In view of the ultrahigh mass of the merger product of around 2.5 M⊙, it is undoubtedly necessary and important to further test the existence of post-merger NSs (Gao et al. 2016; Li et al. 2016, 2017; Ai et al. 2018; Zhu et al. 2018; Sarin et al. 2020; Beniamini & Lu 2021), which can provide a robust constraint on the equation of state of the NS matter and then improve our understanding of the low-energy feature of strong interaction. Besides the GRB 170817A/AT 2017gfo event, searches for possible kilonova emission have already been carried out in the afterglows of many SGRBs since 2013 (Berger et al. 2013; Tanvir et al. 2013; Yang et al. 2015; Jin et al. 2015, 2016, 2018, 2020; Gao et al. 2015, 2017; Kasliwal et al. 2017). Among the SGRBs with a kilonova candidate, GRB 160821B has one of the lowest redshifts, of namely z = 0.162. From its optical/near-infrared(NIR) afterglow, an obvious excess was found. Because of its close distance, the kilonova emission associated with GRB 160821B is in principle detectable and can provide a natural explanation for the observed optical/NIR excess (Lamb et al. 2019; Troja et al. 2019). In view of its luminosity, which is lower than that of AT 2017gfo, the kilonova after GRB 160821B can in principle be modeled with a pure radioactive power. However, it could still be necessary to mention that a significant internal plateau appeared in the early X-ray afterglow during the first few hundred seconds (see the insert in Fig. 1), which indicated that a post-merger NS also exists in this event. According to these observations, Ma et al. (2021) suggested that the post-merger NS could collapse into a black hole and then the subsequent kilonova could be powered by the accretion onto the black hole. Nevertheless, alternatively, as suggested by Yu et al. (2018), the steep decay after the internal plateau may not represent the collapse of the NS, but may simply be caused by the suppression of the magnetic dipole radiation of the NS. In this case, the spin-down of the NS of relatively low luminosity can still power the kilonova emission, which can be generally called a mergernovae (Yu et al. 2013). This scenario can provide a natural explanation for the AT 2017gfo emission. Therefore, in our opinion, this situation could also appear in the case of GRB 160821B. This paper is devoted to testing whether or not there is a nonthermal emission component arising from the interaction between the NS wind and the merger ejecta, as mentioned above for AT 2017gfo.


AFGL 2136 IRS 1 (also referred to as CRL 2136, G17.64+0.16, and IRAS 18196−1331) is a luminous (1.0 × 105 L; Lumsden et al. 2013), high-mass (45 ± 10 M; Maud et al. 2019) protostar that is believed to be in the latter stages of its evolution due to a variety of observed characteristics (Boonman & van Dishoeck 2003; Maud et al. 2018 and references therein). It is located at a distance of 2.2 kpc away from the Sun (Urquhart et al. 2014), and has been extensively observed from centimeter to micron wavelengths, at low and high angular resolution, and low and high spectral resolution. The myriad observations paint a picture where a single, isolated massive protostar is driving a wide-angle bipolar outflow through its natal cloud. The large scale outflow is observed in CO emission at millimeter wavelengths, with both the red and blue lobes being about 100″ in extent (Kastner et al. 1994; Maud et al. 2018). Closer to the central source (2″–10″), the outflow cavity walls are seen in scattered light at near-infrared wavelengths (Kastner et al. 1992; Murakawa et al. 2008; Maud et al. 2018). The cool molecular envelope exhibits ice and dust absorption bands (Willner et al. 1982; Keane et al. 2001b; Dartois et al. 2002; Gibb et al. 2004), as well as molecular emission at millimeter wavelengths (van der Tak et al. 2000a, 2000b), but a much warmer component is also inferred from several different molecules seen in absorption in the near- to mid-infrared (Mitchell et al. 1990; Lahuis & van Dishoeck 2000; Keane et al. 2001a; Boonman et al. 2003; Boonman & van Dishoeck 2003; Goto et al. 2013, 2019; Indriolo et al. 2013a). The presence of a dust disk on small spatial scales was suggested by near-infrared polarization imaging (Minchin et al. 1991; Murakawa et al. 2008) and by mid-infrared interferometric observations (de Wit et al. 2011; Boley et al. 2013). A compact source was marginally resolved at centimeter wavelengths, along with a cluster of nearby 22 GHz H2O masers (Menten & van der Tak 2004), but only with the recent ALMA 1.3 mm continuum observations has the 93 × 71 mas dust disk been fully resolved (Maud et al. 2019). Thermal line emission at 232.687 GHz from the H2O ν2 = 1–1, 55,0–64,3 transition has the same spatial extent as the dust emission, and the H2O gas velocities indicate Keplerian rotation within the disk (Maud et al. 2019). It is ideal that the reader has a clear picture of the AFGL 2136 region in mind to best understand the discussion throughout this paper. In particular, Figure 10 of Maud et al. (2018) provides an up-to-date schematic diagram of the AFGL 2136 region, and Figures 1 and 2 of Maud et al. (2019) present the compact disk observed in dust and gas emission, respectively.


As Parker Solar Probe (PSP) descends deeper into the solar corona on its succeeding orbits, its measurements reveal features of the heliospheric plasma that will significantly increase our fundamental understanding of the workings of the solar corona, the origins of the solar wind, and the behavior of heliospheric energetic particle populations (Fox et al. 2016). In the first several orbits, PSP approached progressively nearer to the range of altitudes at which the accelerating solar wind speed exceeds the Alfvén speed. This critical zone is not a simple surface, but a more irregularly defined region above which (incompressive) magnetohydrodynamic signals, such as Alfvén waves, can no longer return to the lower altitude corona. In this very region, the analysis of heliospheric imaging (HI; DeForest et al. 2016) has described a transition from striated images that appear to be highly collimated due to a structured magnetic field and lower plasma beta to higher altitude images that appeared to be more disordered and isotropic, a condition described as “flocculation.” A number of interesting features have been reported from observations in the region, including periods of near-corotation and, notably, the appearance of magnetic reversals or “switchbacks” (Bale et al. 2019) and accompanying plasma jets (Kasper et al. 2019). Switchbacks have received considerable attention, with a focus on understanding how various plasma properties respond in and near them (Bale et al. 2019; Kasper et al. 2019; Dudok de Wit et al. 2020; McManus et al. 2020; Mozer et al. 2020; Whittlesey et al. 2019). Their origin is also a subject of active discussion, with ideas ranging from distant generation in the lower corona via interchange reconnection (Axford et al. 1999; Fisk & Kasper 2020; Zank et al. 2020) to a roll-up of the magnetic field by vortices in shear-driven turbulence (Ruffolo et al. 2020). Here we examine another important set of PSP observations and their behavior near switchbacks, namely the behavior of energetic particles as measured on PSP by the integrated Science Investigation of the Sun (IS⊙IS) instrument suite (McComas et al. 2016, 2019).


A number of works have tried to explain this conundrum with different ideas, which follow one of three possibilities. When Genzel et al. (1996) first discovered missing RGB stars, they proposed that this might be due to stellar collisions depleting giant stars in the innermost parts through the high stellar densities that are reached near the SMBH. Later, Davies et al. (1998), Alexander (1999), Bailey & Davies (1999), and Dale et al. (2009) addressed this idea in detail and came to the conclusion that it can only explain the absence of the brightest and most extended giant stars. A different suggested possibility to explain the missing stars is that our GC does not only have one, but a binary of two massive black holes. This hypothesised binary could indeed carve a core into the stellar distribution through three-body interactions, as shown by a number of authors (Baumgardt et al. 2006; Portegies Zwart et al. 2006; Matsubayashi et al. 2007; Löckmann & Baumgardt 2008; Gualandris & Merritt 2012). Nonetheless, the mass of the secondary needs to be of the order of
\hbox{${\sim}10^5~M_{\odot}$}
~105M⊙

 to explain the observed core. Such a massive secondary black hole would require the Milky Way to have experienced a major merger relatively recently, which is excluded by observations (see Hansen & Milosavljević 2003; Yu & Tremaine 2003; Chen & Liu 2013). Moreover, the existence of such a massive secondary black hole is largely ruled out from a number of other considerations, for instance, constraints on the proper motion of Sgr A* from radio interferometry (see Gualandris & Merritt 2009). A number of inspiraling smaller-mass black holes can also create a shallow stellar density profile in the centre, which would relax the major merger requirement, as has been shown by Mastrobuono-Battisti et al. (2014). It has also been put forward that a star cluster falling towards the GC could increase the density profile outside of 10′′ , so that within this distance the profile would be like a core (Kim & Morris 2003; Ernst et al. 2009; Antonini et al. 2012; Antonini 2014). However, mass segregation would rebuild a steeper profile in as fast as a quarter of the relaxation time (as shown by Preto & Amaro-Seoane 2010; Amaro-Seoane & Preto 2011). This requirement would hence need a steady inflow of clusters to maintain a weak cusp profile in the centre. Finally, Merritt (2010) and Antonini (2014) found that if the nuclear cluster in the GC formed with an extended enough initial core profile, the current stellar distribution would still not be dynamically relaxed. While this solution is possible, it requires fine-tuning in the initial conditions to produce the density distribution seen in the GC. Amaro-Seoane & Chen (2014) proposed that the discs of young stars observed at the GC (Paumard et al. 2006) are connected to the missing bright giants: the precursor gaseous discmust have gone through a fragmentation phase that produced dense enough clumps to ensure an efficient removal of the outer layers of the giants through collisions, rendering them invisible to observations. Their degenerate cores would nonetheless populate the same area of phase space where the missing bright giants should be. Kieffer & Bogdanović (2016) recently showed that in order to be viable, this scenario requires the total mass of the fragmenting disc to have been several orders of magnitude higher than that of the early-type stars in the stellar discs in the GC.


After a first part of ballistic, high-speed motion, the deceleration of RK1 was rather abrupt, which is something not observed in the majority of discrete ejecta from BH XRBs (e.g Mirabel & Rodríguez 1994; Fender et al. 1999; Miller-Jones et al. 2012). This scenario is consistent with a jet that travels first at constant speed in a low-density region of the ISM, which constitutes a large scale cavity around the system, before hitting the higher density wall of the cavity itself, as already proposed in Hao & Zhang (2009). Radio emission at late times would be produced by the external shocks between the plasma blob and the ISM cavity wall, in analogy with GRB afterglows (Wang et al. 2003). Those cavities have been suggested to exist at ∼pc scales at least for XTE J1550–564 and H1743–322 (Hao & Zhang 2009; Steiner & McClintock 2012; Steiner, McClintock & Reid 2012; Migliori et al. 2017). We obtained the best modelling for the RK1 motion by a combination of a linear motion and a Sedov phase (see Section 3.3), achieved at late times due to the jet sweeping up ISM material on its path, in a similar way as Miller-Jones et al. (2011), which derived it from Wang et al. (2003). We therefore suggest that MAXI J1348–630 is located in a similar cavity, possibly carved by previous jet activity, or resulting from the action of accretion disc winds. However, so far such winds have not been detected for MAXI J1348–630. If we take our estimate of α0 ∼ 25 arcsec, the upper limit on the inclination angle of the discrete ejection of θ1 ∼ 44○ and the lowest acceptable distance of 1.6 kpc, we obtain that RK1 travelled at least ∼0.3 pc before reaching the angular distance α0, which is consistent with what has been observed for other discrete ejections (Corbel et al. 2000; Gallo et al. 2004) and could be taken as a rough lower limit on the size of the cavity.7 As argued by Hao & Zhang (2009), the presence of an underdense cavity could be a common characteristic of BH XRBs environments (Heinz 2002), and its existence could be strictly required for the jet to travel such a long distance (Hao & Zhang 2009).


