to the Jet Power for Multiple-Zone Modeling of the Multiwavelength Data of Quiescent-State Emission from AP Librae The contributions of disk, broadline region (BLR), and torus radiation to the IC emission by the blob and pc-scale jet of AP Librae are considered in earlier papers. The energy of the BLR photons is blueshifted in the rest frame of the blob. The reprocessed BLR emission has been parameterized in Equation (12) of Hervet et al. ( 2015 ). The parameter values presented in Table 3 of Hervet et al. ( 2015 ) have been chosen such that at HE, the EC emission of blob-BLR origin is significant. A similar discussion is given in Zacharias Wagner ( 2016 ). Direct emissions from the disk, BLR, and torus are low as they are not detected, however, EC emission from the blob due to the reprocessed emission could be significant (depending on the parameter values chosen and the distances of the blob and jet from the black hole) after Doppler boosting. Moreover, it is discussed that, due to the outward relativistic motion of the blob and its distance from the accretion disk, the EC emission of blob electrons due to disk radiation is negligible. From Equation (A.6) of Zacharias Wagner ( 2016 ), the energy density of reprocessed emission from the dusty torus in the reference frame of the blob is . Assuming the radius of the region within which the emission is confined to be r DT = 1 pc, luminosity L DT = 10 42 erg s −1 , the Lorentz factor of the blob Γ = 7, the efficiency of reprocessing τ DT = 0.001, and the energy density in radiation u DT = 2 × 10 −8 erg cm −3 , which is much lower than the synchrotron photon energy density inside the blob, 1.28 × 10 −5 erg cm −3 . By adjusting the parameter values suitably, the energy density in reprocessed external radiation could be made even lower. Moreover, the pc jet is assumed to be located beyond the BLR and torus region, which makes EC emission insignificant. 3. Results and Discussions As shown in Figures 2 – 4 , the observed quiescent-state SED of AP Librae has been fitted by the three-zone model adopted in the present work. The optical–UV frequency data in the SED are accounted for partially by the synchrotron emission of electrons from the blob and partially by the blackbody radiation from the accretion disk. The thermal emission from the accretion disk is reproduced by assuming a Shakura–Sunyaev type disk (Shakura Sunyaev 1973 ) with a luminosity of L D = 1.3 × 10 44 erg s −1 . Incidentally, Zacharias Wagner ( 2016 ) used the same estimate for disk luminosity,The jet power requirements from each region are calculated from the expression of P jet presented in Equation ( 11 ). For the parameters used in our model, we find that the required jet power in Zone-1 is 5.7 × 10 47 erg s −1 and in Zone-2 is 3.75 × 10 47 erg s −1 . The jet power requirement in Zone-3 is 4.86 × 10 48 erg s −1 . Assuming a simple power-law proton spectrum of spectral index 2 in the energy range of 10 15 –10 18 eV, we have

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


field for the IC emission, the pionic γ-ray emission in our model is not able to account for both the observed γ-ray luminosities and the spectral shapes of galaxies with low SFRs such as the SMC alone. As diffusive losses become more relevant in these low-density galaxies, this leads to a steepening of the CR proton spectra (depending on the exact energy dependence incorporated in the diffusion time-scale). This necessarily results in steeper pion-decay γ-ray spectra, which would be in conflict with the observations if this were the only relevant emission channel. Hence, a leptonic contribution to the γ-ray emission from IC scattering is indispensable in our models. One of the arguments made in the literature in order to conclude a subdominant leptonic contribution to the total γ-ray emission depends on several underlying assumptions that are only valid in the nuclear regions of starbursts, i.e. for high gas densities, magnetic field strengths, and wind velocities. The magnetic field strength is either deduced from an energy equipartition argument, or from fitting several free parameters in one-zone models (see e.g. Torres 2004 ; Lacki et al. 2010 , 2011 ; Yoast-Hull et al. 2013 ) or axisymmetric two-dimensional models (Buckman et al. 2020 ) in order to simultaneously match the observations. The former approach assumes that the kinetic energy density is equal to the magnetic energy density, . Assuming turbulent velocities of and gas densities of yields in this approach magnetic field strengths of the order of . The fast cooling of CR electrons due to synchrotron emission in these strong magnetic fields has been proposed to be one of the reasons for suppressing the possible leptonic contribution to the γ-ray emission (Lacki et al. 2011 ). In contrast, γ-ray observations of the Galactic Centre suggest that CRs might not be able to penetrate into the densest regions and thus may be far from calorimetry (Crocker et al. 2011a , b ). However, those extreme properties are at most reached in the very central region of our simulated galaxies. Additionally, the energy density of the interstellar radiation field (or its equivalent magnetic field strength, see Fig. 1 , upper panels) persists throughout the whole galaxy. The cooling of the electrons is hence not fully dominated by synchrotron cooling, enabling IC losses to be non-negligible, except in the very central regions of starburst galaxies. In particular, in the low-density ISM of dwarfs, we find that the IC emission might be able to contribute up to 40 per cent of the total γ-ray luminosity, as can be seen in Fig. 4 (middle panels). Still, our models of starburst galaxies M82 and NGC 253 (that are chosen to match the observed SFRs and L γ ) also match their observed radio luminosities at 1.4 GHz. We will address the radio emission of our simulated galaxies in Paper III in more detail. Our findings suggest that SF galaxies are not reaching the calorimetric limit, and depart from this limit even

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


worth noting. Among them, there was a sporadic 10mag fireball, visible in the evening on 2005 October 28 or a similar event on November 30, with an orbit equivalent to the 00241 OUI October Ursae Minorids stream (Molau Rendtel 2009 ). Figure 1. Fireballs from the Southern Taurid shower registered on 2005 October 30 (left) and on 2005 October 31 (right) by the PFN05 Pozna station using the PAVO5 camera. Figure 2. Fireball of 15mag registered on 2005 November 4 at 20:19:42 ut with the Pegasus constellation in the background. Photograph taken by D. Dorosz in PFN09 abikw station (Praktica L2, Vivitar 28mm f /2.5, Konica VX200). Figure 3. Selection of fireballs registered during the peak of activity of the Taurids in 2015. 2.2 Observations in 2015 As in 2005, our research included solar longitudes ranging from 206 to 228. This time, the Moons phases were not as perfect as in 2005 with full Moon on October 27 and new Moon on November 11. From October 20 to 22, our stations did not provide any data because of heavy clouds. Between October 24 and November 4, good weather allowed the PFN to work at its fullest; the nights of November 57 were partially or completely cloudy but the nights of November 8 and 9 were clear in most of the country. Compared to 2005, the number of stations and the quality of our equipment increased significantly. We were able to gather data from 25 stations covering a period of time from October 20 to November 10. We used diverse observation equipment, the sets of the highest speed based on the Mintrons 12V6, which allowed us to observe meteors as faint as 34mag. For the first time, we used the digital DMK23GX236 megapixel camera and the Tamron 2.4-6mm f /1.2 lens. Such a set allows us to observe a field of 1283802 with a limiting magnitude of about 1 to 2 and a resolution of 19201200pixels with 25 frames per second. Table 2 summarizes a list of our stations active in 2015. Table 2. Basic data on the PFN stations that observed the Taurid shower maximum in 2015. In a period from 2015 October 20 to November 10, all PFN cameras registered 6970 meteors out of which we determined 719 orbits. They corresponded to different meteor showers and sporadic centres. Out of that number, 215 orbits belonged to the Southern Taurids and 39 to the Northern Taurids. Fig. 3 shows four bright Southern Taurids captured during 2015 maximum. The first phenomena of high brightness were observed on October 27 (similarly to 2005). Three bright fireballs were also seen on October 30. The night of October 31 brought two other incredibly bright phenomena. At 18:05 ut , a fireball from the Southern Taurid shower appeared over north-western Poland and its absolute magnitude amounted to 16mag. The fireball was visible across Central Europe and was registered by the PFNs network cameras, car cameras and people coincidentally photographing the close fly-by of the asteroid 2015 TB145 (see Olech etal. 2016 for a detailed description). The phenomenon lasted 5.6s

