for further testing and investigation. However, large active regions often last a long time and erupt repeatedly, so there are good reasons to take this hypothesis seriously. For such an active region, the scenario that we have found in the 2012 July case could come up again without much difficulty: the earlier eruptions from the active region can precondition the preexisting ambient solar wind, and the later successive ones from the same active region, while moving through the preconditioned wind, may interact en route to 1 au. This situation could also happen for active regions that are eruptive and close to each other. Historical records of some extreme events seem to support our hypothesis. Around the 1859 Carrington event, which also occurred in a weak solar cycle, long-duration brilliant aurorae were observed from August 28 through September 3. Green Boardsen ( 2006 ) suggest that the active region erupted successively and that two closely spaced CMEs interacted in interplanetary space, leading to the extreme nature of the Carrington event. Similarly, long-duration low-latitude auroral displays were seen for almost nine nights during 1770 September. Hayakawa et al. ( 2017 ) indicate that multiple consecutive eruptions from the same active region, which may have resulted in the “perfect storm” situation as we propose in Paper I , must have occurred for such a long duration of auroral observations. A more recent case, the ultrafast CME in 1972 August, reached the Earth in only 14.6 hr, which is the shortest transit time ever observed. Knipp et al. ( 2018 ) suggest that two earlier eruptions from the same active region likely cleared the path for the subsequent ultrafast event, which is exactly our “preconditioning” idea discussed in Paper I and here in the current work. We speculate that some of the 2003 Halloween storms may also be “perfect storms,” including the preconditioning effect and/or CME–CME interactions, because several large active regions continuously erupted for a long time (e.g., Skoug et al. 2004 ; Gopalswamy et al. 2005 ). We think that the hypothesis is valuable in that it points out the reality of extreme events from today's Sun. They generally are not simple and can involve many reinforcing factors. While the paper appears to stress the importance of interplanetary evolution of CMEs, the “perfect storm” concept also includes solar aspects, such as the persistent eruptive nature of the active region and the simultaneous presence of several big active regions on the disk. A particular instance is that widespread magnetic connectivity between concurrent active regions leads to sympathetic eruptions (e.g., Schrijver Title 2011 ; Jin et al. 2016 ; Wang et al. 2016 ). A nearly “global storm” could be made under this solar-side “perfect storm” scenario. This may have occurred during the 2003 Halloween period, which had a few large active regions, including one that emerged quickly and became connected to 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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-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 O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O B-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 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 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 O O O O O 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 O O O O O O O O O O O O O O O O O O O O O


Analogously to generative adversarial networks (Goodfellow et al. 2014 ), the conditional autoencoder is adversarially trained to generate samples that hinder the critic network’s ability to do its job. The joint distribution p ( x , u , z ) can be expressed using Bayes’ rule asThis can be rewritten asif and only if u is statistically independent from z . If the joint distribution p ( u , z ) is not factorizable, the distributions q ( x , u , z ) and p ( x , u , z ) will be different. It follows from this that u and z are statistically independent if and only if the samples ( x , u , z ) drawn according to p ( x , u , z ) are indistinguishable from those sampled from q ( x , u , z ). How can we generate samples from these two distributions? If we consider our autoencoder to be an idealistic autoencoder capable of perfectly reconstructing its inputs, then the encoder and decoder can be viewed as respectively approximately parameterizing p ( z ∣ u , x ) and p ( x ∣ u , z ), which are both deterministic functions. We can thus draw samples from p ( x , u , z ) = p ( z ∣ u , x ) p ( u , x ) by first randomly sampling from the data set to obtain ( u , x ) and then using the encoder to obtain the associated z . We can similarly draw samples from q ( x , u , z ) = p ( x ∣ u , z ) p ( u ) p ( z ) through reusing our samples drawn from p ( x , u , z ). By scrambling the ( u , z ) pairs within a batch, we can effectively remove any joint information between u and z (Belghazi et al. 2018 ), which results in samples drawn from the marginal distribution ( u , z ) ∼ p ( u ) p ( z ). We can then use the decoder that approximates p ( x ∣ u , z ) to obtain approximate samples q ( x , u , z ) drawn from p ( x ∣ u , z ) p ( u ) p ( z ). As stated above, enforcing statistical independence is the same as finding a latent representation, z , such that samples drawn according to these two procedures are indistinguishable. This bears a strong similarity to the training objective of generative adversarial networks that attempt to train a generator such that generated samples are indistinguishable from samples drawn from a data set. As such, we can take inspiration from existing generative adversarial network architectures to solve our disentanglement objective. In generative adversarial networks (Goodfellow et al. 2014 ), a critic network is trained to distinguish between samples drawn from a data set and samples created by a generator network fed samples from a well-understood probability distribution. The generator and critic network are jointly optimized in a minimax game. That is, the critic attempts to maximally distinguish between the two data streams, and the generator attempts to minimize the critic network’s ability at doing so. The global optimum of this two-player game occurs when both the generator and critic network can no longer improve—when the two data streams are identical. For our disentanglement neural network architecture, we take heavy inspiration

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


reproduces the observed interstellar extinction curve from UV to near-IR (Fitzpatrick 1999 ; Draine 2011 ). The optical results prefer the strong forward scattering with , comparable to the present near-IR values. In the near-IR, the present results can be several times larger than the WD01 prediction. Simply, the discrepancy can be explained if the larger dust grains are more dominant compared to the WD01 model. The WD01 value decreases toward longer wavelengths because the isotropic scattering by the Rayleigh scattering becomes more dominant. In the WD01 model, the typical grain size is (Draine 2011 ), which is much smaller than the near-IR wavelengths. To explain the derived large g -value, a lot of large grains may be required to cancel out the isotropic scattering by the smaller grains. However, the existence of a lot of large grains is expected to conflict with various observed properties of interstellar dust, such as interstellar depletion and wavelength dependence of interstellar extinction and polarization. This may indicate that the actual near-IR g -value is smaller than that obtained in the present study. Figure 2. Optical to near-IR scattering asymmetry factor . The present results at 1.25 and are indicated by filled red circles. The triangle, diamonds, and squares denote the results derived from Lillie Witt ( 1976 ), Witt et al. ( 1990 ), and Mattila ( 1970 ), respectively. The solid curve represents the value expected from the WD01 model with R V = 3.1 Milky Way dust (Draine 2003 ). When interstellar dust grains are exposed to UV photons, continuous near-IR emission is created as a result of the stochastic heating of the small grains and/or fluorescence by large molecules such as PAH. In fact, the UV-excited dust emission component has been observed in reflection nebulae at 1.25– wavelengths (Sellgren et al. 1992 , 1996 ). If such an emission component also exists in the general diffuse interstellar medium, the UV-excited dust emission is expected to be higher toward low Galactic latitudes because, from the Galaxy Evolution Explorer ( GALEX ) data, the near-UV to far-UV ratio in low Galactic latitudes is reported to be smaller than that in high latitudes by more than a factor of two (Figure 10 of Murthy 2014 ). The possible Galactic latitude dependence of the UV-excited dust emission would also contribute to the derived latitude dependence and may reduce the very large asymmetry factor g to the reasonable value. In this sense, the derived latitude dependence in the present study may indicate the first detection of UV-excited dust emission in the diffuse interstellar medium at 1.25 and . Similarly, to explain the very high albedo derived in the galaxy NGC 4826 in the -band, Witt et al. ( 1994 ) suggested the contribution from the near-IR dust emission in addition to the scattered light. To determine the relative contribution of the scattered light and UV-excited dust emission from the derived latitude dependence, detailed