The short gamma-ray burst (GRB) 170817A was observed by the Fermi- Gamma-ray Burst Monitor (GBM; Goldstein et al. 2017). The fact that it was not detected by the Insight Hard X-ray Modulation Telescope (Li et al. 2017) suggests that the burst had a very weak fluence and a soft spectrum. The burst was highly noticeable because of its connection to gravitational-wave (GW) event GW170817, which was detected by the Laser Interferometer Gravitational-wave Observatory, about 1.7 s before the GBM was triggered (Abbott et al. 2017a). To understand the event, it is crucial that we obtain all of the object’s physical properties. Compared with other short GRBs, the luminosity of GRB 170817A was extremely weak, thus suggesting that the jet was off-axis to the line of sight (Albert et al. 2017; Burgess et al. 2017; Fong et al. 2017; Granot et al. 2017a; He et al. 2017; Jin et al. 2017; Margutti et al. 2017; Metzger 2017; Troja et al. 2017; Wang et al. 2017; Xiao et al. 2017). The GW fitting parameters suggest an angle of less than 28° (Abbott et al. 2017a). Given that no prompt X-rays were detected, a number of predictions have been made for the off-axis angle. From observations by the

 and

 telescopes, Evans et al. (2017) suggested that the viewing angle was

. Constraints from deep Chandra observations suggest that it was greater than 23° (Haggard et al. 2017), whereas constraints from radio-frequency observations of a relativistic jet (Alexander et al. 2017) suggested it was

. On the basis of the upper limit from the Atacama Large Millimeter/submillimeter Array (ALMA) and Giant Metrewave Radio Telescope (GMRT) at radio bands, Kim et al. (2017) found the angle to be 41° (or 17°) but did not rule out other values. The modeling for several different bands suggested that the viewing angle was

 (Ioka & Nakamura 2017),

 (Granot et al. 2017a), or

 (Guidorzi et al. 2017). The

 versus

 plot in Pozanenko et al. (2017) shows that GRB 170817A belongs to neither the long nor short GRB groups, thus supporting the idea that it was triggered by an off-axis jet. However, the exact off-axis angle is still hard to predict. If it was derived from the relativistic beaming effect, it would have degenerated with the jet’s Lorentz factor; if it was derived from the parameter fitting of the GW signal, it would have degenerated with the distance.


Among the suggestedmechanisms responsible for the strong damping of the coronal loop oscillations (e.g., Ruderman & Roberts 2002; Ofman 2005, 2009; Morton & Erdélyi 2009) resonant absorption of the MHD waves, which was established first by Ionson (1978), is a strong candidate. Several works developed this theory (e.g., Davila 1987; Sakurai et al. 1991a, 1991b; Goossens et al. 1995; Goossens & Ruderman 1995; Erdélyi 1997; Cally & Andries 2010). The necessary condition for the resonant absorption is a continuum of Alfvén or slow frequency across the loop (Ionson 1978; Hollweg 1984, 1987; Davila 1987; Sakurai et al. 1991a). Resonant absorption occurs when the frequency of the global MHD mode matches at least with one of the frequencies of the background Alfvén or slow continuum at a location called he resonance point. As a result, the energy of the global MHD mode transfers to the local Alfvén modes in a layer around the resonance point, named the resonance layer (Lee & Roberts 1986; see also Goossens et al. 2013; Soler & Terradas 2015). In the absence of dissipation mechanisms, the amplitude of the oscillations diverges at the resonance point. Dissipation is important in the resonance layer, where the oscillations make large gradients. The background Alfvén or slow continuum can be due to the variation of the plasma density (e.g., Davila 1987; Ofman et al. 1994; Ruderman & Roberts 2002; Terradas et al. 2006; Soler & Terradas 2015), twisted magnetic field (Ebrahimi & Karami 2016), or both of them together (Karami & Bahari 2010; Giagkiozis et al. 2016). There are a variety of theoretical works related to the damping of the coronal loop oscillations based on the theory of resonant absorption of MHD waves (e.g., Goossens et al. 2002, 2009; Ruderman & Roberts 2002; Van Doorsselaere et al. 2004; Andries et al. 2005; Terradas et al. 2006; Karami et al. 2009; Karami & Bahari 2010; Soler et al. 2013; Soler & Terradas 2015; Ebrahimi & Karami 2016; Giagkiozis et al. 2016; Jung Yu & Van Doorsselaere 2016). For a good review about the theory of resonant absorption, see also Goossens et al. (2011).


The dust condensations could not arise from a thermal Jeans fragmentation process. If that is the case, with a density of 104–105 cm−3 for the surrounding medium, one may expect the mass of the condensations on the order of 20–50 M⊙ (the Jeans mass at 105–104 cm−3) and the nearest separations between the condensations around 0.2–0.5 pc (the Jeans length at 105–104 cm−3); both are clearly inconsistent with the observations. Alternatively, small dense structures can be temporary density fluctuations frequently created and destroyed by supersonic turbulence (e.g., Elmegreen 1999; Biskamp 2003; Falgarone & Passot 2003). However, σnth is found to be subsonic or at most transonic. Goicoechea et al. (2016) also found that there is only a gentle level of turbulence in the Bar. So the turbulence does not seem to be strong enough to produce the condensations. Another force that could potentially compress the cloud and produce high-density structures is a high-pressure wave from the expansion of the H ii region. Goicoechea et al. (2016) detected a fragmented ridge of high-density substructures at the molecular cloud surface and three periodic emission maxima in HCO+ (4–3) from the cloud edge to the interior of the Bar, providing evidence that a high-pressure wave has compressed the cloud surface and moved into the cloud to a distance of ∼15″ from the dissociation front. The dust condensations are also located within a distance of 15″ from the dissociation front, and thus are very likely over-dense structures created as the compressive wave passed by. The complex clumpy appearance of the condensations is probably related to the front instability of the compressive wave (Goicoechea et al. 2016), or an instability developed across different layers of the Bar (e.g., the thin-shell instability, García-Segura & Franco 1996). The velocity structure of dense gas around the dust condensations may provide insights into the feasibility of this scenario. Figure 10 shows the intensity-weighted velocity map of the H2CS (71,7–61,6) emission. A velocity gradient in a northwest–southeast direction (i.e., along the direction of the propagation of the compressive wave) is seen in the map, and is consistent with the scenario that the gas is being compressed by a high-pressure wave.


Figure 9 presents Fourier power spectrum for wave period P versus height. The initial pulse has a Gaussian spectrum of wave number k which results in a spectrum of period P. The steepening of the magnetoacoustic waves results from the growing wave amplitude with height. Hence, waves with shorter wavelengths and wave periods are present for higher y-values in their Fourier spectra. For the pulse launched from y = y0 = 0 Mm (top), the main wave period of the downward-propagating waves becomes approximately the same for all values of y  0 Mm and is equal to about 250 s. Higher up, however, the period P decays with increasing y, and attains values close to 200 s. As a result of the cut-off only short-period waves can propagate upwards while long-period waves become evanescent. Hence, the relative contribution of long P waves weakens with increasing y. We note that some of our data fits the observational findings of Wiśniewska et al. (2016), represented by diamonds over-plotted on the power spectra, and Kayshap et al. (2018), denoted by dots. The agreement of the theory with the observational data indicates that the results can be used to determine the background structure of the solar atmosphere and confirms that wave generation by the solar granulation in the partially ionized plasma dominates the behavior of the waves. For a pulse at the bottom of the photosphere (y = y0 = 0 Mm, Fig. 9 (top)), a jump in the dominant wave period is observed close to the height y = 1.5 Mm, which reaches a magnitude of 300 s. The signal launched from the bottom of the photosphere with the main period P = 250 s thus reaches the corona with P = 300 s. The wave periods in the photosphere are lower than Pac in this region, because max Pac = 240 s at y = 0.5 Mm, which means that magnetoacoustic waves are evanescent. However, in the corona above y = 2.3 Mm the acoustic cut-off period reaches values larger than P = 300 s. However, this is not the case for a pulse launched at a somewhat greater height, in the middle of the photosphere, namely for y = y0 = 0.25 Mm (see Fig. 9 (bottom)). Moreover, in this case the layers below the photosphere (y  0) oscillate with a dominant wave period of 225 s. In the photosphere, this wave period is also dominant and this time it increases slightly with height in the photosphere. Moreover, in this case there is a second dominant period, namely 250 s. In fact, this wave period is also the dominant one in the upper chromosphere and low corona in this case.


Given the quite strong surface magnetic field of the M7, thermal radiation is expected to be polarized, either if emission is from a bare surface or from an atmosphere (see Turolla et al. 2004; Potekhin 2014). The polarization properties are quite different in the two cases, although there are still uncertainties, especially at optical/ultraviolet (UV) wavelengths. One of the first predictions of quantum electrodynamics (QED), even before it was properly formulated, was vacuum birefringence, and, in particular, that a strong magnetic field affects the propagation of light through it (Heisenberg & Euler 1936; Weisskopf 1936). In thermally emitting INSs, radiation comes from a region comparable with the entire star surface, over which the magnetic field direction changes substantially. In the absence of QED vacuum polarization effects, this would produce a drastic depolarization of the radiation collected at infinity (Heyl, Shaviv & Lloyd 2003, see also Taverna et al. 2015; González Caniulef et al. 2016 and references therein). Vacuum birefringence dramatically increases the linear polarization of the observed radiation, from a level of a few  per cent up to even ∼100 per cent, depending on the viewing geometry and the surface emission mechanism (Heyl & Shaviv 2000, 2002; Heyl et al. 2003; Taverna et al. 2015; González Caniulef et al. 2016). Detecting polarization in the thermal emission from the surface of an INS will be therefore extremely valuable. First, and independently on the physical conditions of the emitting region, the detection of a large degree of linear polarization in the signal would constitute the observational evidence of QED vacuum polarization effects in the strong-field regime. Secondly, the polarization observables can be compared with emission models and help to uncover the physical conditions of INS surfaces and atmospheres, ideally complementing spectral observations (Taverna et al. 2014; González Caniulef et al. 2016).


