INT-G (intermediate gravity) and FLD-G (field gravity) classes defined by Allers Liu ( 2013 ). In Section 2 , we describe the selected sample of objects presented in this paper. In Section 3 , we provide details of the X-shooter observations and data reduction. In Section 4 , we explain the analysis carried out and our results. In Section 5 , we derive the physical parameters for our sample using evolutionary models for substellar objects. Finally, in Section 6 we summarize our results. 2 SAMPLE SELECTION We selected a sample of 20 benchmark objects with confirmed membership of open clusters or associations, with known ages, metallicities and distances. We chose a sample with photometry and optical spectral types confirming membership. In the case of the Pleiades and Praesepe, members are confirmed not only by photometry and optical spectroscopy, but also by proper motion (Lodieu, Deacon Hambly 2012b ; Boudreault et al. 2012 ; Bouy et al. 2015 ). We selected objects in each of the associations or open clusters with magnitude ranging from J = 14.9 to J = 18.1 mag, which allowed us to obtain spectroscopy with a signal-to-noise ratio of between 4 and 53 in the near-infrared, using exposure times of between 40 min and 1.5 h. Our sample has spectral types between M5.5 and L3.5, with at least one target per open cluster or association of each spectral type between M5.5 and L0. To complete our sample in age range, we added three members from the UppSco association, and four from the Cha I region from proposals: 093.C-0109(A) (P.I. Van der Plas), 093.C-0769(A) (P.I. Bonnefoy) and 095.C-0378(A) (P.I. Testi). We list the objects in our sample with their main characteristics in Table 1 . Table 1. List of observed targets with their full name, coordinates, magnitude, spectral types, cluster or association membership, and flag for disc-bearing sources and binary candidates. Notes . References: [1] Boudreault et al. ( 2010 ), [2] Hodgkin et al. ( 1999 ), [3] Boudreault et al. ( 2012 ), [4] Bouvier et al. ( 1998 ), [5] Stauffer et al. ( 1998 ), [6] Bouvier et al. ( 1998 ), [7] Bouvier et al. ( 1998 ), [8] Nagashima et al. ( 2003 ), [9] Lodieu, Deacon Hambly ( 2012a ), [10] Bihain et al. ( 2006 ), [11] Ardila, Martín Basri ( 2000 ), [12] Martín, Delfosse Guieu ( 2004 ), [13] Lodieu et al. ( 2007 ), [14] Persi et al. ( 2000 ), [15] López Martí et al. ( 2004 ). References of disks detections: [16] Luhman Muench ( 2008 ), [17] van der Plas et al. ( 2016 ), [18] Herczeg et al. ( 2009 ), [19] Long et al. ( 2017 ). a NR: the existence of a disc has not been reported for this object. References for spectral type: [20] Alves de Oliveira et al. ( 2012 ), [21] Luhman ( 2007 ), [22] Luhman ( 2004 ), [23] Lodieu et al. ( 2018 ), [24] Slesnick et al. ( 2008 ), [25] Bihain et al. ( 2010 ), [26] Martín et al. ( 1996 ), [27] Stauffer et al. ( 1998 ), [28] Boudreault Lodieu ( 2013 ), [29] West et al. ( 2011 ), [30] Manara et al. ( 2017 ). References for binary candidates:


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


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


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


(− 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


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


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


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


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,


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


, 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


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


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.


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


− 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 )


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


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


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 .


