O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O B-Collaboration I-Collaboration I-Collaboration I-Collaboration I-Collaboration I-Collaboration O B-Formula I-Formula I-Formula I-Formula B-Citation I-Citation I-Citation I-Citation O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O B-Telescope I-Telescope I-Telescope I-Telescope B-Telescope O B-Citation I-Citation I-Citation I-Citation O O O O B-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O B-Telescope B-Telescope B-Telescope O B-Telescope O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

power-law decline begins roughly when the jet centroid comes into view. The sharpness of the light curve peak and the immediate transition to t − p decline implies that we are in the regime 20 20 If ( θ v − θ j ) ≲ θ j there will be a long-lived phase during which the light curve decays as t −1 . θ v − θ j ≫ θ j . We denote by t 1 as the time that we see the edge of the jet, namely Γ( t 1 ) ≃ 1/( θ v − θ j ), and t 2 as the time that we see the jet axis, Γ( t 2 ) ≃ 1/ θ v . Now, ignoring sideways spreading of the jet we can approximate (e.g., Sari et al. 1998 ) to obtain //. Here we use the approximation that θ j / θ v is much smaller than unity. Observationally, t 1 occurs sometime during the transition from the t 0.8 rise to the peak of the light curve and t 2 occurs when the decay phase approaches t − p . Using the results from our MCMC analysis, we find that Δ t / t ≲ 1/3 (68% confidence or better, depending on the where t 1 and t 2 lie), indicating that θ v ≳ 8 θ j . To verify this simple estimate we produced light curves from a top-hat jet using semi-analytic code. 21 21 The semi-analytic code (Soderberg et al. 2006 ) takes proper account of all relativistic effects such as Lorentz boost and light arrival time from each point in the jet and it includes lateral spreading of the jet. Following corollary comparison of the code results to BOXFit (van Eerten et al. 2012 ), we use lateral spreading of 30% of the local thermal speed. We verify that varying the spread velocity, including taking no spreading at all, does not change the result significantly. We find that light curves that fit the transition seen from the peak to the decline of the light curve have θ v ≃ 6 θ j . Together with the upper limit on the observing angle from the Laser Interferometer Gravitational-Wave Observatory (LIGO)-Virgo Collaboration ( θ v ≲ 28°; Abbott et al. 2017a ), our constraint implies θ j ≲ 5°. If instead we use the estimate of Γ ≃ 4.1 ± 0.5 close to the peak of the light curve from the very long baseline interferometry (VLBI) measurement (Mooley et al. 2018a ), then we get θ j ≲ 3° and θ v ≃ 15°. 5. Summary and Conclusions In this companion Letter to our polarization and high angular resolution imaging studies, we have presented deep VLA, ATCA, MeerKAT, and uGMRT observations (Section 2 ) of GW170817 post-peak of the light curve, i.e., between 180 and 300 days post-merger. Our spectral analysis does not yield any evidence for the cooling break to have entered the radio band, or of any achromatic steepening in the light curve indicating the transition of the outflow into the non-relativistic regime (Section 3.1 ). We find that the light curve decay is consistent with t −2.2 (Section 3.2 ), which is a classic signature of a jet where the slope of the decay is equal to the power-law energy index p of the synchrotron-emitting electrons. We also find that the transition from the power-law rise to decay ( t 0.8 to t −2.2 ) is fairly sharp. The data on the light


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

54 value measured for our sample. Fig. 8 shows the distribution of D 34 and D 54 for our program stars. Figure 8. D 34 and D 54 distribution for our program stars. Among 105 stars for which we estimated D 34 values, 19 (≈20 per cent) show D 34 ≥ 2.7. However, D 54 for our stars mostly range between 0.2 and 1.5 (≈70 per cent). Only 19 stars exhibit D 34 1.0, whereas D 54 > 1.5 in 27 cases. Comparing with literature, we find that Dachs et al. ( 1990 ) reported D 34 to lie within 1.2–3.2 for their sample of 26 southern early-type Be stars. However, D 54 for their case range within 0.4–1.0, clustering near 0.7. On the contrary, Slettebak et al. ( 1992 ) obtained D 34 for 41 CBe stars to range between 2.05 and 5.7, while D 54 being always less than 1.0. Both the previous authors also noticed that on an average, weak H α emission (H α EW −25 Å) is usually characterized by flat Balmer decrements ( D 34 2.0, D 54 > 0.6). Our study could not confirm any such trend that is evident from Table 4 . Our result for D 34 fairly agrees with Slettebak et al. ( 1992 ) and Dachs et al. ( 1990 ), although the range of our D 34 is larger. This is possibly due to the larger number of stars for our sample. We found that 19 of our program stars show D 34 ≥ 2.7, implying that the disc for these stars are optically thick in nature. But our result does not match for D 54 . The different range of D 34 and D 54 values obtained in our study might be due to the fact that we considered A V values for calculating the Balmer decrements in our case. This may not have been done by previous authors. Moreover, we estimated D 34 for all 20 weak emitters also that show H α EW −5 Å. 3.4.2 Epoch-wise variation of <italic>D</italic>34 Apart from looking into the H α line, the transient nature of CBe star discs can be identified by studying the epoch-wise variation of estimated D 34 values of those stars where repeated observations are done. For our program stars where previous estimations of D 34 are available (at least two), we compared our estimated D 34 values to those obtained by other authors. We found that only 10 of our program stars have at least two sets of observations for D 34 including our estimations. Only one among them (HR 2142) has three observations for D 34 . Fig. 9 demonstrates the variation of D 34 as observed by us and previous authors. It is seen that our value of D 34 is lower than that of previous authors (e.g. Dachs et al. 1990 , Briot 1971 , Rojas Herman 1958 , Burbidge Burbidge 1953 , and Karpov 1934 ) in every case. Figure 9. Variation of D 34 in 10 of our program stars as observed by us and previous authors. The black line indicates the cut-off value 2.7, adopted from Hummer Storey ( 1987 ), which is assumed to distinguish between an optically thin and thick region that prevails in case B condition defined by Baker Menzel ( 1938 ) and later by Brocklehurst ( 1971 ). The epoch-wise variation study of D 34 for 10 of our program stars certainly imply


