We mentioned that our light curves are characterized by two large gaps of one year and seven months plus eight months, as shown in Table 1. From the table, it is apparent that mean and median observed baseline values, computed for the sources in the main sample for each season, are very close to the maximum observed baseline (when not exactly coincident with it) for the corresponding season. Similarly, the mean and median number of visits for each season are very close to the total number of visits (when not exactly coincident with it) for the corresponding season. This shows how, for individual seasons, our dataset can take advantage of a dense sampling, which plays a key role in the context of AGN detection efficiency, as shown in De Cicco et al. (2019). Nevertheless, the two gaps affect the shape of our SF with inadequate sampling in correspondence with some timescales. Sparse and/or irregular sampling is a very common issue in SF analysis (e.g., de Vries et al. 2003; Peters et al. 2015; Simm et al. 2016; Sartori et al. 2019). Indeed, there are works from the literature where the cadence is low but the sampling is regular: as an example, Hawkins (2002) uses quasar light curves from a long-term monitoring program with 24 yearly observations per source to investigate the origin of the emission mechanism in AGN. Nonetheless, one of the advantages in the use of the SF is its relative insensitivity to irregular sampling when sources are considered as an ensemble rather than individually (e.g., Hawkins 2007; Kozłowski 2016; Sartori et al. 2019). As mentioned in Sect. 3.2, Bauer et al. (2009) analyze the effect of irregular sampling by means of simulations, and conclude that the turnover that is observed in the light curve is an effect of sparse sampling at longer timescales, and not a real feature in the SF of AGN. Emmanoulopoulos et al. (2010) also resort to simulations in order to assess whether and to what extent the SF is robust against the presence of gaps in the light curves. They simulated a single light curve and then investigated the effect of three different gaps in the data, representing three different situations: almost periodic data gaps, dense and sparse sampling, and purely sparsely sampled data, corresponding to 57%, 83%, and 92% of the data being removed from a single simulated light curve that is 2000 time units long, respectively. They then used bootstrapping to extract 1000 light curves from each of the obtained light curves with gaps, then compared the results obtained with and without gaps. While they find that the presence of gaps is responsible for the presence of wiggles and bends in the SF, from the right panels of their Fig. 12 we can infer that these wiggles and bends do not alter the slope of the SF obtained from the light curve with no gaps. In this work we are not investigating the turnover as our baseline is not long enough (Sect. 3.2); our analysis is instead focused on the linear region of the SF (and the possible dependence on physical quantities of interest), where the irregularity of the sampling does not constitute a major issue.


With a priori knowledge of speckle evolution lifetime (Milli et al. 2016), more evolved a posteriori algorithms may well calibrate the speckle pattern. However, any such method can directly benefit from an active technique that minimizes the static or quasi-static speckles in each science image during an observation. Active suppression of these speckles requires measurement of the electric field associated with the speckles directly from a coronagraphic image using a focal plane wavefront sensor (FPWFS). Several FPWFSs have been proposed such as phase diversity (Bordé & Traub 2006; Give’on et al. 2007; Sauvage et al. 2012) and the self-coherent camera (SCC; Baudoz et al. 2006, 2012). Once the electric field is measured, one or several deformable mirrors (DM) can then be used to minimize the speckle intensity in a region of the image called the dark hole (Malbet et al. 1995). Very encouraging laboratory results have been obtained on the coronagraphic testbeds simulating the space-related environment. The stellar speckle intensity is shown to be reduced by a factor of up to 105 (Belikov et al. 2007; Trauger et al. 2011, 2012; Mazoyer et al. 2013, 2014) which would enable the detection of planets 1010 times fainter than their host star. Several attempts on ground-based Extreme-AO instruments have been performed with moderate results. The stellar speckle intensity has been suppressed by only a factor of up to ten (Savransky et al. 2012; Martinache et al. 2014; Bottom et al. 2017; Matthews et al. 2017; Wilby et al. 2017; Vigan et al. 2019; Galicher et al. 2019) reaching contrast levels of roughly 10−6. Most of these techniques temporally modulate the speckle intensity to measure their phase and at least three images are needed for each estimation of the electric field. The quasi-static speckles that evolve faster than every four images cannot be correctly estimated and therefore set a limitation for the speckle estimation. Addressing this concern, our team proposed the SCC that spatially modulates the speckle intensity so that the associated complex electric field can be measured in every science image. The drawback is that a finer sampling of the coronagraphic image is required as compared to the temporal modulation techniques. The SCC has been developed and rigorously tested in space-related environments on the THD2 bench at the Paris Observatory (Baudoz et al. 2018).


Ultraluminous X-ray sources (ULXs) have been widely observed in the local Universe, with inferred isotropic luminosities above 1039 erg s−1 (Roberts 2007; Feng & Soria 2011). Those below ∼3 × 1039 erg s−1 can be readily associated with accretion on to stellar mass black holes (BHs) (∼10 M⊙) accreting close to or at their Eddington limit (see Sutton, Roberts & Middleton 2013, and references therein). There is now strong evidence to support this assertion, with the discovery of extremely bright ballistic jets from a ULX in M31 (Middleton et al. 2013; Middleton, Miller-Jones & Fender 2014b), which unambiguously links the flow with Eddington rate accretion (Fender, Belloni & Gallo 2004), and the first dynamical mass measurement of the compact object in a ULX, from M101 ULX-1 (Liu et al. 2013). Observations of such ‘low-luminosity’ ULXs (Middleton et al. 2011b, 2012; Kaur et al. 2012; Soria et al. 2012) have revealed changes in the disc emission that may imply the creation of a radiation pressure supported, larger scaleheight flow in the inner regions (Middleton et al. 2012) or magnetic pressure support (Straub, Done & Middleton 2013). Although emission below ∼2 keV is generally heavily photoelectrically absorbed by material in the Galactic plane (e.g. Zimmermann et al. 2001), similar spectral behaviour may also be seen in a small number of Galactic BH X-ray binaries (BHBs) at high rates of accretion (e.g. Ueda, Yamaoka & Remillard 2009; Uttley & Klein-Wolt, in preparation). Such ‘extreme’ high state BHBs probably dominate the ULX population (Walton et al. 2011), yet a significant number of ULXs can still be found at higher luminosities. Those above 1041 erg s−1 are dubbed hyperluminous X-ray sources (HLXs; Gao et al. 2003) and provide the best evidence (Farrell et al. 2009; Davis et al. 2011; Servillat et al. 2011; Webb et al. 2012) for a population of intermediate-mass BHs (IMBHs; Colbert & Mushotzky 1999). Such IMBHs (with masses above those expected from direct stellar collapse: >100s of M⊙) could potentially be formed in globular clusters (Miller & Hamilton 2002, but see Maccarone et al. 2007), through capturing and tidally stripping a dwarf galaxy (King & Dehnen 2005) or mergers in young super star clusters (Portegies-Zwart, McMillan & Gerhard 2003; Portegies-Zwart et al. 2004).


Models of the ECSN progenitor cores suggest the onset of the electron-capture instability occurs at a unique ONeMg core mass in the mass range of 1.366–1.377 M⊙. (Miyaji et al. 1980; Nomoto 1984, 1987; Podsiadlowski et al. 2005; Takahashi et al. 2013). Electron captures cause the core to contract, and O and Ne burning is ignited in the central regions and propagates outwards in a deflagration front (Schwab et al. 2015), processing material to nuclear statistical equilibrium, where further electron captures and photdissociation accelerates the collapse (Miyaji et al. 1980; Nomoto 1987; Takahashi et al. 2013). Whether the core collapses or the deflagration disrupts the core depends sensitively on the ignition density (Isern et al. 1991; Jones et al. 2016). If the core does collapse, the explosion proceeds via delayed explosion on short timescales (Mayle & Wilson 1988; Kitaura et al. 2006; Fischer et al. 2010), and 2D simulations suggest the explosion occurs before significant convection has had time to develop (Wanajo et al. 2011) and hence a symmetric explosion results. This, coupled with the steep density gradient at the core surface, leads to very little mass loss from the core; estimates of mass loss include of order 10−3 M⊙ (Podsiadlowski et al. 2005), 10−2 M⊙ (Kitaura et al. 2006), and 1.39 × 10−2 M⊙ (1.14 × 10−2 M⊙) for the 1D (2D) models of Wanajo et al. (2009, 2011). Therefore the ONeMg progenitor core mass is a good estimate of the baryon mass MB of the resulting NS (Podsiadlowski et al. 2005). Indeed, PSR J0737-3039A and the companion to PSR J1756-2251 have gravitational masses consistent with baryon masses ∼1.37 M⊙ when their gravitational binding energies are taken into account (Lattimer & Yahil 1989). Population synthesis calculations incorporating the various binary evolution channels that might lead to production of NSs via ECSNe show that J0737-3039B most likely formed in an ECSN, and the companion to PSR J1756-2251 is consistent with such a formation scenario (Andrews et al. 2015). Other systems with candidates for ECSNe formation also exist (Keith et al. 2009; Chen et al. 2011).


An empirical expression for FUV extinction based on UV reddening of a diverse, UV-selected sample of 200 galaxies (Seibert et al. 2005) is
(10)
\begin{eqnarray*}
A_{\rm FUV}(\beta)=3.978(m_{\rm FUV}-m_{\rm NUV})+0.143,
\end{eqnarray*}
where mFUV and mNUV are the respective GALEX AB magnitudes.13 The equation is similar to relations derived by others (e.g. Hao et al. 2011). Fig. 9 shows the SFRS galaxies in the IRX–(mFUV − mNUV) (or equivalently IRX–β) space. There is a correlation between AFUV(β) and AFUV(IRX) with Pearson correlation coefficient r = 0.71 and mean 〈AFUV(β) − AFUV(IRX)〉 = 0.33 mag, but the rms scatter in AFUV(IRX) as derived from AFUV(β) is 0.44 dex. Galaxies with $A_{\rm FUV}(\beta)\lesssim 2$ can have bolometric extinctions as high as 6 mag, and AFUV(β) applied to LFUV greatly underestimates their FIR luminosity and therefore SFR. This is consistent with other results (e.g. Kong et al. 2004; Johnson et al. 2006, 2007), which have shown that galaxies having higher current SFR relative to their past averaged SFR are likely to deviate above the IRX–β relation, i.e. have larger AFUV(IRX) for a given AFUV(β). Despite this qualitative agreement, the Kong et al. mean numerical relation for their UV-selected sample of 50 local starbursts is not a good fit to the FIR-selected SFRS data as shown in Fig. 9. Regardless of numerical values, all these studies agree that galaxies with higher SFR are more obscured at fixed β (also see Iglesias-Páramo et al. 2004; Cortese et al. 2006; Moore et al. 2010). At the low SFR end, galaxies with L60  109.3 L⊙, which at $z$ ≈ 0 are mostly early-type cluster galaxies, form two groups. Around 75 per cent of them are near the mean IRX–β relation, but the rest show AFUV(IRX) ≪ AFUV(β). One possibility is that these galaxies have older stellar populations with intrinsically high values of β. In the middle range 109.3 L60  1010.7 L⊙, there is a general trend for AFUV(IRX) to follow AFUV(β) but with rms scatter ∼0.34 dex. At L60 > 1010.7 L⊙, the scatter is ∼0.56 dex.