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O B-CelestialObject I-CelestialObject O B-Citation I-Citation I-Citation O O O O O O B-CelestialRegion I-CelestialRegion O O O O O O O O O O O O O O O B-Telescope I-Telescope O O O B-Instrument 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 B-Person I-Person O B-Telescope I-Telescope I-Telescope B-Instrument I-Instrument I-Instrument I-Instrument I-Instrument I-Instrument I-Instrument I-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion I-CelestialRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Instrument I-Instrument O O O O O O O O O O O O O O O O O O B-Instrument O O O O B-Instrument I-Instrument I-Instrument I-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 B-Observatory O O O O B-CelestialRegion 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 B-CelestialRegion I-CelestialRegion O O O O B-CelestialRegion I-CelestialRegion O O O O O B-CelestialRegion I-CelestialRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialRegion I-CelestialRegion O O O O B-Location O O O O O O O O O O O O B-Location I-Location O O O O O B-Observatory O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O B-Citation I-Citation I-Citation O O O O O O O O


infrared yielding a water production rate in the range 3.2–3.0 × 10 28 molec. s −1 for the 7–11 September period, just before our IRAM observations. Faggi et al. (2019) , also from infrared observations of H 2 O, found water production rate in the range 2.6–2.8 × 10 28 molec. s −1 for the 8 September–7 October 2018 period. We thus assumed molec. s −1 at the time of IRAM observations ( Table 3 ). Comet 41P outgassing was monitored by several observatories during its 2017 approach, including the Solar Wind ANistropies (SWAN) instrument on the SOHO spacecraft (31 March to 20 April, Combi et al. 2019 ), TRAPPIST (11 March to 24 May for OH, Moulane et al. 2018 ) and with the Nançay radio telescope (4 March–5 June). The comet was not observed at Nançay at the time of the IRAM observations because of poor OH inversion. OH production rates of ≈ 1.1 × 10 28 and 0.6 × 10 28 molec. s −1 were obtained for the 28 March–3 April and 18–30 May, respectively. Most of the observations showed a plateau of activity ±20 days around perihelion with 4, 3 and 8 × 10 27 molec. s −1 respectively. We adopted a median value of molec. s −1 for the time of our observations. For comets 64P and 38P, around the time of our observations, water production rates were estimated from ground-based spectro-photometric observations of OH. D.G. Schleicher (priv. comm.) provided molec. s −1 for 64P on 16 December 2018. For comet 38P his values were molec. s −1 on 3 and 16 December 2018. We adopted water production rates of molec. s −1 for 64P and molec. s −1 for 38P, both to compute collision rates and determine molecular abundances. 64P and 38P were only observed in September and October at Nançay. 6 Production rates and abundances Line intensities have been converted to production rates using our time-dependent non-LTE code taking into account collisions with neutrals and electrons as well as solar radiative pumping via vibrational bands for HCN, CH 3 OH, CS, H 2 CO, CO, and CH 3 CN, as used in previous papers ( Biver et al. 2000 , 2006 , 2012 , 2014 , 2015 , 2016 ). Photolysis constants are also from previous papers and detailed in Biver et al. (2021) . Production rates or upper limits are provided in Table 4 . For species with multiple lines observed at the same time, the weighted average is provided. 6.1 Relative abundances Abundances relative to water were computed using the average water production rates provided in Table 3 . For 41P we assumed a lower water production rate (0.3 × 10 28 molec. s −1 ) for the second day (1.0 May 2017) because HCN and CH 3 OH showed a significant decrease in production rate and Moulane et al. (2018) also found a decrease in the water production rate between 26.1 April and the 28 April–3 May period. For 38P, abundances relative to water assume molec. s −1 . Although no line is detected with a signal-to-noise larger than 2, the combined signal of the 13 strongest methanol lines at 165–170 GHz and 242 GHz yields a formal signal-to-noise of 3.5 and a

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


at PA = 259o as the distance to the source increases. Table 8. Parameters of the continuum and CH 3 CN line best-fitting model, which consists of an Ulrich envelope and a flared disc. Parameters in bold under the last column are the 10 free parameters that can be constrained by the observations. The inner radius depends on the stellar luminosity. a Defined at a height z = 10 4 au. b 2 models had the same best overall ranking value. The parameters of the best-fitting model during the visual inspection step are listed in Table 8 and the ranking and reduced χ 2 values for each observation are listed in Table 9 . The best-fitting model has a type A density distribution (Ulrich 1976 envelope and a flared disc). The envelope radius was well-fitted during this step and has a value roughly a factor of 1.4 smaller than the initial visual inspection model and has a similar size to the model with disc of Johnston et al. ( 2013 ). The disc scale height is smaller by roughly one order of magnitude than those in Johnston et al. ( 2013 ), but this parameter cannot be constrained by our observations, thus it was less explored. The shape of the cavity changed from the initial exponent of 1.5 to 2.0, and its reference density decreased an ∼15 per cent from its initial value and its density exponent did not change. Table 9. Overall ranking and reduced χ 2 values for the continuum best-fitting models of each type. a Average weighted ranking as described in Appendix A1.2 (online). Similarly, in Table 8 and 9 , we list the results for the overall best-fitting model after the grid-fitting step. The disc mass and radius increased with respect to the visual inspection best-fitting model. The former is roughly a third of the disc mass in the control model of Johnston et al. ( 2013 ), but the disc radii are similar. This difference is explained by the difference in the disc scale height. The cavity opening angle is equal to the one from the visual inspection best-fitting model, and the inclination angles differ by 15o. The luminosities are the same between the best-fitting models at each step, whilst the envelope infall rate is ∼1.8 times higher in the overall best-fitting model. The model SED agrees reasonably well with the observations as shown in Fig. 10 . The total mass of the model, M = 2.1 × 10 3 M ⊙ , is enough to fit the 10- μ m silicate feature relatively well at an inclination of 25o and closely fit the submm points. This is 900 M ⊙ more massive than the model with disc of Johnston et al. ( 2013 ), but 600 M ⊙ less massive than their envelope only model. Models with WD01 dust can also fit in the submm with lower masses, however, they underestimate the fluxes between 3 and 8 μ m by a factor of ∼10. The near-IR maps in Fig. 7(a)–(c) show that the near-IR band images are well reproduced. However, Fig. 8 shows that the small scales closer to the star position probed by the speckle observation are not well reproduced. In general, most models with a cavity