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


Sérsic fit, finding good agreement within 2%–3%. Therefore, we did not adjust our stellar mass for missing light. 3. Analysis 3.1. Velocity Dispersion We measure the observed stellar line-of-sight velocity dispersions (LOSVD) of our galaxy sample using pPXF (Cappellari 2017 ), which utilizes a maximum penalized likelihood approach to fitting spectra to a library of stellar or stellar population templates and determines galaxy kinematics. For our analysis, we use the Indo–US stellar library templates (Valdes et al. 2004 ) with R ∼4200, which are smoothed to the binned resolution of the reduced spectra of R ∼3000. We mask out portions of the spectra where telluric atmospheric absorption bands are significant and also where the spectra are potentially impacted by [O ii ] or [O iii ] emission lines. Good fits to the continuum are obtained for all galaxies, as shown in Figure 1 . We do not introduce additional freedom (e.g., additive/multiplicative polynomial) to attempt better match to the continuum. The results are not sensitive to this choice. As our 1D spectra are optimally extracted with a Gaussian kernel based on the PSF, i.e., seeing-limited, we correct our velocity dispersions within the aperture to velocity dispersions within r e as per van de Sande et al. ( 2013 ), resulting in a mean correction of 0.02 dex. The measured velocity dispersions including aperture corrections are shown in Table 2 . We find large velocity dispersions for all galaxies ranging from 200 − 300 km s −1 . We derive LOSVD uncertainties using Monte Carlo simulations. We take the best-fit spectrum to the observed data from pPXF and perturb its flux 1000 times by a random value drawn from a Gaussian with a standard deviation consistent with the uncertainties of the observed spectrum (determined as outlined in Section 2.2 ). The LOSVD for each iteration is determined and the standard deviation of all 1000 Monte Carlo simulations is used as the error for the LOSVD. These errors are larger than the formal pPXF uncertainties by a factor of 1.1–2.2. To test potential systematic errors of our measurements, we ran pPXF for multiple scenarios. We exclude the H β line and find consistent results, suggesting that emission line-infilling is not significant for these galaxies. To explore dependence on stellar library, we use the MILES stellar library (Sanchez-Blazquez et al. 2006 ; Falcón-Barroso et al. 2011 ) and find that the results agree within the uncertainties. To investigate stability and consistency, we take the best-fit spectrum for each galaxy and smooth it to simulate different velocity dispersions, perturbing the flux by observational errors as per the Monte Carlo simulation above. We are able to recover velocity dispersions for the range 150–500 km s −1 within the pPXF uncertainties, which shows that we should be able to recover dispersions and uncertainties from data of this quality. The median residuals for the recovered velocity dispersions are small (≲17 km s −1

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


so rapidly that it becomes useless. This means that simultaneous operations of LISA and radio instruments such as SKA are beneficial for making full use of our multimessenger strategy. Following consideration of the dispersion measure, we determine the steps of trial values for the amplitude and phase of the modulation by requiring that the pulse arrival time changes by the sampling time. The number of required trials for the modulation amplitude is given by and that for the modulation phase is given by Additionally, the uncertainty in the eccentricity of Δ e ≈ 0.003 could change the arrival time by t mod Δ e , and this will require trials of for our fiducial parameters. We expect that extension to a slightly eccentric orbit will be straightforward. We should remark on the spin precession. Its period will be for our fiducial parameters (Barker O’Connell 1975 ), and we expect its effect to be marginal. We leave the careful assessment for future work, and information from LISA will prove useful even when the precession must be corrected for. 3.3 Comparison with an all-sky survey To elucidate usefulness of the multimessenger observation with LISA , we compare its performance with an all-sky survey of radio instruments. To keep the sensitivity fixed, we assume that the integration time per pointing is the same for both observation strategies. We also fix the sampling time. A comparison with an all-sky survey based on the phase-modulation search, with which the sensitivity is not maximal, is briefly made in the end of this section. First, the all-sky survey trivially requires a large number of pointings, and thus the integration time must actually be shortened. If we do not restrict the search to a limited portion of the sky, e.g. the Galactic plane, equation ( 17 ) suggests that O (10 4 ) pointings in terms of a single-dish beam are required to find a limited number of targets. Even if instruments with a large field-of-view are available (Smits et al. 2009 ), the number of pointings may not be reduced below O (10 2 ). If we evaluate the number of pointings in terms of tied-array beams, the all-sky survey requires O (10 8 ) pointings, which is larger by O (10 6 ) compared to the multimessenger observation with LISA , equation ( 20 ). However, results of the all-sky survey can be used for various applications including standard pulsar searches, and thus this comparison is valid only when we focus on detections of pulsars in the shortest period class of binary neutron stars. Next, the coherent integration becomes significantly costly because of brute-force corrections for the orbital modulation. We have to search over a large parameter space of not only the modulation amplitude and phase but also the orbital frequency. By requiring that the phase error caused by the frequency mismatch accumulated during the integration time does not induce a timing error larger than the sampling time, particularly for the harmonic summing to be successful, the step in

O O O O O O O O O O O O B-Instrument O B-Wavelength O O O B-Telescope O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 B-Instrument 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 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 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 B-EntityOfFutureInterest I-EntityOfFutureInterest O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


an oscillatory process, in which two pulses with different directions are superimposed. In the first case, a random velocity with normal distribution is simulated, see upper panel of Figure 8 . In order to apply exactly the same method used with the real data, we filtered the simulated velocity signal employing the EMD (middle panel of Figure 8 ). The polarization of this filtered signal is then visualized through a compass diagram just like what was done in the case of the observed data. Besides, we simulated a simple oscillatory signal of the form:where A is the amplitude of the velocity signal, T 1 is period, and T 2 is long-term modulation to simulate a wave train (see lower panel of Figure 8 ). Figure 8. Top panel: simulated random velocity signal with normal distribution. Middle panel: same velocity signal filtered using the EMD. Bottom panel: simulated velocity signal made with two superimposed pulses in the x and y direction respectively. The two pulses are exactly the same, but slightly shifted and with different amplitudes. The compass diagrams of the two simulated velocity signals are shown in Figure 9 . In comparison with the oscillatory signal, the random process does not display polarization (top panel). This confirms the validity of our findings. In contrast, the same kind of polarization of the compass diagram is indeed obtained with a superposition of two pulses in different directions (bottom panel). Figure 9. Compass diagram of the simulated random velocity signal with normal distribution (top), and the one obtained from a superposition of two velocity pulses in two perpendicular directions (bottom). 4. Discussion and Conclusion The results presented above show low-frequency (5–6 mHz) kink-like horizontal oscillations of SSMEs in chromosphere with an elliptic polarization of the velocity vector (see Figure 1 for a schematic representation) observed in all of the 35 SSMEs analyzed in the quiet chromosphere. This frequency range is inconsistent with residual seeing aberrations. In this regard, it is worth noting that the orientation of the velocity vector in time is not random, but reflects a long-term coherency (several minutes). This timescale is by far longer than the typical timescale of atmospheric turbulence (a few ms). Indeed, Stangalini et al. ( 2016 ) have deeply analyzed the decorrelation timescales of adaptive optic residual aberrations using on-sky data, and found them to be of the order of 10–20 ms at visible wavelengths (∼630 nm). This is consistent with independent works in the literature (see, for example, Davis Tango 1996 ). Since the turbulence timescales at the Ca ii H wavelengths is even shorter (Roddier 1999 ), we expect a large reduction of the turbulence coherence time, resulting in a turbulence timescale that is even more inconsistent with that of the process observed here. In addition, since the seeing residual aberrations are a random process, one cannot expect any coherent helical motion 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Wavelength I-Wavelength 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 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