Previous works (e.g. Holt et al. 2011; Arribas et al. 2014; Villar Martín et al. 2014, 2015) have found very high reddening and densities associated with ionised outflows in local objects (e.g. Hα/Hβ ∼ 4.91 and ne ≳ 1000 cm−3, Villar Martín et al. 2014). Concerning the reddening, although we find that the outflowing gas is generally less affected by dust extinction than the disc, the median value of the total distribution is significantly affected by dust (Hα/Hβ ∼ 4.16), with tails up to Hα/Hβ ≳ 6. Similarly, the outflow density of MAGNUM galaxies is higher than the values in the disc gas, but appears to be far lower than the values found by these authors. This could stem from the fact that the galaxies studied by Holt et al. (2011), Arribas et al. (2014) are local luminous or ultra-luminous infrared galaxies (U/LIRGs), and those of Villar Martín et al. (2014, 2015) are highly obscured Seyfert 2, thus sampling sources that are more gas and dust rich compared to our sample. However, our values are also lower than the outflow densities found in Perna et al. (2017) (ne ∼ 1200 cm−3), who targeted optically selected AGNs from the SDSS, and Förster Schreiber et al. (2018b), who presented a census of ionised gas outflows in high-z AGN with the KMOS3D survey (ne ∼ 1000 cm−3). A possible explanation could be related to the high quality of our MUSE data, which also allows us to detect the faint [S II] emission associated with lower density regions. If we calculate the median densities of the disc and outflow components, weighting for the [S II] line flux, we obtain higher values (ne ∼ 170 cm−3 and ne ∼ 815 cm−3, for disc and outflow, respectively). This shows that previous outflow density values from the literature could be biased towards higher ne because they are based only on the most luminous outflowing regions, characterised by a higher S/N. This could also mean that outflows at high-z could be far more extended than the values we observe.


The scenario presented above has been formulated in various flavors to individually explain several of the properties reported here. The main addition of this work, namely the excitation of CO in distant main-sequence and starburst galaxies, fits in the general picture that we sketched. The ensemble of properties and correlations that we reported here can be also used to revisit the definition of what a starburst is. A standard operational classification is based on the distance from the observed empirical M⋆-SFR correlation, the main sequence. This proved to be a useful distinction and an excellent predictor of several trends (e.g., Sargent et al. 2014), but recent results, including our present and previous analysis (Puglisi et al. 2019), show that the demarcation between starburst and main-sequence galaxies is more blurred that we previously considered. We do detect starburst-like behaviors in galaxies on the main sequence (Elbaz et al. 2018), likely linked to the existence of transitional objects (Popping et al. 2017; Barro et al. 2017b; Gómez-Guijarro et al. 2019; Puglisi et al. 2019, and in prep. to limit the references to recent works based on submillimeter observations). Such transition might well imply an imminent increase of the SFR, driving the object in the realm of starbursts (e.g., Barro et al. 2017b), or its cessation, bringing the system back onto or even below the main sequence (Gómez-Guijarro et al. 2019; Puglisi et al. 2019), with the CO properties potentially able to distinguish between these two scenarios. Regardless of these transitional objects, a definition of starburst based on ΣSFR, rather than ΔMS, would naturally better account for the observed molecular gas excitation properties, dust temperatures and opacities, or SFE (see also Elbaz et al. 2011; Rujopakarn et al. 2011; Jiménez-Andrade et al. 2018; Tacconi et al. 2020). As an example, in Fig. 8 we show the mean SLED of the subsample of galaxies with both CO (2 − 1) and CO (5 − 4) coverage, split at its median ΣSFR. While only tentative at this stage, this suggests a trend of increasing CO excitation with ΣSFR, consistently with Fig. 7 and what mentioned above.


The aforementioned fluid description offers a good starting point to understand the global electric circuit made of charge and current densities. However, it neglects some fundamental kinetic aspects required to self-consistently include single particle acceleration as well as radiation feedback. As kinetic simulations are much more demanding than fluid models, this approach was only scarcely investigated in the last century. Let us mention Krause-Polstorff & Michel (1985) who computed axisymmetric dead pulsar magnetospheres called electrospheres. Due to the axisymmetry of the problem they used rings of charges instead of point particles. Later with the advent on computational power, Smith, Michel & Thacker (2001) showed with slightly more sophisticated simulations that a fully field magnetosphere is unstable and collapse to an electrosphere. The first full three-dimensional electrosphere was constructed by McDonald & Shearer (2009), using an electromagnetic Particle in Cell (PIC) code. They neglect pair creation and therefore did not add any particle injection process. Eventually Philippov & Spitkovsky (2014) computed the first two-dimensional axisymmetric pulsar magnetosphere for an aligned rotator by permanently injecting particle supposed to be released from the surface, avoiding to end to an electrosphere configuration (Pétri, Heyvaerts & Bonazzola 2002). Depending on the volume injection rate, they were able to find any equilibrium between the force-free and the fully charge separated state. Chen & Beloborodov (2014) improved this model by adding a prescription for the pair creation, putting a threshold on the lepton Lorentz factor. Following the same lines, Cerutti et al. (2015) assumed particle injection only from the vicinity of the stellar surface. Belyaev (2015) injected particles from regions where a parallel electric field exists. The first full three-dimensional PIC simulations of a pulsar magnetosphere were performed by Philippov, Spitkovsky & Cerutti (2015b). For an aligned rotator Philippov et al. (2015a) also included general-relativistic corrections with frame-dragging. Soon after some observational signature predictions were added to compute light curves and spectra emanating from curvature and or synchrotron radiation like for instance Cerutti, Philippov & Spitkovsky (2016b) who then included polarization (Cerutti, Mortier & Philippov 2016a). This PIC simulations were then extended to the striped wind well outside the light-cylinder to study its dissipation (Cerutti & Philippov 2017; Cerutti, Philippov & Dubus 2020). The oblique magnetosphere with radiation and general-relativistic correction was eventually computed by Philippov & Spitkovsky (2018). Several other groups performed similar simulations like Brambilla et al. (2018) or Kalapotharakos et al. (2017, 2018) who tried to explicitly connect their simulation results to gamma-ray observations. Alternatively, more simply test particle trajectories can be explored within a fluid code (see for instance Brambilla et al. 2015).


The chemistry of C4H3N isomers in cold molecular clouds was discussed by Balucani et al. (2000), and more specifically by Balucani et al. (2002), based on crossed molecular beam experiments and ab initio calculations. In these studies, it was pointed out that reactions of the CN radical with methyl acetylene and allene are barrier-less and exothermic when producing CH3C3N and CH2CCHCN in the methyl acetylene reaction, and CH2CCHCN and HCCCH2CN in the reaction involving allene. Indeed, the reactions of CN with CH3CCH and CH2CCH2 were measured to be rapid at low temperatures (Carty et al. 2001). This chemical scheme was implemented in a chemical model by Quan & Herbst (2007) to explain the abundance of cyanoallene in TMC-1. Later on, Abeysekera et al. (2015) measured the product branching ratios of the reaction between CN and methyl acetylene at low temperatures using a chirped-pulse uniform flow and found that HC3N is the major product, while CH3C3N accounts for 22% of the products and CH2CCHCN is not formed. These results are in contrast with those obtained from crossed molecular beam experiments (Huang et al. 1999; Balucani et al. 2000, 2002), where CH2CCHCN is observed as a product of the CN + CH3CCH reaction. Therefore, the most stable isomer, CH3C3N, can be formed in the reaction of CN and methyl acetylene, the second most stable isomer, CH2CCHCN, can be formed when CN reacts with CH2CCH2 – and perhaps also with CH3CCH, depending on whether one gives credit to the chirped-pulse uniform flow experiment or to the crossed molecular beam ones – and the least stable isomer, HCCCH2CN, can only be formed in the reaction between CN and allene. These neutral-neutral reactions involving CN are therefore likely routes to the three C4H3N isomers in cold interstellar clouds such as TMC-1, where abundant CN, CH3CCH, and probably CH2CCH2 (non-polar and thus cannot be detected at radio wavelengths) are present. Moreover, the presence of HCCCH2CN (and perhaps also CH2CCHCN) can be used as a proxy of the non-polar C3H4 isomer allene since this isomer is only formed from CH2CCH2 in the aforementioned reactions of CN.


A number of sources of systematic error disproportionately affect the soft X-rays. One important example is absorption by partially ionized material around the AGN. Although the response of the absorbing gas to changes in the irradiating flux from the AGN does contribute its own time lag, this should only influence the lag-energy spectrum for Fourier frequencies lower than those of interest for our analysis (Silva, Uttley & Costantini 2016). The influence of absorption on the soft X-ray region of the spectrum (e.g. Miller, Turner & Reeves 2008; Miller et al. 2010), however, is potentially much more important and can influence the shape of the lag-energy spectrum (I19). It will therefore be prudent to select the AGN with the clearest view of the inner regions. The soft X-ray region of the reflection spectrum is also the most sensitive to modelling assumptions such as vertical disc structure (Nayakshin, Kazanas & Kallman 2000; Done & Nayakshin 2007; Różańska et al. 2011; Vincent et al. 2016). Moreover, X-ray reverberation models currently always assume that the time taken for photons to be reprocessed and reemitted in the disc atmosphere is very small compared with the light-crossing delays. This is a very good assumption for the fluorescence and scattering processes dominant for E ≳ 3 keV. However, the time taken for soft excess photons to be reprocessed will be longer, since these photons undergo enough interactions to approximately thermalize. This thermalization time is still expected to be small, but it is not yet clear if it is small enough to be neglected entirely. It is also important to note that the model we have explored here does not include a warm (kTe ∼ 0.1 keV), optically thick (τ ∼ 10–40) corona in addition to the hot corona, as is often invoked to explain the observed soft excess in AGNs (Czerny & Elvis 1987; Middleton et al. 2009; Done et al. 2012; Petrucci et al. 2018; Ursini et al. 2020). Models 1, 2, and 4 therefore effectively assume that the observed soft excess is dominated by reflection (e.g. Jiang et al. 2018; García et al. 2019). If in reality there is indeed a warm corona, its presence would make it more difficult to constrain the soft X-ray shape of the reflection spectrum (Xu et al. 2021). Since we believe our models to be most robust for E ≳ 3 keV, we ran an alternative fit ignoring E  3 keV (Model 3), and found that the 3σ error on H0 almost doubles (dH0 ≈ 60 km s−1 Mpc−1) compared to the other fits. It is therefore desirable to also include soft X-rays, but it is encouraging that constraints can even be achieved without. Ignoring soft X-rays entirely is an extreme measure. An alternative approach would be to keep the soft X-rays but trial a variety of different models, for instance with and without a warm corona. This approach would likely return uncertainties somewhere between the two extreme scenarios explored here.