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


tens of solar masses (Abbott et al. 2016a ). Based solely on the gravitational-wave signals recorded by two LIGO detectors, the current hypothesis is that GW150914 was the result of a merger of two black holes with initial masses of and at a luminosity distance of Mpc. The Fermi Gamma-ray Burst Monitor ( Fermi -GBM) reported a possible weak gamma-ray transient source above 50 keV at 0.4 s after the GW150914 trigger (Connaughton et al. 2016 ). However, the upper limit provided by the INTEGRAL Advanced Camera for Survey instrument in a gamma-ray energy band similar to the Fermi -GBM energy band is not consistent with a possible gamma-ray counterpart of GW150914 suggested by the Fermi -GBM (Savchenko et al. 2016 ). No electromagnetic counterpart of GW150914 was found in radio, optical, near-infrared, X-ray, or high-energy gamma-rays (Abbott et al. 2016b ). GW151226 (LIGO-Virgo trigger ID: G211117) is the second gravitational-wave candidate identified by both LIGO Hanford Observatory and LIGO Livingston Observatory with a high significance (the false-alarm rate of less than one per 1000 years by the on-line search) at 3:38:53.647 UT on 2015 December 26 (Abbott et al. 2016c ). According to a Bayesian parameter estimation analysis, the event is very likely a binary black hole merger with initial black hole masses of and and a final black hole mass of (Abbott et al. 2016d ). The luminosity distance of the source is estimated as Mpc, which corresponds to a redshift of . As far as the electromagnetic counterpart search of GW151226 in the gamma-ray regime is concerned, Fermi -GBM (Racusin et al. 2016 ), Fermi Large Area Telescope (LAT; Racusin et al. 2016 ), High-Altitude Water Cherenkov Observatory (Wood the HAWC Collaboration 2016 ), and Astrosat -CZTI (Bhalerao et al. 2016 ) reported no detections around the GW trigger time. According to Racusin et al. ( 2016 ), the flux upper limit of Fermi -GBM is from 4.5 × 10 −7 to 9 × 10 −7 erg cm −2 s −1 in the 10–1000 keV band. The Fermi -LAT flux upper limit using the first orbit data after the LIGO trigger is from 2.6 × 10 −10 to 7.8 × 10 −9 erg cm −2 s −1 in the 0.1–1 GeV band. The CALorimetric Electron Telescope ( CALET ; Asaoka the CALET Collaboration 2015 ; Torii et al. 2015 ) mission, which was successfully launched and emplaced on the Japanese Experiment Module—Exposed Facility of the International Space Station (ISS) in 2015 August, was fully operational at the time of GW151226. CALET consists of two scientific instruments. The Calorimeter (CAL) is the main instrument, which is capable of observing high-energy electrons from ∼1 GeV to ∼20 TeV, protons, helium, and heavy nuclei from ∼10 GeV to 1000 TeV and gamma-rays from ∼1 GeV to ∼10 TeV. The field of view (FOV) of CAL is ∼45° from the zenith direction. Another instrument, CALET Gamma-ray Burst Monitor (CGBM; Yamaoka et al. 2013 ), is a gamma-ray burst (GRB) monitor using two different kind of scintillators (LaBr 3 (Ce) and BGO) to achieve a broad

O O B-EntityOfFutureInterest I-EntityOfFutureInterest B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-Instrument 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 B-Observatory B-Telescope I-Telescope I-Telescope O B-Observatory B-Telescope O O O O B-Wavelength O O O B-Wavelength I-Wavelength O O O O O B-CelestialObject O B-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Instrument I-Instrument I-Instrument I-Instrument I-Instrument O O O B-Wavelength O O O O O B-Observatory B-Telescope O O O O O O O O B-Wavelength O O B-CelestialObject O O O B-Observatory B-Telescope B-Citation I-Citation I-Citation I-Citation O O O O O B-CelestialObject O O O B-Wavelength B-Wavelength B-Wavelength B-Wavelength O B-Wavelength I-Wavelength B-Citation I-Citation I-Citation I-Citation O B-CelestialObject B-Identifier I-Identifier I-Identifier I-Identifier O O O O O O O O B-Instrument I-Instrument I-Instrument O B-Instrument I-Instrument I-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O B-Wavelength O O O B-Observatory B-Telescope B-Citation I-Citation I-Citation I-Citation O B-Observatory B-Telescope I-Telescope I-Telescope B-Telescope B-Citation I-Citation I-Citation I-Citation O B-Observatory I-Observatory I-Observatory I-Observatory B-Observatory O B-Telescope I-Telescope I-Telescope O O B-Telescope B-Instrument B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O B-Observatory B-Telescope 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-Observatory B-Telescope O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O B-Telescope I-Telescope I-Telescope O B-Telescope O B-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-Instrument I-Instrument I-Instrument I-Instrument O O B-Mission I-Mission I-Mission B-Mission O O O O O O O O O O B-CelestialObject B-Telescope O O O O O O B-Instrument 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 B-Wavelength O B-Wavelength I-Wavelength I-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O O O B-Telescope B-Telescope I-Telescope I-Telescope B-Telescope B-Citation I-Citation I-Citation I-Citation O O O B-Wavelength I-Wavelength B-Wavelength O O O O O O O B-Instrument I-Instrument B-Instrument O B-Instrument O O O O


except when the wind speed at the orbital separation is so low compared to the orbital speed that the effective cross section given by the BHL formula is larger than the orbital separation and looses any meaning: relying on the Roche lobe instead makes much more sense in this regime. Fig. 3. Comparison of the mass-transfer rates we measure as a function of η (solid lines) to the BHL mass-accretion-rate formula (dashed lines) for a filling factor of 90% and mass ratios of 2 ( upper panel ) and 15 ( lower panel ). The BHL prescription leads to mass-accretion rates much lower than the mass-transfer rates we derive, sometimes by more than an order of magnitude. 3.2. Accretion luminosity Another insight revealed by this analysis is the identification of the configurations where ULXs cannot be the product of mass transfer via wind-RLOF and can be explained only if the star fills its Roche lobe. In Fig. 2 , we represented in black the regions where μ is inferior to 0.2%, the minimum fraction of stellar wind captured under which mass transfer without RLOF is not able to produce a stationary X-ray luminosity of 10 39 erg s −1 , even for a stellar mass-loss rate as high as 10 −4 M ⊙ yr −1 : Given the maximal μ we found at ∼20%, this analysis suggests that mass transfer via wind-RLOF in a ULX is only possible for stellar mass-loss rates above ∼10 −6 M ⊙ yr −1 . We note here that matching a mass-transfer rate Ṁ high enough to reach ULX levels is a necessary but not sufficient condition: the final X-ray luminosity is determined by the physics at stake within the Roche lobe of the accretor, where the flow geometry can be disk-like ( El Mellah et al. 2019 ) or spherical ( Shakura et al. 2012 ) and where, for an accreting NS, the magnetosphere eventually dominates the dynamics ( Bozzo et al. 2008 ). For accreting BHs, powerful disk outflows come into play in the vicinity of the compact object, lowering the final mass-accretion rate ( Pinto et al. 2016 ). Rather than covering the large scope of regimes possible, let us focus on three donor stars in one SgXBs and two ULXs. In the SgXBs Vela X-1, Gimenez-Garcia et al. (2016) reported a stellar mass-loss rate Ṁ ⋆ ∼ 6.3 × 10 −7 M ⊙ yr −1 for the B0.5 Ib supergiant donor star. In M101, Liu et al. (2013) inferred a mass-loss rate of 2 × 10 −5 M ⊙ yr −1 for the Wolf-Rayet donor. In P13, we think the stellar mass-loss rate of the B9 Ia supergiant donor star could have been underestimated: in Motch et al. (2014) , it is assumed that the donor star fills its Roche lobe on the basis that the wind mass-loss rate derived by Kudritzki et al. (1999) would be inferior to 10 −6 M ⊙ yr −1 . However, Kudritzki et al. (1999) did not include late-type B supergiants in their study because of the difficulty to measure their terminal wind speed ( Howarth et al. 1997 ). Vink et al. (2000 , 2001) provided fits for the mass-loss rate and the terminal wind speed which extend below the second bi-stability jump (i.e., for effective