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


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


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


in the bottom panel we show distributions as a function of R and φ . Figure 2. The – plane coloured by mean φ for the simulation described in Section 2.2.1 . The bins have size Δ = 0.05 kpc, and Δ = 3 km s −1 . The bins with fewer than 10 particles are ignored. Fig. 2 shows the – plane coloured by mean φ . Stars at large radii in the – plane, i.e. stars with high E preferrentially come from stars in population 1, which have lower φ , as seen in the bottom panel of Fig. 1 . The initial DF shown in Fig. 2 is perturbed by displacing it by in . The particles are then evolved using a standard leap-frog algorithm for and the results are shown in Fig. 3 . The number density shows the spiral pattern typical of phase wrapping. Stars orbit the – plane in a clockwise sense and since those at large E have a lower vertical epicycle frequency, the DF quickly develops a trailing spiral. Also shown is the – plane coloured by mean R and φ . Here, the pattern is essentially featureless, apart from the imprint of the number density distribution: with our separable potential the in-plane and vertical epicyclic motions completely decouple. Figure 3. Number density and mean radial and azimuthal velocities in the – plane for the toy model considered in Section 2.2.1 (toy model with additively separable potential). Top panel shows the number density. The bins in the middle and lower panels are coloured by R and φ , respectively. The bin sizes and particle number threshold are the same as in Fig. 2 . 2.2.2 Kinematic spirals in a coupled potential Next we consider the addition of a R – term to the toy model potential R s is a constant radius characteristic of the distribution [if a Taylor expansion of the effective potential is performed for each L population, R s is replaced by R c ( L )]. For illustrative purposes, we choose and . These values are consistent with the cubic terms that arise in realistic Milky Way potentials. The main effect of the new term is to introduce a linear dependence in R to the vertical epicyclic frequency. In particular the difference between the vertical frequency for a population 1 star with and a population 2 star with is . As before we sample an initial distribution (equation 3 ) with 500k particles, perturb it and integrate the perturbed distribution for . The results are shown in Fig. 4 . Not surprisingly, the spirals that appear in the – number density distribution are virtually identical to the ones that appear in our separable model. However, the R and φ spirals are qualitatively different. In particular, there are gradients across the spiral arms and along their inner and outer edges. The addition of the ( R − R s ) 2 term implies a coupling between the in-plane and vertical epicyclic motions. Figure 4. Same as Fig. 3 but for the model considered in Section 2.2.2 (toy model with R – coupling included in the potential). 2.3 Realistic Milky Way potential We conclude this section on test-particle simulations by considering a realistic


Right panels present the distributions of the position angles of the magnetic field orientations as a function of distance from the protostars. If multiple protostars are present in one core, the distances between the magnetic field orientations and the protostar closest to the Stokes I intensity peak are calculated. In the middle and right panels, black dashed lines denote the mean magnetic field orientations computed from the averaged Stokes Q and U emission in the area of the dense cores, and red solid and dashed–dotted (if there are multiple outflows) lines show the position angles of the outflows. The names of the protostars are labeled in the order from western to eastern sources above the middle panel in each row. Figure 12.16. L1157 Same as Figures 3 and 4, but left panels only present the magnetic orientations (small orange segments) detected in the 40′′ × 40′′ regions (dashed open squares) around the sample protostars as well as the mean orientations of the magnetic field (long thick orange segments) in the individual dense cores/clumps. Left panels show the Stokes I maps (gray scale) of the dense cores, where the sample protostars are embedded, and green contours delineate the area of the dense cores identified by Clumpf ind . Yellow dots show the locations of the protostars, and blue and red arrows present the orientations of their blue- and redshifted outflows. Black horizontal segments denote the spatial scale of 0.02 pc (or ∼4000 au). Middle panels present the distributions of the position angles of the individual magnetic field orientations detected with the JCMT POL-2 observations. Right panels present the distributions of the position angles of the magnetic field orientations as a function of distance from the protostars. If multiple protostars are present in one core, the distances between the magnetic field orientations and the protostar closest to the Stokes I intensity peak are calculated. In the middle and right panels, black dashed lines denote the mean magnetic field orientations computed from the averaged Stokes Q and U emission in the area of the dense cores, and red solid and dashed–dotted (if there are multiple outflows) lines show the position angles of the outflows. The names of the protostars are labeled in the order from western to eastern sources above the middle panel in each row. Appendix D Dependences of Misalignment on Source Properties Figure 13 compares the measured misalignment angles with the sizes, total fluxes, mean intensities, and mean polarization percentages of the dense cores and the distances to the sources. The total flux and mean intensity are expected to be proportional to the total mass and mean column density of a dense core, respectively. These comparisons show that the measured misalignments do not depend on the mass and density of the dense cores. We note that the magnetic field structures in the nearby sources can be better resolved than in the distant sources. The comparison also


