mixes with nearby gas, producing a sharp peak in the PDF at the high metallicity end. More efficient diffusion tends to push this peak to lower metallicities. This trend is produced by enriched gas losing its metals more rapidly. However, this also depends on the recent star formation history, and is not a monotonic trend with diffusion strength. This peak is not present in Nodiff. Instead, there is a high-metallicity tail, consisting of the small number of particles that have been enriched by very many feedback events. The difference between the metal distributions has no clear impact on the distribution of cooling times, presumably because the number of particles in the high-metallicity tail is small. In general, the gas properties of Shear do not seem to stand out as particularly distinct among the other simulations. The differences between the simulations thus appears to depend only on the strength of diffusion, even when the diffusion coefficient is calculated in different ways. This suggests that diffusion can be accurately calibrated by adjusting the pre-factor, and that it is not necessary to introduce a more complex method for calculating the diffusion coefficient. 3.3. Spatial Distribution of Metals The spatial distribution of metals at t = 750 Myr is plotted in the second column of Figures 3 and 4 . This distribution is strongly affected by the choice of diffusion algorithm. Without any diffusion, the metal distribution is very clumpy as there is no mechanism to smooth out the metals. Highly metal-enriched particles can therefore move over large distances without losing their metals. Metal-rich gas in the Nodiff model at clearly has a large vertical extent, while Disp is more localized (Figure 4 ). We have plotted the mean metallicity, and [O/Fe], in vertical and radial bins in Figure 7 at intervals of 250 Myr to examine more clearly the difference between the diffusion algorithms. The radial metallicity bins are annuli that extend 2 kpc above and below the disk plane, and the vertical metallicity bins are pillboxes of radius 5 kpc. While many observed dwarf galaxies appear to have flat or near-flat metallicity gradients (Crnojević et al. 2010 ; Koleva et al. 2011 ), all of our simulations show significant slopes. This is likely a result of our feedback being weak, resulting in gas (and hence star formation) that is centrally concentrated. Stronger feedback at higher resolution can produce more distributed star formation ( K14 ). This dependence on feedback means that the simulated spatial distributions of metals can not be directly compared with observations, but only compared with other models with similar feedback strength. Figure 7. Metallicity distributions at t = 250, 500, 750, and 1000 Myr (from top to bottom). First column: metallicity as a function of height above the disk plane. Second column: Metallicity as a function of radius. Third column: [O/Fe] as a function of height above the disk plane. Fourth column: [O/Fe]


errors for are 3%–7%. Because there is no physical motivation to assume that the prior distribution of the pressures is uniform, we also tested the inversion with priors that are uniform in the logarithm of pressure. The results of this test, with identical data as above and the Gaussian regularizer included, are shown in the bottom panel of Figure 2 . The top panel of Figure 2 shows that assuming a uniform prior introduces a preference toward higher pressures. On the other hand, assuming that the prior is uniform in the logarithm of pressures biases the results toward lower pressures. The inversion is particularly sensitive to this bias in the low-mass/low-density region of the EoS, where we lack data. Our Gaussian regularizer helps reduce this bias, as shown in the middle and bottom panels of Figure 2 , in which the results are similar for the two types of priors when the regularizer is also included. In the absence of a regularizer, the freedom introduced by using five polytropes in the parameterization combined with this sensitivity to prior distributions could lead to significantly skewed results, or even the false inference of a phase transition with a perceived high statistical confidence. It is therefore important to use a Gaussian regularizer on the second derivative, with a characteristic scale , to avoid this sensitivity to over-fitting. In Figure 4 , we explore potential correlations between the inferred parameters for this test. Specifically, we show the correlations for the inversion using uniform priors and the Gaussian regularizer (i.e., the middle panel of Figure 2 ). There are slight anti-correlations between adjacent inferred pressures, due to fact that, even with the addition of the regularizer, we are still over-parameterizing our model while trying to fit the effectively single-polytrope EoS SLy. Overall, however, the pressures that are not adjacent are uncorrelated with one another. Özel Psaltis ( 2009 ) showed that, for a three-polytrope parameterization, parameterizing with the pressures as free parameters instead of the polytropic indices reduced the correlations between the inferred values. Figure 4 shows that the low levels of correlations are maintained here. Figure 4. Correlation plots for the inferred pressures at our five fiducial densities. The inversion was performed using uniform priors and a Gaussian regularizer (). The red diamonds mark the pressures of the true EoS (SLy) that we are trying to infer. There are slight anti-correlations between adjacent pressures (e.g., P 1 and P 2 ), but the non-adjacent pressures are relatively uncorrelated. The triangular shape of the P 4 vs. P 5 correlation is due to the causality requirement, which is shown as the red line. In order to ensure that the Bayesian inference works well for other underlying EoS and that the regularizer does not adversely limit our ability to detect potential phase transitions, we tested the method on a number of different EoS as well. As an


(top), central detectors of sparse observations (middle), and from mapping observations (bottom) are shown in blue, orange, and violet, respectively. Lines found by the FF employ round markers while those found by the low SNR search routine through line identification use triangular markers (see Section 3.1 ). The |SNR| cutoff in each case is shown by the dotted black line. The axes in each case have been set to the same scale to allow comparison. 5 CONCLUSIONS The extensions of the FF to include spectral observations from off-axis detectors in sparsely sampled single-pointing observations is detailed. An additional 30 720 spectral features with a |SNR| greater than 6.5 are aggregated into the SAFECAT by the inclusion of the analysis and extraction of features from the off-axis detector spectra. We developed a set of postcards to highlight and summarize results from these off-axis detectors in each observation that are of a similar format to the mapping postcards described by Paper I and are available from the ESA Herschel legacy area (see footnote 6). We have also extended the automated SPIRE FF routine ( Paper I ) to identify the atomic or molecular transition that corresponds to the features extracted from HR observations of the SPIRE FTS. This identification of atomic/molecular transitions is done by matching the spectral features to a template of 307 atomic fine structure and molecular features that are commonly found in SPIRE FTS observations. Line identification is reliant on the radial velocity estimates included in the catalogue by Paper II and is able to successfully match 77.3 per cent, 93.1 per cent, and 95.2 per cent of spectral features found by the FF from central detectors of sparse single-pointing observations, off-axis detectors, and mapping observations, respectively, to their atomic/molecular transitions. We find this line identification to be particularly effective at identifying the CO rotational ladder from J = 4–3 to J = 13–12 and the [N ii ] 3 P 1 – 3 P 0 transition in SPIRE FTS observations. The identification of all 15 atomic/molecular species in SPIRE FTS spectra from mapping, off-axis detectors in sparse observations, and central detectors in sparse observations is shown in Fig. 14 . Note that isotopologues and ionization states have all been grouped together for each species. Figure 14. The line identification of all 15 atomic/molecular species contained in the template for mapping and sparse SPIRE observations. The information provided by the line identification is also used to uncover low SNR features that fall below the |SNR| ≥ 5 cutoff that exists nominally in the FF ( Paper I ). This low SNR search routine adds an additional 1516 for the central detectors of sparsely sampled single-pointing observations and 1234 for the off-axis detectors. An additional 370 lines are added by this routine from mapping observations of the SPIRE FTS. APPENDIX: LINE MATCHING TEMPLATE A note on the quantum numbers


size equal to the sum of the number of HDs and CRs. This results in 118 HDs, 47 CRs, and 165 NDs (see Table 1 ). We show the distribution of the three samples in the plane in the right-hand panel of Fig. 1 , which is a zoom-in figure with galaxies with and . As can be seen, all three sub-populations have roughly similar sSFR, with CRs being slightly lower than the other two. In addition, we have also checked and confirmed that the total halo masses of the three galaxy samples are roughly within the same range. Table 1. Number of galaxies in different samples. Columns (1): All z = 0 central galaxies from the IllustrisTNG simulation; also the parent sample of Columns (2)−(5). Column (2): late-type galaxies; Column (3): selected hot disc galaxies (HDs); Column (4): selected counter-rotating disc galaxies (CRs); and Col.(5): control-sample normal disc galaxies (NDs). See Section 2.2 for definition and selection criteria. In Fig. 2 , we show the distributions of the three orbital fractions ( f cold , f hot , and f ccd ) for general late-type galaxies and the three selected samples (HDs, CRs, and NDs). As can be seen, the three samples exhibit distinctive differences in cold, hot, and counter-rotating cold orbital fractions: NDs, which host the highest fractions in f cold , also possess the lowest fractions in f hot and f ccd , while HDs indeed have lower fractions in f cold and f ccd , and CRs have the lowest fractions in f cold and moderate fractions in f hot . This also demonstrates that the three types of galaxies are intrinsically different from each other. Figure 2. Distributions of f cold , f hot , and f ccd (from left to right, see Section 2.1 for definitions) for late-type galaxies (black), NDs (blue), HDs (red), and CRs (green). Black dashed lines represent f cold = 0.4, f hot = 0.31, and f ccd = 0.2, which are used to classify NDs, HDs, and CRs, respectively. 3 WHAT DO THEY LOOK LIKE? 3.1 Morphology of stars and gas To discuss the visually apparent differences in morphologies between HDs, CRs, and NDs, we first present in Fig. 3 the stellar and H i mass density maps from both edge-on and face-on views for typical HDs (the first 2 columns), CRs (the middle 2 columns), and NDs (the latter 2 columns). As can be seen, the two NDs have the flattest stellar and gaseous disc morphologies with their spin axes well-aligned. In comparison, however, both CRs have less flat stellar and gaseous discs, the spins of which exhibit very large misalignment (∼180°); the two HDs possess much thicker stellar discs and display the least established gaseous discs among all three types. Interestingly, very often the optical images of NDs and CRs show clear extended spiral patterns which are absent in the HD samples. Figure 3. Examples of two HDs (ID: 582800, 512569), two CRs (ID: 486917, 532146), and two NDs (ID: 462986, 606707) from left to right. For each example, we show from the top to the bottom rows: (1) the face-on view of the stellar mass density map,