The compact blobs instead likely have a different origin. The fact that compact blobs are unresolved even at the HST resolution, that they are found at ∼1 kpc distance from the galaxy barycentre, that they have relatively small stellar masses (≲15 per cent of the underlying disc), but are actively forming stars suggests that they are star-forming regions likely originated due to disc instability and fragmentation of the galaxy disc (Bournaud et al. 2014; Mandelker et al. 2017). The in situ formation of the compact blobs is further supported by their metallicity. In fact, while the disc properties are consistent with the stellar mass–metallicity relation of z ∼ 2 star-forming galaxies (e.g. Maiolino et al. 2008; Zahid et al. 2014), compact blobs instead show metallicities inconsistent with the mass–metallicity relation (Fig. 7, bottom right panel). They have a comparable metallicity to the discs, but ∼1.5 dex lower stellar masses, so they are ∼1 dex above the mass–metallicity relation. Metallicity measurements for statistical sample of galaxies with M⋆ ∼ 108 M⊙ at z ∼ 2 are still lacking and therefore at the low-mass end we are showing an extrapolation of the mass–metallicity relation derived for galaxies with M⋆ ≳ 109 M⊙. In Fig. 7, we also show the average location of dwarf galaxies with M⋆ ∼ 108 M⊙ at z ≲ 1 (Kirby et al. 2013; Calabrò et al. 2017; Hidalgo 2017). Despite some of them may have gas-phase metallicities up to 12 + log (O/H) ∼ 8.5 (Sánchez Almeida et al. 2018), on average our compact blobs seem to be ∼0.5 dex more metal-rich than dwarf galaxies (Fig. 7). The high metallicity of compact clumps further suggests that they formed in situ, due to the gravitational collapse of pre-enriched gas in unstable regions of the galaxy disc. The young ages of the blobs reported in Fig. 7 support these conclusions. In fact, the metallicity of star-forming regions is altered in about one galactic dynamical time (≳100 Myr), increasing due to the active star formation and internal production of metals. The fact that our sample clumps with metallicity measurements have ages ≲ 50 Myr points towards the conclusion that they formed in situ from metal-rich gas, since this time-scale is too short for the gas to be self-enriched due to internal star formation (Bournaud 2016). Finally, the metallicity of our sample of clumps does not clearly correlate with their star formation rate, as indeed expected if they formed from pre-enriched material, although larger statistical samples are needed to confirm this finding.


The high-resolution imaging observations of TR from IRIS reveal the ubiquitous presence of network jets. We have used three different IRIS observations of the quiet sun, which are located near the disk center. On the basis of careful inspection, 51 network jets are identified from three QS observations and used for further analysis. These 51 network jets are very well resolved and are not affected by the dynamics of other jets. The study is focused on the rotating motion of network jets along with the estimation of their other properties (speed, height, and lifetime). The mean speed, as predicted by statistical distributions of the speed, is 140.16 km s−1 with a standard deviation of 39.41 km s−1. The mean speed of network jets is very similar, as reported in previous works (e.g., Tian et al. 2014; Narang et al. 2016). However, in case of their lifetimes, we found a value that is almost double (105.49 s) that of the previously reported mean lifetime of the network jets (49.6 s; Tian et al. 2014). As mentioned above, we took only those network jets that are very well resolved in space and in the time; these criteria exclude short lifetime network jets. Therefore, our statistical distribution of the lifetime predicts a higher mean lifetime. The mean length of the network jets is 3.16 Mm with a standard deviation of 1.18 Mm. In the case of CH network jets, Tian et al. (2014) have reported that most of the network jets have lengths from 4.0 to 10.0 Mm. However, the mean length for QS network jets is smaller (3.53 Mm; Narang et al. 2016). So, the mean length for QS network jets from the present work is in good agreement with Narang et al. (2016). In addition, the apparent speed and length of these network jets are positively correlated, which is very similar to what has already been reported in previous works (Narang et al. 2016). Finally, we can say that these networks jets are very dynamic features of the solar TR, as revealed by their estimated properties.


Single-photon VUV excitation from the N2(X1

) ground state can only populate the ungerade states. Many of these ungerade states can be coupled by spin–orbit or vibronic interactions. Hence, only the ungerade states of N2 are calculated and presented. Because of the potential diffuse nature of the excited states, their wavefunctions were calculated using a large basis set composed by the aug-cc-pVQZ quality, which is augmented by 3s and 2p diffuse Gaussian-type orbitals (GTOs; Dunning 1989; Kendall et al. 1992; Woon & Dunning 1995). In addition, the expected high density of the electronic states in this energy range should lead to the mixing of their electronic wavefunctions. Therefore, a multiconfigurational approach is adopted where the electronic computations were carried out using the Complete Active Space Self Consistent Field (CASSCF; Knowles & Werner 1985; Werner & Knowles 1985) approach followed by the internally contracted Multi Reference Configuration Interaction (MRCI; Knowles & Werner 1988; Werner & Knowles 1988) technique as implemented in MOLPRO (Werner et al. 2012). We followed the procedure established in Spelsberg & Meyer (2001), Ndome et al. (2008), and Hochlaf et al. (2010a, 2010b). Briefly, the CASSCF active space is constructed by the valence molecular orbitals (MOs) of N2 increased by one sg and one pg MOs. This allows better relaxation of the wavefunctions of the N2 electronic states whose configurations differ in their s and p orbital occupations as those of interest at present. In MRCI, all CASSCF configurations were taken into account as reference. Finally, the CASSCF wavefunctions were used to evaluate the spin–orbit matrix elements. These spin–orbit computations were performed in Cartesian coordinates, where the CASSCF wavefunctions were used as the multielectron basis for the two-step spin–orbit coupling calculation (Llusar et al. 1996; Zeng et al. 2011) through the Breit–Pauli Hamiltonian (Berning et al. 2000) as implemented in MOLPRO.


The EWs were measured with the methods described in Vásquez et al. (2015). As in Paper I, we used the sum of the EWs of the two strongest CaT lines (λ8542, λ8662) as a metallicity estimator, following the Ca II triplet method of Armandroff & Da Costa (1991). Different functions have been tested in the literature to measure the EWs of the CaT lines, depending on the metallicity regime. For metal-poor stars ([Fe/H] ≲ −0.7 dex) a Gaussian function was used with excellent results (Armandroff & Da Costa 1991), while a more general function (such as a Moffat function or the sum of a Gaussian and Lorentzian, G + L) is needed to fit the strong wings of the CaT lines observed in metal-rich stars (Rutledge et al. 1997; Cole et al. 2004). Following our previous work (Gullieuszik et al. 2009; Saviane et al. 2012) we have adopted here a G+L profile fit. To measure the EWs, each spectrum was normalised with a low-order polynomial using the IRAF continuum task, and set to the rest frame by correcting for the observed radial velocity. The two strongest CaT lines were fitted by a G+L profile using a non-linear least squares fitting routine part of the R programming language. Five clusters from the sample of Saviane et al. (2012) covering a wide metallicity range were re-reduced and analysed with our code to ensure that our EWs measurements are on the same scale as the template clusters used to define the metallicity calibration. Figure 5 shows the comparison between our EWs measurements and the line strengths measured by Saviane et al. (2012) (in both cases the sum of the two strongest lines) for the five calibration clusters. The observed scatter is consistent with the internal errors of the EW measurements, computed as in Vásquez et al. (2015). The measurements show a small deviation from the unity relation, which is more evident at low metallicity. A linear fit to this trend gives the relation: ΣEW(S12) = 0.97 ΣEW(this work) + 0.21, with an rms about the fit of 0.13 Å. This fit is shown in Fig. 5 as a dashed black line. For internal consistency, all EWs in this work have been adjusted to the measurement scale of Saviane et al. (2012) by using this relation. In Table 3 we provide the coordinates, radial velocities, and the sum of the equivalent widths for the cluster member stars, both measured (“m”) and corrected (“c”) to the system of Saviane et al. 2012.


The aforementioned form of power-law primordial power spectrum is a prediction of inflation where the scalar field (inflaton) slowly rolls down to the bottom of the flat inflationary potential. With the constraints on the tilt and an upper bound on the amplitude of tensor perturbation with respect to scalar perturbation, various surveys have ruled out a wide class of models. However, fundamental questions such as the energy scale of inflation and the detailed shape of the potential remain unanswered. Note that any changes in the nearly flat potential will eventually lead to certain features in the spectrum. Local glitches in the potential including rapid change of its amplitude, or the break in its first or second derivatives (Starobinsky 1992; Starobinsky 1998; Adams, Cresswell & Easther 2001; Covi et al. 2006; Joy, Sahni & Starobinsky 2008; Joy et al. 2009; Hazra et al. 2010; Miranda, Hu & Adshead 2012; Benetti 2013; Cadavid & Romano 2015; Chluba, Hamann & Patil 2015), false vacuum decay (leading to open inflation, in particular) (Linde 1999; Linde, Sasaki & Tanaka 1999; Bousso, Harlow & Senatore 2014), or an inflection point in the potential (Allahverdi & Mazumdar 2006; Jain et al. 2009), or oscillations in the potential (Ashoorioon & Krause 2006; Pahud, Kamionkowski & Liddle 2009; Biswas, Mazumdar & Shafieloo 2010; Flauger et al. 2010; Aich et al. 2013; Hazra 2013; Peiris, Easther & Flauger 2013; Easther & Flauger 2014; Meerburg, Spergel & Wandelt 2014; Motohashi & Hu 2015; Miranda et al. 2016) all lead to local and non-local oscillations in the spectrum. Direct reconstruction of the primordial spectrum from the Planck data (Hazra et al. 2014c) hints at large-scale oscillations, an intermediate-scale burst of oscillations, and persistent high-frequency oscillations within intermediate to small scales. While these types of features can be obtained by different potentials, in this work we will be using the WWI, which is known the provide these local and non-local features in a unified framework.


Star-forming galaxies at redshifts z ∼ 1–3 probe the cosmic epoch when most of the stellar mass assembly in the universe took place (Madau & Dickinson 2014, and references therein). A better understanding of star formation (SF) during this epoch is therefore imperative to understand SF across cosmic time. Locally, less than 5% of the galaxy population has a star formation rate (SFR) that is significantly higher than the empirical main sequence for star-forming galaxies, i.e., the tight correlation (∼0.3 dex) between the SFR and stellar mass, M⋆ (Brinchmann et al. 2004; Elbaz et al. 2007, 2011; Noeske et al. 2007; Goto et al. 2011; Rodighiero et al. 2011; Sargent et al. 2012; Whitaker et al. 2012, 2014; Salmon et al. 2015). These often-called starburst galaxies, with an IR luminosity LIR ∼ (0.1–5) × 1012 L⊙ (e.g., Sanders & Mirabel 1996; Downes & Solomon 1998), become increasingly more common at high z. In fact, (sub)millimeter number counts reveal that galaxies with LIR > 1012–13 L⊙, at z > 0.5, are many hundreds of times more likely to exist than in the local universe (Blain et al. 2002; Chapman et al. 2005; Berta et al. 2011; Magnelli et al. 2011; Béthermin et al. 2012; Magnelli et al. 2013; Casey et al. 2013, 2014; Geach et al. 2013; Simpson et al. 2014; Strandet et al. 2016; Brisbin et al. 2017). Meanwhile, the cosmic molecular gas density also peaks at z ∼ 1–3 (Decarli et al. 2014, 2016a, 2016b, 2019; Walter et al. 2014; Lentati et al. 2015; Pavesi et al. 2018; Liu et al. 2019; Riechers et al. 2019). This suggests a strong link between molecular gas and SF. Rest-frame far-IR (FIR) measurements of spectral lines and thermal dust continuum emission have been used to investigate the cooling and heating processes of the interstellar medium (ISM) in star-forming galaxies; however, the physical conditions at high z are still, in general, poorly investigated (Popesso et al. 2012; Bothwell et al. 2013; Carilli & Walter 2013; Genzel et al. 2013; Yang et al. 2017; Tacconi et al. 2018, 2020; Aravena et al. 2020; Birkin et al. 2020; Boogaard et al. 2020; Lenkić et al. 2020).


