ) ice particles are important for cold, CO 2 -rich atmospheres. This includes, for example, the present and early Mars (Forget Pierrehumbert 1997 ), the early Earth (Caldeira Kasting 1992 ), or terrestrial exoplanets at the outer boundary of the habitable zone (HZ; Kasting et al. 1993 ; Forget Pierrehumbert 1997 ). Provided that condensation nuclei are available, such clouds would form easily in a supersaturated atmosphere. Such as in the case of water clouds (e.g., Kitzmann et al. 2010 ), the presence of CO 2 clouds will first result in an increase of the planetary albedo by scattering incident stellar radiation back to space, which leads to a cooling effect (albedo effect). In contrast to liquid or solid water, CO 2 ice is mostly transparent with respect to absorption in the infrared (Hansen 1997 , 2005 ). Thus, as argued by Forget Pierrehumbert ( 1997 ) or Kasting et al. ( 1993 ), a classical greenhouse effect by absorption and re-emission of thermal radiation is unlikely to occur for a cloud composed of dry ice. On the other hand, CO 2 ice particles can efficiently scatter thermal radiation back to the planetary surface, thereby exhibiting a scattering greenhouse effect. In their seminal study, Forget Pierrehumbert ( 1997 ) showed that this scattering greenhouse effect of CO 2 ice clouds alone would have been efficient enough to allow for liquid water on the surface of the early Mars. This strong heating effect was also found in later studies by, e.g., Pierrehumbert Erlick ( 1998 ), Mischna et al. ( 2000 ), or Colaprete Toon ( 2003 ). However, by using three-dimensional general circulation models, it has been suggested, that a limiting factor for the impact of CO 2 clouds on early Mars might be the cloud coverage, which could be well below 100% (Forget et al. 2013 ). In particular, the outer boundary of the classical HZ might also be influenced by the formation of CO 2 ice clouds and their corresponding climatic impact. For the Sun, Forget Pierrehumbert ( 1997 ) reported an outer HZ boundary of 2.4 AU for a planet fully covered with CO 2 clouds, which is far larger than the cloud-free value of 1.67 AU Kasting et al. ( 1993 ). The competing radiative cooling and heating effects are individually large, but partly balance each other. That means that small errors in the description of one of these radiative interactions can lead to large errors in a cloud’s net effect. So far, all previous studies on the climatic impact of CO 2 clouds used a simplified treatment for the numerical solution of the radiative transfer equation to determine the atmospheric and surface temperatures. In particular, two-stream


implications for the proposed loose correlation between explosion energy and kick velocity (Bray Eldridge 2016 ; Janka 2017 ; Vigna-Gómez et al. 2018 ). Our results constitute further evidence that this correlation is not a tight one. More likely, the explosion energy only determines the maximum attainable kick velocity, below which one expects a distribution of kicks depending on the degree of unipolarity or bipolarity (Müller et al. 2019 ). This can be accounted for in a more general formulation than in Bray Eldridge ( 2016 ) by a factor that measures the explosion asymmetry (Janka 2017 ). The evolution of the spin-kick angle α in model m39 is noteworthy. Some observations have suggested that the birth spins and kicks of neutron stars tend to be aligned (Johnston et al. 2005 ; Ng Romani 2007 ; Noutsos et al. 2013 ). However, even though hydrodynamic mechanisms for spin-kick alignment have been proposed (Janka 2017 ), no trend towards spin-kick alignment has been observed so far in 3D CCSN simulations of non-rotating progenitors (Wongwathanarat et al. 2013 ; Müller et al. 2019 ). For our non-rotating explosion model y20, we also find a large angle α ≈ 70° between the spin and kick. For the rapidly rotating model m39, however, the spin-kick angle stays at about α ≈ 30°. In this case, spin-kick alignment comes about because the bipolar outflows are aligned with the initial rotation axis, which is not changed appreciably by asymmetric accretion on to the PNS. This suggests that progenitor rotation could play a role in explaining spin-kick alignment (provided that the observational evidence remains robust). However, even for model m39, the spin-kick alignment is not perfect, and is not clear whether the polar alignment of the outflows is a robust feature for rotating progenitors. In fact, some previous 3D supernova simulations of rotating progenitors rather find that the explosion develops preferably in the equatorial plane (Summa et al. 2018 ; Takiwaki Kotake 2018 ). Clearly, more simulations are required to determine the implications of rotation for the explosion morphology and spin-kick alignment. 6 GRAVITATIONAL WAVE EMISSION The gravitational-wave emission for our models, as measured by an observer at the pole and the equator, is shown in Fig. 6 . The high mass and rotation of model m39 results in high gravitational-wave amplitudes of up to 40 cm at the pole and over 100 cm at the equator. Model y20 reaches amplitudes of ∼10 cm at the pole, and ∼18 cm at the equator. Model s18np has a much lower amplitude of ∼5 cm at the equator, due to the lack of shock revival in this model, however its prompt convection signal in the direction of the equator reaches amplitudes as high as model y20. Figure 6. The gravitational-wave emission for our models as measured at the pole (left-hand panel) and the equator (right-hand panel). Top is model m39, middle is model s18np, and bottom is model y20. All models show the rise of gravitational-wave frequency