s −1 ). Figure 2 shows the integrated intensity maps of C 18 O ( J = 1–0) (cyan contours) and 13 CO ( J = 1–0) (color) observed with the NRO 45 m telescope for the entire region of HCL2 (Sunada Kitamura 1999 ). A prominent straight structure is seen in the northern part of HCL2 in the C 18 O map, which also has been pointed out by Narayanan et al. ( 2008 ) and Goldsmith et al. ( 2010 ). Interestingly, the velocity of the blueshifted component detected in the OH 18 cm transition ( km s −1 ) corresponds to that of C 18 O, exhibiting the straight structure, whereas the velocity of the redshifted component seen in OH ( 6–10 km s −1 ) corresponds to that of the southwestern extended gas in the 13 CO map. These two structures are interfacing with each other, suggesting a compressive motion as the origin of the straight structure (Figure 20 ). Such a compressive motion is consistent with the decreasing velocity from southwest to northeast across the straight structure observed in 13 CO and C 18 O. In addition, the existence of an [H i ] cloud in the northeast of TMC-1FN is suggested by the archival data of the Galactic Arecibo L-band Feed Array H i (GALFA-H i ) Survey maps (Peek et al. 2011 ). Furthermore, the 6–10 km s −1 component traces a diffuse warm gas, whereas the 5.5 km s −1 component traces a cold and dense core illuminated by the FIR radiation from dust grains, according to our statistical equilibrium calculation. It is likely that the 5.5 km s −1 component traces cold cores surrounded by the warm envelope gas in HCL2. Figure 20. Schematic illustration of the cross section of TMC-1FN along the line of sight. The cold (∼20 K) and dense core (5 km s −1 ) is formed by compressive motion of the extended warm gas (6–10 km s −1 ). We observe the source from the right-hand side. The 6.5 and 8.2 km s −1 components show the 1612 MHz line absorption, in spite of the FIR pumping effect seen in the 5.5 km s −1 component. This can be explained by the proposed picture of TMC-1FN (Figure 20 ). A warm envelope gas traced by the 6.5 and 8.2 km s −1 components is likely to be illuminated by fainter FIR radiation than the gas traced by the 5.5 km s −1 component. The OH column density for the 6.5 and 8.2 km s −1 components is also lower. According to the results in Appendix C , the FIR intensity at 160 μ m is estimated to be ∼400 and 100 MJy sr −1 at positions 0.5 and 1.0 pc distant from the center of the TMC-1FN filament, respectively. The OH column densities are determined to be 3.6 × 10 14 cm −2 and 1.4 × 10 14 cm −2 for the 6.5 and 8.2 km s −1 components, respectively (Table 3 ). As described in Section 4.1.7 , our calculation shows that the FIR pumping effect is negligible for an OH column density lower than 10 15 cm −2 and I 160 lower than 100 MJy sr −1 . On the other hand, the 1612 MHz line indeed appears in absorption for I 160 lower than 4 × 10 3 MJy sr −1 , if the OH column density is 3 × 10 14 cm −2 (Figure 15 (d)). Hence, even though there might be


represent the 1.3-mm (G09-83808, NGP-190387) and 3-mm (SGP-261206) continuum emission, at 5, 6, 7, 8, 9 × σ. Near-IR emission is seen clearly, coincident or near-coincident with the 1.3- or 3-mm continuum emission. At the depth of the VIKING observations (limiting magnitude, K AB ≃ 21.2), we do not expect to detect dust-obscured distant galaxies. The sources coincident with G09-83808 and SGP-261206 show, therefore, that these two DSFGs are amplified gravitationally by the foreground galaxies seen in the near-IR images. The galaxy in the foreground of SGP-83808 has z spec = 0.778, obtained using X-shooter on the VLT (Fig. 5 ), and is magnified by 8.2 ± 0.3, a factor determined using high-resolution ALMA continuum imaging (see Oteo et al., in preparation-a). The three galaxies revealed by the deeper Gemini imaging of NGP-190387 are considerably fainter, with K AB = 21.0, 22.3, 21.4, yet they are not coincident with the z = 4.42 DSFG and likely constitute a foreground lensing group. Towards G09-81106 we have detected two emission lines, CO(4–3) and CO(5–4), at 83.36 and 104.19 GHz (Fig. 3 ), both at z = 4.531. There is no suggestion of gravitational lensing for G09-81106, either via the presence of unusually bright near-IR galaxies in the field, or via its submm morphology as seen in high-resolution ALMA continuum imaging (Oteo et al., in preparation-a). Towards G09-83808 we have detected two faint emission lines, at 82.02 and 98.39 GHz (Fig. 3 ), corresponding to CO(5–4) and CO(6–5) at z = 6.026 ± 0.001 and 6.028 ± 0.001, respectively, so an average of 6.027 ± 0.001. These lines were also noted by Zavala et al. ( 2017 ) in a spectrum obtained using the Large Millimeter Telescope. G09-83808 is near-coincident with a foreground galaxy, seen clearly in near-IR imaging from the VIKING survey (see Fig. 4 – Edge et al. 2013 ), indicative of gravitationally lensing. This foreground galaxy has a spectroscopic redshift of 0.778, obtained using X-shooter on the 8-m Very Large Telescope (VLT; see Fig. 5 ). A lens model based on the morphology determined by high-resolution ALMA continuum imaging predicts a gravitational amplification of 8.2 ± 0.3 (Oteo et al., in preparation-a). Figure 5. Top: Spectrum of the lensing galaxy in the foreground of SGP-83808, as seen in the optical arm of VLT/X-shooter after integrating for 4 × 20 min on 2013 March 17. Below: The 1D spectrum, in grey, extracted using a simple box-car summation [090.A-0891(A), PI: Christensen]. To identify the lens redshift we binned these data heavily (see Modigliani et al. 2010 ; Christensen et al. 2012 ; Kausch et al. 2014 ), as illustrated in black, with the error spectrum shown in green, then fitted the redshift by χ 2 minimization using a 5-Gyr stellar population model (shown in red) from Bruzual Charlot ( 2003 ). We find z spec = 0.778 ± 0.006. Strong absorption features are labelled. The flux units are 10 −17 erg s −1 cm −2 Å −1 . For NGP-284357, we find at least two emission lines, at


to test this connection more rigorously, but the match is poor, being both too blue and too broad (Fig. 11 ) compared to even the earliest spectra of SN1998bw or SN2002ap (Patat et al. 2001 ; Kinugasa et al. 2002 ), or of the spectrum of SN2008D (Modjaz et al. 2009 ) during its shock-cooling phase. 9 As of yet we have no convincing explanation for the origin of this feature, other than that it implies very fast (nearly relativistic) ejecta. Figure 11. Comparison of an early spectrum of AT 2018cow to the early spectrum of SN 2008D (Ib) and two SNe Ic-BL (top row), and of a later-time spectrum to SN 1998S (IIn) and two tidal disruption events (bottom row). The extremely blue, smooth continuum bears little resemblance to SN Ib/c, even after attempting to subtract the blue continuum. (A power-law plus a constant have been subtracted from AT 2018cow; the reference SN spectra have been subtracted by a constant only. The strength of the features in the SNe after subtraction has been suppressed by a factor of 2.) The later-time spectra are dominated by weak emission features of hydrogen and helium; these features are also present in IIn SNe but are much narrower compared to what is seen in AT 2018cow. These features are seen in known TDEs with similarly broad widths, although typically much greater strengths. The identities of the features seen in later spectra (H and He in broad emission) are secure. In spite of this, these later spectra bear no obvious resemblance to any class of known supernova. The strongest similarities are to Type IIn supernovae (which can also remain hot for several weeks after explosion, and are emission-dominated by definition): in the bottom panel of Fig. 11 , we plot AT 2018cow versus an early spectrum of SN 1998S from Fassia et al. ( 2001 ), which shows a similar blue continuum and most of the same H and He transitions. However, the lines in AT 2018cow are not narrow for most of their evolution ( ∼ 6000 km s −1 , versus a few hundred km s −1 for SN 1998S). Thomson scattering within ionized matter could broaden a line enough to wash out the narrow component, but this would not produce the net redshift in the emission component that we observe. The H and He thus must be in the ejecta itself (and seemingly preferentially in receding ejecta given the net redshift). In fact, the best spectroscopic analogues to AT 2018cow are not supernovae at all. Our spectra bear a striking resemblance to tidal disruption events: the high temperatures, presence of helium and hydrogen features in emission, and moderate velocities all match what is observed for TDEs. The spectral features in AT 2018cow are substantially weaker than in the examples of TDEs that we are aware of (bottom panel of Fig. 11 ; comparison spectra are from Holoien et al. 2014 , 2016 ), but the resemblance to a TDE is much stronger than to any supernova. We summarize the key observational features of AT 2018cow in Table 3 . 5 INTERPRETATION 5.1 Supernova models: A


distribution is the same as for the monodispere case. For the broad distribution between 10 −8 and 10 −4 bar, the single-scattering albedo of the Gaussian distribution () is always higher than that of the monodisperse case (), see the right two plots of Fig. 5 . The increase for the initial broadening around 10 −7 bar is wavelength independentand peaks at ( Fig. 5 , bottom right). The second peak in the increase of the albedo from the monodispserse case occurs at about 10 −5 bar, and this time is wavelength dependent with a significantly lower increase of only a factor of 2 for λ = 0.1 μ m, as opposed to increases by a factor greater than 4 for all longer wavelengths. This is because in this region and the fraction of cloud particles in the Rayleigh scattering regime ( Q sca ∝ λ −4 ) varies for each wavelength for a broad size distribution. Although an increase of half an order of magnitude in albedo seems substantial when the total extinction of the atmosphere is calculated, the peak extinction is dominated by regions with high mass fractions of cloud particles ( ρ d ∕ ρ ). The mass fraction of cloud particles peaks around the millibar level in the atmosphere, which does not significantly overlap with regions of high nucleation rates ( Fig. 5 , bottom left) where the local size distribution is broad. The size distribution therefore has little effect on properties such as optical depth ( Fig. 9 ). Wakeford Sing (2015) also found that for a log-normal distribution, the cumulative effect of transmission spectra of clouds is dominated by larger particles in the distribution. An asymmetric distribution, such as the log-normal distribution, has a greater number of large particles than the Gaussian distribution considered here, and may produce greater deviations from the monodisperse case. It has been found recently to have an effect on retrieved cloud particle size ( Benneke et al. 2019a ). We note, however, that none of the size distributions used in retrieval approaches are based on a consistent cloud model, and therefore no conclusion can be drawn about the shape of the particle size distribution from such retrieval approaches. 5 Optical effects of non-spherical particles To determine the effect of non-spherical cloud particles, we return to the T eff = 1800 K, log ( g ) = 3.0 atmosphere with compact monodisperse cloud particles. When a distribution of hollow spheres is used, as described in Sect. 2.5 , the albedo generally decreases compared to the compact monodisperse case ( Fig. 6 , top right). This is due to the high f hol end of the hollow sphere distribution, where the cloud particles have a large surface area (which is not conserved across the distribution of hollow spheres) and thus increase absorption ( Min et al. 2003 ). Furthermore, Fig. 9 shows that for the compact case (red line), the inclusion of non-spherical particles leads to an increase in optical depth in the silicate features between 10− 20 μ m. This result is in good