Using moving meshes helps reduce the angular momentum errors from advection in grid codes. We have run >200 iterations of this test problem using the public version of fvmhd3d, systematically varying choices like the mesh regularization scheme, mesh ‘drifting’ (whether to use a strictly Lagrangian drift, or locally smoothed velocity, or regularized drift), initial mesh geometry, and boundary conditions. In both fvmhd3d and more limited tests with arepo, we find that running in the ‘simplest’ initial configuration (an initial Cartesian mesh with outflow boundary conditions, with the default mesh regularization scheme used for all other test problems shown here), the disc goes unstable and the angular momentum evolution tends to be corrupted within a few orbits (similar to the fixed-grid cases). Unfortunately, some significant errors in angular momentum evolution are difficult to avoid in moving-mesh codes, as has been discussed extensively in e.g. Duffell & MacFadyen (2012), Ivanova et al. (2013), Mocz et al. (2014) and Muñoz et al. (2014). In a shearing disc, if the cells adapt in a truly Lagrangian manner, then they are inevitably deformed into a highly sheared/irregular shape (Muñoz et al. 2014). This leads to other errors. As soon as they become non-spherical (or more accurately fail to be radially symmetric about their own cell centre of mass), then mass advection between cells necessarily leads to additional angular momentum errors (indeed, the angular momentum of an irregular cell cannot be defined exactly but only to the same order of integration accuracy as the local velocity gradient estimator). This is akin to the errors in our MFV method. More importantly, if some regularization procedure is used to keep the cell shapes ‘regular’ (as is necessary in any moving-mesh code used for this problem), then the regularization means the cells cannot move entirely with the fluid and the gas must be advected over the cells. This re-introduces some of the same (more serious) errors we saw with stationary-grid methods (specifically, see Ivanova et al. 2013, equation 53). This means that the results for moving meshes are quite sensitive to choices like the mesh ‘stiffness’, regularization procedure, and in particular the choice of boundary conditions for the mesh-generating points (since the rigid Voronoi volume partition can lead to a ‘mesh tension’ effect, whereby regularization-induced distortions in the central regions propagate outwards ‘through’ the mesh; Springel 2010). So there are ways to improve the situation on this problem – for this reason, we do not show a single ‘standard’ moving-mesh result, because significantly different results are obtained if we make just small changes to the mesh-regularization procedure in each code. However, like with AMR codes, the most effective methods for eliminating angular momentum errors in moving meshes generally depend on knowing the problem geometry ahead of time. For example, Duffell & MacFadyen (2012) design a moving grid which is a series of cylindrical shells free to rotate independently about a shared axis (the disco code); Muñoz et al. (2013) use a carefully chosen initial grid configuration with a specially designed boundary condition designed to prevent inward propagation of ‘mesh deformation’; these help considerably, but must be fine-tuned to the exact disc configuration.


While there are increasing efforts to try to explain the SFR dependence on the environment, by conducting surveys at high redshift (e.g. Hayashi et al. 2010; Matsuda et al. 2011; Sobral et al. 2011; Muzzin et al. 2012; Koyama et al. 2013; Darvish et al. 2014; Tal et al. 2014), so far such studies have not been able to fully reveal the physical processes leading to the ultimate quenching of (satellite) star-forming galaxies (e.g. Peng et al. 2010; Muzzin et al. 2012, 2014). Several strong processes have been proposed and observed, such as harassment (e.g. Moore et al. 1996), strangulation (e.g. Larson, Tinsley & Caldwell 1980) and ram pressure stripping (e.g. Gunn & Gott 1972; Fumagalli et al. 2014). Observations are also showing a variety of blueshifted rest-frame ultraviolet (UV) absorption lines which indicate that most star-forming galaxies at least at z ∼ 1–2 are able to drive powerful gas outflows (e.g. Shapley et al. 2003; Weiner et al. 2009; Kornei et al. 2012) which may play a significant role in quenching, particularly if those happen in high-density environments. Evidence of such galactic winds have also been seen in e.g. Förster Schreiber et al. (2009) through broad components in the rest-frame optical Hα and [N ii] emission line profiles (e.g. Genzel et al. 2011). Spatially resolved observations allow for constraints on the origin of the winds within galaxies, and on the spatial extent of the outflowing gas, which are essential to derive mass outflow rates. In field environments, it is expected that such outflows will not be able to escape the halo (as long as it is massive enough and it is not a satellite), and in many conditions would likely come back and further fuel star formation (e.g. Hopkins et al. 2014). However, in the most massive clusters, such strong outflows will likely result in significant amounts of gas being driven out of the subhaloes that host star-forming galaxies, enriching the intracluster medium (ICM) and quickly quenching star-forming galaxies with the highest SFRs/highest outflow rates.


The close proximity in the sky of M 16 and M 17, two of the nearest giant HII regions of our galactic neighborhood lying at a similar distance from the Sun, naturally leads to the question of whether they are physically related, and whether they may share a common origin (Moriguchi et al. 2002; Oliveira 2008; Nishimura et al. 2017). Both giant HII regions are projected on the contour of a giant bubble-shaped structure, outlined in the distribution of HI and CO emission as first noted by Moriguchi et al. (2002). Evidence for triggered star formation in M 16 has been examined in detail by Guarcello et al. (2010), who concluded it had been induced externally, and not by the activity of its associated cluster NGC 6611. This suggests that the formation of M 16 and M 17 could have been triggered by the expansion of the bubble, powered by a previous generation of massive stars near its center, thus representing an example of triggered star formation on the scale of several tens of parsecs (Elmegreen 1998). Given the ages of the giant HII regions, the timescale of expansion of a wind-blown bubble, and the short lifetimes of massive stars, it is to be expected that the most massive members of that previous generation may have exploded as supernovae several Myr ago. The spatial dispersion of the members of the association that must have taken place progressively during its existence, combined with the distance of 2 kpc to the M 16–M 17 complex and the large number of unrelated foreground and background stars in that general direction, would make it extremely difficult to identify even its currently hottest members still remaining on the main sequence. Moriguchi et al. (2002) noted the presence of O and early B stars in the area and proposed that they were part of a massive star population responsible for having caused the bubble, but a review of their properties shows them to be generally too bright to be at the distance of the bubble and the giant HII regions, and instead are more likely members of a foreground population.

Moriguchi et al. (2002)
Moriguchi et al. (2002)


The SFR reported in Table C.1 refers to a stellar mass range from Mlow = 0.1M⊙ to Mup = 100M⊙, is averaged over the past Δt = 100 Myr, and was calculated using the standard SFR(LIR) relationship from Kennicutt (1998; here scaled to a Chabrier 2003, IMF) (1)\begin{equation} \label{eq:sfr} \textit{SFR}=10^{-10}\times L_{\rm IR}[{L}_{\sun}]\, {M}_{\sun}~{\rm yr}^{-1}. \end{equation}SFR=10-10×LIR[L⊙] M⊙yr-1.This calibration relies on the starburst synthesis models of Leitherer & Heckman (1995), and it is based on the assumption of solar metallicity, and an optically thick (τdust ≫ 1) starburst region, in which case LIR is a good proxy of the system’s bolometric luminosity (LIR ≃ Lbol), and hence a sound, calorimetric probe of the obscured, current stellar birth rate. A possible caveat is that the contribution to the dust heating by more evolved stellar populations (the cirrus component; e.g. Helou 1986; Lonsdale Persson & Helou 1987; Walterbos & Greenawalt 1996) is not taken into account. If the cirrus ISM component heated by the more general galactic UV radiation field contributes to LIR, then the Kennicutt (1998) relationship overestimates the SFR. Another issue is the fact that some percentage of the UV photons can escape the starburst region without being absorbed, and hence are not reprocessed into IR photons (indeed, some of our SMGs are visible in the rest-frame UV images; Miettinen et al. 2017b). The MAGPHYS code also gives the SFR as an output, and contrary to the aforementioned LIR diagnostic, the model permits for the heating of the dust by older and longer-lasting stellar populations. We found that the SFR(LIR) is somewhat higher on average than SFRMAGPHYS: the SFR(LIR) /SFRMAGPHYS ratio was found to range from 0.47 to 6.92 with a median of \hbox{$1.31^{+0.83}_{-0.17}$}1.31-0.17+0.83, where the ± errors represent the 16th–84th percentile range (see the corresponding panel in Fig. 2). If, instead of Δt = 100 Myr, the aforementioned comparison is done by using the SFRMAGPHYS values averaged over the past Δt = 10 Myr, the median SFR(LIR) /SFRMAGPHYS ratio is found to be \hbox{$1.15^{+0.38}_{-0.27}$}1.15-0.27+0.38, which is consistent with the results obtained by da Cunha et al. (2015). Unless otherwise stated, in our subsequent analysis we use the SFR averaged over the past 100 Myr as calculated using Eq. (1).


We made use of the SALT product data generated by the in-house pipeline called PySALT (Crawford et al. 2010), which mosaics the individual CCD data to a single FITS file, corrects for cross-talk effects, and performs bias and gain corrections. We then carried out further reduction steps using our own custom tools, written in Python/PyRAF, which consist of several modules designed to handle specific steps of processing. First, we trim the regions of the CCD not containing any usable data and then fill the CCD gaps using a gradient fill. To do this, we calculate the gradient across the gap by measuring the flux values of the pixels to the right and the left of the gap, computing the difference and normalizing it to the number of pixels belonging to the CCD gap (the gradient). We then use the gradient to determine the flux values for pixels in each row of the image and replace the zero-value pixels by these flux values. This step is important to prevent discontinuities in the brightness distribution which affect the flat-fielding process which relies on the modelling of the large-scale illumination structure. Another advantage of this gradient fill is seen in the subsequent step of background subtraction. A CCD gap which appears straight in the original images becomes curved as a result of the coordinate transformation step. This causes background subtraction to result in discontinuous patches. By filling the CCD gap, these patches can be avoided. We then remove the cosmic rays using the LACosmic algorithm (van Dokkum 2001). Calibration in wavelength is achieved using arc lamps and has typical error of ±0.35 Å. We use the arc lamp to determine a coordinate transformation to ‘straighten’ frames so that every column corresponds to a unique wavelength making the background sky shape fitting and subtraction possible. Using the spectrophotometric standard data, we determine the relative flux calibration. We then check individual frames for alignment and co-add them. During this step, a standard deviation frame is constructed from which an error frame is obtained. Before the co-addition, to have consistent noise characteristics, we equalize the effective exposures of the frames – this is needed because the pupil of SALT changes by design during the observation. If Oi(x, y) are the individual observed frames, the final spectrum F(x, y) and error spectrum E(x, y) can be written as,
(1)
\begin{equation*}
F(x,y) = \left\langle O(x,y) \right\rangle = \frac{\sum _i^N O_i(x, y)}{N},
\end{equation*}
(2)
\begin{equation*}
E(x,y) = \sqrt{\frac{\sum _i^N (O_i(x,y) - \left\langle O(x,y)\right\rangle)^2}{N-1}}.
\end{equation*}
An alternate way of obtaining the error frames is to start from the raw CCD images whose noise properties are relatively well understood to try to model the effects of every single reduction step on the errors. This is, however, very complicated and so we adopt the above technique of determining our final error frame. Since we are combining only six to eight frames, we might overestimate our errors, but this overestimation does not affect the findings presented in the paper. Our final step is to correct for foreground extinction and this is done using the deredden task in IRAF.


