μ) and Q 0 (0, μ) in the case of ( 1 7 ) are simple: In Table 1 we give the angular distribution J (μ) = I 0 (0, μ)/ I 0 (0, 0) and the degree of polarization p (μ) = − Q 0 (0, μ)/ I 0 (0, μ) per cent at and 1 for the incident non-polarized radiation perpendicular to the surface. Note that negative Q 0 (0, μ) corresponds to the wave electric-field oscillations perpendicular to the plane ( nN ). This holds in our case. Table 1 shows that the chaotic Faraday rotations strongly decrease the polarization and weakly affect the angular distribution. Table 1. The angular distribution J (μ) = I 0 (0, μ)/ I 0 (0, 0) and the degree of polarization p (μ) = − Q 0 (0, μ)/ I 0 (0, μ) per cent at and 1 for the incident non-polarized radiation normal to the surface. Recall that we consider the atmosphere without pure absorption (a conservative atmosphere). It follows from equation ( 13 ) that the zero moments of functions β(μ) and γ(μ) are equal to and , respectively. These moments are μ-integrals over the interval (0,1) (see Silant’ev et al. 2019 ). Taking the integral μ I 0 (0, μ) dμ over the same interval and using equation ( 13 ), we obtain that the flux of outgoing radiation is equal to the flux F I of the incident radiation. For a conservative atmosphere this is the evident result. In Fig. 1 the polarization degree p (μ) of the reflected radiation for different parameters h is given. The angular dependence J (μ) practically does not depend on h . Therefore, we give J (μ) for and 30. The numbers over the curves denote the values of h . Figure 1. The angular distribution J (μ) = I 0 (0, μ)/ I 0 (0, 0) and polarization degree p (μ) = − Q 0 (0, μ)/ I 0 (0, μ) per cent of reflected radiation. The incident radiation is perpendicular to the surface. The numbers denote the values of parameter h . It is of interest to compare the multiple scattered outgoing intensity I 0 and parameter Q 0 to the results for single scattered radiation: The flux of outgoing single scattered radiation is equal to F single = 0.168 F I , i.e. only ≃ 17 per cent of the total flux. The other 83 per cent of the emerging radiation is concerned with two and more scatterings in the semi-infinite atmosphere. In our case, the considered normal incident radiation penetrates deeper into the atmosphere than in other inclinations. It means that F single = 0.168 F I is the minimum value of the single scattered radiation fluxes. The corresponding angular distribution and the degree of polarization have the form The polarization p single (μ) at μ = 0 is equal to 100/(1 + h ) per cent. This result clearly demonstrates the decrease of polarization with increasing parameter h . This decrease holds along the outflow of single scattered non-polarized radiation. Recall that single scattering of non-polarized radiation gives rise to 100 per cent polarization of the scattered one if the scattering angle (the angle between the incident radiation and the scattered one) is equal to 90° (see, for example,

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


mass with a ratio coefficient f : and the accretion rate will be where f may be of the order of 0.5, as argued by van den Heuvel Bitzaraki ( 1995 ). Because the mass statistics of NSs and MSPs illustrate that the accreted mass at least is about for MSP formation (Zhang et al. 2011 ; Kiziltan et al. 2013 ; Ozel Freire 2016 ; Antoniadis et al. 2016 ), we prefer f to be about 0.1−0.2. A NS/LMXB with m = 1.4 and R 6 = 1 for possesses an accretion rate higher than . However, it cannot accrete at a rate over the Eddington limit, namely . With the limit of the accretion rate , it is possible to derive an upper limit companion mass in the main sequence according to equation ( 11 ): With 0.1 f 0.2, will be about to . Hence a possible mass distribution of the companion in the main sequence in a LMXB is , corresponding to an accretion rate of . In such a LXMB, the NS will evolve to be a MSP with a magnetic field of . For , however, the accretion time might be too short for the binary system to produce a MSP. Table 2. The 16 radio MSPs with a low magnetic fields of (data from the ATNF pulsar catalogue). 2.4 On the minimum magnetic fields of AMXPs AMXPs exhibit an X-ray outburst during the accreting phase, with a luminosity a few magnitudes higher than that in the quiescent phase (Wijnands van der Klis 1998 ; van der Klis 2000 , 2006 ; Mukherjee et al. 2015 ). The variation of the luminosity leads to a change in the accretion rate, and thus the magnetic field of AMXPs can be derived by equating the magnetosphere radius with the co-rotation radius R co of the NS (Burderi et al. 1996 ; Zhang Kojima 2006 ): where P −3 is the spin period P of AMXPs in units of milliseconds. When R co equals the NS radius, the AMXP will have the minimum magnetic field. For 19 AMXPs with spin periods in the range ~1.7–6.1 ms (Patruno, Haskell Andersson 2017b ), their R co are in the range of ~24–56 km, which is larger than the radii of NSs of ~10–15 km. Thus, it can be concluded that the magnetic fields of 19 AMXPs have not achieved their lowest values. Another method for judging the minimum magnetic field of AMXPs is comparing their spin frequencies to the kilohertz quasi-periodic oscillation (kHz QPO) frequencies. The upper-limit kHz QPO frequency of a AMXP is believed to be the Keplerian frequency with orbital accreting matter (van der Klis 2000 ; Zhang 2004 ): where G is the gravitational constant. For a NS with m = 1.4 and R 6 = 1.5, the orbital frequency ν k is . Some AMXPs have an upper kHz QPO frequency over (van der Klis 2000 , 2006 ; Wang et al. 2017 ), which is comparable to ν k . However, the spin frequency of 19 AMXPs ranges from 164 to (Patruno et al. 2017a ), which is much lower than the upper kHz QPO frequency or ν k , and hence we conclude that the minimum magnetic fields of 19 AMXPs have not yet been achieved. If the co-rotation radius approaches the stellar radius, AMXPs will obtain the minimum magnetic field through accretion. 2.5 The minimum magnetic

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


which describes the adopted stellar mass ( M ), polar radius ( R p ), polar effective temperature ( T eff,p ), equatorial rotation velocity ( v e ) and inclination angle ( i ). For example, ‘m40r40t150v300i30’ is the case of M = 4.0 M ⊙ , R p = 4.0 R ⊙ , T eff,p = 15 000 K, v e = 300 km s −1 and i = 30°. (2) Polar radius (in R ⊙ ). (3) Equatorial radius (in R ⊙ ). (4) Polar effective temperature (in K). (5) Equatorial effective temperature (in K). (6) Mean effective temperature in K (which was derived by averaging the local effective temperature over the observed stellar disc while weighting according to the local continuum intensity). (7) Product of v e and sin i (in km s −1 ). (8) First-zero frequency of He 4471 (in Å − 1 ). (9) Ratio of to , where is the first-zero frequency of classical rotational broadening function (see, e.g. Gray 2005 ), which is related to v e sin i as (λ: wavelength, c : velocity of light). (10) First-zero frequency of Mg 4481 (in Å − 1 ). (11) Ratio of to . The wavelengths of the reference pseudo-continuum, necessary for reducing the normalized profile, were defined in almost the same way as in Section 4.1: Having found the critical wavelength λ* corresponding to the maximum level between these two lines, we set [, ] = [4471 − (λ* − 4471), λ*] and [, ] = [λ*, 4481 + (4481 − λ*)]. The Fourier transforms were then calculated for the resulting R (λ) profiles of He 4471 and Mg 4481 lines. Fig. 6 illustrates the behaviours of | f (σ)| as function of σ for the same selected cases as in Fig. 5 . The first-zero frequencies (σ 1 ) measured from the computed transforms are presented in Table 2 . Figure 6. Fourier transform amplitudes [| f (σ)|] plotted against σ, for the theoretical profiles of He 4471 (left-hand panels) and Mg 4481 (right-hand panels) computed for six representative models (same as those shown in Fig. 5 ). The upper panels (a) and (b) show the results for T eff,p = 12 000 K, while the lower panels (c) and (d) are for T eff,p = 15 000 K. 5 DISCUSSION 5.1 Characteristics of first-zero frequencies We first discuss the trend of theoretical σ 1 modelled in Section 4.2 . Since this quantity is expressed as σ 1 = 0.660/(λ v e sin i / c ) in the classical approximation, the projected rotational velocity (or the linewidth for the case of rotation-dominated broadening) plays the most significant role for determining σ 1 , though its precise value is affected also by the profile shape. The resulting values of σ 1 corresponding to the theoretical line profiles simulated on the gravity-darkened models are plotted against v e sin i in Fig. 7 , where the classical σ 1 versus v e sin i relation is depicted by a slanted solid line and the observed σ 1 values for six stars are indicated by horizontal dashed lines. Figure 7. The values of theoretical σ 1 , measured from the Fourier transforms of simulated spectra for gravity-darkened models, are plotted against v e sin i . The results for He 4471 (left-hand panels)