where m p = (4/3)ρ s 3 is the particles mass orbiting with velocity A is the particle’s cross section, and is the unit vector pointing to the direction of the radiation. The particles are assumed to be spherical with uniform density equal to 1 g cm − 3 . For transparency we give the explicit form of ω H is Haumea’s rotational frequency, n H is the mean motion about the Sun, and i is the obliquity of the dwarf planet to its orbital plane. The gravitational effect of the Sun is not included in this model because it is fifth order of magnitude weaker than that of Haumea at the distance of the ring. However, Haumea’s orbit is assumed to be circular with a period of 284 yr which is included in the time dependence of the RP. Since the obliquity of the dwarf planet is about 14 deg this implies a long-term modulation in z -component of the RP. In other words, the initial position of the Sun in our calculations is the negative x direction and Haumea’s obliquity stays in this direction during the whole integration. The effect of planetary shadowing (which blocks the stellar radiation impinging on the ring) is neglected since the ring is currently not shadowed because it is in the equatorial plane of the planet which is tilted with 13.8° ± 0.5° to the orbital plane (Ortiz et al. 2017 ). Furthermore, even for longer integration, only a small fraction of the ring will be hided during Haumea’s journey around the sun. We use a 4th order Runge–Kutta numerical scheme with a fixed step size that keeps the relative energy error below 10 −8 . Equation ( 5 ) is integrated for different times in order to cover different dynamical regimes. That is, the simulations are performed for T = 10 3 , 2.5 × 10 4 , and 3.5 × 10 5 rotation periods, yielding ca. 1, 10, 1000 yr, respectively. The calculations also have been done for grain sizes, 1, 1.75, 2.5, and 5 m. The dynamical analysis involves two different setup of initial conditions. In the one hand, when studying the fine resonant structure, particles are placed equidistantly along a line ( x -axis) in radial distance 1 r 11. On the other hand, an initial ring is defined, θ ∈ [0; 2] and r ∈ [0; 5], in order to follow the particle dynamics in general. In both cases grains are initially on circular Keplerian orbits in the equatorial plane of Haumea. 3 RING CHARACTERISTICS Our first analysis explores the lifetime of the particles around the dwarf planet. The grain dynamics yields three different end-states for the particles: (i) Escape : When the semimajor axis of a particle becomes larger than 25 r s (≈ 25575 km) it is taken to be ejected. Ejections occur due the close encounters with Haumea when the particles are perturbed to hyperbolic orbits. (ii) Collision : In our model a collision occurs when the particle approaches the dwarf planet closer than its volume-equivalent radius, 816 km (0.74 r s ) (Ortiz et al. 2017 ). (iii) Bounded motion : When a particle, until the end of the integration, neither collides nor escapes


XTE J1752-223 discovered by the Rossi X-ray Timing Explorer ( RXTE ) and Swift satellites on 2009 October 23 (Markwardt et al. 2009b ) suggested that it is a black hole candidate (Markwardt et al. 2009a ; Nakahira et al. 2009 ; Remillard et al. 2009 ; Shaposhnikov et al. 2009 , 2010 ). Three days after the X-ray discovery, a bright optical counterpart was found by the Magellan Baade telescope (Torres et al. 2009b ). Also, a bright near-infrared (NIR) counterpart was identified immediately (Torres et al. 2009a ). Afterwards, a bright radio counterpart was discovered by the Australia Telescope Compact Array (ATCA) with a flux density of at both 5.5 and (Brocksopp et al. 2009 , 2010 ). The radio light curves of XTE J1752-223 at 5.5 and were measured by ATCA, the European VLBI (Very Long Baseline Interferometry) Network (EVN), the Very Long Baseline Array (VLBA), and the Expanded Very Large Array (Brocksopp et al. 2009 ; Yang et al. 2010 ; Miller-Jones et al. 2011 ). Furthermore, the X-ray outbursts during 2009 October and 2010 July were obtained by the Monitor of All-sky Image (MAXI), RXTE , and Swift (Nakahira et al. 2010 ; Shaposhnikov et al. 2010 ; Curran et al. 2011 ). The long baseline observations of XTE J1752-223 are shown in Figure 1 , in which four jet features marked as A, B, C, and D have been reported by Yang et al. ( 2011 ). Component A appeared first, and then components B1 and B2 emerged, which suggests that components farther from the core can be seen earlier than components nearer the core. Moreover, components A and B were observed after the peaks of the radio light curve. It is of interest to understand such a connection between jet features and light curve. Figure 1. The positions of the components A, B, and D of XTE J1752-223 from the VLBA images (Yang et al. 2011 ) for each observing epoch. Note that components B and C in Yang et al. ( 2011 ) are written as B1 and B2 here. NRAO 150, discovered in the radio band by Pauliny-Toth et al. ( 1966 ), is a prominent quasar from the millimeter to radio band at redshift z = 1.52 (Agudo et al. 2006 ). Observations of this source by VLBI from 2001 October to 2004 April and by VLBA from 1997 June to 2002 June have exhibited a moving core–jet structure as shown in the left panel of Figure 2 . The core–jet structure consists of three components, Q1, Q2, and Q3. The evolution of the relative position of these three components is plotted in the right panel of Figure 2 , where Q1, Q2, and Q3 moved in a counterclockwise direction with respect to the core. The projected angular speed of these components can be up to , which is the first superluminal motion found within the innermost region () of the jet in NRAO 150 (Agudo et al. 2007 ). Figure 2. The ridge line structure of the jet of quasar NRAO 150 and the evolution of the position of components Q1, Q2, and Q3 from left to right (Agudo et al. 2007 ). In this paper, the observations of the kinematics of XTE J1752-223 and NRAO 150 are


descent, that is good for learning acceleration, but can lead to missing the loss minimum), and max_depth (greater values correspond to a large complexity of the trees, and can lead to overfitting). Moreover, GB algorithms usually allow the use of a stop criterion, responsible for the termination of the learning when an overfitting occurs (the so-called, early_stopping parameter). It is expressed via the number of constructed trees, after which the quality of the metric no longer increases. Usually this parameter ranges between 10 and 1000 trees, depending on learning_rate . If the early stopping criterion is met, the GB algorithm accepts the number of trees, satisfied to the best score. Paying particular attention to the early_stopping parameter is the best way to avoid as much overfitting as possible. To quantify, how the quality of the classification changes over the iterations, for XGBoost and CatBoost, it is necessary to define a quality metric. Defining this metric allows one to express the changing of the classification quality against the complexity of the GBDT algorithm and can be easily used to control the overfitting. Widely used quality metrics are accuracy, precision, recall, and F1-score; however, these metrics are sensitive to the imbalance in number of training sources among different classes. Therefore, we decided to use Matthews correlation coefficient (MCC, Matthews 1975 ) which is instead insensitive to this imbalance. Finally, a good way to decrease the number of stars and galaxies classified by the algorithm as quasars is to apply a weight to the loss function of these two classes. In fact, this trick, applied to CatBoost, helped us in the paper to improve the final purity of the quasar selection with a minimal decrease in the completeness of the training set. In particular, we weighted the loss function for the STAR and GALAXY samples in the following way: where w i = 1 if source is a QSO and w i = 4 if source is STAR or GALAXY . A.2. Random Forest Another method of ensemble learning with decision trees is based on the use of an RF ( Breiman 2001 ) algorithm. This was the choice adopted in KiDS DR3 by N19. The basic idea of RF is that a set of decision trees can fit a robust classifier by averaging their decisions. From the performance side, the RF constructs a large number of decision trees and then uses the majority vote among them. The main pipeline of the single decision tree includes the following steps: (1) generation of different samples from the training set with the same size, but using random subsets of all the objects. The repetition of some objects among different subsamples is required to make the sample complete (so-called, random subsample with replacement); (2) let the decision tree learn on the “random subsample with replacement”, generated at step (1), but using randomly selected features. The RF therefore consists of many learning processes, each performed on a single decision tree using different


that the near-isothermal density profiles were found to be broadly consistent with MOdified Newtonian Dynamics (MOND). With this greater sample of total- mass profiles that cover a greater stellar mass range, new tests of MOND and the general mass-discrepancy–acceleration relations can be made. In order to make useful comparisons between simulations and observations, it is necessary that exactly the same measurements are made for each. Currently, there is great difficulty in achieving this, since observational measurements are best constrained in the inner regions of galaxies, while the resolution limitations of cosmological simulations mean that measurements for simulated galaxies are best constrained at radii greater than ∼0.5 R e . This means that while care can be taken to make measurements in the same way, the underlying data are fundamentally different. 8 SUMMARY AND CONCLUSIONS We measure total-mass density slopes for 21 fast-rotator ETGs of the SLUGGS survey (Brodie et al. 2014 ), including a greater number of galaxies in the low-mass range than the previous study by Cappellari et al. ( 2015 ). These measurements are made by conducting dynamical mass modelling on 2D kinematics that extend to large radii. We apply the jam mass-modelling technique (Cappellari 2008 ), using two different parametrizations of mass distribution to recover the total-mass density profiles for individual galaxies. We determine that the best fits of the model kinematics to the input kinematics of each galaxy are produced by the model in which the total mass is separated into its stellar and DM components, where the DM distribution is parametrized as a double power law (as given by equation 2 ). We find that the measured total-mass density slope values are robust to slight variations within the applied modelling, whereas the separation of stellar and DM is much more degenerate, and susceptible to such variations in the modelling. In order to be consistent with Cappellari et al. ( 2015 ), we measure γ tot values for each galaxy by fitting a power-law slope to the stellar plus DM profile in the radial range 0.1–4 R e , and find an average total-mass density slope of γ tot = −2.24 ± 0.05 for our sample of 21 galaxies, identifying no discernable trend with stellar mass. We collate measurements of total-mass density slopes from multiple observational studies, for a comprehensive overview of the γ tot behaviour across a broad range of stellar masses, utilizing an array of data-types and measurement techniques. Overwhelmingly, the studies all tend to produce consistent results when including the central regions, as shown in Fig. 6 . This is despite the fact that the data utilized have varying radial extents for individual galaxies – an indication that these slopes do not display much variation with radius. We find that there tends to be very little trend with stellar mass, and that the slight shallowing of total-mass density slopes we see at lower stellar masses may not


for eccentric and radial orbits in the case M g = 3.2 × 10 11 M ⊙ . In the case e = 0.7, it is worth noting that at every passage at pericentre some stars are stripped away from the GC and tend to move on precessing ellipses whose semi-major axes increase with the number of passages at pericentre. On the other hand, when the GC experiences a ‘head-on’ collision with the SMBH, stars are scattered backwards at different velocities, depending on the impact parameter that characterizes each star–SMBH interaction. This peculiar interaction leads to the formation of a wake behind the former GC, with a structure similar to the propagation of a wave on a water plate. Figure 4. Snapshots at different times (labelled) of the cluster on an eccentric orbit in the case M g = 3.2 × 10 11 M ⊙ . The central black dot represents the BH with mass M BH = 5 × 10 8 M ⊙ . The x–y plane is the GC orbital plane. Figure 5. Same as in Fig. 4 , but for a cluster on a radial orbit. Therefore, although it is quite difficult to identify the ‘core’ of the GC, the interaction between an SMBH and an infalling GC produces debris that hides much informations about the initial orbital parameters of the GC. However, due to the fact that it is almost impossible to identify a centre for the cluster in these cases, we limited our analysis to the estimate of the amount of GC mass which remains confined to an inner region of the galaxy, around the SMBH. When considering the simulations with M g ≥ 10 11 M ⊙ , we found that eccentric and radial orbits allow a more efficient transport of mass, towards the Galactic Centre, than circular orbits do. On these orbits, the GC can carry about 20 per cent of its initial mass to the Galactic Centre, while, on circular orbits, such percentage is limited to few per cent. On the other hand, for lower galaxy masses, M g 10 11 M ⊙ , we found that the major contribution to the deposited mass comes from GC on circular orbits. We will deepen the discussion about these results in Section 4 . 4 DISCUSSION In this paper, we have presented several N -body simulations to study the interaction between a single GC and an SMBH in the Galactic Centre. The results shed light on the actual mechanisms of mass accumulation in the central region of a massive galaxy ( M g ≥ 10 11 M ⊙ ). Fig. 6 shows the GC cumulative mass profile as a function of the distance from the SMBH after the orbital decay process, for all the orbits considered and in the case of M g = 10 10 M ⊙ and M g = 3.2 × 10 10 M ⊙ . Considering our lightest galaxy model, we found that circular and radial orbits are both efficient in the transport of mass towards the Galactic Centre. In such cases, the mass left to the Galactic Centre exceeds 80 per cent of the initial mass of the GC. On the other hand, in heavier galaxy models, only GCs moving on initial nearly radial orbits deposit a non-negligible amount of their mass (∼20 per cent of the initial mass of the GC) in the inner 20 pc of the galaxy.


