et al. 2017 ; Vallini et al. 2017 ), which may affect the density field of GMCs, and ultimately increase the conversion factor. Finally, we compare our inferred conversion factor with the one resulting from the best-fitting formula, X CO /( cm 2 K km s − 1 ) = 6.3 × 10 19 α CO /(M ⊙ K km s − 1 pc 2 ), obtained by Narayanan et al. ( 2012 ). They simulate the hydrodynamic evolution of both isolated and merging disc galaxies finding that . If we substitute and Z = 0.5 Z ⊙ we obtain α CO = 2.9 M ⊙ /(K km s − 1 pc 2 ) in agreement within a factor ≈2 with our results. 4.5 ALMA observability In Section 4.3 we have shown that the peak of the Althæa CO SLED coincides with the CO(7–6) line. As CO transitions with J up ≥ 6 fall in the ALMA bands from z > 6, in what follows, we use the ALMA Sensitivity Calculator to compute the observing time required to detect the CO(7–6) line from (a galaxy similar to) Althæa. The total CO(7–6) luminosity of Althæa is L CO(7-6) = 10 7.1 L ⊙ , i.e. ≈1/16 of its [C] luminosity. If we assume the line width to be equal to that of [C] observations in LBGs at z ≈ 6 − 7 ( Maiolino et al. 2015 ; Knudsen et al. 2016 ; Pentericci et al. 2016 ; Bradač et al. 2017 ), this yields a peak flux density . 8 The ALMA full-array observing time required to detect (resolve over 1/3 × FWHM) the CO(7–6) line with a signal-to-noise ratio S/N = 5 is ≈13 h (≈38 h), i.e. it would be challenging but doable within the maximum observing time ( ≤ 50 h) allowed for ALMA regular programs. This is in line with what was found by Muñoz Furlanetto ( 2013 ), which pointed out that ALMA observations of high- J CO can be performed with reasonable integration times only in those z ≈ 6 galaxies which, like Althæa, are chemically evolved ( Z Althaea > 0.1 Z ⊙ ) and UV-bright ( M UV, Althaea ≈ −22). 5 CONCLUSIONS In this paper we have studied the CO emission properties of galaxies at the end of the Reionization Epoch. First, we have developed a semi-analytical model that, given the internal density field of a GMC and the impinging FUV flux ( G 0 ) at the cloud surface, computes the CO line emission. The density PDF of the GMC is set both by turbulence (parametrized by the Mach number ) and self-gravity (parametrized by t / t ff ). The radiative transfer is performed with cloudy and includes z = 6 CMB radiation. The model takes the mean gas density n 0 , , t / t ff , G 0 as inputs, and it returns the luminosity of the first nine CO rotational transitions. We validated the model with local observations, demonstrating its capability to reproduce: the M vir - relation; the observed CO excitation in local SB galaxies; and the CO SLED of the low-metallicity ( Z ≈ 0.5 Z ⊙ ) molecular cloud N159W in the LMC. We used our validated CO emission model to post-process a cosmological zoom-in simulation of a prototypical z ≈ 6 galaxy ( M ⋆ ∼ 10 10 M ⊙ , SFR ∼ 100 M ⊙ yr − 1 ), Althæa. We have made the following additional assumptions: (i) we adopt a constant CRIR (cfr.

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


Comptonization; case 2: partially absorbed pure reflection spectrum; case 3: partially absorbed Comptonization spectrum with reflection; case 4: partially absorbed Comptonization with reflection and variable local absorber. Parameters are: intrinsic column density associated with the direct (Compton) spectrum and relative covering fraction (pcf and pcf), intrinsic column density associated with the reflection spectrum and relative covering fraction (pcf and pcf), electron temperature, Compton parameter (see text), relative reflection factor, ionization parameter (see text), comp PS normalization, Gaussian line energy, Gaussian line equivalent width, power-law photon index (for the dust scattering halo), power-law normalization (for the dust scattering halo), JEM-X calibration constant and ISGRI calibration constant. All the quoted errors are 1 level ones. Notice that all models include an additional absorber to account for the interstellar absorption ( N H 8.310 21 cm 2 ). The FeK line flux has been expressed in terms of ergcm 2 s 1 instead of equivalent width in order to allow direct comparison with the lines flux from Model 2 (see Section 5 , for which measuring the equivalent width is problematic). 4 SPECTRAL MODELLING MODEL 1: PARTIALLY COVERED REFLECTED COMPTON SPECTRUM 4.1 Case 1: partially absorbed Comptonization We initially fitted our data using the Comptonization model comp PS in xspec (see Poutanen Svensson 1996 ) modified by the interstellar absorption ( tbnew in xspec ; Wilms, Allen McCray 2000 ) with a fixed column density of N H 8.310 21 cm 2 . We left the Thomson optical depth electron temperature kT e and the normalization in comp PS free to vary, while we fixed the seed photon temperature to kT bb 0.1keV (i.e. the seed photons are produced by a multicolour disc blackbody with an inner disc temperature of 0.1keV) and the inclination to 67 (see Khargharia etal. 2010 ). We also fixed to zero the ionization parameter since it only affects the reflection component, which is switched off in this case. We left all the remaining comp PS parameters fixed to their default values. Large residuals indicated that a more complex spectral model was required. Therefore, we added a neutral absorber partially covering the source ( tbnew_pcf ). The addition of a narrow Gaussian line to describe the ironK line (see King etal. 2015 ) was required to account for some residuals around 6.4keV. The line is unresolved in both the Swift /XRT and INTEGRAL /JEM-X spectra; therefore we fixed its width to 0.2keV. This model did not provide satisfactory fits, having 2 = 620.12 with 461d.o.f. and null hypothesis probability = 9.8210 8 . Large residuals especially above 10keV indicate that the spectrum likely shows a significant reflection component. 4.2 Case 2: partially absorbed pure reflection Since the emission from the dust scattering halo was at times significant in the sky region around the source, sometimes outshining the source itself (see

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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-Model O O O O O O O O O O O O O O O O O O B-Instrument 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 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-Model I-Model O O O O O O O O O O O O O O O B-Model I-Model I-Model I-Model I-Model I-Model I-Model O O O O O O O O O O O O O B-Model I-Model I-Model I-Model O B-Software O B-Citation I-Citation I-Citation O O O O O O O B-Model O B-Software O B-Citation I-Citation I-Citation I-Citation O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O O O O O O B-Model I-Model I-Model O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O B-Model I-Model I-Model O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O B-Wavelength O O O O O O O B-Observatory B-Telescope O B-Telescope B-Instrument O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O B-Wavelength O O O O O O O O O O O B-Model I-Model I-Model I-Model I-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O


