With our joint analysis of stellar mass fraction and source size, we find a larger stellar mass fraction than earlier statistical studies. In FigureÂ 2, we compare our determination of the stellar surface density fraction to a simple theoretical model and to the best fit of a sample of lens galaxies by Oguri etÂ al. (2014). The simple theoretical model is the early-type galaxy equivalent of a maximal disk model for spirals. We follow the rotation curve of a de Vaucouleurs component for the stars outward in radius until it reaches its maximum and then simply extend it as a flat rotation curve to become a singular isothermal sphere (SIS) at large radius (see details in the Appendix). The ratio of the surface mass density of the de Vaucouleurs component to the total surface mass density is shown as a dashed curve in FigureÂ 2. We also show as a gray band the best fit for the stellar fraction in the form of stars determined by Oguri et al (2014) in a study of a large sample of lens galaxies using strong lensing and photometry, as well as the best model using a Hernquist component for the stars and an NFW halo for the dark matter with and without adiabatic contraction, also from Oguri etÂ al. (2014). We have used the average and dispersion estimates for the Einstein and effective radii available for 13 of the objects in our sample from Oguri etÂ al. (2014), Sluse etÂ al. (2012), Fadely etÂ al. (2010), and LehÃ¡r etÂ al. (2000; see TableÂ 1) as an estimate of RE/Reff in FigureÂ 2. The average value and dispersion of the sample is RE/Reff = 1.8 Â± 0.8. This also averages over the different radii of the lensed images. The agreement of our estimates with the expectations of the simple theoretical model and with estimates from other studies (Oguri etÂ al. 2014) is quite good. For comparison, the estimate of Pooley etÂ al. (2012; using the Einstein and effective radii estimates for 10 out of 14 of their objects from Schechter etÂ al. 2014) seems somewhat lower than expected at those radii. The range of stellar mass fractions from MED09 for source sizes in the range 0.3â15.6 light days is also shown in FigureÂ 2. In this case, the discrepancy between our estimate and their reported value of Î± = 0.05 is completely due to the effect of the source size. Although accretion disk sizes are known to be smaller in X-rays, recent estimates are in the range of 0.1â1 light-days, depending on the mass of the black hole (see Mosquera etÂ al. 2013), and these finite sizes will increase the stellar surface densities implied by the X-ray data. Another possible origin for this discrepancy is that Pooley etÂ al. (2012) use the macro model as an unmicrolensed baseline for their analysis. It is well known that simple macro models are good at reproducing the positions of images, but have difficulty reproducing the flux ratios of images due to a range of effects beyond microlensing. Recently, Schechter etÂ al. (2014) found that the fundamental plane stellar mass densities have to be scaled up by a factor 1.23 in order to be compatible with microlensing in X-rays in a sample of lenses with a large overlap with that analyzed by Pooley etÂ al. (2012). It is unclear how this need for more mass in stars at the position of the images found by Schechter etÂ al. (2014) can be reconciled with the apparently low estimate of mass in stars at those radii by Pooley etÂ al. (2012). Our estimate of the stellar mass fraction agrees better with the results of microlensing studies of individual lenses (Keeton etÂ al. 2006; Kochanek etÂ al. 2006; Morgan etÂ al. 2008, 2012; Chartas etÂ al. 2009; Pooley etÂ al. 2009; Dai etÂ al. 2010) that reported values in the range 8%â25%, and with the estimates from strong lensing studies (see for example Jiang & Kochanek 2007; Gavazzi etÂ al. 2007; Treu 2010; Auger etÂ al. 2010; Treu etÂ al. 2010; Leier etÂ al. 2011; Oguri etÂ al. 2014) which produced stellar mass fractions in the range 30%â70% integrated inside the Einstein radius of the lenses.


Cassiopeia A (Cas A), which is a remnant of an SN IIb explosion (Krause et al. 2008), is an ideal target for examining the properties of SN dust. It is quite young (∼330 years; Fesen et al. 2006), so the SN ejecta and freshly formed SN dust have not been significantly mixed with the circumstellar/interstellar medium (CSM/ISM), and it is relatively close (3.4 kpc; Reed et al. 1995), so the physical and chemical structures can be resolved. Therefore, Cas A has been a major target of infrared space missions. The first direct evidence for SN dust in Cas A came from the Infrared Space Observatory (ISO), which performed mid-infrared (MIR; 2.4–45 μm) spectroscopic observations toward the bright ejecta shell (Lagage et al. 1996; Arendt et al. 1999; Douvion et al. 2001). The continuum spectra had a strong bump peaking at 21 μm together with a relatively weak bump at 9.5 μm, and Douvion et al. (2001) showed that the spectra can be fitted by two dust components at different temperatures, one at 90 K and the other at 350 K, with pyroxene (MgSiO3), quartz (SiO2), and aluminum oxide (Al2O3) as major components. The composition and distribution of this “warm” SN dust heated by a reverse shock have been studied in detail using the spectral mapping data of the Spitzer Space Telescope (Ennis et al. 2006; Rho et al. 2008; Arendt et al. 2014). These studies showed that the dust emission exhibits distinct spectral characteristics depending on the SN material with which it is associated. The most prominent dust emission is that with strong 9 and 21 μm bumps, which is associated with SN ejecta having strong Ar emission lines. The spectral features agree with the ISO spectra and can be reproduced by Mg protosilicate/MgSiO3, Mg

SiO

, or SiO2. The dust emission associated with SN ejecta having strong Ne lines is smooth without any silicate features and can be reproduced by Al2O3 dust or C glass. There is yet another type of smooth dust emission associated with X-ray Fe emission, but it is probably from swept-up CSM (Arendt et al. 2014). Meanwhile, Nozawa et al. (2010) showed that the observed spectral energy distribution (SED) of dust emission can be fitted by a physical model in which the SNR is expanding into a dense CSM, and the MIR emission is mostly from silicate grains (e.g., MgSiO3, Mg2SiO4, and SiO2) and MgO. The estimated total mass of warm dust ranges from 0.008 to 0.054

.


These data were compared to two different grids of stellar evolution models (see Table 1 for a summary). The first was a grid run using the Yale Rotating Evolution Code (YREC, Pinsonneault et al. 1989, with updates as discussed in van Saders & Pinsonneault 2012). We ran a grid of masses (0.6 M⊙–2.6 M⊙ in 0.1 M⊙ increments), metallicities ([Fe/H] = −2.0 to +0.6 in steps of 0.2), and α-element enhancements (+0.0, +0.2, and +0.4) to generate tracks. These models use a Grevesse & Sauval (1998) elemental mixture, with the updated OPAL equation of state (Rogers et al. 1996; Rogers & Nayfonov 2002), OPAL opacity tables (Iglesias & Rogers 1996) and gray atmospheres. Alpha-enhanced models use alpha-enhanced starting models and opacity tables, but not equations of state. Our models include semiconvection (see Kippenhahn & Weigert 1994), but do not include overshoot or the diffusion of helium or heavy elements. We assumed a Big Bang helium value of Y = 0.2485 at Z = 0 (Cyburt 2004), and did a linear fit to our solar value of Y = 0.272683 at Z = 0.018011 (so

). We convert Z to metallicity assuming

 for a solar mixture, with a correction factor for alpha-enhanced models. We compare to other theoretical models in Section 3. In the initial part of this analysis, we use grids with a solar mixing length (Böhm-Vitense 1958) of 1.72, chosen to reproduce the solar luminosity (3.827 × 1033 erg s−1) and the solar radius (6.957 × 1010 cm) at the solar age (4.57 Gyrs) (Mamajek 2012). For later parts of this study, we interpolate in a grid of models with mixing lengths of 1.22, 1.72, and 2.22. For the analysis in Section 3.2, we varied the initial helium abundance and surface boundary conditions in our model grid to explore their impact on the theoretical uncertainties. We ran models with fixed helium fractions of 0.239, 0.290, and 0.330, in addition to the solar calibrated value of 0.272683. We also created models with different atmospheric surface boundary conditions (defined as the boundary pressure at τ = 2/3): a look-up table from Kurucz (1997) models, and one from Castelli & Kurucz (2004) models, in addition to the gray atmosphere used in our main model grid.


In the last two decades UV, EUV, and X-ray observations from space made it possible to estimate the total mass of prominences reliably without needing to solve problems that occur when using visible light as was described in the previous paragraph. One possibility would be to estimate column mass of hydrogen and/or helium plasma in prominences using spectral observations of UV and visible lines of hydrogen and helium (Balmer and Lyman lines) and sophisticated models in which plasma is assumed not being in the state of local thermodynamic equilibrium (NLTE models; see e.g. Labrosse et al.2010, and references therein). The problem can be a rather high complexity of such NLTE models which depend on various free parameters. Another possibility is to infer column mass and subsequently the total mass from the amount of radiation absorbed by the photoionisation in the prominence plasma at resonance continua of hydrogen and helium. This estimation of the mean column mass of prominences observed near the limb was first made by Kucera et al. (1998) using extreme-ultraviolet (EUV) observations from the Coronal Diagnostic Spectrometer (CDS; Harrison et al. 1995) on board the Solar and Heliospheric Observatory (SoHO) satellite. The advantage of the observations used by Kucera et al. (1998) was that CDS as a spectrograph observed only in spectral lines of interest, but spectrographs are able to obtain spectra from only one slit position during one exposure. Larger fields of view can be scanned by the spectrograph slit, as the CDS does, for example, but in such a case, intensities in different slit positions the scan is composed of were obtained at different times. In contrast, in filtergrams, intensities in all positions of the field of view are obtained at the same time, but the filter has transmission of certain width which can be wider than the spectral line of interest. The first estimation of the prominence mass using filtergrams was made by Golub et al. (1999) using Transition Region and Coronal Explorer (TRACE1) data. Similar studies were made by Gilbert et al. (2005, 2006) using observations of EUV Imaging Telescope (EIT; Delaboudinière et al. 1995) on board SoHO in the 195 Å channel. In those two works it was shown that it is necessary to estimate an amount of coronal emission behind and in front of the prominence (hereafter referred to as background and foreground radiation, respectively) to determine correctly the amount of absorbed radiation. The foreground radiation can be measured at the darkest place at a prominence, where it is assumed that all radiation from behind the prominence was absorbed. Then, the background radiation can be derived from the total coronal emission at the prominence location. Two ways to estimate the total emission were proposed and used. The spatial interpolative approach uses interpolation from intensities measured in the corona near a prominence. The temporal interpolative approach is suitable only for erupting prominences and it uses measurements of intensity in place of prominence after its eruption. In the work of Williams et al. (2013) these two approaches are also used to estimate the column mass of material returning to limb after prominence eruption. They used observations from the Atmospheric Imaging Assembly (AIA) instrument (Lemen et al. 2012) on board the Solar Dynamics Observatory (SDO) in several EUV coronal channels of wavelengths below 228 Å (head of the resonance continuum of He ii).