task of solving equation ( 69 ). The problem then assumes the form of an inhomogeneous Helmholtz equation and the solution becomes particularly simple when expanding the radial dependence in modified spherical Bessel functions that fulfil the boundary conditions. Like in the classical gravity problem, Legendre polynomials remain the representation of choice for the latitudinal dependence. These basis functions allow a very efficient semi-analytical solution to the problem. Each of the calculations presented here required only a few seconds of run time on a standard 4-core notebook. There has been a discussion whether the DSG term could be neglected when inverting high precision gravity observations of Jupiter and Saturn for zonal flow properties. Our new formulation allows us to quantify the relative impact of the DSG for each gravity harmonic, practically independent of the considered zonal flow or background state. A special case arises for degree l = 1. For the background density with polytropic index unity, the l = 1 solution comprises the case where the two buoyancy contributions in the TGWE cancel. This corresponds to the homogeneous solution of the Helmholtz equation. Zonal flow and gravity perturbation then decouple, and it becomes impossible to draw any conclusion on the zonal flows from the respective gravity contribution. Kong et al. ( 2017 ) seem to have noticed the related problems without realizing their origin. However, this is of little practical interest since the origin is generally chosen to coincide with the centre of gravity so that l = 1 contributions vanish. Table 5 compares the relative DSG impact with the precision of most recent gravity measurement for Jupiter and Saturn. The even harmonics J 2 – J 6 are not listed since they are dominated by the rotational deformation of the planet. For Jupiter’s J 3 , J 5 , and J 7 coefficients, the relative impact of DSG is comparable to the error and should thus be taken into account when inverting gravity harmonics for zonal flow properties. This agrees with the results and conclusion by Kong et al. ( 2017 ). The error in the higher order observed moments may decrease as the Juno mission progresses. For Saturn, J 3 , J 5 , and J 10 seem precise enough to warrant including DSG effects. The estimates of Kong et al. ( 2017 ) and Galanti et al. ( 2019 ) for the relative impact of the DSG are compatible with our results. Including the DSG term generally increases the amplitude of the gravity coefficients. Table 5. Relative error of gravity harmonics for Jupiter (Iess et al. 2018 ) (second column) and Saturn (Iess et al. 2019 ) (third column). The fourth column shows S l , the relative impact of the DSG for radial profile f 3 also listed in Table 4. In addition to the TWE, Cao Stevenson ( 2017 ) also solve the Euler equation for a polytrope of index unity and a geostrophic equatorial zonal jet. The respective results not only provide the perturbed density structure but also the


analysis of photochemical models of Titan (Dobrijevic et al. 2008 ). It was found that the chemistry of C 2 H 2 and C 2 H 4 could be bistable although the underlying chemical pathways, involving neutral–neutral processes, differ from those studied here. The physical environment of Titan is significantly different from that of dense interstellar clouds; nevertheless, as H 2 is much less abundant on Titan, this work suggests that Titan’s ion–molecule chemistry could also lead to bistable solutions. Finally, the interstellar chemistry of carbon is much more complex than studied here, where we have only considered hydrocarbons up to C 2 . Autocatalytic processes in addition to those described above are likely present. For example, ethene, when viewed as a dimer (CH 2 ) 2 takes part in autocatalysis for CH 2 in reaction sequences similar to those for acetylene. Although present in our network, we found this played no role in producing bistable solutions. Analysis of larger, more extensive, carbon chemistry networks may lead to the discovery of more deeply embedded, and so less apparent, autocatalytic cycles. If one identifies the higher hydrocarbons as dimers then diacetylene (C 4 H 2 ) and the carbon tetramer (C 4 ) could act as respective intermediates for C 2 H and C 2 autocatalysis. The possibility for autocatalysis involving larger organic molecules remains to be explored; anion chemistry (e.g., Cordiner Charnley 2012 ; McElroy et al. 2013 ) may become as important as the cationic reactions considered here. 5. Conclusions We have found new bistable solutions in reduced chemical sets comparable to simplistic gas-phase chemical models of dense molecular clouds. We have identified several autocatalytic cycles in the ion–molecule chemistry of the major volatile elements: O, N, and C. In nitrogen chemistry there are two possible autocatalytic processes. An autocatalytic cycle driven by the reaction of He + with N 2 produces bistability. We find that this model has bistable solutions at high densities ( n H > 10 5 cm −3 ), which are present at all values of the elemental N abundance considered. The bistable solutions in the reduced model of the oxygen chemistry occur at low densities but are similarly present at all values of elemental O depletion, including none. Thus, bistable solutions are a fundamental property of interstellar chemistry; introduction of other elements, carbon in particular, acts to suppress these solutions by inhibiting autocatalysis through reactions with O 2 and OH. The carbon chemistry exhibits bistable solutions that appear around 10 2 cm −3 , or less, but only when an elemental depletion equivalent to that of the diffuse interstellar medium is adopted. We have identified three possible autocatalytic processes. We find that two autocatalyses occur in the acetylene chemistry, with CH, rather than atomic C, being the autocatalyst. These involve and C 2 H 2 in processes analogous to those found in the oxygen autocatalysis; their


