Σ after core collapse stops. The disk lifetime is close to that shown in Figure 6 . See the text for details. In Figure 8 , we show M disk and M * as functions of t for the disk evolutions ( ω = 0.3 × 10 −14 s −1 , T cd = 10 K, and M cd = 1.0 M ) with and without external FUV fields. The evolutions of M disk and M * are similar to those shown in Figure 3 . Since ω is smaller, more material of the core falls onto the star, which causes the star to grow faster and the disk to grow relatively slower. When the collapse ends, M * is about 0.86 M and M disk is about 0.14 M . Therefore, the gravitational potential well is deeper, which results in the weaker external FUV photoevaporation. Finally, the difference between the final star masses shown in Figure 8 is smaller (0.002 M ). Figure 8. Evolution of M disk (top panel) and M * (bottom panel) as functions of t for the same core properties as those shown in Figures 6 and 7 . The solid lines represent the case for including both internal X-ray and external FUV photoevaporations. The dashed lines represent the case for including internal X-ray photoevaporation only. Figure 9 shows R disk as a function of t for the disk evolutions ( ω = 0.3 × 10 −14 s −1 , T cd = 10 K, and M cd = 1.0 M ). The evolutions of R disk are similar to those shown in Figure 4 . However, the lower ω means that the location of core mass falling onto the disk is closer to the star. So, R disk for the disk without external FUV fields shown in Figure 9 is smaller than that shown in Figure 4 . As discussed in previous paragraphs, the star gets more mass during the core collapse for the case of ω = 0.3 × 10 −14 s −1 . Therefore, R g of the disk with external FUV photoevaporation grows quickly and it can finally reach ∼372 au. Although external FUV photoevaporation is very weak in this case, the gravitational potential well is shallow at the large radius of the disk. The external photoevaporation can still cut off the disk and decrease R disk effectively, as shown in Figure 9 . Figure 9. Evolution of R disk and R g as a function of t for the same core properties as those shown in Figures 6 and 7 . The solid line represents the evolution of R disk in the disk, including both internal X-ray and external FUV photoevaporations. The dashed line represents the evolution of R disk in the disk, including internal X-ray photoevaporation only. The dotted line represents the evolution of R g in the disk, including both internal X-ray and external FUV photoevaporations. Next, we discuss the evolution of external FUV photoevaporating disks with high ω . We first present the results of the disk evolution, including internal X-ray photoevaporation only. Figure 10 shows the evolution of Σ of the internal X-ray photoevaporating disk for the high low ω case that ω = 5.0 × 10 −14 s −1 , T cd = 10 K, and M cd = 1.0 M . In this case, the angular momentum of the pre-stellar core is very high. Most material of the core collapses onto the disk and is far

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


in other directions form gas circulations in the meridional planes, and near the bottom of the AGN bubble, meridional vortexes also appear. At t 700Myr, one can clearly see that the trailing flow is falling back to the cluster centre (see the overplotted velocity vectors), suggesting that the outflow does not leave the cluster eventually, but instead it is confined to the cluster. Figure 8. Temporal evolution of the concentration distribution ( Z ) of the tracer fluid in a simulation where the initial value of Z at t 0 is 1 if r 100kpc and 0 if r 100kpc. Arrows over-plotted in each panel indicate directions of gas velocities. From top to bottom, the time of each panel is t 300, 400, 500, 700Myr. The top colour bar represents Z in linear scale. It is clear that trailing flows behind the AGN bubble form real outflows in the ICM, which fall back to the cluster centre at later times, e.g. at t 700Myr. Trailing outflows play an important role in suppressing or delaying the central cooling catastrophe. As the rarefaction wave propagates away to large radii, gas inflows resume in the inner core region, as can be clearly seen in Figs 3 and 8 and discussed in Section 3.2 . If there are no trailing outflows, the gas density in the cluster centre would rise rapidly and a central cooling catastrophe would then develop. Trailing outflows uplifted by AGN bubbles transport gas from the inner cluster core to outer regions, suppressing gas accumulation at the cluster centre resulting from inflows along other directions and thus averting the central cooling catastrophe, which is delayed until trailing outflows fall back to the cluster centre at later times (see Section 3.6 ). Observational evidence for trailing outflows has been found in some cool-core clusters where the spatial distributions of heavy elements are anisotropic and preferentially aligned with the large-scale radio and cavity axes (Kirkpatrick, McNamara Cavagnolo 2011 ; Kirkpatrick McNamara 2015 ), suggesting that hot metal-rich outflows are indeed lifted up by AGN jets. Hydrodynamic simulations following both the jet and metallicity evolution in galaxy clusters would be helpful to further explore this scenario (e.g. Barai etal. 2016 , which however does not investigate the angular distribution of metals). Along the axes of trailing outflows, gas density is relatively high, as can be seen in the bottom two rows of Fig. 3 , and cold gas may drop out due to local thermal instability, forming cold filaments found in some galaxy clusters (e.g. Mittal etal. 2012 ; Tremblay etal. 2015 ). 3.6 Emerging picture of cyclic cool cores What is the long-term evolution of cool cluster cores after powerful AGN feedback events? After the onset of the AGN jet event, the cool core in our simulation is quickly overheated by shock dissipation, and rarefied by the rarefaction wave which transports energy to large radii. As the bow shock weakens and propagates further away, the inner core region starts to contract again

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


flow pattern is consistent across the diamagnetic cavity boundary in the CSE frame, we suggest that the flow pattern inside the cavity is determined by the flow outside, depending on the local plasma and magnetic field conditions. Fig. 7 Summary of flow pattern of the accelerated ions inside and outside the diamagnetic cavity in the YZ plane of ( a ) the CSEQ frame and ( b ) the CSE frame. The dark gray object at the center of each figure indicates the comet nucleus, and the surrounding light gray shaded area is the diamagnetic cavity. The view of these figures is from the Sun, and the four regions depending on the clock angle of the Rosetta position are also shown. In each region, a main tailward flow and its aberration component are shown by a cross and an arrow, respectively. Figure 8 summarizes the ion flow pattern inside and outside the diamagnetic cavity in the CSE frame. The aberration pattern of the accelerated ions in the - Z CSE direction near the XZ plane seen in Fig. 8 a suggests that they are mass-loaded by local cold cometary ions, which is similar to the mass-loading of the solar wind ( Behar et al. 2016a , b , 2017 ). The mass-loading of the accelerated cometary ions would result in an acceleration of the local cold cometary ions in the + Z CSE direction due to the conservation of momentum in the system, but we did not detect such a flow pattern from ICA data. This suggests that their energy is very low, which would be out of the energy range in this study (40 eV), or more likely, the density of the accelerated ions is much lower than the local cometary plasma, meaning that the earning momentum for the cold cometary ions is negligible. Fig. 8 Summary of the flow pattern of the accelerated cometary ions inside and outside the diamagnetic cavity in ( a ) the XZ plane and ( b ) the XY plane of the CSE frame. Near the XY plane of the CSE frame ( Fig. 8 b), the accelerated ions flow tailward with an anti-cometward aberration. This indicates that the accelerated ions are deflected around the diamagnetic cavity. The mechanism that produces this flow pattern is still unknown, but the accelerated ions may have been deflected when they flew across the upstream boundaries such as the ion-neutral collisionopause or the SWIC boundary. Another possibility is the aforementioned ambipolar electric field that points outward from the nucleus ( Odelstad et al. 2018 ; Bercic et al. 2018 ). This electric field may cause the tailward-flowing ions to be deflected around the diamagnetic cavity, which results in the anti-cometward aberration of the flow in the XY plane in the CSE frame. As seen in observations, the flux of these ions inside the cavity is nearly one order of magnitude lower than that outside the cavity. This suggests that the accelerated ions are only partly transferred from the outside into the inside of the diamagnetic cavity. There may be an energy-filtering effect in the cavity boundary. If the ion transmission into the cavity 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 O O O O O O O O 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObjectRegion O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