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


rate coefficients. Notes. TW18 and MP17 refer to models with nominal values of the oxygen-bearing influx (see Sect. 4 ). ( a ) CO 2 best-fit mixing ratio at 0.15 mbar from photochemical modelling in Orton et al. (2014b ) is 8.0 × 10 −11 . ( b ) Ice grain ablation influx giving rise to 1.2 × 10 5 and 4.5 × 10 3 cm −2 s −1 for H 2 O and CO 2 , respectively. The outcome of this sensitivity test indicates that a CO relative abundance of 7.0 × 10 −9 at 0.4 mbar allows an optimal match of the line core and wings. Table 4 lists different cases where ( D , t impact ) have been tuned to obtain q CO = (7.0 ± 0.1) × 10 −9 at the ~0.4 mbar region, the delivered CO mass (in g), and the CO mixing ratio obtained in 200–100 mbar. The resulting profiles in the 200–100 mbar region reflect that larger impactors give rise to larger CO abundances although below the upper limits in Teanby Irwin (2013) . Table 4 shows that the solution is degenerate; in other words, the same stratospheric CO mixing ratio abundance can be obtanied with pairs of ( D , t impact ) that represent larger impacts having taken place longer ago, or smaller impactors occurred more recently. For instance, the temporal evolution of the material delivered by a cometary impact indicates that the CO currently observed in the Uranus stratosphere could be due to a comet nucleus of 3.5 km diameter that hit the planet 822 yr ago. Figure 4 shows the comparison of the measured spectra and the modelled radiative transfer as a function of the different CO vertical distribution resulting from steady ice grain ablation and cases 3 and 4 for cometary impact. Any other of the cases in Table 4 will give rise to a CO mixing ratio of ~ 7.0 × 10 −9 at the 0.4 mbar pressure level that will give good match to the Herschel data. Stratospheric CO mixing ratio profiles with an abundance larger than the value in the pressure range probed by Herschel (i.e. between 3 and 0.4 mbar) can in principle be discarded as they will overestimate the observations. Similarly, the tropospheric CO mixing ratio profile has to be lower than the upper limit 2.1 × 10 −9 established by Teanby Irwin (2013) . Equations (14) and (15) in Zahnle et al. (2003) , adapted to Uranus where the impact frequency is ~ 4 times smaller than on Jupiter, allow us to plot the frequency of impact versus the impactor size. Figure 5 displays two different scenarios depending on the origin of the impactors: the size-number distribution of impactors is like that inferred at Jupiter (ecliptic comets), and those impactors more representative of nearly isotropic comets (as long-period or Halley-type comets). Zahnle et al. (2003) conclude that known craters on the Saturnian and Uranian satellites are consistent with either case; that is, both kinds of impactors are in the Uranian system and they could have entered the Uranus atmosphere. Also, Zahnle et al. (2003) assume that the impact rate on Uranus is ~ 0.00125 comets per year (i.e. one impact every ~800 yr)

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This observational evidence makes HL Tau an example of a young (∼1 Myr; Briceño et al. 2002 ), embedded, disc-hosting star. HL Tau has therefore become a prime target for studies aiming to characterize young discs (Greaves et al. 2008 ; Carrasco-González et al. 2009 ). In particular, HL Tau was the first circumstellar disc observed with the long baselines of Atacama Large Millimeter/submillimeter Array (ALMA). This revealed an ordered series of concentric rings and gaps in the disc across multiple millimetre wavelengths (2.9, 1.3, and 0.9 mm; ALMA Partnership et al. 2015 ). Many theories have been put forward to explain the origin of these structures (e.g. Zhang, Blake Bergin 2015 ; Okuzumi et al. 2016 ), but one of the most persistent involves the growth of planets within the disc (Dipierro et al. 2015b ). While efforts to detect thermal emission from young planets in the gaps have been unsucessful, the corresponding upper limits on their masses still lie at the higher end of the giant-planet regime (10–15 M Jup ; Testi et al. 2015 ). The combination of the potential for massive planets at large radii, coupled with evidence of a high disc mass (∼0.1–0.13 M ⊙ ; Guilloteau et al. 2011 ; Kwon, Looney Mundy 2011 ), has seen gravitational instability (GI; Boss 1997 ) being invoked to explain both the observed dust structures in HL Tau (Akiyama et al. 2016 ; Takahashi Inutsuka 2016 ), along with the origin of any planetary companions (Nero Bjorkman 2009 ). However, recent measurements of the gas mass in the HL Tau disc using have shown appears to be too low for GI to occur ( M gas = 2–40 × 10 −3 M ⊙ ; Wu et al. 2018 ). In this Letter, we present a detection of the J = 3–2 transition towards the disc around HL Tau. We have demonstrated this line to be a robust tracer of disc gas mass (Booth et al. 2019 ). We use these data to derive a lower limit to the total gas disc mass and discuss how this impacts the gravitational stability of the HL Tau star–disc system. 2 OBSERVATIONS HL Tau was observed by ALMA in Band 7 on 2017 November 24 for 1.46 h with 49 antennae in configuration C43-8 under project code 2017.1.01178.S (PI: E. Humphreys). Baseline lengths ranged from 92 to 8547 m, and the spectral window (SPW) covering the J = 3–2 transition (321.852 GHz) had a native spectral resolution of 0.908 km s −1 (which we note does not resolve the J = 3–2 hyperfine structure). Data (self-)calibration and imaging were performed with casa version 5.1.1 (McMullin et al. 2007 ). Continuum subtraction was performed in the uv -plane using a constant baseline (fitorder 0). Line imaging was performed with the clean algorithm, using a Keplerian mask with the measured position and inclination angles of the disc (e.g. PA = 138° and i = 46°; ALMA Partnership et al. 2015 ). The native resolution of the data resulted in a natural beam size of 0.14 × 0.11 arcsec 2 (−13°). We used a 0.2-arcsec uv -taper, which was found to maximize the signal-to-noise ratio (S/N) of the line