The distances to planetary nebulae (PNe) have always faced the difficulty that nearby targets were lacking that could be reached well by direct methods. Trigonometric parallaxes have been obtained in a homogeneous long time-line campaign by the US Naval Observatory (USNO; Harris et al. 2007) and from the Hubble Space Telescope (HST; Benedict et al. 2009). Other studies (Acker et al. 1998; Smith 2015) showed that Hipparcos spacecraft parallaxes do not seem to be reliable. It was assumed that contamination by the emission of the surrounding nebulae caused these problems. Another model-independent method for distances to PNe are a cluster membership, as studied extensively by Majaess et al. (2007, 2014), and as discussed in Frew et al. (2016). In addition to these model-independent methods, a wide variety of statistical, model-dependent individual distance scales have been derived. The most frequently used of these are certainly those that are based on surface brightness versus angular sizes. They sometimes include optical depth corrections. All these methods have to be calibrated against a data set of nebulae with known distances. The older, widely used method is based on the 6 cm radio continuum flux, either using the ionized mass concept of Daub (1982) in the calibrations of Cahn et al. (1992) and Stanghellini et al. (2008), or by means of the radio continuum brightness temperature as used by van de Steene & Zijlstra (1994) and calibrated with a Galactic bulge sample. The newest model developed by Frew et al. (2016) is based on similar ideas, but makes use of the optical Hα surface brightness and a wide set of various calibrators. Moreover, they use a completely homogeneous data set for the brightness data derived earlier by themselves (Frew et al. 2013). Smith (2015) and Frew et al. (2016) described the underlying physics and assumptions for all these methods in detail. With the upcoming Gaia project (Gaia Collaboration 2016), a new era was expected to start for many classes of objects. The first step into this was described by Stanghellini et al. (2017) based on the combined Tycho + Gaia DR1 solution called TGAS (Michalik et al. 2015). With the second Data Release of Gaia (hereafter GDR2; Gaia Collaboration 2018), a complete homogeneous data set based only on Gaia measurements is available now for the first time. We present here the comparison of this new data set with common previous calibrations of PNe distances. Moreover, we compare it to the preliminary TGAS results in Stanghellini et al. (2017). Finally, we discuss possible caveats using the current GDR2.


Suprathermal electron strahls in the solar wind come from the Sun and are focused along magnetic field lines (Feldman et al. 1975; Rosenbauer et al. 1977; Pagel et al. 2005). Therefore, observations of CSE strahls within MCs can indicate that the flux rope structures are still connected with the Sun’s magnetic field lines on both ends (Gosling et al. 1995; Larson et al. 1997; Shodhan et al. 2000; Feng et al. 2015, 2019). Counterstreaming suprathermal electrons can also be produced by other mechanisms, for example connection to the Earth’s bowshock (Feldman et al. 1982; Stansberry et al. 1988), interplanetary shocks or corotating interaction regions (CIRs; Gosling et al. 1993; Steinberg et al. 2005; Lavraud et al. 2010), and distribution function depletions near the 90° pitch angle (Gosling et al. 2001, 2002; Skoug et al. 2006). Among these mechanisms, the depletion CSEs are often observed on closed or open field lines within ICMEs, but the depletion CSEs are centered on and roughly symmetric to the 90° pitch angle (Gosling et al. 2002), and can be distinguished from CSE strahls. Shodhan et al. (2000) examined the CSE strahl signatures of 52 MCs detected by a spacecraft near 1 AU and determined that approximately 87.5% of MCs exhibit CSE signatures, revealing that most MCs are still attached to the Sun at both ends at 1 AU. Gosling (1990) and Gosling et al. (1995) proposed explanations for how flux ropes arise in terms of three-dimensional reconnection close to the Sun. They illustrate how the original flux rope reconnects to form a helical field line connected to the Sun at both ends. The closed field lines of flux ropes can gradually open and occasionally disconnect from the corona when closed flux ropes expand from the Sun into the interplanetary space (Gosling et al. 1995). The proposal of Gosling et al. (1995) was confirmed by statistical results of Shodhan et al. (2000), namely most MCs exhibit CSE strahls in parts of their durations, and only 6 of the 52 MCs have no CSE. We therefore want to know whether or not nonMC ICMEs have the same CSE strahl signatures. In this study, CSE signatures from the Advanced Composition Explorer (ACE) from 1998 to 2008 are compared between ICMEs with and without MCs, and we discuss whether the CSE signatures are related to the flux-rope structures.


We used the theoretical models by Eggleton et al. (2008), Charbonnel & Lagarde (2010), and Lagarde et al. (2012) for the comparison. They provide quantitative values representing the first dredge-up, thermohaline (TH), and thermohaline and rotation (TH+V) induced mixing. Eggleton et al. (2008) estimated the mixing speed with their formula for the diffusion coefficient and found that a range of three orders of magnitude in their free parameter can lead to the observed levels of 12C /13C. Their predicted value of the 12C /13C ratio for a solar-metallicity 2 M⊙ star at the RGB tip is 17. A more recent model of the thermohaline-induced mixing by Charbonnel & Lagarde (2010) lists for the same stars a higher value of about 20. The model of Charbonnel & Lagarde (2010) of thermohaline instability induced mixing and the model by Eggleton et al. (2008) are both based on the ideas of Eggleton et al. (2006) and Ulrich (1972). It includes developments by Charbonnel & Zahn (2007). Eggleton et al. (2006) found a mean molecular weight (μ) inversion in their 1 M⊙ stellar evolution model, which occurred after the so-called luminosity bump on the RGB, when the hydrogen-burning shell reaches the chemically homogeneous part of the envelope. The μ-inversion is produced by the reaction \hbox{$^3{\rm He(}^3{\rm He}, 2p)^4{\rm He}$}He(33He,2p)4He, as predicted in Ulrich (1972). It does not occur earlier because the magnitude of the μ-inversion is low and negligible compared to a stabilising μ-stratification. Charbonnel & Zahn (2007) computed stellar evolution models including the ideas of Kippenhahn et al. (1980), who extended Ulrich’s equations to the case of a non-perfect gas. Charbonnel & Zahn (2007) also introduced a double diffusive instability (i.e. thermohaline convection) and showed its importance in the chemical evolution of red giants. This mixing connects the convective envelope with the external wing of the hydrogen-burning shell and induces surface abundance modifications in evolved stars (Charbonnel & Lagarde 2010).


Here, we propose a new speculative site for strong r-process nucleosynthesis in which it is formed by jets launched by an NS spiralling-in inside the core of a giant star. These jets will also explode the star. This is a rare evolutionary route and hence complies with the finding of large variations in the abundances of these elements. In this first study, we limit ourselves to present the scenario and show its viability. Most ingredients of our newly proposed scenario were studied in the past but were never put together into a coherent picture to yield a new possible site for the strong r-process. Previously studied ingredients of our proposed scenario include the CE of an NS and a giant (Thorne & Zytkow 1975; Armitage & Livio 2000; Chevalier 2012), the launching of neutron-rich gas from accretion discs around compact objects (e.g. Surman & McLaughlin 2004; Kohri et al. 2005), the launching of jets by NS accreting at a high rate (Fryer, Benz & Herant 1996) and the formation of r-process elements in jets from NS (Fryer et al. 2006). The idea that jets can explode stars under specific conditions was also studied in the past, e.g. in a CE evolution (Chevalier 2012). Another specific class of models are based on magnetic amplification by a rapidly rotating stellar core (e.g. LeBlanc & Wilson 1970; Bisnovatyi-Kogan, Popov & Samokhin 1976; Meier et al. 1976; Khokhlov et al. 1999; MacFadyen, Woosley & Heger 2001; Woosley & Janka 2005; Couch, Wheeler & Milosavljević 2009). This magnetorotational mechanism creates bipolar outflows (jets) around the newly born NS that are able to explode the star. However, the required core's rotation rate is much larger than what stellar evolution models give, hence making most of these models applicable for only special cases. We, on the other hand, claim that all CCSNe are exploded by jets, the jittering-jets model, that also synthesize r-process elements (but not the strong r-process), and hence our newly proposed scenario is part of a unified picture we try to construct for exploding all massive stars and the synthesis of r-process elements. In the jittering-jets model, the explosion of CCSNe is powered by jittering jets launched by an intermittent accretion disc around the newly born NS (Papish & Soker 2014a,b). The intermittent accretion disc is formed by gas accreted from the convective core regions that have a stochastic angular momentum (Gilkis & Soker 2014; Papish & Soker 2014a).


The dynamic viscosity of a fully ionized gas in the absence of magnetic fields (see Spitzer 1962)1(2)
\begin{equation}
\mu _{\rm Spitzer} = 2.21\times 10^{-15}\,\frac{(T\,[\mathrm{K}])^{5/2}A_{\rm i}^{1/2}}{Z^4\ln \Lambda }\,\mathrm{g\,cm^{-1}\,s^{-1}}\,
\end{equation}
is mainly a function of the temperature T. The parameters Ai and Z are the atomic weight and charge, respectively, of the ions. The Coulomb integral ln Λ depends logarithmically on temperature and density, and is commonly approximated by a constant value around 40 for clusters (see Gaspari & Churazov 2013; Smith et al. 2013). Slices of the resulting viscosity are shown in middle panels of Fig. 1 for three stages of the simulated merger. In Fig. 2, radial profiles of volume averages (blue), medians (red) and interquartiles (red shaded) are plotted for the cluster produced by the merger at z = 0. The typical value of the Spitzer viscosity in the WHIM is μSpitzer ∼ 10 g cm−1 s−1, with a gradual increase towards the core. Around the accretion shock (R ≈ 5 Mpc), the viscosity drops rapidly. It turns out that the median profile reflects this drop much better than the volume-averaged (or mass-averaged) profile because averaging a quantity that varies over several orders of magnitude is biased towards high values. Beyond the outer shocks, the values calculated with equation (2) become physically meaningless because the unshocked gas is neutral or only partially ionized. For the ICM, viscosities above 100 g cm−1 s−1 would be representative if it were not for the depression within 100 kpc from the centre. As discussed in Schmidt et al. (2016), this is a consequence of the overpronounced cool cores in our simulations. Feedback, particularly from AGNs, would raise the core temperature and, thus, the viscosity. This is important to bear in mind for the following discussion: In any case, the viscosity following from equation (2) is large enough to significantly affect or even suppress dynamical instabilities in both the ICM and the WHIM. This was also demonstrated by Roediger et al. (2013), Roediger et al. (2015) and ZuHone et al. (2015) in the context of Kelvin–Helmholtz instabilities and gas sloshing induced by minor mergers.