(− z rec for the counter-jet) for which a recollimation shock is formed due to the jet and wind momentum fluxes balancing each other in the y -axis direction (perpendicular to the jet propagation). This condition can be approximately expressed as follows ( Bosch-Ramon Barkov 2016 ): where Ṗ w = Ṁ w v w is the wind thrust. For γ j = 1.2 we obtain z rec = 1.4 × 10 12 cm ≈ 0.47 a , whereas for γ j = 3, z rec = 3.1 × 10 11 cm ≈ 0.10 a . Some combinations of Ṗ w , Ṗ j and γ j yield non-physical (complex) values of z rec in Eq. ( 4 ), which means that for those sets of parameters no recollimation shock is formed, as the momentum flux balance is never reached (see Yoon et al. 2016 , for a non-relativistic simulation where this effect is studied). Electrons are injected at , since the jet displacement in the x and y coordinates is small at z = ± z rec (≲0.005 a in the worst case). The particles are assumed to follow a power-law energy distribution with spectral index −2, typical for acceleration in strong shocks via the Fermi I mechanism (e.g Drury 1983 ), with a minimum energy of MeV. An exponential cutoff is also assumed: where E ′ is the electron energy in the FF. The normalization of Q ′( E ′) is obtained from the condition that the total power available for non-thermal electrons in the FF is . Electrons are convected from along the jet path while they cool down via adiabatic, synchrotron and IC processes. For simplicity, we neglect particle acceleration beyond , even though weak shocks and turbulence may (re)accelerate particles further downstream in the jets. Analytical expressions are used for the energy losses in the FF (see Longair 1981 ; Khangulyan et al. 2014 for synchrotron and IC losses, respectively). The characteristic timescale for adiabatic cooling is , where R j ( l )∝ l is the jet radius. The magnetic pressure at the accelerator (located at ) is characterized in the FF as a fraction η B of the total jet energy density: where and r j, 0 = R j ( z rec ) are the magnetic field and the jet radius at , respectively. For the same , this fraction relates to the ratio of magnetic pressure to stellar photon energy density in the LF as , which is useful to compare the expected radiation outputs of synchrotron and IC processes. This yields for γ j = 1.2, and for γ j = 3. The jet magnetic field is assumed perpendicular to the flow in the FF, since at the scales considered in this work, far from the jet launching point, a dominant toroidal component for the magnetic field is expected (e.g., Pudritz et al. 2012 ). Given the adopted assumptions plus frozen in conditions, the magnetic field at each jet point can be computed as: The cutoff energy is the maximum energy that the electrons can achieve in the accelerator region in the FF, and it is obtained as follows: We compare the acceleration timescale with the cooling timescale , where Ė ′ is the cooling rate accounting for adiabatic, synchrotron and IC losses. In this work we set η acc = 0.1 as a

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


activities during the period of 2012 August 7–September 4. SDO/AIA 211 and 193 Å observations show a series of coronal loops that formed at the heated region between the filament channel and the CH boundary before and after the partial eruptions (Fig. 4 ). Some loops are observed almost simultaneously with the filament plasma flow from its southern to the extreme northern footpoint on August 7 and some loops just before the onset of eruptions. Before and after the formation of these loops, several EUV bright points associated with the small magnetic dipoles appeared and disappeared quickly between the DR and the CH and very close to the filament channel and its southern footpoint. As observed in SDO/AIA 304 Å images (black arrows, Fig. 4 ), the loop formation was accompanied by the plasma motion from the filament channel to the western boundary of CH. Initially, just a few minutes before the eruptions, the filament plasma, related to a part of the central section not involved in filament eruption, moved from the central part of the filament channel, reached the western boundary of CH and induced the onset of CH fading (August 8, 07:15 ut; Fig. 4 ). Later, after the filament partial eruptions and CMEs, several additional loops formed and the evacuated filament plasma moved from the southern part of the filament channel, reached the southern side of CH and led to the disappearance of the dimming region and almost the whole CH (at 20:00 ut ). Furthermore, the analysis of SDO/HMI magnetograms after the partial filament eruptions and the disappearance of DR and CH show the magnetic diffusion at the north side of the erupted northern section of the filament. Figure 4. SDO/AIA 304 Å ( T = 5 × 10 4 K) and SDO/AIA 211 Å ( T = 2 × 10 6 K) images. CH boundaries are enhanced with white colour. Some loops between the filament (blue colour) and CH surroundings are enhanced with green colour. The black rectangle enclosed the CS and NS, as well as the surrounding region of the filament, related with the possible magnetic reconnection between the filament footpoints and the CH boundary. With the black arrows we indicate the plasma that is moving towards the CH. Additionally, in order to study the perturbed region between the filament channel and the CH boundary, we selected a sector (15° × 12°) from this region based on the SDO/AIA 193 Å images and divided it into 11 segments or cuts, parallel to the solar equator (Fig. 5 a). We have used the method, similar to that reported by McIntosh et al. ( 2011 ), Shen, Liu Su ( 2012 ), Verwichte et al. ( 2013 ) and Ma et al. ( 2014 ). We elaborated the time evolution map of each cut during 10 h, starting at 00:00 ut on August 8, which is the preceding period to the CH disappearance. Fig. 5 (b) shows one part of this map that reveals the CH evolution and its disappearance related to the arrived plasma. Generally, all segments of this map show the filament plasma disturbances and wavy behaviour of the longitudinally