K-S tests with respect to the radio properties, and found that the radio sizes of the absorbed and unabsorbed CSO samples could form two populations. In addition, the results of a two-dimensional two-sample K-S test confirmed the possible existence of such two populations. However, we caution that the two-dimensional two-sample K-S test requires a larger number of the absorbed sources (at least twice as many as in the current sample) to be valid. Our results could be interpreted in two ways. It could be that the CSOs with a high intrinsic X-ray absorbing column, N H > 10 23 cm −2 ; 0048+3157, OQ+208, 2021+614, 1511+518, 0108+388) have less evolved radio structures (smaller linear radio size) than X-ray unabsorbed CSOs with the same 5 GHz radio power. Thus, the environment in which a radio source expands might be able to confine the source growth already at the earliest stages of its evolution. This would provide the first observational evidence in the X-ray band that some compact jets may be frustrated by a dense environment and their kinematic ages may be underestimated. An alternative way of explaining the separation visible in Figure 4 is that the X-ray obscured sources have higher radio luminosity than the X-ray unobscured sources for a given radio size. The two factors that drive radio luminosity for a given size of a radio source are environmental density and jet power. Thus, one possible explanation is that the X-ray obscured sources are brighter for a given size because they were born in a denser environment. Another option is that they are brighter than the unobscured CSOs with the same size because they have higher jet power, which is related to central density, through e.g., the accretion rate (e.g., Allen et al. 2006 ; Tchekhovskoy et al. 2011 ; Ghisellini et al. 2014 ), or directly as in the model of Stawarz et al. ( 2008 ). Even though with the current data it is not possible to distinguish between these two explanations, we stress that in both cases the density of the CSO environment plays a key role. Moreover, our results raise a question about the origins of the X-ray emission and the location of the X-ray obscurer. If the CSO X-ray emission originates primarily from an active nucleus that becomes attenuated by obscuring material in the vicinity of the nucleus, then we should also see heavily obscured CSOs with larger radio structures. In contrast, the CSOs in our sample show low intrinsic X-ray absorption for the radio size exceeding a few tens of parsecs. If the CSO X-ray emission is dominated by inverse-Compton emission of the radio lobes (e.g., Stawarz et al. 2008 ; Ostorero et al. 2010 ), then the CSOs would become unobscured once their radio lobes expand beyond the region occupied by the dense material. Thus, it could be that the obscurer is located on scales smaller than a few tens of parsecs. Alternatively, the obscuring material could be destroyed or removed by the expanding radio source. Recently, Ostorero et al.

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


the marked outliers are not reliable enough for searching for flare candidates alone (see Fig. 1 ): it sometimes also marks the beginning of the light-curve windows. Thus we only used the RANSAC estimate of the inlier points for statistics and calculated the standard deviation of the light curve (with the rotational modulation and most of the flare points removed). We considered those points as first-order flare candidates that were above a given detection level (above 3 σ by default). To achieve more robust results, we shifted the search window through the light curve, by default in steps of one-fourth of the light-curve window (see Fig. 2 , e.g.). In this way, every light-curve point was analyzed multiple times (with the exception of those that are at the beginning or at the end of the data set or large observational gaps), and if a light-curve point is considered as an outlier, that is, a flare point candidate, it received a “vote”. A light-curve section was considered a flare when it received enough votes (≥3, by default) in overlapping search windows and had at least a given number (2, by default) of consecutive points. We note that this last step was performed only after evaluating each light-curve segment. These criteria are basically the same as those defined by Eqs. (3a)– (3d) of Chang et al. (2015) and are consistent with adaptations made by Davenport (2016) . When running FLATW’RM from command line, the user can change the number of flare points needed for a flare, the detection level of the flares, and the full with at half maximum (FWHM) that is used for the analytic fit of the events. Optionally, the rotation period can be given as an input to run the code faster, or to fix it to a chosen value if the rotational modulation is too weak, and the polynomial degree can also be fixed. The number of votes needed for a flare candidate to be kept, the window size (compared to the rotation period), and the step length with which the search window is shifted cannot be changed from command line, but can be easily modified if the flare-finding function is imported to another code. Fig. 2. Demonstration of the voting algorithm on a light-curve section of KIC 1722506. The top plot shows the original light curve (in blue, near a normalized flux of 1), and each light-curve segment in individual windows tested by FLATW’RM (each a different color), and the flare candidates are marked for the given run with circles. In the bottom plot , the candidates with one (light gray), two (medium gray), and at least three (black) votes are plotted. In this setup, the flares plotted in black are kept as final flare candidates. 2.4. Summary of the selection process For clarity, we explicitly state the procedure that FLATW’RM steps through in locating the flares in the light curve. A period search is first performed on the input light curve. The input light curve is divided into windows of 1.5 × P that can be effectively fit with polynomials. Each light-curve

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


they are not noticeably affected by the motions of individual stars within binary systems (because PMs provide a measure of the motions of stars integrated over a baseline and not an instantaneous measure of the velocity as RVs do). In the text that follows, we denote the velocity dispersions in RA and Dec. as σ α and σ δ , though technically the velocity dispersions of the PMs in RA and Dec. should be written as and . Fig. 5 shows the vector point diagram of PMs for the majority of Cyg OB2 members. The PMs of non-members of Cyg OB2 are not shown, but these have a similar distribution, implying that Cyg OB2 members cannot be kinematically separated from the field population. A number of outliers with very large relative PMs are evident in this diagram and are discussed in more detail in Section 3.5 . These outliers cause the velocity dispersion (Section 3.1 ) to come out very differently for a Gaussian dispersion compared to that calculated from an outlier-resistant method such as the interquartile range (IQR), and the use of a forward modelling approach (Section 3.2 ) reinforces this. Figure 5. Vector point diagram for members of Cyg OB2 with PMs (note that PMs are not placed on an absolute reference system but are only calculated relative to each other) with the spectroscopically known OB stars shown as red dots. The left-hand panel shows 869 of the 873 stars with PMs (four stars with very high PMs are not shown), highlighting the presence of a number of runaways or possible contaminants with high PMs. The right-hand panel (inset shown in the left-hand panel with a blue box) shows a close-up of the centre of the velocity space, with 822 of the 873 stars shown. 3.1 Calculating the velocity dispersions Fig. 6 shows the binned velocity distribution (over the range covered by the majority of stars), which has a broadly Gaussian distribution with low-amplitude, broad wings. The simplest estimate of the velocity dispersion is the standard deviation, which for our sample of 873 stars gives mas yr −1 and mas yr −1 (uncertainties calculated from a Monte Carlo simulation in which the individual PMs are varied by their estimated uncertainties). These velocity dispersions are considerably larger than the observed distribution because they are being enlarged by a number of outliers with large velocity offsets. There are 23 (17) stars with |μ| > 10 mas yr −1 in the RA (Dec.) dimension, and 1 (2) of these have |μ| > 100 mas yr −1 . These outliers could be removed by a process of ‘sigma clipping’, but this is a procedure fraught with difficulties of subjectivity and irreproducibility. Figure 6. PM velocity distributions along both axes (black histogram) showing the interquartile range velocity dispersions (green dashed lines) and the two-component Gaussian mixture model for the velocity dispersion (red dashed lines). The best-fitting velocity dispersions are listed in each case, which for the Gaussian mixture model is the dominant Cyg OB2 component.