(i) Our capability of reproducing the lensed images down to the noise level without fully correctly modelling the cored central mass density distribution of the lenses indicates some form of the source-position transformation (SPT; Schneider & Sluse 2014), in line with the previous findings by Unruh et al. (2017). As a consequence, our reconstructions lead to a systematic fractional error on the Hubble constant of $25_{-19}^{+37}$ per cent (in comparison to a statical error of $12_{-3}^{+6}$ per cent when the shape of the lensing potential is perfectly known). This result is in agreement with the latest analysis of Blum, Castorina & Simonović (2020) that shows that cored (dark matter) mass density distributions give rise to approximate MSDs, and an error on the inferred Hubble constant. The latest cosmographic analyses (see e.g. Wong et al. 2019) have attempted to break these degeneracies by including the information contained in the kinematic properties of the lens galaxies and the positions of the lensed quasar images. However, the validity of this approach has been recently debated by Kochanek (2020), who has demonstrated that departures from single power-law mass distributions are responsible for a fractional error on the Hubble constant of 30 per cent. While the cores in the simulations analysed in this paper are artefacts related to limited resolution, cored mass density distribution in real galaxies may be developed by the effect of baryonic processes (see e.g. Chan et al. 2015) or changes in the dark matter properties (Schive, Chiueh & Broadhurst 2014; Spergel & Steinhardt 2000). Moreover, similar additional complexities exist in real galaxies are related, for example, to the presence of faint discs (Hsueh et al. 2018), bars, or other (baryonic) structures (Gilman et al. 2018; Xu et al. 2013). More generally, there exist many plausible deviations from a smooth power-law distribution, such as broken power laws (see e.g. Du et al. 2020) or multiple component models (see e.g. Nightingale, Dye & Massey 2018), which can produce comparable degeneracies. Together with the findings of Blum et al. (2020), our results have important implications for the analysis of time delays and a potential solution to the H0 tension (Wong et al. 2019).


In Fig. 1, the state of the corona is shown both before the introduction of Alfvénic perturbations (panels a–c), as well as after the solar wind has reached a quasi-steady state upon the injection of Alfvén waves of the lowest considered pump frequency of 0.3 mHz (panels d–f). The solar wind density, sound speed, and radial speed are shown at these two evolutionary instances for the three flux-tube geometries considered, with expansions of fmax = 3, 5, and 10. The response of a polytropic solar wind (γ  5/3) for different magnetic flux tube expansions in the absence of a pump wave has been described in previous works (Kopp & Holzer 1976; Pinto et al. 2016). Close to the Sun (r  ∼2 RS), the corona is seen to exhibit similar plasma conditions irrespectively of the chosen flux-tube geometry. The heliocentric distance to which these similar plasma conditions persist (r  ∼2 RS in our study) is partly due to the choice of parameters in Eq. (3). At greater heliocentric distances, the mass density is higher for smaller values of fmax, while the opposite is observed for the sound speed and radial velocity. Upon injecting a 0.3 mHz Alfvén wave, we see that the solar wind exhibits no visually discernible perturbations, indicating that this medium-frequency (0.3 mHz) Alfvén wave simply acts as a direct source of momentum (via the wave pressure gradient) and energy to the solar wind. As compared to the steady state, the sound speed and density are lower and radial speed higher for all considered fmax. This behaviour of the solar wind in response to hour-scale Alfvén waves is similarly found in other numerical simulations (Shoda et al. 2018a) and is indicative of the low dissipation of Alfvén waves at these frequencies either by reflections in the medium or by PDI. Such hour-scale Alfvén waves are also seen to dominate observations (Banerjee et al. 2009) as these waves do not dissipate and propagate through the medium as in Fig. 1. The acceleration of the solar wind is discussed in Sect. 4.2.


While different studies devoted to the near-IR spectra of Be stars show low-resolution data, many of them are restricted to a small sample, and some others analyse reduced spectral ranges. For instance, there are only a few studies done in the J band, and they focus mainly on a particular object or a specific spectral line or element (Mathew et al. 2012a,b; Štefl et al. 2009). Also, individual spectral ranges have already been studied for large samples of Be stars. Steele & Clark (2001) presented H-band spectroscopy of Be stars with a spectral resolution of R ≃ 3000. They reported Brackett and Fe ii lines in emission and, from the analysis of the strength ratio of the higher Brackett lines to Brγ, were able to distinguish early- from late-type Be stars. Later, Chojnowski et al. (2015) published high-resolution H-band spectroscopy for a great number of Be stars observed with APOGEE. They found that the Br11 emission line is formed preferentially in a circumstellar disc at an average distance of ~2.2R*, while the higher Brackett lines seem to originate in an innermost region. Several emission lines have been identified for the first time, such as C i λ 1.6895 μm, which is also formed in the inner region of the discs. In a later work, Chojnowski et al. (2017) analysed the variation of the emission strength, peak intensity ratio, and peak separation. Their analysis revealed a variety of temporal variability, including the disappearance and appearance of the line emission on different timescales. In the K band, Hanson et al. (1996), Clark & Steele (2000) and Granada et al. (2010) reported Brγ, Brδ, and Pfund lines in emission together with lines of He i in emission or absorption, and Mg ii, Fe ii and Na i lines in emission. Clark & Steele (2000) related the infrared characteristics to the underlying properties of the stars: objects that present He i features in emission or absorption are B3 or earlier; if the star presents Mg ii in emission but no He i, it is between B2 and b4; objects with Brγ emission but no evidence of He i or Mg ii are B5 or later. Lenorzer et al. (2002b) provided an extensive atlas of early type stars, including a number of Be stars, covering the K and L bands, while Lenorzer et al. (2002a) analysed the H recombination lines of those stars and constructed a diagram of flux ratios of some selected recombination lines: Hu14/Brα and Hu14/Pfγ. In this diagram, the location of the objects gives information about the density of the emitting gas. After that, Mennickent et al. (2009) presented a classification scheme for Be stars based on the intensity of the L-band hydrogen-emission lines. The objects in each group fall in different regions of Lenorzer’s diagram; thus, this classification scheme is probably connected to the density of the disc. Granada et al. (2010) analysed a sample of eight Be stars and classified them with Mennickent’s criterion. They found that for group I objects, the equivalent widths (EW) of Brα and Brγ lines are similar, while for stars in group II the EW(Brγ) is much larger (more than five times) than the EW(Brα). Besides this, Mennickent et al. (2009) and Granada et al. (2010) reported emission lines not only in Brα, Pfγ, and the Humphreys series but also in He i λ4.038 μm and He i λ4.041 μm. Sabogal et al. (2017) showed a sample of L-band Be-star spectra and correlated the infrared features with the optical Hα line behaviour.


where WCRSF is the width of the cyclotron line, Fν is the emergent flux including cyclotron scattering, and F0 the input continuum flux without a CRSF. In the Monte Carlo simulations performed by Schwarm et al. (2017b), only 1–10% of the initial photons undergo resonant scattering, that is, r ≳ 90%. Consequently, we would expect τCRSF ≲ 0.1 for the observed optical depths9. From our best-fit model of the spectra of Epoch II, the calculated residual fluxes after Eq. (10) are ≥78% for all three detected cyclotron lines (see Table 2). These values together with the fitted optical depths of τCRSF ≤ 0.24 (see Table 1) are in excellent agreement with the expectations from the simulations by Schwarm et al. (2017b). Although spawned photons from higher harmonics, which originate from multi-photon scattering and from the radiative de-excitation of electrons excited into higher levels, can affect the shape of the fundamental line (Isenberg et al. 1998), they can only decrease its depth. We note that residual fluxes down to r ≳ 36% have been observed for GX 304−1 (Rothschild et al. 2017), which can be obtained by, for example, a higher optical depth at the line-forming region. However, the CRSFs are not expected to absorb a significant fraction of the total broad-band continuum flux, which is the case for the model by Iyer et al. (2015). We conclude that the CRSF parameters that these latter authors found are due to a degeneracy between the continuum modeling and the CRSF modeling when unphysical values for the CRSF are allowed. In summary, the choice of a phenomenological model for the X-ray spectrum of an accreting neutron star may cause strong discrepancies relative to the theoretically expected values for the CRSF parameters. In particular, an erroneous shape or an overestimation of the X-ray flux is sometimes corrected by the introduction of further strong absorption components, which are probably not real. We stress that we do not claim that our choice of the phenomenological continuum model for 4U 0115+634 describes its true X-ray spectrum best. However, in contrast to other continua the model applied here yields CRSF parameters which are consistent with theoretical expectations. These conclusions desperately call out for a self-consistent model for both the spectral continuum and the cyclotron resonant scattering features.


Despite 20 years of deep submm surveys since Smail et al. (1997), our knowledge of the upper half of the redshift distribution of SMGs remains incomplete. Early attempts to determine redshifts were conducted toward SMGs with radio counterparts because low-resolution (sub)mm images obtained with single dishes require high-resolution radio continuum maps from radio interferometers such as the Karl G. Jansky Very Large Array (VLA) in order to pinpoint source positions (Ivison et al. 1998, 2000, 2002, 2005, 2007; Smail et al. 1999; Borys et al. 2004; Pope et al. 2006; Aretxaga et al. 2011; Biggs et al. 2011; Yun et al. 2012; Umehata et al. 2014). Intensive studies of radio-bright SMGs were able to yield spectroscopic redshifts for those out to z ∼ 3 (e.g., Chapman et al. 2003, 2005). However, at that time, radio sensitivities could not detect SMGs beyond z ∼ 3, and as many as half of the SMGs lacked reliable radio counterparts (see e.g., Ivison et al. 2007; Biggs et al. 2011, cf. Lindner et al. 2011). Later attempts to determine SMG positions and redshifts using near- and mid-IR imaging could not fully overcome the bias toward lower redshifts, since the K corrections there are no more favorable than those in the radio regime, such that high-redshift sources are much fainter (e.g., Wardlow et al. 2011; Yun et al. 2012). Millimeter (mm) spectroscopic surveys toward gravitationally lensed dusty star-forming galaxies, taking advantage of their apparent ultra brightness, revealed a redshift distribution stretching out to z ∼ 5.8 (e.g., Vieira et al. 2013; Weiß et al. 2013; Strandet et al. 2016). These surveys suggested a larger fraction of SMGs at z ≳ 3 than previous studies of unlensed SMGs, perhaps partly because they were selected at 1.3 mm rather than the traditional 0.8–1.1 mm, but also because the requirement for high magnification favors galaxies with a long line of sight. We need to reveal the intrinsic redshift distributions of unlensed SMGs in large contiguous maps to determine their abundance in the early Universe and to study the evolution of the most massive galaxies via abundance matching with other populations, and with cosmological predictions (e.g., Hayward et al. 2013; Cowley et al. 2015).


We can also compare to the models by Dessart, Audit & Hillier (2015), who synthesize light curves and spectra for superluminous SNe IIn with a variety of physical CSM parameters: in their fig. 20, they show the simulated bolometric light curves for their models out to +450 d. Past 200 d, most of the light curves experience a sudden and significant drop in luminosity that we did not observe for SN 2009ip, except for three (xe3m6r, xm3 and xm6). These models are distinguished from the others by having progenitor stars that experienced a more rapid mass-loss rate during the late stages of stellar evolution, and in one case, a CSM that extends to a radius 50 per cent farther than the others. The total bolometric luminosities for these models are ≳3 orders of magnitude higher at late times than SN 2009ip (log Lbol ≈ 40; Fraser et al. 2015) owing to a more energetic underlying explosion driving the interaction. The synthesized early-time spectra for these three models are also qualitatively similar to those of SN 2009ip (see fig. 22 of Dessart et al. 2015). Late-time synthesized spectra are not shown for these three models, but are given for their model X, in a comparison to luminous SN IIn 2010jl (see also Section 3.4). The synthetic spectra exhibit significantly more asymmetry and have a strong, blueshifted component of the H α line, which is even more exaggerated than that seen for SN 2010jl at ∼200 d. Dessart et al. (2015) explain this blueshifted feature as arising from an optically thick, cool dense shell between the reverse and forward shocks in the CSM, but for SN 2009ip we would not expect to see this signature because we found that the CSM exterior to the shock front is not yet optically thin (i.e. Section 3.2.1). Although not every aspect of the models by Dessart et al. (2015) represent the physical scenario of SN 2009ip, where appropriate comparisons can be made they support a moderately energetic explosion into a large and extended mass of CSM.


