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

that models in which the DTD favors long delays. 3. The Stochastic Background The stochastic background is defined as the energy density of gravitational waves per logarithmic frequency interval:where is the critical density of the universe given by . Here H 0 is the Hubble constant, and G is the Newton constant. The spectrum of the SGWB is given by:(Phinney 2001 ), where f and are the observed and rest-frame GW frequencies, respectively. The GW spectrum from a coalescing BNS or BBH is given bywhere is the energy emitted in GWs, is the chirp mass, and f i () and σ are frequencies that characterize the inspiral-merger-ringdown waveforms, are normalization constants chosen to make the waveform continuous, and are the post-Newtonian correction factors (Ajith et al. 2008 ). We model the ensemble distribution of primary black hole masses as a power lawand assume a flat distributionof secondary masses. We set as the lower observed BH mass in low-mass X-ray binaries (Farr et al. 2011 ). We set our fiducial values of α = 1, and ; however, we will explore the effect of varying these two parameters later in the paper. The upper limit on the BH mass is due to the assumption that pair-instability supernovae set an upper limit for the mass of the BHs born from stellar progenitors (Woosley 2017 ). The population analysis using BBH observations from LIGO/Virgo’s first and second observing runs measured the spectral index of the primary BH power law to be at 90% confidence assuming a minimum black hole mass of and a maximum total mass of (Abbott et al. 2018 ). For the BNS systems we assume a uniform distribution between 1.3–1.5 for each of the NSs to be consistent with the range of observed masses of galactic double neutron star systems (Kiziltan et al. 2013 ; Özel Freire 2016 ; Farrow et al. 2019 ), although we note that this choice is in tension with the masses of GW190425 (Abbott et al. 2020 ). 4. Results The results for the two extreme cases of DTDs for both the BBH and BNS systems are shown in Figure 2 . The green shaded region shows the predicted range of for a population of BNS composed of two NSs each with a mass uniformly distributed between 1.3 and 1.5 . The rate of the BNS mergers from LIGO is (Abbott et al. 2020 ). In order to get the full possible range we assign the highest rate to the short DTD model, and the lowest rate to the long DTD model. We do the same for the BBHs where we consider a merger rate between 20 to 110 (Abbott et al. 2020 ). For the BBH systems we considered two models in which (i) the primary BH mass follows bounded between 5 and 50 , and the secondary is uniformly distributed between 5 and m 1 (gray shaded region), and (ii) each BH has a mass of 15 (red shaded region). The average chirp masses of the two BBH population models are the same, , although their predicted differs by a factor of 3 in magnitude. We also show the power-law integrated (PI) curve (Thrane Romano 2013 ) for the detection of the SGWB with an S/N of 3 by


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Citation I-Citation I-Citation I-Citation I-Citation O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O B-Model O O O O O O O O B-Citation I-Citation I-Citation O O O B-Citation B-Citation I-Citation 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 B-Citation I-Citation I-Citation O O O O O O O O O O B-Model O O O O O O O B-Model 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 B-Wavelength O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O 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 B-Citation I-Citation I-Citation I-Citation 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 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 B-Wavelength O O O O O O O O B-Model O O O O O O O B-Database I-Database I-Database B-Citation I-Citation 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-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

the 14th column. f Experimental lifetime of the upper level used to normalize the oscillator strength and the transition probability given respectively in columns 11 and 12. g Reference of the experimental lifetime used to normalize the oscillator strength and the transition probability given respectively in columns 11 and 12. T = this work; B = Bimont etal. ( 2011 ); W = Wnnstrm etal. ( 1988 ); H = Hannaford etal. ( 1982 ). In Figs 2 4 , the present HFRCPOL oscillator strengths are compared with our previous values (Bimont etal. 2011 ), those of Kurucz (Kurucz 2011 ) and the experimental values of Hannaford etal. ( 1982 ), respectively. Although the latter concerns exclusively the decay transitions of low-lying odd-parity levels (Hannaford etal. 1982 ), they nonetheless provide a good test of the present HFRCPOL model. Figure 2. Comparison between the present HFRCPOL log gf values and those of our previous study (Bimont etal. 2011 ). A straight line of equality has been drawn. Fig. 2 shows a good agreement between our two calculations with no systematic effects, as the core-polarization has been taken into account in both models. However, some discrepancies are seen for the weak transitions due to cancellations such as the transition at 733.295nm with log gf 3.08 and a cancellation factor of CF0.07 in this work, compared to log gf 1.98 obtained with our previous model. In this particular case, it is advisable to use our older published value (Bimont etal. 2011 ), i.e. 1.98, that belongs to a smaller set of calculated strong (log gf 2) decay transitions being not affected by cancellation. Besides, Kurucz ( 2011 ) gives a value of 2.87 for that line. We suspect that this oscillator strength is also affected by cancellation as it is calculated 1 dex weaker than the value of Bimont etal. ( 2011 ), similarly to the present calculation. Unfortunately, CF values are not reported in Kurucz ( 2011 ). Fig. 3 shows that the oscillator strengths computed by Kurucz ( 2011 ) are systematically larger than ours by, on average, 0.07 dex for lines with log gf 0. Furthermore, a significant number (92 transitions out of 357) of the lines with log gf 0 are affected by strong cancellation effects (CF0.1) showing discrepancies of one dex or more. Using our log gf -values with CF0.1 is not recommended as these values could be off by a few dex. Moreover, values of Kurucz ( 2011 ) that are weaker than ours by a few dex should be taken with care as we suspect that they are affected by strong cancellation effects similarly to the case of the line at 733.295nm discussed previously. Figure 3. Comparison between the present HFRCPOL log gf values and those of the Kuruczs data base (Kurucz 2011 ). A straight line of equality has been drawn. In Fig. 4 , it is seen that our HFRCPOL log gf -values agree well with the experimental determinations of Hannaford etal. ( 1982 ), the standard deviation of the differences between the two sets being 0.11 dex. From this comparison, one


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

69 Å) per pixel for the G130M (G160M) grating. The resolving power of each individual extraction is quoted as R ∼ 18 000 to 20 000, which corresponds to 15–17 km s −1 for a Gaussian LSF. However, the COS FUV LSF shows the time-dependent non-Gaussianity and the resolving power degraded with time. The spectral resolution can be approximated to ∼19 km s −1 for the COS non-Gaussian LSF at Lifetime Position 1 (see more details in Section 3.2 ). The wavelength regions contaminated by strong Galactic ISM lines are discarded. The typical COS FUV limit is ∼ 13.0. The CalCOS flat-field correction corrects strong wire grid shadow features greater than ∼20 per cent in intensity, but not weak (≤10 per cent in intensity) fixed pattern noise (FPN) produced by the hexagonal pattern of the fiber bundles in the COS FUV micro-channel plate known as MCP Hex (Dashtamirova et al. 2019 ). MPC Hex is supposed to be fixed in the detector pixel space, but not in the wavelength space. In practice, the position of MCP Hex and its intensity change along the pixel space. This sometimes produces false, equally spaced weak absorption-like features in the high-S/N region of the coadded spectrum (Fig. 3 ). It is the most conspicuous when a high-flux Ly α emission region falls on the longer wavelength edge of Segment B of the detector. Due to FPN, the noise is not Gaussian and the conventional way to quote noise as the reciprocal of 1 r.m.s. of the unabsorbed region underestimates true noise (Keeney et al. 2012 ). Since only an individual extraction with 12 shows distinct FPN and the majority of our individual extractions has a lower S/N, we did not correct for MCP Hex (Fitzpatrick Spitzer 1994 ; Savage et al. 2014 ; Wakker et al. 2015 ). Figure 3. Examples of sawtooth-line MCP Hex fixed pattern noise (FPN) in coadded COS spectra. The red vertical ticks spaced at ∼0.4 Å mark the position of Hex FPN. The blue thick tick in the upper panel marks the position of the Milky Way Cl i λ1347.23. When assumed as a H i Ly α, FPN has log N FPN ∼ 12.5. If a weak IGM H i absorption falls on FPN, the apparent increases. 2.6 <italic>FUSE</italic> data Available FUSE spectra (917–1187 Å) were used to obtain a reliable column density of saturated COS FUV H i Ly α lines, since FUSE spectra cover high-order Lyman lines at z ≤ 0.12. The 8th column of Table 3 lists whether the COS AGN has a corresponding FUSE spectrum. The FUSE spectra used in this study are the same ones analysed by Wakker ( 2006 ). They are sampled at ∼0.0066 Å per pixel, weakly dependent on the wavelength. As they are oversampled, we binned the FUSE spectra by 3, 5, or 7 pixels to increase the S/N. The S/N in general increases towards longer wavelengths, i.e. more reliable Ly β profiles than Ly γ profiles. The S/N per resolution element at ∼1050 Å is listed in parenthesis in the 5th column of Table 3 . Since wavelength regions with S/N 5 are not very useful to deblend saturated lines reliably, we excluded these low-S/N