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


a comparison needs to be made statistically using a large sample of stars. Unfortunately measurements are available for very few A and B stars in Kepler and K2 . A comparison using 30 stars with T eff in the range 8300–12 000 K supports the identification of the photometric period with the rotation period (Balona 2017 ). A similar study using TESS observations of B stars comes to the same conclusion (Balona et al. 2019 ). Both these studies involve small numbers of stars. TESS observations have revealed the rotation frequencies of many more A and B stars for which measurements are available. Table 2 shows that there are 274 stars with both rotation frequencies and . In Fig. 1 a comparison between and the photometric v is made for 193 stars with T eff > 8000 K. The temperature limit was chosen to minimize contamination by stars in which surface convection may still be present. Since cannot exceed v , the points are expected to lie below the line in the figure. Figure 1. The projected rotation velocity, , as a function of the equatorial rotation velocity, v , estimated from the photometric period for stars with effective temperatures T eff > 8000 K. The straight line is . The 1σ error bars are shown on the top left. Table 2. The number of stars with known photometric periods, n , and the total number of stars, N , in the given effective temperature range, T eff , is given. The number of stars with both photometric periods and measurements is . The number of stars used in the frequency distribution is . The increase in numbers of stars above the line at low rotation rates is to be expected. Measurements of are mostly obtained by measuring the widths of selected spectral lines and applying a calibration to convert to . The calibration is obtained using high-dispersion spectra and modelling line profiles. The error in is approximately constant at all values of . Analysis of the rotational velocity catalogue of Glebocki Gnacinski ( 2005 ) gives a standard deviation of of about 30 km s −1 . This means that at low values of , the error is comparable to, or larger than, itself and many points will lie above the line. This is further compounded by the fact that is constrained to be greater than or equal to zero, although measurements of line width may lead to negative values of on applying the calibration. As the rotation rate tends to zero, measurements of ever increasing precision are required to ensure that stays below the line. This is clearly not possible to attain. Another consideration is that low photometric frequencies are more difficult to measure because a longer time span is required to resolve the frequency peak in the periodogram. Thus instrumental drift becomes important. This is further compounded by the fact that the periodogram noise increases sharply towards zero frequency. Thus the uncertainty in v increases as v approaches zero, contributing to moving the point above the line. The standard deviation for v is about 40 km s −1 as

O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O B-Mission O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O O O O O B-Telescope O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O B-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 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-TextGarbage I-TextGarbage 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


values of polynomial fits at each pixel and plot the resulting model over the original spectrum. In the lower panel of Fig. 3 , we show the residuals between the model and the input spectrum, with horizontal lines marking the median uncertainty about zero for this spectrum. With just eight principal components, we can model this particular spectrum to within the typical measurement uncertainty. In Fig. 4 , we show the distribution of model residuals for all spectra in our example slice of the red clump for models using zero, four, and eight principal components. As we expect, increasing the number of principal components used in the model causes the residual histogram to become more peaked towards a value of 0, with shallower wings. Given this continual improvement in modelling, it is necessary to define a cut-off to determine when improvements to the model explain variations due to noise, not intrinsic stellar differences. Figure 4. Histograms of the residual normalized flux after subtracting from each spectrum in the example slice a model using 0, 4, and 8 PCs. As more PCs are used, the histogram becomes more sharply peaked in the centre, with shrinking wings. 3.3.2 Assessing principal components We now define some useful statistics that can be computed from the results of EMPCA, which allow us to assess the results of the algorithm. We define V data mean as the mean-based variance of , We define a similar quantity V data MAD as the median absolute deviation (MAD) based variance of where is the p th row of , the operation ‘med’ is taking the median of the data, and the factor of 1.4826 scales the MAD to the standard deviation for normally distributed data, i.e. V data mean = V data MAD for data drawn from a Gaussian distribution. Equations ( 11 ) and ( 13 ) represent the total variance in the data. We wish to compare these to the variance after removing the principal component model produced by EMPCA. To do this, we define two additional quantities that compute the variance in the data after the contribution from the first n principal components has been subtracted out: Here, is the original data set after the model using the first n principal components has been subtracted (equation 10 ), and is the p th row of . Note that in the case where n = 0, V model mean (0) = V data mean and V model MAD (0) = V data MAD . Also note that when the number of components is maximized ( n = min ( N, P ) = n limit ), V model mean ( n limit ) = 0 and V model MAD ( n limit ) = 0, because in that case the model can perfectly represent all of the data. In what follows, we use V data and V model without superscripts when either the mean-based or MAD-based versions could be used. We compare these variances using R 2 ( n ), defined as The R 2 ( n ) curve should increase in height with the number of iterations on the model components. The maximal value for R 2 ( n ) is 1, which indicates the data can be perfectly reproduced by a linear combination of n components

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


by the WIND spacecraft at 1 au on 2011 June 24, with n i = 2.4 cm −3 , V SW = 599.0 km s −1 , and . (a)–(c) Time variations of the magnetic field vector in geocentric solar ecliptic coordinates. (d) Time variation of field magnitude. (e) Power spectrum of the magnetic field obtained from the FFT method with 11-point centered smoothing. The spectrum with spacecraft frequency f 10 −3 Hz is not shown here, since there are not enough points at this domain when smoothing the spectrum. The two red solid lines show the linear fits to the spectrum in the low-frequency and high-frequency ranges, respectively. Red dots indicate the upper and lower frequency limits used to perform the fits. The obtained spectral indices for the low-frequency ( α L ) and high-frequency ( α H ) ranges and their uncertainties are shown, along with the values of f b , f di (blue arrow), f ρi (green arrow), f ri (black arrow), and β . The vertical dashed line denotes the frequency of the spectral break. Panel (e) of Figure 1 shows the power spectrum of the magnetic field fluctuations. The spectrum is computed by applying the Fast Fourier Transform (FFT) on the three components of B . The trace of the spectral matrix gives the total power spectrum (hereafter power spectrum for simplicity). The spectral break frequency is determined as follows. First, we estimate the location of the break point by eye, which is roughly at 0.3 Hz. The break point divides the power spectrum into two parts: a shallower low-frequency part and a steeper high-frequency part. We then perform linear least-squares fit to the spectrum on the two sides of the roughly estimated break point, respectively (see the two red solid lines in Figure 1 (e)). The upper and lower frequency limits (the red dots) used in the fitting procedure are determined by the frequency range that is best fitted by power law based on chi-square minimization. For the low-frequency part, the band used to perform the fit is between 0.008 and 0.1 Hz. The spectral slope as well as its 1 σ uncertainty is estimated as α L = − 1.694 ± 0.025, which is close to the typical Kolmogorov scaling f −5/3 in the inertial range of the solar wind turbulence (Matthaeus et al. 1982 ; Goldstein et al. 1995 ; Tu Marsch 1995 ; Podesta et al. 2006 ). The high-frequency part of the spectrum beyond the break point is also fitted by a red solid line in the same way, but at the frequency range between 0.4 and 1.2 Hz. The intersection of the two red solid lines associated with the power-law fits thus gives the exact frequency of the break point f b = 0.288 Hz (marked by the red vertical dashed line). This method about determining the break frequency has already been used in several previous studies (e.g., Leamon et al. 1998 ; Smith et al. 2006 ; Hamilton et al. 2008 ; Markovskii et al. 2008 ; Bruno Trenchi 2014 ; Wang et al. 2018 ). In addition, we notice that at the frequencies higher than 1.5 Hz, the power spectrum becomes shallower again, which