The most natural explanation is that the Compton-thick nature of some low-luminosity AGNs results in an underestimation of the true LX(2−10 keV) of these sources. These LX(2−10 keV) estimates come from studies using the spectra of LINERs at energies below 10 keV. However, Compton-thick sources show the bulk of the AGN power at energies above 10 keV. The intrinsic luminosity could be 10−70 times higher than the estimated using only energies below 10 keV in the Compton-thick scenario (Maiolino et al. 1998). González-Martín et al. (2009b) classified around 50% of their LINER sample as Compton-thick candidates. Figure 8 shows the AGN-dominated objects in our study attending to their Compton-thin (left) and Compton-thick (middle) classification. Most of the Compton-thin sources are close to the previously reported correlation for AGN. Compton-thick S2s are nicely placed along the AGN correlation found by Asmus et al. (2011). This is expected because the X-ray luminosities included for S2s are all corrected for their Compton-thick nature (most of them included in Goulding et al. 2012), either using X-ray measurements above 10 keV or assuming a factor between the observed and intrinsic X-ray luminosity for other Compton-thick AGNs (see Panessa et al. 2006, for details in this conversion factor). Compton-thick LINER candidates tend to be shifted towards X-ray luminosities lower than predicted for the AGN correlation. However, most of them are not consistent with the SB correlation either. The double arrows of Fig. 8 (middle panel) show their expected locus if the X-ray luminosity were ~10−70 times higher. Most of the Compton-thick LINERs can be placed in the AGN correlation if the correction is applied. The linear fit to the entire sample, once the intrinsic X-ray luminosity is corrected, results in LX(2−10 keV)(intrinsic) = 40 × LX(2−10 keV)(observed) for Compton-thick LINERs (marked as white stars in Fig. 8, right panel), which is very close to the linear relation found for AGN. Nonetheless, four LINERs and one S2 still remain very close to the SB correlation.


A common property of observed transverse coronal loop oscillations is that they are damped quickly, usually within a few oscillation periods. It is now generally accepted that the main damping mechanism is resonant absorption (Sakurai et al. 1991; Goossens et al. 1992, 2002; Ruderman & Roberts 2002), transferring energy from the global kink mode to local azimuthal Alfvén modes in the boundary layer of the loop structure, where the two frequencies match (for a review of theoretical results, see Goossens et al. 2011). Less frequently, nearly undamped or even growing transverse oscillations are observed (Wang et al. 2012). Decay-less low amplitude kink oscillations, which are present in loops before and after a high-amplitude flare triggered damped kink oscillations can be explained in terms of a damped linear oscillator excited by a continuous low amplitude harmonic driver (Nisticò et al. 2013; Anfinogentov et al. 2013). Some examples of observed undamped high amplitude coronal loop oscillations can be found in Aschwanden et al. (2002) and Aschwanden & Schrijver (2011). In the latter paper, it was concluded that this could only happen if the thickness of the boundary layer (a radially inhomogeneous outer layer of the coronal loops) is much smaller than the loop radius, in order to minimize the damping due to resonant absorption. It was also evident from the observations that the loop was cooling during the particular undamped oscillation event. It seemed a rather natural explanation that the amplification due to cooling may counterbalance the damping due to resonant absorption, explaining the undamped oscillations, as it was first suggested in Ruderman (2011b). The most elaborate analytical study regarding time-dependent kink oscillations (Ruderman 2011a) considered the simultaneous effects of both damping due to resonant absorption and amplification due to plasma cooling. The conclusion was that, for typical boundary layer thicknesses, the amplification due to plasma cooling can account for the observed undamped oscillations only if the cooling happens quickly, on a timescale close to the oscillation period. However, in the paper, the effects of cooling and resonant damping have been studied under the assumption that both the characteristic cooling time and damping time are much longer than the characteristic oscillation period, when using the WKB method. Thus, it is questionable whether the derived equations remain valid for rapid cooling, i.e. for cooling times near to the oscillation periods. On the other hand, neglected non-linear behavior may change the outcome considerably, for example the Kelvin-Helmholtz instability at the tube boundary (Heyvaerts & Priest 1983; Ofman et al. 1994; Terradas et al. 2008), and the ponderomotive forces for high amplitudes (Terradas & Ofman 2004). The aim of this study is to further investigate the effects of radiative plasma cooling on the fundamental standing kink oscillation by means of numerical analysis.


The most unique and characteristic observational feature of blazars’ highly variable broadband emission is the broad bimodal SED extending from the lowest accessible EM band, i.e., the radio, to the highest accessible, i.e., GeV-TeV γ-rays. The broadband SED of all blazars can be categorized into three different spectral subclasses: low-energy-peaked (LBL/LSP), intermediate-energy-peaked (IBL/ISP), and high-energy-peaked (HBL/HSP; Fossati et al. 1998; Abdo et al. 2010), based on the location of the low-energy hump. A remarkable property of each spectral subclass is the stability of the location of the two peaks despite huge variations in flux and often spectral shape. Only in a few rare instances has an appreciable shift in the location of the peaks been observed, e.g., the 1997 outburst of Mrk 501 (Pian et al. 1998; Ahnen et al. 2018) and the activity of OJ 287 from the end of 2015 to the middle of 2017 (Kushwaha et al. 2018a, 2018b). Even these two cases are remarkably different. In the case of Mrk 501, the locations of both the peaks shifted to higher energies. On the contrary, in OJ 287, a shift in the location of only the high-energy peak was observed during the 2015–2016 activity (Kushwaha et al. 2018a, 2019), while in 2016–2017 a new broadband emission component overwhelmed the overall emission, appearing as an overall shift in both the peaks as revealed in the detailed study by Kushwaha et al. (2018b). With the SED being the prime observable for exploration of the yet-debated high-energy emission mechanisms, such changes offer invaluable insights about the emission processes. For example, in Mrk 501 the shift in both peaks strongly implies the same particle distribution for the overall emission, while for OJ 287 the shift of only the high-energy peak can be reproduced by either inverse Compton scattering of the broad-line region photon field (Kushwaha et al. 2018a) or emission of hadronic origin (Oikonomou et al. 2019; Rodríguez-Ramírez et al. 2020).


We present the photometry of the companion in Fig. 4 in a color-magnitude diagram. The corresponding numerical values are reported in Table 2. YSES 2b is consistent with a late L to early T spectral type when comparing it to colors of field brown dwarfs from the NIRSPEC Brown Dwarf Spectroscopic Survey (McLean et al. 2003, 2007), the IRTF spectral library (Rayner et al. 2009; Cushing et al. 2005), the L and T dwarf data archive (Knapp et al. 2004; Golimowski et al. 2004; Chiu et al. 2006), and the SpeX Prism Libraries (Burgasser et al. 2004, 2008, 2010; Gelino & Burgasser 2010; Burgasser 2007; Siegler et al. 2007; Reid et al. 2006; Kirkpatrick et al. 2006, 2010; Cruz et al. 2004; Burgasser & McElwain 2006; McElwain & Burgasser 2006; Sheppard & Cushing 2009; Looper et al. 2007, 2010; Muench et al. 2007; Dhital et al. 2011). Object distances were derived from Gaia EDR3 (Gaia Collaboration 2021), the Brown Dwarf Kinematics Project (Faherty et al. 2009), and the Pan-STARRS1 3π Survey (Best et al. 2018). In color-magnitude space, YSES 2b is very close to the innermost three planets of the HR 8799 multi-planetary system (Marois et al. 2008, 2010). These three planets are classified as mid to late L type dwarfs (e.g., Greenbaum et al. 2018), which agrees well with the sequence evolution of the adjacent field brown dwarfs from L to T spectral types3. A similar spectral type in this domain, therefore, seems very likely for YSES 2b, requiring confirmation by measurements at higher spectral resolution. Whereas the masses of the spectrally similar trio of HR 8799 c, d, and e are in the range 7–12 MJup (Wang et al. 2018; Marois et al. 2008, 2010), it is likely that YSES 2b has an even lower mass as the system age of (13.9 ± 2.3) Myr is significantly younger than the age of HR 8799, which is claimed to be member of the Columba association with an age of 30–50 Myr (Zuckerman et al. 2011; Bell et al. 2015). This is supported by the AMES-COND and AMES-dusty models (Allard et al. 2001; Chabrier et al. 2000) that we present in Fig. 4 for a system age of 13.9 Myr. An individual evaluation of these isochrones yielded masses from 5.3 MJup to 8.0 MJup as presented in Table 2. The uncertainties originate from the errors in the system age and planet magnitude that were propagated by a bootstrapping approach with 1000 randomly drawn samples from Gaussian distributions around both parameters. When combining the posterior distributions for the different models and filters we derived a final mass estimate of

$6.3^{1.6}_{-0.9}\,M_{\mathrm{Jup}}$6.3−0.9+1.6 MJup
 as the 68% confidence interval around the median of the sample. This estimate is based on broadband photometric measurements alone; further spectral coverage of the planetary SED will be important to constrain its effective temperature, luminosity, surface gravity, and mass.


Idealized simulations have the advantage of carefully controlled conditions but the disadvantages that the turbulence is driven in an artificially prescribed manner to maintain a fixed overall turbulent amplitude and the processes leading to cloud formation and destruction are not followed. In reality, GMCs form due to a combination of large-scale ISM flows (including turbulence, shear, and epicyclic motion) and gravity (both stellar gravity and self-gravity) that lead to collection of material from a large volume, as mediated by thermal and magnetic pressure, and a change from the atomic to the molecular phase as the gas cools (e.g., McKee & Ostriker 2007; Dobbs et al. 2014; Chevance et al. 2020). Turbulence on scales less than the scale height of the warm–cold ISM likely originates primarily due to the feedback from young stars (Elmegreen & Scalo 2004; Mac Low & Klessen 2004; McKee & Ostriker 2007),3

3
Gravitational instabilities in the combined gas–stellar system (e.g., Jog & Solomon 1984; Romeo 1992; Rafikov 2001; Kim & Ostriker 2007) can drive horizontal motions at very large scales, as seen in numerical simulations (e.g., Kim & Ostriker 2007; Shetty & Ostriker 2008; Agertz et al. 2009; Dobbs et al. 2011; Hopkins et al. 2012; Agertz & Kravtsov 2015, and citations within), but these motions generally do not reach supersonic amplitudes unless they are associated with gravitational collapse. In addition, turbulence at scales less than the disk scale height can be driven by spiral shocks and the magnetorotational instability, but numerical simulations show that the corresponding amplitudes are relatively modest in cold gas (e.g., Wada & Koda 2004; Piontek & Ostriker 2005, 2007; Kim et al. 2006, 2010; Dobbs & Bonnell 2007; Bonnell et al. 2013, and citations within).
 whether inherited from a GMC’s formation stage or produced internally. Considering that GMCs live for at most a few turbulent crossing or freefall times (Kawamura et al. 2009; Kruijssen et al. 2019), it is not clear that internal GMC conditions can control star formation in a way that is entirely divorced from their formation and destruction processes.


