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

beappropriate for an optically thin spectral line with a given formation temperature). At a temperature of 6.3 kK we already see low lying loop structures connecting magnetic field of opposite polarities. There is a multitude of these low lying, short loops but much of the plasma at that temperature is also distributed in structures that are less loop-like. At 10 kK most of the lowest lying loops have disappeared and we have fewer, more pronounced loops that reach higher. At higher temperatures we basically see the same loops, all the way up to 316 kK () when a new set of hotter, higher lying loops start to appear. These loops dominate up to about 1 MK. The maximum temperature in this simulation is 2.2 MK and this hottest plasma is located in loops that do not reach as high as the loops with temperatures up to 1 MK. The lower lying loops with temperatures below 300 kK evolve on shorter timescales than the hotter loops and give rise to the “Unresolved Fine Structure” (UFS) loops discussed in Hansteen et al. (2014) . Fig. 13 Probability density function (PDF) of the electron density as function of height at s ( upper panel ) and at s ( lower panel ). Note the logarithmic electron density scale. 3.5. Ionization balance The simulation includes the effects of non-equilibrium ionization of hydrogen, see Leenaarts et al. (2007) . Figure 13 shows the electron density as a function of height for two times, just 10 s after the non-equilibrium ionization of hydrogen was switched on at s and for the first published snapshot, at s. The non-equilibrium hydrogen ionization leads to much higher electron density in the cool pockets at 0.5–2 Mm and also higher electron densities up to 3.5 Mm height. There is not much change with time of this probability density function after s. 3.6. Velocity field Spectral lines are normally observed to be broader than what the thermal broadening of the opacity profile would give. An extra free parameter, called microturbulence, is often introduced in 1D semi-empirical models to account for this broadening. The “micro” in the name comes from the fact that this parameter is introduced as an extra broadening of the opacity profile, acting in exactly the same way as thermal broadening. This would be a physically correct description in the limit of zero length-scale for the velocity field. It is also often necessary to introduce a second free parameter to account for the observed lineshape. This is called macroturbulence and is equivalent to a Gaussian convolution of the emergent intensity profile (rather than a convolution of the opacity profile as is the case for microturbulence). Realistic 3D radiation hydrodynamic simulations of the solar photosphere give line profiles that are close to the observed profiles without the addition of extra free parameters – the non-thermal broadening comes from Doppler shifts arising from the convective flows and oscillations (e.g., Asplund et al. 2000 ). Also spectral lines formed in the


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

because their terminal velocity increases due to the increasing gravitational field strength at small planetary radii. Only bolides in a very limited size range are large enough that they do not reach the sublimation temperature and yet small enough for their low terminal velocities to render them immune to frictional ablation. Given the uncertainties and limitations (for example, of excluding fragmentation and lateral spread) that enter our modelling, this narrow range may indeed be either somewhat smaller or simply non-existent in a scenario with more modes of ablation. If impacting planetesimals move with hypervelocities beyond the escape velocity of Jupiter of approximately 60 km s −1 , some high φ i bolides can ablate and still escape the upper outer envelope beyond a normalized altitude of 1. Fig. 6 shows the case of bolides impacting at right angles to the local zenith to 126 physical seconds. This time value is 10 times the time required for vaporisation of a 30 m bolide travelling at 100 km s −1 and is a good benchmark time to gauge when all highest velocity planetesimals either escape the system or completely ablate. Planetesimals capable of escaping the Jovian envelope are represented by black stars. Bolides of sizes 30–200 m with ∼80–100 km s −1 completely ablate upon impact, whilst larger bolides with these high kinetic energies manage to escape the Jovian radius (e.g. a 1 km planetesimal retains ∼0.60 of its initial mass in the process). At future times, the region of the plot involving velocities greater than the escape velocity evolves little whilst the low-velocity regime is subject to progressive ablation as in Fig. 5 . The former region does not evolve because we do not model the re-entry of planetesimals that may fall back to the planet due to their decreased velocities. Planetesimals of velocities exceeding Jovian escape offer chemical depositions that should be observable perhaps even in the atmosphere of such planets given the proximity of the 1 bar level and mixing processes. Figure 6. Mass ablation fraction to 126 s for planetesimals incident tangentially with initial velocities exceeding that of Jovian escape. Black stars represent escaped planetesimals. We see that planetesimals of velocities exceeding the Jovian escape should offer chemical depositions that should be observable at the 1 bar level. 5 DISCUSSION Our model is a simple description of planetesimal dynamics with implications for the enrichment of Jovian-like exoplanetary envelopes. There is consequently extensive potential for further improving the sophistication of our model and we here discuss a few examples of potential refinements. First, Nellis ( 1997 ) highlights that there is indeed a continual process of molecular dissociation into a metallic plasma; there is thus no real distinct boundary between molecular layers and monoatomic conductive hydrogen and the band-gap separation is bridged continuously with increasing pressure rather than jumping


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

with Equation ( 5 ). From Figure 1 it is expected that data points at high enough accelerations do not have any sensitivity to e . Indeed, for data points with −10.3 x 0 −9 the distribution of Δ ⊥ gives a null result. Similarly, for galaxies with , the distribution of e (median value) gives a null result. Figure 4. Distributions of Δ ⊥ and e from fitting Equation ( 5 ) to the SPARC galaxies. The top panels show the distributions of orthogonal residuals Δ ⊥ for three acceleration bins from the MCMC results shown in the middle column of Figure 3 . The mean of the distribution is displaced from zero for lower acceleration bins, indicating declining RCs. The bottom panels show the distributions of the e values fitted to the individual galaxies binned by the median values of x 0 within the galaxies. As expected, for the galaxies in the high acceleration bin (), the data do not have any sensitivity to e and so the distribution has a mean of ∼0. For lower acceleration bins the distributions are shifted to positive e with high statistical significance, indicating a preference for the EFE. The broad distributions are due to the broad individual posteriors on e . Data points at low enough accelerations will have sensitivity to e and distributions with nonzero mean value are expected from Figure 3 . For data points with x 0 −11.3 the distribution of Δ ⊥ has a mean of −0.061 ± 0.008 (a bootstrap error) which is statistically significant at more than 7 σ . For a much larger number of data points with x 0 −10.3, Δ ⊥ has a smaller deviation of −0.035 ± 0.003, but the statistical significance of the deviation is more than 11 σ . Figure 5 shows individual e values and their uncertainties for a subset of 113 galaxies with median . Due to the large uncertainties on e , some galaxies can occasionally return negative values. However, the median value of e is 0.052 ± 0.011 (bootstrap error), which represents ≈5 σ detection of positive e . This value is statistically consistent with the median environmental gravitational field for these galaxies ( (bootstrap error)). Furthermore, based on the robust binomial statistic with equal probabilities for e > 0 and e 0, 78 cases of e > 0 out of 113 is 4 σ away from the expected mean of 56.5 cases. Figure 5. Statistical detection of the EFE. The median values of e from rotation-curve fits are compared with e env values from the large-scale galaxy environment (Desmond et al. 2018 ) for 113 galaxies with . The heat map considers the posterior probabilities of individual e measurements. The distributions of e and e env are shown by the top and right histograms. The median value of e is clearly offset from zero, indicating a 5 σ statistical detection of the EFE. The value of is statistically consistent with (see also Appendix B ). The individual galaxies considered in Figure 2 are indicated: for the golden galaxies at exceptionally high e env values, e is significantly different from zero at 8 σ (NGC 5033) and 11 σ (NGC