To determine foreground and background contamination by star-forming galaxies, AGNs, shock emission, and extended PAH emission, as well as field stars, we performed the infrared color selection method described in Gutermuth et al. (2009). In Phase I of this method, we used only GLIMPSE sources that have photometry in all four IRAC bands, and have photometric uncertainties σ  0.2 mag in all four bands, which corresponds to a total of 2723 sources. In Figure 4 we show CCDs from the first step of the Phase I selection method, that allowed us to identify contamination from star-forming galaxies and AGNs. Then, we proceeded to the elimination of shock emission and extended PAH emission contamination, as well as YSO class selection as shown on Figure 5. This procedure resulted in a total of 2702 Spitzer/GLIMPSE sources without contamination. We obtained a total of 42 sources classified as Class I, and 177 sources classified as Class II. We continued with a process similar to the Phase II selection method described by Gutermuth et al. (2009), which we slightly modified due to the use of VISTA/VVV data instead of 2MASS data used in the Gutermuth et al. (2009) paper. In this step, both Spitzer/GLIMPSE and VISTA/VVV data were used. Specifically, the Phase II selection method is applied to Spitzer/GLIMPSE sources that lack [5.8] and/or [8.0] detections. The Spitzer/GLIMPSE sources were first matched with their VISTA/VVV counterparts. We only selected high-quality VISTA/VVV detections with σ  0.1 mag, and Spitzer/GLIMPSE detections with photometric uncertainties σ  0.2 mag in the detected bands for this analysis. A cross-match of both catalogs was done using a search radius of 1″, to create a matched list of 13,309 sources. A further selection on these sources was done using their VISTA/VVV magnitudes. We excluded stars with saturated photometry (Soto et al. 2013), by limiting the magnitudes of the detected VISTA/VVV sources to 13.8, 12.8, and 12.8, for the J, H, and KS bands, respectively. A total of 9974 non-saturated sources were selected. Whenever possible we checked for contamination using similar color–color criteria as described for Phase I in Gutermuth et al. (2009), and ended up with a total of 9844 sources without contamination. We selected this sample of 9844 stars where objects with infrared excesses are expected to be found. To select these infrared excess sources, we used the dereddened color selection criteria detailed in Gutermuth et al. (2009) with [K–[3.6]]0 and [[3.6]–[4.5]]0 colors. Displaying the position of all the new infrared excess candidates showed that they are uniformly distributed in the region, thus we consider that our selected data set might still suffer contamination by foreground sources. To eliminate any possible chance of selecting any contaminant, we therefore applied additional selection criteria to these infrared excess sources candidates, as described in Winston et al. (2011) and Megeath et al. (2012), by plotting two CCDs, as shown in Figure 6. The first selection was done using the CCD J–H versus H–[4.5], with the slope of the reddening band

 (Chen et al. 2013). The second color selection was done using the CCD H–KS versus KS–[4.5] with the slope of the reddening band

 (Chen et al. 2013). We defined as YSOs all sources passing the selection criteria of the first or of the second CCD, and found a total of 1566 YSOs. Initial inspection of this selection indicated that there was still contamination by normally reddened stars, and the limits were moved by 0.2 mag toward the red compared with the formulas given by Winston et al. (2007) and and Jose et al. (2016). To then isolate Class I and Class II YSOs from these sources, we used the Phase II color selection from Gutermuth et al. (2009), with the CCD [KS–[3.6]]0 versus [[3.6]–[4.5]]0 as shown in Figure 7. We obtained a total of 32 Class I YSOs and a total of 385 Class II YSOs.


Finally, the final estimates depend slightly on whether very strong lines with X > −6 are used or not. In Figure 7, very strong lines clearly show a systematic tilt. These strong lines have an impact on the slopes, e.g., seen in Figure 4. The lower

 values of the stronger lines in MB99 would give higher

 values with a fixed ξ, but this would also cause a tilt in Figure 4. A larger ξ is therefore required so that

 values of strong and weak lines get balanced. While this is an important difference between the two line lists, generally speaking, it is suggested that using very strong lines often introduces complications such as non-LTE effects into a chemical abundance analysis (e.g., Kovtyukh & Andrievsky 1999; Gratton et al. 2006; Takeda et al. 2013). Based on synthetic spectra, we found that, in the case of lines with X ≳ −6, the line core does not grow any more with increasing metallicity and the damping wing starts to contribute to the EW at around the solar metallicity. If we run the bootstrap method with the same lines but including those with X > −6, we obtain moderately different results for the MB99 list, as illustrated in Figure 5. Four lines from MB99 have X > −6, and including them leads to higher ξ and lower

 values:

 = (1.47 ± 0.18, 6.94 ∓ 0.05) for Arcturus and (1.61 ± 0.16, 7.71 ∓ 0.06) for μ Leo. The changes caused by including the strongest lines are marginally significant, 1–2σ, for the former but are negligible for the latter. Figure 6 shows that one line, Fe i λ 11973.04, with the largest

 has a particularly strong impact on the slope in the X versus

 diagram for Arcturus with MB99. The same line gives

 ∼ 8.10 dex, which is also higher than the average, for μ Leo. However, the scatter of

 from lines within the low-X range is large, which explains the relatively small effect of including the high-X lines for μ Leo. In contrast, six VALD3 lines that we selected have X > −6, but including them has a negligible impact on the

 measurements. For VALD3, the Fe i λ 11973.046 line leads to

 values that are very close to the average abundances from other lines for both Arcturus and μ Leo. This line corresponds to the rightmost point in Figure 7 and has a very large difference, 0.8 dex, between the

 values in the two line lists. Considering these complications, we decided to adopt the

 values obtained without the lines at X > −6 as our best estimates. Although the

 from individual lines depend on ξ as described above, we found that the [Fe/H] obtained in different works are not correlated with ξ (Figure 8). This is probably because systematic differences in previous works, such as differences in line lists and atmosphere models, introduced a scatter larger than the expected correlation between the two parameters.


The advent of the ESA Gaia satellite for the first time allows the study of young stellar populations on large scales (> 100 pc) in six-dimensional (6D) position and velocity space. For example, using Gaia Data Release 2 (DR2) (Gaia Collaboration 2018a), Kounkel et al. (2018) and Zari et al. (2019) demonstrated that the Orion star-forming region is composed of a variety of populations with different spatial and kinematic properties each that are all likely generated in multiple events instead of in a progressive star formation history (see also Beccari et al. 2017; Jerabkova et al. 2019b; Kroupa et al. 2018, discussing three bursts of star formation in the Orion Nebula cluster). Zari et al. (2018) described the 6D properties and age structures in which young stars are found within a region of 500 pc around the Sun, and a number of other studies focusing on individual star-forming regions have been reported. One example is the large-scale picture of the Gamma Velorum region (Beccari et al. 2018; Cantat-Gaudin et al. 2019). The Gaia DR2 catalogue also led to the discovery of stellar relic filaments. These are spatial structures of a few pc that are more than 90 pc long and consist of stars of equal ages that are younger than a few hundred million years (Jerabkova et al. 2019a; Beccari et al. 2020). A Galaxy-wide survey using the Gaia DR2 catalogue reveals many elongated structures made of coeval stars, many of which are tidal tails of dissolving star clusters (Kounkel & Covey 2019). Meingast et al. (2021) described the nearby extended spatial distribution of stars that co-move with their clusters but are not bound to them. After the release of the Gaia DR2 catalogue, tidal tails have been found around four nearby ( 300 pc) OCs, namely Blanco 1 (≈100  Myr, Zhang et al. 2020), the Hyades (≈600 − 700 Myr; Meingast & Alves 2019; Röser et al. 2019; Douglas et al. 2019; Gossage et al. 2018; Reino et al. 2018; Lodieu 2020; Gaia Collaboration 2018b), Coma Berenices (≈750 Myr; Tang et al. 2019; Fürnkranz et al. 2019), and Praesepe (≈800 Myr; Röser & Schilbach 2019).


In this section, we describe our new compilation of SLS. To construct Dobs, we have chosen only systems with spectroscopically data well measured from different surveys. We have considered 19 SLS from the CASTLES, 107 from SLACS, 38 from BELLS, 4 from LSD, 35 from SL2S, and 1 system from the DES survey. The final list has a total of 204 systems, being the largest sample of SLS to date. We use spectroscopy to select those lenses with lenticular (S0) or elliptical (E) morphologies that have been modelled assuming a SIS ($\sim 3{{\ \rm per\ cent}}$) or SIE ($\sim 97{{\ \rm per\ cent}}$) lens model. Many systems have not been taken into account due to several issues. For instance, the system PG1115+080 (Tonry 1998) from the CASTLES survey has been discarded because the lens mass model is steeper than isothermal. In addition, the system MGJ0751+2716 (Spingola et al. 2018) was also discarded because the main lens belongs to a group of galaxies. From the SLACS survey (Bolton et al. 2008; Auger et al. 2009), we remove the systems SDSSJ1251−0208, SDSSJ1432+6317, SDSSJ1032+5322, and SDSSJ0955+0101 since the lens galaxies are late-type. The same reason is applied to the systems SDSSJ1611+1705 and SDSSJ1637+1439 from the BELLS survey (Shu et al. 2016). We have also discarded the systems SDSSJ2347−0005 and SDSSJ0935−0003 from the SLACS survey and the system SDSSJ111040.42+364924.4 from the BELLS survey because they have large measured velocity dispersions (∼400 km s−1 or bigger values), suggesting the lens might be part of a group of galaxies or that there is substructure in the line of sight. For those systems without reported velocity dispersion error, we assumed the average error of the measurements in the survey subsample as follows. For the nine systems from CASTLES, we consider the average error on σ for this survey, i.e. 14  per cent. In the case of the system DES J2146−0047 (Agnello et al. 2015), we have assumed a 10 per cent error on σ, which is the average error of the entire sample. The LSD survey (Koopmans & Treu 2003; Treu & Koopmans 2004) reports σ corrected by circular aperture using the expression obtained by Jorgensen, Franx & Kjaergaard (1995a,b). A close inspection of the σspec values, with and without aperture correction, presented by Cao et al. (2015) show the differences is smaller than the reported error. Thus, we decided to use the observed values (σ) and the reported error for the sample without the aperture correction. On the other hand, in those systems in which the Einstein radius error was not reported, we followed Cao et al. (2015) and assumed an error of δθE = 0.05, which is the average value of the systems with reported errors in this sample.