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

form the previous iteration, resulting in a final cleanest sample containing 224 245 QSOs with (for which we have Ly free photometry in the -, -, and -bands), 135,953 with (where we can use the -band), and 77 633 QSO with , where we can use all the SDSS bands. We have an estimate of the intrinsic colours , and an estimate of the reddening for each QSO that is retained by the redshift constraints. Even though the unobscured QSO intrinsic colours are computed independently for each band pair, we do obtain consistent results across the band pairs, i.e. holds for all the bands , , and , over all the redshifts considered. Working with the column density maps as an estimate of the extinction instead of the gives very similar estimates of , and is independent of any dust modelling, so this means we did not translate potential dust modelling systematics into our QSO estimates. Fig. B.3 QSO magnitude increase per unit of dust extinction as a function of the QSO redshift. We use an extinction curve with . The and band curves are shown in a thinner trace for and , the redshifts at which the intergalactic Ly line can affect the photometry in these bands. In order to compare the estimate with a QSO estimate, we need to derive a QSO extinction from the different colour excess . We proceed as follows. For a given QSO spectrum and extinction curve shape, we can compute the SDSS magnitude increase per dust extinction for . These ratios depend on the assumed extinction curve and QSO spectral shape, and therefore on the QSO redshift. Using the QSO composite spectrum of Vanden Berk et al. (2001) and the extinction curve presented by Fitzpatrick (1999) parametrized via , we compute the ratios : Figure B.3 shows as a function of the QSO redshift , for the different bands and . Even though the QSO intrinsic colours are strong functions of its redshift, the extinction curves are smooth enough that is mostly redshift independent. Using the extinction curves with (which was also used to constrain the optical properties of the grains used in the DL model), for each redshift , we define: and Finally, for each QSO, we define its as the average of the values for all the band pairs that are allowed by its redshift . Appendix C: Impact of the CIB anisotropies and instrumental noise on the parameter estimation Fig. C.1 Comparison of the original and recovered dust mass under CIBA and instrumental noise simulation in the diffuse ISM for a resolution. Colour corresponds to the density of points (see Fig. 5 ). We study the impact of CIB anisotropies (CIBA) and instrumental (stochastic) noise in our mass estimates in the diffuse ISM (where their effect should be the largest). We simulate data by adding CIBA and instrumental noise to DL SEDs, and fit them with the same technique as we use to fit the observed data. The results quantify the deviations of the recovered parameters from the original ones. We start by a family of four DL SEDs with and , a typical , and . We


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members. These stars were classified as [Fe/H] ∼ −3.0 from measurements of the Ca ii K line. It appears that the strong carbon enhancement of these Sculptor members biased the Ca ii K metallicities in lower-resolution spectra (see Section 5.2 ). For each star in Table 5 , we derived a Mg abundance from the 5172.7 and 5183.6 Å lines if the S/N was sufficiently high. Then, we compared the derived [Mg/Fe] ratio of these stars to the expected [Mg/Fe] ratio for dwarf galaxy stars in their metallicity regime. We would expect to see systematically higher [Mg/Fe] values if the Ca ii K–based metallicities were biased lower, such as in the case of stars with high A(C) values. We consider two examples: stars 10_7_442 and 10_8_1226 have carbon abundances close to the CEMP threshold and Mg line equivalent widths in the linear regime of the curve of growth (reduced equivalent widths ≲−4.45). For these two stars, we measure [Mg/Fe] values of 0.23 and 0.17, respectively. These [Mg/Fe] ratios are roughly at the lower end of the regime of what is expected for dwarf galaxy stars at these metallicities. This suggests that we are not strongly underestimating our [Fe/H] measurements for stars that are near the CEMP threshold. If we include stars from Table 5 with Mg line equivalent width measurements in the nonlinear regime of the curve of growth at face value and adopt the M2FS metallicities and carbon abundances when available, the average [Mg/Fe] of stars with [C/Fe] > 0.50 is 0.43. This [Mg/Fe] ratio is also in the regime of expected values. As mentioned, if the metallicities were substantially underestimated, we would expect to get much larger [Mg/Fe] values. For comparison, all the CEMP-s candidates have [Mg/Fe] ≳ 1.0 if we take the KP-based [Fe/H] measurements at face value. While these Mg abundance estimates may have large uncertainties (up to ∼0.4 dex, as is expected for data of this quality), they suggest that we are not strongly biased in our metallicity estimates for stars without copious carbon enhancement. We also compared our observed MagE spectra to MIKE spectra of CS22892-52 ([Fe/H] = −3.16; T eff = 4690 K) and HD122563 ([Fe/H] = −2.93; T eff = 4500 K) that had been degraded to match the resolution of the MagE data. Measurements of these standard stars are from Roederer et al. ( 2014 ). We find that the strengths of the Mg b lines observed with MagE appear to be roughly consistent with what is expected from our Ca ii K derived metallicities. Thus, only stars with very strong carbon enhancement are incorrectly selected into our M2FS sample. These stars are overwhelmingly likely to have their carbon abundance elevated by accretion from a binary companion (see Figure 10 ) and should already be excluded in a calculation of the CEMP fraction. This confirms that our selection is not biased in favor of CEMP-no stars. Below a fiducial metallicity of [Fe/H] ∼ −3.0 and after excluding CEMP-s, Ba-strong, and CH-strong stars, we can reasonably assume that


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ones before we can unambiguously identify the assembly bias signature in the universe. As discussed in Section 5.1 , the best candidate appears to be , followed by and the mean age (see also the proxy discussed in Lim et al. 2016 ). These in principle could be obtained from high-quality spectra with VESPA, as well as the aforementioned codes, and will be subjects of our future investigation. Inspiration could also come from the analysis of Miyatake et al. ( 2015 ), who have recently claimed a detection of strong assembly bias using galaxy clusters. Their proxy for halo formation time is , the mean projected separation of member galaxies from the cluster center. In principle, it is possible to adopt a similar proxy for galaxy scale halos, although the number of satellites is much smaller, and the membership determination is less certain. We conclude by noting that it is also imperative to better understand theoretically the origin of assembly bias across the mass spectrum of halos. If the cause at low-mass scales is the backsplash halos, then instead of identifying the best formation time indicator, one should look for ways to observationally distinguish such galactic systems, or to take such population fully into account when comparing with theoretical models. Regarding the high-mass end, since it is likely that the physical origin of assembly bias in high-mass halos is believed to be quite different than for low-mass halos (Dalal et al. 2008 ), the detection presented by Miyatake et al. ( 2015 ) is not necessarily inconsistent with the non-detection reported here. It is clear that the assembly bias phenomenon is far richer and complicated than expected, and warrants further investigations, such as exploring better proxies for halo formation time, and the scale dependence of assembly bias (Section 2.4.1 ). 6. SUMMARY As the assembly bias is a robust prediction of the CDM theory of structure formation, establishing it observationally would not only further vindicate this extremely successful theory, but also shed light on the baryonic physics of galaxy formation. In this exploratory study of the detection of assembly bias, we have shown (with the aid of weak gravitational lensing) that some previous claims of detection may be simply due to differences in halo mass of the galaxy samples, rather than a real manifestation of assembly bias (Section 3 ). We have then investigated a couple of ways of constructing galaxy samples with similar mean halo masses, thus facilitating a direct search for assembly bias in the real data (Section 4 ). We focus on the halo mass scale of , where assembly bias is expected to be large, and construct early- and late-forming halo samples by making use of a central galaxy catalog ( Y07 ), under the assumption that the SFH of central galaxies reflects the formation history of underlying halos (which is well supported by a state-of-the-art galaxy formation model; Section 5.1 ). Satellite galaxies living in massive halos