Various surveys of SNRs in our Galaxy and nearby galaxies have been carried out at radio, X-ray, Infrared (IR), and optical wavelengths. The first extragalactic SNR candidates were identified in the LMC by Mathewson & Healey (1964) and later confirmed with a combination of radio and optical techniques by Westerlund & Mathewson (1966). To date, a total of 60 SNRs have been confirmed in the LMC with an additional 14 suggested candidates (Maggi et al. 2016; Bozzetto et al. 2017; Maitra et al. 2019). However, sensitivity and resolution limitations severely reduce the effectiveness of the past and present generations of radio and X-ray searches for SNRs in galaxies beyond the Small and Large Magellanic Clouds (MCs) (Goss et al. 1980; Long et al. 1981; Cowan & Branch 1985; Matonick et al. 1997; Matonick & Fesen 1997; Millar, White & Filipovic 2012; Galvin & Filipovic 2014; Sasaki et al. 2018; Lin et al. 2020; Sasaki 2020). As a result, optical studies have produced the largest number (∼1200) of new extra-Magellanic SNR candidates. Optical extragalactic searches for SNRs are mainly done by using an emission line ratio criterion of the form [S ii]/H α > 0.4–0.5 (Mathewson & Clarke 1973; Dodorico, Dopita & Benvenuti 1980; Fesen 1984; Blair & Long 1997; Matonick & Fesen 1997; Dopita et al. 2010b; Lee & Lee 2014; Vučetić et al. 2019b, a, 2018; Lin et al. 2020). This criterion separates shock-ionization from photoionization in SNRs from H ii regions and Planetary Nebulae (PNe) (Frew & Parker 2010). SNR radiative shocks collisionally excite sulphur ions in the extended recombination region resulting in S+, hence the larger contribution of [S ii] accounting for an increase of the [S ii] to H α ratio. In typical H ii regions, sulphur exists predominantly in the form of S++, yielding low [S ii] to H α emission ratios. Ratios from narrow-band imaging are usually verified spectroscopically, since [N ii] lines at 6548 and 6584 Å can contaminate the H α images at an unknown and variable level. Spectroscopic observations of such emission nebulae also can provide other evidence of shock heating, such as strong [O i] λ6300 emission, elevated [N ii] to H α with respect to H ii regions, or high [O iii] electron temperatures, verifying the candidate as being an SNR (Blair, Kirshner & Chevalier 1981, 1982; Long et al. 1990; Smith et al. 1993; Blair & Long 1997). Although somewhat biased as an isolated criterion, this method is proven and a good way of identifying ordinary radiatively cooling SNRs in nearby galaxies. We note that young, Balmer-dominated SNRs (Chevalier, Kirshner & Raymond 1980) would be missed by this criterion.


Depending on the specific driver, the characteristics of turbulence will then be imprinted within the ISM mainly as three-dimensional density and velocity fluctuations, and these fluctuations have been traditionally studied via correlation functions such as the spatial power spectrum (SPS) (e.g., Crovisier & Dickey 1983), Δ-variance (e.g., Stutzki et al. 1998), and structure function (e.g., Padoan et al. 2002; Burkhart et al. 2015b). In particular, the SPS approach has been applied to observations of various Galactic and extragalactic environments (e.g., Plume et al. 2000; Dickey et al. 2001; Elmegreen et al. 2001; Burkhart et al. 2010; Combes et al. 2012; Zhang et al. 2012; Pingel et al. 2013), showing power spectral slopes β roughly ranging from −2.7 to −3.7 depending on the tracers used (e.g., H i, carbon monoxide (CO), and dust). These slopes essentially provide information on the relative amount of structure as a function of spatial scale and can be compared with theoretical models of turbulence (mainly numerical simulations) to characterize turbulence cascade (e.g., Burkhart et al. 2010), to determine the influence of shocks (e.g., Beresnyak et al. 2005), to reveal the injection and dissipation scales of turbulent energy (e.g., Kowal & Lazarian 2007; Federrath & Klessen 2013; Chen et al. 2015), and to trace the evolution of MCs (e.g., Burkhart et al. 2015a). The proximity and abundance of multi-wavelength observations make MCs in the solar neighborhood an ideal laboratory for probing the impact of turbulence on their formation and evolution. In this paper, we focus on the Perseus MC, which is a nearby (∼300 pc; e.g., Herbig & Jones 1983; Černis 1990), low-mass (∼2 × 104 M⊙; e.g., Sancisi et al. 1974; Lada et al. 2010) cloud. Its star formation activities, as well as atomic and molecular gas content, have been extensively examined over the past decade (e.g., Ridge et al. 2006; Jørgensen et al. 2007; Pineda et al. 2008; Lee et al. 2012, 2014, 2015; Mercimek et al. 2017), revealing that the cloud consists of several individual dark and star-forming regions (e.g., B5, B1, B1E, IC 348, and NGC 1333) and is actively forming low- to intermediate-mass stars (see Bally et al. 2008 for a review).


The IRIS spectra measure the flare in a “sit-and-stare” mode with a roll angle of 45∘. The spectral scale is ∼25.6 mÅ per pixel in the far-ultraviolet (FUV) wavelengths. The IRIS slit crosses the flaring loop and one ribbon (Fig. 1). Two red bars enclose the flaring loop region used to study the quasi-periodic oscillations in this work. IRIS spectrum was pre-processed with the SSW routines of “iris_orbitval_corr_l2.pro” (Tian et al. 2014; Cheng et al. 2015) and “iris_prep_despike.pro” (De Pontieu et al. 2014). To improve the signal-to-noise ratio, we apply a running average over five pixels to the IRIS spectra along the slit (Tian et al. 2012, 2016). We also manually perform the absolute wavelength calibration using a relatively strong neutral line, O I 1355.60 Å (see De Pontieu et al. 2014; Tian et al. 2015; Tian 2017). IRIS observations show that Fe XXI 1354.08 Å is a hot (∼11 MK) and broad emission line and is always blended with many narrow chromospheric lines at the flaring ribbons (Li et al. 2015b, 2016b; Tian et al. 2015; Young et al. 2015; Brosius et al. 2016; Polito et al. 2016). However, the Fe XXI 1354.08 Å line is much stronger than those blended emission lines at the flaring loops (Tian et al. 2016). Figure 2a gives the time evolution of the line profiles of Fe XXI 1354.08 Å, averaged over the slit positions between ∼18.3″ and 21.6″. Figure 2 panels b−f show the spectral line profiles at the time indicated by the yellow lines in panel a. We can see that only the cool line of C I 1354.29 Å is blended with the hot line of Fe XXI 1354.08 Å, but its contribution is negligible. Therefore, double Gaussian functions superimposed on a linear background are used to fit the IRIS spectra at “O  I” window (Tian et al. 2016). Next, we can extract the hot line of Fe XXI 1354.08 Å, as shown by the turquoise profile. The purple profile is the cool line of C I 1354.29 Å. Two orange peaks represent the cool lines of O I 1354.60 Å and C I 1354.84 Å (Tian 2017), which are far away from the flaring line of Fe XXI 1354.08 Å. Finally, the line properties of Fe XXI 1354.08 Å are extracted from the fitting results, that is, Doppler velocity, peak intensity, and line width (Li et al. 2016b; Tian et al. 2016; Tian & Chen 2018).


HATLAS12-00 had already been identified as a candidate gravitationally lensed galaxy as a result of its high submm flux (i.e. F500 > 100 mJy), red Herschel colours and the lack of a bright optical or radio counterpart (see e.g. Negrello et al. 2010 for a discussion of the selection of lens candidates in H-ATLAS and other Herschel surveys). This source was therefore observed spectroscopically in the submm. A CO spectroscopic redshift of 3.26 was first suggested by Z-spec (Bradford et al. 2004) observations, then subsequently confirmed by observations by the CARMA interferometer (Leeuw et al., in preparation) and the Zpectrometer instrument (Harris et al. 2007) on the Greenbank Telescope (Harris et al. 2012; see also Fu et al. 2012). Additional followup observations in the optical, near-IR, submm and other wavelengths were targeted at the lensed z = 3.26 source and the foreground objects responsible for the lensing, resulting in detailed analyses of this lensing system by Fu et al. (2012) and Bussmann et al. (2013). Their conclusions are that the z = 3.26 source HATLAS12-00 is subject to gravitational lensing, with a magnification of 9.6 ± 0.5 in both the submm continuum and CO, and 16.7 ± 0.8 in the K′ band, by two foreground galaxies, one at a spectroscopically determined redshift of 1.22, and another with photometry suggesting that it lies at a similar redshift. The submm photometry of HATLAS12-00 at 890 μm acquired with the Submillimeter Array (SMA) as part of this programme (Fu et al. 2012; Bussmann et al. 2013) is fully consistent with the 870 μm and 850 μm fluxes derived for this source from the LABOCA and SCUBA2 data to be presented here. The spectral energy distribution (SED) of the lensed source, after correcting for the lensing amplification, is well matched by the optically thick SED model for Arp220 from Rangwala et al. (2011), with a lensing-corrected far-IR luminosity of 1.2 ± 0.2 × 1013 L⊙, and an implied star formation rate of 1400 ± 300  M⊙ yr−1. In many ways the unlensed properties of this object match those of the broader population of bright submm selected galaxies first discovered by the SCUBA submm imager (see e.g. Chapman et al. 2005; Clements et al. 2008; Michałowski, Hjorth & Watson 2010). The unlensed 870 μm flux of this object would be ∼7.7 mJy.