and carbon-normal metal-poor stars (red crosses and blue dots, respectively). Because our model is computed for , we restrict our observed sample to stars with iron abundance within a factor of five from the model value, . This selection leaves us with CEMP, CEMP-, and CEMP- stars, that is more than of our entire carbon-rich sample. The theoretical and observed abundances differ in many aspects. 1. Observed carbon-rich and carbon-normal stars appear as two distinct and clearly separated populations. We compute the linear regression of the observed europium and barium abundances weighted with the observational errors, and we determine the following equations for the ratio of barium to europium in carbon-normal and CEMP- stars, respectively, represented in Fig. 2 with blue-dashed and magenta-solid lines. If we compute the linear fit for CEMP- stars with and CEMP- stars separately we find almost identical results as in Eq. ( 2 ). Equations ( 1 ) and ( 2 ) show that the empirical relation between [Eu/Fe] and [Ba/Fe] has almost the same slope in the two classes of stars, and CEMP- stars have [Ba/Fe] on average dex higher than carbon-normal stars at the same [Eu/Fe]. The relations described by Eqs. ( 1 ) and ( 2 ) are likely consequences of the barium-to-europium ratios produced in the - and in the -process, respectively. In contrast, in our simulation there is not a clear separation between the two groups (colour distributions in Fig. 2 ). Because - and -enrichments are independent, the initial [Eu/Fe] and [Ba/Fe] follow approximately the relation described by Eq. ( 1 ), whereas the final abundances depend on the amount of material transferred from the AGB primary stars onto their secondary companions. Higher accreted masses cause stronger abundance enhancements of carbon and barium. Because AGB stars generally do not produce high europium abundances, [Eu/Fe] is essentially determined by its initial value, except for stars with initial [Eu/Fe] less than about . Consequently, for each [Eu/Fe], which is given by the initial -enrichment, we find stars with all barium abundances up to two dex higher than predicted by a pure -process, and the correlation between [Eu/Fe] and [Ba/Fe] described by Eq. ( 2 ) is completely washed out. Lugaro et al. (2009 , 2012) and Abate et al. (2015c) criticise this scenario of independent - and -process contributions with analogous arguments. Fig. 2 [Ba/Fe] vs. [Eu/Fe] in carbon-normal and carbon-rich metal-poor stars (blue dots and red crosses, respectively). Stars enriched in -elements occupy the region above the horizontal and diagonal solid black lines, corresponding to zones A and B of the plot. According to our adopted definitions, CEMP- stars are in zone B. In zone C there are stars with , , and . CEMP- stars and carbon-normal stars with and are in zone D. The dashed-blue and solid-magenta lines are linear fits of the carbon-normal stars and CEMP- stars, respectively. The red and blue distributions represent the


Zanazzi Lai 2018 ). If the initial inclination angle of the disc is small, the result of the evolution is that the disc tends to be coplanar with the binary star. If the initial inclination angle of the disc is large (i.e. >40°; Martin Lubow 2017 ) and the eccentricity of the binary star is non-negligible, then the disc will evolve into a polar orbit. The presence of high-inclination discs indicates that high-inclination CBPs might exist. However, the above conclusions are based on the evolution of the isolated CBD systems themselves. Besides, they can only evolve to high-inclination orbits in specific initial configurations, such as a high initial inclination and a large eccentricity for the binary. Other mechanisms are still needed to explain why the CBD has a large inclination initially. It is worth noting that the semimajor axes of binaries with high-inclination discs found already are relatively large (several tens of au), while the discs around close binaries are nearly coplanar (Kennedy et al. 2012 ; Czekala et al. 2019 ). For the Kepler CBPs, the semimajor axes of their host binaries are small, about 0.1–0.2 au. One possibility is that the discs around well-spaced binaries are susceptible to the surrounding environment, such as th close encounters with fly-by stars. It is generally believed that most stars, and therefore most planetary systems, were born in clusters or associations (Clarke, Bonnell Hillenbrand 2000 ; Lada Lada 2003 ; Pfalzner 2013 ; Hao, Kouwenhoven Spurzem 2013 ; Cai et al. 2017 ). Some open clusters later dissolved, forming the current field stars. A notable example is that our own Solar system may have formed in an open cluster. The chemical composition of objects in the Solar system, along with the orbital elements of Sedna, suggest that the Sun formed in a cluster with roughly 10 3 –10 4 stars (Adams 2010 ). Other work even suggests that the Sun was born in a massive cluster (10 4 –10 5 stars) because a cluster of several thousand stars is much too small to produce a nearby massive supernova (Dukes Krumholz 2012 ). Malmberg, Davies Heggie ( 2011 ) considered the effect of a close encounter between stars on the planetary systems in a single star system. They found that the fly-by of a star is one of the possible mechanisms for explaining the generally high eccentricity of exoplanes (mainly discovered by radial velocity methods). It is interesting to ask how the cluster environment affects CBPs. In fact, the first CBP discovered, PSR B1620–26, is located in a globular cluster (Sigurdsson et al. 2003 ). According to the theory of star formation, it is impossible to form a close binary directly (Moe Kratter 2018 ). One of the explanations for this is that they are formed by interaction with other stars (Martin, Mazeh Fabrycky 2015 ; Hamers, Perets Portegies Zwart 2016 ; Moe Kratter 2018 ), which means that they were in a star-dense environment previously. A cluster provides such a possibility. If a CBP was born in an