et al. ( 2009 ). Similar to the conclusions from Bouwens et al. ( 2009 ), we find that most of the SFR density at z ≳ 3.5 appears to be directly observable in the rest-frame UV (see also Burgarella et al. 2013 ; Bourne et al. 2016 ; Dunlop et al. 2016 ). 5.3. Implications for the Lyman Continuum Photon Production Efficiencies Another consequence of our new ALMA results is for the interpretation of the prominent H α emission lines inferred in galaxies at z ∼ 4–5 based on the observed Spitzer /IRAC 3.6 μ m and 4.5 μ m fluxes (e.g., Schaerer de Barros 2009 ; Shim et al. 2011 ; Stark et al. 2013 ). As first noted by Shim et al. ( 2011 ), the total H α luminosities of galaxies at z ∼ 4–5 are in excess of what one might expect based on their luminosities in the rest-frame UV. The excess is conservatively as large as a factor of 2 using the general z ∼ 4–5 LBG selections (Smit et al. 2015 ) but was earlier reported to be a factor of 6 (Shim et al. 2011 ) using samples selected based on their emission line properties. One explanation for these high luminosities would be if the selected galaxies predominantly had young stellar ages (given that the Ly α emission was prominent in the spectroscopic sample considered by Shim et al. 2011 ) or if dust extinction preferentially had a larger impact on the observed UV-continuum fluxes than it did on the observed H α fluxes (Marmol-Queralto et al. 2016 ; Smit et al. 2015 ). Neither mechanism appears to provide a fully satisfactory explanation for the high H α fluxes in z ∼ 5 galaxies. Dust extinction falls off rapidly toward lower masses, but the H α EWs in these sources remain essentially unchanged (or possibly increase toward lower mass: see Smit et al. 2015 ). Similarly, young ages for the z ∼ 4–5 galaxy population cannot provide an explanation, because a high ratio of H α to UV continuuum is observed for typical star-forming galaxies at z ∼ 4–5 (Marmol-Queralto et al. 2016 ; Smit et al. 2015 ). 31 31 Shim et al. ( 2011 ) had speculated that young ages might explain the high ratios of H α to UV continuum observed in z ∼ 4–5 galaxies they studied that showed strong Ly α emission. However, it is now clear that such ratios apply both to sources that show Ly α in emission and to those that do not (Smit et al. 2015 ). This essentially forces us to conclude that the observed ratio of H α to UV-continuum luminosity must be intrinsic and that star-forming galaxies indeed have very high H α luminosities relative to their luminosities in the UV continuum, particularly in comparison with conventional stellar population models (i.e., Bruzual Charlot 2003 ). It has been speculated that such could be achieved due to binarity or rapid rotation in massive stars, allowing them to output large amounts of ionizing radiation tens of million of years after an initial burst of star formation (e.g., Yoon et al. 2006 ; Eldridge Stanway 2009 , 2012 ; Levesque et al. 2012 ; de Mink et al. 2013 ; Kewley et al. 2013 ; Leitherer et

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


however, and is, therefore, highly dependent on the host galaxy colour, with bluer galaxies having the highest Type Ia SNe rate per unit mass (e.g. Mannucci et al. 2005 ; Mannucci, Della Valle Panagia 2006 ). Type Ia SNe commonly occur in elliptical galaxies, including those with very little recent star formation (e.g. Oemler Tinsley 1979 ; Cappellaro et al. 1999 ; Mannucci et al. 2005 ; Barkhudaryan et al. 2019 ), however, showing at least some progenitors are from older stellar populations. The radial distribution of Type Ia SNe does not correlate with the UV flux distributions at a statistically significant level (see Fig. 4a : p = 0.01 for both NUV and FUV), in agreement with Anderson et al. ( 2015b ). As UV is a useful tracer of moderate- to high-mass stars and, therefore, also a tracer of moderate emission time-scales (e.g. Hygate et al. 2019 ), the divergence of the UV CDF from the dotted normal line in Fig. 4(a) suggests that Type Ia SNe have progenitor systems from different mass and time-scale ranges. 3.2 Type II SNe The radial distribution of Type II SNe shows strong agreement with both UV fluxes ( p = 0.73 and 0.71 for NUV and FUV, respectively) and differs from the R -band and H α light distributions at, or near, statistically significant levels: p = 0.05 and 0.02, respectively (see Fig. 5a and the Appendix). Type II SNe occur throughout the optical disc and examples can be found near or at (see also Figs 6e and f ). Figure 5. CDFs for (a) Type II SNe, (b) stripped-envelope supernova (SE SNe: Types Ib, Ic, Ib/c, and IIb), and (c) the combined Type II and SE SNe sample. See Fig. 4 for further description. Figure 6. Normalized radial flux profiles shown as separate differently coloured lines, with SN locations indicated with small red circle(s): Type Ia SNe (top row), Type II SNe (middle row), and SE SNe (bottom row). The average radial positions for Type Ia, Type II, and SE SNe are marked on each plot using a black cross, circle, and triangle, respectively, and these show the now well-known centralization of SE SNe compared to Type II SNe. To aid comparison, the mean positions of the other SN types are shown with grey symbols. The lack of SE SNe in the outer regions of the UV apertures is evident in panels k, l, with no SE SNe observed in the outer ∼30 per cent of the UV light distribution, compared to the absence of SE SNe in the outer ∼18 per cent of the H α light distribution (panel j). See Sections 3.3.1 and 4.2 for further discussion. The H α CDF for Type II SNe (see Fig. 5a ) has a central section with a reduced slope; just over 10 per cent of Type II SNe are found in 30 per cent of the flux (between 30 and 60 per cent of the total flux – see also Fig. A1b ). Strong bars are known to cause a notable suppression of massive star formation in early-type spirals (see Hakobyan et al. 2016a and references therein) and this could contribute to this CDF feature. No Type II SNe are found in the outer ∼30 per cent of the FUV