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


optical copper lines are free of non-local thermodynamic equilibrium (NLTE) effects (e.g. Mishenina et al. 2002 ). The first indication that something could be wrong with this statement came from Shi et al. ( 2014 ), who noted that the important NLTE mechanism affecting the Cu i spectrum is the ultraviolet (UV) overionization. Later, Yan, Shi Zhao ( 2015 ) investigated copper abundance in 64 late-type intermediate metal-poor stars from Galactic disc and halo. They succeeded in showing that NLTE effects are important for this atom (the correction is about 0.17 dex for metallicity −1.5). The NLTE calculations enhanced the copper abundance obtained in the range of metal-poor stars, giving a flatter distribution of [Cu/H] versus [Fe/H] than was declared in previous works based on the local thermodynamic equilibrium (LTE) assumption. This conclusion was confirmed by Yan et al. ( 2016 ) who stated that NLTE effects are strong for copper in metal-poor stars. Until now, the most comprehensive study of the Galactic evolution of copper in the light of NLTE computation was performed by Andrievsky et al. ( 2018 ). They showed that for a sample of intermediate and extreme metal-poor stars ([Fe/H] from −4.2 to −1.4) the mean [Cu/Fe] value is about −0.22 dex. This is very different from the results of LTE analyses, which show significant underabundance at the early stages of Galactic evolution. Very recently, Roederer Barklem ( 2018 ) performed new work on copper abundance in late-type stars using UV Cu ii lines, which are supposedly free from the influence of the NLTE effect. The Hubble Space Telescope ( HST ) and ground-based spectra were used for this aim. They showed that the mean copper abundance in six warm metal-poor ([Fe/H] from −2.50 to −0.95) dwarfs derived from Cu i and Cu ii lines differs by 0.36 dex (Cu ii lines give higher abundance compared with Cu i lines). Generally, this difference agrees with derived NLTE corrections in metal-poor stars reported by Yan et al. ( 2015 ) and Andrievsky et al. ( 2018 ). In this paper, we examine NLTE copper abundance in a sample of the same six metal-poor stars derived from different Cu i lines (including the far-UV region) and Cu ii lines. We aim to obtain an independent estimate of the reliability of our NLTE corrections, as reported in Andrievsky et al. ( 2018 ). 2 SPECTROSCOPIC MATERIAL We employed UV stellar spectra that were secured with the help of the Space Telescope Imaging Spectrograph (STIS; Kimble et al. 1998 ; Woodgate et al. 1998 ) on board the HST . Observations were made using the E230H echelle grating, the 0.09 x 0.2 arcsec 2 slit and the NUV Multianode Microchannel Array detector.The resolved power was R = 114 000. The investigated Cu i and Cu ii lines are situated in the range 2024−2248 Å. We retrieved archive spectra from the Mikulski Archive for Space Telescopes (MAST). All spectra are centred at 2013 Å. The following lines fall in the spectral range: Cu i 2024 Å and Cu ii 2037, 2055,

B-Wavelength O O O O O B-Model I-Model I-Model 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 B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O B-Model O O O O O O O O B-Wavelength B-Wavelength O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-CelestialObjectRegion I-CelestialObjectRegion 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 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 B-Model I-Model I-Model B-Model O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O B-Model O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O B-Model O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O O O O O B-CelestialObject O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O B-Wavelength O O O O O O O O O O O O B-Model O O B-Telescope I-Telescope I-Telescope O B-Telescope O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O B-Model O O O O O O O O O O O O O O O O O O O B-Wavelength O O O O O O O O O O O O O O O O O B-Model O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O B-Wavelength O O O O O O O O O O B-Instrument I-Instrument I-Instrument I-Instrument B-Instrument B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O B-Telescope O O O O O O B-Instrument I-Instrument I-Instrument O O O O O O O O O B-Instrument I-Instrument I-Instrument I-Instrument I-Instrument O O O B-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O B-Wavelength I-Wavelength O O O O O O B-Archive I-Archive I-Archive I-Archive I-Archive B-Archive O O O O O B-Wavelength I-Wavelength O O O O O O O O O O B-Wavelength I-Wavelength O O O B-Wavelength B-Wavelength


experiments in Rongcheng, along with the measured median profiles, are shown in Fig. 4 . The performance for estimation by the Dewan outer scale is the worst among four models. The estimated by the Dewan model is much smaller than the measured value below 8 km, with an abrupt change occurring at 8 km, and much larger than the measured value above 8 km. For completeness, Appendix A discusses the individual profiles in Rongcheng. The HMNSP99 and Thorpe models have a similar performance for estimation below 12 km, and are consistent with the measured values in both change trend and magnitude. At high altitude, the two models deviate from the measured values by different degrees: a larger deviation above 12 km appeared for sounding experiments for the Thorpe model. The Sθ model has the best prediction results, and it is consistent with the observed median profile in variation trend and magnitude. The relative error profiles for the above four models are illustrated in Fig. 4(b) . The relative error can demonstrate the variation of the deviation between the estimated value and the measured value with altitude. The deviation between the Dewan model and the observed median turbulence is the largest, while that of the Sθ model is the smallest, for all altitudes. The HMNSP99 and Thorpe models have a similar performance in RE (relative error) below 10 km, while HMNSP99 has better results above 10 km. Figure 4. Evaluation of the estimated median profiles (Rongcheng): (a) comparison of the estimated median profiles using the Thorpe (red), HMNSP99 (blue), Dewan (purple) and Sθ (green) models, and the measured profiles (black); (b) relative error of the estimated median profiles. Table 4 presents the RMSE, R xy , and MRE for the estimations of median obtained from the considered four outer-scale models for balloon experiments. The RMSE and MRE of estimated by the Sθ model are better than those for the other three models. It is worth noting that the R xy values of Thorpe, HMNSP99 and Sθ exceed 0.9, which means that the three models may accurately reflect the variation trend of measured turbulence. For the median values, the correlation coefficient of the estimated by the Sθ scale was the highest of all four models. As shown in Table 4 , the average relative error of the median values was generally lower than 1.6%, which meets estimation accuracy requirements for . Table 4. Statistical analysis for the estimation of in Rongcheng using the four outer-scale models, given for median profile. The specific results of the integral statistics of each sounding balloon and median profiles for Rongcheng are tabulated in Table 5 . Clearly, the Sθ scale provides reliable results, close to observed values. As can be seen, our new outer-scale model gives reasonable results when calculating integrated atmospheric parameters. Table 5. Comparison of integrated atmospheric parameters obtained via values observed by meteorological balloons and estimated by the Sθ model

O O B-Location 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 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 B-Location O B-Model O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O B-Model I-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Model I-Model O O O O O O O O O O O O B-Model I-Model O O O O O O O B-Model O B-Model I-Model O O O O O O O O O O O O B-Model O O O O O O O O O O O O O O B-Location O O O O O O O O O B-Model O B-Model O B-Model 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 B-Model I-Model O O O O O O O O O O O O O O O O O O O B-Model B-Model O B-Model O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 B-Location O O O O O O O O O O O O O O O O O O O O O O O O B-Location 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 B-Model I-Model


1843.03. Contours are spaced in 5% intervals in core mass fraction, with darker colors corresponding to high core mass fraction and lighter colors corresponding to low core mass fraction. As expected, denser planets with higher core mass fractions survive to shorter orbital periods. The limiting orbital period of a pure iron planet is approximately 3.8 hr at , 3.6 hr for , and 3.5 hr for . We note that this figure marginalizes over stellar mass because stellar mass only weakly affects the Roche-limiting minimum orbital period (Rappaport et al. 2013 ). The stellar density does, however, affect whether the planet can reach its Roche limit before colliding with the star (i.e., a = R ⋆ ) and thereby the minimum survivable orbital period for the planet. Figure 4. Composition and mass constraints on planets with KOI 1843.03's measured transit radius and host star mass. Colored contours show the values of the planet mass, which increases with decreasing orbital period and increasing core mass fraction. The boundary of the colored contours in the lower left corner corresponds to the Roche limit. The dashed gray line indicates the measured orbital period of KOI 1843.03. Figure 4 displays interpolated planet masses for a range of orbital periods and core mass fractions in systems consistent with KOI 1843.03's host star mass and transit radius. The boundary of the colored contours in the lower left corner corresponds to the Roche limit; as orbital period decreases, the core mass fraction is more tightly constrained. As anticipated, considering a fixed orbital period in Figure 4 , increasing the planet’s iron mass fraction increases the planet’s mass. Less intuitively, at fixed core mass fraction, decreasing the planet’s orbital period also leads to an increase in the inferred planet mass. This is due to the tidal distortion of the planet; at shorter orbital periods, the volume of the planet exceeds by larger and larger factors. As it orbits less than one stellar radius from the host star’s photosphere ( a / R ⋆ = 1.9), KOI 1843.03 will be significantly elongated in the direction of the star due to tidal distortion. Based on the parameters of KOI 1843.03, our models predict that it must be at least 31% longer along the star–planet line than along the perpendicular axes (aspect ratio of about 1.3), and our models support a value up to nearly twice as long along the star–planet line (aspect ratio of almost 1.8); various possibilities are illustrated in Figure 5 . For comparison, Saturn has an aspect ratio of about 1.1. Figure 5. Aspect ratio constraints on KOI 1843.03, as a function of core mass fraction. To the left of the plot, we indicate the maximum and minimum values of aspect ratio supported by the model grid and show three representative planet cross-sections (assuming ellipsoidal shapes); peach and navy represent the iron-dominated core and silicate mantle, respectively. Results are shown both at the measured transit radius 0.61 and the 1 σ limits