the total magnetic fluctuations and of the parallel electric fluctuations, and (top and bottom rows, respectively) for (left column) and β i = 0.2 (right column). A classical intermittency analysis has been performed on both simulations at about the peak of the nonlinear activity. In order to define the large-scale limit of the inertial range, we evaluated the perpendicular and parallel autocorrelation functions, respectively defined as and (Frisch 1995 ). We assumed isotropy in the perpendicular xy -plane, with the parallel direction along B 0 , i.e., along z . The e -folding length approximately gives the integral scale, which is about in the perpendicular direction (corresponding to ), for both regimes. The situation is different in the parallel direction, where the parallel correlation length is for β p = 0.2, while it is for β p = 1 (corresponding to and ∼0.5, respectively). This is in qualitative agreement with the features spotted in Figure 1 and quantitatively with the corresponding spectra (see Figure 4 ), indicating differences already in the large-scale properties of the fluctuations possibly due to a different decorrelation mechanism along the mean field. The level of intermittency can be better quantified by the probability distribution functions (PDFs) of the magnetic field increments at a given scale r , defined asWe show here the statistics of the perpendicular increments, namely, , spanning this increment from lengths larger than the correlation scale , down to the smallest available scale (Δ x ∼ 0.08 d p ). These distributions are reported in Figure 3 (a) for the β p = 0.2 regime for three cases, namely, and 0.08. These PDFs, as expected, become increasingly intermittent going toward smaller scales. In order to compare among cases, and among different times, we measured the scale-dependent kurtosis χ —the fourth-order moment of the increments in Equation ( 4 )—that can be measured asThis quantity is reported in Figure 3 (b), as a function of the perpendicular scale r , for the two values of β , at two distinct times. At large scales, for r > 5 d p , the distribution becomes Gaussian, where χ ∼ 3, in agreement with the computation of the correlation lengths. At small scales, in the inertial range of turbulence, there is an enhancement due to the intermittent nature of the cascade, due to the presence of coherent structures and nonlinear waves. At the smallest scales, a saturation of the multifractality is observed, in agreement with observations in the SW. In fact, the study of high-order structure functions up to the sixth moment and of their exponents, shows deviation from monofractality (not shown here). Here, this process of saturation might also be slightly affected by the presence of artificial dissipation. It is important to note that at scales in the inertial-dispersive range, the case with β p = 0.2 is more intermittent than the β p = 1 regime, indicating a higher degree of coherency in the small-scale fluctuations.


before the analyses pipelines were finalized. Our decision to focus on the NGC exclusively did come after a comparison with S16 had occurred, though we believe that we are well justified in our choice. S16 provide the current best weak lensing mass calibration of redMaPPer clusters, and they discuss in detail how their mass calibration compares to others in the literature. While the constraints on the slope of the mass–richness relation are in good agreement between the two works, there is mild tension on the recovered amplitude assuming our fiducial cosmology, with the clustering-derived constraints preferring a somewhat higher amplitude. At the richness pivot point used in this work, λ 0 = 35, S16 predict log 10 ( M /M ⊙ ) = 14.43 ± 0.04, while our constraints yield log 10 ( M /M ⊙ ) = 14.62 ± 0.08; this discrepancy corresponds to roughly 2.2σ tension. Because the clustering analysis prefers a slightly lower value of α than the weak lensing analysis, this tension is reduced for λ > 35. For λ 35, the tension remains roughly the same since the error bars increase as one moves away from the λ pivot point. We postpone a discussion of the origin of this tension, and a more detailed comparison of the two results, to future work. That is, our current results reflect our best understanding of both the weak lensing and clustering analysis prior to the comparison of the two works. We have also considered a power-law bias–richness relation as per equation ( 10 ). This model has five parameters: A λ , α λ , β λ and two bias parameters for 5 λ 20 clusters in the two redshift bins. Fitting this model to the data, we find A λ = 3.54 ± 0.13, α λ = 0.57 ± 0.08 and β λ = 2.0 ± 1.1 with χ 2 /d.o.f. = 57.7/75. 7 CHARACTERIZING THE UNCERTAINTY IN THE MASS–RICHNESS RELATION The uncertainties on the mass–richness parameters presented in Fig. 6 and Table 1 receive contributions from several sources: statistical noise in the measurement of the angular correlation functions, uncertainty on the parameters of the line-of-sight projection model, uncertainty on the parameters of the assembly bias model and scatter around the b ( M ) relation from Tinker et al. ( 2010 ). In addition to these sources of scatter that are explicitly included in our model, it is also possible that our measurement is affected by systematic biases that we have not modelled. Below, we determine the approximate contributions of both modelled sources of scatter and unmodelled systematic errors to the uncertainty budget of our parameter constraints. 7.1 Statistical noise in the correlation function measurement We first investigate how statistical noise in the measurement of w αβ (θ) contributes to our parameter uncertainties. The contribution of statistical noise to our parameter uncertainties can be determined by setting the parameters of the line-of-sight projection model, the parameters of the assembly bias model and b scaling to constant values rather than allowing these parameters to vary.