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


of 3°–14°. Figure 10. Top panel: Wind simulation with parameter values set to match P04: f x = 0.1, R in = 60 R g , cm/s, T = 2.5 × 10 4 K, and n 0 = 2.5 × 10 9 cm −3 . We also set τ UV = 0, and σ X = σ T as it is done in P04. Bottom panel: Wind simulation with same parameters as the top panel but using the standard τ UV and τ X of Qwind . 4 CONCLUSIONS AND FUTURE WORK We have presented an updated version of the Qwind code ( Qwind2 ), aimed at modelling the acceleration phase of UV line-driven winds in AGNs. The consistency of our approach with other more sophisticated simulations shows that the non-hydrodynamical treatment is well justified, and that our model has the potential to mimic the results of more expensive hydrodynamical simulations. The main free parameters of the model are the initial density and velocity of each streamline, and the inner disc radius from which the fluid elements are first launched. Nomura et al. ( 2013 ) calibrate the initial wind mass loss using the relation from CAK that links the wind mass loss from O-stars to their gravity and Eddington ratio. However, it is not clear whether this relation holds for accretion discs, where the geometry and the radiation field and sources are quite different (Laor Davis 2014 ). To be able to derive these initial wind conditions from first principles, we require a physical model of the vertical structure of the accretion disc. Furthermore, we need to take into account the nature of the different components of the AGN and their impact on the line-driving mechanism. In that regard, we can use spectral models like Kubota Done ( 2018 ) to link the initial conditions and physical properties of the wind to spectral features. We aim to present in an upcoming paper a consistent physical model of the vertical structure of the disc, considering the full extent of radiative opacities involved, that will allow us to infer the initial conditions of the wind. Another point that needs to be improved is the treatment of the radiation transfer. Qwind and current hydrodynamical simulations compress all of the information about the SED down to two numbers L X and L UV; however, the wavelength-dependent opacity can vary substantially across the whole spectrum. This simplification is likely to underestimate the level of ionization of the wind (Higginbottom et al. 2014 ) and motivates the coupling of Qwind to a detailed treatment of radiation transfer. Higginbottom et al. ( 2013 ) construct a simple disc wind model with a Monte Carlo ionization/radiative transfer code to calculate the UV spectra as a function of viewing angle; however, properties of the wind such as its mass flow rate and the initial radius of the escaping trajectories need to be assumed. We will incorporate a full radiative transfer code like Cloudy or Xstar to compute the line driving and transmitted spectra together. This also opens the possibility of having a metallicity-dependent force multiplier and studying how the wind

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


how the SMBH population evolves over cosmic time, we populate the halo tree according to our recipe. When a halo for the first time reaches a mass M c , with chance p it is marked as occupied by a black hole. The occupation is inherited by the merger tree descendant. As a consequence, in our seeding framework black holes are not only “born” in the high-redshift universe. To show this, the left panel of Figure 5 presents birth rates over cosmic time. Seeding is most frequent at early times ( z > 4). Depending on the model parameters, the median seeding time lies in the second, third, or forth billion years. At z 6, the model curve shapes are almost independent of the input parameters. Regarding the normalization, we note that a 100% seeding above mass M c creates a black hole population at a similar rate as 10% seeding at mass 10% × M c (left panel of Figure 5 ). Figure 5. Left panel: the birth rate of black holes over cosmic time. Curves show different seeding fractions p and mass thresholds M 0 . Center panel: merger rate of halos occupied by black holes. The kink at z ∼ 1 is due to the simulation’s cosmic variance, i.e., a large overdensity merging at that redshift. Right panel: the total number of halos with black holes. We compare with space densities of AGN with luminosities (AGN) and (QSOs) measured by X-ray surveys sensitive to unobscured and obscured accretion (Buchner et al. 2015 ). Comparing the model curves and observations, we see that only a very small fraction (1:10 to 1:10,000) of black holes accrete at these luminosities. As halos containing black holes merge, interactions of multiple SMBHs are possible. The middle panel of Figure 5 shows mergers of halos hosting black holes. The normalization again scales as just described for the birth rate. Changes in the critical mass shift the peak slightly. We explore the possible merging of the black holes themselves in the next section. The right panel of Figure 5 presents the total number of massive black holes over cosmic time. For p = 1, this is just the number of halos above the mass threshold. Overall, we find a present-day SMBH space density of >0.01 Mpc −3 (with models not ruled out in Figure 4 ). In the local universe, the fraction of occupied halos is mass-dependent in the way presented in Figure 3 . The comparison between the number of SMBHs to the observed number of AGN provides the fraction of actively accreting black holes in excess of that luminosity threshold. Modern surveys detect hard X-ray emission even in heavily obscured AGN, and recover the intrinsic accretion luminosity using X-ray spectra (e.g., Buchner et al. 2015 ). In Figure 5 we include the space density of AGN at L (2–10 keV) > 3 × 10 42 erg s −1 and >10 44 erg s −1 , which correspond approximately to accretion rates of 5 × 10 6 and 5 × 10 8 M ⊙ Gyr −1 (Marconi et al. 2004 ), respectively, assuming 10% radiative efficiency. The AGN density inferred from observations is 1–3 orders of magnitude below 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 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 B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O B-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 B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-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-Wavelength 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 O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula 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


from four Gaussian functions in the surface brightness − colour plane. Notes. The MP values quoted in the second column are the mixing proportions for each component of the mixture model. For the mean vectors and covariance matrices, the x variable corresponds to the galaxy colour g − r , while the y variable is the surface brightness μ r . Table C.2. Galaxies in the SDSS DR14 photometric catalogue around compact groups that are potential sources of contamination. We measured the surface brightnesses ( μ r ) and observer-frame colours ( g − r ) of each spectroscopic galaxy and of the potentially contaminating galaxies. The surface brightness of each galaxy was computed using the Petrosian radius provided by the SDSS pipeline. After analysing the surface brightness − colour relation, we used the Mclust package ( Scrucca et al. 2017 ) of R software to perform a density estimation based on finite Gaussian mixture modelling. From its application to our data in the surface brightness − colour plane, we observed that, according to the Bayesian Information Criterion, a proper density representation can be obtained using a mixture of four Gaussian functions for a model with ellipsoidal distribution that allows variable volume, shape, and orientation. The best fitted parameters for the obtained Gaussian mixture modelling are quoted in Table C.1 , while the perspective plot of the resulting surface density is shown in the upper panel of Fig. C.1 . Using this surface density, we defined the isodensity contour that enclosed 95% of the spectroscopic galaxies in the surface brightness − colour plane. This region is represented as the grey. shaded area in the lower panel of Fig. C.1 . We also show the scatter plot for the potential sources of contamination (red dots) Photometric galaxies lying outside the grey region are considered non-contaminating galaxies (empty red dots). This criterion allowed us to discard 104 galaxies. Finally, as described in Sect. 4.2 , after a visual inspection of the remaining 81 objects, we confirm that 13 were actually objects misclassified as galaxies by the SDSS pipeline. Therefore, only 68 galaxies are kept as potential sources of contamination. The SDSS object identification numbers of these 68 galaxies are quoted in Table C.2 . Appendix D: New CG catalogue in the SDSS In this appendix we present the tables of HMCGs identified in the SDSS. In Table D.1 we show the content for the table containing 462 HMCGs, while Table D.2 shows the content for the table that contains the information for the 2070 galaxy members. Table D.1. Compact groups identified in the SDSS DR12 using the modified algorithm. Notes. HMCGid: group ID, N : number of galaxy members, RA: group centre right ascension (J2000), Dec: group centre declination (J2000), Redshift: group CMB redshift, Θ G : angular diameter of the smallest circumscribed circle, μ r : r -band group surface brightness, σ v : radial velocity dispersion, r b : r -band observer-frame