O O O O O O O O O B-Observatory B-Wavelength O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Observatory B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-ObservationalTechniques O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O B-Wavelength I-Wavelength O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Wavelength I-Wavelength O O O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


of dust producers (Bolmer et al. 2018 ; Zafar et al. 2018b ) could also change the effect of total Fe on extinction. It is now simple to compute the average total column density of Fe along a sightline back to a given redshift, and then use the fit in Fig. 4 to convert this to an average ‘cosmic dust dimming’ CDD(). In Fig. 6 , we provide this quantity, CDD(), back to a redshift of = 5. Figure 6. The average ‘cosmic dust dimming’, CDD(), is computed as the integrated A V from redshift 0 to . The A V is computed from the average amount of dust along the line of sight based on the distribution of Fe (blue points) shown in Fig. 5 . 4.2 Impact on high-redshift surveys Fig. 6 shows the accumulated effect of dust in random sightlines out to cosmological distances. It is seen that up to redshifts of about 3 the CDD() is smaller than the typical uncertainties on individual A V measurements, and the effect can be ignored without too much impact. At redshifts in excess of 4, in the current paradigm, the CDD() continues to rise despite the dropping metallicity, causing the cumulated effect to become significant. It should be recalled that the curve shows the average, but the effect is highly stochastic. Therefore, corrections and predictions should probably only be considered for statistical samples while the effect on individual objects will be stochastic. 4.3 Inclusion of 2175 Å bump The shape of the extinction curve tells us about the dust grains in the ISM (Draine 2003 ). Carbonaceous dust grains are responsible for the 2175 Å bump and silicates induce the steepness in the extinction curve (Weingartner Draine 2001 ; Draine 2003 ). We here aim to see if different extinction curves carrying different dust grain properties could affect our results. Our sample mostly has preference towards featureless Small Magellanic Cloud (SMC)-type extinction curve. However, 21 cases (3 GRBs and 18 QSO-DLAs) are reported to contain a 2175 Å bump, suggesting carbonaceous dust enriched environments. These cases are highlighted by stars drawn around the data points in Figs 1 – 4 . De Cia et al. ( 2013 ) presented a sample of 18 GRBs (11 measurements and 7 limits) which included a single burst with a 2175 Å extinction feature (GRB 070802). That single burst did not fall on the A V and N (Fe) dust relation of their limited sample, and De Cia et al. ( 2013 ) suggested that objects with the 2175 Å bump might follow a different relation and therefore should not be included. Our larger sample includes 19 sightlines with bumps, and is reaching extinctions 1.8 mag higher than the De Cia et al. ( 2013 ) sample, but we see no evidence that the 2175 Å bump cases follow a different relation. We also find that inclusion of the 2175 Å bump cases strengthens the relation especially at higher extinctions. Depending on the amount of metals available to form dust, different grain compositions and sizes could provide a range of optical extinction laws. 4.4 Dust-to-gas ratios and

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


power of erg s −1 , very similar to that shown by PSR J1908+0839, but its distance is ∼30 times smaller ( d Geminga = 250 pc). Given the similar spin-down power, the nebula PSR J1908+0839 powers should also have a comparable luminosity with respect to Geminga’s PWN, which would lead to a flux around three orders of magnitude smaller than the flux of Geminga and undetectable by HAWC. Therefore, it is unlikely that 2HWC J1907+084* and PSR J1908+0839 are associated with one another. Finally, the closest pulsar to the source 2HWC J1852+013* is PSR J1851+0118, offset by only 0.10°. This pulsar lies at a distance of 5.6 kpc and has a characteristic age of ∼100 kyr (Yao, Manchester Wang 2017 ). If both objects are related the required pulsar velocity is a reasonable value of ∼100 km s −1 , though this may be as high as ∼245 km s −1 when considering the largest offset given by 0.10° ± 0.10 0.13. However, this pulsar has a relatively low spin-down power, erg s −1 , which along with its high characteristic age make it unlikely to accelerate particles that can emit gamma rays in the TeV regime. To quantitatively test this scenario, we use the Naima software 3 to model the relativistic parent population of the non-thermal gamma-ray emission accounting for different radiative models (see Zabalza 2015 ). To obtain the emissivity of the electron population that gave rise to the gamma-ray emission seen by HAWC, we assume that IC is the dominant radiative process and that the electron spectrum is defined by a simple power law. The target photon field for this process is expected to be a combination of cosmic microwave background (CMB) and infrared (IR) photons. The assumed energy densities in each case are standard Galactic values of u CMB = 0.25 eV cm −3 and u IR = 0.30 eV cm −3 . With such features, the total energy carried by electrons above ∼10 TeV needed to explain HAWC detection would be W e (> 10 TeV) ∼ 6.0 × 10 46 erg. Alternatively, we consider the cooling time of these electrons ( t cool ), which is computed as follows (Aharonian 2004 ): where E e = 10 TeV is the electron energy and u is the total energy density of the medium. In this case, we account for IC and synchrotron losses and hence, assuming a temperature of ∼25 K for the IR photon field (Moderski et al. 2005 ), u can be described as where B is the magnetic field. We use the aforementioned energy densities for the CMB and IR photon fields, and for the magnetic field, we assume the minimum possible value given by the interstellar magnetic field, B = 3 μG, as there is no measured value for the source. Under these assumptions, the cooling time is t cool ∼ 57 kyr. Given the spin-down power of PSR J1851+0118, erg s −1 , the total energy released by the pulsar during the t cool period would be erg. Consequently, even assuming that all the energy released by the pulsar was used to accelerate electrons above 10 TeV, there would not be enough energy to power a PWN with the gamma-ray brightness

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Herschel /HIFI guaranteed time CHESS key program (Ceccarelli et al. 2010 ). On the scale of individual envelopes, N 2 D + is seen only towards A (Jørgensen et al. 2011 ). Most recently, the distribution of N 2 D + has been analysed by Murillo et al. ( 2018b ) on the scale of the individual protostars and the circumbinary envelope. C2.31 Glycolonitrile (HOCH2CN), <italic>m</italic> = 57 Glycolonitrile was detected towards source B by Zeng et al. ( 2019 ). C2.32 Aminoacetonitrile (NH2CH2CN), <italic>m</italic> = 56 An upper limit was derived towards source B by Zeng et al. ( 2019 ). C2.33 Formyl cyanide (CHOCN), <italic>m</italic> = 55 An upper limit was derived towards source B by Zeng et al. ( 2019 ). C2.34 Ethenimine (CH2CNH), <italic>m</italic> = 41 An upper limit was derived towards source B by Zeng et al. ( 2019 ). C2.35 Nitrous acid (HONO), <italic>m</italic> = 47 Coutens et al. ( 2019a ) detected HONO towards source B and derived an accurate column density. C2.36 Nitrogen dioxide (NO2), <italic>m</italic> = 46 Coutens et al. ( 2019a ) derived an upper limit for NO 2 towards source B. C2.37 Nitrosyl cation (NO+), <italic>m</italic> = 30 Coutens et al. ( 2019a ) derived an upper limit for NO + towards source B. C2.38 Nitric acid (HNO3), <italic>m</italic> = 63 Coutens et al. ( 2019a ) derived an upper limit for HNO 3 towards source B. C3 S-bearing molecules C3.1 Hydrogen sulphide (H2S), <italic>m</italic> = 34 H 2 S was detected on envelope scales (Blake et al. 1994 ), as was HDS (van Dishoeck et al. 1995 ; Caux et al. 2011 ). It was also observed towards the two protostars individually (Chandler et al. 2005 ; Jørgensen et al. 2011 ). On large cloud and core scales, H 2 S is also observed, but at lower abundances than closer to the binary source (Wakelam et al. 2004 ). H 2 S was detected on envelope scales in the infrared with the Herschel /HIFI guaranteed time CHESS key program (Ceccarelli et al. 2010 ). Baryshev et al. ( 2015 ) reported a line of H 2 S in absorption from the foreground cloud. HDS and HD 34 S were detected towards source B by Drozdovskaya et al. ( 2018 ) with accurate column densities provided. C3.2 Carbon monosulphide (CS), <italic>m</italic> = 44 C 32 S was the second molecule studied in IRAS 16293-2422. Its emission line profile showed strong self-absorption and prominent asymmetry, which was interpreted as a signature of infall (Walker et al. 1986 ; van Dishoeck et al. 1995 ). C 34 S was observed soon thereafter (Menten et al. 1987 ). CS, like CO, is present on the large cloud and core scales; and the smaller circumbinary envelope and disc-A and -B scales (Mizuno et al. 1990 ; Walker, Carlstrom Bieging 1993 ; Blake et al. 1994 ; Narayanan et al. 1998 ; Caux et al. 2011 ; Jørgensen et al. 2011 ; Takakuwa Kamazaki 2011 ; van der Wiel et al. 2019 ). It also traces the outflows (Walker et al. 1990 ; Girart et al. 2014 ), and shocks,