O O O O B-CelestialObject I-CelestialObject O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O B-Observatory I-Observatory I-Observatory I-Observatory B-Observatory O O O O O O O O O O O O O O O O O B-Wavelength B-Wavelength O B-Wavelength I-Wavelength B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O B-Citation I-Citation O O O O O O O O O O O B-CelestialObject I-CelestialObject B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O B-CelestialObject I-CelestialObject O O O B-Observatory O B-Wavelength I-Wavelength O O O O O O O O O O O O O O B-Identifier I-Identifier I-Identifier O B-Person I-Person O O O O O O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength I-Wavelength B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength O O O O O O O O O B-Software B-Identifier I-Identifier B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O B-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


above even a high percentile point necessarily belong to a real filament. The histograms in Fig. 4 g are plotted for the intersection of two sets of pixels, those that are above the 95% percentile of significance (given by the and values) and those that coincide with a real filament (see Fig. 4 d). The RHT parameters are this time optimised manually, only keeping = 10 fixed. This leads to values = 5 and = 0.65. By visual inspection of the results, TM is slightly more successful in highlighting the location of filaments (Fig. 4 c) and estimating their position angles (Fig. 4 g). Fig. 4 Comparison of RHT and TM results in the case of non-linear filamentary structures on a fluctuating background. For the description of individual frames see Fig. 2 . Figure 5 shows how the results change as a function of the parameter values. For TM, the values of and are varied in 30% steps. For RHT, the parameter is kept at a value of 0.65, which was found to give the best results in Fig. 4 , but and are also change in 30% steps around the best parameter combination. The results of TM are less sensitive to these changes in the input parameters. Fig. 5 Change in RHT and TM results as a function of the method parameters. RHT parameters and are varied and parameter is kept at a value of 0.65. 3.2. Reliability and completeness We address questions of TM reliability estimation in the case of the simulation shown in Fig. 4 . equals 2.8 pixels and any two estimates that are separated by approximately five pixels can be considered independent. We first analyse maps similar to those in Fig. 4 but without filaments and with different realisations of noise and of large-scale fluctuations. According to this Monte Carlo exercise, 84%, 97.7%, and 99.9% confidence limits correspond to values of 0.0457, 0.0638, and 0.0850, respectively. This can be compared to the values of the same percentiles that are obtained directly from the input map of Fig. 4 . Those values are 0.057, 0.23, and 0.43 and they would thus result in lower estimates of the statistical significance of a given value. For example, , the apparent value corresponding to the 84% confidence limit, is in reality closer to the 97.7% confidence limit. The values are higher because of the presence of real elongated structures. The more real structures the map has, the more conservative are the limits derived from the statistics of the image itself. For a 360 360 pixel image, one would expect 2981 spurious pixels above the given threshold of . We count as spurious all pixel whose distance to real filaments exceeds three pixels. The number of such pixels is 3174, by 6.5% higher than expected. However, there are still some pixels with that are associated to filaments but are at distances exceeding three pixels. This suggests that the threshold obtained from the Monte Carlo simulations gives a rather accurate estimate of the reliability. For the 97.7% confidence limit, we expect the map to contain 68 instances where two

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


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we find that the median total number of stars that are enriched per event is ∼13, which is comparable to the maximum number of G dwarfs (stars with similar mass to the Sun, 0.8–1.2 M ⊙ ) that were enriched in the more populous clusters studied in Parker et al. ( 2014a ) as are the fraction of enriched G-dwarf stars that were unperturbed (∼0.5 per cent). In an attempt to increase the fraction of enriched stars, we explore a host of initial conditions for the star clusters. However, we find that no initial conditions result in a significantly higher (more than twice) fraction of enriched stars. The principal reason for this is the effects of two-body relaxation. In order to enrich more than half of the stars in a low-mass cluster, the required stellar density at the time of the SN(e) explosion(s) corresponds to a radius of only ∼0.4 pc, which is impossible to achieve after 5 Myr of evolution. Two-body relaxation results from a stellar system attempting to reach dynamical equilibrium and even a moderately dense system (100 stars pc −3 ) such as our default model expands significantly in the first 10 Myr, as shown in Fig. 7 . Here, the coloured lines represent the median local stellar density with time in each of the 20 realizations of these initial conditions. The solid black line is the mean central density across all 20 simulations (where we define the central density as the density within the half-mass radius). Clearly, the clusters have expanded significantly before the SN explosions (shown by the vertical dashed lines). Figure 7. Evolution of the median local volume density in each simulation as a function of time. Coloured lines indicate each of the 20 simulations and the black line indicates the average central density. Vertical dashed grey lines indicate times of the SNe. Irrespective of the initial conditions, the clusters never attain significant enrichment because the initial density is either too high (and two-body relaxation causes significant expansion), or the initial density is so low that despite the initial subvirial motion of the stars, significant clustering of the stars never occurs. The fraction of enriched unperturbed G-dwarf stars across all initial conditions range between ∼0.07 and 0.55 per cent. 3.4 Low-mass clusters containing one massive star The second median cluster chosen from our Monte Carlo sampling contained 113 stars, of which 1 was massive (24 M ⊙ ), resulting in an SN explosion at ∼7 Myr. The same set of initial conditions are focused on (α vir = 0.3, r F = 1.0 pc and D = 1.6) before summarizing the others. An average of six stars were enriched by the SN, a similar number to the median cluster containing two massive stars. The dynamical interaction and cluster density histories were also similar, resulting in ∼0.1–0.4 per cent of G dwarfs being enriched and unperturbed. With almost identical enrichment fractions and dynamical histories, the difference between clusters containing one or two massive stars is

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Strassmeier 2012 ) observed in total 11 transits in five observing seasons using the filters Johnson B and Sloan r ′. The first seven transits were observed with both filters alternating. These r ′ band light curves were already published by Seeliger et al. ( 2014 ). The four light curves from 2014 to 2016 were taken only in Johnson B . WiFSIP holds a back-illuminated 4k × 4k 15 μm pixel CCD and offers a field of view (FoV) of 22 arcmin ×22 arcmin. To minimize the read-out time, a windowing of the CCD was used reducing the FoV to about 15 arcmin × 15 arcmin. A small defocus was applied to spread the point spread function to an artificial full width at half-maximum (FWHM) of about 3 arcsec. One transit was observed with the NOT as a Fast Track program using ALFOSC in imaging mode. ALFOSC contains a 2k × 2k E2V CCD providing an FoV of 6.4 arcmin × 6.4 arcmin. One transit was observed with BUSCA, the four-channel imager at the Calar Alto Observatory 2.2 m telescope (Reif et al. 1999 ). The instrument performs simultaneous photometry in four different bandpasses with an FoV of 11 arcmin × 11 arcmin. For the bandpass of shortest wavelength, we used a white glass filter and the beam splitter defined the limit of λ 430 nm. For the other bandpasses from blue to red, we used a Thuan–Gunn g , Thuan–Gunn r , and Bessel I filter. Unfortunately, the observation of a pre-ingress baseline was lost due to weather, and the observing conditions remained to be non-photometric. We discarded the light curve of shortest wavelength because it exhibited significantly larger correlated noise than the other three light curves. One transit was observed with the IAC80 telescope, owned and operated by the Instituto de Astrofísica de Canarias (IAC), using its wide field imager CAMELOT. It is equipped with a CCD-E2V detector of 2k × 2k, with a pixel scale of about 0.3 arcsec pixel −1 providing an FoV of about 10.5 arcmin × 10.5 arcmin. Two transits were observed with the 70 cm telescope of the AIP, located in the city of Potsdam at the Babelsberg Observatory. The telescope is equipped with a cryogenic cooled 1k × 1k TEK-CCD providing an FoV of 8 arcmin × 8 arcmin. The first transit was observed in Johnson B and Johnson V quasi-simultaneously with alternating filters, the second one in Johnson V only. We applied a 3 × 3 pixel binning to reduce the detector read-out time. Data of an additional transit were taken with the triple beam, frame-transfer CCD camera ULTRACAM (Dhillon et al. 2007 ) mounted at the WHT. The instrument optics allow for the simultaneous photometry in three different bandpasses. We chose the filters Sloan u ′, Sloan g ′, and a filter centred on the sodium doublet at 591.2 nm with a width (FWHM) of 31.2 nm. To avoid saturation of the brightest stars, the exposure time was extremely short with 0.3 s. However, the overheads are negligible owing to the frame-transfer technique. The detectors were read out in windowed mode. For the u ′ channel, 10