O O O O O O O O O O O O O O O O O O O B-Person I-Person B-Person I-Person O B-Person I-Person O O O O O O O O O O O O O O O B-Observatory O B-Identifier B-Identifier O B-Identifier B-Observatory O O O O B-Observatory O O O O B-Organization B-Location O B-Organization B-Location O O B-Organization B-Location O B-Organization O B-Organization B-Location O B-Organization B-Location I-Location I-Location O O O O B-Location I-Location I-Location O B-Observatory I-Observatory I-Observatory O O O B-Observatory B-Organization O B-Observatory O O O O O O O O B-Observatory O O O B-Observatory I-Observatory I-Observatory I-Observatory O B-Observatory O O B-Proposal O O O O O O B-Software O O B-Organization I-Organization I-Organization I-Organization O O O O B-Collaboration I-Collaboration O O O O O O B-Organization I-Organization I-Organization I-Organization O O B-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship B-Person O O O O B-Organization I-Organization I-Organization B-Organization O O B-Location I-Location B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant B-Person O O O O O O B-Organization I-Organization I-Organization O O O O O B-Fellowship I-Fellowship B-Fellowship B-Person O O O O B-Organization I-Organization B-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship I-Fellowship B-Person O O O O B-Location I-Location B-Grant I-Grant I-Grant O O O B-Grant B-Organization B-Grant I-Grant I-Grant B-Person O O O O B-Organization I-Organization I-Organization B-Grant I-Grant I-Grant

Acknowledgements The authors thank the anonymous referee for very helpful comments that improved this paper. The authors further thank A. Ferrara, R. Bouwens and N. Reddy for very helpful discussions related to this work. This paper makes use of the following ALMA data: ADS/JAO.ALMA#2013.1.00151.S, ADS/JAO.ALMA#2013.1.00034.S and ADS/JAO.ALMA#2012.1.00523.S. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada) and NSC and ASIAA (Taiwan) and KASI (Republic of Korea), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ. Based on data products from observations made with ESO Telescopes at the La Silla Paranal Observatory under ESO programme ID 179.A-2005 and on data products produced by TERAPIX and the Cambridge Astronomy Survey Unit on behalf of the UltraVISTA consortium. This work was supported by the Swiss National Science Foundation through the SNSF Professorship grant 157567 ‘Galaxy Build-up at Cosmic Dawn’. ES acknowledges funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 694343). BG gratefully acknowledges the support of the Australian Research Council as the recipient of a Future Fellowship (FT140101202). MTS acknowledges support from a Royal Society Leverhulme Trust Senior Research Fellowship (LT150041). VS acknowledges support from the European Union's Seventh Frame-work programme under grant agreement 337595 (ERC Starting Grant, ‘CoSMass’). OLF acknowledges support from the European Research Council Advanced Grant ERC-2010-AdG-268107-EARLY.


O O B-Person I-Person O B-Person I-Person O O O O B-Telescope O B-Person I-Person I-Person O O O O O B-Person I-Person B-Person I-Person O B-Person I-Person O O O O O O O O O O O O O O O O O B-Person O B-Person O O O B-Organization O B-Grant O B-Telescope O B-Grant B-Grant O B-Grant O O B-Organization I-Organization I-Organization O B-Grant B-Person I-Person B-Person I-Person O O O O O B-Organization I-Organization I-Organization O O B-Grant O B-Telescope O B-Software B-Citation I-Citation O B-Software B-Citation I-Citation O B-Software B-Citation I-Citation I-Citation I-Citation O B-Software B-Citation I-Citation I-Citation I-Citation O B-Software B-Citation I-Citation O B-Software B-Citation I-Citation I-Citation O B-Software B-Citation I-Citation O

We thank Alberto Krone-Martins and Lennart Lindegren for expert advice on Gaia , Floor van Leeuwen for advice about astrometry, and Fred Adams, Michael Grudić, and Anushree Sengupta for useful feedback on the article. We would also like to thank the referee for helpful comments. E.D.F. and K.V.G. are supported by NASA grant NNX15AF42G and Chandra grants AR7-18002X, GO7-18001X, and G06-17015x, and the Chandra ACIS Team contract SV474018 (G. Garmire L. Townsley, principal investigators) issued by the Chandra X-ray Center under contract NAS8-03060. Facility: Gaia. Software: astro (Kelvin 2014 ), celestial (Robotham 2016 ), MVN (Korkmaz et al. 2014 ), R (R Core Team 2018 ), relaimpo (Grömping 2006 ), spatstat (Baddeley Turner 2005 ), TOPCAT (Taylor 2005 ).


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ACKNOWLEDGEMENTS We thank Indranil Banik and Tim Clifton for helpful discussions. CP has been supported by an STFC studentship.


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

the LAEs in each band (AB); (4) lensing magnification factors derived in Shu et al. ( 2016c ) for the first four lensed LAEs, Marques-Chaves et al. ( 2017 ) for BG1429+1202, and in Section 3 for BG1501+3042; (5) stellar UV continuum slope (equation 2 ), UV dust extinction (AB mag, equation 3 ), and colour excess of the stellar continuum assuming the Reddy et al. ( 2015 ) attenuation curve; (6) observed flux (units of 10 −16 erg s −1 cm −2 ), rest-frame equivalent width (Å), and full width at half-maximum (km s −1 ) of the Lyα line; (7) centroid velocity of Lyα and ISM absorption lines (average) relative to the systemic redshift (km s −1 ); (8) low-ISM and H i covering fractions using the depth of the average absorption line profile of ISM lines (Si ii 1260 Å, C ii 1334 Å, and Si ii 1526 Å) and using the relation of Gazagnes et al. ( 2018 ), respectively; (9) intrinsic UV absolute magnitudes (AB) and star formation rates (M ⊙ yr −1 ; equation 4 ); (10) intrinsic Lyα luminosity (units of 10 42 erg s −1 ) and star formation rates (M ⊙ yr −1 ; equation 9 ); and (11) Lyα escape fraction. a The ACAM/WHT i -band data of BG0201+3228 are affected by a high background level. The projected separation between the centroids of the two components in the source plane is about 0.46 ± 0.06 arcsec which at z = 2.645 corresponds to 3.8 ± 0.6 kpc for the adopted cosmology, suggestive of a close interacting/merging system. Nevertheless, we cannot confirm unambiguously the merging scenario as no velocity offset between the lensed images ‘A’ and ‘B’ is clearly detected in the available spectrum (with a resolution of ≃ 450 km s −1 FWHM). The sources have effective radius kpc and kpc. 4 RESULTS FROM IMAGING DATA 4.1 Photometry As seen in Fig. 1 the morphology of the LAEs in this sample consists of complex arc-like features with multiple lensed images seen in the observer plane. Given the typical ∼0.8 arcsec FWHM seeing of the GTC, WHT, and CFHT images, there is light contamination from the foreground lens galaxies. In order to perform a clean photometry of the lensed images, we use the two-dimensional fitting program galfit (Peng et al. 2002 , 2010 ) to model and substract the light distribution of the foreground lens (and in some cases additionally nearby objects). We use Sérsic profiles centred at the centroids of each LRG light emission allowing only two pixels freedom (∼0.5 arcsec). For the four lensed LAEs with HST imaging, we use the models of the foreground lens presented in Shu et al. ( 2016c ) as priors in our modelling (i.e. effective radius, minor-to-major axial ratio, and major-axis position angle). Nearby stars were used as PSF models. We further use SExtractor (Bertin Arnouts 1996 ) to measure the magnitudes in each band. To do so, we use aperture photometry using apertures with diameters of 2.5 times the FWHM of the PSF. Aperture photometry was performed for compact lensed morphologies, such as the lensed images of BG0755+3445, BG1429+1202 and the


