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

O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O B-Telescope B-Instrument O O O O O O O O O O B-Archive I-Archive O O O O O O O O B-Software I-Software I-Software I-Software O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation O O O O O O O O O O O O O O O O O O B-Archive I-Archive O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O B-Software I-Software I-Software I-Software O B-Citation I-Citation I-Citation I-Citation O O O O O O B-Telescope B-Instrument I-Instrument O O B-Citation I-Citation I-Citation I-Citation O B-Telescope B-Instrument O B-Citation I-Citation I-Citation I-Citation O O B-Telescope B-Instrument O O O O O O O O O B-Wavelength I-Wavelength O B-Wavelength I-Wavelength O B-Wavelength I-Wavelength O B-Wavelength I-Wavelength O O O O O O O B-Citation I-Citation O O O O O O O O O O B-TextGarbage O O O O O O O O O O O O O B-TextGarbage O O O O O O O O O B-TextGarbage O O O O O O O O O O O O


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.

O O O B-Dataset I-Dataset O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O B-CelestialObject O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O B-Telescope I-Telescope I-Telescope I-Telescope B-Telescope O O O B-Instrument I-Instrument O O O O O O O O B-Wavelength I-Wavelength O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O B-Telescope I-Telescope I-Telescope B-Telescope O O B-Instrument I-Instrument O O O O B-Wavelength I-Wavelength O O O O O O O O O B-Telescope I-Telescope I-Telescope I-Telescope B-Telescope O O B-Instrument I-Instrument O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O B-Survey O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation O O O O O O O O O O O O O O O O O O O O B-Software B-Citation I-Citation O O O O O O O O O O O O B-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Dataset I-Dataset B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Dataset I-Dataset O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Dataset I-Dataset O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation


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

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


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,

O O O O O O O B-Instrument O O O O O O O O O O B-Survey O O O O B-Wavelength O B-Wavelength O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O B-Survey O O O O O O O O O O O O O O B-Survey O O O B-Wavelength O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O B-Wavelength I-Wavelength O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Wavelength O O B-Wavelength I-Wavelength O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Wavelength O O B-Wavelength I-Wavelength O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O B-Instrument O B-Telescope O O B-Telescope O O B-Observatory I-Observatory I-Observatory B-Observatory O O O O O O O O O O O O O O O O B-Wavelength O O O O B-Wavelength O O B-Wavelength I-Wavelength O O O O O O O O O O O O O B-Survey O O B-Survey O O O O O O O O O O O O B-Proposal B-Proposal B-Proposal B-Proposal B-Proposal B-Proposal O B-Proposal O B-Person I-Person O O B-Proposal O O O B-Wavelength O O B-Survey O B-Proposal O O O O B-Survey O O O O O O O O O O O O O O O O O O B-Survey O O O O O O O O B-Instrument B-Wavelength I-Wavelength B-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument B-Software I-Software B-Citation I-Citation I-Citation I-Citation O O O B-Software I-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


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

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


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

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


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

O O O O O O O O O B-Wavelength B-Wavelength O B-Wavelength O O O O O O O O O B-Wavelength O B-TextGarbage O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O


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

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


in 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

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Tag O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O B-Citation I-Citation O B-Citation I-Citation I-Citation O O O O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation O O B-Citation I-Citation O O O O O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O


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

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


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

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


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,

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


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

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


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

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


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

O O O O O O B-Instrument I-Instrument I-Instrument O B-URL O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O B-Citation I-Citation O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O B-Formula I-Formula I-Formula O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O B-CelestialObject O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O


O O O O O O O O O O O O B-URL O O O O O O O O B-Wavelength O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O B-Wavelength O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O B-Wavelength O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O B-Wavelength O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


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

O O O O O B-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O B-Telescope B-Wavelength O B-Wavelength I-Wavelength O B-Telescope O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


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

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


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

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


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

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


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

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


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

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