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


structure is completely determined by the conservation of rest-mass, energy, and angular momentum of the accreting gas, the Polish donut model is less constrained. It requires the relation between the fluid angular velocity and the fluid angular momentum per unit energy, Ω = Ω ( l ), as well as the fluid angular momentum per unit energy at the inner edge of the disk, l in . The simplest Polish donut model is the configuration with l = constant, which turns out to be marginally stable with respect to axisymmetric perturbations (Font Daigne 2002 ). Accretion disks in the Kerr spacetime only exist for l ms l l mb , where l ms and l mb are, respectively, the angular momentum per unit energy of the marginally stable equatorial circular orbit (or ISCO) and of the marginally bound equatorial circular orbit (Abramowicz et al. 1978 ; Bardeen et al. 1972 ; Li Bambi 2013 ). Indeed, for l l ms , the fluid angular momentum is too low and there is no stable accretion disk (the fluid directly plunges onto the black hole), while, for l > l mb , the fluid angular momentum is too high and there is no accretion (there is just a fluid rotating around the black hole). In the presence of an accretion disk, when , the inner edge of the disk, R in , is between the marginally bound orbit and the ISCO, i.e., R mb R in R ISCO (Bardeen et al. 1972 ; Abramowicz et al. 1978 ; Li Bambi 2013 ); that is, for a given black hole spin, the inner edge of a Polish donut disk is always smaller than the inner edge of a Novikov–Thorne disk. Since the exact location of the inner edge of the disk is crucial in reflection spin measurements, we can already suspect that systematic uncertainties related to the use of an incorrect disk model to fit the data of a source can be important. 3. Simulations and Fits In order to estimate the impact of the disk structure on spin measurements with the iron line method, we use the code presented in Riaz et al. ( 2020 ) to calculate the theoretical reflection spectrum of a Polish donut disk. We use the xillver model (García Kallman 2010 ; García et al. 2013 ) to calculate the nonrelativistic reflection spectrum at the emission point in the rest-frame of the gas in the disk, and we use our ray-tracing code to convolve this nonrelativistic spectrum into a relativistic spectrum of a thick disk. At this point, we need to choose the properties of our source and of our instruments to simulate the observation of a black hole with a thick accretion disk. As X-ray mission, we consider NICER (Gendreau et al. 2016 ), which has a good energy resolution near the iron line and is thus suitable for X-ray reflection spectroscopy measurements. We assume that the source has a very simple spectrum, just a power-law component and a reflection component. In XSPEC language (Arnaud 1996 ):where TBABS takes the Galactic absorption into account (Wilms et al. 2000 ), powerlw is the power-law component generated by inverse Compton scattering of thermal photons from the disk off

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


broadly consistent with the predictions of Fairhurst ( 2011a ). While the inclusion of LIGO-India was not examined in Fairhurst ( 2011a ), we recover a median localization of 9.3 deg 2 for the HIKLV network. 4.3. Comparison with Previous Studies We can compare our result to several studies of advanced network sky localization that have already been performed. We compared our results to those from analytic expectations of Wen Chen ( 2010 ) and Fairhurst ( 2011a ) throughout Sections 4.1 and 4.2 , respectively. The expression used to calculate the expected error regions from Wen Chen ( 2010 ) produces values that are consistent with both Fairhurst ( 2011a ) and our studies. In addition, our study remains broadly consistent with the analytic results of Vitale Zanolin ( 2011 ), recovering similar scalings in localization improvement for successive detector networks for a canonical BNS to our results in Table 2 . Studies such as Singer et al. ( 2014 ) have examined the sky localization capabilities of two- and three-interferometer networks of LIGO and LIGO–Virgo, using more realistic assumptions. In particular, they carried out an end-to-end study of the localizations from the outputs of one compact binary search pipeline used in the first two observing runs (Messick et al. 2017 ). They use a stream of data with colored, but Gaussian, noise and apply a minimum network S/N cut of 12 for each event. Singer et al. ( 2014 ) projected that Virgo would join the LIGO instruments during the second observation run at the sensitivity indicated in Abbott et al. ( 2016b ). They examine a population of BNSs in the HLV configuration, obtaining a median sky localization of 235 deg 2 at the 90% credible level. For our study of NSBH localization, we obtain a median sky localization of 193 deg 2 , seemingly contrary to the expectation that BNS sources are better localized than NSBHs. However, the fiducial networks in our study are have better sensitivities over a given frequency range compared to Singer et al. ( 2014 ), leading to improvements in the effective bandwidth measured by a given instrument. So, our improved localization from that predicted by Singer et al. ( 2014 ) can be attributed to our use of 2018-era instruments as opposed to the less-sensitive 2016 configuration used in Singer et al. ( 2014 ). Rodriguez et al. ( 2014 ) resolve sky localization for a BNS population in which each event realizes a network S/N of 20. On the contrary, our NSBH study samples a wide distribution of network S/Ns, meeting a minimum S/N threshold. 6 6 We require an S/N of at least 5.5 in the second-loudest detector. Therefore, our study probes the S/N regime at which detections are most likely to occur, while Rodriguez et al. ( 2014 ) ignores this low network S/N range. Nevertheless, our Figure 1 is qualitatively comparable to Figures 6 and 7 in Rodriguez et al. ( 2014 ). In particular, the increased isotropy of a three- to four-instrument network and the subsequent,