B-Citation I-Citation O O O O O O O O O O O O O B-Wavelength I-Wavelength O B-Wavelength I-Wavelength I-Wavelength O O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O B-Wavelength I-Wavelength O B-Instrument O O B-Instrument I-Instrument I-Instrument I-Instrument I-Instrument I-Instrument I-Instrument I-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O B-Grant I-Grant I-Grant O B-Instrument O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O B-Instrument O O O O O B-Observatory I-Observatory I-Observatory B-Telescope I-Telescope I-Telescope B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O B-Wavelength I-Wavelength O B-Wavelength I-Wavelength O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope I-Telescope O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization B-Organization O O O O O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope I-Telescope I-Telescope O O B-Organization O O O B-Location I-Location I-Location O O B-Observatory I-Observatory O O O O O O B-Instrument I-Instrument I-Instrument I-Instrument I-Instrument I-Instrument O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O B-Wavelength I-Wavelength O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument B-Citation I-Citation I-Citation I-Citation O O O O B-Telescope O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength B-Wavelength I-Wavelength I-Wavelength O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength I-Wavelength O


results of both the binary pipeline ( Fig. 2 ) and the main GALAH pipeline ( Fig. B.1 ), confirming their close agreement. We observe some trends and biases in these figures, such as the inconsistency for the lowest metallicities in the bottom panel of Fig. 2 , which are a consequence of both the flexibility of the The Cannon model and the adequacy of the training set,where it is difficult to ensure equal representation of spectra in all bins of the modelled parameter space (see Sect. 3.3.1 in Buder et al. 2018 ). 4.2 Photometric validation In this validation check and in Sect. 4.3 , we used the benchmark validation sample, which is a subset of GALAH objects withexternal information about the temperature from the infrared flux method (IRFM; Casagrande et al. 2019 ) and radii (asteroseismology; Stello et al. 2017 ; Sharma et al. 2019 ). This sample of 620 giant stars is therefore suitable for benchmark testing, and is dominated by stars from K2 campaigns C1 and C6 ( Sharma et al. 2019 , see also Fig. 13 ). Compared to the previous spectroscopic validation, this sample has almost no overlap with the training set and hence no SME parameters to compare to. We took the results from the binary pipeline, using only the photometric fit (Eq. ( 7 )), and compared them to the IRFM temperature values and reddening values from SFD (Schlegel, Finkbeiner, David) reddening maps ( Schlegel et al. 1998 ) and 3D reddening maps based on Pan-STARRS 1 photometry ( Green et al. 2018 ; hereafter the Bayestar maps). This comparison is shown in Fig. 3 , where we display results with and without the Gaia magnitudes in the photometric fit. We distinguish the Gaia magnitudes from other photometric passbands used in this work because their uncertainties are approximately an order of magnitude lower. They therefore affect the fit more strongly. Fig. 2 Comparison of SME and The Cannon labels for The Cannon validation sample. The Cannon values produced by the binary pipeline are subtracted from the SME values. Fig. 3 Comparison of T eff (orange) and E ( B − V ) (green) parameters as derived by the binary pipeline (using only the photometric fit) to the literature values (indicated on the horizontal axis). The literature values are subtracted from those given by the binary pipeline. The lighter shaded distributions correspond to results from the binary pipeline when the Gaia magnitudes are excluded from the fit. Figure 3 shows some important problems. The most striking is a bias towards higher temperatures as compared to both the GALAH DR2 values and those from the IRFM. An additional test that we performed using a larger validation sample (without the need for external information about the radii) also shows strong grid effects, which diminish considerably, however, when we exclude Gaia magnitudes. The grid effect has a spacing of about 250 K, and it might originate from the SED model in combinationwith small uncertainties of Gaia data. Excluding Gaia magnitudes from the fit

O O O O B-Software I-Software O O O O O O B-Software I-Software I-Software O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O B-Survey O O O O O O O O B-ObservationalTechniques I-ObservationalTechniques I-ObservationalTechniques B-ObservationalTechniques B-Citation I-Citation I-Citation I-Citation O O O B-ObservationalTechniques B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O B-Mission B-CelestialRegion I-CelestialRegion O B-CelestialRegion O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O O O O O O O O O O B-Software I-Software O O O O O O O O O O O O O O B-ObservationalTechniques O O O O O O B-Dataset B-Dataset I-Dataset I-Dataset B-Dataset I-Dataset O B-Citation I-Citation I-Citation I-Citation O O O O O O O B-Survey I-Survey O O B-Citation I-Citation I-Citation I-Citation O O O B-Dataset I-Dataset O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Software O B-Model I-Model O O B-Dataset I-Dataset I-Dataset I-Dataset B-Model I-Model I-Model O O O B-Software I-Software O O O O B-Software O O O O O O O O O O O B-Wavelength O B-Wavelength O O O O O O O B-Software I-Software O O O O O O O O O O O O O O O O O O O O O O O O B-Software I-Software O O O O O O O O O B-Software I-Software O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O B-Dataset I-Dataset O O O O O B-ObservationalTechniques O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Telescope O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O B-Telescope O O B-Telescope O O O O


membership probabilities for the 7312 sample stars. Figure 8 shows that the stars with high GMM membership probabilities ( P GMM ≥ 0.8) generally have high RF membership probabilities, and the stars with low GMM membership probabilities ( P GMM 0.2) have low RF membership probabilities in general. However, some stars with near zero GMM probabilities still have a certain probability of being RF memberships, indicating that the color and magnitude parameters play non-negligible roles in the RF-based membership determination. In our previous work, we have confirmed that color and magnitude parameters cannot be ignored in the RF-based membership determination (Gao 2018a ). As a model-dependent clustering technique, the GMM method cannot directly handle the color and magnitude parameters since they do not follow Gaussian distributions. Fortunately, the RF method does not require any mathematical model, only a reliable training set is needed. This allows us to easily identify most likely cluster members of M67 in the 11-dimensional parameter space, even if the color and magnitude parameters are taken into account. The 1502 likely cluster members ( P RF ≥ 0.6) are listed in Table 3 , this table is published in its entirety in the electronic edition. It should be noted that Gaia Collaboration et al. ( 2018a ) have investigated M67 using Gaia -DR2 data and obtained 1520 cluster members, but they did not calculate membership probabilities for these stars. Among the 1520 cluster members in Gaia Collaboration et al. ( 2018a ), 1240 (∼82%) and 1201 (∼79%) stars are determined to be likely ( P RF ≥ 0.6) and high-probability ( P RF ≥ 0.8) cluster members by the RF method, respectively. This once again indicates the high effectiveness of the RF method for identifying likely cluster members in high-dimensional parameter space. Figure 8. A comparison between the GMM and RF membership probabilities of the 7312 sample stars. Table 3 A Catalog of Fundamental Information for 1502 Likely Cluster Members with P RF ≥ 0.6 Note. This table contains Gaia -DR2 identifier, positions and RF membership probabilities for the 1502 likely cluster members (≥0.6). Only a portion of this table is shown here to demonstrate its form and content, a machine-readable version of the full table is available. ID: Gaia -DR2 identifier; R.A., decl.: right ascension and declination; P RF : RF membership probability. (This table is available in its entirety in machine-readable form.) Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available. 3. Distance, Proper Motion, and Radial Velocity We have obtained 1361 high-probability cluster members ( P RF ≥ 0.8), 1260 of which have quite high membership probabilities ( P RF ≥ 0.9). We use the 1260 cluster members to calculate the weighted mean parallax (distance) and proper motion of the cluster, but also taking into account the observational errors. Using 687