O O O O O B-Person I-Person O O O O O O O O B-Person I-Person O O O O O O O O O O O O O O O O O O O O O O B-Grant I-Grant

We would like to thank Mathieu Havel for multiple discussions that helped benchmark our results, Konstantin Batygin for comments on the first draft of this paper, and the anonymous reviewer for her/his insights. This work was funded under grant NSERC RGPIN-2014-06567.


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

∼1 month to 27 d, the solar rotation period. An incomplete list of references includes Burlaga Goldstein ( 1984 ), who studied the evolution of plasma flow at 4–5 au and found intermittency in the 5/3 law; they covered a range of 6 months. Marsh Tu ( 1990 ) analysed magnetic field and plasma data from the Helios 1 and Helios 2 spacecrafts between 0.3 and 1 au at the activity minimum of solar cycle 21; they found a −5/3 spectral law, with turbulence better developed in low-speed flows. Espagnet et al. ( 1993 ) computed the power spectra of solar granulation; their energy decreases as a Kolmogorov −5/3 power law in the granulation range (1000–2000 km). Lawrence et al. ( 1995 ) studied ISSN and the 10.7 cm microwave flux; using Fourier and wavelet spectral analysis, they uncovered two regimes of magnetic variability. Cascade (−5/3) behaviour was observed from 2 yr down to 2 d, whereas low dimensional chaotic behaviour was observed at time-scales longer than 8 yr. Abramenko ( 2005 ) worked on images of the photosphere, and extracted the magnetic field of the Sun at times of low flare activity; the study extends over only 60 h. Alexandrova et al. ( 2008 ) computed the power density spectrum using wavelet transforms over a range from 0.1 s to 3 months. McAteer, Gallagher Conlon ( 2010 ) studied turbulence and complexity in order to predict solar flares; using wavelets, these authors found that the PSD of flares is indeed characterized by a −5/3 law. Ashwanden ( 2019 ) recently reviewed models of the solar wind. He noted that, by introducing the reflection of Alfvénic waves, Cranmer van Ballegooijen ( 2005 ) produced ‘a Kolmogorov-like spectrum that does not change dramatically from the photosphere to the solar wind’. The analysis by Plunian et al. ( 2009 ) is the closest to ours and among the most recent ones. As recalled in the Introduction, these authors analysed several kinds of time series of sunspot numbers, concentrations of 14 C in tree rings and 10 Be in polar ice and found two frequency scalings, f − 2/3 when the Sun was active and f − 1 when it was quiescent. These values of exponents are not that expected for Kolmogorov turbulence that should be exactly (within uncertainty) −5/3. Plunian et al. ( 2009 ) suggest that these exponents reflect buoyancy spectra implying values of k − 5/3 and k − 2 for the magnetic energy spectra of the Sun. Plunian et al's ( 2009 ) fig. 3, which displays the PSD of daily and monthly SSN and 10 yr averages of 14 C, ranges from 0.1 to over 10 4 months, shows significant dispersion of the curves, slope changes, and energy peaks at 1 month (27 d) and 10 yr (Schwabe). The −2/3 slope is based on a small range of frequencies (2–20 months). A value of −5/3 (between 1 and 104 months) is not such a bad fit given these uncertainties. But our own results with SSA are much more compelling. 6 CONCLUSION The diverse proxies of solar activity, and in particular solar wind velocity, that have been studied to conclude that


O O B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person B-Person I-Person O B-Person I-Person O O O O O O O O O O O B-Person I-Person O O O O O O B-Person I-Person O B-Person I-Person O O O O O O O O B-Person I-Person B-Person I-Person B-Person I-Person O B-Person I-Person O O O O O O O O B-Person I-Person O B-Person I-Person O O O O O O O O O B-Person I-Person B-Person I-Person O B-Person I-Person O O O O O B-Person I-Person O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O B-Person I-Person B-Person I-Person B-Person I-Person O B-Person I-Person O O O O O O O O O B-Person I-Person O O O O O O O O O B-Person I-Person O O O O O O O O O O B-Software I-Software O B-TextGarbage I-TextGarbage B-URL O O O O O O O O O O O O O O O O O O O O O B-Grant I-Grant I-Grant B-Person O B-Dataset I-Dataset I-Dataset O O O B-Archive I-Archive I-Archive I-Archive O B-Software I-Software I-Software I-Software B-Organization B-Location I-Location B-Software O O O B-Software O O O B-Citation I-Citation I-Citation I-Citation I-Citation O B-Software B-Citation I-Citation I-Citation I-Citation O B-Software I-Software B-TextGarbage I-TextGarbage B-URL O B-Software B-TextGarbage I-TextGarbage B-URL O O B-Software I-Software I-Software B-TextGarbage I-TextGarbage B-URL O O B-Software I-Software I-Software I-Software B-TextGarbage I-TextGarbage B-URL O O B-Software O B-Software O B-TextGarbage I-TextGarbage B-URL


O O O O O O O B-Location I-Location O B-Grant O O O O O O O B-Telescope O O O O B-Telescope O O O O O B-Organization I-Organization I-Organization I-Organization O O O O O O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Archive I-Archive I-Archive I-Archive I-Archive B-Archive B-Organization O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization O B-Grant O O B-Archive O B-Telescope O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Grant O O O O O O B-Person O O O O B-Observatory I-Observatory I-Observatory I-Observatory O O B-Organization I-Organization I-Organization O O O B-Person O B-Person O O O B-Grant O B-Grant I-Grant I-Grant I-Grant O O O B-Organization B-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization I-Organization B-Location O O O B-Observatory B-Telescope I-Telescope O O O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O O B-Grant O O B-Grant B-Person O O O O B-Organization I-Organization I-Organization O O B-Grant O O O O O O B-Person O O O O O O B-Person I-Person

This work has been done under the Indo-South Africa project DST/INT/SA/P-02. This paper includes data collected by the Kepler mission. Funding for the Kepler mission is provided by the NASA Science Mission directorate. The authors wish to thank the Kepler team for their generosity in allowing the data to be released and for their outstanding efforts which have made these results possible. Much of the data presented in this paper were obtained from the Mikulski Archive for Space Telescopes (MAST). STScI is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. Support for MAST for non-HST data is provided by the NASA Office of Space Science via grant NNX09AF08G and by other grants and contracts. LAB wishes to thank the South African Astronomical Observatory and the National Research Foundation for financial support. SJ and ES acknowledges the grants INT/RFBR/P-118 and RFBR Grant no. 12-02-92693-IND_a jointly funded by DST Govt of India and Russian Academy of Science, Russia. Observations on the SAO RAS 6-m telescope are carried out with financial support from the Ministry of Education and Science of the Russian Federation (agreement no. 14.619.21.0004, project ID RFMEFI61914X0004). ES is thankful to the Russian Science Foundation (grant no. 14-50-00043) for financial support of this study. KS acknowledges useful discussion and comments from Philippe Prugniel.