available to be detected by standard methods. These proto-clusters, likely lying at , are assumed to be in an active star-forming phase, but not yet fully virialized. To investigate these earlier evolutionary stages we need different approaches, such as the one presented in this paper. During the past decade, more and more proto-cluster candidates have been detected through different techniques, using X-ray signatures, stellar mass overdensities, Ly emission, and association with radio galaxies (e.g., Brodwin et al. 2005 ; Miley et al. 2006 ; Nesvadba et al. 2006 ; Doherty et al. 2010 ; Papovich et al. 2010 ; Hatch et al. 2011 ; Gobat et al. 2011 ; Stanford et al. 2012 ; Santos et al. 2011 , 2013 , 2014 ; Brodwin et al. 2010 , 2011 , 2013 ). However, only a few detections have been done in random fields (e.g., Steidel et al. 1998 , 2005 ; Toshikawa et al. 2012 ; Rettura et al. 2014 ), and most of these detections are biased towards radio galaxies or quasars ( Pentericci et al. 2000 ; Kurk et al. 2000 , 2004 ; Venemans et al. 2002 , 2004 , 2007 ; Galametz et al. 2010 , 2013 ; Rigby et al. 2013 ; Wylezalek et al. 2013 ; Trainor Steidel 2012 ; Cooke et al. 2014 ; Noirot et al. 2016 ), or obtained over very limited fractions of the sky, e.g., in the COSMOS field, which is 1.65 ( Capak et al. 2011 ; Cucciati et al. 2014 ; Chiang et al. 2014 ) and in the Hubble Space Telescope Ultra-Deep Field ( Beckwith et al. 2006 ; Mei et al. 2015 ) with its area. Since the expected surface density of such massive proto-clusters is fairly small, a few times ( Negrello et al. 2007 , 2010 ), performing an unbiased analysis of this population of sources requires us to explore much larger regions of the sky. This has been initiated, for example with the Spitzer SPT Deep Field survey covering 94 and has yielded the detection of 300 galaxy cluster candidates with redshifts ( Rettura et al. 2014 ). The submm and mm sky has proved to be an efficient window onto star-forming galaxies with redshifts between 1 and 6, since it allows us to detect the redshifted modified blackbody emission coming from the warm dust in galaxies. Taking advantage of the so-called negative k-correction in the submm ( Franceschini et al. 1991 ), which compensates for the cosmological dimming at high redshift in the submm, many samples of high- galaxies and also proto-cluster candidates have been identified or discovered in this frequency range in the last two decades (e.g., Lagache et al. 2005 ; Beelen et al. 2008 ; Smail et al. 2014 ). As predicted by Negrello et al. (2005) , Clements et al. (2014) showed that the proto-cluster population can be efficiently detected in the submm as overdensities of dusty star-forming galaxies, which has been made possible thanks to the the observations of larger fields in the submm and mm range. The first discoveries of strongly gravitationally lensed galaxies at very high redshift (e.g., Walsh et al. 1979 ; Soucail et al. 1987 ) opened another window onto the


of them had a clear impact. RPC-LAP senses a large increase of plasma during each CME passage on September 11 and 19, with elevated plasma density after. We can differentiate the spiky CME signatures in Fig. 4 from the oscillations in September which correspond to seasonal effects. The spikes also do not manifest until approach into the 30 km orbits. By factoring in the CMEs studied by McKenna-Lawlor et al. ( 2016 ), we can remove two of the large spikes in the September data so they do not appear in Fig. 6 . Another possibility relates to excessive variations of the solar EUV radiation, since the current intensities collected by RPC-LAP sweeps depend on the illumination and ultimately on the solar EUV flux. Thus, a variation in EUV flux should be seen as a variation in the collected photoelectron current density by the probe and qualitatively follow each other. Until the end of 2014 August, the solar EUV flux variations match those of the RPC-LAP current measurements, with a slow increase of the photoelectron emission that can be linked directly to the increase in the flux, as the heliocentric distance between Rosetta and the Sun decreases. The 27-d periodicity in the EUV flux, due to the Sun's rotation (e.g. Woods Rottman 2002 ), has an impact on the photoelectron emission yield of the probes, resulting in the EUV flux and the I 1 current density being in qualitative agreement. After the end of 2014 August, this trend starts to be significantly altered, with the I 1 current density exhibiting large variations that do not correlate any more with the solar EUV flux variation. At the time of the transition into the HDR, the solar EUV flux variations stop driving the evolution of the I 1 currents. Thus, some other effects begin to take precedence on 2014 September 9, and the transition found in the RPC-LAP photocurrent measurements is probably not a temporally isolated artefact due to a sudden variation of the solar flux. On the temporal scale that we study in this paper, we see oscillations of the knee potential, as well as traces of this in the ion attraction current I 1 . These signals correspond to the envelopes of the 6.2-h longitudinal oscillations reported by Odelstad et al. ( 2015 ) and Edberg et al. ( 2015 ), and relate to repeated crossings of more active regions on the comet (with increased neutral outgassing). The envelopes correspond to latitudinal variations, where the Northern hemisphere of 67P is the more active one, and can be seen for electrons with RPC-IES as early as in August (Clark et al. 2015 ), but at a smaller energy and density compared to 2014 September. Although part of the reason for the spread seen at 27–29 km from the nucleus is the oversampling of the projections of active regions once Rosetta enters into the 30 km orbit, this does not explain the sudden change of magnitude upon approach to this orbit. Rosina's Double Focusing Mass Spectrometer (DFMS) measurements show increased density of O 2 following entry


metallicity, we illustrate the corresponding comparison in Fig. 11 . It shows that the two samples are similar in metallicity, spanning from −1.4 dex to 0.5 dex. Comparing with LAMOST, KIC metallicities of both samples were underestimated in the metal-poor regime but overestimated in the metal-rich region. In panel (b), we clearly observe this trend with a mean and standard deviation of −0.061 and 0.210 dex, respectively, in the sense of KIC minus LAMOST. This is consistent with the metallicity trend found by Dong et al. ( 2014 ). Figure 11. Same with Fig. 9 but for metallicity. We also checked if the lack of seven independent colours (derived from eight filters: KIC griz , D51 and 2MASS JHK ) contributes to the incorrect KIC-predicted ν max values. However, only three stars do not have a full set of colours and therefore we excluded this effect as a dominant cause for the larger errors in log g . In Fig. 12 , we compare Kepler magnitudes, KIC reddening, asteroseismic masses and spatial distribution for our sample (red data) with the samples from Huber et al. ( 2011 , grey data) and Stello et al. ( 2013 , blue data). Note that we have restricted both comparison samples to seismic gravities in the same ranges as our sample (from 2.2 to 3.5 dex). Figure 12. Histograms for Kepler magnitude K p [panel (a)] and KIC reddening [panel (b)], spatial distribution in Kepler field of view [panel (c)] and histogram of asteroseismic mass [panel (d)]. The red data represents targets of our entire sample, the grey data indicates those from Huber et al. ( 2011 ) while the blue data are targets from Stello et al. ( 2013 ). From Fig. 12(a) , we can see, due to the preferential selection of bright stars by the Kepler Asteroseismic Science Consortium, our sample is systematically fainter by nearly 2 mag, compared to Huber et al. ( 2011 ). We note that Huber et al. ( 2011 ) used data spanning from Q0 to Q6 for long-cadence light curves and Q0 to Q4 for short-cadence light curves, whereas we used data from the entire nominal Kepler Mission (Q0–Q17). Longer time series enhance the probability of detecting oscillations in fainter stars. Both our sample and the Stello et al. ( 2013 ) sample show a sharp cut at K p = 14 mag due to the Kepler selection function (Batalha et al. 2010 ). Panel (b) shows most targets in our sample have reddening around 0.13 mag, which is consistent with the sample of Huber et al. ( 2011 ) but shifted by 0.03 mag compared to the Stello et al. ( 2013 ) sample. Inspection of panel (b) also reveals there are a population of stars with lower reddening peaking at 0.035 mag. To understand if this population of stars reside in special location, we plotted the spatial distribution of targets for our sample (red dots) and Stello et al. ( 2013 , blue dots) in the entire Kepler field of view. We see fewer targets located in the three modules at the bottom-right corner, which are closest to the Galactic plane and have less stars because of the Kepler


range of 1.58, 1.60, and 1.57, respectively. However, the power spectra have flattened in the dissipation range for the whole ICME and the previous AF-rich region, with the spectral indexes of 1.12 and 0.82, respectively, which may be aliased by the instrument noises. The power spectrum for the previous AF-lack region still has a steepening in the dissipation range, with the spectral index of 1.84. Similarly, the break frequencies are also comparable to the frequency corresponding to the ion inertial length. Figure 3. Power spectral density of magnetic fluctuations inside the ICME: (A) the whole ICME observed by Wind at 1.0 au; (B) the AF-rich region of the ICME at 1.0 au; (C) the AF-lack region of the ICME at 1.0 au; (D) the whole ICME observed by Ulysses at 5.4 au; (B) the AF-rich region of the ICME at 5.4 au; (C) the AF-lack region of the ICME at 5.4 au. The dashed colored lines are the power-law fitting results. The red ones are in the inertial range, while the green ones are in the dissipation range. The vertical dashed lines represent the proton gyro-frequency, f pc , the break frequency, f b , and the frequency corresponding to the ion inertial length, f di . The energy cascade rate then can be calculated from Equation ( 1 ). For the whole ICME, the energy cascade rates at 1.0 au are derived to be about 2688.6 J kg −1 s −1 , which is close to the lower limit (2970 ∼ 65,320) estimated by Vasquez et al. ( 2007 ) when the solar wind speed is between 350 and 400 km s −1 . When the ICME propagates to 5.4 au, this value reduces to 274.7 J kg −1 s −1 , suggesting that the capacity of turbulence cascade reduces as the ICME propagates outward. For the AF-rich region, the energy cascade rate drops from 3312.2 to 89.7 J kg −1 s −1 accompanied with the disappearance of AFs, when the ICME propagates from Wind to Ulysses . For comparison, the energy cascade rates for the AF-lack region can be maintained at a certain level, and the values at 1.0 and 5.4 au are 526.9 and 737.3 J kg −1 s −1 , respectively. In addition, Smith et al. ( 2006 ) have found the dependence of the dissipation range spectrum on the rate of energy cascade through the inertial range. Our results are also in agreement with their findings that the steeper spectral in the dissipation range forms from greater cascade rates. Liu et al. ( 2006 ) have taken into account the Coulomb energy transfer between protons and alphas, and derived the equations of the heating rate required for protons ( ε p ) and alphas ( ε α ) to produce the observed temperature profile. The specific expressions are as follows where k B is the Boltzmann constant, T p and T α are the temperature of protons and alphas, m α is the alpha mass, τ pα and τ αp are the Coulomb collision timescales and have a relationship of , n α is the alpha number density, and τ e is the expansion time of the plasma. For more details, please refer to Appendix A in Liu et al. ( 2006 ). The total required heating rate ( ε re ) is