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

line), along with the combined contribution (black dashed line) as given in van Soelen et al. ( 2012 ). A 33,000 K blackbody distribution is plotted for comparison (blue dashed line). 3. Gamma–Gamma Absorption Gamma-ray photons emitted in binary systems are subject to γγ absorption as they pass through the star’s photon field (see, e.g., Dubus 2006 ). The interaction of a γ -ray photon with a low-energy photon can result in electron–positron pair production (Gould Schréder 1967 ), if the energy exceeds the threshold condition for pair production, which is given bywhere and denote the photon energies of the target low-energy photon and the γ -ray photon, respectively, normalized to the electron rest-mass energy, i.e., , and θ is the interaction angle between the two photons. The minimum threshold occurs for a head-on collision (), and for a 1 TeV gamma-ray photon this will require photons with a threshold frequency ofwhich is within the mid-IR regime (where the disk is the primary photon source; Figure 2 ). The γγ optical depth is given by (Gould Schréder 1967 )where l is the distance over which the γ -ray photon travels, , , and is the number density of the low-energy target photons. Here, is the γγ cross section (Jauch Rohrlich 1976 ),whereand is the Thomson cross section. The maximum γγ cross section occurs when the energy of the interacting photons is twice that of the energy threshold (Equation ( 8 )). This implies that for TeV γ -ray photons the γγ interaction is a maximum for IR photons at a frequency We treat the two components of the target radiation field (stellar radiation and circumstellar disk radiation) separately and numerically calculate the γγ optical depth of both components for a γ -ray photon traveling in the direction of the observer. The total optical depth is given by the sum of the optical depths of the two components. Figure 3 shows the optical depth for a γ -ray photon with an energy of 1 TeV as a function of time from periastron. As expected, the γγ optical depth due to the photons from the disk is lower than that due to the star but still results in a decrease of the flux at TeV energies. The total decrease of the flux at 1 TeV due to γγ absorption may reach ∼60%. For the geometrical configuration used in our calculations (see Section 2.1 ) the maximum absorption due to the disk is at ≈4 days prior to periastron and that due to the star is at ≈2 days before periastron. Figure 3. The γγ optical depth of the Be star’s radiation field as a function of time around periastron for a 1 TeV γ -ray photon. The blue dashed line denotes the stellar component, the red dot-dashed line denotes the circumstellar disk component, and the combined effect is shown by the solid black line. 4. TeV Emission We assume that the TeV emission from PSR B1259-63/LS 2883 is produced by relativistic particles accelerated at the termination shock that occurs between the pulsar and stellar winds. The location of the termination shock depends on the


O O O O O O O O O O B-Database O O O O B-Organization B-Location B-Location O B-Archive I-Archive I-Archive I-Archive I-Archive I-Archive I-Archive B-Archive O O B-Organization B-Organization I-Organization I-Organization I-Organization B-Database I-Database I-Database B-Database O O O O B-Organization O O O B-Organization O B-Grant

This research has made use of data obtained from the SIMBAD data base operated at CDS, Strasbourg, France; the High Energy Astrophysics Science Archive Research Center (HEASARC), provided by NASA's Goddard Space Flight Center NASA/IPAC Extragalactic Database (NED). The authors acknowledge the ASI financial support via ASI–INAF grant 2013-025-R.0.


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

novel prediction for the scatter in the mass in the stellar halos. Upcoming surveys (e.g., van Dokkum et al. 2014 ) of stellar halos will help to constrain this picture. The scatter of the SMHM relation contains valuable information on the galaxy formation process. It deserves careful consideration in both observations and simulations in the future. At the high-mass end (), the scatter is a generic consequence of the hierarchical assembly. Different simulations should be able to produce consistent scatter of the SMHM relation in this mass range. At lower halo mass () the scatter gradually becomes dominated by baryonic processes involved in the in situ buildup, and has potentially more constraining power on the underlying theory. Two different processes, in situ and ex situ growth, are needed to produce the apparent flat scatter in the SMHM relation. However, the similar magnitude of the observed scatter at the low and high-mass end is likely a coincidence. Other works (e.g., Boylan-Kolchin et al. 2012 ; Garrison-Kimmel et al. 2014 ; Dutton et al. 2015 ; Sawala et al. 2015 ) have shown that at the regime of dwarf galaxies, the scatter of the SMHM relation may be much larger than that in more massive systems. More stringent observational constraints on the mass dependence of the scatter would be valuable. We end this section by highlighting several caveats and areas for future improvement. The Bolshoi simulation has a limited resolution (one particle mass ), so halos with mass smaller than may not be properly described in the Bolshoi simulation. As shown in Figure 1 , a fraction of satellite galaxies are possibly affected by this limited resolution. The result for host halos at the low-mass end () should be treated with caution. However, as discussed earlier, since the stellar component in such halos should be very small, based on the SMHM relation, this should only have a small effect on our result. Moreover, we adopt a simple assumption that when a subhalo disrupts, all of its stellar content is accreted to the host halo, while in reality, the accretion of stellar mass could be delayed (Wetzel White 2010 ). We also do not distinguish between the stellar mass in the central galaxy and that in the ICL. Since most observations only include the stellar mass measurement of the central part of the host halo, a direct comparison with observations should also be treated with caution. The scatter in the SMHM relations observed should be roughly the quadratic sum of the intrinsic scatter discussed above and the measurement error. Behroozi et al. ( 2010 ) carefully studied different uncertainties in the SMHM relation. The authors included statistical uncertainties in the stellar mass function, cosmological parameters, and the uncertainty within the methodology to construct the SMHM relation, and revealed a ∼0.07 dex (and ∼0.12 dex) observational uncertainty at z = 0 (and z = 1). As shown in Figure 8 , we compare this with the observed scatter at z = 0


O B-Person B-Person B-Person B-Person O B-Person O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O O O O B-Organization O B-Grant O O O O B-Grant I-Grant B-Grant I-Grant O B-Grant I-Grant B-Person O O O O O O B-Fellowship O O B-Organization B-Location O O O B-Grant I-Grant I-Grant I-Grant O O O O O O O O O O O O B-Person B-Person O B-Person O O O O O B-Organization O B-Grant I-Grant I-Grant I-Grant B-Grant O B-Grant O O B-Organization B-Location O B-Organization B-Location B-Person O O O O B-Location I-Location B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant B-Person O O O O B-Location B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O O B-Organization I-Organization I-Organization O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O O B-Grant B-Person O O O O O B-Location O O B-Organization B-Grant O O O B-Location B-Organization O O B-Grant I-Grant I-Grant I-Grant O B-Organization B-Grant B-Person O O O O B-Grant O B-Organization B-Location O O O O O O O O O O O O O O O O O O O O O O O B-Organization I-Organization I-Organization B-Organization O B-Telescope O B-URL O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization B-URL O O O O B-Organization O O O O O O O O O O O O O B-Collaboration I-Collaboration I-Collaboration O O O O O O O B-Database O O O B-Organization B-Location B-Location O O O O O O B-Software I-Software I-Software O B-Citation I-Citation I-Citation I-Citation O B-Software I-Software I-Software O O B-Software O B-Software I-Software O B-Citation I-Citation I-Citation O B-Software I-Software O B-Citation I-Citation I-Citation O B-Software I-Software O B-Citation I-Citation I-Citation O B-Software O B-Citation I-Citation I-Citation I-Citation O B-Software O B-Citation I-Citation I-Citation I-Citation O O B-Software I-Software O B-Citation I-Citation O


O O O B-Person I-Person O O O O O O O O O O O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Location O O O O O O O O O O O O O O O B-Software O O B-Software B-URL 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-Grant I-Grant I-Grant I-Grant O O B-Organization I-Organization I-Organization I-Organization I-Organization O B-Person O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O O O B-Organization I-Organization I-Organization I-Organization B-Grant O O B-Organization O O O O O O O O B-ComputingFacility O O B-Location O B-Organization O O O O O O O O O O O O O O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility O O O O O B-Grant O B-Organization I-Organization O O O O O O O O O O O O

ACKNOWLEDGEMENTS We thank Åke Nordlund for his contributions to the development of the zoom-technique and the modified ramses version used at the Centre for Star and Planet Formation in Copenhagen, and for valuable suggestions and comments to the article. We thank the developers of the python-based analysing tool yt http://yt-project.org/ (Turk et al. 2011 ). Their efforts in providing analysis support for ramses simplified and improved our analysis significantly. We are grateful to the anonymous referee for constructive feedback that helped to improve the manuscript. This research was supported by a Sapere Aude Starting Grant from the Danish Council for Independent Research to TH. Research at Centre for Star and Planet Formation is funded by the Danish National Research Foundation (DNRF97). We acknowledge PRACE for awarding us access to the computing resource CURIE based in France at CEA for carrying out part of the simulations. Archival storage and computing nodes at the University of Copenhagen HPC centre, funded with a research grant (VKR023406) from Villum Fonden, were used for carrying out part of the simulations and the post-processing.