O O O O O B-Model O O O O O O O O O O O B-Model O O O O O O O O O O O O O B-Model O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Model O O O O O O O O O O O O O B-Model O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Model O O O O O O O O O O O B-Citation I-Citation O O O B-Model O O O O O O B-Survey O O B-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula O O O B-Formula I-Formula I-Formula O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O B-Model O O O O O B-Survey O O B-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula O O O B-Formula I-Formula I-Formula O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O B-Model O O O O O O O O O O O O B-Model O O O O O B-Survey O O B-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula O O O B-Formula I-Formula I-Formula O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O B-Model O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O B-Model O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O O

and best detections. Table D20 StackModelFitExp: Contains the Exponential Fit Parameters to Extended Sources Note. See the StackObjectThin table for a discussion of the primary, secondary, and best detections. Table D21 StackModelFitDeV: Contains the de Vaucouleurs ( 1948 ) Fit Parameters to Extended Sources Note. See the StackObjectThin table for a discussion of the primary, secondary, and best detections. Table D22 StackModelFitSer: Contains the Sérsic ( 1963 ) Fit Parameters to Extended Sources Note. See the StackObjectThin table for a discussion of the primary, secondary, and best detections (Sérsic 1963 ). Table D23 StackApFlxExGalUnc: Contains the Unconvolved Fluxes within the SDSS R3 ( r = 103), R4 ( r = 176), R5 ( r = 300), R6 ( r = 463), R7 ( r = 743), R8 ( r = 1142), R9 ( r = 1820), R10 ( r = 2820), and R11 ( r = 4421) Apertures (Stoughton et al. 2002 ) for Extended Sources Note. These measurements are only provided for objects in the extragalactic sky, i.e., they are not provided for objects in the Galactic plane because they are not useful in crowded areas. See the StackObjectThin table for a discussion of the primary, secondary, and best detections. Table D24 StackApFlxExGalCon6: Contains the Fluxes within the SDSS R3 ( r = 103), R4 ( r = 176), R5 ( r = 300), R6 ( r = 463), R7 ( r = 743), R8 ( r = 1142), R9 ( r = 1820), R10 ( r = 2820), and R11 ( r = 4421) Apertures (Stoughton et al. 2002 ) for Extended Sources after the Images Have Been Convolved to a Target of 6 Sky Pixels (15) Note. These measurements are only provided for objects in the extragalactic sky, i.e., they are not provided for objects in the Galactic plane because they are not useful in crowded areas. See the StackObjectThin table for a discussion of primary, secondary, and best detections. Table D25 StackApFlxExGalCon8: Contains the Fluxes within the SDSS R3 ( r = 103), R4 ( r = 176), R5 ( r = 300), R6 ( r = 463), R7 ( r = 743), R8 ( r = 1142), R9 ( r = 1820), R10 ( r = 2820), and R11 ( r = 4421) Apertures (Stoughton et al. 2002 ) for Extended Sources after the Images Have Been Convolved to a Target of 8 Sky Pixels (20) Note. These measurements are only provided for objects in the extragalactic sky, i.e., they are not provided for objects in the Galactic plane because they are not useful in crowded areas. See the StackObjectThin table for a discussion of the primary, secondary, and best detections. Table D26 StackPetrosian: Contains the Petrosian ( 1976 ) Magnitudes and Radii for Extended Sources Note. See the StackObjectThin table for a discussion of the primary, secondary, and best detections. Table D27 StackToImage: Contains the Mapping of Which Input Images Were Used to Construct a Particular Stack Table D28 StackToFrame: Contains the Mapping of Input Frames Used to Construct a Particular stack along with Processing Statistics Table D29 StackDetEffMeta: Contains the Detection Efficiency Information for a Given Stacked Image Note. Provides the number of


O O O O O O O B-Instrument O O O O O O O O O O B-Organization I-Organization B-Location O O B-Organization I-Organization B-Location B-Observatory B-Location B-Organization B-Organization B-Location B-Organization B-Organization I-Organization B-Location B-Organization B-Location B-Observatory I-Observatory B-Location B-Organization I-Organization I-Organization B-Organization B-Organization B-Organization B-Organization I-Organization B-Location O B-Organization B-Organization B-Organization B-Organization I-Organization B-Location O O O O O O O O O B-Organization B-Location B-Organization B-Location B-Organization B-Organization B-Organization B-Location B-Organization B-Location B-Location B-Organization B-Location B-Organization B-Organization B-Location O B-Organization B-Location B-Instrument O O O O O O O O O O B-Organization B-Location O O B-Organization B-Location B-Organization I-Organization B-Organization B-Organization B-Location B-Organization B-Organization B-Location B-Organization B-Location B-Organization B-Organization B-Organization B-Organization B-Location B-Organization B-Location O O O O O O O O O B-Organization B-Location B-Organization O B-Organization B-Location B-Organization B-Location B-Organization B-Location O B-Organization B-Location O O O O O O O B-Organization I-Organization I-Organization O O B-Location I-Location B-Grant I-Grant I-Grant B-Organization B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O O O B-Location B-Organization I-Organization I-Organization O O B-Grant I-Grant I-Grant O O O O O O O B-Database O O O O B-Organization B-Location I-Location O O O O O O O B-Database I-Database I-Database B-Database O O O O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization I-Organization I-Organization

We thank the referee for helpful comments. SPIRE has been developed by a consortium of institutes led by Cardiff Univ. (UK) and including: Univ. Lethbridge (Canada); NAOC (China); CEA, LAM (France); IFSI, Univ. Padua (Italy); IAC (Spain); Stockholm Observatory (Sweden); Imperial College London, RAL, UCL-MSSL, UKATC, Univ. Sussex (UK); and Caltech, JPL, NHSC, Univ. Colorado (USA). This development has been supported by national funding agencies: CSA (Canada); NAOC (China); CEA, CNES, CNRS (France); ASI (Italy);MCINN (Spain); SNSB (Sweden); STFC, UKSA (UK); and NASA (USA). PACS has been developed by a consortium of institutes led by MPE (Germany) and including UVIE (Austria); KU Leuven, CSL, IMEC (Belgium); CEA, LAM (France); MPIA (Germany); INAFIFSI/ OAA/OAP/OAT, LENS, SISSA (Italy); IAC (Spain). This development has been supported by the funding agencies BMVIT (Austria), ESA-PRODEX (Belgium), CEA/CNES (France), DLR (Germany), ASI/INAF (Italy), and CICYT/MCYT (Spain). This work has received support from the European Research Council under the European Union's Seventh Framework Programme (ERC Advanced Grant Agreement no. 291294, ‘ORISTARS') and from the French National Research Agency (Grant no. ANR-11-BS56-0010 – ‘STARFICH'). This research has made use of the SIMBAD data base, operated at CDS, Strasbourg, France. It has also made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.


O O O O O O O O O O O O B-Organization I-Organization O O B-Grant I-Grant I-Grant I-Grant I-Grant O O B-ComputingFacility I-ComputingFacility I-ComputingFacility O B-Grant O B-Grant

This work was supported in part by computational resources provided by the Australian Government through the National Computational Merit Allocation Scheme and the Pawsey Supercomputing Centre (projects g61 and ew6).