The shape of the spectral energy distribution and the emission rates of ionizing photons (see Table 1 of Paper II) depend on the assumed wind mass-loss rates, wind speeds, and wind clumping. These parameters are uncertain. Theoretical predictions are now available (e.g., Krtička et al. 2016; Vink 2017), but they have not yet been thoroughly tested against observations, because only very few stripped stars with sufficiently strong wind mass-loss have been identified and studied in detail so far (e.g., Groh et al. 2008). In Paper I, we showed that variations in wind mass-loss rate primarily affect the predicted emission rate of He II-ionizing photons, while the emission rates of H I- and He I-ionizing photons are not significantly affected. The mass-loss rates assumed in our models were chosen to smoothly connect the mass-loss rates of subdwarfs (Krtička et al. 2016) with the observed mass-loss rates of WR stars (Nugis & Lamers 2000). Our assumed mass-loss rates also match well with the observed mass-loss rate of the stripped star in the binary system HD 45166 (Groh et al. 2008). The recent theoretical predictions by Vink (2017) suggest that the mass-loss rates of stripped stars may be ten times lower than what we assume in this paper. The winds of stripped stars are likely not reaching close to the Eddington limit, in contrary to massive main-sequence and WR stars (cf. Bestenlehner et al. 2014). This suggests that the wind mass-loss rate from stripped stars is lower than that from WR stars and thus not well-described by the recipe for WR stars of Nugis & Lamers (2000). To establish which are the wind mass-loss rates from stripped stars, observations of a sample of stripped stars are necessary. If, as suggested by Vink (2017), the mass-loss rates from stripped stars indeed are lower than what the recipe from Nugis & Lamers (2000) predicts, it would likely imply an increase of the emission rates of He II-ionizing photons presented in this work. The emission rates of H I- and He I-ionizing photons are robust against wind uncertainties.


Understanding how inertial waves interact with co-rotation resonances is thus a key issue in quantifying tidal dissipation, especially since waves may deeply interact with the background flow at this particular location, which in turn may alter the background flow (as was proposed first by Eliassen & Palm 1961, for terrestrial mountain waves). In binary systems and for late-type stars, Goldreich & Nicholson (1989) showed that the angular momentum transported by gravity waves and exchanged at co-rotation can lead to the successive synchronisation of the layers, from the base to the top of the radiative envelope. More generally, a body of work in various domains, from astrophysical disks (e.g. Goldreich & Tremaine 1979; Baruteau & Masset 2008; Latter & Balbus 2009; Tsang & Lai 2009) to geophysical fluid dynamics (e.g. Bretherton 1966; Yamanaka & Tanaka 1984), has tried to understand the properties of wave propagation and dissipation around co-rotation and, more generally, at all special locations in fluids that correspond to singularities in the linear wave propagation equation. We will refer to them as ‘critical levels’ in the following (Maslowe 1986), or as ‘critical layers’ in the case of a viscous medium. This distinction is analogous to the distinction between shear layers and attractors of characteristics that are kinds of singularities for the governing equation of inertial waves in a spherical shell. The aforementioned singularities can act very differently, with either severe absorption at the critical level (as in Booker & Bretherton 1967, for stratified vertical shear flows) or no attenuation if the wave propagates in a peculiar direction (Jones 1967; Acheson 1972; Grimshaw 1975a, for stratifiedvertical shear flows with rotation and magnetism). In other cases, a critical level may even give rise to wave amplification under certain conditions related to the first and second derivatives of the mean flow velocity (Lindzen & Tung 1978; Lindzen & Barker 1985, for barotropic and stratified shear flows, respectively). These studies all used an invariant quantity (the Reynolds stress or thewave action for rotating or magnetic flows) as a diagnostic tool to interpret the role of the critical level in terms of energy transmission and to quantify exchanges between the wave and the mean flow (Eliassen & Palm 1961; Bretherton 1966).


The launch of the Fermi Gamma-ray Space Telescope has spurred on the search for pulsars in γ-rays (Grenier & Harding 2015), yielding over 2001 detections and triggering multiwavelength observations. While pulsars are common targets in the X-rays, they are very challenging targets in the optical and very few of them have been identified (see Mignani et al. 2016, and references therein). Here, we report on Large Binocular Telescope (LBT) observations of an isolated pulsar, PSR J2043+2740 (Taylor, Manchester & Lyne 1993), detected by both AGILE (Pellizzoni et al. 2009) and Fermi (Abdo et al. 2010; Noutsios et al. 2011). It was discovered as a radio pulsar (Ray et al. 1996) and later on as an X-ray source by XMM–Newton (Becker et al. 2004), although X-ray pulsations have not yet been found. PSR J2043+2740 is one of the very few non-recycled pulsars older than 1 Myr detected in γ-rays, with a characteristic age τc = 1.2 Myr, inferred from the values of its spin period Ps = 0.096 s and its derivative $\dot{P}_{\rm s} = 1.27 \times 10^{-15}$ s s−1 (Ray et al. 1996). This also yields a rotational energy loss rate $\dot{E}_{\rm rot} = 5.6 \times 10^{34}$ erg s−1 and a surface dipolar magnetic field Bs = 3.54 × 1011 G.2 Although PSR J2043+2740 does not have a very large spin-down power compared to young (∼1–10 kyr) pulsars (∼1036–1038 erg s−1), it is still a factor of 2 larger than that of middle aged γ-ray pulsars (∼0.1–0.5 Myr), such as Geminga, PSR B0656+14 and PSR B1055−52, all detected in the optical, thanks to their distances ≲ 500 pc (Abdo et al. 2013). The distance to PSR J2043+2740 is uncertain owing to the lack of a radio parallax measurement. The radio dispersion measure (DM = 21.0 ± 0.1 pc cm−3; Ray et al. 1996) gives a distance of 1.8 ± 0.3 kpc from the NE2001 model of the Galactic-free electron density (Cordes & Lazio 2002). A slightly smaller distance (1.48 kpc) is inferred from the model of Yao, Manchester & Wang (2017). The hydrogen column density towards the pulsar obtained from the X-ray spectral fits (NH ≲ 3.6 × 1020 cm−2; Abdo et al. 2013) suggests a distance of a few hundred pc (He, Ng & Kaspi 2013), although these estimates depend on the model X-ray spectrum. Such a distance would make PSR J2043+2740 a viable target for deep optical observations, never carried out until now, and might be compatible with the debated association (Noutsios et al. 2011) with the Cygnus Loop supernova remnant (SNR) at $540^{+100}_{-80}$ pc (Blair, Sankrit & Raymond 2005).


For completeness, we also supplement our reaction scheme with grain-surface association reactions extracted from the publicly available Ohio State University (OSU) network3 (Garrod et al. 2008). For those species important in grain-surface chemical reaction schemes, e.g., the CH3O radical, which are not included in Rate12, we also extract the corresponding gas-phase formation and destruction reactions from the OSU network. The grain-surface network has been further updated to include all studied routes to water formation under interstellar and circumstellar conditions (Cuppen et al. 2010a; Lamberts et al. 2013). The grain-surface reaction rates are calculated assuming the Langmuir-Hinshelwood mechanism only, and using the rate-equation method as described in Hasegawa et al. (1992). We limit the chemically “active” zone to the top two monolayers of the ice mantle. We assume the size of the barrier to surface diffusion is 0.3× the binding energy; in this way, volatile species diffuse at a faster rate than strongly bound species. This value lies at the optimistic end of the range determined by recent off-lattice kinetic Monte Carlo simulations of surface diffusion of CO and CO2 on crystalline water ice (Karssemeijer & Cuppen 2014). This allows the efficient formation of complex organic molecules via radical-radical association reactions at ≳20 K (see, e.g., Vasyunin & Herbst 2013; Walsh et al. 2014). For the lightest reactants, H and H2, we use either the classical diffusion rate or the quantum tunnelling rate depending on which is fastest (see, e.g., Tielens & Hagen 1982; Hasegawa et al. 1992). For the latter rates, we follow Garrod & Pauly (2011) and adopt a rectangular barrier of width 1.5 Å. We also include reaction-diffusion competition in which the reaction probability is determined by the relative rates between the barrier-mediated reaction and thermal diffusion (see, e.g., Chang et al. 2007; Garrod & Pauly 2011). Although still relatively simplistic, this takes into account the increased probability of reaction in the limit where the thermal diffusion of the reactants away from a common binding site is slow compared with the barrier-mediated reaction rate.


“Wiggling” outflows are often observed among young stellar jets and protostellar molecular outflows (Eisloffel et al. 1996; Terquem et al. 1999). Terquem et al. (1999) investigated such binary systems where the accretion disk, from which the jet originates, is inclined to the binary orbital plane. They concluded that the observed jet “wiggling” is a consequence of the jet precession caused by tidal interactions in such non-coplanar binary systems. Nichols & Slavin (2009) as well as Hollis & Michalitsianos (1993) suggested that the precession of the accretion disk around the WD may be responsible for the bending of the wide-angle outflow found in the previous studies. In analogy to these observations of young stellar jets, we suggest that the “wiggling” that we also find here for the R Aqr jet may result from disk precession as well. We estimated the precession period using the theory from Terquem et al. (1999) and the binary parameters taken from Gromadzki & Mikołajewska (2009) – Mh = 0.8M⊙ (the mass of the hot WD companion), Mp∕Mh = 1.65 (where Mp is the mass of the primary companion), D = 15.5 AU (the mean semi-major axis of the system), and e = 0.25 (eccentricity). The value of Rd is unknown in our case and we used Rd = 5 AU giving D∕Rd ≈ 3 which corresponds to the average value of 2 ≤ D∕Rd ≤ 4 (the range taken from Terquem et al. 1999). For this calculation, we assumed that the angle δ between the disk plane and that of the binary orbit is small enough (10°) and we adopted cosδ = 1. Using Eq. (1) from Gromadzki & Mikołajewska (2009), we derived the precession time of T ≈ 530 yr. This value is quite large for the wiggling waves that we see. We estimated the projected spatial wavelength λproj of the “wiggling” wave according to λ = λproj∕sin i, where i is the angle between the jet symmetry axis and the line of sight, and T = λ∕υ, where υ is the jet velocity, from Gromadzki & Mikołajewska (2009). Using i = 72° and υ ~ 100 km/s, we derive λproj ≈ 10 500 AU which is more than 20 times larger than the projected length of the observed wiggling outflow (2′′ ≈ 440 AU). However, we should note that the precessing time strongly depends on the D∕Rd; the T decreases significantly with increasing R. It may also be the case that the “wiggling” model developed for YSO jets is not fitting for R Aqr which consists of evolved objects, and both the WD and the disk where the jet probably forms are much hotter than YSO systems. Furthermore, we cannot exclude that the steady wiggling might be a sequence of dynamical interactions of the two collimated flows tilted to each other.