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3 . The amplitudes of the PCs have been artificially normalized to unity for easier comparison. We find in general that at a particular redshift, an individual PC tends to be smooth and positively correlated along k , and at a particular k shows negative and positive correlations across redshift. This is a reflection of the underlying smoothness of the power spectra across k , and the fact that physical processes such as reionization, X-ray heating, and Ly α coupling tend to produce redshift-dependent peaks and troughs in the power spectrum (see, e.g., Figure 3 ). The reason why the PCs lose strength at high k is because our rescaling matrix downweights our data covariance matrix at high k . As we will see in Section 4.1 , the bulk of a 21 cm experiment’s sensitivity to the power spectrum is located at lower k . Figure 1. Top: scree plot showing the eigenvalues of the 30 principal components formed from the training data of . Bottom: the first nine principal components of the power spectrum data at each unique k – z combination. The color scale is artificially normalized to [−1, 1] for easier comparison. 2.3. GP Regression For the purposes of emulation, we are not interested in merely reconstructing our original training set data at their corresponding points in parameter space j , but are interested in constructing a prediction of a new data vector, new , at a new position in our parameter space, new . We can construct a prediction of the data vector at this new point in parameter space by evaluating Equation ( 7 ) with new ; however, we do not know this weight vector a priori. To estimate it at any point in parameter space, we require a predictive function for each element of spanning the entire parameter space. In other words, we need to interpolate over our parameter space. To do this, we adopt a GP model, which is a highly flexible and non-parametric regressor. See Rasmussen Williams ( 2006 ) for a review on GPs for regression. A GP is fully specified by its mean function and covariance kernel. The GP mean function can be thought of as the global trend of the data, while its covariance kernel describes the correlated random Gaussian fluctuations about the mean trend. In practice, because we center our data about zero before constructing the PCs and their weights (Equation ( 2 )), we set our mean function to be identically zero. For the covariance kernel, we employ a standard squared-exponential kernel, which is fully stationary, infinitely differentiable, produces smooth realizations of a correlated random Gaussian field, and is given in multivariate form aswhere and ′ denote two position vectors in our parameter space, is a diagonal matrix containing the characteristic scale length of correlations l across each parameter, and σ A is the characteristic amplitude of the covariance. is a tunable hyperparameter of the kernel function that must be selected a priori. We discuss how we make these choices in Section 2.3.1 . We set σ A = 1, and

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


, spflg , and rflag were utilized for flagging bad data. Minimal flagging was necessary for L and X bands, however the S -band data were severely hampered by RFI and five of the eight IFs were almost completely flagged. Los Alamos (LA) was used as the reference antenna, with Pie Town (PT) used when LA was unavailable. Imaging and self-calibration was performed using difmap (Shepherd, Pearson Taylor 1994 ). 3 RESULTS The core of 0313−192 is detected at S band with the LBA, and L, S , and X band with the VLBA. The LBA observations detected an unresolved point source with a flux density of 53.6 ± 8.4 mJy. The longer baselines of the VLBA enabled higher resolution images that were able, at all three observed frequencies, to resolve the radio structure. Table 2 provides a summary of the VLBA data. Table 2. Beam size and flux density measurements for the VLBA observations using different imaging weightings. We assume 10 per cent errors, which is standard for VLBI measurements due to the sparse uv -coverage. 3.1 VLBI detection and chance alignment Keel et al. ( 2006 ) were able to constrain the optical and radio positions to within 0.2 arcsec. The X -band VLBA data provide the best positional information due to the smaller beam size. The error in the radio astrometry is dominated by phase calibration errors, resulting in a positional accuracy of approximately 0.48 mas. As stated in Keel et al. ( 2006 ), the coincidence of the VLBI detections of a compact source with the optical centre of 0313−192 effectively eliminates any possibility of the spiral host and DRAGN being in a chance alignment. A ∼30 mJy compact source detected at L band using the VLBA has a brightness temperature of T b > 10 8 , which can only be attributed to the presence of an AGN. The integrated flux of the naturally weighted S -band source agrees within the errors with the S -band LBA observations from 2009 suggesting little variability on this time-scale. The compact radio detection at the position of the optical host, and the detection of jet components, confirms the presence of an active AGN. 3.2 VLBA-detected core and jet Ledlow et al. ( 2001 ) report an inverted spectral index 1 of the radio core of 0313−192 with , which is common for AGN cores. They also note the steeper inverted spectrum between 1.4 and 4.9 GHz, likely due to either free–free or synchrotron self-absorption. The new VLBA observations confirm the inverted nature of the spectral index of the core. We measure a core spectral index of using the L -, S -, and X -band VLBA measurements of the unresolved radio core. Previously published VLA data of 0313−192 at L and X band suggest the presence of a radio jet to the South of the host galaxy (Ledlow et al. 2001 ). Although the diffuse radio lobes are detected on either side of the host galaxy, the putative jet suggests that the radio jets are oriented with the Southern jet emitting towards the line of sight. We detect components of the Southern jet at L, S , and X