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O O O O O O O O B-CelestialObject 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 B-CelestialObject O O O O B-Mission O O O O O O O O O O O O O O O O B-CelestialObjectRegion O O O O O O O O O O O O O B-CelestialObjectRegion O O O O O O O O O B-Citation I-Citation I-Citation O O B-CelestialObjectRegion O O O O O O O O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O B-CelestialObjectRegion O O O O O O O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O B-CelestialObject O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O B-CelestialObject 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 B-Survey O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O B-CelestialObject O O B-CelestialObjectRegion O O O O O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O O O O O

includes several vestoids and inner belt non-vestoids, while the second group includes some inner belt vestoids and non-vestoids, as well as middle/outer belt non-vestoids. It is worth noting that the errors involved in the determination of spectroscopic and polarimetric parameters are usually large. In many cases, the differences observed amongst the samples fall within their 1 uncertainties, making them indistinguishable in practice. In principle, there is no clear relation between these spectroscopic and polarimetric differences and the different dynamical populations. 2.3 Size distribution So far, the clearest evidence that prevents a link between (4)Vesta and (1459)Magnya is the size of the latter, which does not fit within the expected size frequency distribution (SFD) of the ejecta from craterization events (Durda etal. 2007 ; Michel etal. 2015 ) like those that excavated the surface of (4)Vesta. On the other hand, the remaining non-vestoids (from both the spectroscopic and SDSS samples) are all as small as the vestoids and may also have originated from craterization events. Images of Vestas surface taken by the Dawn probe revealed two large basins in the south pole of the asteroid. One of them, named Rheasilvia with 500km of diameter, has been dated 1Gyr ago. The other one, named Veneneia with 400km of diameter, has been dated 23Gyr ago (Marchi etal. 2012 ). While Rheasilvia is the likely source of the current vestoids (Buratti etal. 2013 ; McSween etal. 2013 ), Veneneia could be the source of several non-vestoids (Schenk etal. 2012 ). Pirani Turrini ( 2016 ) studied the formation of large basins on the surface of (4)Vesta during the epoch of the giant planet instability and concluded that any record of such basins would have been erased by the subsequent crater saturation over the age of the Solar system. This is in line with the fact that observed craters on Vestas surface dated less than 4.1Gyr ago (OBrien etal. 2014 ). Therefore, the possibility of a very early craterization event on the surface of (4)Vesta that led to the origin of a Vesta-like family cannot be ruled out. In this context, it is interesting to discuss the SFD of the different dynamical populations of V-type asteroids. This is shown in Fig. 2 for the sample of SDSS V-type candidates, but a similar result was obtained by Nesvorn etal. ( 2008 ) considering the spectroscopic sample. The fugitives population shows a similar SFD to the vestoids, indicating that these two populations may be related and have the same collisional age. On the other hand, the low-inclination population and the middle/outer population show SFDs that differ from the Vesta family, suggesting that these populations have a different origin/age. These populations (excluding (1459)Magnya due to its size) could have been originated by early craterization events on the surface of (4)Vesta, like the Veneneia basin or even older events (Schenk etal. 2012 ; McSween etal. 2013 ). Figure 2. The cumulative


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We thank an anonymous referee for some very helpful and insightful comments. AV is supported by the National Science Foundation Graduate Research Fellowship, Grant No. DGE 1144152. TK thanks Cheryl Healy and Beth Christie for material support in telescope operations and equipment.


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E.V.Q.’s research was partially supported by a NASA Postdoctoral Program Senior Fellowship at the NASA Ames Research Center, administered by Universities Space Research Association under contract with NASA. The simulations presented here were performed using the Pleiades Supercomputer provided by the NASA High-End Computing (HEC) Program through the NASA Advanced Supercomputing (NAS) Division at Ames Research Center. The authors would like to thank Chris Henze for his expertise and assistance in performing simulations on the Pleiades Supercomputer.


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

I -band model at 1% significance. This could be due to blending problems and also to the lack of extinction correction in OGLE-IV data. To perform stability tests, the data are split by dummy variables into two data sets around P = 3.85 days (OGLE-II) and P = 3.5877 days (OGLE-IV), so as to have about half of observations in each set. No evidence of structural breaks is found, because the P -values obtained, by testing versus the hypothesis that at least one of them is not 0 in Equation ( 32 ), are 0.601 (OGLE-II) and 0.453 (OGLE-IV) in the V -band, and 0.810 (OGLE-II) and 0.267 (OGLE-IV) in the I -band. Models explain about 61% and 68% of variability in the V - and I -bands respectively (OGLE-II), and 54% and 65% of variability in the V - and I -bands respectively (OGLE-IV). The estimated parameters of the models and their confidence intervals are reported in Table 6 . Results for the I -band are shown only for information purposes because of their specification problems. Table 6 Optical Leavitt Law for the LMC Note. The reported β estimators are those given by Equations ( 26 ) and ( 27 ). They were obtained by using the MM -regression. Confidence intervals are reported at 95%. The last columns report the values of zero point and the slope obtained by Soszyński et al. ( 2015 ) using the sigma-clipping algorithm and OLS over OGLE-IV data. The OGLE-II and OGLE-IV MM -estimators obtained in the V -band and their respective confidence intervals include at the OLS estimators reported by Udalski ( 2000 ) and Soszyński et al. ( 2015 ). The OGLE-IV LMC data were also split into two around P = 10 days by Equation ( 32 ). No evidence of a structural break is found in the slope, because the P -value obtained is 0.705. However, the zero-point adjustment is significant. As a result, there is evidence of two parallel regression lines. The SMC slope tests for models ( 26 ) and ( 27 ) are significant because the P -values obtained are less than 0.0001 for the V - and I -bands (OGLE-II, OGLE-IV). However, these models show problems. The test of Godfrey and Orme finds enough evidence of specification problems because the P -values obtained are less than 0.0001 for the V - and I -bands (OGLE-II, OGLE-IV). To perform stability tests, data are split around 2.0039 days (OGLE-II) and 1.9429 days (OGLE-IV) so as to have about half of observations in each data set. Enough evidence of structural breaks is found: P -values are less than 0.0001 in both bands (OGLE-II) when testing versus the hypothesis that at least one of them is not 0 in Equation ( 32 ). Besides, when individual significance tests are performed for and , the P -values obtained are less than 0.0001 for in both bands, and 0.0322 and 0.0082 for in the V -band and I -band respectively. As a result, in both bands there are two regression lines at 5% significance (OGLE-II). Unlike OGLE-II models for the SMC, there is not enough evidence to support the idea that OGLE-IV model parameters for the slope are