It is well known that a per cent level understanding of the anisotropy of the redshift-space galaxy clustering is needed to accurately recover cosmological information from the RSD signal in order to shed light on the issue of dark energy versus modified gravity. From a statistical point of view, the source of the anisotropy is the galaxy line-of-sight pairwise velocity distribution. It is therefore important to adopt a realistic functional form for this velocity PDF when fitting models to the data. To this purpose, in Paper I we introduced the GG prescription for the velocity PDF. In this work, we have continued the development of this model by making explicit the dependence of the GG distribution on quantities predictable by theory, namely its first three moments, and extending it to the more general concept of GQG. To keep the model as simple as possible, we have proposed an ansatz with two free dimensionless parameters that describe how infall velocity and velocity dispersion vary when moving from one place to another in our Universe. Since their interpretation is clear, these parameters can be theoretically predicted or, assuming a more pragmatic approach, tuned to simulations or used as nuisance parameters. State-of-the-art PT has proven successful in predicting the large-scale behaviour of the velocity PDF and the correspondent monopole and quadrupole of the redshift-space correlation function (e.g. Reid & White 2011; Wang, Reid & White 2014), at least for massive haloes, M ∼ 1013 M⊙. Unfortunately, by definition, any PT breaks down for small separations. Consequently, alternative approaches have been suggested in the literature, spanning from purely theoretical (e.g. Sheth 1996) to hybrid techniques in which N-body simulations plus an HOD are employed to deal with the issue of non-linearities (e.g. Tinker 2007; Reid et al. 2014). One of the main results from our work is to provide a framework in which perturbation and small-scale theories are smoothly joined, so that all available RSD information can be coherently extracted from redshift surveys. A fundamental requirement for a redshift-space model is that it must be precise on all scales interest, and it should inform the user of the scales on which the model can be trusted. We have compared to N-body simulations the well-known GSM (Reid & White 2011), the more recent ESM (Uhlemann et al. 2015) and the GQG prescription over a broad range of separations, from 0 to 80 h−1 Mpc. Different redshifts, from z = 0 to 1, and different tracers, namely DM particles and two mass-selected catalogues of DM haloes, have been considered. We have concluded that, among the three, QGQ is the only model capable of providing a precise redshift-space correlation function on scales down to ∼5 h−1 Mpc over the range of redshifts covered by future surveys. Keeping in mind that the range of validity of the models depends on tracer, redshift and order of the Legendre multipoles we are interested in, for finiteness, we can say that all the models converge to the expected amplitude on scales ≳30 h−1 Mpc, at least for multipole and quadrupole. Since these scales roughly coincide with the range of validity of state-of-the-art PTs, if we rely only on PT and if we are not interested in higher order multipoles, the most natural choice is the simplest model among the three, i.e. the GSM. As for the ESM, we have found it to be unbiased down to smaller scales and for higher order multipoles than the GSM, thus confirming the results by Uhlemann et al. (2015), but, on the other hand, it seems to behave even worse than the GSM on the smallest scales. We can therefore think of it as a natural extension of the GSM in the perspective of further PT developments. In particular, a better prediction of the third moment of the velocity PDF is required before the ESM can be applied to data on smaller scales. Formally, the same argument holds for the GQG model, none the less, since this latter is meant to include non-linear scales, it could be possible to obtain a prediction for the third moment by interpolating between (very) small and (very) large scales. More precisely, as shown in the lower-right panel of Fig. A1, the functions $c^{(3)}_t$ and $c^{(3)}_r$, which fully characterize the third moment, are peaked at r ≲ 10 h−1 Mpc. By adopting a model for the small-scale limit that includes those separation, most likely using simulations in a similar way to that proposed in Reid et al. (2014), we would then be able to interpolate between these peaks and their large-scale limit, which is trivially 0.


Erwin (2018) showed that, in a sample drawn from the Spitzer Survey of Stellar Structure in Galaxies (S4G), the bar fraction is constant over a range of (g −r) colours and gas fractions. Their bar fraction does not increase, but rather decreases for stellar masses higher than ∼ 109.7M⊙. These results are in contrast to many SDSS-based studies cited above. Erwin (2018) argues that this apparent contradiction can be explained if SDSS-based studies miss bars in low-mass blue galaxies. In Figs 5 and 6, we showed that the newly detected bars in GZD (compared to GZ2) are weak bars in low-mass blue galaxies. Nevertheless, the ‘combined’ bar fraction in Fig. 6 is not constant over (g −r) colour and agrees well with Masters et al. (2011) for redder colours [(g −r) colour > 0.5]. Additionally, our ‘combined’ bar fraction remains roughly constant over stellar mass. As mentioned before, we conclude that strong bars drive the trends of bar fraction with (g −r) colour, stellar mass, and SFR observed in other studies (Nair & Abraham 2010b; Masters et al. 2011, 2012; Vera et al. 2016; Cervantes Sodi 2017). However, the addition of weak bars in low-mass blue galaxies is insufficient to resolve the apparent disagreement between Erwin (2018) and many SDSS-based studies (Masters et al. 2011, 2012; Vera et al. 2016; Cervantes Sodi 2017; Kruk et al. 2018), which instead seems likely to be due to the very different sample selection of the S4G and SDSS galaxy samples. For example, the median stellar mass of the sample used in Erwin (2018) is ∼109.6M⊙ (based on their Fig. 4 and the bins in the top left-hand panel of their Fig. 5). However, the median stellar mass of our sample is 1010.6M⊙. As stellar mass correlates with many parameters (including bar length), this can have major consequences. Additionally, as Erwin (2018) notes, there is also the issue of resolution to consider. With an r-band FWHM of 1.18 arcsec from DECaLS (Dey et al. 2019) and a mean redshift of 0.036, the mean linear resolution of our sample is approximately 834 pc, which is higher than the 165 pc of Erwin (2018). This explains why they observe many sub-kpc bars, while we do not. These differences in stellar mass and resolution will manifest themselves in the conclusions, so a more detailed analysis is needed for a proper comparison with Erwin (2018).


Analyzing optical emission lines, emanating from within the northern lobe, Tylenda et al. (2019) found a reddening with EB − V ≈ 0.9 mag or AV ≈ 2.8 mag, which we assume is mainly circumstellar in origin. Hajduk et al. (2013) observed two stars shining through the southern lobe and found AV = 3.3 − 4.4 mag with unknown contribution from the interstellar component. We assume here that those observations quantify the amount of circumstellar dust that is the main actor in shielding molecules from the central source. We recalculated the lifetimes of molecules assuming AV = 3 mag, and with (1) standard dust properties (i.e. with composition and size distribution as of interstellar dust) or (2) with larger and less opaque grains, at the gas-to-dust mass ratio of 124 (see Heays et al. 2017, for more details on the assumed dust properties). We used shielding functions from Heays et al., which include effects in lines. Results are shown in Cols. (3) and (4) of Table 3. The presence of ISM grains makes it possible for the observed molecules to survive for a very long time, longer than 350 yr. The lifetimes in the presence of the large grains considered by Heays et al. are typically a few times shorter than the age of the remnant. It is uncertain what kind of grains populate the dusty remnant of CK Vul, but given its anomalous elemental and molecular compositions and eruptive history, dust may have a peculiar chemical composition and size distribution. In such a case, the total to selective extinction law would also be different and the assumed AV may not be adequate. Nevertheless, if the molecules formed 350 yr ago and are shielded by big grains, with the calculated lifetimes a considerable fraction of molecular species would survive, except perhaps for a few most fragile ones which indeed are almost absent in the lobes. We conclude that the lifetimes in Table 3 that were calculated with an attenuated ISRF are consistent with the molecule formation 350 yr ago or more recently.


We have used 3.0–75.0 keV NuSTAR data to probe any cyclotron line feature. To describe the continuum of 4U 1700–37, we have applied the NPEX model [cons*TBpcf*(powerlaw*npex+gaus+gaus)], following the previous work of Jaisawal & Naik (2015a). The NPEX model has been created by adding two cutoffpl models with their cutoff energies tied to each other and keeping the photon index of one to be frozen at –2.0. For the best fit, the χ2/d.o.f is found to be 577.64/475. The fit shows some residuals in the overall spectrum. We added a Gaussian absorption model around 39 keV (following the previous work of Jaisawal & Naik 2015a), but the best fit gives the line energy as $15.44^{+0.56}_{-0.53}$ keV with χ2/d.o.f = 487.32/472. The width and the depth of the line are found to be $5.47^{+0.90}_{-0.78}$ keV and $1.29^{+0.51}_{-0.39}$, respectively. The chance probability of the line has been computed using the ftest task in xspec. The F-test with this absorption line gives an F value  = 29.2 and a chance probability of 2.61 × 10−17(Table 3). If we add another Gaussian absorption line at 38.9 keV (Energy value frozen) the best-fitting χ2/d.o.f is found to be 486.8/470. This indicates that the second absorption line is not required for the fit. If we use only one Gaussian absorption line and freeze the line energy at 38.9 keV then the width and the depth of the line are found to be $4.54_{-0.87}^{+0.90}$ keV and $2.87_{-1.05}^{+1.24}$, respectively with a χ2/d.o.f  = 549.2/473. The ftest gives a chance probability of the 38.9 keV line to be 6.4 × 10−6. So, with NPEX model we find two valid model combinations of the data. One, the presence of a Gaussian absorption line at ∼15 keV, two, the presence of a Gaussian absorption line at 38.9 keV. But, the presence of both lines together is not supported by the data. The 10.0–70.0 keV flux of the source is found to be (2.26 ± 0.01) × 10−9 erg cm-2s-1, much lower than the value (5.6 ± 0.3) × 10−9 erg cm-2s-1, previously reported from SUZAKU data (Jaisawal & Naik 2015a).


In the main simulation, we modeled a Cartesian cube 2000 AU in size with 150 grid points in each direction. The cell size of 13.3 AU is comparable to the size of the star, which was represented by a point source. Clumps A to D were simulated as 3D structures of a Gaussian density profile. The choice of a Gaussian distribution was dictated only by the simplicity of the implementation. Whereas observations constrain the clump sizes and overall relative location in two spatial dimensions, the extent of a given feature along the line of sight was a free parameter. We included scattering in the radiative transfer calculations. It turned out early on in the simulations that the dusty medium is very optically thick for visual and ultraviolet (UV) photons making the calculations particularly time-consuming. To speed them up, we used the Modified Random Walk method implemented in RADMC-3D (Robitaille 2010). The number of photons used in the Monte Carlo simulations varied from 105 to 109. For each spatial configuration of dust distribution, first a thermal structure was calculated. Based on this calculation, regions where the dust temperature exceeded the sublimation temperature were removed from the simulation and the thermal structure was calculated once again. In this way we reconstructed images that were further processed in CASA for a direct comparison to ALMA continuum maps. Given a very high number of free parameters (over 40 in the basic version of the simulation), the best configurations were searched through iterative trial-and-error modifications of the models. We aimed to construct only a general 3D model of the dusty environment requiring a minimum dust mass possible. We attempted to reproduce the peak and integrated ALMA fluxes of each feature within the order of magnitude. This aim, however unambitious it may appear, was challenging without increasing further the number of free parameters. For example, better fits to total flux and its distribution would require considering density distributions other than Gaussian.