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 B-Wavelength O B-Wavelength O O O O O O O O O O B-Wavelength O O O O O O B-Dataset I-Dataset I-Dataset I-Dataset O O O O O O O O O O O O O O O O B-Wavelength O O O O O B-Wavelength 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-Software I-Software O O O O O O O O O O O B-Software I-Software O B-Citation I-Citation I-Citation I-Citation O O B-Software I-Software O O O O O O O B-Model I-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software I-Software O O O 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-Survey 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 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 B-Wavelength O B-Wavelength I-Wavelength O O O O O O O O O B-Wavelength O O B-Wavelength I-Wavelength O


a new set of young solar-type stars. See etal. ( 2015 ) analysed the magnetic field topologies of 55 stars with masses in the range 0.11.5M and discovered that the toroidal field scales with the inverse Rossby number more steeply than the poloidal field does. The toroidal field fraction shows two different power-law dependences on the poloidal field for stars above and below 0.5M . Additionally, they found that strong toroidal fields are typically axisymmetric. To set highly resolved solar or simulated magnetic vector maps into the context of ZDI-observed cool stars, Vidotto ( 2016 ) presented a magnetic field decomposition method. The method is compatible to the description used in ZDI studies and decomposes the magnetic field into spherical harmonics of different -modes up to a maximum max . The small -modes describe the large-scale field ( 1 dipolar, 2 quadrupolar mode, etc.) and the higher -modes the small-scale field. This small-scale field can be removed from the simulations or solar observations by selecting low -modes to compare their magnetic field topology with the magnetic field topology of observed stars. In this Letter, we compare the global time-dependent non-potential simulations of Gibb etal. ( 2016 ) based on the surface flux transport model, with the sample of observed stars 1 analysed by See etal. ( 2015 ). In particular, we compare their magnetic field topologies, focusing on the poloidal, toroidal, and their axisymmetric components at different spatial scales. 2 SIMULATIONS AND METHODS The simulations of Gibb etal. ( 2016 ) used a magnetic flux transport model for the photospheric evolution, coupled with a non-potential coronal evolution model described by a magnetofrictional technique. The magnetic flux transport model solves the magnetohydrodynamic induction equation to evolve the surface magnetic flux, whilst a flux emergence pattern, e.g. bipolar starspot pairs, are advectively injected, and then sheared by surface DR, poleward meridional flow, and diffusion (Charbonneau 2014 ). The flux emergence pattern is based on Yeates ( 2014 ) who determined flux emergence properties using solar synoptic magnetograms observed by the US National Solar Observatory, Kitt Peak, between 2010 January and 2011 January. Gibb etal. ( 2016 ) then varied the flux ER using a statistical model, and the DR in the range of 1 ER/ER 5 and 1 DR/DR 5. The variation of the parameters leads us to 17 simulations ranging from solar-like stars up to stars with five times solar flux ER and DR. The immense difference in resolution prevents a direct comparison between the highly resolved simulated and the relatively poorly resolved observed stellar magnetic field vector maps. Vidotto ( 2016 ) presented a method to filter out the small-scale field from highly resolved solar magnetic field vector maps to ease the comparison with stellar magnetic field vector maps. The method decomposes the radial, azimuthal, and meridional magnetic field components into

O O O O O B-EntityOfFutureInterest O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-ObservationalTechniques O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O B-ObservationalTechniques O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O B-Observatory I-Observatory I-Observatory I-Observatory B-Location I-Location O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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


in size. The spectra were reduced with NOSTAR 2 using the standard procedure. For the molecular analysis, we also used SEST CO(2-1) data that were kindly provided to us by A. P. Marston in 2008 (see Marston et al. 1999 ), and NANTEN CO(1-0) obtained in 2001 (see Paper I ). 3.2 H <sc>i</sc> and radio continuum data Current radio surveys are of little use to inspect the surroundings of WR16 with enough resolution and sensitivity. In Paper I , the radio continuum data at 4.8 GHz were obtained from the Parkes-MIT-NRAO (PMN) survey. At the location of WR16, the survey contains observations performed with the Parkes 64-m antenna. However, the beam size (∼5 arcmin × 5 arcmin) is comparable to the diameter of the ring nebula (≲8 arcmin), which hampers a detailed study. To render an acceptable resolution, observations must be performed using interferometeric techniques, and only two radio interferometers, the Australia Telescope Compact Array (ATCA) and the Molonglo Observatory Synthesis Telescope (MOST), offer public surveys covering an area compatible with the Galactic longitude of WR16. The Southern Galactic Plane Survey (SGPS; McClure-Griffiths et al. 2005 ), which includes both H i and continuum emission data from the ATCA, is limited to −1° ≤ b ≤ +1°, and WR16 lies more than 1° away south of this band. On the other hand, the radio continuum emission towards WR16 at 843 MHz from the Molonglo Galactic Plane Survey (MGPS-2; Murphy et al. 2007 ) is affected by strong sidelobes introduced by the bright nearby H ii region RCW 46. To obtain the best possible set of maps, we then processed from scratch archival radio observations performed during 2001 and 2002 towards this region with the Australia Telescope Compact Array (ATCA) in the configurations EW 352 and EW 367 under project C961. The region was observed simultaneously in the H i 21-cm line and in radio continuum. The continuum data consist of 32 channels spanning through a bandwidth of 128 MHz centred at 1384 MHz, while the H i line was recorded over 1024 channels covering a 4 MHz bandwidth (equivalent to 0.82 km s −1 ). Pointings were arranged in an hexagonal mosaic with a 23 arcmin grid separation and were observed as snapshots during 60 s over a wide range of hour angles. All observation parameters are summarized in Table 1 . Table 1. Parameters of ATCA observations. Standard data reduction was performed with the miriad software package (Sault, Teuben Wright 1995 ), using PKS B1934−638 for flux and bandpass calibration and PKS B0843−54 for phase calibration. For the H i data, the continuum component was subtracted by fitting a linear baseline through a set of line-free channels in the Fourier domain. All pointings in the mosaic were cleaned together with a joint approach using the miriad task MOSMEM. For the H i data, the solutions converged for all channels. Finally, the clean components were convolved with a 130 arcsec × 130 arcsec and a 100 arcsec × 100 arcsec beam for the line and