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

length: this value is extracted from Sbordone Ledoux ( 2018 ) and is equal to 50 mas (0.5 per cent of the slit length, 10 000 mas). This accuracy, as well as the one of the binary separation, are considered in our measurements as rectangular distributions, by excess, where we account for the factor to convert them into normal distributions. standard deviation: as stated above, each point is the mean of all the data of 1-nm bins. In the example we show, we had 49 data points to average. We consider the standard deviation of the mean as another source of uncertainty. It is equal to 0.02 pixel in our example. Using equation ( 4 ), we can derive the combined uncertainty on the pixel scale. It is equal to 0.87 mas using equation ( 5 ). where u 1 is the uncertainty on the angular separation in mas, u 2 and u 3 are the uncertainties of the fits and the standard deviation in pixels, respectively, is the distance of the binary system in pixels (18 pixels in our example), and is the distance of the binary system in mas (4680 mas in our example). Instrumental dispersion calibration: The uncertainty of this component is the standard deviation of the measurements (at airmass 1), and is considered constant over the range. It is equal to 8.3 mas. Atmospheric dispersion measurement: This component has similar subcomponents as the ones of the accuracy of the fits as well as the standard deviation. In addition, we take into consideration the total uncertainty of the pixel scale (equation 5 ). The combined uncertainty on the atmospheric dispersion measurement is also derived from equation ( 4 ). It is equal to 16.18 mas using equation ( 6 ). where is the measured atmospheric dispersion in pixels ( in our example), and PS is the computed pixel scale in mas. Figure 8. Top: Measured atmospheric dispersion, before and after correction by the instrumental dispersion in the blue range. We also show the expected dispersion using Filippenko’s model; bottom: Atmospheric dispersion residuals, before and after correction by the instrumental dispersion. The results obtained for the red arm are shown in Figs A3 and A4 . Table 2. Atmospheric parameters at the time of observation. Table 3. Uncertainties budget showing in details what each source of error is introducing. The contribution of each subsource is computed using equation ( 4 ) and show the results at the wavelength 315 nm of one exposure. The total uncertainty of each source is computed using the root sum squared of its contributions. The last column represents the references used in these computations: (1) Pourbaix Boffin ( 2016 ); (2) study with generated data; (3) experimental standard deviation of the mean value; and (4) Sbordone Ledoux ( 2018 ). The final uncertainty of the method listed, taking into consideration the components described above, is computed using equation ( 7 ). The accuracy of the method is as follows: ±18 mas in the blue range, ±17 mas in the red range. These results are for a 1σ interval.


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

and denote the median of each band in the observed spectrum and model, and gives the standard deviation in each band in the observed spectrum. As also described in Manara et al. (2013a) , this does not represent a true distribution as the noise in the template spectrum is neglected. The models are visually compared to confirm that the best-fit model matches the observed spectrum. The uncertainties are estimated from the range of UV-excess fluxes spanned by models that yield a similar -like value as the best-fit model and match the spectrum visually (details are described in Sect. 4.3 ). Table 5 Parameter ranges of the hydrogen slab model. The measured UV-excess flux is converted to accretion luminosity (). The mass accretion rates () are then calculated byunder the assumption that gas accretes from the disk truncation radius in free-fall onto the star, where is adopted for consistency with pre-existing measurements (see review by Hartmann et al. 2016 ). Table 6 Mass accretion properties in the Cha association. Notes. Columns 2–7 list equivalent widths (EW), accretion luminosity (; using conversions from Alcalá et al. 2014 ), and mass accretion rates () for H and H, respectively. The last two columns list and determined from UV excess. 4.3. Description of fits and uncertainties Figures A.1 – A.4 show the best-fit model for each object. The values of and are listed in Table 6 . Uncertainties in the accretion rates are introduced by uncertainties in the stellar parameters, the distance, and in the individual fits (see, e.g., Herczeg Hillenbrand 2008 ; Manara et al. 2013a ). For our sample, uncertainties in are 0.3 dex. Weak accretors, such as RECX 11, have uncertainties of 0.5 dex because the excess is fainter than the photosphere, thereby increasing the uncertainty in bolometric correction. Upper limits on are difficult to estimate and depend on the ability to distinguish any excess emission from the underlying photospheric spectrum and on an uncertain bolometric correction. In order to estimate upper limits of for non-accreting objects, we perform a similar model fit as described above. The upper limits are compared to the detections in Fig. 8 a in terms of the ratio of . For K stars, the upper limit of for non-accreting stars is similar to of RECX 11. For M stars, the upper limits are almost uniform at (see also Manara et al. 2013b ), with the exception of RECX 12 (). Fig. 7 As in Fig. 6 . J0843, J0844, RECX 5 and RECX 9 show clear indications of UV-excess. For RECX 11, a slight excess is seen. Comments on each fit to the spectra of accreting objects are provided below. <italic>J0843 and J0844</italic>: due to the pronounced observed Balmer jump and strong excess in the Balmer and Paschen continua, the slab model parameters and therefore the are well constrained. Models using templates within 0.5 spectral subclasses yield accretion rates that agree to within 10% of these values. <italic>RECX 5</italic>: the best-fit is calculated using the M4


O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Grant I-Grant O B-Location B-Organization I-Organization I-Organization I-Organization O B-Grant O O B-Grant I-Grant I-Grant O O O O O B-Grant O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization B-Grant O O O B-Organization I-Organization I-Organization I-Organization O O B-Grant O O O O O O O O O O O O O O O O

This work was supported by the Russian Foundation for Basic Research (project no. 14-02-92615 KO_a), the UK Royal Society International Exchange grant IE140055, by the President of Russia grant for young scientists (no. MK-733.2014.2), by the programme of the Presidium of Russian Academy of Sciences P21, and by the Saint Petersburg State University research grant 6.37.341.2015. We would like to thank the anonymous reviewer for useful suggestions and comments on the manuscript.


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

GR 290 in the remainder of this paper. The standard deviations are of similar value to our estimated measurement uncertainty of ±30 km s −1 . Since we do not detect variability in our two spectra that is larger than the uncertainty discussed above, we combined the July and August spectra, shifted the average by +179 km s −1 , and remeasured the lines. We list in Table 3 the RV of the emission in Col. 7, the equivalent width in Col. 8, the RV of the absorption component in the case of P Cyg profiles in Col. 9, and the intersection of the P Cyg absorption with the continuum level in Col. 10. The measurements for P Cyg profiles were performed with two-Gaussian fits 6 . We note that the contribution of nebular emission affects the FWHM. For example, in the case of H α , we measure FWHM = 6.6 Å if the line is fit with a single Gaussian while FWHM = 10.2 Å if the line is treated as a blend of a broad stellar line and a narrow superposed nebular emission. Despite this large difference in FWHM, the RV in both cases is nearly the same. The average V edge = −400 ± 144 km s −1 is similar to the value of v ∞ listed in Polcaro et al. (2016) for recent spectra. However, the He I lines have V edge ≃ 620 km s −1 , implying wind speeds that are faster than ever before observed. The Balmer-H lines also show the signs of a relatively fast outflow, as can be seen from the growing asymmetry in the blue wing of the higher excitation lines of this series. This is illustrated in Fig. 4 where H α and H β were scaled in intensity so as to align the red wings with that of H γ . The other lines plotted are H ∊ and H I 3835 Å. This asymmetry results from the same process that leads to P Cyg absorptions in He I but because of the large optical depth of the H-lines a fully developed absorption component is not visible. Fig. 4. Line profiles of the Balmer-H sequence plotted on a velocity scale corrected for the adopted −179 km s −1 systemic velocity. The lines of H α and H β are scaled by factors of 0.17 and 0.48, respectively, so as to align the red wings with that of H γ . The continuous lines show H γ , H ∊ , and H I 3835 Å. The progressive red-shift at shorter wavelengths appears to be a consequence of the increasing strength of the blue-shifted absorption which, in the helium lines, takes on the form of P Cyg absorption. This effect is explained by the fact that the optical depth of the wind is highest for H α and H β and decreases for lines that have smaller transition probabilities. 3.2. Stellar wind models We used the CMFGEN atmospheric modelling code ( Hillier Miller 1998 ) in order to estimate the current stellar parameters of GR 290. This code solves the radiative transfer equation for objects with spherically symmetric extended outflows using either the Sobolev approximation or the full comoving-frame solution of the radiative transfer equation. CMFGEN incorporates line blanketing, the effect of Auger ionization and clumping, which is parametrized by the volume