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, H β and H α , and narrow [O iii ] λλ 4959, 5007, and Balmer lines. The absorption features around 5450 Å are telluric. The arc spectrum shows some narrow emission lines, such as [O ii ] λ 3728, H β , [O iii ] λ 5007, H α , and [N ii ] λ 6583, and some weak absorption lines, such as Ca ii K λ 3933 and Ca ii H λ 3968. The arc spectrum is contaminated by the QSO, showing broad H α and Mg ii lines (see Section 2.2.2 for details). The redshift of the QSO is measured to be 0.3954 ± 0.0001 from the [O iii ] λλ 4959, 5007 emission lines. The redshift of the arc, using the QSO-contamination-subtracted spectrum, is measured to be 0.3970 ± 0.0001 via [O ii ] and H β emission lines, and consistent with the value of 0.3968 ± 0.0003 measured via the Ca ii K λ 3933 and Ca ii H λ 3968 absorption lines. The arc is likely located nearer than the QSO and moving toward it with a line-of-sight velocity of roughly 340 km s −1 . Figure 4. VLT FORS2 spectrum of the QSO PHL 6625 with model components. We fitted the spectrum from 2750 to 7100 Å, where the S/N is high. The windows used to fit the continuum are marked in black bars, and pixels with telluric absorptions around 5450 Å were excluded in the fitting. The dereddened spectrum is shifted to the rest frame of the QSO at z = 0.3954. Purple: power law; yellow: pseudo-continuum = power law + Fe ii templates; red: summed line model; blue: narrow-line components; green: broad-line components. Figure 5. VLT FORS2 dereddened spectrum (black) of the arc galaxy with the QSO contamination (blue), the galaxy population synthesis model (green), and the total model (red). All emission lines and telluric absorptions are masked during the population synthesis fit. The dereddened spectrum is shifted to the rest frame of the arc at z = 0.3970. 2.2.1. Decomposition of the QSO Spectrum The QSO spectrum is decomposed into multiple emission components following Shen et al. ( 2008 ). The fitting is performed in the rest-frame wavelength range of 2750–7100 Å, where the S/N is sufficiently high. First, a pseudo-continuum was fitted to the spectrum in some continuum windows 12 12 2925–3500 Å, 4200–4230 Å, 4435–4700 Å, 5100–5535 Å, 6000–6250 Å, and 6800–6900 Å at the rest frame. , consisting of a power-law component and Fe ii templates in both the Mg ii region (Salviander et al. 2007 ) and the H β region (Boroson Green 1992 ). The continuum-subtracted line spectrum was then fitted with multiple Gaussian components: three Gaussians for each of the H α , H β , and Mg ii broad components; five Gaussians for narrow lines in the H α region; 13 13 Two for [S ii ], two for [N ii ], and one for narrow H α . three near H β; 14 14 Two for [O iii ] and one for narrow H β . and one for narrow Mg ii . All of the narrow lines are imposed to have the same shift and width. The monochromatic continuum luminosity λL λ of the power-law component at the rest frame 3000 and 5100 Å, the power-law spectral index, and the broad-line width derived from the

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


acceleration. Our inference above is qualitatively different from these models in the sense that it is independent of SNe event in a star cluster. We also note that LOFAR observations show PeV CRs to be enriched in low-Z nuclei (Buitink et al. 2016 ), consistent with their being accelerated from CNO enriched wind material in SBs (Thoudam et al. 2016 ). It is also possible that the hard component of CRs due to WTS is the one inferred to be present in molecular clouds (de Boer et al. 2017 ). Therefore, WTSs are potential PeVatrons and they should be studied in detail in this regard. 5.5 Decoupling of grammage from ISM Our proposed scenario can also provide the astrophysical framework for the phenomenologically motivated models of CR propagation in which the grammage traversed by CRs are mostly near the source (Blasi Serpico 2009 ; Cowsik Madziwa-Nussinov 2016 ; Eichler 2017 ; Biermann et al. 2018 ). In these models, the diffusion property of CR particles is assumed to be different inside the ‘cocoons’ surrounding the CR acceleration sites than elsewhere in the ISM in order to alleviate problems associated with secondary production. The scenario of CR acceleration in SBs satisfies the basic premises of these models, since most of the CR collisions occur in the outer shell of shocked ISM, whereas CRs are advected by the wind in the inner regions. The grammage suffered by CRs in the shocked ISM region is ∼10 g cm −2 , comparable to the total grammage of GCR (Gabici et al. 2019 ), since the typical residence time is t r ∼ 1 Myr (∼κ/ v 2 , for a diffusion coefficient κ ∼ 10 27 cm 2 s −1 and v ∼ 50 km s −1 , the typical outer shock speed), and typical density in this region is ∼10 cm −3 . Therefore, CR grammage can be decoupled from Galactic residence time, alleviating a number of outstanding problems (Butt 2009 ; Gabici et al. 2019 ). Instead of listing them all, we mention one of the problems here, that of the observed scaling of light elements with metallicity in halo stars (Parizot Drury 1999 ). In the case of isolated SNRs (which accelerates ISM particles), the Li/Be/B abundance is expected to scale as Z 2 , since both CR and the target gas share the same metallicity. In the case of WTS, the metallicity of CRs is independent of that of the ambient ISM, the abundance of spallation products should scale as Z , as observed (Parizot Drury 1999 ). 5.6 Caveats and future directions In this study, we show the first calculations for estimating the energetics of the wind and SN shocks in isolated stars/star clusters. We have used a shock detection algorithm and three different tracers to quantify the fraction of shock energy processed by wind, SN ejecta, and ambient material. Although in the above sections, we have shown that this study has succeeded in revealing answers to various problems in GCRs, below we highlight some of the limitations of our models and future directions. Non-radiative strong shocks: We have considered the Rankine–Hugoniot

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effect saturates in the DML, so MOND can provide only a limited amount of additional stability even for a galaxy with arbitrarily low surface density. This might explain why low surface brightness disk galaxies often have spiral features (McGaugh et al. 1995 ), usually taken as a sign that disk self-gravity is important (Lin Shu 1964 ; Das et al. 2020 ). The global stability of disks thus offers a promising way to break the CDM-modified gravity degeneracy in galaxies. M33 is one of the nearest galaxies with a rather low surface brightness. S19 recently conducted isolated N -body and hydrodynamical (hydro) simulations of M33 in the CDM context. As with many other galaxies, its observed RC required them to use a cored DM profile. They found it rather difficult to explain the weak observed bar together with the two-armed spiral (Corbelli Walterbos 2007 ) in the presence of a live CDM halo. Weak bars are also observed in many other galaxies (Cuomo et al. 2019 ). They are problematic in the CDM picture because a bar in the baryons creates a response in the live DM halo, which would cause a resonant effect (Athanassoula 2002 ). This was demonstrated explicitly by S19 , who compared their live halo simulations to a “frozen halo” simulation in which the DM particles provide a fixed gravitational potential. 7 7 This can be thought of as the DM particles providing gravity but not moving. S19 showed that M33 would be more stable in a frozen halo, leading to a weak bar similar to that in the observed M33. Such a model is of course unphysical in the ΛCDM context, but useful to better understand the dynamics. Interestingly, a frozen halo is somewhat similar to gravity theories like MOND where galaxies lack hypothetical DM. This is because features in the disk very rapidly become irrelevant to the potential as one moves away from its plane. Consequently, perturbations in the disk have very little effect on the Milgromian “phantom DM” (PDM) halo because its density depends only on the local potential. 8 8 PDM is the DM density distribution that would be needed for the Newtonian gravitational field to equal the MOND one of the baryons alone. The PDM distribution of thin exponential disks was visualized in, e.g., Lüghausen et al. ( 2013 , 2015 ). Indeed, this is why a bare disk can be stable in MOND. The lack of an actual DM halo automatically removes the possibility of bar–halo angular momentum exchange. However, disk self-gravity is enhanced in MOND compared to the case of a frozen DM halo. The presence of an EFE would slightly decrease this enhancement, but would also decrease the spheroidal potential support from the PDM. In general, it would also break the axisymmetry and up–down symmetry of the problem. Clearly, numerical simulations are needed to properly understand how disk stability is influenced by a fundamental modification to the gravity law. Several MOND N -body simulations have considered isolated disks, starting with the seminal work of Brada