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with haloes, and the slight difference is because the two tracer classes do not correspond to exactly the same halo population, since central galaxies are populated in haloes in a random way. Third, for the two cases in which we cross-correlate the dark matter field from the F5 simulation with tracers from the GR simulation (cyan dashed and red dot-dot-dot–dashed), ξ gm decreases towards very small separations ( r ≲ 0.3 h −1 Mpc), and this is because GR tracers usually do not coincide with the highest density peaks in the dark matter field of the F5 simulation so that the highest values of ξ gm appear to be away from the GR tracers themselves. All in all, the test highlights the importance of using carefully constructed mock galaxy catalogues when we compare the predictions of GGL in different models. As an example, the 3D real-space two-point correlation functions and the projected 2D correlation functions in our GR and F5 HOD catalogues agree with each other within 2 per cent–3 per cent in the range of separations considered here, but such agreements are in a statistical, rather than an object-by-object, sense. When cross-correlated with the same (F5) matter field, the ξ gm results by using F5 and GR galaxies are indeed different (cf. blue dotted and cyan dashed curves in Fig. 8 ), in particular at small separations. This indicates that high-resolution simulations enable to accurately resolve the internal structures of haloes and to allow realistic galaxy mocks to be constructed, are necessary in order to make GGL more useful for distinguishing f ( R ) gravity and GR. 3.3 Galaxy bias Finally, we compare the galaxy biases in GR and f ( R ) gravity. We are interested in this comparison this for two reasons. First, in standard ΛCDM, the linear bias factor, defined as is scale-independent on large scales. On the other hand, it is known that f ( R ) gravity, and in general chameleon models, predict a scale-dependent linear growth rate of matter density perturbations, which may result in scale-dependent b lin , because we have tuned the HOD parameters to match ξ gg ( r ) in the two models, while their ξ mm ( r ) can have a scale-dependent difference. We want to check whether, at least for F5, such a scale dependence of b lin is significant enough to make it of interest in observations. Secondly, assuming that the linear bias factor b lin gives a correct quantification of galaxy bias at some given scale r , the galaxy–matter cross-correlation coefficient R gm , defined as is equal to 1. This offers an opportunity to derive the matter correlation function ξ mm from observational determinations of ξ gg and ξ gm . We want to see whether the minimum length-scale R min above which this can be performed without worrying about the non-linear effects in galaxy bias is significantly different in GR and in F5. Fig. 9 shows the results of our tests to answer these questions. The top bunch of curves in each panel (left for GR and right for F5) show the

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of the α-effect and the angular velocity profile, the star with the rotation period of 30 d is slightly above the large-scale dynamo instability threshold. Table 1 lists the integral parameters for the kinematic dynamo models. Our results are in general agreement with the results of the previous paper by Pipin ( 2015 ). The models show a decrease in the dynamo period with an increase in the rotation rate. Fig. 3 shows the time–latitude diagrams for the large-scale toroidal magnetic field evolution at r = 0.9 R in the kinematic models. The models with a period of rotation longer than 10 d show solar-like butterfly diagrams. The star rotating with a period of 10 d shows a double dynamo wave pattern, where the high-frequency high-latitude cycles merge into long cycles at low latitudes. A similar pattern is found for the star rotating with the period of 8 d. For a star with a higher rotation rate, the dynamo wave patterns divide into two: the high-latitude wave drifts to the equator and the low-latitude wave migrates toward the poles. This property becomes very clear for the M5, M2 and M1 models. All these models show a mix of the magnetic parity modes and different systems of the dynamo waves at high and low latitudes. The complicated dynamo wave patterns in these models result in multiple dynamo periods (see Table 1 ). For example, the model M1 shows three different dynamo waves. There are two high-frequency waves migrating toward the poles below 50°. The third wave is a quasi-periodic high-latitude wave migrating toward the equator. We deduce the dynamo periods using the time–latitude diagrams of the toroidal magnetic field in the subsurface layer r = 0.9 R , the variations of the toroidal magnetic field flux F S , and the Poynting flux luminosity L P . To identify the dynamo periods, we employ the standard wavelet package of the scipy distribution (see www.scipy.org ). All these parameters indicate the unique dynamo period for the models in the range of rotational periods from 15 to 30 d. The models for a rotational period of less than 15 d start to show long-term variations. The different dynamo parameters show the different sets of periodic variations. For the long period, we choose the minimal value that is found both in F S and L P and in the time–latitude diagrams. Also, the models for fast rotating stars, M1, M2 and M5, show the short-term periodicity of the L P parameter. Its period is about two times less than the main dynamo period. Figure 3. The time–latitude diagrams for the near-surface ( r = 0.9 R ) toroidal magnetic fields for the kinematic dynamo models. Table 1. The integral parameters of the kinematic dynamo models. The numbers in the model names correspond to the period of rotation in days, which is rounded to the nearest integer. P rot is the period of stellar rotation. Ro* is the estimation of the Rossby number. F T is the magnitude of the total magnetic flux in the convection zone. F S is the magnitude of the

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and lower values of , respectively. 3.4. Constraining H0 with BAO plus Deuterium Abundance in ΛCDM Obtaining a constraint on H 0 from the BAO requires adding information to break the degeneracy. One way to do this is to add a constraint on the baryon density (e.g., Addison et al. 2013 ; Aubourg et al. 2015 ; Wang et al. 2017 ). We assume that the photon energy density, or, equivalently, the CMB mean temperature, is also known. The CMB temperature was measured precisely by COBE /FIRAS (Fixsen et al. 1996 ; Fixsen 2009 ) and we view this result as independent of the CMB anisotropy measurements performed by more recent experiments. Note that while the H 0 in the H ( z ) in the denominator of (1) cancels in the product, some residual H 0 dependence still exists because the decoupling redshift and the sound speed depend on the physical matter and radiation densities, and , respectively, while the expansion rate H ( z ) depends on the fractional densities and . In the BAO fit with an external baryon density prior, performs double duty. It not only goes into determining the late-time expansion ( D M and H at the BAO survey redshifts) but also controls the expansion history in the early universe prior to baryons decoupling from photons, since the photon and neutrino properties (with ) are held fixed. As well as providing an indirect H 0 constraint, the BAO+ fit also serves as something of a self-consistency test of early and late-time expansion. The most precise constraints on independent of the CMB power spectrum come from estimates of the primordial deuterium abundance. In standard Big Bang nucleosynthesis (BBN), the abundance of light nuclei is determined by a single parameter, the baryon-to-photon ratio η (see recent review by Cyburt et al. 2016 , and references therein). Taking the photon number density as fixed from the CMB temperature, a measurement of the primordial deuterium abundance in conjunction with knowledge of BBN physics provides a constraint on . Precise estimates of the primordial deuterium abundance have been made in recent years using extremely metal-poor damped Ly α (DLA) systems along sight lines to high-redshift quasars (e.g., Pettini Cooke 2012 ; Cooke et al. 2014 , 2016 ; Riemer-Sørensen et al. 2017 ). Cooke et al. ( 2016 ; hereafter C16 ) reportby combining six such systems. The reaction rate plays a key role in the conversion from D/H to . Using the theoretical calculation for this rate from Marcucci et al. ( 2016 ), C16 findwhich is lower than the Planck value (assuming a standard model throughout). Using instead an empirically derived rate, C16 findwhich has a larger uncertainty but is in better agreement with CMB-derived values. We performed fits to the galaxy-plus-Ly α BAO data with the addition of each of the Gaussian priors on in ( 6 ) and ( 7 ) in turn. We show parameter constraints in Table 3 , including the WMAP 9-year and Planck 2016 CMB anisotropy constraints for comparison. Table 3 Constraints