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

to all disc particles and obtained f x , f y , f z , and f R , which are frequencies of oscillations along x , y , and z coordinates and cylindrical radius R . In Fig. 1 xy , xz , and yz snapshots for the whole BL model are presented at the time moment t = 450. A barlens is clearly seen in the xy snapshot, while a thick B/P structure is visible in the xz view. Fig. 1. Face-on, side-on, and end-on views of the considered model at t = 450 (6 Gyr). 3. Edge-on structure In Smirnov et al. (2021) , the BL model was disassembled into several orbital groups to analyse the face-on morphology of an overall bar. We assume that each individual group is characterised by a unique set of frequency ratios f R / f x and f R / f y . In Smirnov et al. (2021) , we focus on the face-on morphology of the inner parts of bars in our models. For this purpose, at the initial stage of our orbital analysis, we discarded orbits from the rest of the disc (outside the ring at the co-rotation radius (CR) R c ≈ 3) as well as of the thin part of the bar itself. Orbits from the thin part of a bar are located inside the CR and can be distinguished by the frequency ratio f z / f x > 2.25 ( Smirnov et al. 2021 ). Although the fraction of the 4 kk particles in these orbits is about 14%, all these orbits do not contribute to the thick B/P bulge, but only to the most remote and vertically thin parts of the bar (see Fig. 2 ). For the thick part of the bar, we identified all separate orbital groups (see Fig. 3 ) based on frequency ratios f x / f R and f y / f R and show that the structures to which they contribute are completely different in morphology. In this Letter, we analyse the edge-on morphology of the thick bar and its components in our BL model. Fig. 2. Side-on views of particles in the considered model at t = 450 (6 Gyr). Left : vertically thick part of the bar. Middle : all particles inside the co-rotation. Right : remaining particles which form a vertically thin structure. Fig. 3. Distribution of all orbits in the bar over the ratios of dominant frequencies f x / f R and f y / f R for the considered model at t = 450 (6 Gyr). The annotations illustrate the separation of orbits into orbital groups. Smirnov et al. (2021) identified the following components constituting a complex bar with a barlens: a ‘classic’ elongated bar ( f R / f x = 2.0 ± 0.1, 21.8% of particles from 4 kk) and two components contributing to the barlens (bl u orbits, in our notation, with f R / f x ≤ 1.9, 9.2%, and bl o orbits, with f R / f x ≥ 2.1, 13.5%). A ‘classic’ bar can be further divided into two subsystems. One is assembled from the x 1-like orbits ( f y / f x = 1.0 ± 0.1, 11.4%), and another one is the so-called boxy bar with orbits that are characterised by the ratio f y / f x ≥ 1.1 (10.4%). In Fig. 3 , all these orbital groups occupy separate regions (a spot and straight rays) and can be easily distinguished. The x 1-like bar has a complex structure itself. Three main orbital blocks, which


O O O O O O O O O O O O O O O O O O O O O O O O O B-Organization O O O O O B-Person I-Person O B-Person I-Person O O O O O O O O O O B-Person I-Person O O O O B-Telescope O O O O O O O O O O O B-Telescope B-Wavelength O O O O O O O O B-Organization I-Organization O B-Organization I-Organization O O O O O O O B-Wavelength O O B-CelestialObject I-CelestialObject O O B-Person O O O O B-Person I-Person O B-Person I-Person O O O O O O B-Telescope I-Telescope I-Telescope I-Telescope O O O B-Organization I-Organization I-Organization I-Organization O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization O B-Grant I-Grant O O O O B-Organization O O B-Grant B-Grant B-Grant O B-Grant O O B-Organization I-Organization I-Organization I-Organization O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization I-Organization O B-Organization O B-Grant I-Grant B-Person O O B-CelestialObject I-CelestialObject O O O O B-Organization O B-Grant O B-Grant

ACKNOWLEDGEMENTS We acknowledge helpful comments from the referee, which helped to clarify several aspects of the observations and analysis presented in this paper. We thank STScI science and technical staff members Peter McCullough and Amber Armstrong for special assistance in planning the DD time observations and Joe DePasquale for producing the colour HST image in Fig. 2 and the similar image superposed on the Chandra X-ray image in Fig. 6 . We thank both Kenji Hamaguchi and Mike Corcoran for discussions over many years concerning the X-ray emission from η Car’s outer shell. JM appreciates helpful discussions with John Raymond and Pat Hartigan. Based on observations made with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. Support was provided by NASA through grants GO-15596, GO-15289, GO-14768, and AR-14586 from the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. NS’s research on Eta Carinae also received support from NSF grants AST-1312221 and AST-1515559.


O O O O O O O O O B-Grant B-Grant O O O O O B-Organization I-Organization I-Organization O B-Grant B-Person O B-Organization B-Grant I-Grant I-Grant I-Grant O B-Person O O B-Grant I-Grant I-Grant O O O O O B-Person I-Person B-Person I-Person I-Person O B-Person I-Person O O O B-Dataset I-Dataset I-Dataset I-Dataset O O O

The work was a part of the research project RVO:61388963 (IOCB) and was supported by the Czech Science Foundation (grant P209/15-10267S). SY thanks ERC Advanced Investigator Project 267219 and AO thanks the UCL Impact scheme. The authors are grateful to Luciano Fusina, Gianfranco Di Lonardo and Adriana Predoi-Cross for providing their 15 NH 3 data prior to publishing.


O O B-Person I-Person O B-Person I-Person 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 B-Person I-Person O O O B-Instrument O O B-CelestialObject B-Person O O O O O O O O O O O O O O O O O O O B-Person O B-Person I-Person O O O O O O O O O O O O O O O O O B-Person O O O O O B-Organization B-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant I-Grant O B-Organization O O O O O O O B-Grant I-Grant B-Person O B-Location I-Location B-Grant I-Grant I-Grant I-Grant O O O O O O O O O B-Observatory O O O B-Observatory I-Observatory O O B-Grant B-Grant B-Grant B-Grant B-Grant B-Grant B-Grant O B-Grant O O O O O O O O O O B-Telescope I-Telescope I-Telescope O O O O O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization I-Organization O O O O O O O O O B-Telescope I-Telescope I-Telescope I-Telescope O O O O O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization B-Organization I-Organization I-Organization O O O B-Organization I-Organization I-Organization I-Organization I-Organization O O O O O O O B-Database O O O B-Organization B-Location I-Location O O O O O B-Organization O O O O B-Citation I-Citation I-Citation O O O O O O O O O O B-Observatory I-Observatory I-Observatory I-Observatory O O O O O O O O O B-Organization I-Organization I-Organization I-Organization O B-Organization I-Organization I-Organization O O B-Organization I-Organization I-Organization I-Organization I-Organization O O O O O O O O O O O O B-Organization I-Organization I-Organization I-Organization