O O O O O O O O O O O O B-Wavelength O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength O B-Wavelength I-Wavelength O O O O O O O O O O B-Wavelength O O O B-Wavelength O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O B-Wavelength O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O B-Citation I-Citation I-Citation O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O B-Wavelength O O O O O O O O O O O O O O O O B-Dataset I-Dataset O O O O O O O B-Wavelength O O O O O O O O O O O B-Wavelength O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O B-Survey O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

the emitting electrons through the inverse Compton mechanisms and that weakens their radio emission. However, the regions of the jet producing the 1.4 GHz radio flux (≳7 GHz rest frame) are not affected by the ‘quenching’ of the radio due to the CMB radiation. This is because they have a magnetic energy density much larger than the CMB one, even taking into account the Γ 2 enhancement due to the relativistic motion of the emitting plasma. At z = 4, the CMB energy density is U CMB ∼ 2.6 × 10 −10 erg cm −3 . In the comoving frame, this is enhanced by a factor ∼Γ 2 , thus reaching U ′ = 2.6 × 10 −8 (Γ/10) 2 erg cm −3 . Most of the observed radiation from the jet is produced in a compact region, where the magnetic field is around 3 G, and the observed self-absorption frequency is ν t ∼ 3 × 10 12 Hz (rest frame, see e.g. Ghisellini Tavecchio 2015 ). In the case of a flat radio spectrum, the self-absorption frequency scales as R −1 , where R is the distance from the black hole. This is the same dependence of the dominant component of the magnetic field B . Therefore in the region self-absorbing at 7 GHz (rest frame) B should be ∼6 mG, and its energy density U B = B 2 /(8π) ∼ 1.4 × 10 − 6 . Since , there is no ‘quenching’ of the synchrotron emission of the jet. 4.1 The proposed scenario To solve the tension between predicted and observed sources, we propose a scenario that follows the ideas put forward by Fabian ( 1999 ). At redshifts larger than ∼4, jetted sources hosting a black hole with mass M ≳ 10 9 M ⊙ 1 are completely (i.e. 4π) surrounded with obscuring material (see the cartoon in Fig. 1 ). Only the jet can pierce through this material and break out. Observers looking down the jet can see the nuclear emission from the accretion disc and the broad emission lines. For observers looking with viewing angles even only slightly larger than θ j ≈ 1/Γ, the optical emission (including broad lines) is absorbed, the flux is fainter, and the source cannot enter the SDSS Catalog. The absorbed radiation is reradiated in the infrared. Even if the hotspots or the lobes were indeed emitting a radio flux above the 1 mJy level at the observed 1.4 GHz frequency, there would be no source in the SDSS to match with if the jet is only slightly misaligned. The quasi-spherical dusty structure (hereafter ‘obscuring’ or ‘dark bubble’) can cover the nuclear region until the accretion disc radiation pressure blows it away. This can occur at a threshold luminosity . 5 DISCUSSION Let us assume that the obscuring bubbles exist not only in jetted sources, but are common to all high-redshift quasars, including radio-quiet ones. The evolution in time of the obscuring bubbles and the central black hole mass could however be different in jetted and non-jetted sources. In fact, the presence of a jet could affect the accretion efficiency η d , defined as : part of the dissipation of the gravitational energy could amplify the magnetic field instrumental to launch the jet. In other


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O B-URL O O B-Observatory B-Telescope I-Telescope I-Telescope I-Telescope I-Telescope B-Telescope B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O B-Instrument B-Wavelength I-Wavelength O O O O O O O O O O B-Telescope O O O O O O O O O O O B-Instrument B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O B-Tag O B-CelestialObject O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O B-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O B-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

plotted the intensity increase and decrease in Figure 6 (a). The base-subtracted images show that strong coronal dimming appears in the west of the active region from 03:10 UT, which is 18 minutes after the GOES peak time. The dimming reached the peak at 04:10 UT, which is 78 minutes after the GOES peak time. Coronal mass ejections (CMEs) are often associated with coronal dimming (Sterling Hudson 1997 ). Therefore, in this case, a CME was likely to occur as well, even though the CME catalog 3 3 https://cdaw.gsfc.nasa.gov/CME_list/ by the SOHO /Large Angle and Spectrometric COronagraph (LASCO; Brueckner et al. 1995 ) does not show any CME. Figure 6. (a) Spatially integrated intensity increase (thick black) and decrease (dashed red) of the 195 Å intensity measured on EIS 195 Å images from 01:46:55 UT. The vertical dotted line indicates the GOES peak time at 02:52 UT. (b) Intensity and base-subtracted maps of EIT 195 Å. The observation time is shown at the top right of each image. The base-subtracted images are the difference from the image at 01:46:55 UT shown in the top plot. The red boxes show the field of view of Figure 3 . 5. Summary and Discussions In this section, we summarize our results from the statistical and event studies and discuss the chance to observe the linear polarization in H α and its origin. 5.1. Infrequent Occurrence of Significant Linear Polarization at H<italic>α</italic> in Solar Flares We found only one event that showed significant linear polarization signals among 71 H α flares including 64 GOES flares with the spatial and temporal samplings of 10′′ × 10′′ and 40 s, respectively. Many preceding papers reported the characteristics of the linear polarization in H α only for the events that show significant polarization signals. In the cases where the polarization was not detected, it has been considered that the sensitivity of the polarimetry was insufficient. On the other hand, Bianda et al. ( 2005 ) reported that they did not find significant linear polarization signals in 30 flares, even though they used a high-sensitivity instrument. Based on their preliminary analysis of dozens of flares, Hanaoka ( 2004 , 2005 ) also found that one flare showed significant linear polarization signals, while most other flares showed none. In our study, we used the polarimeter with higher accuracy described in the papers by Hanaoka ( 2004 , 2005 ) and confirmed their preliminary results. Furthermore, although the analyzed samples include some large flares such as 4 X- and 13 M-class events, the results are basically negative. The high-frequency modulation techniques reduce spurious signals caused by the seeing effect and by flaring structures evolving in time, and data obtained by these techniques are more reliable than data that were taken by low-frequency modulation techniques. Thus, our results proved that the linear polarization does not appear in most of the flares, but there are a few flares that actually show the polarization.


O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O B-Organization O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O B-Instrument O O O B-Organization O O O O O O O O O O O O O O O O O O O B-Wavelength O B-Wavelength O O B-Archive O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O B-Wavelength O O O O B-CelestialObject I-CelestialObject O O B-Wavelength O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O B-Wavelength B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model O B-Model I-Model I-Model I-Model O O B-Model I-Model I-Model I-Model O O O O O O O B-Model I-Model O O B-Software O O B-Software O O B-Citation I-Citation I-Citation B-Software I-Software I-Software I-Software I-Software I-Software O B-Software O O B-URL O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O B-Wavelength O O O B-Wavelength O O O O O O O O O O O O O O O B-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