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


reliable results (e.g., Henry 1999 ). Lastly, the number of genuinely SLS bright enough to measure with modest (meter-class) telescopes is small. As measured by the number of stars in a meaningful volume of hyperspace similar to the Sun (Radick et al. 1998 ), considerable work would be needed to identify new, dimmer targets. There remains the nagging question of whether the Sun is different from other SLS (Gustafsson 1998 ). Radick et al. ( 2018 ) conclude “it may be unusual in two respects: (1) its comparatively smooth, regular activity cycle, and (2) its rather low photometric brightness variation relative to its chromospheric activity level and variation...” These authors speculate that facular brightening may nearly balance sunspot darkening, explaining the second point. Egeland ( 2017 ) pointed out that the Sun has the most regular cycle of all SLS measured so far. The question of whether the Sun acts (magnetically) as other SLS is difficult to answer. If all such stars are indeed magnetically similar, it implies that stars have a consistent magnetic variability over timescales of several Gyr (the age range of our sample) to ∼100 million years. The latter is close to the uncertainty in ages of older main sequence stars obtained using the best available methods. It is impossible to verify or refute the question for the Sun, even using a cosmogenic proxy record, which presently stretches only 0.01 million years into the past (Wu et al. 2018 ). Certainly, the most Sun-like of the stars found so far, 18 Sco (HD 146233) has clear differences in metallicity and starspot cycle length. Nevertheless, there is hope that a carefully selected stellar ensemble can represent the activity of the Sun in middle and old age. van Saders et al. ( 2016 ) demonstrated that rotation rates of middle-aged and old GV stars converge as a result of weakened magnetic breaking. Unlike younger stars, there is perhaps a good physical reason to believe that magnetic dynamos of older Suns, and their effects, should be similar. 3. Time Series from a Solar “Reconstruction” The limits of our analysis due to the lack of longer time series can be illustrated through a comparison of our results with a “reconstruction” of solar variations with extraordinary and significant forcing of ≈6 W m −2 from 1600 to 2010 (Shapiro et al. 2011 ). Figure 5 highlights two extended periods of near-monotonic large changes predicted over 15 and 50 yr. The first is compatible with several stars (HD 126053, 52711, 50692, 143761; Table 2 ). The second (50 yr) period is compatible with about half of the stars listed. Figure 5. Variations from a model by Shapiro et al. ( 2011 ) are shown, in which variations in radiative forcing since 1750 are of the order of 3 W m −2 , far larger than the IPCC estimate of −0.30 to +0.10 W m −2 Myhre et al. ( 2013 ). (The relationship between Strömgren magnitudes and irradiance is linear, taken from the model computations. The factor differs from the values

O O O B-Citation I-Citation O O O O 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 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 O B-CelestialObject O O O O B-EntityOfFutureInterest B-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O B-CelestialObject O O O O O O O B-EntityOfFutureInterest O O O O O O O O B-CelestialObject O O 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 O O O O O O O O O O O O O O O O O O O O O O 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 B-Citation I-Citation I-Citation I-Citation O O O O B-EntityOfFutureInterest O O O O O O B-CelestialObject I-CelestialObject 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 B-CelestialObject O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O 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 B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject 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 B-CelestialObject I-CelestialObject B-CelestialObject B-CelestialObject B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Model O O O O O O O O O O O


as follows. The observations are described in Sect. 2. Sections 3 and 4 give reduction techniques and results of analysis of the obtained spectroscopic and photometric data. Discussion on the derived results can be found in Sect. 4. Brief conclusions are presented in Sect. 5. 2. Observations 2.1. Photometry December, 2006. Spectrophotometric observations were carried out on December 12, 2006 with the multi-mode focal reducer SCORPIO attached to the prime focus of the 6 m Big Telescope Alt-azimuth (BTA) operated by Special Astrophysical Observatory (SAO) of the Russian Academy of Sciences (Russia). The focal reducer provided both photometric mode and long-slit spectroscopic mode ( Afanasiev Moiseev 2005 ). A CCD chip EEV-42-40 of pixels was used as a detector. The focal reducer converts the focal ratio to /2.6, providing a pixel scale of 018 per pixel and field of view of . To increase the signal-to-noise ratio (S/N) of measured signal, on-chip binning of 2 in the spatial direction was applied. s image of the comet was obtained through a broadband filter (center wavelength nm, full width at half maximum ( FWHM ) nm); s images were taken through a broadband Rc filter ( nm, nm). A field of standard stars (PG 0231) was observed at approximately the same airmasses as the comet to perform the photometric calibration ( Landolt 1992 ). Reference zero points and color terms for transformation to the standard photometric system were calculated using the standard stars with a scatter of less than 0.03 mag on average. The difference between the comet and standard field airmasses was considered to be small and was compensated for with the mean monochromatic extinction coefficients measured for Peak Terskol Observatory, which is located in the same mountain region ( Kulyk et al. 2004 ). The twilight sky was observed through the filters used to construct flat field images. November, 2007. Another data set was obtained on November 9, 2007 with the 6 m Telescope. The observation set-up was similar to that described in the previous paragraph. s images were acquired with a broadband filter ( nm, nm). The spectrophotometric standard star Feige 34 was observed at the similar airmasses as the comet airmasses to carry out absolute photometric calibration ( Oke 1990 ). We used the mean monochromatic coefficient to compensate the first order of extinction, neglecting the color member, which is small in the -band and comparable to the uncertainty of the main extinction itself. A set of exposures from the evening and morning twilight sky was obtained to create a flat field image. October, 2008. To collect images of the comet, we used the 2 m RCC Telescope at Peak Terskol Observatory operated by the International Center for Astronomical, Medical and Ecological Research (IC AMER, Terskol, Kabardino-Balkaria, Russia). A focal reducer mounted at the prime focus converted the initial focal ratio of to , providing an image scale of 099 per pixel and useful field of view of 94.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Telescope I-Telescope I-Telescope I-Telescope I-Telescope B-Telescope O O B-Observatory I-Observatory I-Observatory B-Observatory O O B-Organization I-Organization I-Organization I-Organization B-Location O O O O O O O O O O O O B-Citation I-Citation I-Citation 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 B-Wavelength O O O 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 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 B-Observatory I-Observatory I-Observatory 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 B-Telescope I-Telescope I-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject 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 B-Telescope I-Telescope I-Telescope I-Telescope O B-Observatory I-Observatory I-Observatory O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Organization I-Organization B-Location I-Location I-Location O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


are needed to perform the analysis of cTTS. In this investigation we analyse rather weak spectral lines, with equivalent width (EW) of about 10 mÅ, so we need high-resolution, high S/N spectra of template stars of different spectral type. In order to minimize the errors of measurements, we prefer to use a grid of synthetic spectra. This way we avoid possible spectral peculiarities from the real stars that could affect our results. 3.1 Template synthetic spectra The synthetic spectra were produced by the software package Spectroscopy Made Easy (SME; Valenti Piskunov 1996 ). It was initially used to confirm the spectral type of each cTTS, with the estimation of T eff , as well as for the determination of v sin i and v rad . Two sets of synthetic spectra with spectral resolution R = 50 000 were produced. The first set corresponds to a grid of narrow-band spectra withseveral values of stellar parameters, which was used in the determination of spectral type, as well as v sin i and v rad . Then, specific spectra for each star in a wider wavelength band between 4500 and 7000 Å were produced. This second set of synthetic spectra corresponds to our templates and was used to measure EWs of hundreds of spectral lines for comparison with the same lines in the spectra of cTTS. The spectral type determination, described in detail in Sect. 3.2 , allowed us to gather information mainly about T eff . The usual criteria of surface gravity (log g ) can hardly be used in the case of highly veiled spectra with strong lines in emission. Due to that we are assuming the value log g = 3.75 dex for these stars (see Sect. 3.2 ). We also assume a priori a solar-like metallicity ([M/H] = 0.0). Besides the mentioned stellar parameters, SME also needs input information about the microturbulence velocity ( v mic ) and macroturbulence velocity ( v mac ), as well as the instrumental resolution. For the v mic parameter we assume a value that is typical for cool stars and wTTS (e.g. Padgett 1996 ; Rojas et al. 2008 ; James et al. 2006 ; Taguchi et al. 2009 ): v mic = 1.0 km s −1 . For the v mac value we assume a value based on the T eff value, as reported by Valenti Fischer (2005) . The three stars have spectral types between K1 and G5 corresponding to temperatures between 4900 and 5500 K for sub-giant stars ( Table 1 ). For this range of temperatures we assume a value of v mac = 2.8 km s −1 , consonant to an average T eff = 5000 K. To create the synthetic spectra we use the Kurucz grids of stellar atmospheric models, considering local thermodynamic equilibrium (LTE) conditions. The line list used by SME to create the synthetic spectra was extracted from the Vienna Atomic Line Database (VALD) database using the “Extract stellar” option ( Ryabchikova et al. 2015 ). Since we measured several hundred spectral lines, we did not apply any corrections to the log gf and Van der Waals damping parameters. 3.2 Spectral type determination The spectral types of our targets were determined