We thank S. Antonellini and I. Kamp for providing water emission spectra from their ProDiMo model explorations, and for insightful discussions on water emission in disks and on its dependence on disk model parameters. We also thank A. Carmona for providing the CRIRES spectrum of HD139614. A.B. wishes to thank all colleagues who made this work possible through their pioneering work in infrared spectroscopy of disks. A.B. thanks Simon Bruderer for the seminal work he did in 2011–2012, which provided knowledge and tools to enable this work. A.B. acknowledges financial support by a NASA Origins of the Solar System grant No. OSS 11-OSS11-0120, a NASA Planetary Geology and Geophysics Program under grant NAG 5-10201. E.v.D. acknowledges European Union A-ERC grant 291141 CHEMPLAN. This work is partly based on observations made with ESO telescopes at the Paranal Observatory under programs 179.C-0151, 093.C-0432, 088.C-0666, 079.C-0349, 081.C-0833, 091.C-0671, 082.C-0491, and 088.C-0898. This work is partly based on observations made with the Spitzer Space Telescope , which is operated by the Jet Propulsion Laboratory, California Institute of Technology. This publication makes use of data products from the Wide-field Infrared Survey Explorer, which is a joint project of the University of California, Los Angeles, and the Jet Propulsion Laboratory/California Institute of Technology, funded by the National Aeronautics and Space Administration. This research has made use of the VizieR catalog access tool, CDS, Strasbourg, France. The original description of the VizieR service was published in AAS 143, 23. This work is partly based on observations obtained at the W. M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California, and the National Aeronautics and Space Administration. The observatory was made possible by the generous financial support of the W. M. Keck Foundation.


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

an injection of excess twist into the filament from one footpoint could drive a combination of longitudinal and rotational plasma motions (Uchida et al. 2001 ; Vršnak et al. 2007 ). However, when the Alfvén-wave packet caused by the injection is reflected at the opposite footpoint, the direction of rotational motions is expected to reverse, but in our case, the Doppler pattern persists (Figure 4 ). Moreover, we found no sign of twisting motions in the surge. Hence, we dismissed the wave-packet interpretation for the current observation. But we cannot dismiss the possibility that the observed rotational motion is a manifestation of unwinding relaxation; in other words, magnetic twist is propagating out of rather than into the filament, which could happen when the twisted filament field reconnects with the ambient, untwisted field (Okamoto et al. 2016 ). Additionally, Jing et al. ( 2003 , 2006 ) speculated that a mass perturbation in a fine thread would propagate along the spine across the obliquely stacked threads making up the filament. In our high-resolution observations, it is clear that mass motions involved in longitudinal oscillations are directed along individual threads, but it is obscure whether there are any perturbations propagating across the threads. To conclude, this study has demonstrated a promising methodology to diagnose the magnetic configuration of filaments and has substantiated the presence of the double-decker configuration with a flux rope atop a sheared arcade (Liu et al. 2012 ). Since no discernible separation is seen inside the filament studied, such a configuration might be more common than previously thought. With this configuration, however, one expects normal polarity in the lower atmosphere but inverse polarity in the higher atmosphere; because of the mixed signs of helicity, one also expects two pairs of plasma draining sites if the filament fully erupts, except that double-decker filaments often erupt partially (e.g., Liu et al. 2012 ; Cheng et al. 2014 ; Zhu et al. 2015 ). These predictions remain to be verified by future observation. Appendix Extraction of Oscillatory Patterns From the representative TD maps selected along the spine (Figure 6 ), we extracted the oscillatory pattern through a semi-automatic procedure that starts by visually choosing 20 points outlining the entire discernible pattern (Figure 7 (b)). Next, we applied a cubic spline to interpolate the intermediate points (Figure 7 (b)). We further refined the interpolations if the intensity profiles deduced from the TD maps could be well fitted by a Gaussian function ( gaussfit.pro ; Figure 7 (c)). Each intensity profile is 20 pixels wide, centering on the minimum intensity location within ±15 pixels of the original interpolated location. The full-width-half-maximum of the best-fit Gaussian function is considered as the uncertainty of the oscillation amplitude. We then fitted the extracted oscillation pattern by the exponentially


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 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 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 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

Disks The lack of correlation in Figure 9 implies a decoupling of the mm grains and gas. We can test this further by assuming instead that there is no decoupling, and by comparing the inferred gas content of the inner disk with the accretion rate. Assuming a standard ISM gas-to-dust ratio, we compare the dust mass and accretion rate in Figure 12 and overplot the resulting timescale for the gas and dust content of the inner disk to accrete onto the star. Similar to Figure 9 , no correlation appears to be present ( r corr = − 0.24 ± 0.26), which is again consistent with decoupling of the mm grains and accreting gas. Second, we find that the lifetimes of most inner disks are relatively short compared to the lifetime of the disk, typically less than 10 4 yr, assuming an ISM gas-to-dust ratio of 100. Figure 12. Inner disk dust mass vs. accretion rate. 0.5 dex of error is assumed for the accretion rate. An ISM-like gas-to-dust ratio of 100 is assumed for the inner disk, the validity of which is discussed in Section 4.5 . No correlation appears to be present ( r corr = − 0.24 ± 0.26), which is again consistent with decoupling of the mm grains and accreting gas. Assuming a gas-to-dust ratio of 100, the lifetime of the inner disks is typically less than 10 4 yr, well below the typical lifetime of a protoplanetary disk. Given the high occurrence rate of inner disks in our sample, a short lifetime would require that the inner disk is regularly replenished by episodes of enhanced accretion from the outer disk. However, depletion of dust in the inner disk due to radial drift such as suggested in the previous section may cause the gas-to-dust ratio of the inner disk to be several orders of magnitude larger (Pinilla et al. 2012 ), implying proportional longer lifetimes. While we do not have a direct measurement of gas content of the inner disk to assess this scenario, viscous accretion disk theory predicts a link between the gas surface density, accretion rate, and viscosity, which we can use to estimate the gas content. We assume the following relations:with ν the disk viscosity, α the viscosity parameter, c s the sound speed, H the vertical height, Ω( r ) the angular velocity, k B the Boltzmann constant, μ ≈ 2 the mean molecular weight, m p the proton mass, G the gravitational constant, and M * the stellar mass. The third equation assumes that the disk is vertically isothermal. These equations result in a relation between the gas surface density and the accretion rate (Manara et al. 2014 ):The gas surface density profile is derived from the dust profile where ξ inner and ξ outer are the gas-to-dust ratios for inner and outer disks, respectively:while for the temperature profile, we use Equation ( 4 ). This means that we can express the gas-to-dust ratio ξ inner :withand equivalently, we can express viscosity α as We note that both quantities α and ξ inner are independent of r and can be evaluated at any radius, and we can compute either quantity while