O O B-Mission O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest I-EntityOfFutureInterest B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation 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


resolution. In order to compare clumps in our galaxies with those in high-redshift galaxies, we identified clumps by visual inspection of the z = 2 images in the F435W band. Measurements were made on the original non-redshifted images since the simulated redshifted images were Gauss-blurred and re-pixelated with artificial noise added, so flux would have been difficult to determine accurately. Instead, contour plots were made on the local images and compared with the z = 2 images where the clumps were distinct. In practice, the contours at 10× sky σ on the local images matched the clumps in the high -z images, so that is where the boxes were defined for photometry. The IRAF task imstat was used to determine total pixels and mean counts per pixel within the boxes. Magnitudes were then determined for each clump, using the zero-points from the WFC3 and ACS handbooks. There was no background subtraction, because the photometric fitting described below included an underlying component plus the star-forming component, described further below. This is the same procedure as we used in measuring clumps in high-redshift galaxies (Elmegreen et al. 2009b ), so our results for clumps in our galaxies can be directly compared to the high-redshift results. For the galaxies in this paper, this means the clump boundaries sometimes contain more than one large clump, since some get blended at high z . The measured clumps are indicated as boxes in Figure 8 . For Haro 11, contour plots are also shown as an example of how clumps were identified. The right-hand contour plot is on the simulated z = 2 F435W image, where the three clumps are distinct. The middle contour plot on the original image has an arrow indicating the ∼10× sky σ contour where the boxes were then drawn. A total of 51 clumps were identified in the seven galaxies (the number in each galaxy is listed in Table 1 ). The average absolute B- band magnitude of the clumps for the seven galaxies in this sample is −15.4 ± 2.6, while the average ( B − V ) color is 0.4 ± 0.5. The clump diameters are approximated by the square root of the area of the boxes defined for photometry, and range from 170 pc to 2.9 kpc, with an average of 1.0 ± 0.7 kpc. Figure 8. The seven galaxies studied here are shown in the F555W filter. Boxes identify the clumps that were measured; see Figures 1 – 4 for physical scales. For Haro 11, contour plots are also shown to indicate how clumps were identified. Measurements were done on the non-redshifted images for the boundaries determined from the redshifted images. In practice, these boundaries were at a surface brightness ∼10× sky σ in the F435W image, as indicated in the middle image. The right-hand contour plot is for the simulated z = 2 F435W image, where the three clumps are distinct. 4.2. Clump Ages and Masses The photometric measurements of the clumps were used to determine ages, masses, and extinctions through spectral energy distribution (SED) fitting, as detailed in Elmegreen

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


is undetected in one scenario, an upper limit on its abundance can suffice to disfavour biological production for certain molecules. Fig. 7 shows the posterior distributions for the mixing ratio of each molecule from our retrievals. A 10 Prism transit campaign suffices to constrain the CO 2 and CH 4 abundances of the modern Earth to within an order of magnitude (0.78 dex and 0.85 dex, respectively); for the prebiotic Earth only CO 2 is constrained (0.62 dex). An increase to 20 Prism transits offers two new results: (i) an order of magnitude constraint on the H 2 O abundance for the prebiotic Earth (0.70 dex); and (ii) a upper limit on the prebiotic Earth CH 4 abundance in tension with the confidence interval of the modern Earth CH 4 abundance. The latter is a diagnostic difference between the modern and prebiotic scenarios accessible with only 20 transits. A further increase to 100 Prism transits offers dramatic improvements: constraints on the CO 2 , H 2 O, and CH 4 abundances to ∼ a factor of 2 (0.3 dex), and an order of magnitude constraint on the modern Earth N 2 O abundance (0.78 dex). Constraints on the O 3 abundance of the modern Earth can be obtained, to within an order of magnitude, with either 100 Prism + 100 MIRI transits (0.63 dex), or 200 Prism transits (0.59 dex). However, 200 Prism transits result in significantly better constrained abundances for the other molecules. As above, we recommend additional Prism transits instead of dividing time between the Prism and MIRI. Figure 7. Retrieved atmospheric composition from simulated JWST observations of TRAPPIST-1e. The predicted mixing ratio constraints for CO 2 , H 2 O, CH 4 , N 2 O, and O 3 for the 1 bar modern Earth (green) and prebiotic Earth (orange) are shown by the marginalized posterior histograms. Each row corresponds to a different JWST observing campaign, ranging from 10 NIRSpec Prism transits (top) to 200 Prism transits (bottom). Various combinations of NIRSpec Prism + MIRI LRS transits are also included. Predicted detection significances for each molecule are annotated (green text for the modern Earth; orange text for the prebiotic Earth). Abundance constraints (error bars) are overlaid, with the interval annotated where constraints 1 dex are possible. For non-detections, abundance upper limits are shown (vertical lines with arrows). The prebiotic and Modern scenarios can first be distinguished with 20 Prism transits via the CH 4 abundance (the prebiotic upper limit precludes the modern abundance). Similarly, the N 2 O abundance can be differentiated with 200 Prism transits. Even 200 Prism transits (or 100 Prism + 100 MIRI transits) are insufficient to distinguish the O 3 abundances. O 2 is unconstrained in all cases. Adding MIRI data slightly increases the detection significances of O 3 , but adding the same quantity of Prism transits produces tighter constraints on all other atmospheric parameters. Our analysis demonstrates that the most effective way to

O O O O O O O O O O O O O O O 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 B-CelestialObject O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O B-CelestialObject O O O O O O O O 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 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 B-CelestialObject 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-Instrument O O B-Instrument O O O O O B-Instrument O O O O O B-Instrument 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 B-Instrument O B-Instrument O O O O O O O B-Telescope 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-CelestialObject O O O B-CelestialObject O O O O O O O O O O O O O O B-Telescope O O O O O B-Instrument B-Instrument O O O O B-Instrument O O O O O B-Instrument B-Instrument O B-Instrument B-Instrument O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O B-CelestialObject O O O O O O O O O O O O O O O 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 B-Instrument O O O B-Instrument O O O B-Instrument O O B-Instrument 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 B-Instrument O O O O O O O O O O O O O O O O O O


is evaluated. The θ = 0 plane corresponds to the equatorial plane of the system. Bottom : angular ejection distribution after the most energetic interaction. Other elements in the plots are the same as in the top three plots. In contrast, we find that Pops. II and III are more isotropically distributed. These are the stars that come from outer regions on centrophilic orbits, and therefore the effect of random motion of the black holes does not play a role, like it does in the case of Pop. I. We notice that the third and especially second population show a prevalence of ejections along the SMBH binary orbital plane. This is in agreement with previous studies which find that HVSs are primarily ejected near the SMBH binary orbital plane when their SMBH orbital plane is aligned with the rotational place of the system (e.g., Sesana et al. 2006 ; Wang et al. 2014 ; Zhong et al. 2014 ; Lezhnin Vasiliev 2019 ; Rasskazov et al. 2019 ). Our findings show that not all of our three populations are uniformly distributed in the azimuthal direction. While there is some disagreement in the literature over the existence of a preferential ejection direction in eccentric binaries ( Rasskazov et al. 2019 ), in the case of a circular SMBH binary like ours, previous studies report a uniform distribution of ejected stars in the orbital plane ( Rasskazov et al. 2019 ; Lezhnin Vasiliev 2019 ; Sesana et al. 2006 ). We argue that the motion of black holes around the center can result in anisotropic ejections for the central population of stars (Pop. I), while stars originating from outside of the SMBH binary influence sphere are uniformly distributed (Pop. II and III). From the apocenter distribution in Fig. 11 , we conclude that Populations II and III correspond to stars on centrophilic orbits that are responsible for repopulating the loss cone. Depending on the shape and degree of nonsphericity of the nuclei (e.g., axisymmetric or triaxial), different orbital families may fulfil this role ( Merritt 2013b ). We can distinguish between the different orbital families if we look at their angular momentum at a time significantly before the interaction. Namely, because of the symmetries of different geometries, we can distinguish between spherical, axisymmetric, and triaxial orbits. Spherical orbits have conserved angular momentum, and in order to satisfy Eq. ( 12 ) are necessarily contained at all times within the bottom dashed square region of the top panel of Fig. 12 . Axisymmetric orbits, such as the saucer and tube orbits, in turn have conservation of the z -component of angular momentum and are therefore necessarily contained in the | L z / L crit | 1 region of phase space, denoted by vertical dashed lines in the same figures. Finally, triaxial orbits (pyramids, boxes or chaotic orbits) can have arbitrarily small or large values in the ( L , L z ) plane as a result of a lack of an integral of motion in that plane. This simple classification scheme is inspired