luminosity an excellent proxy of the star formation rate. In Arp 220, the L ′ CS(7–6) -to- L ′ CS(4–3) ratio is equal to 0.76. Using the calibration of Zhang et al. ( 2014 ), this leads to an L IR estimate of 1.6 × 10 12 L ⊙ , consistent with the L IR determined by Rangwala et al. ( 2011 ) using Herschel /Spectral and Photometric Imaging Receiver (SPIRE) data (i.e. 1.8 × 10 12 L ⊙ ). The relation linking L CS(4–3) and L IR can now be calibrated with SEPIA Band 5. H 2 O – submillimetre water line emission is considered to be an important gas cooling mechanism in warm molecular clouds and the H 2 O line (ν rest = 183.3 GHz) only requires moderate densities ( n (H 2 ) = 10 4 –10 5 cm −3 ) and low temperatures ( T ∼ 40K) to be excited (Cernicharo et al. 1994 ). We confirm the detection of H 2 O(3 3,1 –2 2,0 ) emission in Arp 220 (Fig. 1 , middle), with a peak flux of 0.14 Jy and a width at half-power of 332±31 km s −1 . These values are consistent with the peak flux (0.17 Jy) and width at half-power (310 km s −1 ) obtained with IRAM data by C06 (see section 4.1 for further analysis). CH 3 OH – extragalactic methanol maser emission has been detected towards many objects (Henkel et al. 1987 ; Sjouwerman et al. 2010 ). In particular, millimetre methanol transitions are known to be sensitive (but sometimes degenerate) tracers of temperature and density. Millimetre CH 3 OH emission has been detected in Arp 220 by Martín et al. ( 2011 ), particularly the 5–4 group (241.8 GHz). Salter et al. ( 2008 ) also report an absorption feature from the 6.7 GHz methanol line. Our SEPIA observations give us an access to the 193.5 GHz methanol (4–3) group (Fig. 1 , bottom). The peak flux is 68 mJy. The water and methanol lines have similar widths (equal to 333 km s −1 for CH 3 OH). We note that this is at the lower end of the line width range (280–590 km s −1 ) estimated from thermal molecules in Arp 220 by G09 . HC 3 N – molecules from the cyanopolyyne family like HC 3 N are standard tracers of the dense gas in Galactic star-forming regions but are also detected in extragalactic environments (Aladro et al. 2011 ; Lindberg et al. 2011 ) in many transitions (from 9–8 to 28–27). Arp 220 is one of the very few ‘HC 3 N-luminous’ galaxies (i.e. that the HC 3 N(10–9) line intensity is at least 15 per cent of the HCN(1–0) line intensity; Aalto et al. 2002 ; Martín et al. 2011 ). The HC 3 N(20–19) line is narrow and detected at 16 per cent of the HNC(2–1) luminosity. Its profile looks symmetric but its peak is shifted. This is consistent with the asymmetry observed in the 10–9 transition by Aalto et al. ( 2002 ) and could suggest that most of the emission emerges from the eastern nucleus. C 34 S – we observe a strong and broad C 34 S(4–3) line at 192.8 GHz. The line is unfortunately at the edge of the velocity range observed. An HC 3 N vibrationally excited line resides in a similar frequency range (192.6 GHz; see Fig. 1 , bottom)). Vibrationally excited emission of this