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

with black open circles. We warn the reader that we cannot rule out the presence of other binaries with no obvious s -elements and/or RV differences among our remaining 15 giants. Another stellar population that may affect the appearance of the ChMs and likely has a connection to binary stars is the blue stragglers (BSs). In particular, we consider their evolved counterparts that lie close to the RGB. In Figure 7 , we use blue symbols to represent the candidate BS stars of NGC 3201 in the CMD. The objects marked with blue asterisks are possible BSs selected on the CMD that are evolving toward the RGB phase, which clearly displays lower values in the diagram (top right panel). The BSs in GCs are tightly linked to the cluster binary populations (Knigge et al. 2009 ). The BSs in open clusters themselves have a very high binary fraction (Mathieu Geller 2009 ), and preliminary evidence suggests the same is true in NGC 3201 (Giesers et al. 2019 ). When we include the evolved BSs in the ChM (bottom panel of Figure 7 ), they populate a well-defined sequence on the blue extension of the 1G sequence. We conclude that, based on RVs and s -process element abundances, the three bluest 1G stars that we analyzed spectroscopically are binary systems. Some of them are possibly associated with the BS population of NGC 3201, as evolved BSs would contribute to the bluest extension of the 1G sequence in the ChM. Figure 7. Top panels: CMD (left) and diagram (right) of NGC 3201. Bottom panel: ChM of NGC 3201, similar to Figure 1 but extended to show the evolved BSs. In all panels, the green dots represent our analyzed spectroscopic targets, the open blue circles are the BSs, and the blue asterisks are the evolved BSs. 6.1. Noninteracting Binary Simulations To investigate the effect of noninteracting binaries formed by pairs of 1G stars, we reproduce in Figure 8 five isochrones, I1—I5, with [Fe/H] = −1.50, [ α /Fe] = 0.4, and an age of 13 Gyr from Milone et al. ( 2018 ). These isochrones are constructed with a different combination of He, C, N, and O to represent the typical chemical pattern of different stellar populations in GCs. We used the isochrone I1, which correponds to the 1G, to generate a stellar population of 1G–1G binaries that we represent with black points in Figure 8 . Figure 8. Left panels: simulated CMD, with five isochrones corresponding to different stellar populations with different He, C, N, and O. Here I1 is the isochrone corresponding to the first population; I2 has the same abundance of C, N, and O as I1 but different He; and in I3, I4, and I5, the abundances of He, C, N, and O have been varied to represent the second population chemical pattern. Right panel: location of the five different stellar simulated populations at a reference magnitude on the ChM plane. The black points are noninteracting binaries formed by pairs of I1–I1 stars. Binaries can contribute to the width of the 1G in the ChM, but only binaries with a large mass ratio ( q ≳


We thank the anonymous referee for useful discussion.


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 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 B-Wavelength 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 B-Wavelength 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 B-Wavelength O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O O B-Identifier 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-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 B-CelestialObject I-CelestialObject 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 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 B-Wavelength 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 B-Wavelength O O O O O O O O O B-Wavelength O O O O B-Observatory O B-Telescope O O O O B-Wavelength O O O O O O O O

cool via synchrotron and IC losses. Following Murase ( 2012 ), the deflection angle during the radiation cooling time is given bywhere t syn is the synchrotron cooling time, r L is the Larmor radius, and the Lorentz factor of pairs in the black hole rest frame is . Only synchrotron cooling is considered, because the IC cooling is suppressed for such high-energy electrons and positrons. The above equation implies that the pairs lose their energy after they become isotropized. Note that the X-ray emission is doubly suppressed, because the deflection is larger than the jet opening angle, i.e., , and the time spread in the cascade emission is longer than the intrinsic flare duration, i.e., . Also, the CR neutrons do not produce extra pairs via the Bethe–Heitler process. In addition, in the np scenario, X-rays could also be isotropized via the Compton scattering. Thus, X-rays from the neutral beam can be highly suppressed if the CR energy is lower than UHE energies, and the associated hadronic cascade signatures can be masked by the GeV γ -ray emission from the blazar zone. Note that the UHE neutron beam, if it exists, can also produce beamed cascade emission at TeV energies. The resulting synchrotron pair-echo emission (Dermer et al. 2012 ; Murase 2012 ) is expected to have some time delay. We also remark that the very high energy flare seen by MAGIC was detected about 10 days later after IceCube-170922A. 4. Summary We considered implications of the high-energy neutrino flares from TXS 0506+056 by examining various constraints. Flaring blazars could be the brightest sources in the neutrino sky, while the observations can most naturally be reconciled with existing theoretical models, if the blazars are subdominant (∼1%–10%) in the diffuse neutrino intensity. Interestingly, within the standard leptonic scenario of γ -ray emission, we found that the blazar neutrino emission itself can readily be dominated by flaring episodes. This could explain why the significant neutrino signals from TXS 0506+056 were found only in the time-dependent search and that the steady component that typically dominates γ -ray emission has not been seen yet in neutrinos. Bright neutrino flares like the ones observed for TXS 0506+056 could contribute only up to a few percent of the INB. If the association with this blazar is physical, such flares can be detected with a rate of by dedicated time-dependent searches in the near future. Based on analytical considerations, we also showed the importance of X-ray constraints to test the physical models of TXS 0506+056. An efficient electromagnetic cascade is unavoidable in the canonical blazar models based on the single radiation zone, which also predicts that the 2014–2015 neutrino flare found in the archival data should be accompanied by X-ray emission with . This can readily be tested by X-ray sky monitors such as Swift and MAXI . Nondetection of the X-ray flares will necessitate more complicated models involving multizone


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It is a pleasure to acknowledge fruitful discussions with Fatima Ebrahimi, Eero Hirvijoki, Hantao Ji, Russell Kulsrud, Roscoe White, and Yao Zhou. This research was supported by NSF Grant Nos. AGS-1338944 and AGS-1460169 and by DOE Grant No. DE-AC02-09CH-11466.


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

drop in the abundances, which is and . A KS test suggested that the two distributions are different (-value of 3%), consistent with a radial movement of the gas as the cause of this feature. Finally, of the galaxies displaying this inner abundance drop neither showed evidence of a star-forming ring nor of a bar. This suggests that another mechanism related to radial movements is responsible for causing this feature. To shed some further light on this question, we investigated the presence of this feature depending on the integrated stellar mass of the galaxies. We conclude that the galaxies displaying the strongest oxygen abundance inner drop are the most massive ones (Fig. 9 ), suggesting that stellar mass plays a key role in shaping the inner abundance profiles. In summary, this is the first study that analysed the oxygen abundance distribution for a sample of face-on spiral galaxies spaxel by spaxel. Our final sample of 122 galaxies provided more than 185 000 oxygen abundance values (8200 of them beyond two disc effective radii) to carry out the analysis. The results were compared to those obtained following the classical procedure of detecting H ii regions, leading to equivalent results that point to the same conclusions: (i) the existence of a common abundance gradient, independent of other properties of galaxies, in particular the presence of bars, which seems not to have the flattening effect predicted by numerical simulations; (ii) the existence of a flattening of the abundance gradient in the outer regions of discs, which seems to be a common property of disc galaxies; and (iii) the existence of a drop of the abundance in the inner regions of disc galaxies, only visible in the most massive ones and most probably associated to radial movements of the gas (sometimes a bar or a circumnuclear star-forming ring). These results support the scenario in which disc galaxies present an overall inside-out growth. However, clear deviations were shown with respect to this simple scenario that affect the abundance profiles in both the innermost and outermost regions of galaxies. The agreement between the two methods arises because the spaxel size of the CALIFA datacubes is of the order of the size of a typical H ii region. However, this is not expected for IFS data with better spatial resolution and a smaller spaxel size, where different areas of the H ii regions can be resolved and even abundance gradients can be found. Different procedures that can accomodate data that are capable of resolving H ii regions may be needed. Appendix A: Fundamental parameters and oxygen abundance information In this section we present a table with general information and derived oxygen abundance information for all the galaxies in the sample. The meaning of each column is indicated in the notes below. Table A.1 Fundamental properties and oxygen abundance information. Notes. (a) The galaxy name; (b) the morphological type; (c) -band absolute magnitude; (d) the