length of just 0.5 kpc, the gas will have cooled and recombined before escaping. These baryons will therefore become visible to Lyman series absorption studies and the oxygen will be visible to O i absorption (e.g., at 1302 Å). APPENDIX MATCHING THE POINT-SPREAD FUNCTION The diffuse halo of O vi emission could be mimicked if the F125LP PSF is broader than that of F140LP. We used custom software to match images to a common PSF. Point sources (stars) that are bright in the FUV are rare, making empirical studies of the SBC PSFs challenging, and the models available from STScI severely underestimate the power in the extended wings of the PSF (at radii larger than 1 arcsec). We instead build empirical PSF models by examining multi-epoch calibration data of the globular cluster NGC 6681. These were obtained under many programs by the ACS instrument team at STScI, stretching back to 2002 when the instrument was first mounted. We have obtained all the calibration images taken in F125LP and F140LP from the MAST, drizzled and stacked them using the same methods as for our science data. The total exposure time in F125LP is 13,530 and 7350 s in F140LP. The brightest star in NGC 6681 has a FUV AB magnitude of 18.0, giving a countrate of 22 counts per second in the brightest pixel in F125LP. This is just below the nonlinear regime of the SBC detector, indicating that calibration data are as good as possible for deriving the PSF. We then selected 45 (48) stars in the F125LP (F140LP) images, extracted stamps, and stacked them to produce a very deep point-source image. A model PSF consisting of a combination of three 2D functions (an elliptical Moffat function, a radially symmetric Gaussian function, and a symmetric fourth-order polynomial function) was fitted to the stacked image using least-squares fitting with the LMFIT package for Python. 6 6 Newville et al., LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python, 2014, doi: 10.5281/zenodo.11813 . The stacking was then redone iteratively with the contribution from nearby stars removed by subtracting the model PSF. The final stacked images in the two filters were normalized to have a total sum of 1 and are presented in Figure 12 , while the final best fitting models were used to compute the matching convolution kernel. Figure 12. Point-spread function of the SBC filters. The top left panels show the empirical PSF of the F125LP (left-hand side) and F140LP (right-hand side) filters in log scale. The bottom left panels show the relative difference map, (F125LP–F140LP)/F140LP, without any PSF matching on the left and with PSF matching on the right. Note that the 2D PSF models are only trustworthy (at a level) out to a radius of about 1.3 arcsec. The top right panel shows the surface brightness profiles of the two empirical PSFs with the shaded regions showing the errors per annulus, and the inset showing the inner 0.5 arcsec of the profile. The lower right panel shows the signal-to-noise


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

dex) that led us to speculate about the possibility that the assumption for young MC clusters to have metal contents similar to the mean galaxy present-day metallicities is justified for statistical purposes. Otherwise, when young clusters are studied to search for chemical abundance anomalies, light element abundance variations, binary fraction, extended main sequence turnoffs, among others, the knowledge of their actual metallicities could have an impact. This could be the case, for instance, of NGC 1844, NGC 1847, and NGC 330, for which Milone et al. ( 2013 ), Niederhofer et al. ( 2015 ) and Milone et al. ( 2018 ) adopted, respectively, more metal-rich metal abundances to show evidence of multiple populations. In order to see whether a better tracking of the split main sequences can be achieved, it would be worth trying to match their CMDs with theoretical isochrones with metallicities similar to those derived in this work. In the case of NGC 1850, a cluster with a large population of near-critically rotating stars, a slightly more metal-rich value has usually been adopted (Bastian et al. 2017 ). The existence of a spread in metallicity within the younger stellar populations of both MCs is well known. Piatti and Geisler ( 2013 ), using an homogeneous age/metallicity compilation, showed that the FWHM of such a scatter is 0.51 dex for the LMC and 0.32 dex for the SMC (see also Choudhury, Subramaniam Cole 2016 ; Choudhury et al. 2018 ); the MC cluster populations also exhibit a noticeable scatter at their younger end (see also Perren, Piatti Vázquez 2017 ). In this context, most of the present studied clusters are within the expected metallicity range, while others fall at the edge of the known metallicity distributions. This is the case of NGC 330, the most metal-poor young SMC cluster ([Fe/H] = −1.15 dex) so far. In the LMC, NGC 1847 resulted to be the most-metal poor young cluster ([Fe/H] = −0.91 dex) ever known, while NGC 1711 turned out to be at the metal-rich end of the LMC cluster’s metallicities ([Fe/H] = −0.06 dex). These relatively extreme metallicity values tell us that the gas out of which these young clusters were formed was not well mixed. Note that there has been speculations about the role of infall of unenriched (or less enriched) gas into the MCs leading to an unexpectedly large spread in cluster abundances at a relatively constant age (see e.g. Da Costa Hatzidimitriou 1998 ). We looked at the cluster positions in their respective host galaxies in order to search for any link of their derived metallicities with the chemical evolution histories of the MCs, particularly of those with more extreme values. Fig. 2 depicts with black points the spatial distributions in both MCs of all the clusters catalogued by Bica et al. ( 2008 ). The studied clusters are drawn with big filled circles. As a spatial reference, we have also included the areas defined by Harris and Zaritsky ( 2009 ) in the LMC main body (the bar is traced with a


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

in denser environments, for example, star clusters ( Varri et al. 2018 ) or the Galactic bulge, where thousands of NSs may be present (e.g. Fragione et al. 2018 ). The encounter velocities originating from SN kicks will be significantly higher than the virialised velocities that have been used in published simulations (e.g. Wang et al. 2020 ). In fact, they are closer to what would be expected for a high-velocity star in the Solar neighbourhood ( Laughlin Adams 2000 ). An estimate of the gravitational capture distance, assuming that the intruder can be bound in the centre of mass frame, is given by . This scales as where ‘I’ represents the impactor. For reference, the value for the lowest velocities in our simulations is r grav, BH ≈ 10 −3 pc and r grav, NS ≈ 2 × 10 −4 pc. For b BH, NS ≲ r grav , we found alterations in both the inclination and eccentricity of virtually all retained planets regardless of the incidence angle and encounter velocity (see Appendices B and C ). The most efficient captures for both scenarios occurred in the range 60° ≲ θ BH, NS ≲ 120°, with up to eight planets for b BH, NS ≲ 10 −5 pc and the lowest impact velocity (see f cap in Figs. 2 and 3 ). Eccentricities of the captured planetary orbits, e cap , were very high – around 0.8 for the BH and 0.65 for the NS. Fig. 3. Outcomes of the NS scenario for v NS = 10 km s −1 . For each impact parameter (coded by colours and symbols) and incidence angle (columns), we plotted the final distribution of semi-major axes, eccentricities, and inclinations of planets that were either retained by the Sun or captured by the NS ( top six rows , for each planet from Mercury ☿ to Neptune ♆). Bottom two rows : fraction of retained and captured planets. Each variation in the initial parameters was averaged over nine pre-evolved states of the SS, see Sect. 2 . Detailed plots for all v NS and θ NS are in Figs. C.1 – C.8 . There was a difference between the prograde ( θ BH, NS = 0°) and retrograde ( θ BH, NS = 180°) encounters with the SS in both scenarios. A low-velocity NS showed no directional preferences for planetary capture, but it was most destructive for a retrograde fly-by with b NS ≲ 10 −5 pc; in 60% of the cases, the SS did not survive and in the remaining 40% the Sun was left with only one terrestrial planet (see f ret and f cap in Fig. 3 ). In contrast, a low-velocity BH was generally more disruptive and also more efficient in capturing planets for a prograde encounter (see f ret and f cap in Fig. 2 ). The greatest difference between the NS and BH case was found in the change of the orbital inclinations of the retained planets, i ret , as the BH is more likely to completely flip the orbits of even massive planets. Based on the positions of the planets during the encounter, both intruders were able to capture planets on prograde, retrograde, or 90° orbits while approaching from θ BH, NS = 0° (see i cap ). It was, however, impossible for the NS to capture a retrograde planet


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T.M. and E.R. are supported by DOE grant DE-SC0015975. E.R. acknowledges additional support by the Sloan Foundation, grant FG-2016-6443. J.L.T. and R.H.W. acknowledge support of NSF grant AST-1211889. J.D., R.H.W., S.M., and M.R.B. received support from the U.S. Department of Energy under contract number DE-AC02-76SF00515. Y.Y.M. is supported by the Samuel P. Langley PITT PACC Postdoctoral Fellowship. This research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. Software: Python, Matplotlib (Hunter 2007 ), NumPy (van der Walt et al. 2011 ), SciPy (Jones et al. 2001 ), emcee (Foreman-Mackey et al. 2013 ), george (Ambikasaran et al. 2015 ), CAMB (Lewis Bridle 2002 ), CLASS (Lesgourgues 2011 ), Rockstar (Behroozi et al. 2013 ), GADGET (Springel 2005 ), 2LPT (Crocce et al. 2006 ).