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little variation of A e with rotation. The peak values are also quite different: 150 per cent for HD 37776, 50 per cent for HD 189775, and only 10 per cent for HD 175362. Stars with highly variable A e likely exhibit greater surface abundance anisotropies than stars in which A e is less variable. In order to obtain a single number with which to characterize the average strength of deviations between the magnetic curves derived for different elements for a given star, we used the idl curvefit routine to generate second-or third-order harmonic best fits, which were then integrated as functions of rotational phase. The significance of this integrated value is then A e /σ e , which is given for each star in the second-last column of Table 2 , where σ e is the mean uncertainty in the individual A e measurements. If A e /σ e 1, it can be concluded that differences in 〈 B z 〉 between different elements are a consequence of noise rather than real variations. It is this significance in which we are interested, as it will help to decide whether accurate measurements are available using metallic lines, or whether H lines should be used instead. Fig. 9 shows the histogram of A e /σ e for all stars. For the full sample (top panel), the median significance is 2.7σ. For the sub-sample of He-weak and He-strong Bp stars, the median of the distribution is at 2.9σ (second panel from the top). Amongst pulsating β Cep and SPB stars (third panel from the top) and the remainder of the sample with no apparent peculiarities (bottom panel), only one star, HD 96446, has A e /σ e ≥ 3: as HD 96446 is also a He-strong star, this likely reflects the star's chemical peculiarities. The medians of these distributions are 1.4σ and 1σ, respectively. While there are only eight non-chemically peculiar stars for which A e could be measured, these results are consistent with an origin of the effect in distortion due to chemical spots, and confirm that when chemical peculiarities are not present, there is no significant difference in 〈 B z 〉 when measured using different chemical elements. Even amongst the Bp stars, although there are several stars for which A e /σ e ≫ 3, differences in 〈 B z 〉 measured from different elements are negligible for many of the stars. Figure 9. Significance histogram for A e for (top–bottom) all stars in the sample for which A e could be measured, Bp stars, pulsating stars, and chemically normal, non-pulsating stars. The dashed line marks 3σ significance. Approximately half the sample shows at least a 3σ spread in 〈 B z 〉 measurements conducted with different elements. All of these are Bp stars: the only pulsator with A e /σ e ≥ 3 is HD 96446, which is also a He-strong star. It should be noted that while the mathematical treatment of A e is based upon random uncertainties, these variations are in fact systematic . Unfortunately, it is not obvious what simple mathematical tools might be utilized in order to capture the systematic variations between

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5.2. Comparison with the IRSF monitoring data in the SMC The NIR monitoring data for three stars has recently been published by Ita et al. (2018) using the InfraRed Survey Facility (IRSF, Kato et al. 2007 ). These data were not used in our LC analysis and can therefore serve as an independent test. The K -band data ( H band for 12.627600 −72.858307) were analysed in the same way as the VMC data and literature data. Table 2 compares the periods and amplitudes. For the first two stars the agreement is good. In the last case the periods do not agree within their mutual error bars, but this is a faint source for the IRSF survey ( K ∼ 15.5 mag), while our analysis might be hampered by the relatively small number of data points (18 in total). Table 2. Comparison with three sources in the IRSF survey. Notes. (a) In the K band. 5.3. LPVs with periods over 1000 days Of the likely AGB stars, 34 stars have periods longer than 1000 days 6 . The longest period we find is 3108 d, but this object has alternative periods that are much shorter. Six other stars also have shorter possible periods, and therefore the periods beyond 1000 days are only tentative in these cases. It will be interesting to analyse the IRSF data for the LMC objects when they become available (cf. the SMC data presented in Ita et al. 2018 ). Nine stars with periods over 1000 days in the MCs were previously reported by Wood et al. (1992) and Whitelock et al. (2003) based on NIR observations. Recently, Menzies et al. (2019) presented a compilation of Miras with periods over 1000 days in the Milky Way (17), SMC (3), and LMC (18), while Karambelkar et al. (2019) published a list of 417 luminous IR variables, of which 86 have periods over 1000 days, located in seven galaxies (the majority in M 83 (49 objects), and M 81 (11 objects)). The compilation by Menzies et al. (2019) was based on Wood et al. (1992) and Whitelock et al. (2003) , OGLE data in the SMC and LMC ( Soszyński et al. 2011 , 2009a ), and GS18 (which is partly based on a preliminary analysis of VMC data). Of the 21 MC objects, 18 are confirmed with updated periods. Three objects are not in our list. One object (IRAS 05506−7053) is too red; the period in GS18 is based on WISE data. The two others (HV 888 and HV 11417) are too blue to have passed the selection criteria, and both have been classified as RSGs (GS18, Kraemer et al. 2017 ). The longest period in the study of GS18 of almost 400 AGB stars with Spitzer IRS spectra is 1810 d based on a re-analysis of OGLE-III data for MSX SMC 055 (also known as OGLE-SMC-LPV-08137 and IRAS 00483−7347). No errors on the period are given in GS18 because they are very hard to reliably estimate for these long periods. The period in the OGLE-III release is 1859 d, which gives some indication of the uncertainty. In Groenewegen et al. (2009) such a long-period has been recognised based on OGLE-II data and, it was suggested that the object may be a candidate super-AGB star, based on its

O O O O B-Telescope O O O O B-CelestialObject O B-Wavelength O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O O B-Telescope I-Telescope I-Telescope B-Telescope B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O B-Wavelength I-Wavelength O O B-Wavelength I-Wavelength O B-CelestialRegion I-CelestialRegion O O O O O O O O B-Survey O O O O O O O O O O O O O O O O O O O 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 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 B-Survey I-Survey 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 B-Telescope O O O B-CelestialObject O O O O O O O B-CelestialObject 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-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O B-Wavelength O O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O B-CelestialObject I-CelestialObject O B-CelestialObject O O B-CelestialObject O O B-Citation I-Citation I-Citation I-Citation O O O O O O B-Wavelength O O O O O O O O O O O O O O O O B-CelestialObject I-CelestialObject O O O B-CelestialObject I-CelestialObject O O O O O B-Citation I-Citation I-Citation I-Citation O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O B-Survey O O O B-CelestialObject O B-CelestialObject O B-Citation I-Citation I-Citation I-Citation O B-Citation O O B-Citation O O O O O O O O O B-Survey 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 B-Citation O O O B-Telescope O O O O B-CelestialObject I-CelestialObject O B-CelestialObject I-CelestialObject O O O O O O O O O O O O O O O O B-Citation B-Citation I-Citation I-Citation I-Citation O O O O O O O O B-Citation O O O O O O B-Telescope B-Instrument O O O O O O O O O B-Survey O O B-CelestialObject I-CelestialObject I-CelestialObject O O O B-CelestialObject O B-CelestialObject I-CelestialObject 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 B-Survey 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-Survey O O O O O O O O O O O O O O O O O