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

used the local Maxwellian approximation to generate their ICs, which can lead to artificial relaxation in the centre of the subhalo (Kazantzidis et al. 2004 ). Overall, it appears that the fits from Green van den Bosch ( 2019 ) perform slightly better than all other models, but our model is at least comparable to, if not more accurate than the models presented in Hayashi et al. ( 2003 ) and Peñarrubia et al. ( 2010 ). Figure 1. Comparison of different model descriptions of the density, enclosed mass, and circular velocity profiles of the bound satellite remnant after one orbit in the Slow (left-hand panel) and Fast Simulation (right-hand panel). Simulation results are shown with points, and the models are shown with lines. The thick dashed curve shows the original, untruncated NFW profile. The residuals in the fits are calculated as ( y model / y simulation − 1), where y is the density, mass, or circular velocity profile. Our model from Paper I is described in Section 2 , and the other models in Appendix B . In all cases, the models are dependent on one parameter, the bound mass fraction, which we calculate as the self-bound mass in the simulation, as described in the text. We note that since all of these methods are dependent on the bound mass, they are sensitive to the method used for defining bound particles. Also, bound mass calculations include mass that is only temporarily bound, but is leaving the system (e.g. Peñarrubia et al. 2009 ). Most of this temporarily bound mass is at larger radii, which may explain why the mass-loss models all fail to match the bound mass profiles from the simulations beyond 4–5 r unit in Fig. 1 . A more accurate normalization procedure for our model might be to fit the radius enclosing some fraction of the mass, or to fit the peak circular velocity; rather than take either of these approaches, we will later use the mass-loss model in Section 6 to predict theoretically. 5 OUR MODEL ASSUMPTIONS The truncation method described in Section 2 determines which particles will remain bound, and which will be ejected from the system, given a tidal truncation energy . As shown in the previous section, this approach predicts the density (or equivalently the mass or the circular velocity) profiles of the remnants quite well, but appears to be more accurate when mass-loss is slower. Our goal in this section is to understand why this is the case, focusing on the Fast and Slow Simulations described in Section 3 . Suppose we consider a simple model where mass-loss is primarily an energy-based process, as proposed by Choi et al. ( 2009 ). Three main simplifying assumptions are: Mass-loss occurs episodically around the pericentre of the orbit; after each episode the system returns to equilibrium, with the modified spherically symmetric, isotropic distribution function predicted by the energy truncation method. Individual particles are lost or retained based solely on their energy with respect to the rest of the


O O O O B-Person I-Person B-Person I-Person O O O O O O O O O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Grant B-Grant B-Grant B-Grant B-Grant B-Grant O B-Grant B-Organization I-Organization I-Organization I-Organization I-Organization O B-Grant O B-Organization I-Organization I-Organization I-Organization O O B-Grant I-Grant I-Grant O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O B-Grant O B-Grant B-Person O O O O O B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant B-Grant B-Person O B-Person I-Person O O O O O O O O O O O O O O O O O O O O O B-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility I-ComputingFacility O B-Observatory I-Observatory I-Observatory

We are grateful to Eugene Churazov, Sergey Komarov, and an anonymous referee for insightful comments and suggestions. This work was supported partially by Natural Science Foundation of China (grant Nos. 11633006, 11725312, 11643001, U1431228, 11233003, 11421303, and 11703022), Natural Science Foundation of Shanghai (No. 18ZR1447100), and Chinese Academy of Sciences through the Hundred Talents Program and the Key Research Program of Frontier Sciences (Nos. QYZDB-SSW-SYS033 and QYZDJ-SSW-SYS008). G.M. acknowledges the support by the Fundamental Research Funds for the Central Universities (WK2030220017). X.E.F. thanks Zhen-Yi Cai for the help on scientific plotting. Some simulations presented in this work were performed using the high-performance computing resources in the Core Facility for Advanced Research Computing at Shanghai Astronomical Observatory.


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

there are ≈100 M ⊙ of hot gas in the X-ray-emitting bright regions (see Table 3 ). There have been a variety of simulations that predict the amount and isotopic composition of debris from SN explosions. For example, Seitenzahl et al. ( 2013 , hereafter Sei ) list 17 models for a Type Ia explosion of a 1.4 M ⊙ white dwarf, and Woosley Weaver ( 1995 , hereafter WW ) simulate the gravitational collapse of 78 stars with zero-age main-sequence mass ranging from 11 to 40 M ⊙ s and metallicity from zero to solar values. Table 6 lists a few selections of predictions from these references. The WW examples have been chosen because of higher values for the amount of Si ejecta and to show a general trend. Table 6 LMC Abundances and Ejecta Mass The abundances of elements in the LMC ISM have been taken from Schenck et al. ( 2016 ), who give values for material swept up by the brighter LMC SNRs. Table 6 compares our abundance values with these. Although our uncertainties are not small, the elements O, Ne, Mg, and Fe appear to be present in amounts expected from the ISM. The only enhancement measured by the Chandra ACIS is the abundance of Si, which is 1–2× solar. Table 6 lists the Schenck abundances, our ACIS abundances, the mass of each element in 100 solar masses of material with solar abundances, the masses in 100 solar masses of material with LMC ISM abundances, the masses in 100 solar masses of X-ray-emitting material in J0453-6655 as determined by ACIS, and, in the last four rows, masses predicted by four models of SN explosions. In the 100 solar masses of diffuse gas we find ≈0.13 ± 0.05 M ⊙ of Si. Values for other elements are close to those expected for the ISM. Uncertainties are listed in Table 6 only for the element Si, but Table 2 gives all uncertainties in the spectral fits. There is good agreement between ACIS and EPIC results, but there is a dependence on model used, which could be a factor of 2. This is not important for the conclusions to be drawn here. The elements produced in an SN Ia are predominantly Fe (the 56 Ni produced quickly decays to 56 Fe), O, Si, and S. Almost all models yield several tenths of a solar mass of Fe. Our ACIS analysis finds 10× less, including the ISM contribution. Based solely on the lack of Fe, an SN Ia is an unlikely origin. An SN II, from gravitational collapse of a massive star, will have dispersed several solar masses of ejecta, and the amount of material ejected increases with stellar mass. The Si/O ratio generally decreases with increasing pre-SN star mass, but there is considerable variation from model to model. The predominant element ejected in the WW core-collapse simulations is O. All stars with mass above 20 M ⊙ and solar metallicity eject more than 1 M ⊙ of O, well above the ACIS measurement of 0.11 M ⊙ , indicating that the pre-SN star almost certainly is 20 M ⊙ in size. The data also favor an explosion that ejects at least 0.07 M ⊙ of Si and less than 0.1 M ⊙ of O. None of the WW simulations fit


O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O B-Wavelength O O O O B-Wavelength O O O O B-Instrument O O O O O O O O O O O O O O B-Wavelength O B-Wavelength O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O B-Model 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 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 B-Wavelength O B-Wavelength O O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength O O O O O O O B-Wavelength I-Wavelength 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 B-Wavelength I-Wavelength O O B-Wavelength O O O O O O O O O O B-Wavelength I-Wavelength O O O O B-Wavelength O O O O O B-Wavelength I-Wavelength O O O O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O B-Wavelength B-Wavelength O O B-Wavelength I-Wavelength O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength O O O O O O B-Citation I-Citation I-Citation O O O O O O O O B-Wavelength B-Wavelength O O O O O O B-Citation I-Citation I-Citation O O O O O O O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength O O O O B-Wavelength O O B-Instrument O O O O O O O B-Wavelength O O O O O O O O B-Wavelength O O O O O O O B-Wavelength I-Wavelength O B-Wavelength I-Wavelength O O O O O O O O O B-Wavelength O O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O B-Wavelength O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O B-Wavelength I-Wavelength O O B-Wavelength B-Wavelength I-Wavelength O O O O O O O O O O O O O O O B-Wavelength I-Wavelength