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

in gas phase is still debated. In dark cores, only about 0.05% is locked in the S-bearing molecules detected at millimeter wavelengths (see the fractional abundances derived for S-bearing species towards the dark cloud TMC1-CP in Table 5 ). Unfortunately, most of the plausible major sulphur reservoirs such as S, HS, and S 2 are either not observable or very difficult to observe at millimeter wavelengths and one needs to trust to chemical models to estimate the exact amount of sulphur in the gas phase. It is widely accepted that most of the sulphur is locked in icy grain mantles. This is corroborated by the observations of S-bearing species in comets. In a recent compilation, Bockelée-Morvan Biver (2017) estimated that the S/O elemental ratio in the comet ice is about 1.5%, which is consistent within a factor of approximately four with the solar value, H 2 S being the main sulphur reservoir. Hot cores are compact warm regions where the icy mantles evaporate releasing the sulphur budget to the gas. Orion KL is the best-studied hot core, with full spectral surveys at millimeter and submillimeter wavelengths. In Table 5 , we show the abundances of sulphur species that have been derived in this prototypical hot core. Gas phase H 2 S is the main sulphur reservoir in this hot core and the elemental gas-phase sulphur abundance is ~ 1.6 × 10 −6 ( Crockett et al. 2014 ). Fuente et al. (2019) obtained a similar value for the sulphur gas phase abundance of ~10 −6 in the edges of the TMC1 molecular cloud. Table 5 Comparison of fractional abundances with observational templates. References. TMC1: Agúndez Wakelam (2013) ; Cernicharo et al. (2018) and references therein. Orion-KL: Tercero et al. (2010) ; Esplugues et al. (2014) ; Crockett et al. (2014) . Comets: Calmonte et al. (2016) ; Bockelée-Morvan Biver (2017) . Fig. 5 Abundances of NS + as a functionof N (H 2 ). Black pointscorresponds to the detections reported by Cernicharo et al. (2018) . Red points corresponds to the core and PDR positions in the Horsehead. The black solid line depicts a linear fit to the data. Based on the WHISPER survey, we have determined a significant inventory of sulphur species and their abundances in the Horsehead PDR. Only one H 2 S line has been observed and the estimated value of the H 2 S abundance (~0.3−5 × 10 −9 ) is hence uncertain. It seems clear, however, that the abundance of gaseous H 2 S is far from that observed in Orion-KL. One possibility is that a large fraction of H 2 S remains in the solid state. This is expected since the dust temperature in this PDR is around ~20–30 K in the PDR ( Goicoechea et al. 2009 ), which is below the sublimation temperature of H 2 S, ~80 K ( Jiménez-Escobar Muñoz Caro 2011 ). The detections of SO + and NS + suggest that a significant fraction of sulphur is in the form of S + in the outer layers of this cloud. Sulphur chemistry is still poorly known, and especially surface chemistry reactions need further understanding. Oba et al.


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We are grateful to our colleague P. Briand from the laboratory of mathematics LAMA of Université de Savoie Mont-Blanc for his kind help and for having provided us with a proof of the generalized central limit theorem. We also thank P. Mertsch who contributed by drawing our attention to the role of stable laws in cosmic ray physics.


O O B-Person I-Person O B-Person I-Person I-Person O O O O O O O O O B-Person O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Person O O O B-Organization O B-Grant O B-Grant O O O B-Survey O B-Survey O O O O O B-Organization I-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization O B-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Survey O O O B-URL O O B-Survey O O O O B-Collaboration I-Collaboration I-Collaboration O O O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization B-Telescope B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization B-Organization O B-Organization I-Organization I-Organization B-Organization B-Organization I-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization B-Organization I-Organization O B-Observatory I-Observatory I-Observatory I-Observatory O O B-Organization I-Organization I-Organization O O O O O O O B-Instrument O O O O B-Telescope O B-Organization O O B-Telescope I-Telescope B-Telescope O O O O O B-Organization I-Organization I-Organization B-Organization O B-Location O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O B-Location O O B-Organization I-Organization I-Organization O O O O O O O O O O O B-Software O O O B-Organization I-Organization I-Organization I-Organization O O O O B-Survey I-Survey I-Survey I-Survey O O O O B-Organization O B-Organization

We thank Jo Bovy and Timothy D. Brandt for insightful discussions on statistical modeling of our results. C.P. acknowledges financial support from the Natural Sciences and Engineering Research Council of Canada. D.J.S. is supported by NSF grants AST-1412504 and AST-1517649. Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England. The SDSS Web Site is http://www.sdss.org/ . The SDSS is managed by the Astrophysical Research Consortium for the Participating Institutions. The Participating Institutions are the American Museum of Natural History, Astrophysical Institute Potsdam, University of Basel, University of Cambridge, Case Western Reserve University, University of Chicago, Drexel University, Fermilab, the Institute for Advanced Study, the Japan Participation Group, Johns Hopkins University, the Joint Institute for Nuclear Astrophysics, the Kavli Institute for Particle Astrophysics and Cosmology, the Korean Scientist Group, the Chinese Academy of Sciences (LAMOST), Los Alamos National Laboratory, the Max-Planck-Institute for Astronomy (MPIA), the Max-Planck-Institute for Astrophysics (MPA), New Mexico State University, Ohio State University, University of Pittsburgh, University of Portsmouth, Princeton University, the United States Naval Observatory, and the University of Washington. Based in part on observations obtained with MegaPrime/MegaCam, a joint project of CFHT and CEA/IRFU, at the Canada–France–Hawaii Telescope (CFHT) which is operated by the National Research Council (NRC) of Canada, the Institut National des Science de l’Univers of the Centre National de la Recherche Scientifique (CNRS) of France, and the University of Hawaii. This work is based in part on data products produced at Terapix available at the Canadian Astronomy Data Centre as part of the Canada–France–Hawaii Telescope Legacy Survey, a collaborative project of NRC and CNRS.


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We acknowledge the support from the ERC Consolidator Grant funding scheme ( project STARKEY , G.A. n. 615604). L.G. and T.S.R. acknowledge partial support from PRIN INAF 2014—CRA 1.05.01.94.05.