within the assumed cosmological prior for the parameters . As specified above, in this investigation we assume very conservative prior h ∈ [0.6, 0.85] and Ω m ∈ [0.04, 1] (fixing ). Therefore, F − ( z ) = 0.6[0.04(1 + z ) 3 + 0.96] 1/2 and F + ( z ) = 0.85(1 + z ) 3/2 . Secondly, because of peculiar velocities v p , the apparent redshift z obs of the GW host might be different from the cosmological redshift z determined by the Hubble flow, thus adding a further uncertainty term to the estimated redshift. To account for this effect, for each event defined by D l ± Δ D l , we assign a possible host redshift range . We assume v p = 500 km s −1 , consistent with the standard deviation of the radial peculiar velocity distribution observed in the Millennium run (Springel et al. 2005 ). We neglect additional contributions to the apparent redshift of the GW event coming from kicks at the compact binary formation, which can be as high as 360 km s −1 (Kelley et al. 2010 ), thus comparable with our choice of the peculiar velocity. The support Θ that enters in the evaluation of the galaxy likelihood function in equation ( 8 ) is the error-box defined by . To perform the proposed statistical D l – z reconstruction, we now need to attach a realistic distribution of galaxy to each of those error-boxes. We use the simulated observed light cones of Henriques et al. ( 2012 ) constructed from the Millennium run. The simulation assumes a Λ CDM cosmology with (which justifies the cosmological parameters assumed above to construct the BHB population). Because of the resolution of the simulation, galaxy distributions extracted from it are reliable only down to M * = 10 9 M ⊙ . We checked that at the magnitude cut imposed by Henriques et al. ( 2012 ), their reconstruction of the all-sky galaxy map is complete down to this mass limit out to z ≈ 0.15. The all-sky galaxy map provides sky location, stellar mass, cosmological redshift z , and observed redshift z obs (i.e. inclusive of peculiar velocities) for each galaxy. To select galaxy counterpart candidates to each GW event, we proceed as follow: we fix the cosmological parameters to the values of the Millennium run and we select all galaxies with a cosmological redshift (i.e. excluding peculiar velocities) in the volume shell z ± Δ z consistent with the LISA measurement D l ± Δ D l ; we randomly choose one of those galaxies to be the ‘true host’ of the GW signal. Note that this amounts to say that the true host can be anywhere in the interval D l ± Δ D l , i.e. we are not centring the error-box around the true host; we consider the error-box defined by , where ΔΩ is centred at the sky location of the selected ‘true host’; and we list all the galaxies with M * > 10 9 M ⊙ that fall within the error-box. In doing this, we make sure that their observed redshift z obs lies within the selected range. Each galaxy z obs is the relevant z j that enters in equation ( 8 ). In fact, in a real cosmological measurement one can


collisions in this specific case. Table 1. Percentage of collision, escape survivors and the cases of secondary disruption for every mass ratio q . This percentage is out of 90 different initial obliquity θ. Survivors mean cases that the lifetime is larger than 200 yr. We simulated 1260 different initial conditions and found that secondary fission should occur in 16 per cent of the cases and collisions in 22 per cent of cases. So, a significant part of the results are candidates to become a stable binary system. Interesting results are the spin fission phenomena in cases with q > 0.20. The cases with q > 0.20 have at least a few percentage of secondary disruption. Jacobson Scheeres ( 2011 ) did not find secondary spin fission in cases of q > 0.20 and their conclusion is that the chaotic systems with q > 0.20 can only become a stable binary through tidal process or BYORP process, but with our results we show that for the non-planar case this is not true. In other words, it is possible get a stable binary for q > 0.20 through a dynamical process (secondary disruption), but with low probability. It means that non-planar systems with large mass ratio can become a stable binary following the small ratio mechanisms outlined in Jacobson Scheeres ( 2011 ), expanding this route to forming binaries. We also analysed the rotational mode of the secondary characterized by the dynamic inertia I D (Scheeres et al. 2000 ) for all escape cases, where I D = H 2 /2 E k , H is the magnitude of rotational angular momentum and E k is the rotational kinetic energy. The parameter I D tells whether the body is in a tumbling or non-tumbling state, and in the tumbling case whether it is in a long-axis mode (LAM) or short-axis mode (SAM). Uniform rotation (non-tumbling) can be about the largest moment of inertia I D = C or about the smallest moment of inertia I D = A , and for all values of I D between A and C the body is tumbling and will have precession and nutation. The condition for a body to be in a SAM rotation mode is ( B I D C ), while the condition for it to be in an LAM rotation mode is ( A I D B ). We choose nine equal regions between the values of A and C and computed the percentage of cases that the values of I D finished in each region, so we made a plot of these percentage of cases as a function of for all mass ratios studied, as shown in Fig. 14 . We can conclude that all of the bodies are in some state of tumbling after escape. Most of them are in SAM, and are closer to uniform rotation about the maximum moment of inertia. The bodies between B and A are in a LAM, and will likely take longer to settle into the principal axis rotation. We note that the most probable state seems to be close to rotation about the intermediate axis, followed by a SAM state and followed by a LAM state. In contrast we find all of the primary body spin states to be in a SAM state, with small excitation. Figure 14. A bar graph of percentage cases as a function of . The vertical


typically multi-periodic oscillators that can show very rich pulsation frequency spectra that challenge asteroseismic analyses and the theoretical interpretation of the observed pulsation frequencies. A- and F-type stars can also show a combination of pressure ( p -), gravity ( g -), and Rossby ( r -) modes (e.g. Uytterhoeven et al. 2011 ; Saio et al. 2018 ). Hence, we investigated all available photometric data sets of β Cas for the presence of g - and r- modes in addition to the already described p -modes. g -modes would be found in the range of ∼3.3 to 0.3 d −1 in frequency (corresponding to ∼0.3 to 3.0 days in period; Kaye et al. 1999 ); r- modes appear as a group of peaks below m times the rotational frequency. BRITE-Constellation and SMEI data are known to allow the detection of g -mode pulsations when the standard procedures for data reduction are applied (e.g. Kallinger et al. 2017 ; Zwintz et al. 2017 ). The BRITE-Constellation and SMEI data for β Cas do not show any signs for g -mode pulsations. We also checked the TESS data for the potential presence of g -modes before we applied the Gaussian filter to remove the instrumental signal, and also did not find any evidence for them (see Fig. B.1 ). In all our data sets, we do not detect a frequency that can be attributed to the rotation of β Cas or a group of peaks typical for r -modes. There are two prominent physical effects that complicate the asteroseismic analysis of δ Scuti stars. One effect is moderate to fast rotation, which can cause a splitting of the pulsation modes with the same n and l values but different m values (e.g. Lignières et al. 2006 ). The second effect is the presence of magnetic fields, which is a rather recent discovery for δ Scuti stars (e.g. Neiner Lampens 2015 ; Neiner et al. 2017 ). In this context, β Cas is a special case because observationally it shows only three independent p -mode pulsation frequencies and not several dozen to hundreds of modes. The reason might be connected to the inclination angle of only 19° ( Che et al. 2011 ) and the presence of the magnetic field. Despite the rather high rotational speed of β Cas, no sign of a rotational splitting can be detected in the present observational material. We calculated the pulsation constant, Q , based on our values for the three independent frequencies, F 1 , F 2 , and F 4 , and our fundamental parameters, T eff = 6920 K and log g = 3.53 cgs. The pulsation constant Q ( Petersen 1976 ; Stellingwerf 1979 ) can be expressed as: where P is the pulsation period in days and M bol is the bolometric magnitude, which is defined as M bol = M V + BC. The absolute magnitude of 1.14 mag is calculated from the distance of 16.8 pc, and the bolometric correction, BC, can be calculated from the relation given by Reed (1998) . The pulsation constant has a value of 0.033 for fundamental mode pulsation ( n = 0), 0.025 for the first overtone ( n = 1), 0.020 for the second overtone ( n = 2), and 0.017 for the third


F336W, F438W) = 0.0 and Δ(F275W−F814W) = 0.0 in the chromosome maps. The results are plotted in the two panels of Fig. 2 . We display on the horizontal axis the different chemical compositions investigated. The vertical axis displays the indices ΔC(F275W, F336W, F438W) and Δ(F275W−F814W) for all our synthetic populations. The results are quite clear. The index Δ(F275W−F814W) is affected essentially only by variations in Y; instead, the ΔC(F275W, F336W, F438W) index is in comparison weakly sensitive to Y, but is mainly affected by variations in N (e.g. Piotto et al. 2015). The range of Δ(F275W−F814W) values for P1 stars observed in several clusters like M 3 and NGC 2808 discussed here is therefore due to a range of Y abundances. This is however not found in other clusters, for example NGC 288. The extended P1 sequences in the chromosome maps also display a tilt towards increasing ΔC(F275W, F336W, F438W) for decreasing Δ(F275W−F814W) (e.g. Milone et al. 2017 ). Based on Fig. 2 , this can possibly be explained by a narrow range of N amongst P1 stars. We conclude that the spread in P1 stars indicates that a relatively wide spread of Y is present within this population, possibly accompanied by a narrow range in N. Fig. 2. Expected chromosome map indices of RGB stars with P1 chemical composition (squares), P1 with He enhanced by ΔY = 0.05 (triangles up), P1 with He enhanced by ΔY = 0.15 (triangles down), P2 extreme (crossed squares), P2 extreme with ΔY = 0.05 (stars), and P2 moderate with ΔY = 0.05 (crossed circle); see text for details. In summary, P1 stars are defined by their location on the chromosome maps, which is consistent with the position of stars with homogeneous and field-like [O/Fe] and [Na/Fe] measurements in the clusters like M 4 and NGC 2808 investigated here. These P1 stars are often called first-generation stars in the literature, according to the proposed cluster self-enrichment scenarios. We have shown here that P1 stars in clusters with extended P1 in their chromosome maps, such as NGC 2808 and M 3, show a spread of initial Y and a small range of N. In other cases, like NGC 288 with a non-extended P1 in the chromosome map, the Y and N abundances are also homogeneous, like O and Na. The former behaviour is entirely unexpected in the context of all scenarios for the origin of MPs. 3.2. Distribution of the subpopulations along the RGB An independent test for He-abundance variations among P1 stars is to look at the optical colour distributions of each of the identified subpopulations. Bolometric corrections in optical filters are negligibly affected when moving from typical P1 to P2 metal distributions (e.g. Sbordone et al. 2011 ), but an increase in Y shifts the RGB towards bluer colours because isochrones with enhanced He have hotter T eff values. For each cluster, we first identified different RGB subpop-ulations from the chromosome maps in Fig. 1 . The mean values of the ΔC(F275W, F336W, F438W) and Δ(F275W−F814W)