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


surface term for stellar models is the method proposed by Kjeldsen et al. ( 2008 ). They note that the offset between observed and best model frequencies turns out to be closely fitted by a power law. However, there are issues with many of the surface-term corrections, even for main-sequence stars; and most models perform very badly in the subgiant and red-giant region. Schmitt Basu ( 2015 ) found that the two-term model proposed by Ball Gizon ( 2014 ) works better than other models across a large portion of the HR diagram, and consequently we adopt that for this work. 4. Results and Discussions We show the evolutionary track of our models in Figure 3 . The figure also shows the two error boxes. T eff = 4766 ± 200 K and have been used for the large error box while T eff = 4974 ± 161 K and for the smaller error box. We find that many models fall into the two error boxes. In order to obtain the best-fit model for KIC 8263801 from among these models, we calculated the likelihood for each model and determined the model with the highest likelihood. The likelihood function is defined aswherewith the quantity indicating the observed T eff , [Fe/H], and frequency ν n , l ; while the corresponds to these values of the model. The quantity σ i represents the observational error of . In the study, we use the function as follows:where In the above expression, are the surface-term corrected frequencies of the models. The values of likelihood function for model of KIC 8263801 as a function of mass, metallicity, age, and radius are shown in Figure 4 . We choose the model that maximizes as a candidate for the best-fit model. The model parameters are shown in Table 5 . To clearly compare all of the theoretical frequencies of the best-fit model with observed frequencies, we show the échelle diagram of the best-fit model in Figure 5 . In the figure, open symbols are the model frequencies corrected for the surface term, the filled symbols refer to the observable frequencies. Circles are used for l = 0 modes and squares for l = 2 modes. Figure 4. Likelihood values for models of KIC 8263801 as a function of mass, metallicity, age, and radius, corresponding to panels (a)–(d) respectively. Figure 5. Échelle diagrams for the best-fit model. Open symbols are the surface-term corrected frequencies of the best-fit model; filled symbols refer to the observed frequencies. Circles are used for l = 0 modes, squares for l = 2 modes. Table 5 The Parameters of the Best-fit Model Finally, we derive the parameters of star as the likelihood weighted mean and standard deviation from the models and obtain a mass of , age of t = 1.48 ±0.21 Gyr, and radius of R / R ⊙ = 10.53 ± 0.28. Our best-fit model has an age of 1.596 Gyr, the age as determined from the likelihood weighted average is not too different, and thus the question arises as to whether this star can be a member of NGC 6866. There are a number of results about the age of NGC 6866. For example, Loktin et al. ( 1994 ) derived

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


well-studied extragalactic radio source Cygnus A to demonstrate the applicability of our code. This is one of the nearest Fanaroff–Riley type I (FR II) galaxies and has a well-defined jet and counterjet with a jet inclination angle thought to be between 55 ○ and 85 ○ (Bartel et al. 1995 ), with a redshift of z = 0.0562 ± 0.000067 (Carilli Barthel 1996 ). There is observational morphological evidence to suggest that the jets are precessing ( K19 ). We visually identified 48 jet points (with an astrometric error of 0.4 arcsec from VLA data) from the 5-GHz map of Perley, Dreher Cowan ( 1984 ), as shown in Fig. 5 . Jet points are taken to be any discrete, distinct feature that appears to be part of the jet; this includes both compact knots and sub-regions of more extended bright parts of the jet. For longer sub-regions of the jet, we placed multiple points, spaced by at least the resolution of the image, in order to constrain the curvature of the jet in these regions. Figure 5. Locations of visible jet knots within Cygnus A used in the model. Note the curvature in both the jet and counterjet paths. The final points in both the jet and counterjet lie above the primary hotspots of the two lobes, as discussed in the text. The inner, straighter points of the jet used in Fig. 7 are identified as being within the indicated brackets. One important constraint on the application of the MCMC model to real-world data is the requirement for the precessing jet to stay within the lobes. Since the model does not take lobe structure into account beyond the terminal hotspot, the constraint was implemented by a joint prior on position angle and precession cone opening angle. This dual parameter calculates the two extreme edges of the cone for any given position angle, and keeps them within the lobes, which are approximately 25 ○ across at their widest point. Without this additional prior, we found that unphysical jet paths were permitted as part of the fit, broadening the credible interval on precession period. As with the tests described in earlier sections, the priors were flat within the permitted ranges. We initially fitted the model to all identified points (see Fig. 6 ), including the terminal hotspot, which in both lobes is taken to be the more compact or ‘primary’ hotspot; we do not include the larger, brighter secondary hotspot since the position of this is almost certainly dominated by post-shock hydrodynamics (Cox, Gull Scheuer 1991 ). Then, with respect to the potential for hydrodynamic influences to dominate the jet path within the lobes, we fitted the model only to the straight portion of the jet, terminating just inside the lobes (Fig. 7 ). The full number of regions produced a peak in the posterior distribution corresponding to a precession period of 1 Myr. Figure 6. Main: ‘Corner plot’ of one-dimensional and two-dimensional marginalized posterior probability distributions for the model parameters, given the observed jet path of Cygnus A, including