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

by each successive refinement splitting a cell into two, and a refinement level of RL leads to cell sizes decreased by 1/2 RL . The maximum value of RL is taken as 13. This can lead to very small cells, with a commensurate decrease in the time step required for numerical stability. However individual loops can be simulated for reasonable real times (a few hours). Further details of the HYDRAD numerical method, including the finite difference schemes used, can be found in Appendix A.2 of BC13 and references therein. Such a “brute force” method is unlikely to be a viable way of running multi-dimensional codes. To this end we have developed an alternative approach, tested on one-dimensional problems ( Johnston et al. 2017a , b ), that treats the lower TR as an unresolved layer. By integrating the energy equation across this layer, and imposing a closure condition, we are able to provide rapid solutions to 1D problems with an accuracy that compares well with HYDRAD results. The details are found in Johnston et al. (2017a) , and we refer to this as the UTR method. It is incorporated into a one-dimensional version of the Lagrangian remap (Lare) code whose computational details are discussed in Arber et al. (2001) , referred to as “LareJ”. 2.2. Influence of numerical resolution We start by exploring the effect of numerical resolution on TNE cycles in coronal loop models. We model a coronal loop of total length 180 Mm with a small chromosphere attached to each end and select the largest grid cells in our calculations to have a width of 1 Mm. Thus, at the highest refinement level, the minimum cell width is 122 m. 2.2.1. Steady footpoint heating: HYDRAD simulations Representative of the conditions necessary to induce TNE in coronal loop models (e.g. Müller et al. 2003 ; Antolin et al. 2010 ; Peter et al. 2012 ; Mikić et al. 2013 ; Froment et al. 2018 ), we first consider the case of steady footpoint heating where the spatial profile is given by the sum of two Gaussian peaks (one at each loop leg), each defined as, These peaks are localised between the base of the corona and base of the TR with a maximal value at z = 12.5 Mm and we take z H = 1.5 Mm as the length scale of heat deposition. This is shown in Fig. 1 as the blue curve. We note that in this part of the paper a small spatially uniform background heating term is always present so that Q ( z ) = Q bg + Q H ( z ). This is commonly done in 1D loop models to ensure that T and n remain positive: here Q bg = 6.8682 × 10 −6 J m −3 s −1 and the effect of including a range of values of Q bg will be examined in Sect. 2.4 . Moreover, in order to avoid unrealistic pile up of condensations at the loop apex due to the symmetry of the model, the spatial symmetry of the heating profile is perturbed by adding a small enhancement of 0.4% to the Gaussian peak at the left-hand leg of the loop. The initial state of the loop is determined using just Q bg , leading to a temperature of order 1 MK. The footpoint


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Based on observations carried out as part of the Large Program ASAI (project number 012-12) with the IRAM 30 m telescope. IRAM is supported by INSU/CNRS (France), MPG (Germany) and IGN (Spain). This work was supported by the CNRS program ‘Physique et Chimie du Milieu Interstellaire’ (PCMI) and by a grant from LabeX Osug@2020 (Investissements d'avenir – ANR10LABX56). EM acknowledges support from the Brazilian agency FAPESP (grant 2014/22095-6 and 2015/22254-0 ). IJ-S acknowledges the financial support received from the STFC through an Ernest Rutherford Fellowship (proposal number ST/L004801/1 ).


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

evolution. The transition occurs at the same time as light curve evolves on to the linear tail. Similar evolution, across a similar time-scale, is seen in Type IIb SN 2008bo (Bianco et al. 2014 ), with the sole difference over the first 120 d being that SN 2008bo has an initial blueward evolution until ∼12 d after explosion that is not seen in SN 2018gjx. This blue/red/blue evolution is commonly seen in SE-SNe (Prentice et al. 2016 ). However, SNe with strong shock-cooling tails in their light curves (e.g. SNe 1993J, 2013df, 2016gkg; Richmond et al. 1994 ; Morales-Garoffolo et al. 2014 ; Tartaglia et al. 2017 ) evolve straight from blue to red at these early times, and it is to these that SN 2018gjx is most similar. Comparatively, SNe Ibn show great diversity in their colour evolution. SN 2015G is most like SN 2018gjx and is plotted using the estimated explosion date of 3 d prior to the discovery date (2015-03-23.778, but see Shivvers et al. 2017b , for a discussion on t exp ). SN 2006jc displays an inverted evolution to that of SN 2018gjx, and two other SNe Ibn LSQ13ddu (Clark et al. 2020 ) and SN 2014av (Pastorello et al. 2016 ), appear to follow the trend of blue to red, albeit from a bluer starting point. 3.2 Pseudo-bolometric and absolute <italic>r</italic>-band light curves An optical pseudo-bolometic light curve was constructed by converting the dereddened multicolour photometry to flux and building spectral energy distributions (SEDs) for each date. These SEDs were then integrated over 4000−10 000 Å, covering the effective range of the griz bandpasses and converted to pseudo-bolometric luminosity using a fixed luminosity distance of 35 Mpc. This method is described in more detail in Prentice et al. ( 2016 ). The pseudo-bolometric light curve of SN 2018gjx is shown in Fig. 4 in comparison with SNe IIb and SNe Ibn. It is a requirement of the bolometric light-curve methods that the transients are observed in BVRI, gri , or equivalent and while some interpolation and extrapolation can be done to account for missing data, we find that many SNe Ibn are only well-sampled in one or two bands, which limits our comparison sample. The peak luminosity of ∼1.4 × 10 42 erg s −1 places the first peak in a similar range to that of the SNe IIb that show shock-cooling tails. After this, the light-curve evolution diverges and fails to rise a second peak. It instead tracks the evolution of SN 2008bo, although with a steeper linear decline of ∼0.026 mag d −1 . The decline is steeper than for most SNe IIb (Prentice et al. 2019 ). Figure 4. Upper panel: The pseudo-bolometric light curve of SN 2018gjx compared with SNe IIb. The unusual SN IIb 2008bo has a remarkably similar light curve after 10 d. Lower panel: Absolute R / r LCs of SNe Ibn (squares) and SNe IIb (diamonds) in comparison with SN 2018gjx (black stars). Type Ibn SN 2015G (orange), Type IIb SN 2008bo (red), and Type IIb SN 2018ivc (gold) show similar evolution. The dramatic decline of SN 2006jc is


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A.T. is supported by the DFG Emmy Noether grant Hi 1495/2-1 and the Bonn-Cologne Graduate School of Physics and Astronomy. I.G. would like to thank the science department and “International Research Fellow” programme of ESA-ESTEC in Noordwijk for the partial support during the completion of this paper. A.C.S. acknowledges the receipt of CNPq/BJT-A fellowship 400857/2014-6. The authors would like to thank Sophia Lianou for kindly providing us with their photometic tables and measurements of the IKN field RGB stars metallicities. We are also grateful for the helpful discussions with Søren Larsen and the anonymous referee. This research made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration. We acknowledge the use of the HyperLeda database ( http://leda.univ-lyon1.fr ).


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We thank the anonymous referee for helpful comments. We thank Katherine Alatalo and David Meier for helpful discussions. Y.C. and T.W. acknowledge support from NSF through grants AST-1139950 and AST-1616199. E.R. is supported by a Discovery Grant from NSERC of Canada. Support for CARMA construction was derived from the Gordon and Betty Moore Foundation, the Eileen and Kenneth Norris Foundation, the Caltech Associates, the states of California, Illinois, and Maryland, and the NSF. CARMA development and operations were supported by funding from NSF and the CARMA partner universities.