the 12 CO line profiles are dominated by infall and outflow motions and we find no significant evidence of rotation in the outflow. As mentioned in Sect. 3.2 , however, CH 3 OH and SO 2 do show clear evidence for rotation within ~16 au ( Fig. 8 ). This emission originates in the central region, where it appears that material is infalling and rotating simultaneously. Even so, the velocity gradients measured from the CH 3 OH and SO 2 lines are consistent with one another, and thus one might expect that the outflow should rotate in the same sense. A 12 CO moment 1 map ( Fig. A.3 ) and line profiles at different positions ( Fig. 4 ), meanwhile, do not show any significant difference in the velocities between northern and southern outflow cavity walls. In the redshifted outflow, however, there is a blueshifted component at small separations (≲30 au) south-west of the protostar ( Fig. 3 ), consistent with the inferred rotation seen in SO 2 and CH 3 OH. Likewise, a redshifted component is observed in the blueshifted outflow on comparable scales, but this component is seen along the jet axis and not the north-western side as would be expected if this component was due to rotation in the outflow. Attributing the inner features to rotation is in any case difficult since the outflow is nearly in the plane of the sky, and expansion of the outflow, deviations of the outflow axis from axisymmetry, or internal shocks (e.g. Fendt 2011 ) can produce similar features. Hints of expansion are indeed seen in the lowermost PV diagram of Fig. 9 , where an extended U-shaped structure is observed at blueshifted velocities. Although this emission structure barely exceeds the 3 σ threshold, itis clear that the velocity is increasing towards the outflow axis. A similar feature is found on the redshifted side at slightly lower S/N, and lower velocities. While an onion-layered velocity structure (whereby velocities close to the outflow axis are high and then fall off with distance) is expected for a rotating, magnetically-launched wind (e.g. Bacciotti et al. 2002 ; Pudritz et al. 2006 ), the symmetry of the PV diagram w.r.t. the zero position offset in the lowermost panel of Fig. 9 is not consistent with this picture. It is, however, consistent with expanding cavity walls. The rotation and expansion velocity at different offsets from the protostar can be estimated using the method presented in Lee et al. (2018) , assuming that only two velocity components are present. While this is an oversimplification of reality, assuming the outflow velocity does not change significantly over the considered distances, it does provide a useful method to deduce any trends in rotation and expansion. We fit 2D Gaussians to several PV diagrams with cuts perpendicular to the outflow axis but with different offsets. One example of such a fit (at zero offset from the continuum peak) is presented in the uppermost panel of Fig. 9 ). We only consider pixels where the emission is above 3 σ ,

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


2009 ), which assumes that all LyC flux converts to unbinding the atmosphere. The LyC flux corresponds to the energy-limited mass-loss rate . In this case, the adiabatic cooling rate is and still has a less than 15% effect in the region of main concern. 8.2. Comparing with Other Hot Jupiter Upper Atmosphere Models Christie et al. ( 2013 ).—The present study agrees with the conclusion in Christie et al. ( 2013 ) that the 2 p occupation is set by radiative excitation and de-excitation, and as an improvement, we include an Ly α radiation transfer inside the atmosphere instead of applying a constant solar Ly α intensity. Because of the ∼30 times stronger stellar Ly α intensity of HD 189733 compared to the Sun and considering the Ly α photons generated inside the atmosphere owing to collisional excitation and recombination cascades, the Ly α mean intensity should be ∼100 times larger for the majority of the atomic layer. In addition, because Christie et al. ( 2013 ) underestimate n 2 p by a factor of 20 owing to a math error, n 2 p should be significantly larger in the whole simulation domain, and thus the atmosphere is optically thick to H α mainly owing to the absorption of H(2 p ). The observed H α absorption width agrees well with an optically thick atmosphere model. Because of the much larger , the photoionization of H(2 l ) is larger compared to photoionization of the ground state in the atomic layer. Hence, n e and n p in this work are ∼10 times larger. Considering the proton collisional l -mixing process with a rate ∼10 times larger than the electron collisional process, as well as the large H(2 p ) population, the creation of 2 s hydrogen is dominated by l -mixing rather than collisional excitation considered in Christie et al. ( 2013 ). As a result, 2 s and 2 p reach collisional equilibrium. In addition, it is shown that the metal lines are crucial in cooling the atmosphere. Assuming solar abundance, lines of Mg and Na can cool the atomic layer by ≃2000–3000 K. Menager et al. ( 2013 ).—Menager et al. ( 2013 ) investigate the Ly α emission and reflection by the atmosphere of HD 189733b. The temperature and electron, hydrogen, and helium number density profiles of HD 189733b from the Koskinen et al. ( 2011 ) unpublished model were applied. The temperature, n e , n p , and are in broad agreement with the profiles presented in this paper in the corresponding pressure range. According to a similar model of HD 209458b presented in Koskinen et al. ( 2013a ), it should be a one-dimensional hydrodynamic model of the upper atmosphere considering hydrogen and helium constructed on top of a full photochemical model of the lower atmosphere. They chose the average solar flux as their stellar spectrum, which is ∼10 times smaller than the synthetic spectrum from MUSCLES. Different from the photoelectron heating efficiency calculated at the fixed ionization fraction x e = 0.1 throughout the model, or a constant η applied in Koskinen et al. ( 2013a ), a

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


spectrum (Figs. 2 and 3 of Ho et al. 2003 ), while atomic hydrogen transitions may produce additional features. That may explain some of the observed multiple lines. In view of the limited significance of the line detections it appears difficult to make specific assignments. Another way to explain multiple lines is to invoke – beyond the radiation from the hot cap at the magnetic dipole – separate hot spots on the stellar surface having higher multipolar magnetic fields. The first strong evidence for this comes from the discovery of strongly phase-variable absorption lines which are visible only for about 20% of the neutron star rotation. The lines were detected in the X-ray spectra of RX J0720.4−3125 and RX J1308.6+2127 ( Borghese et al. 2015 , 2017 , respectively) and have energies a factor of ∼2.5 higher than the broad lines (Table 3 ). Such multipole fields must be quite young compared to the age of the NS. They may be formed by extracting magnetic energy from the toroidal field that resides in deep crustal layers, via Hall drift (e.g., Geppert Viganò 2014 ). We conclude that proton cyclotron lines produced in strong magnetic fields of isolated neutron stars can explain the absorption-type features observed in the soft X-ray spectra of young isolated neutron stars of the M7 class. More accurate measurements in the future in combination with further theoretical work on magnetized atmospheres and the magneto-thermal evolution of neutron stars are required to make further progress in this exciting field. 9. Summary With this contribution we attempt to provide a review on the current state of our knowledge about X-ray sources that show cyclotron line features in their spectra – both for electron cyclotron lines (this is by far the larger part) and for proton cyclotron lines. We concentrate on the observational aspects, providing a number of Tables that contain detailed informations on all sources that we consider reasonably well secured regarding the existence of cyclotron lines. In the case of electron cyclotron lines – observed from binary X-ray pulsars, highly magnetized accreting neutron stars in binaries – we also give a Table with candidate sources, mostly objects for which a detection of a cyclotron line was claimed some time ago, but had not been confirmed in subsequent observations, or sources that were observed rather recently, but only once and with somewhat peculiar properties. On the other hand: for some of the objects listed in the main Tables, the existence of a cyclotron line still needs confirmation (or not) through re-measurements (with a finite probability that they have to be moved into the candidates category). We try to address the basic physics underlying the cyclotron line phenomenon, including a large number of references to theoretical work, with some coverage of specific theoretical modeling. Since the discovery of the first CRSF in Her X-1 in 1976, a new field of Cyclotron Line Research has evolved. With the rather