Analyzing the fraction of quenched galaxies for centrals and satellites as a function of stellar mass and environmental parameters has emerged as a fruitful way of gaining insights into the phenomenology and the physical processes of quenching. However, one of the difficulties in interpreting this fraction is that many of the environmental parameters are statistically correlated both with each other or with the stellar mass of the galaxy. For example, there is good evidence that halo mass correlates with the mass of the central galaxy (e.g., Yang etÂ al. 2009), that the local overdensity correlates with the group-centric distance (e.g., Peng etÂ al. 2012; Woo etÂ al. 2013), and that the local overdensity also correlates with halo mass (e.g., Haas etÂ al. 2012; Carollo etÂ al. 2013b). These correlations among the parameters can introduce spurious dependencies, i.e., dependencies which have no direct causal relation to quenching, if the quenched fraction is regarded as a function of certain parameters in isolation. Therefore, in principle one has to study the quenched fraction in the full parameter space and to vary only one parameter at a time, while keeping the others fixed (see, e.g., the discussion in Mo etÂ al. 2010; Section 15.5). However, this approach does also not necessarily guarantee that the measured dependence of the quenched fraction on a certain parameter is directly related to a physical quenching process, since the red fraction may also depends on the history of the galaxy, i.e., how the galaxy is moving through the parameter space. Therefore, interpreting trends of the quenched fraction even in the full parameter space has turned out to be quite difficult and has led to some confusing and apparently inconsistent statements in the literature. In this paper, we use the Sloan Digital Sky Survey (SDSS; York etÂ al. 2000) and the group catalog of Yang etÂ al. (2012) to take a new look at some of the issues that have been recently raised.


In our investigation we were looking for alignment of galaxy clusters in a sample of 1056 low redshift ACO clusters with known Bautz–Morgan type. We found a statistically significant effect for structures with separation distance 30  R ≤ 45 h−1 Mpc. This allowed us to conclude that, for the analyzed clusters, the effect has a range to about 45 h−1 Mpc. We found a stronger alignment of elongated clusters of BM type I (an excess of small values of the Δθ angles is observed), having a range to about 45 h−1 Mpc. The alignment for BM I is probably connected with the origin of a supergiant galaxy. One should note that during studies of the isolated Abell groups (Flin & Olowin 1991; Trevese et al. 1992; Kim 2001; Niederste-Ostholt et al. 2010), only a rudimentary alignment was found and related only to the brightest cluster members. Gonzalez-Sanchez & Teodoro (2010) interpreted the alignment of just the brightest galaxies within a cluster as the effect of gravitational tidal forces. Correlation between the orientation of the brightest galaxy within a cluster and the cluster’s large axis was also found by Sastry (1968), Carter & Metcalfe (1980), Binggeli (1982), Struble & Peebles (1985), Rhee & Katgert (1987), West (1989, 1994), van Kampen & Rhee (1990), Plionis (1994), Fuller et al. (1999), and Kim et al. (2002). The role of a much more massive central galaxy is related to the problem of galaxy mergers in a cluster. This, in turn, is due to the fact of (generally speaking, random) interaction between cluster members and the dynamic evolution of structures near to specific cluster members. The problem of dynamic evolution can be studied by combined studies of the Binggeli effect, i.e., the relation between the positions of major axes in groups or clusters of galaxies and the directions toward their neighbors, and of the mutual orientation of the brightest galaxy (and other bright galaxies) in a structure relative to the position of cluster major axes or even examination of structure ellipticity redshift dependence, especially in the enlarged observational samples.


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).


However, using the well-assessed new post-AGB evolutionary models, we confined the main-sequence ages of our halo sample to be mostly ∼2–5 Gyr, with the oldest being ∼6–8 Gyr, while the outer-disk sample are mostly ≲1–4 Gyr. We thus conjecture that our targets probably formed prior to the encounter with M33. Obviously, our sample represents the population that is different from the underlying, smooth, extended (and mostly metal-poor) halo component of M31 (Ibata et al. 2007, 2014), which was formed through the repeated accretion of smaller galaxies in the distant past. These bright PNe seem to resemble the younger, metal-rich population in the outer stream of M31, as revealed by HST pencil-beam pointings on the Giant Stream (Brown et al. 2006a; Bernard et al. 2015b). The metallicity of the stream fields was enriched continuously from [Fe/H] ∼ −1.5 to at least solar level about 5 Gyr ago (Bernard et al. 2015b). This timeline of metal enrichment is generally consistent with the stellar ages of our metal-rich sample. N-body simulations suggested that the Giant Stream and other stream-like features in the halo are debris of a massive (≳109–

) progenitor that was recently disrupted during the course of a merger (e.g., Ibata et al. 2004; Fardal et al. 2006, 2007, 2008, 2013; Font et al. 2006; Geehan et al. 2006; Mori & Rich 2008; Sadoun et al. 2014). The extended star formation history and the broad range of metallicity (−1.5 ≲ [Fe/H] ≲ 0.2) discovered in the stream fields can be explained by a disk galaxy progenitor (Brown et al. 2006a, 2006b; Bernard et al. 2015b). If the stellar streams in M31's halo indeed have a common origin, our sample of halo PNe then probably formed through extended star formation in this possibly massive, disk-like progenitor. Moreover, some simulations predict that the remnant of the disrupted satellite resides in the NE Shelf (e.g., Fardal et al. 2008, 2013; Sadoun et al. 2014); PN17 in our sample is located in this region and might be associated with this substructure (see Section 4.4).


The galaxy NGC 7213 benefits from a detailed SED decomposition performed by G16, which allowed us to disentangle the relative contributions of AGN and SF activity to the global IR outcome of the source, providing a characterisation of the host galaxy in terms of stellar and dust content (M⋆ and Mdust, respectively), and ongoing SF (SFR). Here, we briefly introduce the photometric data collected from the archive and the SED decomposition procedure adopted by G16. The homogenised catalogue of total fluxes, from the UV to the FIR, is presented by G16 (see also their Table A.1: the flux densities are corrected for the aperture and magnitude zero point). In the case of NGC 7213, the photometric data included in the analysis are: the U, B, V, and R bands from de Vaucouleurs et al. (1991); the near-infrared measurements from the catalogue by Jarrett et al. (2000); the IRS spectrum re-binned by Gruppioni et al. (2016) and the photometry by Gallimore et al. (2010) and Moshir et al. (1990) in the MIR; and the FIR photometry by Spinoglio et al. (2002). The adopted SED fitting code was SED3FIT5 (Berta et al. 2013), which reproduces the stellar emission and the emission of the dust heated by the stars and the torus emission simultaneously. The code used the library by Bruzual & Charlot (2003) for the stellar contribution, that of da Cunha et al. (2008) for the IR dust-emission, and the library of smooth AGN tori by Fritz et al. (2006), updated by Feltre et al. (2012). In order to limit the degeneracy among the torus parameters, in G16 the AGN configurations of obscured sources were excluded for NGC 7213 (as supported by optical observations of the source and by the X-ray spectral properties presented in Sect. 3.1.2). The best fit model and the decomposition in the different components is presented in Fig. 5. The host-stellar contribution and the dusty SF dominate over the AGN in the optical bands and in the entire IR band, respectively. While this could appear to be in contrast with the type 1/broad-line nature of the AGN, it is in agreement with the relatively weak nuclear activity observed in NGC 7213 (revealed also through the X-ray spectral analysis reported Sect. 3.1.2).


A comparison between the constraints in Figure 2 and those found from the analysis of the reflection spectrum of the disk of other sources in previous studies is not straightforward because these measurements are quite sensitive to the specific source and the quality of the data, so it may be dangerous to generalize the results found from our analysis of 17 RXTE observations of LMC X-1. In general, a correlation between the estimates of a* and α13 is common even when we analyze the reflection spectrum. However, such a degeneracy can be broken when the inner edge of the disk is very close to the compact object (Tripathi et al. 2018, 2019b; Zhang et al. 2019). For example, Tripathi et al. (2019a) analyzed simultaneous XMM-Newton and NuSTAR observations of MCG–6–30–15 obtaining

 and

 (90% confidence level for one relevant parameter). Even if there is a correlation between these measurements of a* and α13, see Figure 6 in Tripathi et al. (2019a), we can get quite stringent constraints on both parameters. This is not the case with the analysis of the thermal component presented in this paper. When we assume the Kerr metric, observations 7, 12, and 14 of LMC X-1 give quite high spin values (see left column of Table 1), comparable to the XMM-Newton and NuSTAR observations of MCG–6–30–15. However, when we leave α13 free it is not easy to constrain a* and α13 at the same time. While the limited energy resolution of RXTE with respect to XMM-Newton may have some effect, the key-point is in the difference between the reflection spectrum and the thermal one. The former is characterized by many features, notably, but not only, the iron Kα complex around 6–7 keV. Such features help to break the parameter degeneracy, even if the reflection spectrum has several parameters to fit. The thermal spectrum, on the contrary, has quite a simple shape and there is an intrinsic degeneracy among the model parameters. This is true even when we assume the Kerr metric: it is possible to measure the black-hole spin only when we have independent estimates of the black-hole mass, distance, and inclination angle of the disk. If we want to use the continuum-fitting method to test the Kerr metric and we add a deformation parameter, the problem of degeneracy between a* and α13 should not be a surprise.


In principle, Fig. 5, central panel G, shows that (469219) 2016 HO3 may have been locked in a Kozai–Lidov resonance with ω librating about 270° for nearly 100 kyr and probably more. Because of the Kozai–Lidov resonance, both e (central panel E) and i (central panel F) oscillate with the same frequency but out of phase (for a more detailed view, see Fig. 4, panels E and F); when the value of e reaches its maximum the value of i is the lowest and vice versa ($\sqrt{1 - e^2} \cos i \sim$ constant, see Fig. 4, panel B). During the simulated time and for the nominal orbit, 469219 reaches perihelion and aphelion the farthest possible from the ecliptic. Fig. 5, G-panels, show that for other incarnations of the orbit of 469219, different from the nominal one, ω may librate about 90° as well during the simulated time interval. However, is this a true Kozai–Lidov resonance? Namouni (1999) has shown that the secular evolution of co-orbital objects is viewed more naturally in the erωr-plane, where er and ωr are the relative eccentricity and argument of perihelion computed as defined in Namouni's work (see equations 3 in Namouni 1999); these are based on the vector eccentricity and the vector inclination. Fig. 6 shows the multi-planet erωr-portrait for the nominal orbit of this object. It clearly resembles figs 13 and 19 in Namouni (1999). Asteroid 469219 librates around $\omega _{\rm r}=-90{^\circ }$ for Venus, the Earth, and Jupiter. This behaviour corresponds to domain III in Namouni (1999), horseshoe-retrograde satellite orbit transitions and librations (around $\omega _{\rm r}=-90{^\circ }$ or 90°). For a given cycle, the lower part corresponds to the horseshoe phase and the upper part to the quasi-satellite or retrograde satellite phase. This is not the Kozai–Lidov resonance; in this case, the Kozai–Lidov domain (domain II in Namouni 1999) is characterized by libration around $\omega _{\rm r}=0{^\circ }$ (or 180°) which is only briefly observed at the end of the backwards integrations (see Fig. 6). The Kozai–Lidov resonance is however in action at some stage in the orbits displayed in Figs 5 and 8. Our calculations show that the orbital evolution followed by 469219 is the result of the dominant secular perturbation of Jupiter as the periodic switching between co-orbital states ceases after about 8 kyr if Jupiter is removed from the calculations. Fig. 7 shows that, without Jupiter, 469219 switches between the Kozai–Lidov domain and that of horseshoe-quasi-satellite orbit transitions and librations (including both −90°and 90°). Jupiter plays a stabilizing role in the dynamics of objects following orbits similar to that of 469219. It is not surprising that Jupiter instead of the Earth or Venus is acting as main secular perturber of 469219. Ito & Tanikawa (1999) have shown that the inner planets share the effect of the secular perturbation from Jupiter; in fact, Venus and our planet exchange angular momentum (Ito & Tanikawa 2002). In their work, these authors argue that the inner planets maintain their stability by sharing and weakening the secular perturbation from Jupiter. Tanikawa & Ito (2007) have extended this analysis to conclude that, regarding the secular perturbation from Jupiter, the terrestrial planets form a collection of loosely connected mutually dynamically dependent massive objects. The existence of such planetary grouping has direct implications on the dynamical situation studied here; if Jupiter is removed from the calculations, the overlapping secular resonances and the recurrent dynamics disappear as well.