Similarities Similarities Similarities Similarities


Among the most viable mechanisms of cusp-core transformation that require changes to the assumed cosmogony is one that was proposed specifically as a possible solution to the cusp-core problem. It proposes that the DM is in fact not collisionless but self-interacting (SIDM; Spergel & Steinhardt 2000; Yoshida et al. 2000; Davé et al. 2001; Colín et al. 2002; Vogelsberger, Zavala & Loeb 2012; Rocha et al. 2013; see Tulin & Yu 2018 for a review). In SIDM, particles can exchange energy and momentum through elastic scattering, causing an outside-in energy redistribution within the centre of DM haloes, resulting in the formation of an isothermal core. The time-scale on which an initially cuspy SIDM halo forms a flat and isothermal core is roughly given by the time it takes for each DM particle in the inner halo to scatter at least once (Vogelsberger et al. 2012; Rocha et al. 2013). The strength of the self-interaction in SIDM models is parametrized in terms of the momentum transfer cross-section per unit mass, σT/mχ. Depending on the specific SIDM model, σT/mχ can either be constant or dependent on the relative velocity between the two scattering DM particles. SIDM is an efficient mechanism of cusp-core transformation in dwarf-size haloes for $\sigma _T/m_\chi \gtrsim 1\, {\rm cm^2g^{-1}}$, whereas SIDM haloes are virtually indistinguishable from CDM haloes if $\sigma _T/m_\chi \lesssim 0.1\, {\rm cm^2g^{-1}}$ (Zavala, Vogelsberger & Walker 2013). The most stringent and precise constraints on the self-interaction cross-section have been put on the scales of galaxy clusters (e.g. Robertson, Massey & Eke 2017; Robertson et al. 2019) and large elliptical galaxies (Peter et al. 2013), where observations require that $\sigma _T/m_chi \lesssim 1\, {\rm cm^2g^{-1}}$. On smaller scales, Read, Walker & Steger (2018) concluded that $\sigma _T/m_\chi \lesssim 0.6\, {\rm cm^2g^{-1}}$, based on their findings that the central density profile of the MW dwarf spheroidal galaxy Draco is cuspy (see also the SIDM results of Valli & Yu 2018). Moreover, based on a DM only analysis of the updated too-big-to-fail problem, Zavala et al. (2019) concluded that SIDM models with a constant cross-section of $\sigma _T/m_\chi \sim 1\, {\rm cm^2g^{-1}}$ fail to explain the apparently large central densities of the host haloes of the ultra-faint satellites of the MW (Errani, Peñarrubia & Walker 2018). It should be pointed out that the constraints on σT/mχ on the scale of dwarf galaxies are affected by significantly larger systematic uncertainties than on the scales of galaxy clusters or elliptical galaxies. Moreover, Zavala et al. (2019) demonstrate that SIDM with a strongly velocity-dependent self-interaction cross-section may provide a natural explanation for the observed diversity in the rotation curves of the MW dwarf spheroidals (see also Correa 2021). The strong dependence of the self-interaction cross-section on the typical DM velocities would create a bimodal distribution of rotation curves in the MW satellites in which the heavier haloes have constant density cores while the lighter haloes have undergone gravothermal collapse and have very steep central cusps as a consequence. The same mechanism of gravothermal collapse might be accelerated by tidal interactions in the environment of the MW leading to an agreement between constant cross-section SIDM models with $\sigma _T/m_\chi \sim 3\, {\rm cm^2g^{-1}}$ and the internal kinematics of MW satellites (e.g. Kahlhoefer et al. 2019; Sameie et al. 2020).


While new data will refine our understanding of the interplanetary medium, it is necessary for future models to be consistent with both new and archival data. It is precisely this need that motivates the COSMOGLOBE project1, which aims to create a framework that will allow for the refinement of astrophysical models jointly with the raw data from complementary experiments. This form of joint analysis is already being explored within the framework of WMAP (Watts et al. 2022) and LiteBIRD (Aurlien et al., in prep.), in combination with Planck Low Frequency Instrument data (BeyondPlanck 2022). ZE is an especially promising direction for joint analysis, in part because HFI made observations of ZE at complementary wavelengths to DIRBE. While the DIRBE model was modified during the HFI analysis, no attempt was made to improve upon the geometrical representation of the model components using the larger effective dataset. Our understanding of the interplanetary medium has improved since the development of the DIRBE IPD model (see, e.g., Reach et al. 1997; Reach 2010a,b). The AKARI satellite, which observed in the infrared at wavelengths between 6 and 180 µm, detected small-scale structures in the ZE which were not well-characterized by the DIRBE model (Ootsubo et al. 2016). While the DIRBE model has been successful in describing the large-scale diffuse ZE, modern high-resolution high-frequency and infrared experiments will require IPD models that can more effectively resolve the small-scale structures in the ZE. As such, an update of the community state-of-art ZE model is long overdue. In this COSMOGLOBE framework, such a model refinement is a natural byproduct of a joint analysis of DIRBE, HFI, and other data. To improve upon this model, it is essential to have the model agree with the data at all wavelengths. The modeling of ZE is in the process of being implemented in the Commander framework, which will ultimately be used for the joint processing of HFI and DIRBE data. However, a stand-alone code is useful for agile model building and data analysis. As such, ZodiPy will function as the first step toward this goal in the COSMOGLOBE framework, in addition to making ZE corrections on arbitrary data more accessible to the community.


Amongst the oldest stellar systems known to exist in the Milky Way (MW) are metal-poor globular clusters (GCs). These accumulations of stars do not seem to have undergone substantial star formation for extended periods. Given the limited quality of the available data, for a long time color-magnitude diagrams (CMDs) of GCs appeared to be narrow and could be readily described by a single isochrone. These observations have justified the establishment of the long-lasting paradigm that considers CGs as prime examples of simple stellar populations (SSPs), that is, the results of very short bursts of star formation in their natal clouds. However, improved photometric precision indicates the presence of sub-populations in the cluster CMDs that are inconsistent with the SSP assumption, for a number of luminous GCs in a variety of bandpasses. Thus, early detections of chemical abundance variations (e.g., Cohen 1978) could be more easily explained in a scenario involving several populations. Moreover, in recent years evidence has grown supporting the statement that GCs are generally composed of two or three chemically distinct populations. These subpopulations are separated by a few tens to hundreds of Myr in age and show vastly varying abundances of light elements such as C, N, O, Na, Mg, and Al (see, e.g., Carretta et al. 2009b; Gratton et al. 2012, and references therein). Theoretical considerations (see, e.g., D’Ercole et al. 2008, 2011) imply that GCs could have lost the majority of the initial stellar content of the first population, which consequently should have ended up in the Galactic halo. In fact, numerous studies found metal-poor GCs to be consistent with the abundance trends of the MW halo at equally low metal content (e.g., Pritzl et al. 2005; Koch et al. 2009; Koch & McWilliam 2014; Villanova et al. 2016). We address this scenario by adding NGC 6426 to the short list of metal-poor clusters with available information on detailed chemical abundances. There are only two GCs in the Harris catalog (Harris 1996, 2010 edition) more metal poor than NGC 6426. At 12.9 ± 1.0 Gyr, the cluster is the oldest in the age compilation by Salaris & Weiss (2002). At a galactocentric distance of Rgc = 14.4 kpc and a galactic latitude of 16.23° it is located in the transition region between inner and outer halo. Previous studies found consistent [Fe/H]1 values: −2.20 ± 0.17 dex (Zinn & West 1984), −2.33 ± 0.15 (Hatzidimitriou et al. 1999), and −2.39 ± 0.04 dex (Dias et al. 2015). The latter value originates from the very first spectroscopic analysis of NGC 6426 at low resolution, which also stated [Mg/Fe] = 0.38 ± 0.06 dex. To date, there has been no study further addressing the detailed metal content of this cluster.


Optical extragalactic searches for SNRs are mainly done by using an emission line ratio criterion of the form [S ii]/H α > 0.4–0.5


We need to build data sets to train and evaluate the model. Then the data sets are prepared in the following way: (1) if the AR does not flare within 24 hr after the observation time, the No-flare (weaker than C1.0) label is assigned to the magnetogram sample in the same AR. (2) If the C/M/X-level flare occurs within 24 hr after the observation time, the corresponding flare label (i.e., C, M, or X) is assigned to the magnetogram sample. Note that there are a number of ARs producing recurring flares with different flare levels within 24 hr. For the first flare of one AR, the corresponding flare label is assigned to the magnetogram sample within 24 hr after the observation time. Then for the following flares of the same AR, the corresponding labels are assigned to the magnetogram sample in the period from the end of its prior flare to the end of this flare. (3) We adopt a four-level AR classification scheme based on the maximum GOES-level flare an AR ever yields (Song et al. 2009; Yuan et al. 2010; Liu et al. 2017). In other words, ARs are further categorized into four levels (i.e., No-flare, C, M, and X) if they yield at least one flare with such GOES-level criterion but no flares with higher GOES-level criterion: “Level = X” indicates that an AR yields at least one X-level flare; “Level = M” indicates that an AR yields at least one M-level flare but no X-level flares; “Level = C” indicates that an AR yields at least one C-level flare but no M/X-level flares; “Level = No-flare” indicates that an AR only yields microflares (weaker than C1.0 flares). Finally, we gather 870 ARs and 136134 magnetogram samples in total, including 443 X-level, 6534 M-level, 72412 C-level, and 56745 No-flare level samples. Note that the magnetogram samples with multiple ARs (Bobra et al. 2014) are not included in our work. For the ≥M class, magnetogram samples of M/X-level flare in an AR are defined as positive class, while all the others are defined as negative class. For the ≥C class, magnetogram samples of C/M/X-level flare in an AR are defined as positive class, while all the others are defined as negative class.


Among the odd Z elements, we derived the abundances of Na, Al, K, and Sc using the high-resolution spectra and the details of the lines are given in Table A1. The Na D lines were not used as the lines are too strong for deriving the abundances. So, we depended on the weaker lines 5682 Å and 5688 Å to derive the Na abundance. The NLTE corrections for these Na i lines were performed from Lind et al. (2011) whenever available and the average values are listed in Table 3. Al i lines at 6696 and 6698 are used for deriving the Al abundance and these lines have negligible contributions from NLTE effects (Baumueller & Gehren 1997; Nordlander & Lind 2017). For the case of K, whenever the feature at 7698.98 Å has contributions from telluric features, the abundance from 7664.87 Å is quoted, otherwise the average of the abundances from both the lines is quoted in Table 3. Both these lines are sensitive to NLTE effects (Takeda et al. 2002; Kobayashi et al. 2006; Andrievsky et al. 2010; Prantzos et al. 2018; Reggiani et al. 2019) and the NLTE corrections depend on the effective temperature and surface gravity of the model. Using the NLTE grid provided in Reggiani et al. (2019), we have estimated the NLTE corrections for the program stars and the NLTE corrected values are given in Table 3. The NLTE grid does not cover very low log g values, so we could not estimate the NLTE corrections for HE 1152−0355 and HE 0314−0143. We could not measure the K abundance in HD 5223 due to the contamination from telluric features. For the case of Sc abundance, we could not find any study of Sc line formation in NLTE except in Zhang, Gehren & Zhao (2008) where they have studied the NLTE effects only for the sun and identified negligible NLTE effects for Sc ii lines. So, we report only LTE results for this element in Table 3. The resolution of the NIR spectra was too low to resolve the HF feature from the nearby features, so we could not derive F abundance in these stars.