The short-term (seconds to hours) temporal properties of ULXs are quite different from those observed in Galactic X-ray binary systems and are not related to specific spectral states (e.g. Heil et al. 2009): even if the amplitude of short-term variability is larger in soft ultraluminous sources than in hard ones (Sutton et al. 2013), the variability appears to be poorly predictable, i.e. it is not found in all sources with a soft spectrum and, when detected in a source, it is not necessarily found in all the observations of that ULX. Such variability was explained with the existence of optically thick and non-uniform winds, radiatively ejected by the accretion disc, which stochastically intersect our line of sight (e.g. Middleton, Sutton & Roberts 2011; Middleton et al. 2015a). Observational evidences of these winds come from the detection of blue-shifted absorption lines in the high-quality grating spectra of some ULXs (e.g. Pinto, Middleton & Fabian 2016; Kosec et al. 2018) and by the nebulae observed in the radio (e.g. Cseh et al. 2012), optical (e.g. Pakull, Soria & Motch 2010) or X-ray band (Belfiore et al. 2020). Long-term flux variability (days to months) is also observed in most of the monitored ULXs. Such variability, in some cases, can be as high as several orders of magnitudes, implying that these sources are transients (detected at least once in the ultraluminous state, Lx > 1039 erg s−1, and either once at a significantly smaller luminosity or undetected below the instrumental sensitivity; e.g. Soria et al. 2012; Pintore et al. 2018a). Often the pulsating ULXs (PULXs) show large flux variations, implying they can be considered as transient ULXs. A bimodal flux distribution is sometimes observed in the long-term light curves of PULXs (e.g. Walton et al. 2015a; Motch et al. 2014). A possible explanation for this long-term behaviour may be the propeller effect: when the magnetospheric radius of the NS becomes larger than the corotation radius of the accreting matter in the disc, a centrifugal barrier prevents the accretion on to the NS, with a corresponding decrease in the X-ray flux (Illarionov & Sunyaev 1975; Tsygankov et al. 2016; Grebenev 2017). The propeller effect can act only if the accretor is an NS with a strong magnetic field, so a bimodal flux distribution can be used to identify candidate PULXs, even when pulsations are not detected (e.g. Earnshaw, Roberts & Sathyaprakash 2018; Song et al. 2020). Furthermore, long-term monitored ULXs revealed possible (super-)orbital variability (e.g. Foster, Charles & Holley-Bockelmann 2010; An, Lu & Wang 2016; Fürst et al. 2018), the origin of which is still a matter of debate. Super-orbital periods are also observed in the light curves of the PULXs, with periods of tens to hundreds days (e.g. Walton et al. 2016; Brightman et al. 2019, 2020). The detections of such long-term periodicities were only possible thanks to the flexibility and performance of the Neil Gehrels Swift Observatory (hereafter Swift; Gehrels et al. 2004).


X Persei (4U 0352 + 309) is a binary stellar system at a distance of ∼0.95 kpc (Telting et al. 1998) and consists of a slowly spinning neutron star (White, Mason & Sanford 1977, Pspin ∼ 837 s) that is accreting matter from its Be-star companion (Lyubimkov et al. 1997). The source is peculiar in that it is a persistent source and does not show Type-I outbursts as are commonly observed in other Be-/X-ray binaries. But X-ray flares and variability in the X-ray light curve of the source have been observed (La Palombara & Mereghetti 2007; Lutovinov, Tsygankov & Chernyakova 2012). The orbital period of the binary system is long, $P_{\text{orb}}\sim 250 \rm {d}$, but the orbital eccentricity is only e ∼ 0.11 (Delgado-Martí et al. 2001). The long orbital period and the low X-ray luminosity of the source support the assumption that the neutron star in this binary is accreting quasi-spherically by capturing matter from the stellar wind of the Be-star (Shakura et al. 2012). The X-ray spectrum of X Persei is also unlike most accreting X-ray pulsars, the latter can usually be modelled with a power law and a cutoff in the range 10–30 keV (White, Swank & Holt 1983). Instead, X Persei has a peculiarly hard X-ray spectrum, making the source detectable at energies higher than 100 keV (Lutovinov et al. 2012). Thus, a single-component spectral model is insufficient to model the source continuum spectrum, making it necessary to include a second high-energy component to explain the emission at harder X-rays. Several authors have used several different models to explain the observed spectrum, of which we note the following works. The RXTE observations were modelled using a blackbody component at lower energies and a power-law component with an exponential cutoff at higher energies (Coburn et al. 2001). A cyclotron resonance scattering feature (CRSF) was also required to account for an absorption-like feature seen around 30 keV. The spectrum obtained from BeppoSAX observation was modelled with two power-law components with exponential cutoffs at low and high energies and did not require any CRSF (Di Salvo et al. 1998). The INTEGRAL observations used thermal Comptonization and bulk motion Comptonization to account for the observed spectrum at the low and high energies, respectively (Doroshenko et al. 2012). The INTEGRAL observations also did not require any CRSF to improve the spectral model. Thus, the presence of CRSF noted in the RXTE observations was not detected in either the BeppoSAX or the INTEGRAL observation and hence needs to be verified. There is also no clear agreement on the unusual nature of the X-ray spectrum with respect to the continuum model.


The lower panel of Figure 9 shows the SFR density against the H2 mass density for each pixel (black dots) and the average value found within each of the analyzed region as colored symbols. Red dashed lines are fixed depletion times, while the blue dashed line is the one derived from the 30 nearby disk galaxies of the HERACLES survey by Bigiel et al. (2011) at 1 kpc scale resolution. The red dots, corresponding to regions D1, D2, and D3 located within the disk, lie below the local galaxies relation (in blue), i.e., they show low SFE. This confirms that this galaxy is forming new stars in the disk at a very low rate (see also Vulcani et al. 2018), given that the measured values of

 are those typically found in galaxy bulges (Fisher et al. 2013). Lower values of αCO (5–10 times lower than the Milky Way value adopted here) have been found in the central part of some HERACLES galaxies (Sandstrom et al. 2013), but only in the central kiloparsec, while regions D1, D2, and D3 span a larger extent of the galaxy disk. In particular, the central kiloparsec is dominated by AGN-like line ratios (Poggianti et al. 2017a; Radovich et al. 2019), according to different indicators (Poggianti et al. 2019a), and we therefore excluded it from the calculation. Our data confirm that local conditions play an important role in determining the star formation process, as already shown in the nearby galaxy M51 (Bigiel et al. 2016), and in 29 other nearby galaxies where dense gas tracers were available (Usero et al. 2015). Ram pressure then works in JW100 by enhancing the gas density in the disk and at the same time suppressing the global SFR, resulting in long depletion times both in the tail and in the galaxy disk (as already suggested in Moretti et al. 2018a). Whether this is accompanied also by an enhancement of the molecular gas fraction, as in Nehlig et al. (2016), cannot be stated yet. Ongoing H i observations with MeerKAT will shed light on this issue. It is worth noticing, though, that in the GASP jellyfish galaxy JO206, the H i depletion time turned out to be shorter than expected (Ramatsoku et al. 2019), showing the opposite trend with respect to the molecular gas in JW100.


In the modelling, it is assumed that the low-energy peak (from radio to optical–UV) is due to synchrotron emission from ultrarelativistic electrons in the jet with an energy distribution as given by equation (2). Instead, the HE peak is due to the IC scattering of internal (SSC; Ghisellini et al. 1985; Maraschi et al. 1992; Bloom & Marscher 1996) or external photons (EIC; Sikora et al. 1994; Błażejowski et al. 2000; Ghisellini & Tavecchio 2009). The IC scattering of external photons is considered, since the SEDs of FSRQS are better explained by EIC, as shown by the previous studies (e.g. Abeysekara et al. 2015; Ahnen et al. 2015; Hayashida et al. 2015b; Gasparyan et al. 2018; MAGIC Collaboration 2018), and the CD is evident in the SEDs of the considered sources (Fig. 6). Localization of the emission region in the jet is an open question and along the jet, depending on the distance from the central black hole, different photon fields can be dominant for the IC scattering (Sikora et al. 2009). In this paper, we assume that the emitting region is outside the broad-line region (BLR) where the dominant photon field is the IR emission from the dusty torus. Sikora et al. (2002) showed that in MeV blazar SEDs the shift of the peak of the HE component to lower energies is most likely due to the Comptonization of IR photons from the dusty torus. The IR radiation from the dusty torus is assumed to have a blackbody spectrum with a luminosity of LIR = 0.6 Ldisc (see Ahnen et al. 2015) where Ldisc is the accretion disc luminosity, which fills a volume that for simplicity is approximated as a spherical shell with a radius of RIR = 2.5 × 1018 (Ld/1045)1/2 cm (Nenkova et al. 2008) with the energy density of $u_{\rm IR}=0.6\:L_{\rm d}/4 \pi R_{\rm IR}^2\:\delta ^2$ in the co-moving frame of the jet. In Ghisellini et al. (2011) and Marcotulli et al. (2017), the HE component in the SED of distant blazars was modelled by IC scattering of BLR reflected photons, adopting a smooth broken power-law shape of the emitting electrons. We refer the reader to these papers for details on the modelling when BLR reflected photons are considered.


Silicon monoxide (SiO) is predicted to be the most abundant Si-bearing molecule in the entire 1–10 R* range in the atmospheres of M stars. In S-type atmospheres, the calculated abundance of SiO decreases by two orders of magnitude in the 1–5 R* but retains a very high abundance beyond, and the same occurs in C-rich atmospheres, although in this case, the abundance drop in the 1–5 R* is even more pronounced (see Fig. 2; see also Agúndez & Cernicharo 2006). Observations indicate that the abundance of SiO does not differ significantly between envelopes around M-, S-, and C-type stars, although in all them the SiO abundance decreases with increasing mass-loss rate (González Delgado et al. 2003; Schöier et al. 2006; Ramstedt et al. 2009; Massalkhi et al. 2019, 2020). This decline in the SiO abundance with increasing envelope density is not a consequence of chemical equilibrium (Massalkhi et al. 2019), but has been interpreted as evidence that SiO disappears from the gas phase at high densities to be incorporated into dust grains (González Delgado et al. 2003; Schöier et al. 2006; Ramstedt et al. 2009; Massalkhi et al. 2019, 2020). It therefore appears that the gradual abundance decline calculated for SiO in the 1–5 R* region from stellar type in the sense M → S → C does not have a direct consequence in the SiO abundance that is injected into the expanding wind. However, this behavior predicted by chemical equilibrium probably explains why SiO masers are observed in M-type stars but not toward carbon stars (e.g., Pardo et al. 2004). Except for these details, chemical equilibrium and observations agree in the fact that SiO is one of the most abundant carriers of silicon in the atmospheres of M-, S-, and C-type stars. Calculations and observations also agree for SiS in that it is an abundant molecule regardless of the C/O. However, observations indicate a differentiation between C- and O-rich envelopes, with SiS being on average one order of magnitude more abundant in carbon-rich sources (Schöier et al. 2007; Danilovich et al. 2018; Massalkhi et al. 2019, 2020). Moreover, in some oxygen-rich envelopes, the fractional abundance of SiS relative to H2 is as low as ~10−8, which is well below the predictions of chemical equilibrium (Danilovich et al. 2019; Massalkhi et al. 2020).