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

spectroscopy leads to more detailed models being needed to fully describe the data. Our knowledge of many aspects of these models is not yet complete (for example the possible presence of additional astrophysical components in the line of sight towards the source and imperfect atomic data) and we also have to deal with imperfect instrumental calibration, systematic effects and statistical fluctuations, so there will necessarily be differences between the data and the best physical model that can be found. As discussed in Blustin et al. (2002) , the use of goodness-of-fit statistics when modelling RGS data must be coupled with careful consideration of the physical meaning of the models, as physical self-consistency is more important than reaching a nominally “acceptable” goodness-of-fit value. 3.1. Testing the 2012–13 stacked spectrum with continuum model and Gaussian lines As Braito et al. (2014) have previously analysed the Jan. 2013 observation (Obs. 3, the least absorbed of the four 2012–13 observations), we began our analysis using their continuum and absorption model. Their use of EPIC data allows much better contraints of the continuum than is possible using just the RGS data. As observation 3 has lower absorption than the other 2012–13 observations, it reveals ionised absorber phases not previously seen. For this we used a power law model, absorbed by three ionised absorbers ( of 3.77, 2.15 and 0.17, as in their Table 4). We allowed our power law normalisation to vary, and fixed to a value of 2.1 to match their EPIC fits. At this stage we have not fitted any of the emission lines, so have an unacceptable -statistic value of 7000. Table 2 Narrow emission line best fit intensities from the 2012–2013 stacked spectrum and 2004–2007 stacked spectrum. Notes. A star marks uncertainty in the assigned transition. Overall -statistic 1445 (2012–13) and 1548 (2004–07). (a) r, i and f represent the resonance, intercombination and forbidden lines of an He-like triplet, respectively. Fig. 1 2012–13 RGS spectrum and line labels for detected emission lines. r, i and f represent the resonance, intercombination and forbidden lines of a He-like triplet, respectively. A * indicates uncertainty in the line identification. The data are binned by two for display purposes. The data are shown in black, and the model in red. For details of the model shown here, see Sect. 3.5 . We then fitted Gaussian lines to the data, adding a Gaussian if the best fit -statistic improves by , corresponding to a 90% confidence level for three extra free parameters (normalisation, width and central wavelength of each Gaussian model). These Gaussian models are only absorbed by our Galactic , and none of the absorption intrinsic to NGC 1365. For the He-like triplets in this wavelength range we included three components (resonance, intercombination and forbidden) if at least one was detected at the 90% level. These “triplets” really include four components, but at RGS resolution


O O O O O O O O O O O O O O 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 B-Citation I-Citation I-Citation I-Citation 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 B-Model O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-CelestialObject O O O O O O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O B-CelestialObject O B-CelestialObjectRegion I-CelestialObjectRegion O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Instrument O O B-Telescope O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O B-CelestialObject I-CelestialObject O O O O O B-CelestialObject O O O O O O O O O O O O B-CelestialObject O O O O O O O B-Instrument O O O B-Citation I-Citation I-Citation I-Citation O O B-Telescope O O O O O O O O O O O O B-Location I-Location I-Location 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 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

molecules released from the nucleus and an additional source of D-poor water molecules from sublimating icy grains (see dash-dotted line in Fig. 2 ). Laboratory experiments on samples of pure ice show small deuterium fractionation effects ( Lécuyer et al. 2017 ). In experiments with water ice mixed with dust, the released water vapor is depleted in deuterium, explained by preferential adsorption of HDO on dust grains ( Moores et al. 2012 ). This effect goes in the opposite direction to the observed trend, while conversely the VSMOW D/H value from subliming icy grains is likely representative of buried nucleus water ice. Alternatively, a non-steady-state regime of water ice sublimation could explain the factor 2 − 3 deuterium enrichment in water vapor released from the nucleus with respect to VSMOW ( Podolak et al. 2002 ). However, this would occur in episodic time intervals along the comet orbit ( Podolak et al. 2002 ), whereas the HDO/H 2 O values measured for comet 67P at different periods are very uniform ( Altwegg et al. 2017 ). 5. Conclusion Enlarging the number of accurate D/H measurements in both Jupiter-family and Oort cloud comets is required to better constrain the observed correlation. Taking these measurements from the ground is challenging. Nearly simultaneous spectroscopic observations of low-energy rotational lines of and HDO in a matching field of view encompassing a large fraction of the coma using the GREAT spectrometer aboard SOFIA can play a key role in this endeavor. In this context, the next close apparition of comet 67P/Churyumov-Gerasimenko in 2021 November will offer an excellent opportunity to re-measure the D/H ratio in this comet using spectroscopic techniques. The understanding of the observed correlation calls for detailed investigations of the mechanisms leading to dust and chunk ejection, and cometary hyperactivity. Further experimental and modeling work on evaporative fractionation is also clearly needed, and may ultimately establish that all comets share the same Earth-like water D/H ratio, with profound implications on the early solar system and the origin of the Earth’s oceans. Appendix A: Observations and modeling A.1. Observations The observations of comet 46P/Wirtanen reported here were carried out using the GREAT heterodyne spectrometer ( Heyminck et al. 2012 ) aboard SOFIA during five flights between 2018 December 14 and 20 UT, out of Palmdale, CA, USA. The instrument was operated in its upGREAT HFA/4GREAT (HFA/4G) configuration ( Risacher et al. 2018 ; Durán et al. 2017 ), which allows simultaneous observations at five different frequencies. The lowest frequency band, 4G-1, was used for the observations reported here. The tuning setup and the basic instrument characteristics are summarized in Table A.1 . Although several other transitions of interest were covered in the higher-frequency channels, only OH was detected at a low signal-to-noise ratio, and the other upper limits are not constraining


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

we cannot trust them since these very large parameters produce synthetic profiles with a significant portion being out of the observed spectral range (Figure 15 ). The inversion code combined a strongly shifted two-lobed Stokes V profile with an unshifted one to recreate the observed three-lobed Stokes V profile, without any information about what the profiles would look like outside the spectral range. Figure 14. Right panels: observed and best-fit Stokes profiles (black and red, respectively). Left panels: atmospheric parameters inferred for the fast (blue) and the slow components (magenta) from the inversion. The filling factor of the fast component is shown in the lower left corner of the top panel. Figure 15. Synthetic profiles resulting from the fast and the slow atmospheres (blue and magenta lines, respectively) plotted in Figure 14 . The gray line shows the blue one multiplied by a scale factor for better visibility. As a reference, the observed and best-fit profiles are also shown here in black and red, respectively. The dotted vertical lines delimit the observed spectral range. To solve this situation, we decided to repeat the inversion considering as initial models the atmospheric stratifications obtained from a nearby pixel unaffected by this problem whose Stokes V profile is similar. The results are shown in Figure 16 . Although the fit is not as good as in the previous inversion, it is still reasonable. The inversion now finds strongly shifted and reversed two-lobed Stokes V profile, together with an unshifted profile, whose combination reproduces the observed spectral signatures, being a more reliable solution. Figure 16. Best-fit profiles and atmospheric parameters inferred from an inversion of the same pixel as in Figure 14 considering as initial models the results from a close pixel with a similar Stokes V profile. The layout is the same as in Figure 14 . Although these structures resemble Evershed clouds (e.g., Rimmele 1994 ; Shine et al. 1994 ; Cabrera Solana et al. 2006 , 2007 ), we do not find any indication of two velocity packets inside the patch traveling outward as a whole. In addition, Cabrera Solana et al. ( 2007 ) found that the two Evershed cloud packets have opposite magnetic polarities when they cross the sunspot border, which has not been found in our observations. A number of physical mechanisms are known to be able to drive supersonic flows in the penumbra, including siphon flows (Thomas 1988 ) and moving magnetic tubes (Schlichenmaier 2002 ). Both mechanisms might well explain our observations, but a detailed comparison is difficult because the theoretical results are based on idealized models that are often simplistic and do not consider the actual conditions of the penumbra (in particular, the fact that it is a stratified atmosphere with temperatures, pressures, and magnetic fields varying both vertically and horizontally). The 3D radiative MHD simulations of Rempel ( 2012 ), on the other hand, show


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

This research is partly supported by the following grants: Royal Society-Newton Mobility grants NI160149, CIC-UMSNH 4.9, and CONACyT 258726 (Fondo Sectorial de Investigación para la Educación). The simulations were carried out in the facilities of the CESCE-UNAM, Iceberg HPC Cluster and the Big Mamma cluster at the LIASC-IFM. V.F. and G.V. thank the STFC for their financial support. Visualization of the simulations data was done with the use of the VisIt software package.