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− K )/ E ( J − K ); Indebetouw et al. 2005 ; Jiang et al. 2006 ; Zasowski et al. 2009 ; Xue et al. 2016 ) and absolute (right, A ( λ )/ A ( K ); Rieke Lebofsky 1985 ; Rieke et al. 1989 ; Indebetouw et al. 2005 ; Chiar Tielens 2006 ; Fritz et al. 2011 ; Wang Chen 2019 ; Hensley Draine 2020 ) measurements. Real variations are seen in the relative measurements indicating different MIR extinctions between the diffuse and dense ISM. The variations in the absolute measurements are likely due to a combination of real variations and uncertainties in deriving the total column normalizations. Note that the Lutz ( 1999 ) work presented preliminary results that were finalized in Fritz et al. ( 2011 ). In the case of the E ( λ − K )/ E ( J − K ) measurements, these differences are likely due to the relative contribution between diffuse and dense material in the sight lines studied. This can be seen from the Zasowski et al. ( 2009 ) measurements that encompass the full range of values with higher extinctions seen toward the Galactic Center ( l = 10–15) and lower extinctions well away from the Galactic Center ( l = 90). Zasowski et al. ( 2009 ) interpret this as less dense material in the l = 90 case compared to the l = 10–15 case, and this would be consistent with much of the previous work probing denser material given their biases toward high dust column sight lines. In the case of the A ( λ )/ A ( K ) measurements, some of the differences can be due to uncertainties in deriving the total column. The absolute level for the Chiar Tielens ( 2006 ) curves was set by fiat to that of Indebetouw et al. ( 2005 ) and Lutz ( 1999 ) and, hence, their overall high MIR extinction may just be due to this normalization. Similarly, Hensley Draine ( 2020 ) used Fitzpatrick et al. ( 2019 ) to set the absolute level of the Cyg OB2 12 extinction. However, the differences between the Rieke et al. ( 1989 ) and Fritz et al. ( 2011 ) results are enigmatic. The Br α /Br γ ratio for the former reference agrees well with the measurements by Wade et al. ( 1987 ); between these references, the ratio is measured for eight sight lines (one twice) and the (weighted) average Br α /Br γ ratio is 16 ± 1. Some of the flux in the beams used may originate from luminous early-type stars, which typically have a Br γ equivalent width of order 6 × 10 −4 μ m (Hanson et al. 1996 ). The result could be that the ratio is overestimated by about 5%. Fritz et al. ( 2011 ) determined a ratio value of 11.6 ± 2 from the ISO spectrum (for Br α ) and a ground-based spectral image (for Br γ ). The difference in these two measurement approaches suggests that the best value is toward the large end of the ones permitted by Fritz et al. ( 2011 ) and that the Galactic Center extinction in Figure 10 probably lies between that shown for Fritz et al. ( 2011 ) and ours (and the point from Rieke et al. ( 1989 ). Only Rieke Lebofsky ( 1985 ), Rieke et al. ( 1989 ), Chiar Tielens ( 2006 ), and Hensley Draine ( 2020 )

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


photometry for the faintest variable. Multi-epoch data were also used to investigate color–magnitude and Bailey diagrams for M53 RR Lyrae at NIR wavelengths. No significant overlap is seen in the color–magnitude plane between RRab and RRc stars, suggesting that horizontal branch evolution occurs toward the red edge of the instability strip (Arellano Ferro et al. 2012 ). RR Lyrae in the Bailey diagrams follow the expected locus of RRab in a typical OoII cluster. New NIR photometry for RR Lyrae in the metal-poor M53 GC provided an opportunity to constrain the metallicity dependence of their PLRs by means of a quantitative comparison with relatively metal-rich GCs. While single-epoch data for RR Lyrae are available for several GCs, for example from 2MASS, homogeneous JHK s -band time-series photometry is limited to only a few GCs. Time-series data are crucial to determine precise mean magnitudes and the PLRs for RR Lyrae with a dispersion of ∼0.04 mag, thus allowing a rigorous comparison of GCs with different mean metallicities. Combining precise K s -band PLRs in GCs covering a metallicity range of Δ[Fe/H] = 0.9 dex, we determined a metallicity dependence of the PLRs and simultaneously estimated distances to the GCs adopting different calibrations based on theoretical models and Gaia EDR3 data. The quantified metallicity dependence of ∼0.15–0.17 mag dex −1 is in good agreement with theoretical predictions for the relation from Marconi et al. ( 2015 ). When excluding the calibrator relations, the metallicity dependence of the PLRs in the GCs was found to be sensitive to the adopted spectroscopic metallicities, the RR Lyrae sample size, and the number of clusters, and can vary between 0.07 and 0.15 mag dex −1 . Therefore, homogeneous NIR time-series data in additional GCs, particularly in metal-rich ([Fe/H] > −1.0 dex) and more metal-poor ([Fe/H] −2.1 dex) GCs, is required to extend the metallicity baseline and the statistics of both the number of RR Lyrae and the GCs. Our analysis has shown that a robust constraint on the effects of metallicity on the PLRs and precise RR Lyrae distances to GCs can be obtained simultaneously, provided a statistically significant sample of GCs covering a wide range of mean metallicities is available. However, the calibration of the RR Lyrae PLZ relation in the Milky Way is still hampered by uncertainties and a possible zero-point offset in the parallaxes even with Gaia EDR3. Using theoretical PLZ relations to predict parallaxes for Galactic RR Lyrae, we found a small parallax zero-point offset of −7 ± 3 μ as in EDR3, which is significantly smaller than the value (−32 ± 4 μ as) obtained using the recipe of Lindegren et al. ( 2020a ). We note that our estimated parallax offsets are in agreement with the values provided by the corrections of Lindegren et al. ( 2020a ) for faint and distant RR Lyrae stars that have small parallaxes (0.5 mas). When Gaia EDR3 parallaxes were corrected using the formulae of Lindegren et