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion O O O O O B-CelestialObject O B-CelestialObject O O O O O O O O O B-CelestialObjectRegion O O O O O O O O O B-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

At every rotational phase, a cross-section – or ‘great circle’ – is defined by a west longitude and an east longitude 180° to the east. The first step in calculating the cross-sectional area is finding the distance from the centre of the planet to every point on the projected silhouette. This distance might not necessarily be the elevation at the point on the great circle because the silhouette could be dominated by a taller point that sits on a longitude that isn’t used to define the great circle. In other words, a taller point might be behind or in front of the point on the great circle from our point of view. To account for this projected geometry issue, we first define an ‘α angle’, which is the number of degrees a planet would have to rotate in order for its tallest feature to disappear below the horizon after it appears on the great circle. For example, Everest is the tallest mountain on Earth, and Earth would have to rotate 32 from the time when Everest is on the great circle before the tip of Everest would no longer appear in the planet’s silhouette. Here, l is the latitude of the highest point on the planet and h is the elevation of the highest point. For both the west and east longitude lines used to define the great circle, we step through in latitude, and at every latitude, we find the maximum projected height. The projected height of point A is where d is the actual elevation of point A and β is the angle between A and the point along the great circle. β ranges from −α to +α. The projected heights give us the distances from the centre of the planet to every point along the silhouette. The area of the silhouette can then be found using trapezoidal integration. Once the planet’s cross-sectional area is found, the transit depth can be calculated using equation ( 1 ). 3.5 Defining scatter The projected geometry method described above provides a list of transit depths for every rotational phase, so σ B is easily defined as the std of all of the depths. We use these σ B values to derive the general relationship between B an σ B in Section 3.6 . In the Earth’s case, a transit would last for up to approximately 13 h – more than half a rotational period – and thus we would observe the full range of phases necessary to calculate σ B . However, other transiting planets may not last long enough for us to observe a sufficient fraction of a planet’s rotation. Instead, individual transits will show various ranges of rotational phases, which may or may not overlap depending on the planet’s rotational period. Unfortunately, this means that we might not observe every rotational phase. When this is the case, the σ B we find in our observations may be less accurate than the ‘true value. In this section, we merely describe the two ways to evaluate σ B . The first way is to find the average depth of each individual transit (see Fig. 4 ), and take the std of those averaged depths. The second way is to fold the light curve and take the std of the


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S.H.L. acknowledges support from NASA grant NNX11AK61G. C.J.N. acknowledges support provided by NASA through the Einstein Fellowship Program, grant PF2-130098. R.G.M.'s support was provided under contract with the California Institute of Technology (Caltech) funded by NASA through the Sagan Fellowship Program. We thank the referee for suggesting improvements in the description of the results.


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have been active for . The projection has a depth of and is centred on the BH. This disc galaxy provides the initial conditions for simulations with a disc galaxy in an NFW halo. In the left-hand panel of Fig. 12 , we plot the mass of the baryonic components, i.e. gas, stars, metals, and dust, of the halo with r 200 as a function of time. After , a stellar disc with a mass has formed in the xy plane of the halo with a radial extent of . Over the first , a dust mass rapidly forms, after which the dust mass grows much more slowly and the final halo has a dust mass . The build-up of gaseous metals initially occurs at a slower rate, but after the dust and metal content of the halo is roughly similar, with a cumulative dust-to-metal ratio of 1.15 within r 200 . Figure 12. Properties of the initial disc galaxy. Left : Gas (red solid), stellar (blue dash–dotted–dotted), metal (purple dash–dotted), and dust (pink dashed) mass components with r 200, crit . The global halo properties are reasonable for a disc galaxy. Centre : Radial dust mass surface density profile for the relaxed NFW halo with D = 0.01 (blue dash–dotted–dotted), the NFW halo with a disc galaxy and D = 0.01 (light purple dash–dashed), and the NFW halo with a disc galaxy and self-consistently modelled dust (red solid). Right : Dust-to-gas ratio radial profile as a function of time for the NFW halo with a central disc galaxy and self-consistently modelled dust. We plot t = 0.5 (blue dash–dotted–dotted), 1.0 (purple dash–dotted), 1.5 (light purple dash–dashed), 2.0 (pink dashed), and (red solid). Dust is confined to the disc due to the lack of feedback and satellite mergers during its formation. The formation of the disc galaxy leads to a contraction of the halo. The central panel of Fig. 12 shows the radial dust surface density profile, where the halo has been projected along the z -axis of the simulation (i.e. the galaxy is face on). For the initial NFW halo with a constant dust-to-gas ratio D = 0.01, the surface density of the dust decreases strongly with radius from at to 5 × 10 −4 at r 200 . After the formation of the disc, still assuming D = 0.01, central dust surface density of dust at increases to . However, due to material condensing to form the disc galaxy the dust surface density is lower than the initial NFW halo beyond . Modelling the formation of dust we find that its central surface density increases still further, reaching a dust surface density of at . The lack of feedback during the formation of the disc galaxy means that we achieve higher than typically observed central dust densities. In addition, the idealized nature of the simulation results in the circumgalactic medium (CGM) of the halo being free from dust because dust is not produced in the CGM but instead is acquired through in-falling satellites. The evolution of the dust-to-gas ratio radial profile during the formation of the disc galaxy is shown in the right-hand panel of Fig. 12 . The dust initial forms in a


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

in the literature. However, as time progresses the action is conserved with less accuracy, as indicated by the increase of the standard deviation up to the value of 50% after 6 Gyr of evolution. This also holds for a subset of stars that radially migrates by resonant scattering at corotation. These results have implications for the vertical structure of the disk when stars radially migrate to the outer part of the disk. In this model stars migrating outwards are a heavily biased subset of stars with preferentially low vertical velocity dispersion. Thus, extreme migrators outwards are characterized by having a have small amplitude of their vertical excursion, independent of the conservation of the vertical action. In the MW-like galaxy model, disk 2 , the bar formation causes large angular momentum changes, with significant in-plane and vertical heating. Thus, in the presence of the formation of the bar and combined with significant disk heating, our results show that the vertical action cannot be assumed a constant of motion. Indeed, in this case the fractional changes in the estimates of the action for a set of stars progressively increase by time, with a standard deviation that approaches 80% after 6 Gyr of disk evolution. If confirmed, this result casts doubts on the possibility of predicting the vertical structure of the disk for a set of extreme migrators outwards, by assuming that their vertical action is conserved. APPENDIX MEASURING THE VERTICAL ACTION The vertical action j z is defined as:where z and v z describe the position and velocity along the orbit, respectively. If the potential is nearly axisymmetric this quadrature can be calculated using the algorithm described in (Solway et al. 2012 ). We adopted here a similar prescription as explained below: 1. At a given time t the gravitational potential Φ, its radial gradient , and vertical gradient are computed on a polar grid centered at the minimum of the (fixed) halo potential. The grid dimension is , with the cylindrical coordinates ranging as follows: (logarithmically spaced), , and , where is the softening length. Note that these ranges span six times the scale-length and twenty times the scale height. The potential is numerically calculated at each node of the grid using a tree algorithm that includes up to the quadrupole contribution. We do not impose a symmetry about the galactic mid-plane, in fact, modest asymmetries that can develop over time are naturally captured by the grid. 2. At each point ( R , z ) the potential is calculated by averaging over the azimuthal points:Equivalent expressions are derived for and . This approximation relies on the fact that the potential is nearly axisymmetric, this however may not be the case after if a bar grows at the center of the galaxy. Once the potential is computed at t time, for each star particle the following quantities are evaluated: the vertical angular momentum L z , the guiding radius as the solution to the equation:and the