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

range to obtain the constant horizontal polarisation pattern we are looking for. If these structures have an optical depth that is too low or too high, the central belt shows multiple scatterings as seen in both Figs. 12 and 13 . In extreme cases with very high optical depth in the outer torus, we have no photons in this region, a case close to the simulations of model 2 (see Fig. 7 ). These two conditions seem to be important to produce the features we are expecting. A last remark is that the photons detected from the ionisation cone are no longer just scattered once at high optical depth in the cone ( Fig. 12 ). However, the centrosymmetric pattern seems to be approximatively conserved for double scattering in the cone. 4.4 Reproducing the NGC 1068 observations Based on previous simulations, we tried to reproduce the SPHERE observations of NGC 1068. As we observed constant polarisation orientation in the core of NGC 1068 in both the H and Ks bands, we need in our simulation an optical depth τ ≥ 20 at 2.2 μ m to be able to generate such polarisation features. We changed our previous model 5 to adapt it to these larger wavelengths. Here, the torus has an optical depth τ Ks = 19, which gives τ H = 35 and τ V =169. We note that this is in therange of the current estimation of the density of dust in the torus (see Sect. 5.6 ). For this simulation we used a mixture of silicates and graphites to rely on a realistic dust composition for an AGN, inspired by Wolf Henning (1999) . We adapted their mass ratio to a number ratio according to Guillet (2008) leading to 57% silicates, 28.67% parallel graphites, and 14.33% orthogonal graphites. With these parameters, the maps in Fig. 14 are now able to reproduce some of the observed features. Namely, the nearly constant horizontal polarisation in the central part is similar to that observed on NGC 1068 at 1.6 and 2.2 μ m. We are, however, not yet able to reproduce the ridge that appears at the very centre of the SPHERE observations. Fig. 14 Maps of the observed averaged number of scattering with an inclination angle of 90 ° at 1.6 ( top ) and 2.2 μ m ( bottom ). Polarisation vectors are shown, their lengths being proportional to the polarisation degree and their position angles representing the polarisation angle. 5 Discussion 5.1 Photons significance One major concern is the simulation strategy of conserving the packets until they exit the simulation box, whatever their number of interactions.We must verify to what extent the detected photons are relevant. The energy of each packet is decreased according to the albedo at each interaction, as is the number of photons in the packet. Therefore, it is common at the end to record photon packets with energies 10 4 times lower than the initial energy. If a high energy packet reaches a pixel previously populated only with low energy ones, it will totally dominate the pixel so that Q and U values and the polarisation parameters will be essentially linked to this


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

free of atmospheric perturbations, regularly produced by the 50 cm Solar Optical Telescope (SOT) on-board the satellite HINODE between November 2006 and February 2016, are now available. These images have been used in this paper to investigate the variation of the solar granulation over the activity cycle with more accuracy than before. After a presentation of the HINODE/SOT synoptic program in Sect. 2 , the method of analysis of the blue continuum images is described in Sect. 3 . The results are presented in Sect. 4 and discussed in Sect. 5 . 2. Observations: HINODE/SOT synoptic program The HINODE synoptic program provided broadband images obtained at the disk center with the Optical Solar Telescope (e.g., Tsuneta et al. 2009 ). They were taken a few seconds apart in blue, green and red continuum windows at 450.45, 555.05, 668.40 nm respectively, in the G -band lines of the CH molecule at 430.50 nm, in the CN band head at 388.35 nm and in the Ca II H line at 396.85 nm, in general once or twice a day. In this work we have only used the blue continuum images. During the observations, the focus position was controlled in the G -band; when optimized in this wavelength, it is also optimized in the nearby blue continuum 0.4 nm window. But unfortunately, this set of images is not as homogeneous as expected, because a significant number of them appear to be blurred to a varying degree; the cause of blurring may be inaccurate focusing or/and optical aberrations as one will see in Sect. 4 . Consequently, great care is taken in this investigation to only select the sharpest images, in order to get the most homogeneous set of high resolution granulation images currently available, spanning nearly one solar cycle (although the minimum of activity between cycle 23 and cycle 24 was longer than usual). Before February 2008, when a serious telemetric problem occured, between two and four images were taken every day in each wavelength; after that month and until September 2009 the cadence was reduced to about one image taken every two days, but then on increased again to a cadence of about one observation per day. Two adjacent cameras with 2048 × 2048 square pixels of nominal scale 0′′̣055, took rectangular images of nominal size 228′′ × 114′′. We have taken into account the annual variation of the Earth-Sun distance by changing the pixel scale accordingly. After the telemetric problems which occurred in January 2008, the images of the synoptic program were binned by a factor of two. Fortunately, this is not a problem in this work, since the images taken before this date were binned by a factor of two for analysis. So the size of all the analyzed images is 2048 × 1024 pixels. The program ended in February 2016, when both cameras broke down. All images were calibrated with the standard solar reduction software distributed under SSWIDL, which corrects for bad pixels, readout errors, dark current and flat field. A 1024 × 512 pixel subfield of a calibrated image is


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

that model A is strongly favored by the data, while model B is preferred for . It is somewhat indicative to relate values of the odds ratio to σ -levels of Gaussian measurements:where erf is the error function. 4.1.1. Mock Observations We want to assess the number of observations N obs needed to discriminate between the two models, assuming that one of them is a faithful representation of reality. To understand how each parameter impacts the analysis, we run our statistical pipeline assuming we only measure either , , or . In practice, this implies that the integral in Equation ( 18 ) is evaluated on the selected variables while marginalizing over the others. Regarding the production of mock data: we generated 10 3 sets of observations for each value of N obs , in order to produce a statistical estimation on our results. Each of the mock observations was sampled from the model and included in the observation set with probability p det . In Figure 2 , we show values of the odds ratio O AB where the set of observed events is generated from model A, so that O AB is expected to increase as N obs grows. We present results for observations generated from the dynamical (orange) and isolated (blue) models, both for aLIGO/aVirgo (left panels) and ET (right panels). Figure 2. Evolution of the odds ratio as a function of the number of simulated observations generated from the dynamical (orange) and isolated model (blue). The odds ratios are defined such that the posterior of the true model is at the denominator. Equivalent σ levels are reported with dotted lines. The four rows correspond to analysis done with M t , q , , and (from top to bottom); the left and right panels refer to aLIGO/aVirgo and ET, respectively. For each scenario, the thick lines are the median values, while the surfaces represent the 90% credible regions. Let us focus first on the top row, where only the total mass is considered in the analysis. In the case in which the dynamical model is assumed to be true (orange) with aLIGO/aVirgo, the upper limit of the 90% credible interval presents high values even for small N obs . This is because the isolated model only predicts merging BBHs with M t 70 M ⊙ . As a result, any observation where the entire support of the total mass posterior distribution is above 70 M ⊙ can only be described by the dynamical model. Another interesting feature is that the lower bound of the credible interval has values of starting at , which is consistent with our models. In fact, as the number of dynamical BBHs with M t > 70 M ⊙ in our dynamical catalog is equal to 16 (out of 229), the probability of not observing any massive BBHs in 50 observations generated from the dynamical model is equal to p = 1.9 × 10 −3 . It is also interesting to see that the results obtained are similar when observing with ET, suggesting that the differences in total mass range of our models is the dominant effect in the analysis. In contrast, the evolution of the odds ratio for


O O O O O O O O O B-Person I-Person B-Person I-Person O B-Person I-Person O O O B-Model I-Model O O O O O O O O O O O O O O O O O B-Organization I-Organization I-Organization O B-Grant I-Grant I-Grant

We would like to acknowledge the pioneering work of Adam Burrows, Hans-Thomas Janka, and Matthias Liebendörfer, whose contributions to CCSN theory were directly inspirational to the work presented here. This material is based upon work supported by the National Science Foundation under Grant No. 1313036.