of gravitational wave after supernova explosion. In this study, since we consider only one progenitor model and one EOS, it is difficult to say how this relation is independent of the models, i.e. equation ( 7 ) cannot be used to analyse data from future gravitational wave observations. Even so, this relation seems to be independent of the models at least in the early phase, as shown in Fig. A2 in Appendix A . Anyway, additional models should be considered in the future. Figure 6. In the left-hand panel, frequencies of the f - and g 1 -modes are shown as a function of the square root of the PNS average density, where the thick solid and the thick dotted lines are the fitting formula given by equations ( 7 ) and ( 8 ). In the right-hand panel, frequencies of the f - and g 1 -modes are shown as a function of the surface gravity of the PNS, where the thick-solid line denote the fitting formula given by equation ( 9 ). The relation similar to equation ( 7 ) has already been proposed, as a function of x in Sotani Sumiyoshi ( 2019 ): and as a function of in the unit of M ⊙ km −2 in Torres-Forné et al. ( 2019b ): although in Torres-Forné et al. ( 2019b ) the ramp up signal is identified as g 2 -mode in their classification. Equation ( 8 ) is derived for the f -mode frequency after the avoided crossing with the g 1 -mode with the PNS models provided by the 1D numerical simulations, which are eventually collapsed into black hole. In the left-hand panel of Fig. 6 , we also plot the thick dotted line given by equation ( 8 ). From this figure, we find that the f -mode frequency is well identified by equation ( 8 ) up to f ≃ 1.4 kHz, which corresponds to T pb ≲ 0.6 s from Fig. 5 (or Fig. 2 ), but it deviates for T pb ≳ 0.6 sec. This may come from that the PNS models for deriving equation ( 8 ) become more compact in the later phase due to the massive progenitor model. On the other hand, in order to see the correspondence between the eigenmodes calculated in this study and equation ( 9 ), we show the f - and g 1 -mode frequencies as a function of in the right-hand panel of Fig. 6 . This fitting formula seems to correspond to the f -mode rather than the g 1 -mode in the very early phase and also in the late phase, at least for comparing to our results. Finally, we make a comment with respect to the previous results about the gravitational wave signals, especially obtained via the general relativistic 3D simulation (Kuroda et al. 2016 ), which is done with a 15 M ⊙ progenitor model (Woosley Weaver 1995 ) and SFHx EOS (Steiner et al. 2013 ). Unlike most of the other simulation results, several modes of gravitational wave signals have been found in this simulation. The characteristic gravitational wave frequencies extracted by the time-frequency analysis (Kawahara et al. 2018 ) are shown in the left-hand panel of Fig. 7 , where the signal A corresponds to the ramp up signals. Nevertheless, considering the results with the PNS asteroseismology shown in Fig. 2


HO (under laboratory conditions), which is consistent with the astronomical observation of solid CO in water-rich environments. Neill et al. ( 2014 ) performed a sensitive line survey of Sgr B2(N), and based on the HOCO species, they estimated a CO/CO ratio in the colder external envelope of between 0.010.1, implying a CO gas-phase abundance of 10–10, consistent with the finding of Minh et al. ( 1988 , 1991 ). Their lower limit to the CO gas-phase abundance of 10 relative to H indicates that the CO abundance in the gas is clearly enhanced, while most of the water is still frozen out in ices in the Sgr B2 envelope. Table 1 Properties of the observed HOCO and DOCO lines ( K). Notes. The upper limits have been computed using the rms around the line. The errors in the fluxes include the calibration and statistical uncertainties from the Gaussian fits of the lines. As part of the IRAM-30 m Large Program ASAI 1 (Lefloch et al., in prep.), we carried out a highly sensitive, unbiased spectral survey of the molecular emission of the L1544 prestellar core with high spectral resolution. This source is a prototypical starless core in the Taurus molecular cloud complex ( pc) on the verge of the gravitational collapse (Caselli et al. 2002 , and references within). It is characterised by a central high density ( cm) and a low temperature (7 K). We reported the detection of many oxygen bearing complex organic molecules produced through the release in the gas phase of methanol and ethene through non-thermal desorption processes (Vastel et al. 2014 , hereafter Paper I). The sensitivity of these IRAM observations also led to the detection of the hyperfine structure of CHCN (Vastel et al. 2015a ). In the present study we report on the detection of the HOCO ion in the L1544 prestellar core, as well as a tentative detection of its deuterated form, DOCO. 2. Observations and results The observations were performed at the IRAM-30 m towards L1544 () using the broad-band receiver EMIR at 3 mm, connected to an FTS spectrometer in its 50 kHz resolution mode. The beam of the observations is 29 and 23 at 85 and 106 GHz, respectively. Line intensities are expressed in units of main-beam brightness temperature (see Paper I for more details). The frequencies and other spectroscopic parameters of the HOCO transitions have been retrieved from the JPL database 2 from laboratory measurements by Bogey et al. ( 1988 ). Two lines of HOCO (the 4–3 and 5–4 at 85.531 and 106.913 GHz, respectively) lie in the frequency range covered by the ASAI survey for upper level energies lower than 30 K and were detected. Their spectra are shown in Fig. 1 . Table 1 reports the spectroscopic parameters as well as the properties of the two detected lines, obtained by Gaussian fitting. For the deuterated form of HOCO, DOCO, we used the JPL database with the spectroscopic parameters from Bogey et al. ( 1986 , 1988 ). Three transitions lie in the frequency range for upper level energies lower than 30 K.