O O O O O O O O B-Tag O B-Model I-Model I-Model I-Model O B-Model O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest 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 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 B-Wavelength O O O O O O B-Wavelength O O O O O B-Telescope B-Instrument B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation O O O O O O O O O O B-Wavelength O O O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Survey I-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 O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest 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 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 B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength B-Wavelength 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 O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation O O B-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation B-Citation O O O O O B-Telescope 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 B-Wavelength O O O O O O B-Wavelength I-Wavelength B-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 B-Dataset I-Dataset O B-Dataset I-Dataset B-Wavelength O O O O O O O


by scaling relations between the H i content and other intrinsic properties of galaxies. These H i scaling relations can be useful in identifying galaxies that have either more H i than expected or less H i than expected, as galaxies like these may have been affected by recent processes including the removal or accretion of gas. One way to characterize the H i gas content of galaxies is with H i deficiency. H i deficiency is the logarithmic difference between the observed H i mass and the expected H i mass: where M H i exp is the expected H i mass calculated from scaling relations, and M H i obs is the measured H i mass taken from observations (Haynes Giovanelli 1984 ). Generally, a galaxy is considered to have a normal H i gas content if its H i deficiency is between −0.3 and 0.3 (Dénes, Kilborn Koribalski 2014 ), with an H i excess if −0.3 and H i deficiency if >0.3. Studies use H i -selected samples combined with SDSS optical properties to derive scaling relations. With the GASS survey, Catinella et al. ( 2012 ) found that a good predictor of the H i content is the linear combination of stellar surface density and NUV− r colour. We examine the H i deficiency of our sample adapting results using the H i to stellar mass fraction function shown in fig. 8 from Catinella et al. ( 2012 ): with a = −0.285, b = −0.366, and c = 2.872. This function is the relation between H i mass fraction and a linear combination of stellar mass surface density and NUV − r colour with the relation obtained using the subset galaxies with NUV − r ≤ 4.5 mag. The stellar mass surface density is calculated from the formula where R 50 z is the radius containing 50 per cent of the Petrosian flux in z- band from SDSS DR7, and NUV − r is the GALEX (Martin et al. 2005 ) NUV magnitude minus the SDSS DR7 r -band magnitude. Figure 8. H i deficiency using scaling relations from Catinella et al. ( 2012 ). A solid grey line is drawn for deficiency = 0 and a dotted grey line for deficiency = +0.3 and −0.3. Fig. 8(a) shows the H i deficiency in relation to the log of stellar mass. Fig. 8(b) shows the H i deficiency in relation to the distance from filamentary structure based on the DisPeSE topological algorithm. Open symbols are small galaxies with uncertain stellar masses. The results for H i deficiency are shown in Fig. 8 . A solid grey line is drawn for deficiency = 0 and a dotted grey line for deficiency = +0.3 and −0.3. Figs 8(a) and (b) show the H i deficiency in relation to stellar mass and distance to filament, with no obvious trends. In Catinella et al. ( 2012 ), the results are for a sample of galaxies with stellar mass greater than 10 10 M ⊙ . Since only three galaxies (1204837, 1437568, 969633) are above stellar mass 10 10 M ⊙ , this method is not well calibrated for our lower mass sample. With that said, none of the galaxies are H i deficient and half of the sample has H i excess. This is of course not surprising for a small H i -selected sample. 4.3 H <sc>i</sc>

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Survey B-Wavelength O O O O O O O B-Survey I-Survey 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 B-Wavelength 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-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Formula I-Formula I-Formula B-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O B-Wavelength O B-Wavelength 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 B-Wavelength O O O O O O O O O O O O B-Wavelength I-Wavelength O B-Dataset I-Dataset O B-Wavelength O B-Wavelength O O B-Telescope B-Citation I-Citation I-Citation I-Citation O B-Wavelength O O O B-Dataset I-Dataset B-Wavelength I-Wavelength 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 B-Software I-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 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 B-CelestialObject B-CelestialObject 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 O O O O O O O O O O O O O B-Tag


versions of these methods as described in Patiño-Álvarez et al. ( 2013 ). To establish a significance to the correlation coefficients we performed Monte carlo simulations following Emmanoulopoulos, McHardy Papadakis ( 2013 ) and Patiño-Álvarez et al. ( 2018 ). The confidence intervals (at 90 per cent) in the delay were obtained as in Patiño-Álvarez et al. ( 2018 ). To determine the truthfulness of the delays obtained with the cross-correlation analysis, we performed an alias check via Fourier analysis (Press et al. 2007 ). 9 The resulting delays obtained from the cross-correlation analysis are summarized in Table 3 . Table 3. Delays obtained via cross-correlation analysis, for the entire time-range of study. Delays are in units of days. All correlations are at a confidence level , unless otherwise stated. The uncertainty is at a 90% confidence level. a All delays observed were found to be alias. b Inconclusive analysis. It is important to mention that there are non-conclusive results for some of the light curve pairs, where lag periods from 200 to 1000 d, appear as significant correlations (see Fig. 9 ). We explain this effect by taking into account the low-amplitude variability over large periods of the light curves. When the cross-correlation coefficient is calculated for every lag, light curves in quiescent states will be very similar to each other, regardless of the time axis-shift. The same issue also contaminates cross-correlation functions for correlated signals. Figure 9. Example of inconclusive cross-correlation result. The noisy lines represent the significance of correlation at 90, 95, and 99 per cent, below and above correlation coefficient zero. The smooth line is the interpolated cross-correlation function (ICCF). 5.1 <italic>V</italic> band and 15 GHz anticorrelation In Section 5 , we reported finding a weak anticorrelation between the V band and 15 GHz. We decided to investigate this further by analysing the normalized light curves, then we noticed that during the time period JD 245 = 4860–5760, the behaviour of the V band and the 15 GHz light curves is contrary (see Fig. 10 ). However, this anticorrelation does not hold for the entirety of the time-frame studied in this work; which is the likely reason why it only appeared as a weak anticorrelation on the analysis mentioned above. Figure 10. Normalized light curves for the V band and the 15 GHz emission in the period JD 245 = 4860–5760. Moreover, we decided to test it with a cross-correlation analysis, restricted to the period mentioned above. The analysis results in an anticorrelation at a delay of 39.6 ± 3.2 d, with the V band leading the 15 GHz emission (see Fig. 11 ). In blazars, the V band is usually dominated by synchrotron emission from the jet; however, 3C 273 has a history of being dominated by the accretion disc in the optical bands (e.g. Shields 1978 ; Ghisellini et al. 2010 ). This fact that the optical emission is mostly dominated by thermal emission from