spiral and elliptic galaxies, with the type assigned by visual recognition from archival optical images. For all 31 sources we found the spectral signature of the re-emission by an obscuring torus. From the peak frequency and luminosity we can derive a mean dust temperature of T T ∼ 300 K and a mean covering factor of q T = cos θ T = 0.3; most of the sources have q T 0.4. Therefore, from Eq. ( 7 ), we obtain a mean radius of R T ∼ 5 parsec. To best describe the SED of all the 20 unknown AGN sources with data in the millimeter and submillimeter wavelength band, we had to consider a second emitting toroidal structure at a larger distance from the black hole. It is reasonable to interpret this component as a dust belt inside the galaxy rather than a proper dusty torus surrounding the black hole. The mean obtained value for the temperature distribution is T DB ∼ 50 K, the mean covering factor q DB = 0.6, and the distance distribution shows a peak at ∼150 pc, where some sources reach ∼1 kpc. In Fig. 8 we show the distribution of the emitting structures distance. In evaluating the absorption and consequent re-emission on this scale, we must take into account the contribution of stars. It is reasonable to think that a large fraction of the radiation heating the dust does not come from the AGN, but from nearby stars. Nonetheless, since the dust belt blackbody has a peak luminosity that is, on average, equal or larger than the host galaxy peak luminosity, we can comfortably assume that the stars alone cannot provide enough energy to explain the measured emission. Furthermore, a heavily obscured accretion disk, whose presence is highly suggested by the X-ray spectral emission, could easily provide the necessary energy to heat the dust emitting this spectral feature. This is a clear clue that the host galaxy environment plays a key role in obscuring the AGN. Fig. 8. Distance distribution from the black hole of the IR and submillimeter emitting structures found in our work. The blue columns represent the radius of the classical obscuring torus in the AGN inner region; the red line indicates the radius of an emitting dust belt, of which we have found traces in 20 out of 31 sources. The distances are derived from Eq. ( 7 ). Furthermore, we can make two considerations about the general slope of the SED in these 31 sources. First, all but five sources show a clear sign of absorption in the soft-X ray energy range. Those that do not are SWIFT J0317.1+1542, SWIFT J0329.4−2157, SWIFT J1643.4+0986, SWIFT J2004.6−1111, and SWIFT J0302.2+6853. Of these, only the last source shows no signs of re-emission in the submillimeter band, which in our model is interpreted as the emission from a dust belt. These sources need more in-depth studies, in particular obtaining optical spectra could be very useful. Also, regarding the low-energy emission, most of the sources with data at submillimeter wavelengths show an IR-to-optical luminosity ratio of about one, with a few


the differing resonance profiles converging on to differing threshold positions. The present calculation has shifted the thresholds to lie in their exact observed positions listed in Table 1 . In Fig. 6 we present the effective collision strengths for some higher lying transitions, the 3d 7 4 F 9/2 –3d 7 2 G 9/2 (1 → 8), 3d 7 2 P 1/2 –3d 7 2 H 9/2 (11 → 13) and 3d 7 2 G 7/2 –3d 7 2 H 9/2 (9 → 13). Excellent agreement is evident for all three transitions when a comparison is made with the data of Storey Sochi ( 2016 ) across all temperatures where a comparison is possible. The collision strengths and effective collision strengths for all 42 486 forbidden and allowed lines are available from the authors on request but we present in Table 4 the effective collision strengths for all transitions among the lowest 11 3d 7 fine-structure levels across nine temperatures of astrophysical importance. 1 Figure 6. The effective collision strengths, Υ 1 → 8 (top), Υ 11 → 13 (middle) and Υ 9 → 13 (bottom), presented as a function of temperature in K (bottom). Solid black lines with stars are the current data set and the dashed line with crosses represent the results from Storey Sochi ( 2016 ). Table 4. Effective collision strengths as defined by equation ( 5 ) are presented between an upper ( j ) and lower state ( i ), across a range of nine temperatures (K), 3800 T 25 100 K. We have denoted ( a ) ≡ ×10 a . 3.3 Line ratios Combining the electron-impact excitation rates with the decay rates ( A -values), it is possible to investigate important infrared and visible line ratios. For simplicity and purpose of this study, we neglect the recombination and ionization process from the neighbouring ion stages and focus on the populating mechanisms solely of Co iii . Assuming local thermal equilibrium and detailed balance, we can derive the collisional radiative modelling approach detailed in (Griffin et al. 1997 ). We can therefore investigate selected transitions that have been suggested as temperature or density diagnostics. We present in Table 5 a comparison of emissivities (ρ ij ) between our current results, and those from Storey Sochi ( 2016 ) for particular transitions at electron densities N e = 10 4 cm −3 and N e = 10 7 cm −3 . The emissivities are calculated relative to the H β line [see equation ( 1 ) in Storey Sochi ( 2016 )], where the effective recombination coefficients can be found in Hummer Storey ( 1987 ) and Storey Hummer ( 1995 ). The wavelengths are those from National Institute of Standards and Technology (NIST) and we use our current set of A -values. In general there is excellent agreement for all emissivities considered with the major outlier ρ 1 → 2 found to be around 30 per cent at N e = 10 4 cm −3 . This is evident from the strong Υ 1 → 2 from Fig. 5 (a) at T = 10 4 K. By replacing this one effective collision strength to Υ 1 → 2 ( T = 10 000) = 4.18, then the ρ 1 → 2 differences are within a much more agreeable 8 per cent. A similar


therefore agree. At 5.5 z 5.9, the GOLD distribution lies between the bounds shown in Fig. 8 . At z > 5.9, the difference is attributable to the small sample size of the sub-samples (see the text). The differences between the SILVER and GOLD samples at 5.7 z 5.9 are due to the small sample size of the GOLD sample. The difference in number of lines of sight in this range is a factor of 2.5, which reflects the fact that very high-quality spectra are harder to obtain for quasars at z > 6.0. The SILVER and GOLD sample are marginally consistent according to a KS test( p 0.2). On the other hand, the sizes of the SILVER and GOLD samples are similar at 5.9 z 6.1, and agree with each other well. However, the additional lines of sight included in the BRONZE sample are of insufficient quality to distinguish opacity beyond τ eff ≳ 3. Since the mean opacity measured in the SILVER sample is roughly τ eff ∼ 4.5, these S/N 5 spectra yield upper limits (equal to twice the error) which are very poor in comparison. The small sample size in this bin (8 measurements in the GOLD sample, and 16 in the BRONZE one) mitigates the significance of this discrepancy, with the KS level indicating only mild discrepancy ( p 0.2). In addition, two of the BRONZE lines of sight do show tentative signs of residual transmission. The z = 6.34 quasar J1148+0702 displays a transmission peak within 6 Å of the formal end of the proximity zone, while the z = 6.23 quasar J2325 displays such a peak outside of its proximity zone but has an S/N of 1.8, making it impossible to definitely rule of reduction issues. Further scrutiny of these objects is required in order to determine whether these peaks may be related to particularly long and sporadic proximity zones. In light of these results, we decide to adopt the SILVER distribution in every instance in this paper where the data are presented or analysed in the form of a CDF. The maximum-likelihood method described above has been explicitly designed to account for observational errors and sensitivity, and we accordingly use the BRONZE sample only in Section 6 . 5 COMPARISON WITH MODELS In this section, we compare the updated CDFs of Lyman-α transmission in 50 cMpc h −1 windows with three simulations. Here, we briefly describe these simulations and outline their most relevant features. When comparing predictions from these numerical simulations to observational results, it is important to keep in mind a few caveats. First, all of the following numerical models explicitly rescale the ionizing background intensities to match the observed mean effective optical depth of the observations presented in this paper, 〈 F 〉 obs , by freely choosing a parameter A suchthat: At low redshift ( z ≲ 5.7), this rescaling is small and is somewhat justified by the difficulty of self-consistently generating the ionizing UVB. In the following analysis, all simulation snapshots have been rescaled in this way to observed 〈 F 〉 obs for each redshift bin. The


and Fig. 6 , we have shown that the radial density profile of the ejecta is well described by a power-law function of the velocity v with an exponent 6. This distribution is shallower than those of expanding envelopes in normal SNe (from n 9 to 12 as assumed in our model), which is clearly a consequence of the additional energy injection. The density distribution of freely expanding ejecta is a key to distinguishing existing models of SLSNe and other extraordinary SNe. In the following, we discuss how ejecta with such density structure form in the presence of the central energy source. For simplicity, we restrict ourselves to the Newtonian limit. We consider the following idealistic case. In normal SNe, the strong blast wave driven by a point explosion is the only way to transport the explosion energy to the outermost layer. As a result, only a small fraction of the energy is deposited in the outer envelope, while the inner ejecta possess the bulk of the energy, leading to a steep kinetic energy distribution (Matzner McKee 1999 ). In contrast to normal SNe, the central engine deposits an energy much larger than the supernvova ejecta for a time-scale much longer than the expansion time-scale of the ejecta. In our setting, the additional energy is injected at a constant rate L . Therefore, if the energy is continuously transferred throughout all the layers of the ejecta without loss or stagnation, the kinetic energy flux v 3 of the ejecta powered by the energy injection at a radius R 0 roughly proportional to the energy flux . The presence of relativistic flows leaking from the hot bubble makes the efficient energy transport possible. The flows can directly bring and deposit the additional energy throughout different layers. Thus, the following relation, is expected to hold for SN ejecta with a sufficiently long-term energy supply. In other words, the kinetic luminosity of the flow is constant. This relation gives the density distribution immediately after the ejecta are affected by the energy injection. We denote the time when the ejecta following this relation are created by t 0 . The ejecta are not freely expanding at this time. As the ejecta expand to the surrounding space, the density distribution would gradually be modified. Our goal is to derive the density distribution at the freely expanding stage. We regard the radial velocity v as a Lagrangian coordinate and derive the density distribution as a function of v . We consider a concentric shell with inner and outer velocity coordinates v and v v . The inner and outer boundaries are located at R R 0 ( v ) and R R 0 ( v v ) at t 0 . The width l s of the shell is initially given by, where the last expression is obtained for a sufficiently small v . The boundaries travel at the velocities v and v v with time and reach R R 0 ( v ) v ( t t 0 ) and R R 0 ( v v )( v v )( t t 0 ) at t . For t much longer than t 0 , the initial radius R 0 ( v ) can be neglected and the inner and outer radii are