( 2015 ) galaxies are compatible with our simulations] then the slope of the reddening law required to explain the data is much steeper than the SMC extinction law. For example, the position of the stack of undetected galaxies would require n −20, much steeper than any attenuation, or even extinction law, ever observed. Given this discrepancy, it is worth considering the potential systematics that could be affecting the Capak et al. ( 2015 ) and Bouwens et al. ( 2016 ) results. One possibility is an underestimation of the dust temperature, which is taken to be 35 K in both cases. It has been suggested that dust temperature may increase with redshift due to an increase in the intensity of the radiation field heating the dust (e.g. Béthermin et al. 2015 ), 1 and typically an upper limit of 45 K has been assumed (Schaerer et al. 2015 ). In this case, L IR will be underestimated by a factor ≈2 and the resulting IRX underestimated by ≈0.3 dex. The magnitude of this shift is illustrated by the arrow in the bottom right-hand corner of Fig. 16 . It would bring the Capak et al. ( 2015 ) and Bouwens et al. ( 2016 ) data into better agreement with our model, however it is not enough to fully account for the discrepancy. There are other potential systematic issues affecting the determination of the UV continuum slopes, and estimated upper limits on L IR , which we will discuss in detail in a future work (McLure et al. in preparation). 6.2.5 SMC-like attenuation at lower redshifts? In Fig. 16 , we have not included data at lower redshifts ( z ∼ 2–3) which also support steeper, SMC-like, attenuation laws. In particular, Reddy et al. ( 2010 ) find that galaxies with young mass-weighted ages and typically lower masses (age ≲ 100 Myr; M/M ⊙ 10 10 ) have a smaller IRX, at a given β, relative to older galaxies at the same redshift. Finally, similar conclusions have also been reached using small numbers of individual lensed galaxies (e.g. Baker et al. 2001 ; Siana et al. 2009 ). In Reddy et al. ( 2010 ), these young galaxies represented ≈13 per cent of their full star-forming galaxy sample, and in our simulated sample ≈6 per cent of galaxies have ages 100 Myr. However, since our method involves comparing to the observed LF, it can only be applied to the full galaxy population complete down to a given UV magnitude, and cannot be applied to populations split by age. Therefore, we cannot rule out the possibility that certain populations (e.g. the youngest galaxies), or any given individual galaxy, will follow a steeper attenuation curve. We also note that, since the absolute attenuations decrease towards fainter, lower mass galaxies, the uncertainties on the form of the attenuation law will correspondingly increase, as the difference in absolute attenuation between curves becomes more difficult to distinguish. Therefore, our conclusions are most robust at high masses. Nevertheless, our current analysis suggests that, on average, a Calzetti-like attenuation curve