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


the cooling time depends on the gas density, it is expected to vary according to location. This is clearly visible in the top panel of Fig. 16 , where the spherically averaged temperature profiles of galaxies only models are plotted. Here, the temperature in the inner part of the H ii region is lower than the gas temperature immediately behind the I-front, 11 and the spread is large (see the difference in the spread in the temperaturedensity relation inside H ii regions shown in Figs 13 and 17 ). Figure 16. Spherically averaged temperature profiles of galaxies only models (top panel) GAL_0.5R (blue dotted line), GAL_R (black solid), GAL_2R (red dashed), and galaxiesQSO models (bottom panel) GAL_0.5RQSO_UVXsec (blue dotted), GAL_RQSO_UVXsec (black solid), GAL_2RQSO_UVXsec (red dashed). The shaded regions indicate the 1 scatter around the mean. Figure 17. Temperaturedensity diagram for galaxies only models GAL_0.5R, GAL_R, GAL_2R and galaxiesQSO models GAL_0.5RQSO_UVXsec, GAL_RQSO_UVXsec, GAL_2RQSO_UVXsec. The red (blue) colour indicates the H ii (H i ) regions defined as cells with (0.5). The contours are overlaid as a guide. To emphasize the temperaturedensity relation both in H ii and H i regions, two different y -axis scales are used. On the other hand, the thermal structure in the neutral regions is nearly identical in all galaxies only models, as, similarly to Section 4.1 , hydrodynamical processes, and not UV photons, are responsible for controlling the temperature in the neutral gas. 4.3.2 Heating by galaxies and a QSO Fig. 15 shows that as the QSO increases the extent of the fully ionized region, the radius at which the gas is heated to 10 4 K is larger than in the corresponding galaxies only models. However, both the average profiles (Fig. 16 ) and the overall temperaturedensity relations (Fig. 17 ) are similar to those of the corresponding galaxies only models. This indicates that a QSO plays a small role in controlling the thermal state in the inner parts of the H ii region, where the pre-existing galaxies have ionized the IGM before the QSO activity. On the other hand, the top panels in Fig. 17 show that galaxiesQSO models reach temperatures that are typically higher than those in the corresponding galaxies only models. The differences become less evident with increasing ionizing emissivity from the galaxies (from left to right in the three rightmost panels). The reason for this is that when both the H ii and He iii I-fronts from the QSO are larger than the pre-existing H ii region due to galaxies, the gas experiences the highest heating. However, when only the H ii I-front from the QSO is larger than the pre-existing H ii region (but the QSO He iii I-front is still inside it), the portion of the gas newly heated up by H i photoionization of a QSO has not yet undergone QSO-driven He ii photoionization. This lack of He ii photoionization by the QSO results in a slightly lower temperature. This non-linear heating process, which

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


being only due to reflection by dust in the coma. The fitted one-dimensional dust spectrum was used to determine the scaling factor for the dust profile by measuring the relative strength of the continuum in the centre of the emission band compared to that in the centre of the dust region. The scaled dust profile was subtracted from the emission profile to leave the contribution due to the gas only. The measured spatial fluxes were converted to column densities using the fluorescence efficiencies for each species. The fluorescence efficiencies for the OH (0-0), NH (0-0) and CN (0-0) features are strongly dependent on the heliocentric velocity of the comet due to the Swings effect (Swings 1941 ), and were determined using D. Schleicher’s online tool 2 . The C 3 (λ4050) and the C 2 (Δ = 0) fluorescence efficiencies were taken from AH95 and C12 , while the NH 2 (0,3,0) fluorescence efficiency was that used by Fink ( 2009 ). The fluorescence efficiencies were scaled as . The Haser model (Haser 1957 ) describes the photodissociation of parent molecules into daughter molecules in a spherically symmetric coma. The column density of the daughter molecules N d as a function of distance from the nucleus ρ for a molecular production rate Q is given by the equation where K 0 ( y ) is a modified Bessel function of the second kind. The quantities l p and l d are the scalelengths of the parent and daughter molecules, respectively, and is the radial outflow velocity which is calculated using the equation from Cochran Schleicher ( 1993 ): A model Haser profile was fit to the measured column density profile of each observed species to determine its production rate. The nucleus was placed at the centre of the slit for each exposure, and therefore the extracted profiles have components at ρ values either side of the nucleus. As the Haser model assumes spherical symmetry in the coma, the profiles in the two directions were averaged and the production rates were determined using these average profiles. A series of model profiles for different values of the production rate were generated, and the model profile where the χ 2 statistic was minimized gave the best-fitting production rate. The additional uncertainty in Q was determined by finding the difference between the best-fitting production rate and the model production rate where (Hughes Hase 2010 ). We measured the molecular production rates using scalelengths from two sources, which are given in Table 4 . The production rates in Table 5 were determined using the scalelengths from AH95 , while those in Table 6 used the scalelengths from C12 . We chose to use the same set of fixed scalelengths as previous authors to allow direct comparison of our abundance ratio measurements with the ratios determined in those studies. The parent and daughter scalelengths are usually scaled as , but Langland-Shula Smith ( 2011 ) note that the theoretical scalelength variation should instead be . Power-law fitting can be carried

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Wavelength I-Wavelength O B-Wavelength I-Wavelength O O O O O O O O O O O O O O B-Model I-Model B-Citation I-Citation O O O O O B-Person I-Person O O O O O O O B-Wavelength O O O O B-Formula I-Formula I-Formula O O O O O B-Citation O B-Citation O O O B-Wavelength I-Wavelength I-Wavelength O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Model I-Model B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation 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 B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Citation 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 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


dependent on the grain shape or composition. Indices fall between −2.4 and −2.74, which gives slightly less steep fits than in the analysis in LH07 , where a spectral index −3 provides the best fit for a severely more limited set of shapes. Therefore, while RAT scaling predictions can be done with a simple power-law estimate, our study suggests that a power-law index −2.6 should be used for a general fit. Figure 20. Q Γ (Θ = 0) as a function of λ / a eff for the silicate base shapes. The shaded area around the mean indicates the range of all samples. The power-law fit is done for data between λ / a eff = 2 and 20. Figure 21. Same as Figure 20 , but for coated silicates. Figure 22. Same as Figure 20 , but for carbonaceous shapes. Due to the limited wavelength range available, Figures 20 – 22 cannot show whether or not the RAT efficiency is best fitted by a constant below λ / a eff = 1.8, an estimate of the threshold between constant and power-law fits that originates from LH07 . The region λ ∼ a eff is not possible to account for properly using the limited wavelength range. Due to this, the full RAT fit provided in LH07 cannot be confirmed for the ensembles. Finally, we consider the precession-inducing RAT component Q e 3 . From LH07 , we know how to estimate Q e 3 for the AMO spheroid, here chosen to have an aspect ratio a : b = 2:3, aswhere e is the spheroid eccentricity, a is its minor axis, and K is a fitting factor. For rough estimates of the maximum value , which are found at cos Θ = ±2 −1/2 , LH07 showed that K is near unity. We study the wavelength-dependent normalized values of for the silicate oblate and prolate ensembles. Using Equations ( 3 ) and ( 4 ) with K ≈ 1, we also study the deviation from the estimated functional form of AMO. The results, presented in Figure 23 , reveal that there exists a critical value of λ / a eff ≈ 5, where the maximal value and shape deviation against AMO of Q e 3 are clearly anticorrelated, such that the maximum value of Q e 3 is noticeably less and the shape is considerably different than what AMO predicts. Such a clear discrepancy against AMO was identified to be a property of only the Q e 3 component. Above λ / a eff ≈ 5, quickly peaks, after which it gradually decreases. Also, below the critical value, another strong decrease is visible, although it is limited by the wavelength range used. That behavior, which is almost identical for the two different shape ensembles, can possibly be identified as being due to changing scattering regimes. To fully understand the universality of the critical grain size, which implies that in some situations certain grain size groups may exhibit a different types of alignment, further studies are needed. Figure 23. Top panels: mean values of the component, normalized with the corresponding AMO component, as a function of λ / a eff , for the silicate oblate and prolate ensembles. The bars represent 1 standard deviation around the mean. Below: mean deviation from AMO

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