While the properties of the SLSN hosts themselves are of interest, they are most diagnostic when compared to other classes of extragalactic transient whose progenitors are better understood. To this end, we employ a comparison sample of LGRB and CCSN3 host galaxies. In principle, CCSNe should trace all core-collapse events, although the mass function means they will be dominated by stars at the lower mass end (∼8 M⊙ to ∼25 M⊙). There also remains a possibility that some very massive stars can undergo core collapse without yielding a LSNe (e.g. Smartt 2009; Ugliano et al. 2012; Kochanek 2014) such that CCSNe samples might only provide a census of lower mass core collapsing stars (e.g. 8  M*  20 M⊙). Indeed, constraints from explosion parameters have shown the majority of CCSNe to be consistent with lower mass progenitors, as opposed to more massive Wolf–Rayet stars (Cano 2013; Lyman et al. 2016) GRBs likely represent a population with rather larger initial masses (Larsson et al. 2007; Raskin et al. 2008). LGRBs are now known to be associated with the core collapse of massive stars, and broad line SN Ic are near ubiquitously associated with low-z events (where such signatures can be seen; Hjorth et al. 2012). When compared to the hosts of CCSNe they are generally smaller and of lower luminosity, consistent with an origin in galaxies of lower metallicity (Fruchter et al. 2006; Svensson et al. 2010). In relatively local examples, where spatially resolved gas phase metallicities can be obtained, these indeed appear to be lower for GRBs than for CCSNe, even in cases where the luminosity of the galaxy is relatively high (i.e. the GRB host galaxies lie off the mass–metallicity relation; Modjaz et al. 2008; Graham & Fruchter 2013). Hence, comparing the hosts of SLSNe to these events allows us to test the large-scale environments of SLSNe against those of the bulk core-collapse population and a subset which appears to derive largely from massive stars at lower metallicity, although we note that agreement on this matter is not complete (e.g. Podsiadlowski, Joss & Hsu 1992; Eldridge, Izzard & Tout 2008; Smartt 2009; Drout et al. 2011). By exploiting both LGRB and CCSN host samples we can ascertain if there is a strong metallicity dependence in SLSN production, and if this is more or less extreme than that observed in GRB hosts.


The snowlines of various volatiles (sublimation temperature Tsub ≲ 160 K) play a major role for planet formation. Beyond the snowline, the high abundances of solids allow for efficient sticking to form larger bodies, which is further enhanced by the presence of ices (e.g., Stevenson & Lunine 1988; Ros & Johansen 2013). Extensive studies have investigated the snowline in protoplanetary disks around pre-main-sequence stars similar to the nebula out of which the solar system is assumed to have formed (e.g., Lissauer 1987; Pollack et al. 1996). In such models, the water snowline is located at a radius of a few AU. It is thought that the early pre-solar nebula was hot (>1500 K), such that both volatiles and refractories (Tsub ≳ 1400 K) are in the gas phase out to larger distances (Cassen 2001; Scott 2007; Davis et al. 2014; Marboeuf et al. 2014). The evidence of such a hot solar nebula comes from the history of the refractories, but the volatile content of comets seems to indicate that a part of the disk remains cold (Bockelée-Morvan et al. 2000; Mumma & Charnley 2011; Pontoppidan et al. 2014). The evolution of the snowline due to disk and star evolution and its accretion rate clearly affects the chemical composition in the region relevant to planet formation (e.g., Lodders 2004; Davis 2005; Öberg et al. 2011b). The most relevant volatiles are the known major ice species: H2O, CO2, and CO. Observations (Meijerink et al. 2009; Zhang et al. 2013) and models (e.g., D’Alessio et al. 1998; Dullemond et al. 2007) of protoplanetary disks around pre-main sequence T Tauri stars indicate that such disks are not warm enough to have gas-phase volatiles in the midplane beyond 30 AU, as claimed in some early solar nebula models, and, for the case of H2O, a snowline of only a few AU is typically found. Higher temperatures at large radii might be achieved, but only during the deeply embedded phase of star formation when the accretion rate is high. The question remains how hot an embedded accreting disk can be when the accretion rate is high (≥10-6M⊙ yr-1, see Dunham et al. 2014, for a recent review).


There are still several sources of systematics we do not consider in this paper. For instance, whether the use of a different mass distribution models for these lenses could significantly affect the final result. Therefore, we performed a sensitivity analysis and repeated the above calculation using the extend power law (EPL) lens model, in which the luminosity density profile [v(r) ∼ r−δ] is different from the total mass (luminous plus dark matter) density profile ρ(r) ∼ r−α. Such lens model has found widespread astrophysical applications in the literature (Cao et al. 2016a; Xia et al. 2017; Qi et al. 2019), considering the anisotropic distribution of stellar velocity dispersion β (Koopmans 2005; Cao et al. 2017b; Chen et al. 2019). With the EPL lens parameters (α, β, δ) modelled by Gaussian distributions α = 2.00 ± 0.08, δ = 2.40 ± 0.11, and β = 0.18 ± 0.13 (Gerhard et al. 2001; Bolton, Rappaport & Burles 2006; Graur et al. 2014; Schwab, Bolton & Rappaport 2010), the scatter plot of the deviation Tzs in EPL model is shown in Fig. 4. Our results provide the deviation Tzs = 0.974 ± 0.017 [corresponding to c(zs) = 2.922(± 0.051) × 105 km s−1], and the median value Med(Tzs) = 0.983 with the median absolute deviation MAD(Tzs) = 0.259 for the full lens sample. Therefore, our results show that the assumed lens model has a slight impact on the SOL constraint, which highlights the importance of auxiliary data (such as more high quality integral field unit) in improving constraints on the density profile of gravitational lenses. More detailed models of mass distribution, such as Navarro–Frenk–White density profile (suitable for dark matter distribution; Navarro, Frenk & White 1997), Sersic-like profile (suitable for stellar light distribution) (Sérsic 1968), pseudo-isothermal elliptical mass distribution, could also be considered in this context (Kassiola & Kovner 1993). However, strong lensing observables we used are determined by the total mass inside the Einstein radius. Hence, they are not so sensitive to the details of the very central distribution like cusps (besides the extremal cases). Moreover, the Einstein rings of the lenses we used corresponded to less than 10 kpc hence the NFW profile of the dark halo would not likely be manifested.


Herschel imaging observations have shown that filamentary structures are truly ubiquitous in the cold interstellar medium (ISM) of the Milky Way (Molinari et al. 2010), dominate the mass budget of Galactic molecular clouds at high densities (≳104 cm−3) (Schisano et al. 2014; Könyves et al. 2015), and feature a high degree of universality in their properties. In particular, detailed analysis of the radial column density profiles indicates that, at least in the nearby clouds of the Gould Belt, molecular filaments are characterized by a narrow distribution of crest-averaged inner widths with a typical full width at half maximum (FWHM) value Wfil ∼ 0.1 pc and a dispersion of less than a factor of ∼2 (Arzoumanian et al. 2011, 2019; Koch & Rosolowsky 2015). Another major result from Herschel (e.g., André et al. 2010; Könyves et al. 2015; Marsh et al. 2016) is that the vast majority (> 75%) of prestellar cores are found in dense “transcritical” or “supercritical” filaments for which the mass per unit length, Mline, is close to or exceeds the critical line mass of nearly isothermal, long cylinders (e.g., Inutsuka & Miyama 1997),

M

line,crit

=

2

c
s
2

/G~16
M
⊙

$ {M_{{\rm{line}},{\rm{crit}}}} = \,2{\mkern 1mu} c_{\rm{s}}^2/G{\mkern 1mu} \sim {\mkern 1mu} 16{\mkern 1mu} {M_ \odot } $

 pc−1, where cs ∼ 0.2 km s−1 is the isothermal sound speed for molecular gas at T ∼ 10 K. Moreover, most prestellar cores lie very close to the crests (i.e., within the inner 0.1 pc portion) of their parent filaments (e.g., Könyves et al. 2019; Ladjelate et al. 2019). These findings support a filamentary paradigm in which low-mass star formation occurs in two main steps (André et al. 2014; Inutsuka et al. 2015): (1) multiple large-scale compressions of cold interstellar material in supersonic magneto-hydrodynamic (MHD) flows generate a cobweb of ∼0.1 pc-wide filaments within sheet-like or shell-like molecular gas layers in the ISM and (2) the densest molecular filaments fragment into prestellar cores (and then protostars) by gravitational instability near or above the critical line mass, Mline, crit, corresponding to

Σ

gas

crit

∼

M

line
,
crit

/

W
fil

∼
160

M
⊙

$ \Sigma_{\mathrm{gas}}^{\mathrm{crit}} \sim M_{\mathrm{line, crit}}/W_{\mathrm{fil}} \sim 160\,M_\odot $

 pc−2 in gas surface density (AV ∼ 7.5) or nH2 ∼ 2 × 104 cm−3 in volume density. This paradigm differs from the classical gravo-turbulent picture (Mac Low & Klessen 2004) in that it relies on the anisotropic formation of dense structures (such as shells, filaments, cores) in the cold ISM and the unique properties of filamentary geometry (see Larson 2005).