1966 ) and the effect on measured image quality was seen by the smaller FWHM of star images at redder wavelengths compared to 4900 Å in the MUSE cubes. Given that the wave feature of the extinction maps occurs where the surface brightness decreases by a factor 2 over a distance of a few spaxels (0.5), then the effect of the different image FWHM between the wavelengths of the H Balmer lines would modulate the ratio image which forms the basis of the extinction determination. For example for a step function across the shell, the ratio map H/H would be expected to show a trough, since the image FWHM at H is lower than at H. On the 10 s MUSE cube the measured FWHM of the central star varies from 0.53 to 0.50 between H and H. In order to determine if this effect could be responsible for the observed wave-trough appearance across the inner shell, the H image was convolved with a Gaussian to the same measured FWHM as the H image and the extinction map redetermined. The strength of the trough is slightly decreased, by 0.02 in , and the wave increased by a lesser amount, but the features remain. A repeat of this test but with the 120 s H map showed a similar result. Having rejected instrumental or seeing effects as causing the pattern in extinction, astrophysical effects are now examined. 3.4. Balmer v. Paschen line ratios The He II Pickering series 6g-4f 6560.10 Å line is within 2.7 Å of the H line and at the resolution of the MUSE spectra, and given the very large flux ratio (100), will be included in the flux of the fitted H line. Thus the H flux needs to be corrected for the contamination of the He II line (1% of the H surface brightness in the bright He II core of the nebula). The He II Pickering 7g-4f 5411.52 Å line was measured in all the cubes and from the Case B ratio 6560.1/5411.5 Å ratio, the 6560.1 Å observed line flux was computed using Storey Hummer (1995) and a reddening map. The observed value of the He II 6560.10 Å line of 0.0338 F(H) tabulated by Fang Liu (2011) appears to be too large (the theoretical ratio 6560.1/5411.5 Å is 1.75 at 10 K whilst Fang Liu 2011 have a dereddened ratio of 2.92). Similarly the Pickering He II 8g-4f 4859.32 Å line is blended with H at the MUSE resolution, so its contamination of the measured H flux should also be corrected (similarly 1% of H in the core). The theoretical ratio of 4859.3 Å to 5411.5 Å was again used. Applying both these corrections to the H and H flux maps, the derived extinction map was re-computed. The He II line is indeed only strong inside the inner rim and is very weakly present outside the rim, so the effect of the correction to H and H fluxes for He II is insignificant where the strongest features of the extinction are present. Inside the inner rim, where the He II is brightest, the effect on the extinction map is small, . The Paschen lines higher than P9 (9229.0 Å) are also available for extinction determination. These lines also have the advantage that the contaminating He II


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O O O O B-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 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 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 B-Observatory O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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

large SEP events (e.g., Gopalswamy 2018 ). SEP events need to be magnetically connected to the observer in order to be detected; type II bursts do not have such a requirement. Only 2 of the 44 cycle-23 limb halos are not associated with DH type II bursts; they are slow (800 km s −1 on 2000 October 24; 896 km s −1 on 2002 January 4) compared to the average speed of CMEs associated with cycle-23 DH type II bursts (1219 km s −1 ). The 2002 January 4 CME is associated with a metric type II burst, while the 2000 October 24 CME is radio-quiet. Nine cycle-24 halos have no DH type II association (see Table 1 ): five have metric type II bursts, three are quiescent filament-eruption events (which are only occasionally associated with DH type II bursts, Gopalswamy et al. 2015a ), and the slowest cycle-24 halo (2012 February 23). The four radio-quiet halos are slow (505 to 919 km s −1 ) compared CMEs associated with cycle-24 DH type II bursts (1059 km s −1 ). Thus, an overwhelming majority of limb halos (cycle 23: 98%; cycle 24: 90%) have type II bursts indicative of electron acceleration. 4. Discussion and Summary We analyzed large samples of limb-halo CMEs observed in cycles 23 and 24. We found that cycle-24 halos are slower than the cycle-23 ones. The limb CMEs that revealed wider width in cycle 24 did not show the speed difference (Gopalswamy et al. 2014a ). We introduced a new parameter—the height at halo time is readily determined for limb halos, but not for disk halos (the CME nose is hidden by the occulting disk of the coronagraph). The cycle-24 halo heights are significantly smaller. Combined with the result that cycle-24 halos are slower, we conclude that halos form at shorter heliocentric distances at lower speeds. Furthermore, we ruled out the possibility that the difference in CME properties is due to solar-source characteristics represented by soft X-ray flare size. Thus, we can pin down the heliospheric state as the main cause of the anomalous CME expansion in cycle 24. The number of limb halos (44) in cycle 23 is only slightly larger than the number (38) in cycle 24. This corresponds to a drop of only 14% in cycle 24. There was a 4 month SOHO data gap in cycle 23 (3 month in 1998 and one month in 1999). Assuming that the limb halos occurred at the cycle-averaged monthly rate (0.3 per month), we expect only one additional CME during the data gap. Then the drop is only 16%. This is much smaller than the 40% drop in the cycle-averaged total SSN from 81 to 49. Normalizing to SSN, we see that there are ∼42% more limb halos per SSN in cycle 24. This result was previously obtained by considering all LASCO halos in the first half of the two cycles (Gopalswamy et al. 2015b ). The effect of the heliospheric state on CMEs has important implications for space weather: lower geoeffectiveness is expected in SC 24 because lower speed and weaker CME magnetic field (due to expansion) result in a weaker storm. Furthermore, milder space weather is


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Acknowledgements The authors would like to thank Dr Sven Buder for his useful comments and discussion about Na abundances. Based on observations made with the Italian Telescopio Nazionale Galileo (TNG) operated on the island of La Palma by the Fundación Galileo Galilei of the INAF (Istituto Nazionale di Astrofisica) at the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofisica de Canarias. CARMENES is an instrument for the Centro Astronómico Hispano-Alemán de Calar Alto (CAHA, Almería, Spain) funded by the German Max-Planck-Gesellschaft (MPG), the Spanish Consejo Superior de Investigaciones Científicas (CSIC), the European Union through FEDER/ERF FICTS-2011-02 funds, and the members of the CARMENES Consortium. This work is partly financed by the Spanish Ministry of Economics and Competitiveness through project ESP2016-80 435-C2-2-R. G.C. acknowledges the support by the National Natural Science Foundation of China (Grant No. 11503088, 11573073, 11573075) and by the project “Technology of Space Telescope Detecting Exoplanet and Life” from National Defense Science and Engineering Bureau civil spaceflight advanced research project (D030201). F.Y. acknowledges the support of the DFG priority programme SPP 1992 “Exploring the Diversity of Extrasolar Planets (RE 1664/16-1)”. A.F. acknowledges the support from JSPS KAKENHI Grant Number JP17H04574. This work is partly supported by JSPS KAKENHI Grant Numbers JP18H01265 and 18H05439, and JST PRESTO Grant Number JPMJPR1775. This article is based on observations made with the MuSCAT2 instrument, developed by ABC, at Telescopio Carlos Sánchez operated on the island of Tenerife by the IAC in the Spanish Observatorio del Teide. This work made use of PyAstronomy and of the VALD database, operated at Uppsala University, the Institute of Astronomy RAS in Moscow, and the University of Vienna.