iron. Finally, the microturbulent velocity (ξ t ) is established by erasing any trend between the abundance from Fe i and EWr. The same approach to constrain ξ t is used consistently in the three independent analysis. The atmospheric parameters are then set in an iterative fashion, first setting the temperature, and then revisiting T eff as the gravity and microturbulence are tweaked. The error associated with the determination of ξ t is estimated by propagating the uncertainty in the slope in the rEW versus Fe abundance plane. This uncertainty is of the order of ≃0.07 km s −1 . The derived T eff are typically based on more than ≃70–130 Fe i lines and have internal uncertainties of about 50–60 K, while the internal uncertainties in log g are of the order of ≃0.06 dex. The derived atmospheric parameters and [Fe i /H] and [Fe ii /H] abundances are listed in Table 2 , along with their associated uncertainties. The left-hand panel of Fig. 2 illustrates how they compare to Y14 results. We observe that our T eff , log g , and ξ t estimates are in excellent agreement with those listed in Y14 , being the average difference between our and Y14 estimates Δ T eff = −19 ± 8 K, Δlog g = −0.0 ± 0.0 dex, Δξ t = −0.09 ± 0.02 km s −1 . The agreement between our [Fe i /H] and [Fe ii /H] abundances and those listed in Y14 is also very good. In particular, we note that the metal-poor stars identified by Y14 , i.e. see Table 1 , are also the most metal-poor stars in our analysis (see Table 2 ). Additionally, the four stars with [Fe/H] ≃ −1.0 dex are the same metal-rich stars in Y14 . In the left-hand panel of Fig. 3 , we plotted the histograms of the [Fe i /H] and [Fe ii /H] distributions when the full spectroscopic analysis is performed. Our ability to portrait the [Fe i /H] and [Fe ii /H] distributions for this small data set critically depends on the adopted bin size (Δ). To adequately represent the shape of the underlying distribution, in Fig. 3 we selected Δ as the value which minimize C (Δ) = (2 me − va )/Δ 2 ; where me and va are the mean and variance of the data set. As one can see, we obtain an iron dispersion that mirrors the dispersion measured by Y14 . We find a large (Δ[Fe/H] ≃ 0.8 dex) iron distribution with two prominent peaks at [Fe/H] ≃ −1.7 and −1.0 dex and a smaller component at [Fe/H] ≃ −1.5 dex. The iron dispersion within the metal-poor stars is larger (Δ[Fe/H] ≃ 0.4 dex) than that expected from observational errors alone, indicating the presence of two separated subpopulations with different metallicity. Photometric analysis . We use VI WFI photometry to derive photometric T eff and log g * estimates. 2 Input T eff values have been computed by means of the ( V − I ) 0 – T eff transformation by Alonso, Arribas Martínez-Roger ( 1999 ) adopting a colour excess E ( B − V ) = 0.02 mag taken from the most update version (2010) of the McMaster catalogue (Harris 1996 ). Surface gravities have been computed assuming the photometric T eff , the


pressure wherever a shock is detected (see Fig. 2 ) since shocks are the acceleration sites for CRs. The following conditions (Gupta, Nath Sharma 2018b ) have been used to detect whether a particular region within the simulation box is shocked or not: ; Δ x |∇ p |/ p > δ tolerance ; ∇ T .∇ρ > 0. Figure 2. Comparison of density and thermal pressure between TH and TH+CR runs for M12 galaxy at ≈20 Myr simulation time. The three sets of plots (from left) are for SFR = 0.1, 1, and 10 . We also show the CR pressure in a separate plot. Green dots show the shock locations. In the TH+CR runs, these are the locations where CR energy is injected. For all our simulations, we have used δ tolerance = 0.5. Wherever a shock is detected, we redistribute the total pressure between thermal and CR component following the CR pressure component fraction w = p cr /( p th + p cr ). In all our models, we have used w = 0.2. 3 RESULTS To understand the properties of outflowing gas between the models with and without CRs, we investigate (i) the morphology of the outflowing gas, (ii) outer shock position, (iii) mass-loading factor, and (iv) temperature distribution of the gas. These quantities have been used in previous studies to quantify the dynamical impact of CRs. Here we present the results from our simulations of three different galaxies with halo masses of , and using three different constant SFRs: 1 0.1, 1, and 10 . To represent runs with and without CRs, we have used two different labels: ‘TH+CR’ and ‘TH’, respectively. Note that we have used our simulation for M11 galaxy as the fiducial run. The used parameters are given in Table 1 . 3.1 Outflow morphology In Figs 2 , 3 , and 4 , we show the morphology of outflowing gas for three different halo masses for TH and TH+CR runs. For all runs, we find that the shape of the outflow is nearly spherical in nature. For M8, the shape is expected to be more spherical because, in this case, the galactic disc is much smaller than the outflow length-scale and the disc is not included in our simulation. For all cases, the forward and reverse shocks are prominently distinguishable, except for SFR = 0.1 in M12 galaxy. In this case, the outflow has an irregular shape and does not show a prominent reverse shock; the locations of shocks are rather distributed inside the bubble. This can be seen from the shock locations, as displayed by the green dots in the second rows of Figs 2 , 3 , and 4 . Figure 3. Same as Fig. 2 , for M vir = 10 11 M ⊙ . Figure 4. Same as Fig. 2 , for M vir = 10 8 M ⊙ . For SFR = 0.1 (first column of Figs 2 , 3 , and 4 ), a comparison of different snapshots among three haloes shows that for M12 galaxy, before the outflow breaks out of the central region, an acoustic wave propagates from the central region. This can be understood as follows. In our set-up, CRs are initially confined in the galactic disc and the halo has very low CR pressure. Due to the pressure gradient, the CRs start to diffuse out of the disc


expects stalled bubbles (and consequently, a size distribution with slope ≈−2.7) in the presence of cooling, or if this depends on the ambient pressure. In order to answer the question, we have run our simulations for two different pressures. Fig. 12 shows the scatter plot of bubbles (similar to Figs 6 and 8 for our fiducial ISM pressure) for two different values of ISM pressures, at 30 Myr. Essentially, we have decreased the non-thermal contribution in the ambient pressure, by reducing the equivalent temperature from 4 × 10 4 to 2 × 10 4 K (left-hand panel) and then to 10 4 K (right-hand panel). Comparing with Figs 6 (adiabatic case) and 8 , we find that the bubbles in these two cases are not dominated by stalled bubbles, as was the case for Fig. 8 . For the left-hand panel, we find that bubbles with L ∼ 5 × 10 36 erg s −1 stall after a time-scale of ∼7 Myr, and bubbles bigger than that at latter times. When the pressure is further lowered, in the right-hand panel, all bubbles keep growing until 30 Myr, and the circumstance is similar to Fig. 6 . We recall that, in these cases of domination by growing bubbles, the size distribution is likely to be steeper than 1 − 2β, as we confirm below. Figure 12. Scatter plot for bubbles for ambient pressure p 0 = 1.38 × 10 −12 dyne cm −2 (left), and 6.9 × 10 −13 dyne cm −2 (right), at 30 Myr. We show in Fig. 13 the size distribution of the bubbles for these values of pressure at two different times after the onset of star formation (10 and 30 Myr). In general, we find that lowering pressure steepens the size distribution, by allowing low -luminosity bubbles to grow to larger sizes. This trend is shown in Fig. 14 , for two different epochs, 10 and 30 Myr. At lower pressures, there is an evolution of the slope between these time-scales, since bubbles keep growing in low ambient pressure, compared to high-pressure environments. Figure 13. Size distribution of bubbles for ambient pressure p 0 = 2.76 × 10 −12 dyne cm −2 (blue), 1.38 × 10 −12 dyne cm −2 (red), and 6.9 × 10 −13 dynes cm −2 (green), at 10 and 30 Myr. Figure 14. The slope of size distribution as a function of ISM pressure, for two different epochs, 10 Myr (green) and 30 Myr (red). The distributions at lower (non-thermal) pressures also show a positive part at small sizes, in addition to the falling numbers at large sizes as we have seen earlier. The rising part comes from growing young bubbles whose age is smaller than the stalling time of the bubble with the lowest luminosity. This generates a peak in the distribution. The peak depends upon the radius of the stalled bubble with the lowest luminosity at the time being observed. Fig. 13 shows that at higher pressures the peak radius is independent of time but starts varying with time as soon as we start decreasing the pressure. This occurs due to the fact that at higher pressures (such as, at 2.76 × 10 −12 dyne cm −2 ), the bubbles with low luminosities stall much before 10 Myr hence the peak


to a predicted final binding energy equal to E bin ∼ 2.4 E bin,0 in very good agreement with what shown in Fig. 7 . 3.3 Radial variation of the binary fraction Fig. 8 shows the radial profiles of the binary fraction (defined as the ratio of the number of binaries for each population to the total number of binaries and single stars in the cluster) for all binaries, for FG binaries, and for SG binaries. The low ionization rate of the compact binaries we are considering, facilitates the central accumulation of binaries segregating from the outer regions and results into an increasing binary fraction in the cluster inner regions. It is interesting to note that the evolved binary fraction radial profiles are in general qualitative agreement with those found in the recent observational study of Milone et al. ( 2016 ). Figure 8. Time evolution of the radial profiles of the binary fraction (defined as the ratio of the number of binaries to the total number of binaries and single stars) for the model MPr5f1x3-800. Each profile is calculated by combining three snapshots around the time indicated in the legend. Top, middle, and bottom panels show, respectively, the profiles for all the binaries, for FG binaries, and for SG binaries. The horizontal dashed line in the top panel shows the initial binary fraction. The three panels of Fig. 9 show the cumulative and the differential radial profiles of SG-to-FG binary ratio and the differential SG-to-FG ratio for single stars. The interplay among ionization, ejection and segregation towards the inner regions results into a progressive decrease of the SG-to-FG binary number ratio in the cluster inner regions. The global SG-to-FG binary number ratio decreases with time due to the dominant effect of the preferential ionization or ejection of SG binaries; it is interesting to note that this is opposite to what happens to the global SG-to-FG number ratio for single stars which increases with time because for single stars the preferential evaporation of FG stars (see also Vesperini et al. 2013 ) drives the evolution of this number ratio. Figure 9. Time evolution of the radial profile of the cumulative number ratio of SG to FG binaries (top panel), the differential SG-to-FG binary number ratio (middle panel), and the differential number ratio of SG to FG single stars (bottom panel) for the model MPr5f1x3-800. Lines with different colour and style correspond to the different times indicated in the legend, and the horizontal lines show the global SG-to-FG ratio for binaries (middle panel) and single stars (bottom panel). (Each profile has been calculated using three combined snapshots around the times indicated in the legend.) As shown in Fig. 9 , the SG-to-FG binary number ratio depends on the distance from the cluster centre. It is important to identify the radius R glob , where the local SG-to-FG ratio is equal to the global value of this ratio. In paper I , we have already shown that R glob depends on the initial