In Sifón et al. (2013), we used the σ–M200 scaling relation of Evrard et al. (2008) to estimate dynamical masses. As discussed in Section 1, the scaling relation of Evrard et al. (2008) was calibrated from a suite of N-body simulations using DM particles to estimate velocity dispersions. However, the galaxies, from which velocity measurements are made in reality do not sample the same velocity distribution as the DM particles. They feel dynamical friction and some are tidally disrupted, which distorts their velocity distribution and biases their dispersion (e.g. Carlberg 1994; Colín et al. 2000). Recent high-resolution hydrodynamical simulations of ‘zoomed’ cosmological haloes have shown that there is a significant difference between the velocity distributions of DM particles and galaxies themselves; whether galaxies (i.e. overdensities of stars in hydrodynamical simulations) or DM subhaloes are used makes comparatively little difference (Munari et al. 2013). Results from state-of-the art numerical simulations depend on the exact definition of a galaxy and the member selection applied, but the current consensus is that galaxies are biased high (i.e. at a given mass the velocity dispersion of galaxies or subhaloes is larger than that of DM particles) by 5–10 per cent with respect to DM particles (Lau et al. 2010; Munari et al. 2013; Wu et al. 2013), translating into a positive 15–20 per cent bias in dynamical masses when using DM particles. This is illustrated in Fig. 5: DM particles are not significantly impacted by either dynamical friction or baryonic physics; therefore, the scaling relations for DM particles are essentially the same for all simulations. In contrast, DM subhaloes are affected by baryons in such a way that including baryonic feedback (most importantly feedback from active galactic nuclei – AGN, but also from cooling and star formation) makes their velocity dispersions much more similar to those of simulated galaxies. This means we can rely on our analysis of the previous section, based on DM subhaloes, to correct the velocity dispersions measured for ACT clusters, and then estimate dynamical masses using predictions obtained either from galaxies or subhaloes. The difference between the Saro et al. (2013) and Munari et al. (2013) galaxy scaling relations depends on the details of the semi-analytic and hydrodynamical implementations used in Saro et al. (2013) and Munari et al. (2013), respectively. The different cosmologies used in the Millenium simulation (in particular, σ8 = 0.9; Springel et al. 2005) by Saro et al. (2013) and the simulations by (Munari et al. 2013, σ8 = 0.8) may also play a role.


When the size of the logarithmic redshift bin is small enough, we can use fluxes in place of luminosities, performing a test on the (non-)evolution with redshift that is completely independent from any assumption on cosmology. Risaliti & Lusso (2019) analysed in detail the choice of the bin size and verified that, as long as Δlog(z)≤0.1, the slope in the relation does not depend on it. Thanks to the statistics available, we chose Δlog(z)=0.06 and we limited our analysis to the redshift bins with more than five objects. We performed the same analysis for bins of size Δlog(z)=0.05 and Δlog(z)=0.07, finding no significant difference (see Fig. 9 for a comparison of the results for different sizes of the redshift bins). For our selection in Γ and the choice of the threshold for the Eddington bias, the division yielded 17 redshift bins. To perform the fitting to the data, we adopted the Python package emcee (Foreman-Mackey et al. 2013), a pure-Python implementation of Goodman & Weare’s Affine Invariant Markov chain Monte Carlo (MCMC) Ensemble sampler. To check that the results were independent from the employed method, we also performed the analysis using the Linmix package (Kelly 2007), an algorithm that makes use of a Bayesian approach to linear regression and takes into account the errors in both the x and y variable. We performed the fit a first time, then applied a 3σ clipping to the data, repeating this sequence for a total of three times. This yielded no significant difference with respect to the analysis without σ clipping. The results are shown in Figs. 7 and 9, and summarised in Table 3. In Fig. 7, red points indicate when the observations are characterised by an SN  5 in the soft band. Most of them are (X-ray) fainter objects at intermediate redshifts. This confirms that data points that passed our selection criteria, even if with a low SN, follow the relation and are representative of the population of blue quasars.


Figure 6 compares the IR SED of SN 2014C with the SEDs of all other interacting SNe for which observations beyond 5 μm are available in the literature. Apart from SN 2014C, only four other strongly interacting SNe IIn have been observed in the mid-IR. Three of these were observed at epochs comparable to the epoch at which SN 2014C was observed in the mid-IR. SN 2005ip was observed at 936 days post-explosion during the cryogenic phase of Spitzer. It was the only interacting SN with an InfraRed Spectrograph (IRS; Houck et al. 2004) mid-IR spectrum from 5 to 12 μm and IRAC photometry at 5.8 and 8 μm (Fox et al. 2010). SN 2006jd was observed at 1638 days, an epoch very similar to that of SN 2014C, with Spitzer/IRAC and WISE (Stritzinger et al. 2012). SN 2010jl was observed at 1279 days with Spitzer/IRAC and SOFIA/FORCAST (Herter et al. 2018) at 11.1 μm, resulting in a deep upper limit after 6400 s of total integration time (Williams & Fox 2015). In all three cases, the photometry and spectra from 1 to 10 μm are well fitted by purely carbonaceous dust models, which we overplot in Figure 6 using dust parameters from the literature. Lastly, SN 1995N was observed at more than 10 yr post-explosion by Spitzer/IRAC and WISE (Van Dyk 2013). Its SED shape differs markedly from those of the other three SNe observed at earlier epochs. The carbonaceous dust model that Van Dyk (2013) fitted to the data is shown in Figure 6. However, we note that the shallow slope from 3 to 10 μm cannot be fitted with a single-temperature dust model, regardless of composition, and would require a range of dust temperatures. Given the late epoch of the observation, one might also consider a nonthermal origin for the IR emission from SN 1995N, as the SED can also be described with a broken power law (Fν ∝ ν−3; also overplotted) with a knee at around 12 μm. In addition to these H-rich interacting SNe, the H-poor interacting SN 2006jc (Ibn) was also observed beyond 5 μm with AKARI  (Sakon et al. 2009). Its SED was also best fitted with a two-temperature amorphous carbon dust model. This comparison highlights SN 2014C’s unique SED shape among other interacting SNe for which data are available beyond 5 μm at comparable epochs, showing for the first time an evidence for a silicate dust feature in the IR SED of an interacting SN. It also accentuates the need for observations of interacting SNe at late times, out to decades post-explosion, in the near- to mid-IR, which will be enabled by the upcoming James Webb Space Telescope (JWST).


As mentioned above, the magnetic reconnection is introduced as breaking and reconfiguration of the oppositely directed magnetic field lines in highly conducting plasma. The magnetic field lines collapse near the X-point and form an extended magnetic singularities known as a current sheet. There are two mechanism of the current-sheet formation. The first kind of current-sheet formation is associated with the MHD instabilities (e.g., resistive tearing mode and ideal kink mode) known as spontaneous magnetic reconnection (e.g., White 1984; Baty 2000; Vekstein 2017). The second kind of current sheet can be formed in the MHD stable configuration, where some external perturbations trigger the forced magnetic reconnection (Hahm & Kulsrud 1985). The forced magnetic reconnection may be activated by nonlinear MHD waves, which may be caused by explosive solar activities (e.g., Sakai et al. 1984; Dewar et al. 2013; Beidler et al. 2017). The forced magnetic reconnection may be developed due to boundary perturbations, which induce a surface current in such a way that it opposes the progress of the reconnection (Ishizawa & Tokuda 2000, 2001; Fitzpatrick 2003). The multimode simulation approach has been adopted to investigate the thinning of the current sheet induced by forced magnetic reconnection (Birn et al. 2005). The motion of the photospheric footpoints of the coronal magnetic field may also trigger the forced magnetic reconnection, which may be caused by the explosive solar coronal events (e.g., Vekstein & Jain 1998; Jain et al. 2005; Vekstein 2017). Although there is a remarkable development in the theory of the forced magnetic reconnection, Jess et al. (2010) have suggested that there is no observational evidence of explosive flare or coronal activities triggered by forced magnetic reconnection. They have observed a microflare activity driven by forced magnetic reconnection. The lower solar atmosphere (photosphere & chromosphere) is dominated by cool, partially ionized and collision dominated plasma. Most of the energy releases during the forced magnetic reconnection may be consumed by such plasma systems (e.g., Litvinenko 1999; Chen et al. 2001; Chen & Ding 2006; Litvinenko et al. 2007).


RX J1347.5–1145 is one of the most luminous X-ray galaxy clusters and is located at a redshift of z = 0.451. It was thought to be a relaxed cluster when it was discovered in the ROSAT all sky survey (Schindler et al. 1997). Komatsu et al. (1999) made the first measurements of the Sunyaev–Zel’dovich effect (SZE: Sunyaev & Zeldovich 1972) toward this cluster with the James Clerk Maxwell Telescope at 350 GHz as well as with the 45 m Nobeyama Radio Telescope at 21 and 43 GHz. A higher angular resolution observation of the SZE was performed by Komatsu et al. (2001) using the Nobeyama Bolometer Array and they found a prominent substructure which has no counterpart in the soft X-ray image from ROSAT. The presence of the substructure has been confirmed by Chandra and XMM-Newton (e.g., Allen et al. 2002; Gitti & Schindler 2004) as well as by more recent SZE measurements (Mason et al. 2010; Korngut et al. 2011; Plagge et al. 2013; Adam et al. 2014; Kitayama et al. 2016). Allen et al. (2002) measured the mean temperature of the ICM to be over 10 keV, which is relatively high compared to other typical clusters. Kitayama et al. (2004) and Ota et al. (2008) found a very hot (>20 keV) component of the ICM in this cluster. In addition, the radial profile and spatial distribution of the ICM temperature indicate that the temperature drops to ∼6 keV toward the cluster center so that the cool core is formed (e.g., Allen et al. 2002; Ota et al. 2008; Kreisch et al. 2016). A disturbed morphology is further supported by radio synchrotron observations (e.g., Ferrari et al. 2011) and gravitational lensing maps (e.g., Köhlinger & Schmidt 2014). The total mass of RX J1347.5–1145 within r200 is estimated to be ∼1.5 × 1015 h−1

  using weak-lensing analysis, where r200, the radius within which the mean mass density is 200 times the critical density of the universe, is 1.85 h−1 Mpc (Lu et al. 2010) for this galaxy cluster.18

18
They adopted the Hubble constant of 70 km s−1 Mpc−1.


For decades, the metallicity and the above chemical abundance ratios have been estimated in samples of star-forming galaxies (SFGs), by using their emission line ratios to calculate the abundances of the different elements that originate them. Many techniques were developed for such studies, such as the use of the Te-method, photoionization models, or optical calibrations based on strong emission lines (see the review by Maiolino & Mannucci 2019 for a more detailed discussion). By using these techniques, some studies show a correlation between both 12 + log (O/H) and log (N/O) (Vila-Costas & Edmunds 1993; Masegosa, Moles & Campos-Aguilar 1994; Andrews & Martini 2013). On the other hand, it is also important how the different properties of the host galaxies correlate with their chemical abundances. For instance, preliminary studies of the Local Group of galaxies (McClure & van den Bergh 1968; Lequeux et al. 1979) revealed the existence of a relation between the luminosity of an SFG and its metallicity, the so-called luminosity–metallicity relation (the most luminous galaxies have the higher chemical abundances), which has been later studied in further detail (Garnett & Shields 1987; Skillman, Kennicutt & Hodge 1989; Brodie & Huchra 1991; Vilchez 1995; Mateo 1998). Later on it was probed that the luminosity–metallicity relation was in fact the result of a more fundamental mass–metallicity relation (Garnett 2002; Pérez-González et al. 2003; Pilyugin, Vílchez & Contini 2004). This relation has been probed in large sample of SFG both at low-redshift (Contini et al. 2002; Melbourne & Salzer 2002; Lamareille et al. 2004; Tremonti et al. 2004) and at high-redshift (Erb et al. 2006a; Pérez-Montero et al. 2009, 2013; Izotov et al. 2015; Gao et al. 2018; Torrey et al. 2019). In addition, it has been reported that the star-formation rate is also related to gas-phase Z in SFG (Lara-López et al. 2010; Mannucci et al. 2010; Yates, Kauffmann & Guo 2012). Morphological type may also be related with the chemical abundances, as early-type galaxies, despite some of them can present episodes of on-going star-formation (Zhu, Blanton & Moustakas 2010), tend to have on average older stellar populations than late-type galaxies (Kennicutt 1998; Trager et al. 2000; Gebhardt et al. 2003; Schiavon 2007), being thus more chemically evolved.