Classically, the explosive α-capture at the bottom of the former convective He-shell activates a neutron burst peaking up to 1018–20 neutrons cm−3, produced by the 22Ne(α, n)25Mg reaction. This nucleosynthesis process was called the n-process (Blake & Schramm 1976; Thielemann, Arnould & Hillebrandt 1979). Much later, its signature was identified in heavy elemental abundances measured in presolar SiC-X grains such as large excesses of 58Fe, 88Sr, 96Zr, 95, 97Mo, and 138Ba (e.g. Meyer, Clayton & The 2000; Pellin et al. 2006; Pignatari et al. 2018) and in the production of the radioactive isotope 32Si (Pignatari et al. 2015). However, this scenario has been discounted as a way to explain the r-process because it could not reproduce the r-process abundance pattern in the Solar system (Blake et al. 1981). The presence of H in the He-shell during the SN explosion may lead to a suppression of the n process, where it becomes more probable to destroy 22Ne by proton capture than by the 22Ne(α, n)25Mg reaction (Pignatari et al. 2015). The production of 44Ti and 40Ca in the C/Si zone along with the possible strong depletion of 40Ca by neutron capture predicts abundances consistent with the observation of large 44Ca/40Ca in the C-rich grains discussed (Pignatari et al. 2013a). It is still matter of debate if in presolar grains the abundance signatures of H-ingestion coexist with the neutron-capture signature of the n-process. Indeed, the n-process activation would be compatible with the 30Si- and 32S-enhancements measured in in some putative nova grains (Liu et al. 2016; Hoppe et al. 2018), and with the 32Si- and 50Ti-enhancements found in a sample of SiC–AB grains (Liu et al. 2017a). On the other hand, measurements of the Sr, Mo, and Ba isotopic abundances in SiC–AB grains seem to be compatible with the pre-explosive s-process abundances in the He shell, and not with the n-process (Liu et al. 2018b). In the first case, major asymmetries triggered by the H ingestion in the pre-explosive He shell structure would be required in order to explain for the same single grain the signatures of both the n-process and of a late H-ingestion event leaving H behind in the former He shell material. While this may be a natural expectation from multidimensional simulations, it cannot be captured by 1D stellar simulations. Additionally, those abundance signatures of high neutron-density exposures could also be the effect of a local activation of the intermediate neutron-capture process (i-process; Cowan & Rose 1977), following the H ingestion event. The i-process has been proposed as a nucleosynthesis source active in massive stars at low metallicities (e.g. Roederer et al. 2016; Banerjee, Qian & Heger 2018; Clarkson, Herwig & Pignatari 2018), but it also has been proposed as a source of anomalous signatures in presolar grains for Ti isotopes (HD graphites; Jadhav et al. 2013), Ba isotopes (in some mainstream SiC grains; Liu et al. 2014) and 32Si-enrichments (in SiC AB grains; Fujiya et al. 2013). In order to verify all of these different scenarios, new abundance observations are required for more presolar grains of different types.


Since polycyclic aromatic hydrocarbons (PAHs) were first hypothesized to be carriers of the unidentified infrared bands (Léger & Puget 1984; Allamandola et al. 1985), a great deal of effort has been devoted to understanding the chemical processes leading to the formation of these molecular species (see e.g. Joblin & Cernicharo 2018). Circumstellar envelopes around carbon-rich asymptotic giant branch (AGB) stars have been suggested as the factories of PAHs (Cherchneff et al. 1992). The detection of benzene in the carbon-rich protoplanetary nebula CRL 618 (Cernicharo et al. 2001) suggests a bottom-up approach in which the small hydrocarbons that formed during the AGB phase, such as C2H2 and C2H4, interact with the ultraviolet (UV) radiation produced by the star in its evolution to the white dwarf phase (Woods et al. 2002; Cernicharo 2004). Other hypotheses involve the processing of dust grains around evolved stars, either through UV photons (Pilleri et al. 2015) or by chemical processes (Martínez et al. 2020). Hence, it has been surprising to see that cyanide derivatives of PAHs have been found in the cold pre-stellar core TMC-1, which is well protected against UV radiation (McGuire et al. 2018, 2021). It is unlikely that these PAH cyanides arise from a reservoir of PAHs that has existed since the early stages of the cloud since these relatively small PAHs would not have survived the diffuse cloud stage. Although McGuire et al. (2021) propose a reasonable chemical network starting with the phenyl radical that could explain the observed abundances of cyanonaphthalene, the chemical routes leading to benzene itself are still unclear. An in situ formation mechanism for benzene must involve abundant hydrocarbons containing from two to four carbon atoms. Moreover, some of these species have to permit an easy cyclization in two to three steps to have an efficient yield of benzene or phenyl radical. The propargyl radical (CH2CCH) was recently found in TMC-1 by Agúndez et al. (2021) with an abundance close to 10−8 relative to H2. In addition, complex hydrocarbons such as vinyl and allenyl acetylene have also been observed in very large abundances (Cernicharo et al. 2021a,b). These hydrocarbons may hold the key to the formation of initial aromatic rings, from which larger PAHs can grow.


For the sources with the full JHKs photometric information (309 objects out of 507 found in the 2013 HKs catalogue), we first check the source's position in the CCD diagram. In Fig. 4(c), the solid black line represents evolutionary models, the dashed black and grey lines the locus of T-Tauri stars and the corresponding uncertainties (Meyer et al. 1997), whereas the dash–dotted rectangle represents the locus of Herbig AeBe stars (Hernández et al. 2005). The dotted red lines are the reddening vectors (Cardelli et al. 1989), encompassing the regions where the colours are consistent with reddened evolutionary models (region A), CTTSs (region B) and Herbig AeBe stars (region C). If the star falls in region A of the CCD, its extinction and corresponding mass are derived by de-reddening its photometry to the 1 Myr isochrone in the J, (J − H) CMD. In region B, the extinction is derived by de-reddening the colours to the CTTS locus (Meyer et al. 1997). We note that the objects in region A could also be part of the CTTSs; however, the derived AV differences are typically smaller than the derived uncertainties, and for simplicity we decide to only consider the evolutionary models. The derived extinction is then used to convert the J-band photometry to the absolute J-band magnitude, which is in turn compared to the models to derive the mass. For the stars in region B, in addition to the interstellar extinction, we also correct for an excess due to the circumstellar disc or envelope, chosen randomly in the interval 0–0.7 mag for the J band (Cieza et al. 2005). In the case that the derived mass is larger than 2 M⊙ (upper mass limit for T-Tauri stars), the procedure is repeated by de-reddening the colours to the Herbig AeBe locus (Hernández et al. 2005). The intrinsic colour in this case is a randomly chosen value within the dash–dotted box shown in Fig. 4(c), falling along the reddening line. The same procedure is performed if the object falls within region C. Finally, if the object falls to the left of region A, or to the right of region C, the extinction and mass cannot be derived.


A great deal of this progress is attributed to reverberation mapping (RM) campaigns since the 1980s, with the underlying principle proposed by Bahcall et al. (1972) and Blandford & McKee (1982). Photons of emission lines from structured ionized gas trace different paths to observers, leading to time lags (τ) of the emission lines with respect to the ionizing photons. Such RM campaigns focusing on broad Balmer lines had detected the anticipated lags in a number of Seyfert galaxies (e.g., Peterson 1993; Peterson et al. 1998; Bentz et al. 2013; Barth et al. 2015; U et al. 2022) and quasars (e.g., Kaspi et al. 2000; Du et al. 2014, 2018a; Shen et al. 2019) over the past few decades. Along with the growing investment of observing resources and the development of analytical algorithms, the general geometry and kinematics of BLRs in some AGNs have been revealed by velocity-resolved delay analysis (e.g., Bentz et al. 2010; Denney et al. 2010; Grier et al. 2012, 2013; Du et al. 2016a; U et al. 2022), velocity-delay maps (e.g., Xiao et al. 2018; Horne et al. 2021), or dynamical modeling (e.g., Bottorff et al. 1997; Pancoast et al. 2014; Li et al. 2018; Williams et al. 2020). Many resolved BLRs have a disk-like geometry of their Hβ line region (the other have inflow or outflow, or a kind of mixture of the three configurations)1. Moreover, the repeat RM observations of the same emission line and the RM results of the emission lines with different ionization in a few AGNs (e.g., NGC 5548, 3C 390.3, NGC 3783, NGC 7469, Mrk 817 etc.) approximately demonstrated the relation VFWHM ∝ τ−1/2, demonstrating evidence for potential of SMBHs (e.g., Peterson & Wandel 2000; Peterson et al. 2004; Lu et al. 2021), where VFWHM is the full-width-half-maximum (FWHM) of the emission lines. Considering the disk-like geometry of BLRs in some AGNs, this relation probably indicates a nearly Keplerian rotation of the disk BLRs. More recently, the GRAVITY instrument mounted in Very Large Telescope Interferometer (VLTI) spatially resolved the BLRs in several AGNs (e.g., 3C 273, NGC 3783, IRAS 09149 by GRAVITY Collaboration 2018, 2020b, 2021, respectively) and also found that their BLRs are approximately characterized by Keplerian rotating disks.


We combine theoretical prescriptions with realistic simulations of asteroseismic observations to construct the first magnetic detection method based on the period spacing of mixed modes. This study opens the way for an extensive search of magnetic fields inside evolved stars with solar-like oscillations. Due to the known effect of magnetic fields on mixed-mode frequencies from Bugnet et al. (2021), the magnetic signature on local measurements of the period spacing of g-modes investigated here should not get mistaken for another known physical process also leading to frequency shifts (e.g., latitudinal differential rotation, centrifugal effects, glitches, near-degeneracy effects). Such a detection of magnetic-field signatures from the measurement of the period spacing of g-modes can then be inverted to get an estimate of the radial magnetic-field strength inside RGs following Mathis et al. (2021), as it is already possible for the internal rotation (e.g., Deheuvels et al. 2017, 2020). Our methodology is well-suited for stars observed with low-inclination angles or observed pole-on, as it is based on azimuthal order m = 0 components to avoid additional signatures in the LS periodogram resulting from the distinct periodicity of m = ±1 modes. As long as the magnetic-field amplitude remains moderate, the method presented here can be applied even if the field is inclined inside the star (see Appendix F). From the statistics on the amplitudes of oscillations on the RGB (e.g. Stello et al. 2016a), intermediate-mass stars seems more likely to host strong magnetic fields than low-mass stars during the RGB. There are a few stars in the study of Gehan et al. (2020) that are observed with low-inclination angles, with a mass above 1.3 solar masses, and that present a rather low value of ΔΠ1 from the study of Vrard et al. (2016). The detection of magnetic fields inside these stars is out of the scope of this paper and its focus on methodology, but we are able to identify these stars as the best sample for the search of buried magnetic fields. The observational search is made possible thanks to the theoretical progress made in this study. Such a detection would be game-changing for improving the understanding of all stars of low and intermediate mass, as they are described as non-magnetic bodies in current stellar evolution models. The presence of strong internal magnetic fields inside the radiative interior of stars along their evolution would modify stellar age estimates and would thus affect many astrophysical areas – from planet habitability2 studies to galacto-archeology (Rauer et al. 2014; Chaplin et al. 2020).