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


only investigate H 2 –H 2 O atmospheres, the sole opacity sources in the cloud-free models are the vibration-rotation bands of water vapor in the near- and mid-IR, collision-induced absorption (CIA), and Rayleigh scattering off of H 2 and H 2 O gas (see Freedman et al. 2008 , 2014 and Lupu et al. 2014 for a more detailed description of the opacity data). Exo-Transmit includes H 2 –H 2 CIA opacities but not H 2 –H 2 O or H 2 O–H 2 O. The non-inclusion of H 2 O CIA should not affect our results because these opacities tend to be only weakly wavelength dependent. For our cloudy models, the cloud opacity is treated as an infinite opacity source at the location of the cloud deck. 2.2. Modeling JWST Observations and Instrumental Noise We simulate three different instrument modes: the NIRISS Single Object Slitless Spectrometer (SOSS) ( R = 700, 0.7–2.7 μ m), NIRSpec G395H+f290lp ( R = 2000, 2.8–5 μ m), and the MIRI Low Resolution Spectrometer (LRS) ( R = 100, 5–14 μ m). To calculate the flux and background rates, and , we use the beta version of Space Telescope Science Institute’s online Exposure Time Calculator 6 6 https://devjwstetc.stsci.edu (ETC). The ETC does not contain a systematic noise floor, which has been suggested to be anywhere from 20 to 30 ppm for the near-IR instruments and 50 ppm for MIRI (Greene et al. 2016 ). These noise estimates may shift somewhat but will not impact the conclusions in this paper. The duty cycle is calculated by determining the number of allowable groups in an integration before detector saturation. A group, in JWST terminology, is one or more consecutively read frames—all exoplanet spectroscopy modes have a single frame per group. To determine the number of groups per integration, n grp , we sequentially increase n grp in the ETC, until a single pixel on the detector becomes saturated. The duty cycle is calculated by . We compute noise simulations for a GJ-1214-like host star with a magnitude J = 8, as a realistic system that might be observed with JWST and also discovered by TESS (Sullivan et al. 2015 ). Additionally, a GJ-1214-like star at J = 8 will have a distance of 6.6 pc, which acts as an optimistic comparison with de Wit Seager’s ( 2013 ) assumed system at 15 pc. We calculate , 9, and 29 for NIRISS SOSS, NIRSpec G395M, and MIRI LRS, respectively, corresponding to duty cycles d = 0.33, 0.80, and 0.93. Using the duty cycle, the total shot noise is F out is the flux (e − /s) for the host star computed from the JWST ETC. F in is the in-transit flux, , where is obtained from the transmission spectrum model described in Section 2.1 . The in-transit and out-of-transit time components, t in and t out , are the transit duration and the out-of-transit observing time, respectively, multiplied by the duty cycle. We compute the total noise viawhere n int is the total number of integrations during the entire transit, B λ is the extracted background rate (observatory background plus dark current in e − /s), computed in

O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O O O O 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 O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Telescope O O O O O O O O O O O B-Instrument I-Instrument I-Instrument I-Instrument I-Instrument B-Instrument O B-Formula I-Formula I-Formula B-Wavelength I-Wavelength I-Wavelength B-Instrument B-Wavelength O B-Formula I-Formula I-Formula B-Wavelength I-Wavelength I-Wavelength O O B-Instrument I-Instrument I-Instrument I-Instrument B-Instrument O B-Formula I-Formula I-Formula B-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O O O O O B-Organization I-Organization I-Organization I-Organization O B-Software I-Software I-Software O O B-URL 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 B-Wavelength O O O O O B-Instrument 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-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 B-Software 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 O O B-Formula I-Formula I-Formula O O O O O O O O O B-Telescope O O O O B-Telescope B-Citation I-Citation I-Citation I-Citation O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O B-Formula I-Formula I-Formula 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 B-Instrument I-Instrument B-Instrument B-Wavelength O B-Instrument I-Instrument O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope B-Software 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 O O O O O O O O O O O O O O O O O O O O O O O O


density). From the 2D plot, it is seen that the distribution of the dust averaged velocity also has the filamentary structure with several minima of the V d,av, z -component. Positions of these velocity minima correspond to positions of maxima of the number density (it is clear from Fig. 7 B), i.e. dust accumulates in the regions of its deceleration. This is consistent with the continuity equation. Thus, dust number density is not uniform in the astrosphere due to periodical deceleration and acceleration of the dust grains. This non-monotonic behaviour of the dust velocity is caused by gyrorotation around magnetic field lines. For example, for the trajectory started at point P 0 gyrorotation takes place in the ( Z , Y )-plane, and during each rotation at the point with maximal y , velocity vector of gyromotion is opposite to the plasma velocity and, hence, the total individual dust velocity has a minimum; oppositely, at the point with minimal y , total velocity has a maximum (see the schematic illustration of this effect in Fig. 8 ). Figure 7. A. 2D distribution of the averaged dust z -velocity component (absolute value) in the ( ZX )-plane obtained for the perpendicular case. B. Dust number density and averaged velocity (absolute value of the z -component) along the Z -axis ( x = 0, y = 0). All results are presented for the dust grains with a d = 1.8. Distances are normalized to R 0 . Figure 8. Schematic picture of dust grain motion in the uniform perpendicular magnetic field. Green dots correspond to maxima of the local dust velocity, blue dots correspond to the local minima (see the text for details). The distance between the density maxima and their number depend on the period of gyrorotation of dust grains (see Fig. 8 ). Namely, in the case of the uniform electromagnetic field, the distance between two adjacent maxima of y ( z ) along the trajectory is equal to D gyr v p , z T gyr , where the dimensionless period of gyrorotation is T gyr 2/( Ba d ). In our case, when v p , z and B change along the trajectory, the distance between the density maxima depends on the averaged D gyr at each part of the trajectory (values of D gyr averaged over the whole trajectory are given in Table 2 ). Fig. 9 A shows y ( z ) along the trajectories (started at P 0 ) for different a d . It is seen that the grains are involved in the gyrorotation with corresponding gyroradius (given in Table 2 ). Distance between adjacent maxima of y ( z ) along the trajectory correspond to the distance between maxima of the dust number density in Figs 5 and 6 . Fig. 9 B shows D gyr as a function of z for the trajectories started at P 0 and the all considered values of a d . Note that D gyr decreases with approaching to the AP because the magnetic field B increases (see Fig. 3 B). This is why the dust density filaments become more frequent close to the AP (see Fig. 5 ). Figure 9. A. The trajectory ( y ( z )) started at P 0 is shown for dust grains with four different a d .