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


This holds true in particular for CO line emission which is optically thick. A second parameter to explore is , the power-law index of the surface density distribution. Models with different values are presented separately in the lower panels of Fig. A.1 . The line luminosities produced by models with and are almost indistinguishable, while differences can be found comparing these with models with . In particular in the intermediate disk mass regime, models for show three different populations that reflect models with different values. This effect is less clear for models with . Finally, it is interesting to investigate how much the central star influences the CO isotopologues emission in the disk. Models with the same physical disk parameters, but irradiated by a T Tauri-like and a Herbig-like star are presented in Fig. 2 (respectively in the left and in the right panel) and in Fig. 3 . For the Herbig disks, the derived line intensities are higher for more massive disks and lower for less massive disks compared with those obtained for the T Tauri disks. Since Herbig disks are warmer, less material is frozen-out onto grains in the higher mass regime and can contribute to the total emission enhancing the line luminosity. Also, the higher temperatures enhance the moderately optically thick CO lines. On the other hand, the strong UV flux coming from the Herbig star is very efficient in photodissociating CO isotopologue molecules for lower mass disks (, ) where the column densities are not high enough for shielding the photons. This combination of high UV field and low column densities reduces the line luminosities, thus they are lower than those from T Tauri disks. 3.2.4. Dependence on gas-to-dust ratio To test the sensitivity of the results to the gas-to-dust ratio for a fixed gas mass, we ran two T Tauri disk models ( au, , , , , ) with reduced gas-to-dust ratios of ten and one. The ray-traced line intensities for CO isotopologues are presented in Fig. A.3 as functions of the gas-to-dust ratio, normalized to the value at gas-to-dust =100. For the disk the optically thin CO intensities increase by a factor of 3.5 if the gas-to-dust ratio is lowered by a factor of 100. This can be understood by the fact that if the dust mass is enhanced for a fixed gas mass, the FUV flux will be more efficiently attenuated. Accordingly CO and its isotopologues survive more easily and their lines are brighter for low gas-to-dust ratios, especially if their emission is optically thin. In addition, if the dust opacity dominates over the line mutual shielding, isotope-selective processes are minimized. The CO and CO emission on the other hand stay the same within 30% because they are more optically thick. There are also small temperature differences of order 20% between the models in the emitting layer which can affect their line intensities. For the disk the trend is opposite: line intensities decrease if the gas-to-dust ratio is lowered for all three

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O B-EntityOfFutureInterest O O O O O O O O O O O O O O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O O O O O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest I-EntityOfFutureInterest O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model I-Model O B-TextGarbage I-TextGarbage I-TextGarbage I-TextGarbage I-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 B-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


et al. 2017 ). This implies that low- and intermediate-mass stars in such a late evolutionary phase are often old and hence metal-poor on average. The distributions of [Fe/H] and [S, Zn/H] are very similar in the LMC and in our Galaxy (see Fig. 7 ), indicating that depletion and hence dust-gas segregation and subsequent gas accretion, is very similar in both environments. On average the LMC has a lower metallicity than the Galaxy but it does not affect the efficiency of the depletion process. Additionally, in none of the systems, there is an evidence that the abundances of the s-process elements, systematically deviate from the abundance of elements with similar dust-condensation temperature. A good tracer of the depletion which is independent of the initial metallicity is the [Zn/Ti] abundance ratio. Zn and Ti are both Fe-peak elements and have the same nucleosynthetic history. If only nucleosynthesis determines the abundances ratios, (i.e. no selective depletion of elements), then [Zn/Ti] will remain zero. Since Ti is likely to be more strongly depleted than Zn, [Zn/Ti] is an ideal indicator of depletion. Therefore, we define the efficiency of depletion as a function of [Zn/Ti]. In principle [Zn/Fe] can also be used as a proxy for depletion; however, Ti has a higher dust condensation temperature and hence more easily depleted than Fe. So we define the efficiency of depletion as a function of [Zn/Ti]. Strongly depleted sources are defined such that [Zn/Ti] ≳ 1.5. Mildly depleted sources are defined as those with 0.5 ≲ [Zn/Ti] ≲ 1.5 while sources with [Zn/Ti] ≲ 0.5 are considered to show little or no depletion. In Fig. 8 we show the spread in [Zn/Ti] abundance ratios as a function of T eff for the LMC post-AGB sources (left-hand panel) and the depleted Galactic sources (right-hand panel). We find that the LMC as well as Galactic post-AGB stars show a large spread in depletion patterns, ranging from strongly depleted to stars with mild and no depletion. The plots also show that there is no clear trend in the efficiency of depletion with respect to T eff . The advantage of the LMC sample is their accurately derived luminosities. The derived photospheric luminosities of the LMC sample of depleted objects show that chemical depletion is active over a range of luminosities (see Section 5 and Fig. 8 , left-hand panel). Hence we can conclude that there is also no clear trend in the efficiency of depletion with respect to luminosity ( L ph ) of the star. Figure 8. Left: The [Zn/Ti] abundance as a function of T eff for the depleted sources in the LMC. Right: The [Zn/Ti] abundance as a function of T eff for the depleted post-AGB stars in the LMC (black filled circles) and their Galactic analogues (magenta filled squares). The dashed line represents the limit of what we call ‘strongly depleted’ while the dotted line marks our definition of ‘mild depletion’. In the case of the Galactic sources, majority of these objects show the presence of a stable