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


multilayer system. In general, unlike the symmetric case studied, e.g., by Roberts ( 1981b ), the dispersion relation Equation ( 15 ) cannot be decoupled into two equations that correspond to the well-known sausage (oscillations at the slab boundaries in antiphase, that correspond mathematically to the equation containing ) and kink (perturbations of the slab boundaries oscillating in-phase that correspond to the equation with ) MHD waves. Solutions to Equation ( 15 ) will provide modes modified by the density difference at the sides of the magnetic slab similar to a single asymmetric slab investigated by Allcock Erdélyi ( 2017 ). We adopt the notions of quasi-sausage and quasi-kink to describe these eigenmodes, because they have mixed characters. The slab cross-sectional width, that is constant for symmetric kink modes, is affected for asymmetric kink modes and the line of zero perturbation is shifted for asymmetric sausage modes when compared to the symmetric case, namely, the center of the slab. Furthermore, both the sausage and kink modes can be further categorized as body and surface modes. Surface waves exist when , which corresponds to evanescent solutions of Equation ( 5 ), while body waves exist when , which corresponds to spatially oscillatory solutions. This nomenclature for wave classification was introduced by Roberts ( 1981b ) for symmetric and Allcock Erdélyi ( 2017 ) for asymmetric equilibria. Let us now consider some specific cases of an asymmetric multilayered plasma slab structure that are analytically solvable and have potential for solar application. First, by setting p = q = 0, we verify that the dispersion relation reduces to that which governs the asymmetric slab configuration of Allcock Erdélyi ( 2017 ), namely,We will now focus on cases of two layers (one magnetic and one nonmagnetic), and three (a magnetic layer sandwiched between two nonmagnetic) slabs, respectively, and investigate how the multilayered structure affects the eigenmodes and their eigenfunctions. 2.1 Two-slab Case Let us first consider the case of two slabs, represented by p = 1 and q = 0, which is illustrated by Figure 2 . The width of the nonmagnetic and magnetic slabs are denoted as and d 0 , respectively. Such a model could be useful for modeling MHD waves in MBPs of the solar photosphere (as shown on Figure 3 ). MBPs are approximately vertical magnetic structures between supergranule convection cells of different densities and temperatures. Since neighboring granular cells affect the MBP, we can apply a two-slab description to analyze what will change when comparing eigenmodes to MHD waves in a single slab case. Figure 2. Equilibrium configuration for a two-slab case: a magnetic slab, , and a nonmagnetic slab, . Figure 3. Asymmetric multislab approximation for an elongated MBP, based on Figure 11 of Liu et al. ( 2018 ), observed by the New Vacuum Solar Telescope in TiO 7058 Å. From condition ( 15 ), we obtain the dispersion relationNote, that the

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


been identified by IE methodology, where the IE is less than 1.5%. c ( N IE /Total) × 100%. The same study explained in the above paragraph was performed with two other identifiers of MCs (see Huttunen et al. 2005 , their Table 2, and Wu et al. 2003 , /WIND list). In Table 3 , the results are shown in the last two columns. The low successfulness (55.5%) with Huttunen et al. ( 2005 ) has an explanation. The IE methodology was unsuccessful in four events: one event was identified as a cloud candidate (cl) with a time extension of eight hours; two events were classified as MCs, however, on that date ICMEs were not reported; and the last MC was also identified by Wu et al. ( 2003 , /WIND list, event 42 (September 21) with poor quality (3) and with a time extension of seven hours. 4.1.5. False Alarm Cases Furthermore, we saw false alarm cases. False alarm cases are grouped into three categories: (1) non-MC ICMEs according to the catalog of Richardson Cane ( 2010 , Table 3) (20 of these cases were identified); (2) stream interaction regions (SIRs) according to the catalog of Jian et al. ( 2006 , p. 367–371), where 36 SIRs were identified; (3) other cases (non-MC ICMEs and non-SIRs). In Table 4 , the previous categories are shown. In the first category, 15% of false alarms are reported. This is important and can save time, e.g., when a specialist wants to identify new MCs in a large data period. These three cases could be MC-ICME; however, they are not studied in this work. Table 4 Summary of Events That Are Not MCs Reported in 1999 and False Alarm Cases in the IE Analysis Notes. a Number of false alarm cases, i.e., where . b Percent of false alarm cases /Total) × 100%). c Adapted from Richardson Cane ( 2010 , Table 3), from 33 ICMEs: 13 were MCs-ICMEs and 20 were non-MC ICMEs. d Jian et al. ( 2006 , p. 367–371). In the second category, there is only one false positive case. In summary, the IE methodology is not useful to identify SIRs. Finally, five cases are in the third category. These cases are interesting because disturbances in the IMF can be observed. In addition, we are left with two open questions. What really are these events? Why do they have low IE values, similar to an MC? We think that these cases could be flux ropes. However, further study should be done to investigate the above cases. In summary, the IE methodology identified 9 from 13 MCs, and nine false alarm cases are emitted. In a year (1999), a total of 788 windows of 2500 values exist, which means that the percent of false alarms was 1.14%, which is a good result. However, we prefer to propose it as a preliminary result because one year is considered poor statistics to accept the result as a robust identifier of MCs. Despite the difficulties, we can conclude that the IE methodology is useful for studying MCs, and in the next section, the IE methodology is used to identify two MCs. 4.2. Results: Part II After tests on efficiency, the methodology is applied to study some SW

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


an order of magnitude lower just by increasing the disc viscosity by a factor of 3–6 (Stehle 1999 ). Therefore, while increasing the disc temperatures increases the opening angle of the resulting spiral arms (e.g. Makita, Miyawaki Matsuda 2000 , and references therein), increasing the disc viscosity seems to have a similar (and seemingly stronger) effect. The point we make here is that wide open spiral arms may be more a signature of a high viscosity disc than of a hot disc, and that a large disc viscosity might lead to detectable, wide open tidally induced spiral density waves even when the disc is relatively cool and small. Thus, the detection of spiral arms in V2051 Oph during quiescence suggests that its quiescent accretion disc has high viscosity. This is in line with the results of Baptista Bortoletto ( 2004 ) – which inferred a high viscosity α ≃ 0.1−0.2 for the quiescent accretion disc of V2051 Oph – and with those of Baptista et al. ( 2007 ) – which suggest that the outbursts of V2051 Oph are the result of bursts of enhanced mass transfer on to a high-viscosity accretion disc. 5 SUMMARY Infrared JHK s quiescent light curves of V2051 Oph after removal of the ellipsoidal contribution from its mass donor star show an out-of-eclipse double-wave modulation the amplitude of which increases with wavelength. Eclipse maps derived from these light curves reveal two asymmetric arcs extended in azimuth at the intermediate/outer disc regions, which are reminiscent of those seen in eclipse maps of the dwarf nova IP Peg in outburst and are similarly interpreted as tidally induced spiral density waves in the V2051 Oph accretion disc. In agreement with this interpretation, the maxima of the double-wave modulation coincide with the binary phases where the spiral arms are seen face-on. The spiral arms are located at different distances from disc centre; the inner arm is at an average radius of (at a corresponding Keplerian velocity of ), while the outer arms is at . We estimate the opening angle of these spirals to be θ s = 21° ± 4°. The detection of wide open spiral arms in V2051 Oph during quiescence suggests that its quiescent accretion disc has high viscosity. Broad-band JHK s disc spectra were extracted for concentric annular disc regions. The inner disc atmosphere () is made of hot and tenuous gas ( and surface densities ), suggesting that either an extended hot and tenuous chromosphere veils the emission from an underlying, colder accretion disc or that the inner disc itself has evaporated into a hot and tenuous corona. The disc gas becomes cold and opaque in its outer regions (). The spiral arms are hotter and have lower column densities than the disc at same radial range, with differences within the 2σ confidence level. The JHK s best-fitting hydrogen continuum emission models are in very good agreement with the B -band observations of Baptista Bortoletto ( 2004 ), suggesting that the inner disc regions were also optically thin and with

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