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


a coronal loop in our model) is significantly lower. While our whole computational domain covers more grid points () than the Rappazzo et al. (2008) models (up to ), in their model they describe only a single loop structure (straightened out), and consequently can reach significantly higher Reynolds numbers. Table 1 Exponents for different coronal heating scaling laws as used in Eqs. ( 10 ) and ( 11 ) together with the fitting results from Sect. 5.3 . The coronal heating scaling law we fit to our model data indicates a dependency on the magnetic field that lies between the exponents given by Rappazzo et al. (2008) and van Ballegooijen et al. (2011) . We also find that the homogeneous atmospheric background in the MHD-turbulence setup of Rappazzo et al. (2008) may be problematic when estimating the coronal magnetic energy input or braiding of field lines because the Alfvén crossing time , which determines their scaling law exponents, varies strongly within our stratified atmosphere. In a recent study van Ballegooijen et al. (2014) speculate that the quasi-static behavior of the coronal magnetic field found in models like ours is due to the limited spatial resolution of the photospheric magnetic driving. They suggest that in the case of increased resolution, the heating might be wave-dominated. Certainly, with increasing resolution AC heating will also be present, but this does not automatically imply that the DC heating becomes less efficient. To the contrary, models that employ reduced MHD (allowing for a higher spatial resolution) show that MHD turbulence will lead to a DC-type heating by the build-up of current sheets also for high spatial resolution (e.g., Rappazzo et al. 2008 ). This is backed by the argument that in the coronal part of the atmosphere a field line will adapt quickly to any wave excitation from below because coronal Alfvén speeds are at least one order of magnitude faster than within the lower atmosphere (cf. Fig. A.1 and Table A.1 ). More realistic full MHD simulations with increased resolution will have to show the relative merits of AC and DC heating based on the photospheric driving. The temperature scaling laws we tested against our model field lines ( Rosner et al. 1978 ; Serio et al. 1981 ) indicate only general trends for the most heated field lines and EUV-emissive loops. This puts all attempts to set up scaling laws of the coronal heating into their context, namely that these laws are deduced from and are only applicable to a small subset of coronal field lines, namely the ones that are bright in EUV or X-rays. Non-emissive and weakly heated field lines are often not consistent with scaling laws intended for 1D loop structures. Some of their plasma parameters need to be determined differently, for example, through self-consistent 3D MHD simulations. It is an interesting question whether such observationally motivated scaling laws would benefit from new and much more precise observations of hot coronal loops. We

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


reflecting enhanced and variable N abundances locally in the circumstellar material (CSM) surrounding many of the individual SNRs. There are some indications that the abundances in the twice solar models begin to have some unexpected impacts on relative line intensities. For example, the twice solar models show [O iii ]/H β as already being strong at 100 km s −1 and decreasing dramatically to 200 km s −1 and above, which is exactly opposite to the lower-abundance models over this same range. Also, more salient to the above discussion, the ratio of [N ii ]/[S ii ] varies by over 40% from 100 to 300 km s −1 shocks, whereas this ratio is nearly constant for lower-abundance sets over the same velocity range. As abundances increase, the balance of energy transfer and cooling being carried by the various ions must be changing in ways that are different from the lower-abundance models. From even this cursory comparison, it seems likely that the elevated abundances may contribute both to the high ratios and to the observed scatter of line ratios we observe in M83. Figures 32 and 34 of Allen et al. ( 2008 ) show their 2× solar abundance grids projected onto the same line ratio plots as shown in the middle and right panels of Figure 10 . Allen et al. apply these models to AGN situations, where one attempts to separate shocked emission from photoionized regions, but they should apply to SNR shocks as well. The majority of the SNRs in all three galaxies plotted in Figure 10 lie within the classical shock-heated region toward the upper right in these diagrams, but a significant number of objects appear toward the lower left region nominally ascribed to H ii regions. However, note that the model grids extend significantly down into the nominally photoionized regions of the plots at lower left. (Presumably lower shock velocities might extend even further into this regime.) Here again, we see evidence that at the higher abundances assumed in these models some of the traditional expectations begin to break down. We encourage further investigation of the properties of shock models at elevated abundances that can further elucidate this interesting and so far little-explored region of parameter space. 4.2. Ramifications The high metallicity of M83 has ramifications for the massive stars that are the precursors to many of the SNRs we have observed. It has long been known that abundances affect both the momentum transfer and mass loss in the stellar winds of massive stars (e.g., Vink et al. 2001 ; Kudritzki 2002 ), though the situation is complicated (Smith 2014 ). While most such studies consider only solar abundances and below, the trends with increasing abundance are clear, with higher abundances giving rise to significantly stronger and more massive winds. Coupling this with the hot, high pressure ISM in M83 that was inferred from X-ray data (Long et al. 2014 ), one might expect this wind mass loss to be constrained to the region immediately surrounding the

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


The signal source comes from a quasi-monochromatic Continuous Wave HeNe laser emitting at 3.39 μm. Figure 2. Description of the experimental setup. M: injection mirrors for the infrared signal at 3.39μm; L1: focusing lens for the MIR injection into the Periodically Poled Lithium Niobate (PPLN) waveguide; L2: focusing lens for the converted signal into a fibre single mode at 810 nm; L3: collimating lens for the pump signal; P: off-axis parabola; D: dichroic mirror used to separate converted signal from pump signal; BS: beam splitter used to separate the MIR signal in two separated ways. The 3.5 mW signal is shared equally between the two interferometric arms thanks to a pellicle beam splitter BS. Over the MIR stage, a set of mirrors and objectives allow the injection of the signal into frequency converters in each arm. These converters consist of periodically poled Ti-indiffused waveguides in LiNbO 3 . The waveguides are designed to provide low-loss single-mode guiding in the MIR range. Poling periods around 22 μm enable the phase-matching for the SFG process. The entire length of the non-linear conversion section is 92 mm. The non-linear stages are powered by a distributed feedback laser laser emitting at 1065 nm to generate a wave at 810 nm through the SFG process. On each interferometric arm, the maximum power conversion efficiency is measured in the range of 3·10 −5 when each non-linear crystal is powered by a 60 mW pump power. Notice that this overall throughput includes the non-linear efficiency and the whole losses resulting from the launching and collimating stages, including the stringent spatial filtering. This current low conversion efficiency is to be improved for future application, e.g. by using pigtailed techniques as demonstrated by Büchter (Büchter, Herrmann Sohler 2011 ) The pump signal is injected backward using a taper, and is then back-reflected towards the output of the Periodically Poled Lithium Niobate (PPLN) waveguide thanks to a dichroic mirror directly deposited at the waveguide endface [Anti-Reflection (AR) at 3.39 μm and High-Reflection (HR) at 1065 nm, see Fig. 3 ]. The waveguide taper allows us to ensure a better control of the pump beam geometry leading to the optimal spatial overlapping in the non-linear crystals between the pump at 1065 nm and the signal at 3.39 μm. Figure 3. PPLN injection scheme. The pump wave at 1065 nm propagates in the reverse direction, and is coupled into the waveguide thanks to a taper. After a back-reflection by a dichroic mirror, the pump field interacts with the signal at 3.39 μm to generate the converted wave at 810 nm. We define the normalized conversion efficiency curve of the SFG process as the ratio between the converted power and the signal one as a function of the signal wavelength. This curve depends on the crystal's optical and geometrical parameters (Fig. 4 ) and can be tuned by a fine control of its temperature. The full width at half-maximum of the conversion

O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O B-Wavelength O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Person B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O B-Wavelength I-Wavelength O O O O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O B-Wavelength I-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