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


not correspond to the velocity expected from the kinematical model presented in this work. We thus conclude that the clumps of the EHVO seen in Fig. 7 correspond to material that was swept up by a different outflow, which is faster and likely older than the HVO. Additionally, there seems to be traces of entrained material of the EHVO outflow that appear as “horns” of the HVO and confined within the region traced by the CO( J = 1 → 0) emission. Therefore, it is likely that the extension of the region traced by the CO( J = 1 → 0) emission determines the radius of CO photo-dissociation by interstellar UV radiation. 4.3 Kinetic energy and scalar momentum of molecular outflow Since our model is fundamentally different from the one presented by Sahai et al. (2017) , here we re-calculate the scalar momentum and kinematic energy of the molecular outflow. To obtain the kinetic energy and scalar momentum, in principle, it is possible to use the mass spectrum shown in Fig. 6 . However, the velocity offset in this plot is simply the component of the expansion velocity on the line-of-sight. The 3D expansion velocity is necessary for the calculations. To circumvent this problem, one can take advantage of the morphology adopted for the emitting region, which has an elongated, narrow shape. In such a case, it is possible to de-project the velocity vectors by multiplying the velocity offsets by a factor of 1/sin θ inc , with θ inc = 45°. This is not strictly true for all the velocity vectors, since the gas is not really moving along one single line. Particularly, for the gas located close to the central source, which might be expanding along the line-of-sight, the expansion velocity will be overestimated by a factor of 1/sin θ inc . For such gas, this leads to an overestimation of the scalar momentum by a factor of and for the kinetic energy by a factor of 2. In addition, there is an uncertainty due to the optical depth of the CO( J = 3 → 2) emission since it was assumed to be optically thin to obtain the mass spectrum of Fig. 6 . If the emission is optically thick the estimated value of the mass simply represents a lower limit. Having this in mind, we proceeded to calculate the kinetic energy and scalar momentum in the manner introduced by Bujarrabal et al. (2001) and described inthe following. Firstly, we multiplied the mass in each channel by the square of the corresponding velocity to obtain the kinetic energy per channel. By adding the kinetic energy of all the channels we obtain K LVC = 8 × 10 44 erg and K HVC = 1 × 10 45 erg for the LVC and HVC, respectively. Similarly, the derived scalar momentum is 1.6 × 10 38 gm cm s −1 and 6 × 10 37 gm cm s −1 for the LVC and HVC, respectively. The total kinetic energy and scalar momentum in the outflow are of the same order of magnitude as the values calculated by Sahai et al. (2017) . Subsequently, the scalar momentum in the molecular outflow transferred by the jet, Δ P , is obtained by subtracting the scalar

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


the maximal error is roughly 6 times smaller than this upper limit. Table 2. In this table we compare nonlinear correction spectra computed with EuclidEmulator (EE) on the one hand and with an emulator based on Takahashi’s HALOFIT (THF) on the other hand to nonlinear correction spectra of full N -body simulations for 36 cosmologies outside the ED over the entire k and range. The numbers in the table correspond to the relative errors in per cent between the emulated and simulated nonlinear corrections. We find that the errors predicted with the THF emulator are broadly consistent with the EE errors. This implies that the configuration of the EE based on a HALOFIT emulator is actually valid and that there is no need to make a huge investment to run N -body simulations just for the configuration study of an emulator. This result is particularly important for finding the size of the ED (see Fig. 5 ). 4.2 Sensitivity analysis Sobol’ indices (Sobol’ 1993 , 2001 ) measure how sensitive the eigenvalues λ i (ω b , ω m , n s , h , 0 , σ 8 ) (introduced in equation 9 ) are to each single input parameter as well as to any of their interactions. For an introduction into Sobol’ sensitivity analysis, we refer to the previous references or to Marelli et al. ( 2017 ) and Le Gratiet, Marelli Sudret ( 2016 ). Sobol’ indices are based on the Hoeffding-Sobol’ decomposition, which states that any square-integrable function over a hypercube input parameter space can be cast as a sum of a constant, a set of univariate functions of each input parameter, another set of bivariate functions, etc. This decomposition is unique and the various terms are orthogonal with each other (with respect to the uniform probability measure over the hypercube). The variance of the output can then be apportioned to each input parameter, each pair, triplets, etc.: these contributions are called Sobol’ sensitivity indices S . Although their classical estimation relies on costly Monte Carlo simulations, Sobol’ indices can be computed analytically from a PCE as in equation ( 9 ), see Sudret ( 2008 ). In our case, we get one such Sobol’ expansion for each principal component. Each Sobol’ index corresponds to the fraction of the total variance of the respective eigenvalue that is caused by the parameter(s) under consideration. The bigger this number, the more λ i depends on the considered set of input parameters. Fig. 7 shows the first-order (no interactions) Sobol’ index plots for the first and fifth principal components (see Fig. A1 in Appendix A ). It is interesting to notice that the input parameter ω b has no leading-order effect on the output nonlinear correction. The nonlinear correction starts to show non-vanishing sensitivity to this parameter only at fifth order and higher. This is explained by the fact that baryons are treated as a background quantity that only come into the simulation data via the transfer function. As they are not directly evolved themselves in PKDGRAV3 , their

O 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-Software O O O O O O O O O O B-Person B-Software B-Software O O O O O O O O O O B-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software I-Software O O O O O B-Software O O O O O O O O B-Software O O O B-Software I-Software O O O O O O O O O O O O O O O O B-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation O B-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O


disc. Fig. 7 confirms that the time lag increases with increasing R acc and with increasing ξ, and does not change significantly with τ r and τ w . Observations show time lags of about 50–250 Myr which are reproduced by most of our simulations, but a few of our simulations produce time lags that have values of up to 550 Myr. Such large time lags have not been directly observed yet. However, Wild et al. ( 2010 ) only measure the average time lag of a sample of about 400 galaxies with a result of 250 Myr, thus some of the galaxies involved will have time lags that exceed this average value. Fig. 8 shows SFR, BHAR and AGNAR versus time for different levels of resolution. We increase the number of particles by a factor of 2 and a factor of 4, respectively. For the former resolution level the gravitational softening length for the halo particles is 0.64 kpc and 0.4 kpc for all other particles, for the latter resolution level the gravitational softening length for the halo particles is 0.5 kpc and 0.32 kpc for all other particles. Figure 7. Time lag between starburst and AGN activity with the values of R acc , ξ, τ r and τ w from our parameter study (Table 2 ) and our reference model. Figure 8. SFR, AGNAR and BHAR as functions of time for different resolution levels. Left: particle number increased by a factor of 2, right: particle number increased by a factor of 4. The vertical lines mark the peak of the SFR and the peak of the BHAR, respectively. Both resolution levels show the same features as our reference model: the simulations produce a starburst and a peak in the BHAR, and a time lag between these phenomena of about 200 Myr. However, there are still small differences between these simulations, to further reduce these deviations additional adjustments to the respective resolution levels would be necessary. For instance, Hopkins, Narayanan Murray ( 2013 ) argue that the critical density for the onset of star formation ρ crit has to be adjusted for resolution. But as the above mentioned key features are already reproduced we refrain from such a fine tuning of our simulation parameters. 5 SUMMARY With only one model setup we were able to reproduce three observational findings that have been identified in galaxies. The observed time lag between starburst and AGN activity is, in our work, principally caused by a viscous time lag the gas needs to flow through the AGN's accretion disc until it reaches the central black hole. Our results match the observed M BH -σ correlation, but additionally include the aforementioned time lags. As, e.g. Di Matteo et al. ( 2005 ) or Debuhr et al. ( 2011 ) have already shown, AGN feedback is responsible for this relation. The large scatter of the M BH -σ correlation is, in our work, caused by the continuing evolution of the black hole mass after the merging event. The time lag does not only occur between starburst and AGN activity, but also between the peak in the AGNAR and the peak in the BHAR. Thus it is