Recently filaments, in particular the warm hot intergalactic medium (WHIM) in filaments, have been the pivot of several studies. Using emission in the soft X-ray bands, such studies estimate the WHIM temperature in filaments to be ∼3–8 keV (Eckert et al. 2015; Akamatsu et al. 2017; Parekh et al. 2017; Tanimura et al. 2017). Furthermore, the cosmic microwave background map from the Planck together with the Canada–France–Hawaii Telescope Lensing Survey, as well as the Two-Micron All-Sky Redshift Survey of galaxies suggest that at least half of the missing baryons in the Universe may reside as WHIM in large-scale filaments tracing the dark matter distribution (Van Waerbeke, Hinshaw & Murray 2014; Génova-Santos et al. 2015). Therefore, undeniably it is crucial to characterize the large-scale structure (LSS) of the Universe and comprehend the impact of the cosmic-web on properties of galaxies. The Coma supercluster is one of the richest large-scale structures (Chincarini & Rood 1976) in the nearby Universe comprising two clusters of galaxies, connected by a web of large-scale filaments around $30\,h_{70}^{-1}$ Mpc long (e.g. Fontanelli 1984). The two clusters, Coma (Abell 1656) and Abell 1367, along with the filaments of galaxies dispersed with several small galaxy groups span ∼500 deg2 on the sky (Mahajan et al. 2010). The large-scale filaments in the Coma supercluster have not just been observed by means of the galaxy distribution in the optical wavebands (Gregory & Thompson 1978; Mahajan et al. 2010), but also diffuse emission in the radio continuum (Kim et al. 1989). Studies of clusters and groups at $z$ ∼ 0 have evidently shown that outskirts of groups and clusters (Zabludoff & Mulchaey 1998; Wang, Owen & Ledlow 2004; Rines et al. 2005; Cortese et al. 2007; Tran et al. 2009; Gavazzi et al. 2010; Smith et al. 2010; Sun et al. 2010; Coppin et al. 2011; Mahajan, Raychaudhury & Pimbblet 2012; Verdugo et al. 2012; Mahajan 2013) and filaments of galaxies (Porter & Raychaudhury 2007; Boué et al. 2008; Fadda et al. 2008; Porter et al. 2008; Edwards et al. 2010a; Biviano et al. 2011) are favourable sites for galaxy transformations. Based on a study using optical data from the Sloan Digital Sky Survey (SDSS) data release (DR) 7, Mahajan et al. (2010) found that the star formation (SF)–density relation in the Coma supercluster for the giant galaxies is much weaker than their dwarf counterparts. However, the fraction of star-forming galaxies for both declines to ∼0 at the centre of the clusters (also see Mahajan, Haines & Raychaudhury 2011). Cybulski et al. (2014) further study the star formation in the Coma supercluster by combining a complementary optical data set from SDSS DR 9, with IR data from the Wide-Field Infrared Survey Explorer (Wright et al. 2010) and UV data from the Galaxy Evolution Explorer (GALEX; Martin et al. 2005). Cybulski et al. (2014) corroborated the results of Mahajan et al. (2010, 2011) by probing both obscured and unobscured star formation down to ∼0.02 M⊙ yr−1, in order to quantify the effect of different types of large-scale environments: groups, clusters, filaments, and voids, on quenching SF in galaxies. In the absence of dust in star-forming galaxies, the UV emission is a good tracer of massive (>10 M⊙) star formation. On the other hand, optical emission lines such as H α probe instantaneous star formation over a time-scale of ≲20 Myr (Kennicutt 1998). Assuming that the UV luminosity is not overwhelmed by contribution from the old stellar populations due to the UV upturn such as in massive early-type galaxies (O’Connell 1999), the UV luminosity measures star formation over a time-scale of ∼100 Myr (Kennicutt 1998). Hence, the star formation rate (SFR) estimated from optical emission lines delineates the continuous SF in a galaxy, while the SFR determined from the UV is representative of its recent SF activity. But even though GALEXand its predecessor UV imagers have been used to investigate individual galaxies within clusters and groups (e.g. Hicks & Mushotzky 2005), or galaxy populations therein (e.g. Donas et al. 1990; Donas, Milliard & Laget 1995; Cornett et al. 1998; Boselli et al. 2005b), limited work has been done to analyse the UV properties of galaxies in the large-scale cosmic-web. Since the Coma supercluster is one of the most well studied regions in the nearby Universe, many other authors (e.g. Bernstein et al. 1995; Mobasher et al. 2003; Hammer et al. 2012; Smith et al. 2010; Smith, Lucey & Carter 2012b) have made use of optical and UV data to study the Coma and Abell 1367 clusters and their surroundings. With the advent of large redshift surveys, several studies (Gavazzi et al. 2010; Mahajan et al. 2010, 2011; Gavazzi et al. 2013; Cybulski et al. 2014 ) have also used multiwavelength data at optical, UV, and 21 cm continuum to study the properties of galaxies in the entire supercluster region. In this paper, we make use of similar data sets: UV data derived from GALEX and optical spectroscopic and photometric data from the SDSS for the entire Coma supercluster to further explore the impact of environment on the properties of galaxies. Conventionally, the ‘environment’ of galaxies is quantified as the projected density of galaxies in a fixed 2D or 3D region of the sky (e.g. Dressler 1980). Muldrew et al. (2012) combined 20 published methods of defining environment into two methods: (i) method that uses nearest-neighbours to probe the underlying galaxy density and (ii) fixed aperture methods. Muldrew et al. (2012) found that while the former are better suited for quantifying internal density within massive haloes, the latter fixed-aperture methods are better for probing the large-scale environment. Therefore, in order to characterize the large-scale cosmic-web, a combination of these methodologies is required to quantify the environment on different scales. In this work, we implement their result by making use of two different algorithms to define the large-scale filaments, and high density nodes of the cosmic-web characterized as clusters and groups. We also present a catalogue of all spectroscopically confirmed galaxy members of the Coma supercluster detected in the UV. This paper is organized as follows: in the next section we describe our data sets, followed by definition of environment in Section 3. In Section 4, we analyse the broad-band colours of galaxies as a function of environment, while in Section 5 we study the impact of the large-scale filaments on the properties of galaxies. Finally, we discuss our results in the context of the existing literature in Section 6 and summarize our results in Section 7. Throughout this paper, we use concordance Λ cold dark matter cosmological model with H0 = 70  km s−1 Mpc−1, $\Omega _\Lambda =0.7$, and Ωm = 0.3 to calculate distances and magnitudes. We note that at the redshift of the Coma cluster ($z$ = 0.023) our results are independent of the cosmological model used.


Adaptive optics (AO, Roddier 1999) is a game changer in the quest for high-angular resolution, especially for ground-based astronomical observations that face the presence of wavefront aberrations introduced by the atmosphere (Roddier 1981). Thanks to AO, the point spread function (PSF) delivered by an optical instrument is much narrower, by a factor up to 50 on the full width at half maximum (FWHM), than the seeing-limited scenario (Roddier 1981). Still, some correction residuals persist and render the AO PSF shape complex to model. Consequently, standard parametric models that reliably reproduce the seeing-limited PSFs, such as a Moffat function (Trujillo et al. 2001; Moffat 1969), become inefficient at describing the AO PSF. Moreover, contrary to seeing-limited observations, AO-corrected images suffer from the anisoplanatism effect (Fried 1982) that strengthens the spatial variations of the PSF on top of instrument defects. Determining the AO PSF is necessary for two major reasons. Firstly, understanding and accurately modeling the PSF morphology is key to diagnosing AO performance. From the PSF, we can identify the major contributors to the AO residual error (Beltramo-Martin et al. 2019; Ferreira et al. 2018; Martin et al. 2017). Secondly, the image delivered by an optical instrument depends on both the science object we want to characterize and the PSF. In order to estimate the interesting astrophysical quantities, one can either use a deconvolution technique (Fétick et al. 2020, 2019a; Benfenati et al. 2016; Flicker & Rigaut 2005; Mugnier et al. 2004; Fusco et al. 2003; Drummond 1998) or include the PSF as part of a model, as is performed in PSF-fitting astrometry/photometry retrieval techniques (Beltramo-Martin et al. 2019; Witzel et al. 2016; Schreiber et al. 2012; Diolaiti et al. 2000; Bertin & Arnouts 1996; Stetson 1987) and galaxy kinematics estimation (Puech et al. 2018; Bouché et al. 2015; Epinat et al. 2010) for instance.


Investigation of solar wind outflow velocities is generally performed by the analysis of UV spectrometric observations. The UVCS/SOHO instrument has provided H I Lyα spectral line data over a longer time than a whole solar activity cycle (1996–2012), giving the possibility of studying coronal dynamics in different activity phases. The analysis of UVCS daily Lyα synoptic data, in combination with electron densities derived from the white-light RS observations, has allowed to derive H I outflow speed maps (see e.g. Dolei et al. 2018, 2019). One of the methods based on the synergy between UV and WL observations is the Doppler dimming technique (Hyder & Lites 1970; Noci et al. 1987; Withbroe et al. 1982). It exploits the progressive UV intensity reduction of the coronal resonantly scattered component of the coronal H I Lyα line emission with increasing outflow velocities. The line emission depends on the physical quantities involved in the Lyα resonant scattering process, such as, for instance, the coronal electron density and temperature, and the chromospheric Lyα radiation that excites the coronal H I atoms. The Lyα intensity is also sensitive to the speed of the outflowing plasma from about 50–500 km s−1, that are the typical velocities for neutral hydrogen atoms in the inner corona. Following the approach of Withbroe et al. (1982) and Noci et al. (1987), the intensity of the resonantly scattered Lyα line can be also numerically computed by iteratively tuning the plasma speed value in order to reproduce the observed UV line intensity. The best match between computed and observed Lyα intensity provides an estimate of the solar wind H I outflow velocity. Figure 9 shows an example of 2D outflow velocity map, in the range of heliocentric distances between 1.5 and 4.0 R⊙, obtained via Doppler dimming technique (Dolei et al. 2018). The speed values radially increase with altitude up to about 150–200 km s−1 in the equatorial regions and 400 km s−1 in the polar regions. These values are in agreement with the expected latitudinal distribution of slow and fast solar wind components, corresponding to equatorial regions, and mid-latitude and polar regions, respectively. The methodology put in place throughout this project will be applied later to the data acquired by the Solar Orbiter’s Metis instrument, giving an unprecedented daily picture of the coronal dynamics, see Antonucci et al. (2020) for a detailed description of diagnostic techniques for Metis data.