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


i.e., the prior distribution of BBH source parameters θ conditional upon some hyperparameters Λ. For this work, we are concerned with the prior distribution of ( D L , m 1 , m 2 ) ∈ θ that is dependent on cosmological hyperparameters ( H 0 , Ω m ) ∈ Λ via Equation ( 6 ). The conditional priors is denoted as π ( θ ∣Λ). The hyper-likelihood is related to the regular likelihood by:where h denotes the GW data. In hierarchical inference, we have access to the posterior distribution of parameters of individual BBHs P ( θ ∣ h ), which is related to the regular likelihood through the Bayes’ theoremwhere is the evidence and π ( θ ) is prior used for the parameter estimation of individual events. Rewriting Equation ( 8 ) by replacing the integral with the summation over discrete posterior samples (e.g., Hogg Foreman-Mackey 2018 ), we obtainwhere n is the number of posterior samples for individual events. Combining N independent events, we obtain the total likelihoodwhere h denotes the collection of data { h i }. The hyper-posteriors are given by , with π (Λ) being the prior distribution of hyperparameters. In order to perform model selection, it is also necessary to calculate the hyper-evidence given a model M The Bayes factor (BF) between model M 1 and model M 2 isWe impose a threshold of the natural logarithm of BF at as the point when one model is significantly favored against another (e.g., Mackay 2003 ). 4. Results In this section, we present results of hyperparameter estimation and cosmological model selection using the simulated BBH population that is expected to be detected by third-generation detectors such as ET. 4.1. Hyperparameter Estimation Figure 3 shows the joint posterior distribution of H 0 and Ω m using 10 3 BBH events detected with ET, while ignoring the delay time between binary formation and binary merger and assuming we know the cosmic star formation rate and black hole mass distribution a priori. In our analysis, uniform priors are used: H 0 ∈ [40, 105] km s −1 Mpc −1 and Ω m ∈ [0, 0.75]. In this example, the Hubble constant is measured with a precision of 5.6%. By performing this analysis for a range of N (the number of BBH events) assuming zero measurement uncertainty of luminosity distance and black hole masses (which we call zero-error injections), we find the measurement precision of H 0 scales linearly with . We expect that one year operation of ET, yielding ∼10 5 BBH detections, will allow H 0 to be measured within ≈ 0.6%. However, this result is too optimistic as it does not account for uncertainties in cosmic star formation rate, delay time distribution and black hole mass distribution. In Figure 6 of the Appendix , we show that the estimates of ( H 0 , Ω m ) are biased if an incorrect model of star formation rate is used. Figure 3. Joint posterior distribution of the Hubble constant ( H 0 ) and matter density (Ω m ) in the ΛCDM model estimated using 10 3 BBH events. The 2D contour regions denote the 1 σ , 2 σ, and 3

O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O 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 O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O O O O O O O O O O O O O O O O O O O O O O O B-EntityOfFutureInterest I-EntityOfFutureInterest O B-EntityOfFutureInterest I-EntityOfFutureInterest 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


and thus star formation (see Gnedin 2000 ; Wise Abel 2008a ). Lastly, because ionizing radiation originates from massive stars, the fraction of halos generating escaping photons, shown in the right panel of Figure 22 , follow a similar trend as the stellar occupation fraction. Figure 22. Fractions of halos with active star formation (left; stars younger than 20 Myr) and photons escaped from their virial radius (right) as a function of the halo mass for the Rarepeak region (dashed blue) at z = 15, Normal region (solid black) at z = 15, 12.5, and Void region (red solid with boxes) at z = 15, 10, 8. 4.5. Comparison to Other Work Early efforts to constrain the escape fraction with simulations found wildly varying f esc values over a range of halo masses 10 7 –10 12 , ranging from less than 1% to unity (e.g., Fujita et al. 2003 ; Razoumov Sommer-Larsen 2006 ; Gnedin et al. 2008 ; Wise Cen 2009 ; Paardekooper et al. 2011 ; Yajima et al. 2011 ). However, in the past few years with higher resolution simulations that resolve star-forming clouds, there has been some convergence, showing that low-mass () halos have higher mean f esc values ≳25% (Wise et al. 2014 ; Paardekooper et al. 2015 ) that then decrease with halo mass to approach ∼5%–15% in more massive (log M vir / = 8–11) galaxies at z ≥ 6 (Kimm Cen 2014 ; Ma et al. 2015 ). Using the star formation surface density as a proxy to f esc , Sharma et al. ( 2016 ) suggested that the brightest galaxies dominated the photon budget at the end of reionization with 50% of the photons originating from galaxies with UV absolute magnitudes M 1500 ≤ (−18, −16.5) and at z = (6, 8), respectively. Our results are in agreement with these latest works with f esc decreasing with halo mass, given that M vir ≲ 10 9 . Here we only compare the mean values, but in reality, it should be noted that escape fractions greatly vary between galaxies and temporally. In the smallest galaxies, mean f esc values are ∼50% in the range of 10 7 –10 7.5 with a large scatter (see Wise et al. 2014 ; Paardekooper et al. 2015 ), spanning the full range from zero to unity, depending on previously discussed conditions. This then decreases to ∼0.05 at higher halo masses, agreeing with Kimm Cen ( 2014 ) and Ma et al. ( 2015 ). The Void simulation at z = 8 contains two galaxies with M ⋆ ≃ 3 × 10 7 contained in halos with M vir = 2 × 10 9 that have escape fractions of 25% that are undergoing strong starbursts. These galaxies may be analogs of the ones explored in the “brightest galaxies reionized the universe” scenario posed by Sharma et al. ( 2016 ). In the same data, we are also in agreement with Sharma et al., where we both find that 50% of the ionizing photons (see Figure 18 ) come from galaxies with an SFR ≥ 0.1 yr −1 in halos M vir ≥ 10 9 at z = 8. 5. CONCLUSIONS In this paper, we have quantified the properties and the UV escape fraction of galaxies during the epoch of reionization, expanding upon the work of Wise et al. ( 2014 ) with

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it is not objectively easy to determine the optimal deblending performance because it is not fundamentally trivial to determine if an object is actually composed of two galaxies or a single morphologically disturbed galaxy with two cores. This fundamental problem is unfortunately not unique to our morphological measures, but can occur in any qualitative or quantitative investigation of morphology. Fortunately, we only have two deblending statuses, i.e. ‘deblended’ or ‘blended’, therefore the effect of ‘deblending ability’ remains roughly constant down to a certain ‘deblending limit’, then it drops. Note also that this deblending limit is independent from a particular choice of desired morphological measure. Furthermore, this deblending ability can be roughly characterized only by the apparent size of an object (e.g. the number of pixels of a galaxy), because the average surface density of galaxies (or the inverse of average separation between two galaxies) is related to the apparent magnitude of galaxies, and this magnitude is approximately correlated to the number of pixels of a galaxy. Because of this simplicity, when we plot the mean value of each measure versus the number of pixels of an object inside the entire image, one can find that the mean value of any measure is approximately flat down to a certain number of pixels, then an object consists of smaller number of pixels starts to show much different (usually bigger) mean value. By monitoring the sudden change in the morphological measures, such as the concentration and the asymmetry of a galaxy, for various input npix values, we estimated that the optimal minimum number of pixels related to this deblending ability should be set around npix = 50 for the nominal setting related to ‘deblending’ of our extracting software, sextractor . Note that the minimum number of pixels related to a single object, explained earlier in this section, varies among various morphological measures. Therefore, the ‘overall’ minimum number of pixels should be determined by comparing the two types of minimum number of pixels (i.e. one type related to a single galaxy, and another related to ‘deblending’) on measure-by-measure bases, and that overall threshold, usually ranging between 20 and 100 pixels, should be applied to a different set of measures for various analyses. 3.3 Variation in detection fraction To investigate variations in the detection and measuring ability of sextractor , we performed a simulation through adding of galaxies into random positions of the each real cluster image. These added galaxies were randomly selected from a list of galaxies satisfying the specific selection conditions (e.g. magnitude and colour ranges) identical to each of the investigations in the next section. The list was constructed from the outer part (2 Mpc or more from the cluster centre) of the same cluster image. The exclusion of galaxies inside 2 Mpc radius was to ensure that added galaxies were free from any

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