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


in the range 0.4%–0.5%. For the dwells with mHz detections, the symbol size is proportional to the fractional amplitude (rms). 3. Properties of mHz Oscillations Since the power spectra (Figure 3 ) from the two 2017 September dwells with strong mHz oscillations are consistent with rather coherent oscillations during these intervals, we computed phases for all events in each of these dwells separately using the frequencies corresponding to the peak Fourier power obtained from each dwell. To combine the two dwells we first found a constant phase offset for the second dwell that maximized the signal power of the sum of both dwells (Buccheri et al. 1983 ). The resulting phase-folded pulse profile in the 0.4–7.5 keV band is shown in Figure 8 . We fit a model of the form and find an amplitude B / A = 1.12 ± 0.05%. The fit is good with a minimum χ 2 = 11.0 for 13 degrees of freedom, and the best-fitting model is also plotted in Figure 8 (red curve). To explore the energy dependence we also computed profiles for different energy bands and then fit them with the same model as above. Figure 9 shows the derived amplitudes, B / A , and phases, φ 0 , versus energy. The amplitude shows a modest increase from about 0.7% at 1 keV to ≈2% at 7 keV. There is no strong evidence for a variation in φ 0 with energy. Figure 8. Average, phase-folded mHz oscillation profile from the two NICER dwells shown in Figure 2 . The profile includes all events in the 0.4–7.5 keV band. The best-fitting model, , is also shown (red curve). Phase ranges used to extract spectra are indicated by the vertical lines. See Section 3 for additional discussion. Figure 9. Fractional pulsed amplitude (top) and reference phase, φ 0 (bottom), obtained from fits to the phase-folded mHz oscillation profile are shown as a function of energy. The dashed line in the bottom panel marks the mean reference phase value. This constant value provides an acceptable fit to the distribution of values, with a χ 2 = 6.9 for 5 degrees of freedom. To explore the pulse-phase spectrum we extracted two spectra, from regions around the pulse minimum and maximum. The phase ranges used for these extractions are indicated by the dashed and dashed–dotted vertical lines in Figure 8 , respectively. In each case, we used a range of pulse phase equal to 0.25 cycles, so that each spectrum has an exposure of 0.25 × (2(2200)) = 1100 s. We used XSPEC version 12.9.1 with version 1.02 of the NICER instrument response, and we fit the spectra in the range 0.6–9 keV. We use a model comprising thermal comptonization ( comptt in XSPEC) for the persistent accretion-driven emission and a blackbody ( bbodyrad in XSPEC) to capture the neutron star thermal emission (Thompson et al. 2008 ; Chenevez et al. 2016 ). To model Galactic absorption we employ the tbabs model with abundances from Wilms et al. ( 2000 ), and we fix (freeze) the value of n H = 0.4 × 10 22 cm −2 based on prior measurements, since the source is in the same (soft) state

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O B-TextGarbage I-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 B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O B-Software I-Software I-Software O B-Identifier I-Identifier O O B-Model I-Model I-Model O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O B-Model O B-Software O O O O O O O B-Model O B-Model O B-Software O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O B-CelestialObject O O O O B-Model I-Model O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O


low-density conditions ( Westermann et al. 2001 ). It allows operation at 10 −10 –10 −6 mbar and can be used in a static background mode in molecular-beam mode to simulate the outflow of cometary gases ( Graf et al. 2004 ). To calibrate aliphatic and aromatic hydrocarbons in the DFMS laboratory model, the compounds were transferred from liquid into gas phase by heating the sample tube to 323 K at low pressure in the range of 10 −6 mbar. The gas was introduced through a leak valve into CASYMIR/DFMS where measurements were performed. This procedure was repeated at three different pressure levels p = 3 × 10 −9 mbar, 2 × 10 −8 mbar, and 1 × 10 −7 mbar to cover a maximum density range. In addition, background measurements were performed and subtracted from the actual measurements. Calibration of DFMS on aliphatic and aromatic hydrocarbons was necessary for several reasons: (I) in addition to charging neutral molecules positively, the electron impact ionization used in mass spectrometry also breaks molecular chains and thus leads to a detection of the fragments and the parent molecule in the mass spectra. This process is called fragmentation and depends on the electron energy used for ionization. It results in a fragmentation pattern with species-dependent abundances, which can be used to identify or exclude species in mass spectra. However, the pattern also depends on the molecular structure of the ionized species and thus can be used to distinguish isomers such as n-butane and isobutane. Compounds such as pentane, heptane, and octane with higher masses are significantly affected, leading to complex fragmentation patterns. (II) The DFMS sensitivity on a compound is calculated from the detected number of ions. Therefore pressure conditions must be stable over the measurement period. This can be especially challenging for volatile organic compounds. Thus, a thermal valve-control system was used to stabilize the partial pressure of the component in CASYMIR during the calibration cycle. The DFMS calibration campaign included the saturated aliphatic compounds up to octane (integer mass/charge 114 u/e). The calibration campaign on butane, pentane, hexane, heptane, and octane was made with unbranched molecule version (e.g., n-pentane), while for methane, ethane, and propane, no differentiation in terms of structural isomerism appears. For benzene, the DFMS calibration was not performed because the compound is highly toxic in the gas phase. In addition to the fragmentation, the DFMS calibration campaigns were performed to derive the sensitivity of DFMS for measured compounds. Hereby the ratio of the ion current to the molecular density was derived for each pressure level. The slope between ion current and density for each of the three pressure levels is the sensitivity factor. As an alternative, when no calibration could be obtained, the sensitivity was calculated based on the ionization cross-section of the molecule. The sensitivities used in

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


higher post-outburst luminosities lead to shorter durations (∼hours to days) when DNB contributes significantly to the total luminosity and surface temperature. The total amount of energy available from burning hydrogen is set by the initial hydrogen column, and corresponds to the integral of the elevated luminosity cooling curves, which is constant in all cases with the same initial hydrogen column. For the initial hydrogen column of y H ∼ 1.2 × 10 6 g cm −2 , the total amount of energy that is released from hydrogen burning is 10 38 erg (i.e. ∼7 MeV nucleon −1 ). Without residual accretion or a large helium buffer that may slow down the depletion of hydrogen, the times when DNB significantly increases the observed surface temperature for an H–C envelope are ∼0.1–80 d from the end of the accretion outburst, depending on the initial hydrogen column and cooling luminosity. For larger initial cooling luminosities (and thus higher surface temperatures), the initial change in surface temperatures increases, while the relevant duration decreases, as the available hydrogen is consumed more rapidly. 4.2 Effect on cooling curves due to changing composition In addition to releasing energy through nuclear reactions, DNB can alter the observed cooling after accretion outbursts by altering the light element column in the envelope over time. In Section 2.1 , we show the effect on the T s – T b temperature relations for varying hydrogen column sizes in H–C envelopes (see Fig. 1 ). The decreasing hydrogen column due to DNB will only affect the cooling curve when the hydrogen column is varied in the transition region (as shown in Fig. 2 ). At the relevant temperatures for NSs in quiescence (with initial post-outburst surface temperatures T s > 8 × 10 5 K), this means that the same boundary temperature (at the bottom of the envelope) corresponds to different surface temperatures when the hydrogen column varies in the range 10 4 ≲ y H ≲ 10 7 g cm −2 . When the initial hydrogen column after the accretion outburst is smaller than y H ∼ 10 4 g cm −2 , a further decreasing hydrogen column will not affect the cooling curve. When the initial hydrogen column is larger than y H ∼ 10 4 g cm −2 , the cooling curve transitions from relatively hydrogen-rich envelope temperature relations towards those for a hydrogen-poor envelope. We show this effect in Fig. 8 , where we ignore the effect of heat released by DNB and only show the effect of a changing envelope composition. The dashed cooling curves in Fig. 8 correspond to fixed hydrogen columns, while the solid cooling curves correspond to the scenario where the hydrogen column decreases over time due to DNB. When DNB is taken into account, all the plotted cooling curves (irrespective of initial column density) correspond to that of a hydrogen-poor envelope after ∼50 d. Note that for larger post-outburst luminosities, it can take less time (∼1 d) to decrease the hydrogen column below y H ∼ 10 4 g cm −2 (see e.g. the

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