unexpected to condense from a gas cooling from high temperature (Grossman et al. 2012 ). The Fe content of these minerals is an increasing function of oxidation state. Even in an oxygen-rich condensing gas, these minerals are expected to be very Fe-poor, with fayalitic contents (=Fe/(Fe+Mg)) of no more than 4% (Grossman et al. 2012 ). Before the return of samples from comet Wild 2, it was thought that oxidation of crystalline silicates might have occurred within the parent bodies of meteorites, during aqueous alteration or thermal metamorphism. However, olivines returned from comet Wild 2 show a very broad and nearly flat distribution in fayalitic content from 0 to ∼40%, and a range of fayalitic content from 0% to 97% (Frank et al. 2014 ), so the oxidation appears to have taken place in a nebular environment, through an unknown mechanism. We note that all three collections of cometary materials have the potential to have suffered oxidation state change, or the appearance of oxidation state change through sample bias, between release from the parent body and analysis in the laboratory. Samples from comet Wild 2 were captured in the coma at 6.1 km s −1 , which may have led to reduction of Fe through smelting: the arrow in Figure 3 indicates that the original material may have been less reduced than observed in laboratory analyses. Cometary materials captured in the stratosphere may suffer from biases against metal-rich, high-density particles, because of their shorter residence time. This is consistent with the metal-poor composition of individual small CP-IDPs, in contrast to the relatively metal-rich composition of particles from giant cluster IDPs. However, none of these capture or sample bias effects go in a direction to reconcile cometary oxidation state with that of the ISM. 5.2. Summary A comparison of Fe L-edge absorption spectrum of continuum X-rays from Cygnus X-1 with extinction spectra derived from synchrotron X-ray microprobe analyses of mineral standards leads to the following conclusions: 1. Observations are consistent with the hypothesis that Fe is sequestered principally in metals, at least in this line of sight. The data are marginally consistent with Fe evenly divided between sulfide and metal, a composition that would be expected if Fe and S reside entirely in metal and sulfide, e.g., in a high-temperature condensation sequence. Less than 38.5% (2 σ ) of Fe resides in amorphous silicates. 2. The observations are inconsistent with the hypothesis of Ishii et al. ( 2018b ) that interstellar silicates consist of GEMS or their subcomponents as found in chondritic-porous IDPs. This conclusion is robust even if some Fe is oxidized between residence in the ISM and observation in the laboratory. 3. Fine-grained cometary material, as represented by FGM returned by the Stardust mission from comet 81P/Wild 2, with a WD01 size distribution predicts an extinction spectrum that is inconsistent with Chandra observations. 4. Our conclusions


) within 3 arcsec of the new variables and (ii) manually check OGLE-II DIA light curves of nearby sources to make sure none of them show brightness trends mirroring the new variables. 3.6 Digitized photographic plates (66 Oph) Photographic images of the sky obtained in late 19th and 20th centuries contain a wealth of information about historical positions (e.g. Laycock et al. 2010 ; Vicente et al. 2010 ; Berezhnoi 2013 ; Robert et al. 2014 ) and brightness (e.g. Kolesnikova et al. 2008 ; Tang et al. 2013 ; Sokolovsky et al. 2014c ) of celestial objects. The efficient use of this information requires it to be converted to a digital form using purpose-built digitizing machines (Simcoe et al. 2006 ; De Cuyper et al. 2012 ) or a commercially available flatbed scanners capable of working with transparent materials (Vicente, Abad Garzón 2007 ; Simcoe 2009 ; Tuvikene et al. 2014 ). We use an Epson Expression 11000XL flatbed scanner operating at 2400 dpi resolution (1.4 arcsec pixel −1 , 16 bits per pixel colour depth) to digitize a 1.26 × 1.26 deg 2 area centred at α J2000 = 17:57:44.7 δ J2000 = +04:59:54 (66 Oph field; Kolesnikova et al. 2010 ) on 227 photographic plates obtained in 1976–1995 with the 40 cm astrograph. The digitized images were processed with vast following the procedure described by Sokolovsky et al. ( 2014b ). APASS B -band photometry of 1600 UCAC4 stars in the magnitude range B = 10–16 is used to calibrate the instrumental magnitude scale using the relation between aperture photographic and photoelectric magnitudes proposed by Bacher, Kimeswenger Teutsch ( 2005 ). We identify 23 variable stars including five not previously known (Table 4 , Fig. 2 ) by means of period search and visual inspection of light curves standing out in the magnitude versus σ w plot. 3.7 Light-curve filtering Often raw photometric data have to be pre-processed before computing the variability indices discussed in Section 2 . This may include (i) removing outliers from a light curve (possibly by applying iterative σ-clipping or median filtering); (ii) removing systematic effects from a set of light curves by applying local zero-point corrections (e.g. Nascimbeni et al. 2014 ) and/or the sysrem algorithm, decorrelating each light curve with external parameters such as airmass, seeing, object position on a CCD, detector temperature (e.g. Pál 2009 ; Bakos et al. 2010 ; López-Morales et al. 2010 ; Hartman et al. 2011 ; Burton et al. 2012 ; Guterman, Mazeh Faigler 2015 ; Baade et al. 2016 ) or de-trending the light curves if one is interested only in fast variability (e.g. Kovács, Bakos Noyes 2005 ; Weingrill 2015 ). A smaller-than-expected number of detections is an indirect indication of many photometry problems including the object being close to an image edge, a cosmetic defect, a bright star, a detection or saturation limit. Objects systematically affected by any of these problems can be removed from the analysis by discarding light curves having less than a