The data presented here comprise quasi-simultaneous observations during secondary eclipse of WASP-33 b around the V and Y bands. The predicted planet-star flux ratio in the V-band is 0.2 ppt, four times lower than the accuracy of our measurements. Therefore, we can neglect the planet imprint and use this band to measure the stellar pulsations, and most specifically to tune their current phases (see phase shifts in von Essen et al. 2014). Particularly, our model for the light contribution of the stellar pulsations consists of eight sinusoidal pulsation frequencies with corresponding amplitudes and phases. Hence, to reduce the number of 24 free parameters and the values they can take, we use prior knowledge about the pulsation spectrum of the star that was acquired during von Essen et al. (2014). As the frequency resolution is 1/ΔT (Kurtz 1983), 3.5 h of data are not sufficient to determine the pulsations frequencies. Therefore, during our fitting procedure we use the frequencies determined in von Essen et al. (2014) as starting values plus their derived errors as Gaussian priors. As pointed out in von Essen et al. (2014), we found clear evidences of pulsation phase variability with a maximum change of 2 × 10-3 c/d. In other words, as an example after one year time a phase-constant model would appear to have the correct shape with respect to the pulsation pattern of the star, but shifted several minutes in time. To account for this, the eight phases were considered as fitting parameters. The von Essen et al. (2014) photometric follow-up started in August, 2010, and ended in October, 2012, coinciding with these LBT data. We then used the phases determined in von Essen et al. (2014) during our last observing season as starting values, and we restricted them to the limiting cases derived in Sect. 3.5 of von Essen et al. (2014), rather than allowing them to take arbitrary values. The pulsation amplitudes in δ Scuti stars are expected to be wavelength-dependent (see e.g. Daszyńska-Daszkiewicz 2008). Our follow-up campaign and these data were acquired in the blue wavelength range. Therefore the amplitudes estimated in von Essen et al. (2014), listed in Table 1, are used in this work as fixed values. This approach would be incorrect if the pulsation amplitudes would be significantly variable (see e.g., Breger et al. 2005). Nonetheless, the short time span of LBT data, and the achieved photometric precision compared to the intrinsically low values of WASP-33’s amplitudes, make the detection of any amplitude variability impossible.


We use the set of wind solutions (density and velocity distribution of gas in the wind) for primordial discs (i.e. gas-rich, optically thick discs, which do not have an evacuated inner cavity) calculated by Owen et al. (2010, 2011) and EO10 for a 0.7 M⊙ star and X-ray luminosities (0.1 ≤ hν ≤ 10 keV) of LX = 2 × 1028, 2 × 1029 and 2 × 1030 erg s−1. These were obtained by means of two-dimensional hydrodynamic calculations using the zeus code (Stone & Norman 1992; Stone, Mihalas & Norman 1992; Hayes et al. 2006), modified to include the effects of X-ray irradiation with a parametrization of the gas temperature as a function of the local ionization parameter. The dust radiative transfer and photosionisation code mocassin (Ercolano et al. 2003; Ercolano, Barlow & Storey 2005; Ercolano et al. 2008a), modified according to Ercolano et al. (2008b), was used produce the temperature parametrization. The atomic data base of the mocassin code included opacity data from Verner et al. (1993) and Verner & Yakovlev (1995), energy levels, collision strengths and transition probabilities from Version 5.2 of the CHIANTI data base (Landi et al. 2006, and references therein) and hydrogen and helium free–bound continuous emission data of Ercolano & Storey (2006). The ionizing spectrum used to calculate the temperature parametrization was calculated by Ercolano et al. (2009), using the plasma code of Kashyap & Drake (2000) from an emission measure distribution based on that derived for RS CVn type binaries by Sanz-Forcada, Brickhouse & Dupree (2002), which peaks at 104 K and fits to Chandra spectra of T-Tauri stars by Maggio et al. (2007), which peaks at around 107.5 K. This spectrum has a significant EUV component (13.6 eV ≤ hν ≤ 0.1 keV), with roughly LEUV = LX. Solar abundances (Asplund, Grevesse & Sauval 2005), depleted according to Savage & Sembach (1996) were assumed, namely (number density, with respect to hydrogen): He/H = 0.1, C/H = 1.4 × 104, N/H = 8.32 × 105, O/H = 3.2 × 104, Ne/H = 1.2 × 104, Mg/H = 1.1 × 106, Si/H = 1.7 × 106, S/H = 2.8 × 105. More details about the codes and setup of the models can be found in Ercolano et al. (2008b, 2009) and Owen et al. (2010).


Low-mass X-ray binaries (LMXBs) which either contain a black hole (BH) or a neutron star (NS), accreting matter from its low-mass companion star (≲1M⊙) are ideal natural laboratories for studying the physics of accretion and jet around a BH or an NS (e.g. Migliari & Fender 2006). According to the timing and spectral features in the X-ray band, LMXBs are generally divided into two main spectral states, i.e. the high/soft state and the low/hard state (Gilfanov 2010, for review). For BH-LMXBs, when they are in the high/soft state, the accretion flow is widely believed to be dominated by the optically thick, geometrically thin, cool accretion disc (Shakura & Sunyaev 1973), and the X-ray spectrum can be well described by a multicolour blackbody spectrum (e.g. Mitsuda et al. 1984; Makishima et al. 1986; Merloni, Fabian & Ross 2000). Whereas, for NS-LMXBs, besides the emission from the disc, there is a significant thermal emission from the boundary layer between the accretion disc and the surface of the NS (Popham & Narayan 1992; Inogamov & Sunyaev 1999; Popham & Sunyaev 2001; Gilfanov & Sunyaev 2014, for review). Observationally, for both BH-LMXBs and NS-LMXBs, when they are in the low/hard state, generally, the accretion flow is suggested to be dominated by the optically thin, geometrically thick, hot, advection-dominated accretion flow (ADAF) (Done, Gierliński & Kubota 2007, for review). Theoretically, the ADAF solution has been studied in detail by several researchers since it was discovered in 1970’s (Ichimaru 1977; Rees et al. 1982; Narayan & Yi 1994, 1995a,b; Abramowicz et al. 1995; Chen et al. 1995; Yuan & Narayan 2014, for review). In the BH case, the ADAF solution is a kind of radiatively inefficient accretion flow, in which a fraction of the viscously dissipated energy will be advected into the event horizon of the BH. While in the NS case, the viscously dissipated energy advected onto the surface of the NS will eventually be radiated out, so the ADAF solution is radiatively efficient (Narayan & Yi 1995b). Qiao & Liu (2018b) calculated the structure and the corresponding emergent spectrum of the ADAF around a weakly magnetized NS within the framework of the self-similar solution of the ADAF. The authors compared the electron temperature of the ADAF around a NS and a BH, it is found that the electron temperature of the ADAF around an NS is systemically lower than that of a BH, which is consistent with observations (Burke, Gilfanov & Sunyaev 2017; Qiao & Liu 2018b). Meanwhile, the authors compared the Compton y-parameter (defined as $y={{4kT_{\rm e}}\over {m_{\rm e}c^2}} \rm {Max}(\tau _{\rm es}, \tau ^2_{\rm es})$, with Te being the election temperature, me being the electron mass, c being the speed of light, and τes being the Compton scattering optical depth) of the ADAF around an NS and a BH, it is found that the Compton y-parameter of the ADAF around an NS is systemically lower than that of a BH, producing a softer X-ray spectrum, which is also consistent with observations (Wijnands et al. 2015; Parikh et al. 2017; Sonbas, Dhuga & Göğüş 2018; Qiao & Liu 2018b).


The final location of close-in giant planets in our models reflects the strength of the tides that we include in our modeling, which play a very important role in the decay of planetary orbits. These are dynamical tides (e.g., Lai 1997; Ivanov & Papaloizou 2004, 2007, 2011) and in our simulations we used a formulation given by Ivanov & Papaloizou (2007) as described inSect. 2. However, the impulse approximation used in the evaluation of dynamical tides becomes a poor approximation when the circularization proceeds (e.g., Mardling 1995a,b) and the eccentricity becomes low. Equilibrium tides become then effective (e.g., Beaugé & Nesvorný 2012 and references therein) and the tidal evolution may occur on a longer timescale. In short, at the beginning of the orbital evolution that leads to the formation of hot/warm Jupiters, dynamical tides are important in forcing the decay of the orbit. In the last part of the dynamical evolution when the eccentricity has become low, equilibrium tides are more important in determining the location where the planet stops. Unfortunately, at present it is not known when and how the two tides switch. When we change the magnitude of two tides, the final location of the planets can be adjusted (Beaugé & Nesvorný 2012). However, rather than introducing artificial effects, we continue to use dynamical tides in our simulations even for low eccentricities but we stop our simulations when the energy, decreasing from the tide at the pericenter, overcomes the orbital energy leading to a clustering of tidally circularized planets around 0.02 au. However, the final distribution of the inclination of the planets does not depend on this choice and highly misaligned planets would be produced anyway. Since the tidal evolution of planets with arbitrary inclinations is still not well known, we assume that planetary inclination is not significantly changed during tidal evolution (Barker & Ogilvie 2009). Thus, the planets maintain the inclination they have when the circularization begins.


As a first step, we need to specify the photoelectron sheath features. In this course, we first evaluate the steady state potential over the lunar surface (equation 4), and then after, we use this as a boundary condition to solve the Poisson equation (equation 2) and estimate the photoelectron sheath profile. In calculations, Lyman α (λ ∼ 121.57 nm, 10.29 eV, Λ ∼ 3 × 1011 cm–2 s–1) spike of solar photon radiation (Bauer 1973) is considered as the dominant source for the generation of photoelectrons from the lunar surface. The work function of the regolith material is taken from Grobman & Blank (1969), where it is suggested to vary in the range ϕr ∼ (4–6) V for the region across the subsolar point and limb. Moreover, Draine’s formulation is accounted to determine the lunar surface’s photoelectric efficiency (Draine 1978; Draine & Salpeter 1979) – its spectral dependence can be represented as ${\chi _{\nu r}} = {\chi _o}[1 - ({\phi _r}/{E_\nu })]$. For instance, for the Lyman α radiation χνr = 0.042 for optimum efficiency χo = 0.1 (Sickafoose et al. 2001) and ϕr = 6 V (Grobman & Blank 1969). Another significant parameter is the surface temperature which describes the electron population within the lattice available for the photoemission. Lunar Reconnaissance Orbiter based measurements (Williams et al. 2017) suggest that the surface temperature may vary from the equator (∼400 K) to the terminator (poles, ∼150 K). In order to take this account, we use the latitude (θ) dependent empirical relation ${T_\theta } = {T_0}[1 - (5/4\pi )\theta ]$; for instance, at θ = 70°, and To ≈ 205 K. These three parameters, viz., ϕr, To, χν, and Λ drive the photoemission current from the lunar regolith. The nominal solar wind plasma parameters are considered for calculating collection current over lunar regolith; the constituents are considered as40-41nes ≈ nis = 8.7 cm–3 and Tes ≈ Tis = 1.4 × 105 K (Mann et al. 2011; Kureshi et al. 2020). These solar radiation and wind plasma parameters might vary widely during active solar events and alter surface charging and sheath features. Popel et al. (2018) suggest the dust number density may also vary in a wide range depending on lunar altitude and particle size; for instance, nd ∼ 800 cm–3 for the particles of size 100 nm ≤ ao ≤ 200 nm and θ = 77°. Note that the secondary electron emission (Seitz 1940; Misra, Mishra & Sodha 2013) from the lunar regolith (and floating dust) is ignored, as it minimally contributes to the charging of sunlit surfaces (Mishra & Bhardwaj 2020). These parameters, along with equation (4), yield steady state potential over the sunlit locations. This estimate of the surface potential is used as a boundary condition (i.e. at l = 0, υ = υo) alongwith υ’ = υ = 0 as $l \to \infty $ to solve the Poisson equation (equation 2) numerically – using this framework, the sheath structure is derived in terms of electric potential (υ), electric field (Es), and photoelectron population density (npe).