O O O O O O O B-Software O O B-Organization B-Location O B-Location I-Location O O O O O O

The figure production made use of the PGPLOT software at NRC Canada in Victoria, BC. I thank the referee for clarification.


B-Person O O O O B-Organization I-Organization I-Organization O B-Location I-Location O O B-Grant I-Grant

J.L. acknowledges support from the Research Grants Council of Hong Kong through grant HKU 703512P.


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

cooling break signature does not appear in the spectrum. Since some young PWNe have a soft injection spectrum of p 2 ∼ −3.0, we also study such PWNe. Figure 2 shows model spectra for the small magnetic field cases ( B , p 2 ) = (3 μ G, −3.0). The braking index is different for the left ( n = 3) and the right ( n = 2) panels, and then we search for the value of γ b for the calculated X-ray flux to be close to F O11 . In both cases, a large TeV γ -ray flux is predicted when compared with Figure 1 without increasing the energy density of the ISRF ( u IR , u OPT ). 4. DISCUSSION AND CONCLUSIONS Considering the plasma outflows from the magnetar, we build a broadband emission model of MWNe based on the one-zone model of young PWNe around RPPs ( TT10 , TT11 , TT13b ). The model is simplified for application to MWNe that have less observational information than PWNe. We apply the model to the MWN around 1E 1547.0-5408, which is the most promising object for detecting MWNe among all the known magnetars because of its large L spin and its small distance to the Earth. Because of poor current observational constraints on the MWN around 1E 1547.0-5408, various combinations of parameters are allowed. However, here, we compare Models 1 and 2 based on past studies of young PWNe, especially focusing on Kes 75 around PSR J1846-0258, which is the only HBP showing a magnetar-like behavior (Gavriil et al. 2008 ). Model 1 has η and γ b similar to Kes 75, while Model 2 has a similar magnetic field strength B . It is known that the mean magnetic field B is very different for each young PWN 3 ≲ B ≲ 80 μ G (e.g., TT13b ; Torres et al. 2014 ). On the other hand , TT11 and TT13b showed that η ∼ 10 −3 is common among young PWNe, except for Kes 75, by using almost the same model as this study, i.e., adopting ( α R , α B ) = (1.0, −1.5) in Equations ( 7 ), ( 8 ), and ( 10 ). Kes 75 has an exceptionally small η compared to other young PWNe for our model and also for other models, although the values of η are different among models (Bucciantini et al. 2011 ; Torres et al. 2014 ). We favor Model 1 over Model 2 because we expect that magnetars have the wind property η and γ b similar to HBPs, where γ b is related to the bulk Lorentz factor of the wind just upstream the termination shock (e.g., Kennel Coroniti 1984 ; Bucciantini et al. 2011 ). Models 3 and 4 are cases for the soft injection spectrum p 2 = −3 and the large break Lorentz factor ( γ b ≫ 10 6 ), although such γ b and p 2 are not typical among young PWNe ( TT13b ). Both models are interesting because they predict a larger TeV γ -ray flux than Model 1 without increasing the local ISRF ( u IR , u OPT ). For example, the γ -ray flux increases if the photons from the nearby star-forming region contribute to the local ISRF ( Torres et al. 2014 ). Model 3 is brighter than Model 2 in TeV γ -rays because the injection of the high energy particles is an increasing function of γ b . Model 4 predicts larger TeV γ -ray flux


O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Observatory O O O O O O B-Telescope I-Telescope I-Telescope B-Wavelength I-Wavelength O O O O B-CelestialObject O O O B-Survey I-Survey I-Survey O O O O B-Person I-Person O O B-Grant O O O O O O O O O B-Survey I-Survey O O O B-Wavelength I-Wavelength I-Wavelength 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 B-CelestialObject O O O O O O B-CelestialObject O B-CelestialObject I-CelestialObject I-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O O B-Observatory O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Survey I-Survey I-Survey I-Survey I-Survey O B-Survey I-Survey I-Survey O B-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Dataset I-Dataset 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 B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula I-Formula I-Formula O O B-Formula I-Formula I-Formula I-Formula I-Formula O O O B-Formula I-Formula I-Formula B-Citation I-Citation I-Citation I-Citation O O B-Dataset I-Dataset O O O B-Observatory O O O B-Telescope O B-Citation I-Citation I-Citation I-Citation O O O O O O B-Instrument I-Instrument I-Instrument O B-Telescope B-Wavelength 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 B-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion B-CelestialObject I-CelestialObject B-CelestialObject B-CelestialObject O O B-CelestialObjectRegion I-CelestialObjectRegion I-CelestialObjectRegion B-CelestialObject I-CelestialObject B-CelestialObject B-CelestialObject B-CelestialObject B-CelestialObject O O O O O B-CelestialObject I-CelestialObject B-CelestialObject B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Observatory 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 B-Observatory 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

analysis of the visibility weights in order to ensure robust uncertainties in the measured flux. Future work on identifying variability in deeply embedded protostars is underway. A Cycle 6 ALMA proposal for 4 epochs of stand-alone Atacama Compact Array Band 7 observations of variables in Serpens identified by the JCMT Transient Survey has been accepted (PI: Logan Francis, project code 2018.1.00917.S ). These observations will complement results from the contemporaneous Transient Survey by observing at 850 μ m with a resolution of 38 (compared to the 146 resolution of the JCMT), sufficient to reach the scale of the inner envelopes (∼1500 au) of protostars in Serpens. Appendix Discussion of Individual Fields in Serpens Main The Serpens Main cluster has been extensively surveyed at a variety of wavelengths and resolutions over the past 30 yr. Our ALMA observations provide some of the highest resolution and most sensitive maps of deeply embedded protostars in the cluster to date. In many of our fields, we are thus able to resolve single sources at the scale of the accretion disks, uncover significant extended structure, and identify previously unknown faint sources. Here, we discuss each field in the context of past and recent observations, and compare the positions of our sources with YSOs identified in the Spitzer “cores to disks” (c2d) and “Gould Belt” (GB) surveys (Dunham et al. 2015 ). Table 14 lists the properties of all c2d/GB YSOs in our fields associated with our millimeter sources in Table 5 . Table 14 Properties of the Serpens c2d+GB YSOs Note. This table adapted from Table 2 of Dunham et al. ( 2015 ). a Classes are defined by the extinction corrected spectral index α ′ as Class 0 + I: α ′ ≥ 0.3, flat spectrum: −0.3 ≤ α ′ 0.3; Class II: −1.6 ≤ α ′ −0.3; and Class III: α ′ −1.6 (Greene et al. 1994 ). The Ser-emb objects targeted by our ALMA and the earlier CARMA observations (Enoch et al. 2011 ) were originally defined from large-scale Bolocam 1.1 mm and Spitzer mid-IR surveys, and classified according to their bolometric temperature (Enoch et al. 2009 ). Most of our targets lie in two dense clusters: the northern Main Cluster (Ser-emb 4, 6, 8) and the southern Cluster B (Ser-emb 3, 7, 9, 11, 17). Three sources are relatively isolated (Ser-emb 2, 5, 15) from either cluster. An overview of the region showing these clusters and the locations of the targeted embedded sources can be found in Figure 1 of Enoch et al. ( 2011 ). Our Figures 9 – 11 show the continuum maps with the full field of view for each of our ALMA pointings, and indicate the positions and IDs of c2d/GB YSOs by green pluses (Class 0 + 1, flat spectrum) and orange crosses (Class II). Red squares show the location of the postage-stamp views in Figures 2 and 3 . Figure 9. Full maps of our ALMA observations of Serpens protostars. Red squares indicate the field of view for the postage stamps in Figures 2 and 3 . The maps are shown with primary beam correction to indicate