gravitational lensing distortion matrix ( 1 ) across the image, on the employed weight function W , and also the employed ellipticity definition. In the case of a flat weight, W ()const., and the centre of light as image centre, equations ( 9 ) and ( 13 ) yield unweighted moments. The observed ellipticity ( 10 ) and the intrinsic ellipticity ( 14 ) are then related by An advantage of based on unweighted moments is that for g 1, one may use the observed ellipticity as an unbiased estimator, for the reduced shear g , i.e. , where angular brackets denote averages over the galaxy intrinsic ellipticity distribution (which is assumed rotation invariant), regardless of the details of the intrinsic ellipticity distribution (Seitz Schneider 1997 ). Unweighted moments and ellipticities derived from them are susceptible to image noise in the outer image regions [due to the factor i j in the integral in equation ( 9 )]. Moreover, unweighted moments and ellipticities are strongly affected by errors in the separation of the galaxy light from the light of neighbouring galaxies. Ellipticity estimation from real galaxy images thus often employs down-weighting of the outer regions of the image. The drawback of such radially weighted moments is that they complicate the relation between observed and intrinsic ellipticities. For a general choice of ellipticity definition and weight function W (), and sufficiently small reduced shear g , the observed ellipticity as a function of reduced shear g can be approximated by a linear response in g : where the intrinsic ellipticity , and the shear polarizability If P can be estimated with sufficient accuracy (e.g. from the observed galaxy image itself) and is invertible, one may obtain an unbiased shear estimator by applying P 1 as a shear polarizability correction factor: If the average shear polarizability P for the observed galaxy population is known, another unbiased shear estimator can be constructed that employs P 1 as polarizability correction: The above image ellipticity-based shear estimators can be treated in a uniform manner, 7 with appropriate definitions for the observed ellipticity and intrinsic ellipticity . For example, equation ( 17 ) suggests with and from unweighted moments. For e computed from unweighted moments, one obtains (e.g. Bernstein Jarvis 2002 ) 8 A simplified version of the estimator by Kaiser, Squires Broadhurst ( 1995 , KSB) yields with and from moments with a Gaussian radial weight function, and estimated from the individual observed galaxy images. As for the shear, the ellipticities and can be decomposed into tangential and cross components with respect to a given angular direction or comoving transverse direction : with , , and . 2.4 Density and intrinsic shape correlations The intrinsic shapes of galaxies may have a preferred orientation towards nearby other galaxies and matter overdensities. The preferred orientation of galaxies towards matter overdensities may be quantified by the

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


for a cold flow such that (equation B1 in Appendix B , with ω = 1). This expression provides the two solid blue curves shown in Fig. 4 , computed in two extreme cases for the location of the Alfvén surface: near the SM surface with x SM = 2, namely (lower curve) and much further out with for the upper one (as in typical near-equipartition cold flows). For a given magnetic lever arm λ (mostly determined by ξ), κ must be large enough. This rules out all super-SM solutions located at the left-hand side of these curves. It can be seen right away that the parameter space of super-A solutions for near-equipartition fields ( n = 0) will be very small, with mass loads κ smaller than 0.1, disc ejection efficiencies ξ smaller than 0.08, and magnetic lever arms larger than ∼7, in agreement with Ferreira ( 1997 ). On the other hand, MRI-like driven flows at small μ seem to allow mass loads larger than unity with small λ. These isothermal flows could be of great interest for reproducing dense outflows (ξ > 0.1) with low asymptotic speeds ( u p ∞ ∼ Ω K o r o ). In other words, a weakly magnetized disc is better suited for a massive ejection than a near-equipartition disc, not only by providing the necessary bending at the disc surface through the MRI-like mechanism, but also by bringing the Alfvén surface closer to the disc (see the discussion on the role of Ψ A in Appendix B ). Nevertheless, not all super-SM solutions located at the right-hand side of the solid curves in Fig. 4 can become super-A. For a given ξ, λ is roughly determined and so is the cylindrical radius r A = r o (λ/ω) 1/2 of the Alfvén point. But equation ( 21 ) shows that κ also depends on p and μ. For a given toroidal current density p , the SM constraint provides μ so that κ is fixed. On the other hand, p also determines the radial magnetic field component at the disc surface and thereby the initial jet bending (see Fig. B3 ). As a consequence, playing with p not only affects the disc vertical equilibrium (SM point) but also this initial jet angle. Not all couples (κ, λ) fulfil the Grad–Shafranov equation ( 30 ). If a solution is not possible, this means that there is no altitude A of the Alfvén point that can be found starting from the conditions provided at the base of the jet (SM point). Changing the value of p leads to a slight modification of κ, λ as well as the jet angle at the SM point, allowing thereby to (possibly) meet the A condition. This translates into an adaptation of the altitude A of the Alfvén point (thus the angle Ψ A ) according to the disc conditions. The necessary condition highlights this aspect. When λ is large, r A / r o is large and gravity plays a negligible role so that is satisfied whenever λ > 3 (dashed line in Fig. 4 ). But gravity cannot be neglected anymore at lower values of λ, as can be seen in equation ( 31 ). In that case, providing requires to increase sin Ψ A , namely to bring the Alfvén surface closer to the disc surface. The closer it is to the

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


to be aligned with its projected morphological major axis. The coincidence in PAs from the kinematics and morphology is thus generally a criterion in determining the nature of a galaxy. In practice, complications arise for a variety of physical reasons (e.g., presence of nonaxisymmetric structures, nearby companions with overlapping outer isophotes, spatially nonuniform extinction), compounded by surface brightness sensitivity and spatial resolution limitations for high-redshift galaxies. We examined the agreement between the derived kinematic position angle PA kin (Section 4.3 ) and the morphological position angle PA morph , quantified via the “kinematic misalignment” . We exclude GMASS-2540 here because it is not fully covered by the SINFONI AO data and because of its low H α surface brightness emission hampering a reliable PA kin determination. Following the same motivation as in Section 6.1 , we adopted as PA morph the PA from the H -band morphologies, when available, and from the H α maps otherwise. As noted in Section 5.4 , the PA H α and PA H are similar within 1.5 σ , and we verified that our conclusions would not be affected by instead adopting PA H α for all objects. For our sample, the mean and median ΔPA are 23 and 13 , respectively. For 73% of the galaxies, the alignment is better than 30 . Figure 8 shows the PA offsets as a function of the adopted axis ratio q and effective radius R e . Not unexpectedly, and as seen in other high-redshift samples (e.g., Wisnioski et al. 2015 ; Harrison et al. 2017 ), our galaxies broadly follow a trend of increasing ΔPA for more face-on and smaller sources. Of the 10 objects with ΔPA > 30°, eight are compact sources with distortions/extensions in their outer isophotes, asymmetric light distributions in their inner brighter regions, or little or irregular velocity structure (Q1623-BX502, Q1623-BX513, GMASS-2303, SA12-6339, ZC400528, ZC401925, ZC404221, and ZC411737). The other two sources are large, massive, and fairly face-on disks for which the misalignment can be attributed to morphological features (a noncircular ring with a clump on one side for Deep3a-6004 and clumps in a tail-like structure for ZC400569N; see Section 7.2 for more details). Figure 8. Kinematic misalignment ΔPA as a function of morphological axis ratio q for the SINS/zC-SINF AO sample. The symbols are color-coded and sized according to the effective radius R e of the galaxies. The five compact objects with ill-defined axis ratios and to which we assigned q = 0.64, corresponding to the for randomly oriented disks (Section 6.1 ), are plotted as squares connected with red dotted lines to their nominal best-fit q , shown as circles with a red arrow pointing toward the adopted value. Most of the well-resolved objects show very good agreement between their kinematic and morphological PAs, especially for the more edge-on systems. A larger proportion of the compact sources have ΔPA > 30°, reflecting ill-defined PAs due to