As given in equations (1)–(3), ϕ(r) and i(r) are needed when deriving the LOS model velocity at a projected sky position (x, y). Specifically, equations (2) and (3) imply that
(4)
\begin{eqnarray}
r &=& \Biggl [\biggl \lbrace -(x-x_{C}) \, \sin \phi + (y-y_{C}) \, \cos \phi \biggr \rbrace ^2 \nonumber \\
&&+\,\biggl \lbrace \frac{(x-x_{C}) \, \cos \phi \ + (y-y_{C}) \, \sin \phi }{\cos i} \biggr \rbrace ^2\Biggr ]^{\!1/2}.
\end{eqnarray}
If ϕ and i are independent of r, the latter can be directly derived from equation (4). However, if not, adequate functional forms that provide a sufficient approximation to the radial variations of ϕ and i should be assumed. As discussed earlier, kinematic ϕ and i can vary with galaxy radius due to dynamical structures in galaxies including lopsidedness, warps, bars, spiral arms and non-circular motions. The combined effect of such structures tends to result in random variations of ϕ and i which are not necessarily described by any specific functional form. To remove any unphysical discontinuities of ϕ and i and regularize their radial variations, we use the basis spline (de Boor 1978), also called the ‘B-spline’. This is a piecewise radial polynomial function of degree n where the order n is less than the number of rings in the tilted-ring model. The radial extent of the galaxy is broken up into some number of intervals where each interval has two endpoints, called ‘breakpoints’. For continuity and smoothness, these breakpoints are converted to ‘knots’ which constitute a knot vector
(5)
\begin{equation}
\displaystyle {\boldsymbol t} = \{t_{0}, t_{1}, \ldots, t_{n+k-1}\},
\end{equation}
where n is the number of basis splines of order k.
(6)
\begin{eqnarray}
\displaystyle B_{m,1}(r) &=& \left\lbrace \begin{array}{rl}1 & \qquad t_{m} \le r < t_{m+1} \\
0 & \qquad \rm {otherwise} \end{array} \right.
\end{eqnarray}
(7)
\begin{eqnarray}
B_{m,k}(r) &=& \frac{r-t_{m}}{t_{m+k-1} - t_{m}}B_{m,k-1}(r) \nonumber \\
&&+\,\,\frac{t_{m+k} - r}{t_{m+k} - t_{m+1}} B_{m+1,k-1}(r),
\end{eqnarray}
where m = 0, 1, …, n − 1. Constant, linear, quadratic
and cubic B-splines are given by k = 1, 2, 3 and 4, respectively. The models of ϕ and i used in the new algorithm are given by expanding the B-spline functions as follows:
(8)
\begin{equation}
\phi (r) = \sum _{l=1}^{U} c^{\phi }_{u}B^{\phi }_{l, k}(r),
\end{equation}
(9)
\begin{equation}
i(r) = \sum _{m=1}^{V} c^{i}_{v}B^{i}_{m, k}(r),
\end{equation}
where U and V are the numbers of B-splines, and $c^{\phi }_{m}$ and $c^{i}_{m}$ are the coefficients of the B-splines for ϕ and i, respectively. Similarly, the expansion velocity, vEXP, can also be modelled by the expansion of W B-spline functions,
(10)
\begin{equation}
v_{\rm EXP}(r) = \sum _{n=1}^{W} c^{v_{\rm EXP}}_{w}B^{v_{\rm EXP}}_{n,k}(r).
\end{equation}


The GMC associated with G305 is one of the most massive and luminous clouds in the Milky Way (Fig. 1). It is located in the Galactic plane at l ~ 305°, b ~ 0° and at a kinematic distance of 4 kpc (derived from a combinationof radio and Hα observationsby Clark & Porter (2004); Davies et al. (2012) measured its spectrophotometric distance to be 3.8 ± 0.6 kpc and most recently Borissova et al. (2019) measured the Gaia DR2 average distance to be 3.7 ± 1.2 kpc); this places it in the Scutum-Crux spiral arm. Given this distance, the complex has a diameter of ~ 30 pc (Clark & Porter 2004) and a molecular mass of ~6 × 105 M⊙ (Hindson et al. 2010). The G305 complex consists of a large central cavity that has been cleared by the winds from massive stars belonging to two visible central clusters (Danks 1 and 2) and the Wolf-Rayet star (WR48a; Clark & Porter 2004; Davies et al. 2012). The cavity is surrounded by a thick layer of molecular gas (traced by CO and NH3 emission; Hindson et al. 2010, 2013). Radio continuum observations by Hindson et al. (2012) have revealed that the cavity is filled with ionized gas and identified six ultra-compact HII (UC HII) regions and also one bright rimmed cloud (BRC) at the periphery of the cavity, indicating molecular gas irradiated by UV radiation (Sugitani & Ogura 1994; Thompson et al. 2004), which may cause implosion (Bertoldi 1989) or evaporation. A number of studies havereported star formation tracers (water and methanol masers, HII regions and massive young stellar objects, MYSOs; Clark & Porter 2004; Lumsden et al. 2013; Urquhart et al. 2014; Green et al. 2009, 2012). Furthermore, Hindson et al. (2010) found the concentration of star formation tracers to be enhanced inside a clump of NH3 bearing molecular gas that faces the ionizing sources, which is consistent with the hypothesis that the star formation has been triggered. Analysis of the stellar clusters in the complex reveals them to have ages of 1.5 Myr for Danks 1 and 3 Myr for Danks 2,with the former possibly being triggered by the latter (Davies et al. 2012). Additionally, a diffuse population of evolved massive stars was also found to exist within the confines of the G305 complex that had formed around the same time as the two clusters (Leistra et al. 2005; Shara et al. 2009; Mauerhan et al. 2011; Davies et al. 2012; Faimali et al. 2012; Borissova et al. 2019).


From the plot, we can see that there are some outliers in the sample. We will discuss these systems specifically in the following. For the system with an open circle, it is more likely to have a WD mass larger than 0.48 $\rm M_{\odot }$ and could have a CO WD rather than a He WD. Among these observed data, there are three systems with small orbital periods (log(Porb/days)  −1.2) (open squares). For the two systems with orbital periods ($\rm {log} (P/\rm {days})$) around –1.6, their sdB masses roughly equal to 0.3 $\rm M_{\odot }$ (Burdge et al. 2020). Because only these sdB progenitors with non-degenerate cores can ignite the helium when their core masses are around 0.3 $\rm M_{\odot }$ (Han et al. 2002, 2003). Their progenitor masses of sdB stars are likely to be larger than $2.0\,\,\rm M_{\odot }$. For these progenitors, they have a larger binding energy of envelopes leading to smaller orbital periods after CE ejection. For the system PTF1 J0823, Kupfer et al. (2017) claimed that the progenitor of the sdB star in this system is likely to have a non-degenerate core. For the three systems with minimum WD masses smaller than $0.20\,\,\rm M_{\odot }$, it is unclear how the systems formed if the WD masses are confirmed to be less than 0.2 $\rm M_{\odot }$. In principle, stellar objects with such a low mass could be also low-mass MS stars but the fact that no reflection effect in their light curves has been detected excludes this possibility (Maxted, Morales-Rueda & Marsh 2004; Kupfer et al. 2015). As we mentioned in the first paragraph of this section, it is possible that some WDs with masses smaller than 0.48 $\rm M_{\odot }$ in the sample are non-pure He WDs. For these kind of systems, the progenitor of WDs have masses larger than 2.0 M⊙ and non-degenerate He core ignition on the RGB. After their H envelopes are stripped, they can evolve into WDs with CO cores. With a binary population synthesis method, we estimate that the contribution of low mass (0.48 M⊙) non-pure He WD + sdB binaries to low mass (0.48 M⊙) WD + sdB binaries is less than $5{{\ \rm per\ cent}}$.


To overcome these limitations, in our previous paper (Chatzistergos et al. 2018b, Paper I, hereafter) we introduced a novel approach to process the historical and modern Ca II K observations, to perform their photometric calibration, to compensate for the intensity centre-to-limb variation (CLV, hereafter), and to account for various artefacts. By using synthetic data, we also showed that our method can perform the photometric calibration and account for image artefacts with higher accuracy than other methods presented in the literature. More importantly, we showed that, as long as the archives are consistent with each other, for example, they are centred at the same wavelength and employing the same bandwidth for the observations, the method can be used to derive accurate information on the evolution of plage areas without the need of any adjustments in the processing of the various archives (Chatzistergos et al. 2019b, Paper II, hereafter). In Paper II, we applied our method to 85 972 images from 9 Ca II K archives to derive plage areas and produce the first composite of plage areas over the entire 20th century. In particular, we analysed the Ca II K archives from the Arcetri, Kodaikanal (8-bit digitisation), McMath-Hulbert, Meudon, Mitaka, Mt Wilson, Rome/PSPT, Schauinsland, and Wendelstein sites. Five out of the nine analysed archives were amongst the most studied and prominent ones, while the remaining archives were from less studied data sources. There are, however, many other Ca II K archives that are available and still remain largely unexplored. These archives harbour the potential to fill gaps in the available plage series as well as to address inconsistencies among the various archives and within individual archives (e.g. change in data quality, or in the measuring instrument with time). Moreover, since the work presented in Paper II, more data from various historical and modern archives became available in digital form. In particular, historical data that have been made available in the meantime include those from the latest 16-bit digitisation of the Kodaikanal archive, Catania, Coimbra, Kenwood, Kharkiv, Kyoto, Manila, Rome, Sacramento Peak, and Yerkes observatories, as well as additional data from the Meudon and Mt Wilson archives. In this light, here we present results from the most comprehensive analysis to date of historical and modern Ca II K observations taken between 1892 and 2019 from 43 different datasets for the purposes of producing a composite plage area series.