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

mass profiles are extrapolated based on the best-fitting temperature profile model beyond the extent of the temperature profile. The median extent of the temperature profiles is 1.25 R 500 . Profiles of the mass ratios beyond that point are less robust. In Fig. 4 , the ratio of the hydrostatic to caustic masses at the radius R 500 determined from the hydrostatic mass profile is shown for each cluster. Again, the ratios are computed as . At this radius, the two mass estimators agree well, with κ = 0.080 ± 0.046, corresponding to . The intrinsic scatter between the hydrostatic and caustic mass estimators at this radius is , corresponding to an intrinsic scatter of . The RCC and NRCC subsamples show consistent results, albeit with weaker constraints. Figure 4. Ratio of hydrostatic to caustic masses at the hydrostatic R 500 for each cluster (computed as ). Points are coloured to indicate RCC (blue triangles) and NRCC (red circles) clusters. The solid line and shaded band show the mean bias between the hydrostatic and caustic masses and its uncertainty. These summary statistics are captured in Table 3 , along with the same quantities derived in a fixed aperture of for each cluster. The parameter values are insensitive to the choice of aperture, demonstrating that our results are not significantly influenced by scaling the caustic profiles to the hydrostatic estimate of R 500 . Table 3. Summary statistics of the ratio of the mean bias between hydrostatic and caustic masses, measured in the hydrostatic estimate of R 500 and in a fixed aperture of . The second column gives the subset being considered and the third column gives the mean bias. The mean bias is expressed as the mean ratio of masses in column four, and the intrinsic scatter between the mass estimators (converted to a percentage) is given in column five. Note that the quantities in columns four and five are summaries of a lognormal distribution using a median and percentiles as described in Section 3.3 . 5 DISCUSSION 5.1 Biases in hydrostatic and caustic masses We have performed one of the first comparisons between mass profiles of galaxy clusters determined from their hot gas via hydrostatic assumptions, and the dynamics of their galaxies via the caustic method. These two methods are completely independent, and are subject to different assumptions and systematics. We found that, while significant scatter is present between the two estimators, the average agreement is good. As demonstrated in Fig. 2 , the masses agree to better than ≈20 per cent on average over the full radial range sampled by both techniques. Importantly, neither of the mass measurement techniques assumed a functional form for the mass profile (although the hydrostatic analysis did use parametric temperature and density profiles). The agreement we find is not a consequence of a common parametrization of the mass profile. This good average agreement is somewhat surprising given that various observational and


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ACKNOWLEDGEMENTS We are grateful to the anonymous referee for her/his very useful comments and suggestions that helped us to clarify and improve this work. OLD and ACK are grateful to FAPESP and CNPq. AFM is grateful to CAPES. MVC and GFH are grateful to CONICET. OLD is grateful to Dr. Sameshima and Dr. Miller for making their BLR metallicity estimations and α ox values available, respectively.


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the main object, respectively, and Na 1, Na 2, Ne 1, and Ne 2 are factors that take place in eccentric orbits and are defined by 5.2 General relativistic effect The important effect derived from General Relativity theory (GRT) on the dynamic of planetary systems is the precession of ω ( Einstein 1916 ). In our case, we considered that only the main object contributes with relevant corrections. As we worked in the reference frame of the star, the associated correction in the acceleration of the embryo is with c the speed of light. Eq. ( 19 ) was proposed by Anderson et al. (1975) , who worked under the parameterize post-Newtonian theories. The authors obtained a relative correction associated with two parameters β and γ , which are equal to unity in the GRT case. This expression has been used in several works that included relativistic corrections (e.g., Quinn et al. 1991 ; Shahid-Saless Yeomans 1994 ; Varadi et al. 2003 ; Benitez Gallardo 2008 ; Zanardi et al. 2018 ). The timescale associated with the precession of the longitude of periastron is given by 5.3 Test simulations We made a set of N -body simulations in order to test the agreement between the external forces that we incorporated in the M ERCURY code and the timescale associated with them. To test the precession of ω , we developed two simulations: one that included the tidal distortion term, and another that included the GR correction. In Fig. 5 we show the apsidal precession timescale of a planet with 1 M ⊕ orbiting a 1 Myr substellar object of 0.08 M ⊙ with initial values a = 0.01 au and e = 0.1 for the two simulations we made. Our results show that the apsidal precession of 360° is completed in 14 750 and 3060 yr, respectively, which agrees with the time predicted by the timescales associated with each correction term in Eqs. ( 20 ) and ( 8 ). These timescale values depend on the physical parameters of the protoplanetary embryos and the substellar object, as well as on the initial orbital elements. For instance, if the protoplanets are smaller than Earth in mass and radius, then the relativistic effect is more relevant than the tidal distortion regarding the precession of ω . Fig. 5 Apsidal precession due to tidal distortion (solid red line) and GR effects (dotted blue line) in a system composed of a 1 M ⊕ planet around a 0.08 M ⊙ BD with initial a = 0.01 au and e = 0.1. In this example, the argument of periastron completes an orbit in ~14 750 yr when is affected by GR and in ~3060 yr when is affected by tidal distortion. Fig. 6 Evolution of e , a , and the pseudo-synchronization period of a 1 M ⊕ around a 0.04 M ⊙ BD. Solid lines indicates the results considering the initial orbital elements from Bolmont et al. (2011) . The dashed lines indicate the evolution of r corot ( middle panel ) and the rotational period of the BD, P ⋆ ( bottom panel ). To test the analytic expressions for the tidal dissipation with the timescales of e and a decay, we developed a N -body simulation


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scaled-down AGN jet model based on equipartition assumptions and applied it to observationally well defined samples of galactic and extragalactic sources. They find that the jet powers of their studied sources were comparable to their accretion disk luminosities providing evidence for a disk-jet coupling holding from stellar mass BHs to low-luminosity AGN. Merloni Heinz (2008) present a synthesis model for the AGN evolution where they studied how SMBHs grow and evolve through the age of the Universe. In this model, AGN with high Eddington ratios may display either only radiative feedback (high-radiative mode, HR) or both radiative and kinetic feedback (high-kinetic mode, HK). In this context, HLAGN with low radio AGN fractions ( f AGN 0.5) would be those which display mostly radiative feedback, while those with high radio AGN fractions ( f AGN ≥ 0.5) also produce kinetic feedback in the form of radio-detectable features, such as cores, jets and lobes. Radiative feedback is expected to arise in galaxies hosting rapidly accreting SMBHs, where the energy released by the growth of the SMBH can influence the properties of the hosts (e.g., see a review by Fabian 2012 ). The models of galaxy evolution usually find the AGN bolometric luminosity density to increase from the local redshift out to a peak around z ∼ 2 − 3, followed by a decrease toward higher redshifts (e.g., Croton et al. 2006 ; Merloni Heinz 2008 ). For the ∼38% of HLAGN for which we estimated a radio luminosity arising from AGN emission (Sect. 3.2 ) we compare the radiative luminosity density to literature expectations (e.g., Croton et al. 2006 ; Merloni Heinz 2008 ). We binned the radiative luminosities derived from the SED-fitting decomposition (see Delvecchio et al. 2017 ) into nine redshift bins, finding typical values of bolometric luminosity density to be 1% of those found from the literature for all radiatively efficient AGN. This confirms that X-ray and MIR selected AGN detected in radio are not the dominant contribution to the total bolometric output expected for radiatively efficient AGN. In the following sections, we describe how the number and luminosity densities of HLAGN change through cosmic time. By scaling the 1.4 GHz AGN luminosity into kinetic luminosity, we calculate the kinetic luminosity density and compare it to semi-analytic model predictions. 6.2. Cosmic evolution of radio AGN To calculate the number and luminosity density, we use where Φ( L 1.4 GHz ) is the redshift evolved luminosity function, using both best-fit evolution parameters derived from the redshift binned and continuous fitting. Here we take the lower and upper limits of the integral to be L 1.4 GHz = 10 22 WHz −1 and L 1.4 GHz = 10 28 WHz −1 , respectively. The normalizations of the number and luminosity density evolution curves are affected by the chosen limits of integration. For example, a decrease of the lower limit to L 1.4 GHz = 10 21 WHz −1 would produce a number density higher by a factor