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


O B-CelestialObject O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O B-CelestialObject I-CelestialObject O B-Instrument O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O B-Wavelength O B-TextGarbage I-TextGarbage O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Tag I-Tag O B-Tag I-Tag O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O B-Wavelength O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-TextGarbage I-TextGarbage O O O B-Wavelength O O O B-Wavelength


maximum grain size is determined by the fragmentation barrier (Eq. ( 3 )) and particles can reach centimetre sizes, but small particles are continuously reproduced. For a more massive planet, the location of the pressure maximum (and therefore the peak of mm dust concentration) occurs further away at 30, 44, and 54 AU for 1, 5, and 15 , respectively, as previously shown by Pinilla et al. (2012) . The radial range in which mm-sized grains are concentrated becomes wider. For the case, the second peak is caused by a transient density feature that in reality would be short-lived and would not function as a pressure maximum that can effectively concentrate particles. This issue has no impact on our results since we focus on the inner disk. In the regions inside the planetary gap ( AU) where the gas surface density steeply decreases outwards (and therefore the pressure gradient is negative), the maximum grain size is determined by radial drift (Fig. 2 ), and only close to the snow line ( AU) does the fragmentation barrier drop below the drift barrier due to the change in at . With the decrease in at , the maximum grain size is a few centimetres and the Stokes number of the particles at that location is much lower than unity (), thus they are better coupled to the gas, their radial drift velocities are lower (Eq. ( 2 )), and they move with at a similar speed to the gas (see also Brauer et al. 2008 ). If does not change at , the maximum grain size is dominated by radial drift, reaching values of the Stokes number of around , which would lead to very high drift velocities () depleting the inner disk on very short time scales (100–1000 yr). Therefore, when the inner disk is constantly resupplied from the outer disk, the changes of at allows replenishment of warm, small, and optically thick dust near , for which the drift velocities are slow. In the case of a mass planet, the micron-sized particles (1–10 m), are not perfectly trapped at the outer edge of the planet-gap, and they move continuously through the gap via turbulent diffusion. This partial filtration of dust grains supports a constant replenishment of dust from the outer to the inner disk, which together with variations of at extends the lifetime of a detectable inner disk reaching the life of the disk (5 Myr). In the cases of and mass planets, there is more efficient trapping of particles at the outer edge of the planetary gap, filtering all particle sizes (from 1m, which is the minimum grain size in our setup). The dust inside the planetary gap ( AU) is the dust that was initially within the gap. These particles grow, drift and fragment when they reach the snow line. Although there is a considerable amount of dust in the inner disk for all cases (1, 5, and 15 ) after 1 Myr, after 5 Myr of evolution the inner disk is practically depleted of dust for a disk hosting a and a mass planet. The dust density distribution after 5 Myr of evolution for AU is almost identical for and because the

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


et al. 2015b ). The contaminated regions of the SMICA map were further removed with the Galaxy, point-source, and SMICA -specific temperature and polarization masks, which leave ≈67% of the sky for the minimum-variance lensing reconstruction analysis. Given the sensitivity and angular resolutions of the Planck mission, the analysis thus results in the most significant measurement of the CMB lensing potential map to date. The online data provided by the Planck science team are in the standard HEALPix format (Górski et al. 2005 ). The spherical harmonics coefficients of lensing convergence, , are given for multipoles up to instead of the lensing potential, . We use the standard definition of lensing convergence to calculate fromWe then use the HEALPix synfast package to synthesize the lensing potential map, . The generated map has a resolution of (i.e., pixels). The projected lensing potential map is shown in Figure 1 . This reconstructed lensing potential map is used to cross-correlate with the cosmic void catalog, where the azimuthally averaged potential around each void is extracted, scaled, and then combined to constrain the void density profile. For our analysis, we shall use only those regions that pass the analysis mask (Galaxy + point-source + SMICA ). Figure 1. Lensing potential map, , constructed from Planck lensing convergence, . The gray shaded area marks the rejected pixels excluded by the analysis mask. 2.2. Cosmic Void Catalog In this work, we use the “Public Cosmic Void Catalog” (Sutter et al. 2012b ) constructed using a modified and extended version of the watershed algorithm ZOBOV , called “Void IDentification and Examination” (VIDE; Sutter et al. 2014b ). We applied the code to the SDSS Data Release 7 (Abazajian et al. 2009 ) main galaxy sample and SDSS-III Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 10 (Ahn et al. 2014 ) LOWZ and CMASS samples. This results in individually detected voids. The samples represent volume-limited catalogs of voids at various redshift bins. To minimize any possible evolution of the profile parameters, we choose to work with voids in individual redshift bins and do not stack voids across the bins. In order to have as many voids in a single bin as possible, we chose a high-redshift bin to increase the volume. Here, we report on the analysis using the “dr10cmass1” (, , ) and “dr10cmass2” samples (, , ), hereafter called “cmass1” and “cmass2,” respectively. We therefore stacked the Planck lensing potential map (Section 2.1 ) around the central positions of cosmic voids taken from the Sutter et al. ( 2014b ) “dr10cmass1” and “dr10cmass2” samples as two separated measurements. However, during our analysis we found that considerable numbers (106 and 303 for cmass1 and cmass2, respectively) of the voids are located in the negative lensing potential regions, which could be due to a number of reasons and warrants further investigations. We therefore restrict our analysis to 123 and

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age uncertainties of these stars (that can be substantial as these solar twin stars are located on the upper main sequence). The diagonal line shows the relationship between Li and stellar age from Carlos et al. (2016) . 3.7. Li in stars with planets Since King et al. (1997) claimed a possibility that the low Li abundances in the Sun and 16 Cyg B relative to 16 Cyg A could be due to the presence of planetary companions in the former two, several studies have presented disparate results regarding whether or not stars with detected planets have different Li abundance patterns compared to those with no thus-far detected planets. Studies that support the idea that there is no difference include Ryan (2000) , Luck Heiter (2006) , Baumann et al. (2010) , Ghezzi et al. (2010) , Ramírez et al. (2012) , and Pavlenko et al. (2018) , while those that find that indeed there is a difference include Israelian et al. ( 2004 , 2009 ), Takeda Kawanomoto (2005) , Chen Zhao (2006) , Gonzalez ( 2008 , 2014 , 2015 ), Figueira et al. (2014) , Delgado Mena et al. (2014) , and Mishenina et al. (2016) . To see whether this study can add some further clues to this controversy the exoplanets website 1 ( Han et al. 2014 ) was queried on February 14, 2018. We find that 36 stars in our sample have detected exoplanets, that 18 of those have well-determined Li abundances, and that 6 have upper limit Li detections. These 18 + 6 stars are marked in red in Fig. 8 . They span a range of effective temperatures from about 5600 K to 6500 K. The bottom panel in Fig. 8 shows the differences between the Li abundance of the exoplanet stars and the mean Li abundance of other stars in the sample that have effective temperatures within ±75 K, log g within ±0.25 dex, and [Fe/H] within ±0.25 dex of each exoplanet star. Due to the low number statistics of stars with similar atmospheric parameters at higher T eff , the temperature range was expanded to ±200 K for stars with T eff > 6100 K. As stars at these temperatures have less Li depleted atmospheres, this expansion should not affect the results. The stars with detected exoplanets have on average 0.08 dex higher Li abundances than those without planet detections, with a dispersion of 0.36 dex. Using the median instead gives a Li-enhancement of 0.04 dex. These numbers are well within the uncertainties and our sample reveals no statistically significant difference in Li abundances between stars with and without exoplanet detections. Fig. 8. Upper panel : red circles mark the 18 stars in the sample that have exoplanets detected and good Li measurements. Bottom panel : difference between the A (Li) for individual stars to the mean A (Li) for stars that have no exoplanet detections and that have effective temperatures, surface gravities, and metallicities, within ±75 K, ±0.2 dex, and ±0.2 dex. For stars with T eff > 6100 K, the temperature range is expanded to ±200 K. 3.8. Li trends in the thin and thick disks It is not straightforward

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