We made use of the Pipe3D pipeline (Sánchez et al. 2016a,b, 2018) to perform the spatially resolved stellar population analysis of the data cubes. We note that Pipe3D is based on the stellar population synthesis code FIT3D (Sánchez et al. 2016a,b), which uses the GRANADA and MILES simple stellar population (SSP) libraries in the current implementation to model and subtract the stellar spectrum and fit the emission lines. The GRANADA and MILES (gsd156) stellar library is a combination of the empirical stellar library of Vazdekis et al. (2010) and the theoretical stellar libraries of González Delgado et al. (2005) and González Delgado & Cid Fernandes (2010). The SSPs use a Salpeter (1955) initial mass function and cover 39 stellar ages (from 1 Myr to 14.1 Gyr1) and four metallicities (Z = 0.002, 0.008, 0.02, and 0.03). It is important to note that FIT3D performs the SSP fitting within the wavelength of 3500 Å –7000 Å. In addition, FIT3D considers the effects on dust extinction during the stellar population synthesis using a Cardelli et al. (1989) extinction law. FIT3D provides the SSP decomposition of the modeled stellar spectra of each spatially resolved region of the galaxies. With this decomposition, we can estimate the respective SFHs and the cumulative mass temporal distributions (or mass growth histories; e.g., Ibarra-Medel et al. 2016, 2019; Sánchez et al. 2019). In order to estimate the contemporary (local and integrated) SFR values, we smoothed the SFHs within a period of 30 Myr. These quantities are independent of SFR estimations that use the Hα emission line flux. For star-forming galaxies, both estimates are very similar, showing that the SFR calculated in the last 30 Myr is related to massive young stars, contributing to the Hα emission. For retired galaxies, the SFR calculated from the Hα flux is likely overestimated because this flux is dominated by effects of post-AGB stars rather than of young stars (see, e.g., Bitsakis et al. 2019; Sánchez et al. 2019). However, in these galaxies, the SFR derived from the stellar population synthesis with Pipe3D should also be considered as an upper limit. To fit the emission lines, Pipe3D subtracts the modeled stellar spectra and fits a series of Gaussian profiles for each line (Sánchez et al. 2016b). With those fits, Pipe3D provides the total flux, dispersion, and the kinematics of each emission line. The quality of the emission line fits of Pipe3D (and other codes) was tested using MUSE data (Sánchez-Menguiano et al. 2018; Bellocchi et al. 2019; López-Cobá et al. 2020). With the use of the adjacent continuum windows (from the modeled stellar spectra) for each emission line, Pipe3D estimates the stellar continuum flux and provides the equivalent width of each emission line.


The observed QPOs are generally attributed to oscillations of the star excited by an explosion of magnetic origin that creates the flare. The oscillating stellar surface should modulate the charge density in the magnetosphere, creating variations in the optical depth for resonant Compton scattering of the hard X-rays that accompany the flare (Timokhin et al. 2008; D’Angelo & Watts 2012). In this connection, the problem of finding the oscillatory modes for a strongly magnetized neutron star has received much attention, and has proven to be a formidable problem. To make the problem tractable, most theoretical treatments of the QPO problem have assumed smooth field geometries, usually dipolar or variants (e.g., Glampedakis et al. 2006; Levin 2006, 2007; Sotani et al. 2008a, 2008b; Cerdá-Durán et al. 2009; Colaiuda et al. 2009; Colaiuda & Kokkotas 2011; Gabler et al. 2011, 2012, 2013a, 2013b, 2014; van Hoven & Levin 2011, 2012; Passamonti & Lander 2013). Smooth field geometries support a problematic Alfvén continuum that couples to the discrete natural spectrum of the crust. As pointed out by Levin (2006), if energy is deposited in the crust at one of the natural frequencies of the crust, and this frequency lies within a portion of the core continuum, the energy is lost to the core continuum in less than 0.1 s as the entire core continuum is excited. The crust excitation is effectively damped through resonant absorption, a familiar process in MHD; see, e.g., Goedbleod & Poedts (2004). The problem has been addressed by assuming field geometries with gaps in the Alfvén continuum. Under this assumption, long-lived quasi-normal modes can exist inside the gaps or near the edges of the Alfvén continuum. van Hoven & Levin (2011) showed for a “box” neutron star that introduction of a magnetic tangle breaks the Alfvén continuum. Link & van Eysden (2015) showed that for magnetic tangling in a spherical neutron star the problematic Alfvén continuum disappears.3

3
Sotani (2015) added general relativity in the treatment of the magnetic field, and confirmed some of the results of Link & van Eysden (2015).
 They found that the star acquires discrete normal modes, and quantified the mode spacing. It is clear from these investigations that the unknown magnetic field geometry is the most important ingredient in determining the oscillation spectrum of a magnetar.


To understand the 3D magnetic properties of the FC observed here, we reconstructed the coronal magnetic field of the source region based on the nonlinear force-free field (NLFFF) assumption using the HMI photospheric vector magnetogram as the bottom boundary (Yan et al. 2001; Canou et al. 2009; Wiegelmann & Sakurai 2012; Yang et al. 2016b; Zhong et al. 2019; Qiu et al. 2020). We first tried the extrapolation method (Guo et al. 2010; Zhu et al. 2016) and found that it is difficult to reproduce the magnetic field comparable with the morphology of the observed filament threads. We then resorted to the magnetic flux rope (MFR) embedding method based on regularized Biot-Savart laws (RBSL; Titov et al. 2014, 2018; Guo et al. 2019). The procedure was divided into four steps. First, we took advantage of the 304 Å images at 05:24 UT to derive the path of the FC, as shown in Fig. 7a. According to previous statistics (Tandberg-Hanssen 1995; Filippov & Den 2000; Engvold 2015), the height of active region filaments ranges from 5 Mm to 30 Mm. We therefore set the height of the MFR axis to 30 Mm and the MFR minor radius to 25 Mm, assuming that the lower half of the MFR is fully filled by cool material. The 3D path of the MFR was estimated according to Guo et al. (2021a). Second, we calculated a potential field utilizing the normal magnetic field component, where the projection effect was corrected (Wiegelmann et al. 2006; Guo et al. 2017). Third, we set the physical parameters of the RBSL model including the average value of unsigned magnetic flux at the two MFR footprints (1.72 × 1021 Mx) and the strength of the electric current following Eq. (12) in Titov et al. (2018). Finally, we inserted the MFR derived by the RBSL model into the potential field along the path of the FC and then performed a relaxation using the magnetofrictional code (Guo et al. 2016a,b). After relaxation, the force-free metric was σJ = 0.28, and the divergence-free metric was ⟨|fi|⟩ = 1.47 × 10−4, which were sufficiently small and generally acceptable according to Guo et al. (2021a)1.


The theory of angular momentum evolution due to mass transfer via Roche lobe overflow and gravitational wave radiation is well established and leads to quantitative predictions (Landau & Lifschitz 1958; Paczyński 1967; Faulkner 1971; Verbunt 1993). However, angular momentum losses due to emission of gravitational waves only dominate at short orbital period (Porb ≲ 2 h), while other mechanisms, such as magnetic braking, are invoked to explain the orbit evolution at longer periods. The theory at the heart of the magnetic braking model is based on the same physical principles through which magnetic stellar winds are known to decelerate the rotation of low-mass stars (e.g. Kraft 1967; Skumanich 1972; Soderblom 1983). In synchronized binaries (typically the case of LMXBs), the angular momentum loss from the companion star is continuously re-distributed to the angular momentum of the whole binary system, therefore affecting its orbital period and binary separation (e.g. Tauris 2001). Large uncertainties are involved in the extrapolation of magnetic braking from isolated low-mass stars to the case of synchronized companion stars in LMXBs (e.g. see discussion in Knigge, Baraffe & Patterson 2011). Indeed, despite the large allowed range of model parameters (possibly translating into more than one order of magnitude on efficiency of angular momentum removal), magnetic braking often fails to reproduce measured values of the orbital period derivative, at least in the case of conservative mass transfer (Di Salvo et al. 2008; Hartman et al. 2008, 2009; Hu, Chou & Chung 2008; Burderi et al. 2010; Jain, Paul & Dutta 2010; González Hernández, Rebolo & Casares 2012, 2014). Additional mechanisms, typically involving outflows, are generally necessary to explain these discrepancies (Di Salvo et al. 2008; Hartman et al. 2008, 2009; Burderi et al. 2010). We also note that some of the best-monitored sources (i.e. EXO 0748−676; Wolff et al. 2009) show erratic variations of the orbital period with amplitudes of ΔP/P ∼ 10−5 and possible trends recurring on time-scales of years-to-decades, such as those observed in e.g. Algols systems (Kreiner & Ziolkowski 1978; Hall 1989). These variations are thought to be the consequence of the torque provided by the magnetic activity of a sub-surface magnetic field in the companion star with convective envelope. The latter induces a cyclic exchange of angular momentum between the inner and outer parts of the companion star causing a change in the gravitational quadrupole moment (Applegate 1992; Applegate & Shaham 1994; Lazaridis et al. 2011).


Several observational pieces of evidence confirmed the existence of a relativistically blurred reflection component in AGNs. In particular, X-ray spectroscopy has proven to be a powerful tool to identify the reflection features in AGNs X-ray spectra, allowing us to probe the innermost regions of AGNs (e.g. Fabian et al. 2009). Additionally, this technique may provide estimates of black hole spins (e.g. Risaliti et al. 2013; Marinucci et al. 2014; Walton et al. 2014). This was achieved thanks to the high-quality spectra provided by XMM–Newton (Jansen et al. 2001) and NuSTAR (Harrison et al. 2013) in the 0.3–80 keV range. The first observational X-ray feature associated with relativistic effects was the anomalous shape of the aforementioned iron K α line detected in type-1 AGNs, where the observer has a direct view of the central engine through the polar direction of the system (e.g. Matsuoka et al. 1990; Pounds et al. 1990). The shape of the iron line, with an extended red wing spanning over several keV was soon associated with special and general relativistic effects blurring the signal (e.g. Tanaka et al. 1995; Iwasawa et al. 1996; Nandra et al. 1997). By fitting the observed iron line with relativistic models, it became possible to determine the spin of the black hole (BH), its mass and inclination (see e.g. Miller 2007, for a review). Yet, an alternative interpretation, based on partial covering absorption, has been proposed in order to explain the apparent red wing of the Fe line and the spectral curvature at hard X-rays (e.g. Miller, Turner & Reeves 2008, 2009). The two scenarios have different advantages: on the one hand, blurred reflection is able to explain the spectral and timing properties of accreting systems for a wide range of BH mass. On the other hand, the Compton-thin to Compton-thick (and vice versa) rapid transitions that are observed in “changing-look” AGNs (Matt, Guainazzi & Maiolino 2003) is suggestive that partial covering should be also taken into consideration. In addition, several occultation events, associated with both Compton-thin and Compton-thick clouds in the broad-line region (BLR), have been reported in AGNs (e.g. Risaliti et al. 2007, ; Nardini & Risaliti 2011; Sanfrutos et al. 2013; Torricelli-Ciamponi et al. 2014). Markowitz, Krumpe & Nikutta (2014) estimated the probability to observe an X-ray eclipse (of any duration between 0.2 d and 16 yr) in a given source to be in in the ranges 0.003–0.166 and 0.039–0.571, for type I and type II AGNs, respectively. By studying X-ray eclipses, it might be possible to constrain the importance of partial obscuration, together with the geometry and location of the distant obscuring clouds. This is particularly relevant since obscuration events from BLR clouds do not affect only the AGNs light curves but they show also a strong impact on their spectroscopic and polarimetric properties. Risaliti et al. (2011) investigated the effects of successive eclipses of the receding and approaching parts of the accretion disc on the shape of the iron line. In fact, due to special and general relativistic effects, obscuring various parts of the disc will result in a variability in the profile of the observed emission line, which provides a new probe of the innermost regions of the disc. In a similar fashion, Marin & Dovčiak (2015) explored the effects of such events on the polarimetric signal. The authors showed that eclipses induce a variability in the polarization signal due to the covering of different parts of the disc emitting a non-uniformly polarized light, mainly due to relativistic effects.