in Sect. 3 are indicated as blue circles filled with gray, while values for the average stacks in Table A.1 are indicated as open blue circles. The correlation between EW(CIII]) and EW(Ly α ) appears to be very strong ( r P = 0.99, r S = 1) and hides the wide range of properties of CIII] vs. Ly α . As a comparison with the literature, we plot the observed values from the different Ly α samples of Shapley et al. (2003) (green stars, average for Ly α samples), Rigby et al. (2015) (purple diamonds), and Stark et al. (2014 , 2015) (orange squares). This behavior is somewhat expected as the radiative transfer of Ly α or CIII] photons is markedly different. As a striking example we point to object 520391642 (second from the top in Fig. 1 ), which shows strong CIII] (EW > 20), as well as CIV, HeII, or NV, but only weak Ly α emission. Our results compare well with the literature when the large spread of the relation between EW(CIII]) and EW(Ly α ), the selection, and the size of different samples is taken into account. The average properties from stacks show that our results agree well with those of Shapley et al. (2003) . VUDS galaxies span a broad range of properties, including galaxies with and without Ly α in emission, expanding from smaller and possibly biased samples for which a stronger correlation between Ly α and CIII] is reported ( Stark et al. 2014 , 2015 ; Rigby et al. 2015 ; Guaita et al. 2017 ). We find that the chance of emitting CIII] and CIV at an appreciable level (EW > 3 Å) for galaxies with EW(Ly α ) > 25 (the broadly used definition of a LAE) is 42% and 20%, respectively. For galaxies that emit both Ly α and CIII] at these levels, the median EW(CIII]) is 7.7 Å, compared to a median EW(CIV) of 3.4 Å for the average LAE emitting CIV. The overall weak correlation that is observed between CIII] and Ly α emission strength for individual galaxies is in line with findings from photoionization models (e.g., Jaskot Ravindranath 2016 ; Zackrisson et al. 2017 ; Nakajima et al. 2018 ) when a broad range of conditions such as ionizing fields, geometry, and dust opacity is taken into account. 5. Distribution of EW(CIII]) To answer the question of how frequently CIII] emission is observed in UV-selected galaxies, we seek to establish the fraction of CIII] emitters in the VUDS sample as a function of EW(CIII]). While it is straightforward to identify strong CIII] emitters, it is more difficult to separate weak emitters from noise. We therefore proceed with a statistical analysis of the distribution of CIII] emission for the 3899 VUDS galaxies with 2 z 3.8. If CIII] emission is absent and in the presence of noise, the line measurement resulting from the process presented in Sect. 2.2 could result in either a false-positive or negative EW. As CIII] is only expected in emission, we use the distribution of EW measurements that indicates absorption as an estimate of how many CIII] emission lines could be produced from noise spikes, under the


the minimum comoving scale R = 8 h −1 Mpc. This cut is translated to an angular harmonic mode on each tomographic bin using the Limber relation l max = k max × χ(〈 z i 〉), where is the mean redshift for the i th tomographic bin of the analysis and χ( z ) the comoving distance computed on the fiducial cosmology of the analysis. Similar approaches were taken in Nicola et al. ( 2020 ) and Doux et al. ( 2020 ). We fix , which yields l max = 80, 127, 172, 215, and 246 for the five redshift bins for DES-Y1 cosmology. We checked these cuts do not change significantly when using a FLASK cosmology. We also keep l min = 43 for all bins based on the impact of binning for our modelling. In order to verify whether these scale cuts are effective to mitigate the effects of nonlinear bias we perform a simple χ 2 test comparing two data vectors: a fiducial data vector generated with a linear bias and a data vector contaminated with nonlinear bias. More specifically, we generate a contaminated data vector with an additional quadratic bias parametrized as a function of the linear bias as in Lazeyras et al. ( 2016 ). Using the FLASK covariance matrix we find that Δχ 2 = 0.2 for the physical cuts, where well below the criterion Δχ 2 1 adopted in Abbott et al. ( 2019a ). Hence the nonlinear biases as modelled above are mitigated by the physical scale cuts. Just for comparison, for the naive scale cuts, we find that Δχ 2 = 14.31 and therefore this further justifies our fiducial analysis choice for the physical scale cuts. 7 RESULTS ON MOCKS In order to validate our pipeline, we ran the implemented nested sampling algorithm using as input a random mock realization as well as the average of the set of mocks. We explored the parameter space: where b i is the constant linear galaxy bias in the redshift shell z i with a flat prior (0.8 b i 3.0), and Δ z i is the respective shift in the mean of the photometric redshift distribution for each redshift bin i : n i ( z ) → n i ( z − Δ z i ). The Gaussian priors are centred in Δ z i = 0 (for the synthetic data used in this section) and width as in Elvin-Poole et al. ( 2018 ). We use the FLASK covariance matrix as the fiducial one. We show that the CosmoLike theoretical covariance matrix yields very similar results in Fig. 4 . 11 In this section, we use the average of the FLASK mocks as a proxy for a noiseless data vector, as used in simulated likelihood analyses (Krause et al. 2017 ). The use of the FLASK covariance matrix gives the uncertainty one would expect for the real data likelihood analyses, which is the goal of the comparison between the harmonic and configuration space performed in the DES-Y1 data in Section 8 . The recovery of unbiased cosmological parameters in this case also shows that the Gaussian likelihood approximation is adequate. Figure 4. Comparison of the bias constraints to the average of the FLASK mocks using either FLASK (DES-Y1 run) or CosmoLike (quick run) covariance matrices with physical scale cuts


the AGN luminosity, or the distance from the BH. For simplicity we vary only one of these, the density, while keeping the others fixed. As discussed in following sections, this change, while simple, does serve to illustrate the types of SEDs that will filter through the wind. Changes in the mass-loss rate of the wind can cause changes in the hydrogen density of the equatorial obscurer. We examine the effects of such variations upon the transmitted SED in Figure 3 , which shows three typical SEDs. As the figure shows, the shape of the SED is highly sensitive to the value of the hydrogen density. Figure 3. SED transmitted through equatorial obscurer and incident upon the BLR is shown for three different values of the hydrogen density. The unextinguished SED is also shown. The SED is dramatically dependent on the hydrogen density of the obscurer. High hydrogen densities produce strong absorption in the XUV region and strong emission in the FUV/optical regions. The density and flux parameters chosen here do not matter in detail. The transmitted SED actually depends on the ionization parameter, which is the ratio of the ionizing flux to the hydrogen density (Osterbrock Ferland 2006 ). Increasing the hydrogen density lowers the ionization parameter inversely. Particular values of the density and flux do not matter as long as the ratio giving the ionization parameter is kept constant. As the ionization parameter increases the level of ionization of the gas increases. The gas opacity decreases as the number of bound electrons decreases. The ionization structure changes in ways that produce the three characteristic SEDs shown in Figure 3 . These are the three cases: 1. Case 1 has the lowest density and the highest ionization, and is shown in black. This wind is fully ionized, has no H or He ionization fronts, and nearly fully transmits the entire incident SED. 2. Case 2 has an intermediate density and is shown in blue. This has a He 2+ − He + ionization-front but no H ionization-front. The incident SED is heavily absorbed for the XUV energies, 11 11 We refer to the region 6–13.6 eV (912–2000 Å) as FUV, 13.6–54.4 eV (228–912 Å) as EUV, and 54.4 eV to few hundred eV (less than 228 Å) as XUV. although most of the hydrogen-ionizing radiation is transmitted. 3. Finally, Case 3 is shown with the red line and has the highest density. The wind has both H and He ionization-fronts, and much of the light in the EUV and XUV regions is absorbed. 4. The Response of the BLR to Changes of the Transmitted Continuum We now show how the EWs of the BLR lines in Figure 2 are affected by changes in the transmitted SED of the equatorial obscurer. Figure 4 shows how the EW of the strongest observed lines reacts as the density, n (H), of the equatorial obscurer varies. These changes are due to variations in the SED filtering through the equatorial obscurer. The three general types of SED shown in Figure 3 produce the three different BLR regimes shown in Figure 4 . We


dissociation of TiO and VO in the limb even at the lower altitudes probed by our data, reducing the log VMR of both species to −10, well below the detection limits we set with our injection tests. It is also interesting to note that the work of Evans et al. (2017 , 2018 ) and Mikal-Evans et al. (2019) infers the presence of VO, but not TiO, when both were predicted as inversion-drivers by Hubeny et al. (2003) and Fortney et al. (2008) and were largely expected to occur together. It has been shown in the models of Goyal et al. (2019) that greater abundance of VO over TiO is only expected in a very narrow temperature range: ~ 1700–1800 K assuming rainout condensation, or ~1200–1400 K assuming local condensation. This highlights the importance of robust detections and non-detections of TiO and VO as a diagnostic for temperature and condensation processes in the atmospheres of ultra-hot Jupiters. Despite our non-detection of TiO and VO, Evans et al. (2018) still show a feature in their transmission spectra at 600–800 nm consistent with the presence of VO (or perhaps another molecule absorbing strongly in this range). Additionally, their emission spectra ( Evans et al. 2017 ; Mikal-Evans et al. 2019 ) are still best-fit with models containing VO and clearly show water emission features consistent with the presence of a temperature inversion. It was theorised by Spiegel et al. (2009) that a hot Jupiter witha solar carbon-to-oxygen ratio would require TiO of at least solar abundance to cause a temperature inversion, a level which both we and Evans et al. (2018) rule out in our analysis. Our analysis in this paper now seems to rule out the presence of VO also, although again we emphasise that VO cannot be robustly ruled out using high-resolution cross-correlation methodology until a more suitably accurate line list is published. Nevertheless, although TiO and VO were long thought to be the predominant cause of temperature inversions in hot Jupiters, it may now be time to look for other culprits. Recent theoretical work has postulated a range of potential optical absorbers such as SiO, Fe, Mg, AlO, CaO and metal hydrides ( Lothringer et al. 2018 ; Lothringer Barman 2019 ; Gandhi Madhusudhan 2019 ), some of which (such as AlO) have absorption bands in the 600–800 nm range. Gandhi Madhusudhan (2019) also suggested a theoretical link between the C/O ratio and the presence of a temperature inversion, postulating that a reduced infrared opacity due to a low H 2 O abundance in WASP-121b could contribute towards the existence of an inversion layer; the presence of H 2 O emission features, however, would appear to rule out this possibility. Finally, the transmission spectrum presented by Evans et al. (2018) shows a strong upward trend in the blue optical much steeper than would be consistent with Rayleigh scattering, which they tentatively identify as due to the presence of SH, another molecule known to absorb strongly in the optical and thus